Ejercicios resueltos del libro de estructuras metálicas de McCorman

UNIVERSIDAD TÉCNIC

FACULTAD DE CIENCIAS MATEMÁTICAS

ESCUELA DE INGENIERI

RESOLUCIÓN DE E DEL CAPÍTU DOCENTE:

ING. MARCOS ZE

ESTUDIANTE:

VÉLEZ CEVALLOS

ASIGNATURA:

ESTRUCTURAS M

 NIVEL:

NOVENO “H”

JUNIO 2016 - SEPTIEMB

RSIDAD TÉCNICA DE MANABÍ

TAD DE CIENCIAS MATEMÁTICAS, FÍSICAS Y QUÍMICA ESCUELA DE INGENIERIA CIVIL

LUCIÓN DE EJERCICIOS DEL CAPÍTULO 4 ING. MARCOS ZEVALLOS VÉLEZ CEVALLOS JEAN CARLOS ESTRUCTURAS METÁLICAS NOVENO “H” JUNIO 2016 - SEPTIEMBRE 2016

CALDERERO PANCHANA MARIA JOSE ESTRUCTURAS METALICAS

Seleccione perfi les para las condiciones descritas, usando Fy = 50 klb/plg2 y Fu = 65 klb/plg2, a menos que se indique lo contrario y sin considerar el boque de cortante. 4-1

Seleccione el perfi l más ligero W12 disponible para soportar cargas de trabajo a tensión de PD = 120 klb y PW = 288 klb. El miembro tiene 20 pies de largo y debe tener dos hileras de agujeros para tornillos de 3/4 plg en cada patín. Habrá por lo menos tres tornillos en cada línea a 3 plg entre centros DATOS PD= PW= L= tf= #HILERAS= Diámetro= aumento(1/8)= # línea = s=

W12X35

TORNILLO Fu= Fy=

3 4

TORNILLO

120.00 Klb 288.00 Klb 20.00 pies 0.52 plg 2.00 0.75 plg 0.13 plg 4 3.00 plg

COMBINACIONES DE CARGA LRFD

240.00 plg asume

ASD ��=�+0,6�

��=1,2�+1,0� Pu=

432.00 k

Pa=

292.80 k

65.00 Klb/plg2 50.00 Klb/plg2 ∅_�=

MÉTODO LRFD �= ∅_�=

0.9

�_� ��� =�_�/(∅_� �_� )

0.85 CASO 7 0.75

�_� ��� =�_�/(∅_� �_� �)+�_������� =

Agmín reque=

9.60 plg2

Agmín reque=

� ��� =�/���=

12.25 plg2

r mín=

0.80 plg

COMPROBACIÓN

W12X45

PROBAR Ag= d= bf= tf= ry=

FLUENCIA DE LA SECCIÓN DE ACERO 13.10 plg2 12.10 plg 8.05 plg 0.58 plg 1.95 plg

LRFD

∅�=

�_�=�_� �_�= Pn=

1.67

��/�

655.00 Klb LRFD= 589.50 k RESISTENCIA DE FRACTURA A LA TENSIÓN

wt6x22.5 x=y= L=

ASD Ω�=

0.9 ����=��∗��

1.13 plg 6.00 plg

11.09 plg2

71.53 cm2

432.00 k

X= U=

392.22 k

OK

0.75 ����=��∗��

Caso 2

Ae=

9.00 plg2

58.06 cm2

LRFD=

0.85

612.58 k

392.22 k 292.80 k

∅�= ��<2/3 �

1.13 plg

U=

>

LRFD

0.81

Pn=��∗�e Pn=

ASD=

OK

FUERZA DE RUPTURA �=1−�/�

��=�∗�n An=

589.50 k

>

459.44 k

Ae=

9.42 plg2

>

60.80 cm2

459.44 k 432.00 k

OK

ASD Ω�=

2

��/�

RELACIÓN DE ESBELTEZ L ry

=

240.00 plg 1.95 plg

123.08

USAR:

W12X45

<

300

OK

PARA

LRFD ASD

ASD= 306.29 k >

4-3

306.29 k 292.80 k

OK

Seleccione la WT7 más ligera disponible para soportar una carga factorizada de tensión Pu = 250 klb, Pa = 160 klb. Suponga que hay dos líneas de tornillos de 7/8 plg en el patín (con tres tornillos por lo menos en cada línea de 4 plg centro a centro). El miembro tiene 30 pies de largo DATOS Pu= Pa= L= tf= #HILERAS= Diámetro= aumento(1/8)= # línea = s=

WT7X26.5

TORNILLO Fu= Fy=

7 8

TORNILLO

250.00 Klb 160.00 Klb 30.00 pies 0.66 plg 0.88 plg 0.13 plg 2 4.00 plg

COMBINACIONES DE CARGA LRFD

ASD

360.00 plg asume Pu=

250.00 k

Pa=

160.00 k

65.00 Klb/plg2 50.00 Klb/plg2 ∅_�=

MÉTODO LRFD �=

0.9

0.85 CASO 7 0.75

∅_�=

�_� ��� =�_�/(∅_� �_� )

�_� ��� =�_�/(∅_� �_� �)+�_������� =

Agmín reque=

5.56 plg2

Agmín reque=

� ��� =�/���=

7.35 plg2

r mín=

1.20 plg

COMPROBACIÓN

WT7X26.5

PROBAR Ag= d= bf= tf= ry=

FLUENCIA DE LA SECCIÓN DE ACERO 7.80 plg2 6.96 plg 8.06 plg 0.66 plg 1.88 plg

W14X53 13.90 plg

LRFD

∅�=

�_�=�_� �_�= Pn=

LRFD=

1.38 plg 8.00 plg

6.48 plg2

41.81 cm2

351.00 k

>

250.00 k

X= U=

��/�

∅�=

0.83

U=

233.53 k 160.00 k

0.75 ����=��∗��

Caso 2 5.36 plg2

34.59 cm2

5.51 plg2

35.54 cm2

0.85 Ae=

OK

LRFD

W14X53

��<2/3 �

1.38 plg Ae=

Pn=��∗�e 358.02 k

ASD= 233.53 k >

OK

FUERZA DE RUPTURA �=1−�/�

��=�∗�n An=

Pn=

1.67

390.00 Klb 351.00 k RESISTENCIA DE FRACTURA A LA TENSIÓN

WT7X26.5 x=y= L=

ASD Ω�=

0.9 ����=��∗��

LRFD= 268.52 k

>

268.52 k 250.00 k

OK

ASD Ω�=

2

��/�

RELACIÓN DE ESBELTEZ L

=

360.00 plg

191.49

<

300

OK

ASD=

179.01 k

ry

CALDERERO PANCHANA MARIA JOSE 300 OK ESTRUCTURAS METALICAS

191.49

1.88 plg

ASD= 179.01 k >

USAR:

WT7X26.5

PARA

179.01 k 160.00 k

OK

LRFD

CHEQUEAR WT7X24 PARA ASD Ag= d= bf= tf= ry=

WT7X24

7.07 plg2 6.90 plg 8.03 plg 0.60 plg 1.88 plg

ASD Ω�=

ASD= 211.68 k > USAR:

4-5

ASD 1.67

Ω�=

��/�

211.68 k OK

160.00 k WT7X24

2

ASD= 174.53 k >

PARA

160.00 k

��/�

174.53 k OK

ASD

Seleccione el perfi l C más ligero que soporte con seguridad las cargas de servicio de tensión PD = 65 klb y PL = 50 klb. El miembro tiene 14 pies de largo y debe tener dos líneas de agujeros para tornillos de 3/4 plg Ø en el alma. Considere por lo menos tres agujeros en cada línea de 3 plg centro a centro. Use acero A36. DATOS PD= PW= L= tW= #HILERAS= Diámetro= aumento(1/8)= # línea = s=

C8X18.7

TORNILLO Fu= Fy=

3 4

TORNILLO

65.00 Klb 50.00 Klb 14.00 pies 0.49 plg 0.75 plg 0.13 plg 2 3.00 plg

COMBINACIONES DE CARGA LRFD

168.00 plg asume

ASD ��=�+�

��=1,2�+1,6� Pu=

158.00 k

Pa=

115.00 k

58.00 Klb/plg2 36.00 Klb/plg2 ∅_�=

MÉTODO LRFD �=

0.9

0.9 CASO 7 0.75

∅_�=

�_� ��� =�_�/(∅_� �_� )

�_� ��� =�_�/(∅_� �_� �)+�_������� =

Agmín reque=

4.88 plg2

Agmín reque=

� ��� =�/���=

4.89 plg2

r mín=

0.56 plg

COMPROBACIÓN

C8X18.7

PROBAR Ag= d= X= tw= ry=

FLUENCIA DE LA SECCIÓN DE ACERO 5.51 plg2 0.57 plg 0.49 plg 0.60 plg

LRFD

∅�=

�_�=�_� �_�= Pn=

1.67

��/�

198.36 Klb LRFD= 178.52 k RESISTENCIA DE FRACTURA A LA TENSIÓN

WT7X26.5 x=y= L=

ASD Ω�=

0.9 ����=��∗��

0.57 plg 6.00 plg

4.66 plg2

30.05 cm2

158.00 k

ASD= 118.78 k >

OK

FUERZA DE RUPTURA �=1−�/�

��=�∗�n An=

178.52 k

>

X= U=

W14X53 ∅�=

0.91

0.75 ����=��∗��

Caso 2

Ae=

4.22 plg2

27.22 cm2

Ae=

4.22 plg2

27.22 cm2

LRFD= 183.53 k

Pn=

244.71 k

OK

LRFD

��<2/3 �

0.57 plg

Pn=��∗�e

118.78 k 115.00 k

>

183.53 k 158.00 k

OK

ASD Ω�=

2

��/�

RELACIÓN DE ESBELTEZ L ry

=

168.00 plg 0.60 plg

280.94

USAR:

C8X18.7

<

300

OK

PARA

LRFD ASD

ASD= 122.36 k >

4-7

OK

Seleccione el perfi l C más ligero que soporte con seguridad las cargas de servicio de tensión PD = 20 klb y PL = 34 klb. El miembro tiene 12 pies de largo y debe tener solamente una soldadura transversal al fi nal de la canal. Use acero A36. DATOS PD= PW= L= tW= #HILERAS= Diámetro= aumento(1/8)= # línea = s=

C6X10.5

TORNILLO

3 4

TORNILLO

20.00 Klb 34.00 Klb 12.00 pies 0.31 plg 0.75 plg 0.13 plg 2 3.00 plg

Fu= Fy=

COMBINACIONES DE CARGA LRFD

144.00 plg asume

ASD ��=�+�

��=1,2�+1,6� Pu=

78.40 k

∅_�=

MÉTODO LRFD �= ∅_�=

0.9

1 CASO 3 0.75

�_� ��� =�_�/(∅_� �_� �)+�_�������−�����=

Agmín reque=

54.00 k

2.42 plg2

Agmín reque=

3.00 plg2

r mín=

0.48 plg

OK

FLUENCIA DE LA SECCIÓN DE ACERO 3.08 plg2 6.00 plg 0.50 plg 0.31 plg 0.53 plg

� ��� =�/���=

��=�����=�∗��

3.00 plg2< 3.08 plg2 COMPROBACIÓN PROBAR Ag= d= X= tw= ry=

Pa=

58.00 Klb/plg2 36.00 Klb/plg2

�_� ��� =�_�/(∅_� �_� )

C6X10.5

122.36 k 115.00 k

LRFD ∅�=

�_�=�_� �_�=

ASD 0.9

1.67

Ω�=

��/�

����=��∗�� Pn=

110.88 Klb LRFD= 99.79 k RESISTENCIA DE FRACTURA A LA TENSIÓN

>

FUERZA DE RUPTURA ��=�∗�n

99.79 k 78.40 k

ASD= 66.40 k >

OK

W14X53

66.40 k 54.00 k

LRFD

OK

An=

1.88 plg2

CALDERERO PANCHANA MARIA JOSE ESTRUCTURAS ��=�∗�n METALICAS

12.15 cm2

X= U=

∅�= ��<2/3 �

0.00 plg 1.00

Pn=��∗�n∗U

0.75 ����=��∗��

Caso 2

Ae=

1.88 plg2

12.15 cm2

Ae=

1.88 plg2

12.15 cm2

LRFD= 81.95 k

Pn=

109.27 k

>

81.95 k 78.40 k

OK

ASD Ω�=

2

��/�

RELACIÓN DE ESBELTEZ L ry

=

144.00 plg 0.53 plg

272.21

USAR:

C6X10.5

<

300

OK

PARA

LRFD ASD

ASD= 54.64 k >

54.64 k 54.00 k

OK

Seleccione la sección más ligera para cada una de las situaciones descritas en la Tabla 4.1. Suponga tornillos a 3 plg entre centros (a menos que se indique otra cosa). No considere bloque de cortante. Determine U de la Tabla 3.2 de este libro (excepto si se da). 4-9

Perfil W8, PD=75klb, PL=100klb, longitud=24 pies, acero A992, Dos lineas de tornillos de 5/8plg (3 en una línea a 2 1/2 plg centro a centro en cada patín

DATOS PD= PW= L= tf= #HILERAS= Diámetro= aumento(1/8)= # línea = s=

W8X28

TORNILLO Fu= Fy=

5 8

TORNILLO

75.00 Klb 100.00 Klb 24.00 pies 0.47 plg 0.63 plg 0.13 plg 4 2.50 plg

COMBINACIONES DE CARGA LRFD

288.00 plg asume

ASD ��=�+�

��=1,2�+1,6�

s

2

Pu=

1 2

250.00 k

Pa=

175.00 k

65.00 Klb/plg2 50.00 Klb/plg2 ∅_�=

MÉTODO LRFD �= ∅_�= �_� ��� =�_�/(∅_� �_� �)+�_������� =

0.9

�_� ��� =�_�/(∅_� �_� )

Agmín reque=

5.56 plg2

0.85 CASO 7 0.75

Agmín reque=

� ��� =�/���=

7.43 plg2

r mín=

0.96 plg

COMPROBACIÓN

W8X28

PROBAR Ag= d= bf= tf= ry= x=y=

x=y= L=

FLUENCIA DE LA SECCIÓN DE ACERO 8.24 plg2 8.06 plg 6.54 plg 0.47 plg 1.62 plg 0.73 plg

LRFD ∅�=

�_�=�_� �_�=

ASD Ω�=

0.9

1.67

��/�

����=��∗�� Pn=

412.00 Klb LRFD=

WT4X14

370.80 k RESISTENCIA DE FRACTURA A LA TENSIÓN

0.73 plg 5.00 plg

6.85 plg2

44.16 cm2

250.00 k

X= U=

W14X53 ∅�=

0.85

OK

0.75 ����=��∗��

Caso 2

Ae= U=

5.84 plg2

37.68 cm2

6.16 plg2

39.75 cm2

LRFD=

0.90

400.43 k

246.71 k 175.00 k

LRFD

��<2/3 �

0.73 plg

Pn=��∗�e Pn=

ASD= 246.71 k >

OK

FUERZA DE RUPTURA �=1−�/�

��=�∗�n An=

370.80 k

>

300.32 k

Ae=

>

300.32 k 250.00 k

OK

ASD Ω�=

2

��/�

RELACIÓN DE ESBELTEZ L ry

=

288.00 plg 1.62 plg

177.78

USAR:

W8X28

<

300

OK

PARA

LRFD ASD

ASD= 200.22 k >

4 - 11

200.22 k 175.00 k

OK

Perfil W12, PD=150klb, PL=175klb, longitud=26 pies, acero A36, Dos lineas de tornillos de 7/8plg (2 en una línea a 4 plg centro a centro en cada patín

DATOS PD= PW= L= tf= #HILERAS= Diámetro= aumento(1/8)= # línea = s=

W12X58

TORNILLO Fu= Fy=

7 8

TORNILLO

150.00 Klb 175.00 Klb 26.00 pies 0.64 plg 0.88 plg 0.13 plg 4 4.00 plg

COMBINACIONES DE CARGA LRFD

312.00 plg asume

ASD ��=�+�

��=1,2�+1,6�

s

4

Pu=

0 1

460.00 k

Pa=

325.00 k

58.00 Klb/plg2 36.00 Klb/plg2 ∅_�=

MÉTODO LRFD �= ∅_�=

0.9

�_� ��� =�_�/(∅_� �_� )

0.75 CAS2- SOLO2 0.75

�_� ��� =�_�/(∅_� �_� �)+�_������� =

Agmín reque=

14.20 plg2

Agmín reque=

16.66 plg2

� ��� =�/���=

r mín=

1.04 plg

COMPROBACIÓN

W12X58

PROBAR Ag= d= bf= tf= ry= x=y=

FLUENCIA DE LA SECCIÓN DE ACERO 17.00 plg2 12.20 plg 10.00 plg 0.64 plg 2.51 plg 1.03 plg

LRFD ∅�=

�_�=�_� �_�=

ASD 0.9

1.67

Ω�=

��/�

����=��∗�� Pn=

612.00 Klb LRFD=

WT6X29

550.80 k

>

550.80 k 460.00 k

OK

ASD= 366.47 k >

366.47 k 325.00 k

OK

CALDERERO PANCHANA MARIA JOSE METALICAS

RESISTENCIA DE FRACTURA A LAESTRUCTURAS TENSIÓN

x=y= L=

1.03 plg 4.00 plg

FUERZA DE RUPTURA �=1−�/�

��=�∗�n An=

14.44 plg2

93.16 cm2

X= U=

∅�=

0.74

0.75 ����=��∗��

Caso 2

Ae=

Pn=��∗�e

LRFD

W14X53

��<2/3 �

1.03 plg 10.72 plg2

69.17 cm2

LRFD= 466.39 k

Pn=

621.86 k

Ae=

10.72 plg2

>

69.17 cm2

466.39 k 460.00 k

OK

ASD Ω�=

2

��/�

RELACIÓN DE ESBELTEZ L ry

=

312.00 plg 2.51 plg

<

124.30

300

OK

ASD= 310.93 k <

USAR:

W12X58

PARA

x=y= L=

0.99 plg 4.00 plg

16.68 plg2

107.61 cm2

X= U=

WT6X32.5

0.75

729.21 k

ASD

W14X53

Ω�=

2

��/�

��<2/3 �

0.99 plg

Pn=��∗�e Pn=

19.10 plg2 12.10 plg 12.00 plg 0.61 plg 3.02 plg 0.99 plg

FUERZA DE RUPTURA �=1−�/�

��=�∗�n An=

NO

LRFD

REDISEÑAR PARA ASD Ag= d= bf= tf= ry= x=y=

W12X65

310.93 k 325.00 k

Caso 2

Ae=

12.57 plg2

81.11 cm2

Ae=

12.57 plg2

81.11 cm2

ASD= 364.60 k >

325.00 k

364.60 k OK

RELACIÓN DE ESBELTEZ L ry

4 - 13

=

312.00 plg 3.02 plg

103.31

USAR:

W12X65

<

300

OK

PARA

ASD

Perfil W8, PD=100klb, PL=80klb, longitud=30 pies, acero A992, Soldadura transversal solamente en los patines

DATOS PD= PW= L= tf= #HILERAS= Diámetro= aumento(1/8)= # línea = s=

W8X24

TORNILLO Fu= Fy=

COMBINACIONES DE CARGA

TORNILLO

100.00 Klb 80.00 Klb 30.00 pies 0.40 plg 0.13 plg 4 -

LRFD 360.00 plg asume

ASD ��=�+�

��=1,2�+1,6� Pu=

0

s

248.00 k

Pa=

180.00 k

65.00 Klb/plg2 50.00 Klb/plg2 ∅_�=

MÉTODO LRFD �= ∅_�= �_� ��� =�_�/(∅_� �_� �)

0.9

�_� ��� =�_�/(∅_� �_� )

Agmín reque=

5.51 plg2

1 caso3 0.75

Agmín reque=

� ��� =�/���=

5.09 plg2 2

5.09 plg2

2.54 plg2

r mín=

1.20 plg

COMPROBACIÓN

W8X24

PROBAR Ag= d= bf= tf= ry= x=y=

FLUENCIA DE LA SECCIÓN DE ACERO 7.08 plg2 7.93 plg 6.50 plg 0.40 plg 1.61 plg 1.03 plg

Af 2.60 plg2

LRFD ∅�=

�_�=�_� �_�=

ASD 0.9

Pn=

LRFD=

318.60 k

> 318.60 k RESISTENCIA DE FRACTURA A LA TENSIÓN

WT6X29

1.03 plg #VALUE!

248.00 k

ASD= 211.98 k >

OK

5.20 plg2

33.55 cm2

211.98 k 180.00 k

0.75

∅�=

X= U=

1.03 plg 1.00 Ae=

Pn=��∗��∗�

��<2/3 �

Caso 2 5.20 plg2

����=��∗��

33.55 cm2

LRFD= 253.50 k

338.00 k

Ae=

5.20 plg2

>

33.55 cm2

253.50 k 248.00 k

2

RELACIÓN DE ESBELTEZ =

360.00 plg 1.61 plg

223.60

USAR:

W8X24

<

300

OK

PARA

LRFD

ASD= 169.00 k <

W8X28

REDISEÑAR PARA ASD Ag= d= bf= tf= ry= x=y=

8.24 plg2 8.06 plg 6.54 plg 0.47 plg 1.62 plg 0.99 plg

WT6X32.5

OK

ASD Ω�=

L ry

OK

LRFD

W14X53

��=�∗�n An=

Pn=

��/�

354.00 Klb

FUERZA DE RUPTURA x=y= L=

1.67

Ω�=

����=��∗��

��/�

169.00 k 180.00 k

NO

CALDERERO PANCHANA MARIA JOSE ESTRUCTURAS METALICAS FUERZA DE RUPTURA x=y= L=

0.99 plg #VALUE!

ASD

W14X53

6.08 plg2

39.24 cm2

X= U=

Pn=��∗�e Pn=

395.34 k

��/�

��<2/3 �

0.99 plg 1.00

2

Ω�=

��=�∗�n An=

Caso 2

ASD=

Ae=

6.08 plg2

39.24 cm2

Ae=

6.08 plg2

39.24 cm2

197.67 k >

197.67 k 180.00 k

OK

RELACIÓN DE ESBELTEZ L ry

4 - 15

=

360.00 plg 1.62 plg

222.22

USAR:

W8X28

<

300

OK

PARA

ASD

Perfil WT6, PD=80klb, PL=120klb, longitud=20 pies, acero A992, Soldadura longitudinal solamente en el patín, 6plg de longitud

DATOS PD= PW= L= tf= #HILERAS= Diámetro= aumento(1/8)= # línea = s=

WT6X25

TORNILLO Fu= Fy=

7 8

TORNILLO

80.00 Klb 120.00 Klb 20.00 pies 0.64 plg 0.13 plg 4 6.00 plg

COMBINACIONES DE CARGA LRFD

240.00 plg asume

ASD ��=�+�

��=1,2�+1,6�

s

6

Pu=

0 1

288.00 k

Pa=

200.00 k

65.00 Klb/plg2 50.00 Klb/plg2 ∅_�=

MÉTODO LRFD �= ∅_�= �_� ��� =�_�/(∅_� �_� �)

0.9

�_� ��� =�_�/(∅_� �_� )

Agmín reque=

6.40 plg2

0.85 CAS2- SOLO2 0.75

Agmín reque=

� ��� =�/���=

6.95 plg2

r mín=

0.80 plg

COMPROBACIÓN

WT6X25

PROBAR Ag= d= bf= tf= rx= x=y=

FLUENCIA DE LA SECCIÓN DE ACERO 7.30 plg2 6.10 plg 8.08 plg 0.64 plg 1.60 plg 1.17 plg

LRFD

ASD 0.9

∅�=

�_�=�_� �_�= Pn=

LRFD=

328.50 k

> 328.50 k RESISTENCIA DE FRACTURA A LA TENSIÓN

WT6X25

288.00 k

1.17 plg 6.00 plg

ASD= 218.56 k >

OK

∅�= ��<2/3 �

1.17 plg 0.81

Pn=��∗�e 381.97 k

0.75

Ae=

5.88 plg2

37.91 cm2

Ae=

5.88 plg2

37.91 cm2

LRFD=

286.48 k 288.00 k

2

ASD=

=

190.99 k <

REDISEÑAR PARA ASD y LRFD Ag= d= bf= tf= rx= x=y=

7.78 plg2 6.03 plg 10.00 plg 0.58 plg 1.51 plg 1.02 plg

FLUENCIA DE LA SECCIÓN DE ACERO

350.10 k

1.67

Ω�=

350.10 k

>

288.00 k

ASD= 232.93 k >

OK

FUERZA DE RUPTURA 1.02 plg 6.00 plg

X= U= Pn=��∗�e 419.73 k

232.93 k 200.00 k

OK

0.83

2

Ω�=

��/�

��<2/3 �

1.02 plg Caso 2

ASD=

Ae=

6.46 plg2

41.66 cm2

Ae=

6.46 plg2

41.66 cm2

RELACIÓN DE ESBELTEZ =

��/�

ASD W14X53

�=1−�/�

��=�∗�n

L ry

NO

����=��∗��

389.00 Klb

LRFD=

Pn=

190.99 k 200.00 k

ASD 0.9

∅�=

Pn=

��/�

WT6X26.5

LRFD

�_�=�_� �_�=

NO

ASD Ω�=

WT6X26.5

OK

����=��∗��

Caso 2

286.48 k <

Pn=

218.56 k 200.00 k

LRFD

W14X53

�=1−�/�

��=�∗�n X= U=

x=y= L=

��/�

365.00 Klb

FUERZA DE RUPTURA x=y= L=

1.67

Ω�=

����=��∗��

209.87 k >

209.87 k 200.00 k

OK

LRFD 0.75

∅�=

����=��∗��

240.00 plg 1.51 plg

158.94

USAR:

WT6X26.5

<

300

OK

PARA

LRFD ASD

LRFD= 314.80 k >

314.80 k 288.00 k

OK

CALDERERO PANCHANA MARIA JOSE ESTRUCTURAS METALICAS 4 - 17

Usando acero A36 seleccione el miembro más ligero consistente en un ángulo individual de alas iguales para resistir una carga de tensión de PD = 45 klb, PL = 25 klb y PW = 88 klb. El miembro se conectará por un ala con dos líneas de tres tornillos de 3/4 plg Ø a 3 1/2 plg centro a centro. La longitud del miembro es de 24 pies. Desprecie el bloque de cortante. (Resp. L6 * 6 * 1/2 para LRFD y ASD.)

DATOS PW= L= PD= PL= PS= T= adreajust ACERO

A36 GRADO

88.0 Klb 2 pies 45.0 Klb 25.0 Klb 65.0 Klb 0.75 0.88

COMBINACIONES LRFD P1 63 P2 94 P3 66.5 P4 98 P5 154.5

36

PU

a) Min Aq =

COMBINACIONES ASD P1 P2 P3 P4

154.50 k

Pa

PERFILES L4*4*3/4 L5*5*5/8 L6*6*7/16

4.77 plg2

c)

45.0 Klb 70.0 97.8 103.35

AREA 5.44 5.9 5.08

L6*6*1/2 A X rmin Wt U A)

103.35 k

X 1.27 1.47 1.65

5.77 1.67 1.18 19.6 0.761

RMIN=r2 0.774 0.915 1.18

WT 18.5 20 17.2

Pn = 26 Klb

Revisar

ASD , Pn/Ω=

18 Klb

Ok

B)

Ruptura U An= AE= Pn=

Ω=

0.76 5.77 Plg² 4.39 Klb 254.68KIPS

L6*6*1/16 U

B) Ruptura Min Aq =

0.76

5.41 plg2

Ok

LRFD , øRn=

191.007195

Ok

ASD , Rn/Ω=

127.33813

Ok

244.068

Ok

C) L/R

USE L6*6*1/2 LRFD Y ASD

4 - 19

Seleccione el perfi l de canal C6 más ligero para usarse como un miembro a tensión de 12 pies de longitud para resistir las siguientes cargas de servicio, PD = 20 klb y PL = 32 klb. El miembro se conecta mediante una soldadura transversal solamente en el extremo de la canal. Use acero A36 Grado 36 con Fu = 58 klb/plg2. (Resp. C6 * 10.5 LRFD y ASD.)

Datos : PD = PL = Acero = Fu =

CHEKEAR : 20 Klb 32 Klb 36 58 klb/Plg²

LRFD , Pu = ASD , Pa =

75.2 Klb 52 Klb

A)

Pn =

A) Min Aq=

2.32 plg2

B)

B) RUPTURA

110.5 Klb

LRFD , øRn=

99.5 Klb Ok

ASD , Rn/Ω=

66.2 Klb Ok

Ω=

U= 1 Pn =

U =1

109.3 Klb

An = tw (d) = Aconn LRFD , øRn=

82.0 Klb ok

TRATAR C6x10.5 ASD , Rn/Ω= Aq=

3.07 Plg²

d= 6 plg

tw=

54.6 Klb revisar

0.314 plg l/r=

Aconn = 1.88 Plg²

rmin = ry =

Min Aconn =

4 - 21

1.73 Plg²

usar C6 x 10.5

por LRFD y ASD

Seleccione un perfi l ST que va a usarse como un miembro a tensión de 20 pies de longitud que soporte con seguridad las cargas de servicio en tensión: PD = 35 klb, PL = 115 klb y PS = 65 klb (nieve). La conexión es a través del patín con dos líneas de tres tornillos de 3/4 plg Ø entre centros. Use acero A572 Grado 50. Desprecie el bloque de cortante. (Resp. ST10 * 33 LRFD y ASD.)C DATOS

L= PD= PL= PS= T= adreajust ACERO

272.21 ok

0.529 plg

ok

LRFD1, PU ASD.Pa=

20 pies 35.0 Klb 115.0 Klb 65.0 Klb 0.75 0.88 A572 GRADO 50 Min Aq =

258.50KIPS 170.00KIPS

B)

5.74 Plg²

Ruptura U An= AE= Pn=

0.65 8.31 Plg² 5.4 Klb 350.37KIPS

LRFD , øRn=

262.7772011719

Ok

ASD , Rn/Ω=

175.1848007813

Ok

201.6806722689

Ok

0.75 0.659 C) Min Aq =

8.22 Plg²

L/R USE ST10*33 LRFD Y ASD

9.7 Plg² 0.80plg 1.19plg 2.81plg 8.00plg A)

4 - 23

Pn =

485.00KIPS

LRFD , øPn=

437 Klb

Ok

ASD , Pn/Ω=

290 Klb

Ok

Ω=

1.67

Un miembro a tensión consta de dos canales C10 y dos PL 1/2 * 11, dispuestos como se muestra en la Figura P4-23 para soportar las cargas de servicio, PD = 200 klb y PL = 320 klb. La longitud del miembro es de 30 pies y debe tener cuatro líneas de tornillos de 3/4 plg Ø. Suponga U = 0.85. Todo el acero será A36. Desprecie el bloque de cortante

B)

Tratar con C10x25

A= Min Aq=

7.35 Plg²

tf =

0.436 plg

23.61 Plg²

TRATAR 2c10x25 + 2PL 1/2 x 11 Aq =

25.7 Plg²

Chequear : A) Datos: PD = PL =

200 Klb 320 Klb

Pn =

925 Klb

LRFD , øRn=

833 Klb

Ok

ASD , Rn/Ω=

554 Klb

Ok

Ω=

5.42 Plg²

29.31KIPS

LRFD , øPn=

� ��� =�/���= 0.96 plg

Min Aq =

1.67

1.67

1.67

Ok

L= T= U= Fy = Fu =

30 pies 3/4 plg 0.85 36 58

360

CALDERERO PANCHANA MARIA JOSE ESTRUCTURAS METALICAS

plg

B) LRFD, Pu=

752 Klb

ASD, Pa=

520 Klb

A) 23.21 Plg²

A2c's =

EACH =

0.85

An= Pn=

Estimacion del area de dos canales Min Aq =

Ruptura =

22.58 Plg² 1,113.3 Klb

LRFD , øRn=

835.0 Klb

ok

ASD , Rn/Ω=

556.7 Klb

ok

12.21 Plg²

6.1 Plg² C)

l/r

calcular rx , ry

Ix =

485.62 Plg4 rx =

Iy=

4.64 plg

467.62 Plg4 ry= l/r=

usar 2-C10x25

4 - 25

Pu= Fu = ø= Pa = Ω=

Seleccione una barra redonda estándar roscada para soportar una carga de tensión factorizada de 72 klb (carga de servicio a tensión = 50 klb) usando acero A36. (Resp. Barra de 134 plg Ø LRFD y ASD.) Datos : 72 Klb 58 0.75 50 Klb 2

LRFD Min Ao =

2.21 Plg²

barra roscada=

1 3/4 plg

Arosca =

2.41 Plg²

Rn =

104.6 Klb

LRFD , øRn=

78.5 Klb

Ok

ASD , Rn/Ω=

52.3 Klb

Ok

4.55 plg 79.11

por LRFD y ASD

ok

Shape W44X335 W44X290 W44X262 W44X230 W40X593 W40X503 W40X431 W40X397 W40X372 W40X362 W40X324 W40X297 W40X277 W40X249 W40X215 W40X199 W40X392 W40X331 W40X327 W40X294 W40X278 W40X264 W40X235 W40X211 W40X183 W40X167 W40X149 W36X800 W36X652 W36X529 W36X487 W36X441 W36X395 W36X361 W36X330 W36X302 W36X282 W36X262 W36X247 W36X231 W36X256 W36X232 W36X210

A 98.5 85.4 76.9 67.7 174 148 127 117 109 107 95.3 87.4 81.4 73.3 63.4 58.5 115 97.5 96 86.3 82 77.6 69 62 53.3 49.2 43.8 236 192 156 143 130 116 106 97 88.8 82.9 77 72.5 68.1 75.4 68.1 61.8

d 44 43.6 43.3 42.9 43 42.1 41.3 41 40.6 40.6 40.2 39.8 39.7 39.4 39 38.7 41.6 40.8 40.8 40.4 40.2 40 39.7 39.4 39 38.6 38.2 42.6 41.1 39.8 39.3 38.9 38.4 38 37.7 37.3 37.1 36.9 36.7 36.5 37.4 37.1 36.7

tw 1.03 0.865 0.785 0.71 1.79 1.54 1.34 1.22 1.16 1.12 1 0.93 0.83 0.75 0.65 0.65 1.42 1.22 1.18 1.06 1.03 0.96 0.83 0.75 0.65 0.65 0.63 2.38 1.97 1.61 1.5 1.36 1.22 1.12 1.02 0.945 0.885 0.84 0.8 0.76 0.96 0.87 0.83

bf 15.9 15.8 15.8 15.8 16.7 16.4 16.2 16.1 16.1 16 15.9 15.8 15.8 15.8 15.8 15.8 12.4 12.2 12.1 12 12 11.9 11.9 11.8 11.8 11.8 11.8 18 17.6 17.2 17.1 17 16.8 16.7 16.6 16.7 16.6 16.6 16.5 16.5 12.2 12.1 12.2

W36X194 W36X182 W36X170 W36X160 W36X150 W36X135 W33X387 W33X354 W33X318 W33X291 W33X263 W33X241 W33X221 W33X201 W33X169 W33X152 W33X141 W33X130 W33X118 W30X391 W30X357 W30X326 W30X292 W30X261 W30X235 W30X211 W30X191 W30X173 W30X148 W30X132 W30X124 W30X116 W30X108 W30X99 W30X90 W27X539 W27X368 W27X336 W27X307 W27X281 W27X258 W27X235 W27X217 W27X194 W27X178

57 53.6 50.1 47 44.2 39.7 114 104 93.6 85.7 77.5 71 65.2 59.2 49.5 44.8 41.6 38.3 34.7 115 105 95.8 85.9 76.9 69.2 62.2 56.3 51 43.5 38.9 36.5 34.2 31.7 29.1 26.4 159 108 98.9 90.4 82.9 76 69.4 64 57.2 52.5

36.5 36.3 36.2 36 35.9 35.6 36 35.6 35.2 34.8 34.5 34.2 33.9 33.7 33.8 33.5 33.3 33.1 32.9 33.2 32.8 32.4 32 31.6 31.3 30.9 30.7 30.4 30.7 30.3 30.2 30 29.8 29.7 29.5 32.5 30.4 30 29.6 29.3 29 28.7 28.4 28.1 27.8

0.765 0.725 0.68 0.65 0.625 0.6 1.26 1.16 1.04 0.96 0.87 0.83 0.775 0.715 0.67 0.635 0.605 0.58 0.55 1.36 1.24 1.14 1.02 0.93 0.83 0.775 0.71 0.655 0.65 0.615 0.585 0.565 0.545 0.52 0.47 1.97 1.38 1.26 1.16 1.06 0.98 0.91 0.83 0.75 0.725

12.1 12.1 12 12 12 12 16.2 16.1 16 15.9 15.8 15.9 15.8 15.7 11.5 11.6 11.5 11.5 11.5 15.6 15.5 15.4 15.3 15.2 15.1 15.1 15 15 10.500 10.500 10.5 10.5 10.5 10.5 10.4 15.3 14.7 14.6 14.4 14.4 14.3 14.2 14.1 14 14.1

W27X161 W27X146 W27X129 W27X114 W27X102 W27X94 W27X84 W24X370 W24X335 W24X306 W24X279 W24X250 W24X229 W24X207 W24X192 W24X176 W24X162 W24X146 W24X131 W24X117 W24X104 W24X103 W24X94 W24X84 W24X76 W24X68 W24X62 W24X55 W21X201 W21X182 W21X166 W21X147 W21X132 W21X122 W21X111 W21X101 W21X93 W21X83 W21X73 W21X68 W21X62 W21X55 W21X48 W21X57 W21X50

47.6 43.1 37.8 33.5 30 27.7 24.8 109 98.4 89.8 82 73.5 67.2 60.7 56.3 51.7 47.7 43 38.5 34.4 30.6 30.3 27.7 24.7 22.4 20.1 18.2 16.2 59.2 53.6 48.8 43.2 38.8 35.9 32.7 29.8 27.3 24.3 21.5 20 18.3 16.2 14.1 16.7 14.7

27.6 27.4 27.6 27.3 27.1 26.9 26.7 28 27.5 27.1 26.7 26.3 26 25.7 25.5 25.2 25 24.7 24.5 24.3 24.1 24.5 24.3 24.1 23.9 23.7 23.7 23.6 23 22.7 22.5 22.1 21.8 21.7 21.5 21.4 21.6 21.4 21.2 21.1 21 20.8 20.6 21.1 20.8

0.66 0.605 0.61 0.57 0.515 0.49 0.46 1.52 1.38 1.26 1.16 1.04 0.96 0.87 0.81 0.75 0.705 0.65 0.605 0.55 0.5 0.55 0.515 0.47 0.44 0.415 0.43 0.395 0.91 0.83 0.75 0.72 0.65 0.6 0.55 0.5 0.58 0.515 0.455 0.43 0.4 0.375 0.35 0.405 0.38

14.000 14.000 10 10.1 10 10 10 13.7 13.5 13.4 13.3 13.2 13.1 13 13 12.9 13 12.9 12.9 12.800 12.8 9 9.07 9.02 8.99 8.97 7.04 7.01 12.6 12.5 12.4 12.5 12.4 12.4 12.3 12.3 8.42 8.36 8.300 8.270 8.24 8.22 8.14 6.56 6.53

W21X44 W18x311 W18x283 W18x258 W18x234 W18x211 W18x192 W18X175 W18X158 W18X143 W18X130 W18X119 W18X106 W18X97 W18X86 W18X76 W18X71 W18X65 W18X60 W18X55 W18X50 W18X46 W18X40 W18X35 W16X100 W16X89 W16X77 W16X67 W16X57 W16X50 W16X45 W16X40 W16X36 W16X31 W16X26 W14X730 W14X665 W14X605 W14X550 W14X500 W14X455 W14X426 W14X398 W14X370 W14X342

13 91.6 83.3 75.9 68.8 62.1 56.4 51.3 46.3 42.1 38.2 35.1 31.1 28.5 25.3 22.3 20.8 19.1 17.6 16.2 14.7 13.5 11.8 10.3 29.5 26.2 22.6 19.7 16.8 14.7 13.3 11.8 10.6 9.13 7.68 215 196 178 162 147 134 125 117 109 101

20.7 22.3 21.9 21.5 21.1 20.7 20.4 20 19.7 19.5 19.3 19 18.7 18.6 18.4 18.2 18.5 18.4 18.2 18.1 18 18.1 17.9 17.7 17 16.8 16.5 16.3 16.4 16.3 16.1 16 15.9 15.9 15.7 22.4 21.6 20.9 20.2 19.6 19 18.7 18.3 17.9 17.5

0.35 1.52 1.4 1.28 1.16 1.06 0.96 0.89 0.81 0.73 0.67 0.655 0.59 0.535 0.48 0.425 0.495 0.45 0.415 0.39 0.355 0.36 0.315 0.3 0.585 0.525 0.455 0.395 0.43 0.38 0.345 0.305 0.295 0.275 0.25 3.07 2.83 2.6 2.38 2.19 2.02 1.88 1.77 1.66 1.54

6.5 12 11.9 11.8 11.7 11.6 11.5 11.4 11.3 11.2 11.2 11.3 11.2 11.1 11.1 11 7.64 7.590 7.560 7.53 7.50 6.06 6.020 6.000 10.4 10.4 10.3 10.2 7.12 7.07 7.04 7 6.99 5.53 5.5 17.9 17.7 17.4 17.2 17 16.8 16.7 16.6 16.5 16.4

W14X311 W14X283 W14X257 W14X233 W14X211 W14X193 W14X176 W14X159 W14X145 W14X132 W14X120 W14X109 W14X99 W14X90 W14X82 W14X74 W14X68 W14X61 W14X53 W14X48 W14X43 W14X38 W14X34 W14X30 W14X26 W14X22 W12X336 W12X305 W12X279 W12X252 W12X230 W12X210 W12X190 W12X170 W12X152 W12X136 W12X120 W12X106 W12X96 W12X87 W12X79 W12X72 W12X65 W12X58 W12X53

91.4 83.3 75.6 68.5 62 56.8 51.8 46.7 42.7 38.8 35.3 32 29.1 26.5 24 21.8 20 17.9 15.6 14.1 12.6 11.2 10 8.85 7.69 6.49 98.8 89.6 81.9 74 67.7 61.8 55.8 50 44.7 39.9 35.3 31.2 28.2 25.6 23.2 21.1 19.1 17 15.6

17.1 16.7 16.4 16 15.7 15.5 15.2 15 14.8 14.7 14.5 14.3 14.2 14 14.3 14.2 14 13.9 13.9 13.8 13.7 14.1 14 13.8 13.9 13.7 16.8 16.3 15.9 15.4 15.1 14.7 14.4 14 13.7 13.4 13.1 12.9 12.7 12.5 12.4 12.3 12.1 12.2 12.1

1.41 1.29 1.18 1.07 0.98 0.89 0.83 0.745 0.68 0.645 0.59 0.525 0.485 0.44 0.51 0.45 0.415 0.375 0.37 0.34 0.305 0.31 0.285 0.27 0.255 0.23 1.78 1.63 1.53 1.4 1.29 1.18 1.06 0.96 0.87 0.79 0.71 0.61 0.55 0.515 0.47 0.43 0.39 0.36 0.345

16.2 16.1 16 15.9 15.8 15.7 15.7 15.6 15.5 14.7 14.7 14.6 14.6 14.5 10.1 10.1 10 10 8.06 8.03 8 6.77 6.75 6.73 5.03 5 13.4 13.2 13.1 13 12.9 12.8 12.7 12.6 12.5 12.4 12.3 12.2 12.2 12.1 12.1 12 12 10 10

W12X50 W12X45 W12X40 W12X35 W12X30 W12X26 W12X22 W12X19 W12X16 W12X14 W10X112 W10X100 W10X88 W10X77 W10X68 W10X60 W10X54 W10X49 W10X45 W10X39 W10X33 W10X30 W10X26 W10X22 W10X19 W10X17 W10X15 W10X12 W8X67 W8X58 W8X48 W8X40 W8X35 W8X31 W8X28 W8X24 W8X21 W8X18 W8X15 W8X13 W8X10 W6X25 W6X20 W6X15 W6X16

14.6 13.1 11.7 10.3 8.79 7.65 6.48 5.57 4.71 4.16 32.9 29.4 25.9 22.6 20 17.6 15.8 14.4 13.3 11.5 9.71 8.84 7.61 6.49 5.62 4.99 4.41 3.54 19.7 17.1 14.1 11.7 10.3 9.12 8.24 7.08 6.16 5.26 4.44 3.84 2.96 7.34 5.87 4.43 4.74

12.2 12.1 11.9 12.5 12.3 12.2 12.3 12.2 12 11.9 11.4 11.1 10.8 10.6 10.4 10.2 10.1 10 10.1 9.92 9.73 10.5 10.3 10.2 10.2 10.1 10 9.87 9 8.75 8.5 8.25 8.12 8 8.06 7.93 8.28 8.14 8.11 7.99 7.89 6.38 6.2 5.99 6.28

0.37 0.335 0.295 0.3 0.26 0.23 0.26 0.235 0.22 0.2 0.755 0.68 0.605 0.53 0.47 0.42 0.37 0.34 0.35 0.315 0.29 0.3 0.26 0.24 0.25 0.24 0.23 0.19 0.57 0.51 0.4 0.36 0.31 0.285 0.285 0.245 0.25 0.23 0.245 0.23 0.17 0.32 0.26 0.23 0.26

8.08 8.05 8.01 6.56 6.52 6.49 4.03 4.01 3.99 3.97 10.4 10.3 10.3 10.2 10.1 10.1 10 10 8.02 7.99 7.96 5.81 5.77 5.75 4.02 4.01 4 3.96 8.28 8.22 8.11 8.07 8.02 8 6.54 6.5 5.27 5.25 4.01 4 3.94 6.08 6.02 5.99 4.03

W6X12 W6X9 W6X8.5 W5X19 W5X16 W4X13 M12.5X12.4 M12.5X11.6 M12X11.8 M12X10.8 M12X10 M10X9 M10X8 M10X7.5 M8X6.5 M8X6.2 M6X4.4 M6X3.7 M5X18.9 M4X6 M4X4.08 M4X3.45 M4X3.2 M3X2.9 S24X121 S24X106 S24X100 S24X90 S24X80 S20X96 S20X86 S20X75 S20X66 S18X70 S18X54.7 S15X50 S15X42.9 S12X50 S12X40.8 S12X35 S12X31.8 S10X35 S10X25.4 S8X23 S8X18.4

3.55 2.68 2.52 5.56 4.71 3.83 3.63 3.4 3.47 3.18 2.95 2.65 2.37 2.22 1.92 1.82 1.29 1.09 5.56 1.75 1.27 1.01 1.01 0.914 35.5 31.1 29.3 26.5 23.5 28.2 25.3 22 19.4 20.5 16 14.7 12.6 14.6 11.9 10.2 9.31 10.3 7.45 6.76 5.4

6.03 5.9 5.83 5.15 5.01 4.16 12.5 12.5 12 12 12 10 10 10 8 8 6 5.92 5 3.8 4 4 4 3 24.5 24.5 24 24 24 20.3 20.3 20 20 18 18 15 15 12 12 12 12 10 10 8 8

0.23 0.17 0.17 0.27 0.24 0.28 0.155 0.155 0.177 0.16 0.149 0.157 0.141 0.13 0.135 0.129 0.114 0.098 0.316 0.13 0.115 0.092 0.092 0.09 0.8 0.62 0.745 0.625 0.5 0.8 0.66 0.635 0.505 0.711 0.461 0.55 0.411 0.687 0.462 0.428 0.35 0.594 0.311 0.441 0.271

4 3.94 3.94 5.03 5 4.06 3.75 3.5 3.07 3.07 3.25 2.69 2.69 2.69 2.28 2.28 1.84 2 5 3.8 2.25 2.25 2.25 2.25 8.05 7.87 7.25 7.13 7 7.2 7.06 6.39 6.26 6.25 6 5.64 5.5 5.48 5.25 5.08 5 4.94 4.66 4.17 4

S6X17.2 S6X12.5 S5X10 S4X9.5 S4X7.7 S3X7.5 S3X5.7 HP14X117 HP14X102 HP14X89 HP14X73 HP12X84 HP12X74 HP12X63 HP12X53 HP10X57 HP10X42 HP8X36

5.06 3.66 2.93 2.79 2.26 2.2 1.66 34.4 30 26.1 21.4 24.6 21.8 18.4 15.5 16.8 12.4 10.6

6 6 5 4 4 3 3 14.2 14 13.8 13.6 12.3 12.1 11.9 11.8 10 9.7 8.02

0.465 0.232 0.214 0.326 0.193 0.349 0.17 0.805 0.705 0.615 0.505 0.685 0.605 0.515 0.435 0.565 0.415 0.445

3.57 3.33 3 2.8 2.66 2.51 2.33 14.9 14.8 14.7 14.6 12.3 12.2 12.1 12 10.2 10.1 8.16

W, M, S, and HP Se tf 1.77 1.58 1.42 1.22 3.23 2.76 2.36 2.2 2.05 2.01 1.81 1.65 1.58 1.42 1.22 1.07 2.52 2.13 2.13 1.93 1.81 1.73 1.58 1.42 1.2 1.03 0.83 4.29 3.54 2.91 2.68 2.44 2.2 2.01 1.85 1.68 1.57 1.44 1.35 1.26 1.73 1.57 1.36

k(des) 2.56 2.36 2.20 2.01 4.41 3.94 3.54 3.38 3.23 3.19 2.99 2.83 2.76 2.60 2.40 2.25 3.70 3.31 3.31 3.11 2.99 2.91 2.76 2.60 2.38 2.21 2.01 5.24 4.49 3.86 3.63 3.39 3.15 2.96 2.80 2.63 2.52 2.39 2.30 2.21 2.48 2.32 2.11

k(det) 2.625 2.4375 2.25 2.0625 4.5 4 3.625 3.5 3.3125 3.25 3.0625 2.9375 2.875 2.6875 2.5 2.3125 3.8125 3.375 3.375 3.1875 3.0625 3 2.875 2.6875 2.5 2.3125 2.125 5.5625 4.8125 4.1875 4 3.75 3.4375 3.3125 3.125 3 2.875 2.75 2.625 2.5625 2.625 2.4375 2.3125

k1 1.3125 1.25 1.1875 1.1875 2.125 2 1.875 1.8125 1.8125 1.75 1.6875 1.6875 1.625 1.5625 1.5625 1.5625 1.9375 1.8125 1.8125 1.75 1.75 1.6875 1.625 1.5625 1.5625 1.5625 1.5 2.375 2.1875 2 1.875 1.875 1.8125 1.75 1.75 1.6875 1.625 1.625 1.625 1.5625 1.3125 1.25 1.25

T 38.75 38.75 38.75 38.75 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 31.375 31.375 31.375 31.375 31.375 31.375 31.375 31.375 31.375 31.375 31.375 31.375 31.375 32.125 32.125 32.125

gage 5.5 5.5 5.5 5.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 5.5 5.5 5.5

1.26 1.18 1.1 1.02 0.94 0.79 2.28 2.09 1.89 1.73 1.57 1.4 1.28 1.15 1.22 1.06 0.96 0.855 0.74 2.44 2.24 2.05 1.85 1.65 1.5 1.32 1.19 1.07 1.18 1 0.93 0.85 0.76 0.67 0.61 3.54 2.48 2.28 2.09 1.93 1.77 1.61 1.5 1.34 1.19

2.01 1.93 1.85 1.77 1.69 1.54 3.07 2.88 2.68 2.52 2.36 2.19 2.06 1.94 1.92 1.76 1.66 1.56 1.44 3.23 3.03 2.84 2.64 2.44 2.29 2.10 1.97 1.85 1.83 1.65 1.58 1.50 1.41 1.32 1.26 4.33 3.27 3.07 2.88 2.72 2.56 2.40 2.29 2.13 1.98

2.1875 2.125 2 1.9375 1.875 1.6875 3.1875 2.9375 2.75 2.625 2.4375 2.25 2.125 2 2.125 1.9375 1.8125 1.75 1.625 3.375 3.125 2.9375 2.75 2.5625 2.375 2.25 2.0625 2 2.0625 1.875 1.8125 1.75 1.6875 1.5625 1.5 4.4375 3.375 3.1875 3 2.8125 2.6875 2.5 2.375 2.25 2.0625

1.1875 1.1875 1.1875 1.125 1.125 1.125 1.4375 1.375 1.3125 1.3125 1.25 1.25 1.1875 1.1875 1.1875 1.125 1.125 1.125 1.125 1.5 1.4375 1.375 1.3125 1.3125 1.25 1.1875 1.1875 1.125 1.125 1.125 1.125 1.125 1.125 1.0625 1.0625 1.8125 1.5 1.4375 1.4375 1.375 1.3125 1.3125 1.25 1.1875 1.1875

32.125 32.125 32.125 32.125 32.125 32.125 29.625 29.625 29.625 29.625 29.625 29.625 29.625 29.625 29.625 29.625 29.625 29.625 29.625 26.5 26.5 26.5 26.5 26.5 26.5 26.5 26.5 26.5 26.5 26.5 26.5 26.5 26.5 26.5 26.5 23.625 23.625 23.625 23.625 23.625 23.625 23.625 23.625 23.625 23.625

5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5

1.08 0.975 1.1 0.93 0.83 0.745 0.64 2.72 2.48 2.28 2.09 1.89 1.73 1.57 1.46 1.34 1.22 1.09 0.96 0.85 0.75 0.98 0.875 0.77 0.68 0.585 0.59 0.505 1.63 1.48 1.36 1.15 1.04 0.96 0.875 0.8 0.93 0.835 0.74 0.685 0.615 0.522 0.43 0.65 0.535

1.87 1.76 1.70 1.53 1.43 1.34 1.24 3.22 2.98 2.78 2.59 2.39 2.23 2.07 1.96 1.84 1.72 1.59 1.46 1.35 1.25 1.48 1.38 1.27 1.18 1.09 1.09 1.01 2.13 1.98 1.86 1.65 1.54 1.46 1.38 1.30 1.43 1.34 1.24 1.19 1.12 1.02 0.930 1.15 1.04

2 1.875 2 1.8125 1.75 1.625 1.5625 3.625 3.375 3.1875 3 2.8125 2.625 2.5 2.375 2.25 2.125 2 1.875 1.75 1.625 1.875 1.75 1.6875 1.5625 1.5 1.5 1.4375 2.5 2.375 2.25 2 1.9375 1.8125 1.75 1.6875 1.625 1.5 1.4375 1.375 1.3125 1.1875 1.125 1.3125 1.25

1.1875 1.125 1.125 1.125 1.0625 1.0625 1.0625 1.5625 1.5 1.4375 1.4375 1.375 1.3125 1.25 1.25 1.1875 1.1875 1.125 1.125 1.125 1.0625 1.125 1.0625 1.0625 1.0625 1.0625 1.0625 1 1.3125 1.25 1.1875 1.1875 1.125 1.125 1.125 1.0625 0.9375 0.875 0.875 0.875 0.8125 0.8125 0.8125 0.8125 0.8125

23.625 23.625 23.625 23.625 23.625 23.625 23.625 20.75 20.75 20.75 20.75 20.75 20.75 20.75 20.75 20.75 20.75 20.75 20.75 20.75 20.75 20.75 20.75 20.75 20.75 20.75 20.75 20.75 18 18 18 18 18 18 18 18 18.375 18.375 18.375 18.375 18.375 18.375 18.375 18.375 18.375

5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 3.5 3.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 3.5 3.5

0.45 2.74 2.5 2.3 2.11 1.91 1.75 1.59 1.44 1.32 1.2 1.06 0.94 0.87 0.77 0.68 0.81 0.75 0.695 0.63 0.57 0.605 0.525 0.425 0.985 0.875 0.76 0.665 0.715 0.63 0.565 0.505 0.43 0.44 0.345 4.91 4.52 4.16 3.82 3.5 3.21 3.04 2.85 2.66 2.47

0.950 3.24 3.00 2.70 2.51 2.31 2.15 1.99 1.84 1.72 1.60 1.46 1.34 1.27 1.17 1.08 1.21 1.15 1.10 1.03 0.972 1.01 0.927 0.827 1.39 1.28 1.16 1.07 1.12 1.03 0.967 0.907 0.832 0.842 0.747 5.51 5.12 4.76 4.42 4.10 3.81 3.63 3.44 3.26 3.07

1.125 3.4375 3.1875 3 2.75 2.5625 2.4375 2.4375 2.375 2.1875 2.0625 1.9375 1.8125 1.75 1.625 1.5625 1.5 1.4375 1.375 1.3125 1.25 1.25 1.1875 1.125 1.875 1.75 1.625 1.5625 1.375 1.3125 1.25 1.1875 1.125 1.125 1.0625 6.1875 5.8125 5.4375 5.125 4.8125 4.5 4.3125 4.125 3.9375 3.75

0.8125 1.375 1.3125 1.25 1.1875 1.1875 1.125 1.25 1.25 1.1875 1.1875 1.1875 1.125 1.125 1.0625 1.0625 0.875 0.875 0.8125 0.8125 0.8125 0.8125 0.8125 0.75 1.125 1.0625 1.0625 1 0.875 0.8125 0.8125 0.8125 0.75 0.75 0.75 2.75 2.625 2.5 2.375 2.3125 2.25 2.125 2.125 2.0625 2

18.375 15.5 15.5 15.5 15.5 15.5 15.5 15.125 15.125 15.125 15.125 15.125 15.125 15.125 15.125 15.125 15.5 15.5 15.5 15.5 15.5 15.5 15.5 15.5 13.25 13.25 13.25 13.25 13.625 13.625 13.625 13.625 13.625 13.625 13.625 10 10 10 10 10 10 10 10 10 10

3.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 5.5 5.5 5.5 5.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 (3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3)

2.26 2.07 1.89 1.72 1.56 1.44 1.31 1.19 1.09 1.03 0.94 0.86 0.78 0.71 0.855 0.785 0.72 0.645 0.66 0.595 0.53 0.515 0.455 0.385 0.42 0.335 2.96 2.71 2.47 2.25 2.07 1.9 1.74 1.56 1.4 1.25 1.11 0.99 0.9 0.81 0.735 0.67 0.605 0.64 0.575

2.86 2.67 2.49 2.32 2.16 2.04 1.91 1.79 1.69 1.63 1.54 1.46 1.38 1.31 1.45 1.38 1.31 1.24 1.25 1.19 1.12 0.915 0.855 0.785 0.820 0.735 3.55 3.30 3.07 2.85 2.67 2.50 2.33 2.16 2.00 1.85 1.70 1.59 1.50 1.41 1.33 1.27 1.20 1.24 1.18

3.5625 3.375 3.1875 3 2.875 2.75 2.625 2.5 2.375 2.3125 2.25 2.1875 2.0625 2 1.6875 1.625 1.5625 1.5 1.5 1.4375 1.375 1.25 1.1875 1.125 1.125 1.0625 3.875 3.625 3.375 3.125 2.9375 2.8125 2.625 2.4375 2.3125 2.125 2 1.875 1.8125 1.6875 1.625 1.5625 1.5 1.5 1.375

1.9375 1.875 1.8125 1.75 1.6875 1.6875 1.625 1.5625 1.5625 1.5625 1.5 1.5 1.4375 1.4375 1.0625 1.0625 1.0625 1 1 1 1 0.8125 0.75 0.75 0.75 0.75 1.6875 1.625 1.625 1.5 1.5 1.4375 1.375 1.3125 1.25 1.25 1.1875 1.125 1.125 1.0625 1.0625 1.0625 1 0.9375 0.9375

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10.875 10.875 10.875 10.875 10.875 10.875 10.875 11.625 11.625 11.625 11.625 11.625 9.125 9.125 9.125 9.125 9.125 9.125 9.125 9.125 9.125 9.125 9.125 9.125 9.125 9.125 9.125 9.125 9.125 9.25 9.25

(3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3) (3) 7.5 (3) 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 3.5 3.5 3.5 2.75 2.75 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5

0.64 0.575 0.515 0.52 0.44 0.38 0.425 0.35 0.265 0.225 1.25 1.12 0.99 0.87 0.77 0.68 0.615 0.56 0.62 0.53 0.435 0.51 0.44 0.36 0.395 0.33 0.27 0.21 0.935 0.81 0.685 0.56 0.495 0.435 0.465 0.4 0.4 0.33 0.315 0.255 0.205 0.455 0.365 0.26 0.405

1.14 1.08 1.02 0.820 0.740 0.680 0.725 0.650 0.565 0.525 1.75 1.62 1.49 1.37 1.27 1.18 1.12 1.06 1.12 1.03 0.935 0.810 0.740 0.660 0.695 0.630 0.570 0.510 1.33 1.20 1.08 0.954 0.889 0.829 0.859 0.794 0.700 0.630 0.615 0.555 0.505 0.705 0.615 0.510 0.655

1.5 1.375 1.375 1.1875 1.125 1.0625 0.9375 0.875 0.8125 0.75 1.9375 1.8125 1.6875 1.5625 1.4375 1.375 1.3125 1.25 1.3125 1.1875 1.125 1.125 1.0625 0.9375 0.9375 0.875 0.8125 0.75 1.625 1.5 1.375 1.25 1.1875 1.125 0.9375 0.875 0.875 0.8125 0.8125 0.75 0.6875 0.9375 0.875 0.75 0.875

0.9375 0.9375 0.875 0.75 0.75 0.75 0.625 0.5625 0.5625 0.5625 1 1 0.9375 0.875 0.875 0.8125 0.8125 0.8125 0.8125 0.8125 0.75 0.6875 0.6875 0.625 0.625 0.5625 0.5625 0.5625 0.9375 0.875 0.8125 0.8125 0.8125 0.75 0.625 0.5625 0.5625 0.5625 0.5625 0.5625 0.5 0.5625 0.5625 0.5625 0.5625

9.25 9.25 9.25 10.125 10.125 10.125 10.375 10.375 10.375 10.375 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 8.25 8.25 8.25 8.375 8.375 8.375 8.375 5.75 5.75 5.75 5.75 5.75 5.75 6.125 6.125 6.5 6.5 6.5 6.5 6.5 4.5 4.5 4.5 4.5

5.5 5.5 5.5 3.5 3.5 3.5 2.25 2.25 2.25 2.25 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 2.75 2.75 2.75 2.25 2.25 2.25 2.25 5.5 5.5 5.5 5.5 5.5 5.5 3.5 3.5 2.75 2.75 2.25 2.25 2.25 3.5 3.5 3.5 2.25

0.28 0.215 0.195 0.43 0.36 0.345 0.228 0.211 0.225 0.21 0.18 0.206 0.182 0.173 0.189 0.177 0.171 0.129 0.416 0.16 0.17 0.13 0.13 0.13 1.09 1.09 0.87 0.87 0.87 0.92 0.92 0.795 0.795 0.691 0.691 0.622 0.622 0.659 0.659 0.544 0.544 0.491 0.491 0.425 0.425

0.530 0.465 0.445 0.730 0.660 0.595 0.563 0.563 0.563 0.563 0.500 0.563 0.563 0.438 0.563 0.438 0.375 0.313 0.813 0.500 0.563 0.500 0.500 0.500 2.00 2.00 1.75 1.75 1.75 1.75 1.75 1.63 1.63 1.50 1.50 1.38 1.38 1.44 1.44 1.19 1.19 1.13 1.13 1.00 1.00

0.75 0.6875 0.6875 0.8125 0.75 0.75 0.5625 0.5625 0.5625 0.5625 0.5 0.5625 0.5625 0.4375 0.5625 0.4375 0.375 0.3125 0.8125 0.5 0.5625 0.5 0.5 0.5 2 2 1.75 1.75 1.75 1.75 1.75 1.625 1.625 1.5 1.5 1.375 1.375 1.4375 1.4375 1.1875 1.1875 1.125 1.125 1 1

0.5625 0.5 0.5 0.4375 0.4375 0.5 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.3125 0.375 0.25 0.25 0.25 0.5 0.375 0.375 0.375 0.375 0.375 -----------------------------------------

4.5 4.5 4.5 3.5 3.5 2.625 11.375 11.375 10.875 10.875 11 8.875 8.875 9.125 6.875 7.125 5.25 5.25 3.375 2.75 2.875 3 3 2 20.5 20.5 20.5 20.5 20.5 16.75 16.75 16.75 16.75 15 15 12.25 12.25 9.125 9.125 9.625 9.625 7.75 7.75 6

---

6

2.25 2.25 2.25 2.75 2.75 2.25 ------------------------2.75 ----------4 4 4 4 4 4 4 3.5 3.5 3.5 3.5 3.5 3.5 3 3 3 3 2.75 2.75 2.25 2.25

0.359 0.359 0.326 0.293 0.293 0.26 0.26 0.805 0.705 0.615 0.505 0.685 0.61 0.515 0.435 0.565 0.42 0.445

0.813 0.813 0.750 0.750 0.750 0.625 0.625 1.50 1.38 1.31 1.19 1.38 1.31 1.25 1.13 1.25 1.13 1.13

0.8125 0.8125 0.75 0.75 0.75 0.625 0.625 1.5 1.375 1.3125 1.1875 1.375 1.3125 1.25 1.125 1.25 1.125 1.125

-------

4.375 4.375 3.5

--------1.0625 1 0.9375 0.875 1 0.9375 0.875 0.875 0.9375 0.8125 0.875

2.5 2.5 1.75 1.75 11.25 11.25 11.25 11.25 9.5 9.5 9.5 9.5 7.5 7.5 5.75

--------------5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5

W, M, S, and HP Section Properties from AISC Version 13.0 CD Database (Dec. 2005) and AISC 13th Edition Manu wt./ft. 335 290 262 230 593 503 431 397 372 362 324 297 277 249 215 199 392 331 327 294 278 264 235 211 183 167 149 800 652 529 487 442 395 361 330 302 282 262 247 230 256 232 210

bf/(2*tf) 4.50 5.02 5.57 6.45 2.58 2.98 3.44 3.66 3.93 3.99 4.40 4.80 5.03 5.55 6.45 7.39 2.45 2.86 2.85 3.11 3.31 3.45 3.77 4.17 4.92 5.76 7.11 2.10 2.48 2.96 3.19 3.48 3.83 4.16 4.49 4.96 5.29 5.75 6.11 6.54 3.53 3.86 4.48

h/tw 38.0 45.0 49.6 54.8 19.1 22.3 25.5 28.0 29.5 30.5 34.2 36.8 41.2 45.6 52.6 52.6 24.1 28.0 29.0 32.2 33.3 35.6 41.2 45.6 52.6 52.6 54.3 13.5 16.3 19.9 21.4 23.6 26.3 28.6 31.4 33.9 36.2 38.2 40.1 42.2 33.8 37.3 39.1

Ix 31100 27000 24100 20800 50400 41600 34800 32000 29600 28900 25600 23200 21900 19600 16700 14900 29900 24700 24500 21900 20500 19400 17400 15500 13200 11600 9800 64700 50600 39600 36000 32100 28500 25700 23300 21100 19600 17900 16700 15600 16800 15000 13200

Sx 1410 1240 1110 971 2340 1980 1690 1560 1460 1420 1280 1170 1100 993 859 770 1440 1210 1200 1080 1020 971 875 786 675 600 513 3040 2460 1990 1830 1650 1490 1350 1240 1130 1050 972 913 854 895 809 719

rx 17.8 17.8 17.7 17.5 17 16.8 16.6 16.6 16.5 16.5 16.4 16.3 16.4 16.3 16.2 16 16.1 15.9 16 15.9 15.8 15.8 15.9 15.8 15.7 15.3 15 16.6 16.2 16 15.8 15.7 15.7 15.6 15.5 15.4 15.4 15.3 15.2 15.1 14.9 14.8 14.6

194 182 170 160 150 135 387 354 318 291 263 241 221 201 169 152 141 130 118 391 357 326 292 261 235 211 191 173 148 132 124 116 108 99.0 90.0 539 368 336 307 281 258 235 217 194 178

4.81 5.12 5.47 5.88 6.37 7.56 3.55 3.85 4.23 4.60 5.03 5.66 6.20 6.85 4.71 5.48 6.01 6.73 7.76 3.19 3.45 3.75 4.12 4.59 5.02 5.74 6.35 7.04 4.44 5.27 5.65 6.17 6.89 7.80 8.52 2.15 2.96 3.19 3.46 3.72 4.03 4.41 4.71 5.24 5.92

42.4 44.8 47.7 49.9 51.9 54.1 23.7 25.7 28.7 31.0 34.3 35.9 38.5 41.7 44.7 47.2 49.6 51.7 54.5 19.7 21.6 23.4 26.2 28.7 32.2 34.5 37.7 40.8 41.6 43.9 46.2 47.8 49.6 51.9 57.5 12.1 17.3 18.9 20.6 22.5 24.4 26.2 28.7 31.8 32.9

12100 11300 10500 9760 9040 7800 24300 22000 19500 17700 15900 14200 12900 11600 9290 8160 7450 6710 5900 20700 18700 16800 14900 13100 11700 10300 9200 8230 6680 5770 5360 4930 4470 3990 3610 25600 16200 14600 13100 11900 10800 9700 8910 7860 7020

664 623 581 542 504 439 1350 1240 1110 1020 919 831 759 686 549 487 448 406 359 1250 1140 1040 930 829 748 665 600 541 436 380 355 329 299 269 245 1570 1060 972 887 814 745 677 627 559 505

14.6 14.5 14.5 14.4 14.3 14 14.6 14.5 14.5 14.4 14.3 14.1 14.1 14 13.7 13.5 13.4 13.2 13 13.4 13.3 13.2 13.2 13.1 13 12.9 12.8 12.7 12.4 12.2 12.1 12 11.9 11.7 11.7 12.7 12.2 12.1 12 12 11.9 11.8 11.8 11.7 11.6

161 146 129 114 102 94.0 84.0 370 335 306 279 250 229 207 192 176 162 146 131 117 104 103 94.0 84.0 76.0 68.0 62.0 55.0 201 182 166 147 132 122 111 101 93.0 83.0 73.0 68.0 62.0 55.0 48.0 57.0 50.0

6.49 7.16 4.55 5.41 6.03 6.70 7.78 2.51 2.73 2.94 3.18 3.49 3.79 4.14 4.43 4.81 5.31 5.92 6.70 7.53 8.50 4.59 5.18 5.86 6.61 7.66 5.97 6.94 3.86 4.22 4.57 5.44 6.01 6.45 7.05 7.68 4.53 5.00 5.60 6.04 6.70 7.87 9.47 5.04 6.10

36.1 39.4 39.7 42.5 47.1 49.5 52.7 14.2 15.6 17.1 18.6 20.7 22.5 24.8 26.6 28.7 30.6 33.2 35.6 39.2 43.1 39.2 41.9 45.9 49.0 52.0 50.1 54.6 20.6 22.6 25.0 26.1 28.9 31.3 34.1 37.5 32.3 36.4 41.2 43.6 46.9 50.0 53.6 46.3 49.4

6310 5660 4760 4080 3620 3270 2850 13400 11900 10700 9600 8490 7650 6820 6260 5680 5170 4580 4020 3540 3100 3000 2700 2370 2100 1830 1550 1350 5310 4730 4280 3630 3220 2960 2670 2420 2070 1830 1600 1480 1330 1140 959 1170 984

458 414 345 299 267 243 213 957 864 789 718 644 588 531 491 450 414 371 329 291 258 245 222 196 176 154 131 114 461 417 380 329 295 273 249 227 192 171 151 140 127 110 93 111 94.5

11.5 11.5 11.2 11 11 10.9 10.7 11.1 11 10.9 10.8 10.7 10.7 10.6 10.5 10.5 10.4 10.3 10.2 10.1 10.1 10 9.87 9.79 9.69 9.55 9.23 9.11 9.47 9.4 9.36 9.17 9.12 9.09 9.05 9.02 8.7 8.67 8.64 8.6 8.54 8.4 8.24 8.36 8.18

44.0 311 283 258 234 211 192 175 158 143 130 119 106 97.0 86.0 76.0 71.0 65.0 60.0 55.0 50.0 46.0 40.0 35.0 100 89.0 77.0 67.0 57.0 50.0 45.0 40.0 36.0 31.0 26.0 730 665 605 550 500 455 426 398 370 342

7.22 2.19 2.38 2.56 2.76 3.02 3.27 3.58 3.92 4.25 4.65 5.31 5.96 6.41 7.20 8.11 4.71 5.06 5.44 5.98 6.57 5.01 5.73 7.06 5.29 5.92 6.77 7.70 4.98 5.61 6.23 6.93 8.12 6.28 7.97 1.82 1.95 2.09 2.25 2.43 2.62 2.75 2.92 3.10 3.31

53.6 10.4 11.3 12.5 16.8 15.1 16.7 18.0 19.8 22.0 23.9 24.5 27.2 30.0 33.4 37.8 32.4 35.7 38.7 41.1 45.2 44.6 50.9 53.5 24.3 27.0 31.2 35.9 33.0 37.4 41.1 46.5 48.1 51.6 56.8 3.71 4.03 4.39 4.79 5.21 5.66 6.08 6.44 6.89 7.41

843 6970 6170 5510 4900 4330 3870 3450 3060 2750 2460 2190 1910 1750 1530 1330 1170 1070 984 890 800 712 612 510 1490 1300 1110 954 758 659 586 518 448 375 301 14300 12400 10800 9430 8210 7190 6600 6000 5440 4900

81.6 624 565 514 466 419 380 344 310 282 256 231 204 188 166 146 127 117 108 98.3 88.9 78.8 68.4 57.6 175 155 134 117 92.2 81 72.7 64.7 56.5 47.2 38.4 1280 1150 1040 931 838 756 706 656 607 558

8.06 8.72 8.61 8.53 8.44 8.35 8.28 8.2 8.12 8.09 8.03 7.9 7.84 7.82 7.77 7.73 7.5 7.49 7.47 7.41 7.38 7.25 7.21 7.04 7.1 7.05 7 6.96 6.72 6.68 6.65 6.63 6.51 6.41 6.26 8.17 7.98 7.8 7.63 7.48 7.33 7.26 7.16 7.07 6.98

311 283 257 233 211 193 176 159 145 132 120 109 99.0 90.0 82.0 74.0 68.0 61.0 53.0 48.0 43.0 38.0 34.0 30.0 26.0 22.0 336 305 279 252 230 210 190 170 152 136 120 106 96.0 87.0 79.0 72.0 65.0 58.0 53.0

3.59 3.89 4.23 4.62 5.06 5.45 5.97 6.54 7.11 7.15 7.80 8.49 9.34 10.2 5.92 6.41 6.97 7.75 6.11 6.75 7.54 6.57 7.41 8.74 5.98 7.46 2.26 2.45 2.66 2.89 3.11 3.37 3.65 4.03 4.46 4.96 5.57 6.17 6.76 7.48 8.22 8.99 9.92 7.82 8.69

8.09 8.84 9.71 10.7 11.6 12.8 13.7 15.3 16.8 17.7 19.3 21.7 23.5 25.9 22.4 25.4 27.5 30.4 30.9 33.6 37.4 39.6 43.1 45.4 48.1 53.3 5.47 5.98 6.35 6.96 7.56 8.23 9.16 10.1 11.2 12.3 13.7 15.9 17.7 18.9 20.7 22.6 24.9 27.0 28.1

4330 3840 3400 3010 2660 2400 2140 1900 1710 1530 1380 1240 1110 999 881 795 722 640 541 484 428 385 340 291 245 199 4060 3550 3110 2720 2420 2140 1890 1650 1430 1240 1070 933 833 740 662 597 533 475 425

506 459 415 375 338 310 281 254 232 209 190 173 157 143 123 112 103 92.1 77.8 70.2 62.6 54.6 48.6 42 35.3 29 483 435 393 353 321 292 263 235 209 186 163 145 131 118 107 97.4 87.9 78 70.6

6.88 6.79 6.71 6.63 6.55 6.5 6.43 6.38 6.33 6.28 6.24 6.22 6.17 6.14 6.05 6.04 6.01 5.98 5.89 5.85 5.82 5.87 5.83 5.73 5.65 5.54 6.41 6.29 6.16 6.06 5.97 5.89 5.82 5.74 5.66 5.58 5.51 5.47 5.44 5.38 5.34 5.31 5.28 5.28 5.23

50.0 45.0 40.0 35.0 30.0 26.0 22.0 19.0 16.0 14.0 112 100 88.0 77.0 68.0 60.0 54.0 49.0 45.0 39.0 33.0 30.0 26.0 22.0 19.0 17.0 15.0 12.0 67.0 58.0 48.0 40.0 35.0 31.0 28.0 24.0 21.0 18.0 15.0 13.0 10.0 25.0 20.0 15.0 16.0

6.31 7.00 7.77 6.31 7.41 8.54 4.74 5.72 7.53 8.82 4.17 4.62 5.18 5.86 6.58 7.41 8.15 8.93 6.47 7.53 9.15 5.70 6.56 7.99 5.09 6.08 7.41 9.43 4.43 5.07 5.92 7.21 8.10 9.19 7.03 8.12 6.59 7.95 6.37 7.84 9.61 6.68 8.25 11.5 4.98

26.8 29.6 33.6 36.2 41.8 47.2 41.8 46.2 49.4 54.3 10.4 11.6 13.0 14.8 16.7 18.7 21.2 23.1 22.5 25.0 27.1 29.5 34.0 36.9 35.4 36.9 38.5 46.6 11.1 12.4 15.9 17.6 20.5 22.3 22.3 25.9 27.5 29.9 28.1 29.9 40.5 15.5 18.7 21.2 19.1

391 348 307 285 238 204 156 130 103 88.6 716 623 534 455 394 341 303 272 248 209 171 170 144 118 96.3 81.9 68.9 53.8 272 228 184 146 127 110 98 82.7 75.3 61.9 48 39.6 30.8 53.4 41.4 29.1 32.1

64.2 57.7 51.5 45.6 38.6 33.4 25.4 21.3 17.1 14.9 126 112 98.5 85.9 75.7 66.7 60 54.6 49.1 42.1 35 32.4 27.9 23.2 18.8 16.2 13.8 10.9 60.4 52 43.2 35.5 31.2 27.5 24.3 20.9 18.2 15.2 11.8 9.91 7.81 16.7 13.4 9.72 10.2

5.18 5.15 5.13 5.25 5.21 5.17 4.91 4.82 4.67 4.62 4.66 4.6 4.54 4.49 4.44 4.39 4.37 4.35 4.32 4.27 4.19 4.38 4.35 4.27 4.14 4.05 3.95 3.9 3.72 3.65 3.61 3.53 3.51 3.47 3.45 3.42 3.49 3.43 3.29 3.21 3.22 2.7 2.66 2.56 2.6

12.0 9.00 8.50 19.0 16.0 13.0 12.4 11.6 11.8 10.8 10.0 9.00 8.00 7.50 6.50 6.20 4.40 3.70 18.9 6.00 4.09 3.45 3.20 2.90 121 106 100 90.0 80.0 96.0 86.0 75.0 66.0 70.0 54.7 50.0 42.9 50.0 40.8 35.0 31.8 35.0 25.4 23.0 18.4

7.14 9.16 10.1 5.85 6.94 5.88 8.22 8.29 6.81 7.30 9.03 6.53 7.39 7.77 6.03 6.44 5.39 7.75 6.01 11.9 6.62 8.65 8.65 8.65 3.69 3.61 4.16 4.09 4.02 3.91 3.84 4.02 3.93 4.52 4.34 4.53 4.42 4.16 3.98 4.67 4.60 5.03 4.75 4.91 4.71

21.6 29.2 29.1 13.7 15.4 10.6 74.8 74.8 62.5 69.2 74.7 58.4 65.0 71.0 53.8 56.5 47.0 54.7 11.2 22.0 26.4 33.9 33.9 23.6 25.9 33.4 27.8 33.1 41.4 21.1 25.6 26.6 33.5 21.5 33.2 22.7 30.4 13.7 20.6 23.1 28.3 13.4 25.6 14.1 22.9

22.1 16.4 14.9 26.3 21.4 11.3 89.3 80.3 72.2 66.7 61.7 39 34.6 33 18.5 17.6 7.23 5.96 24.2 4.72 3.53 2.86 2.86 1.5 3160 2940 2380 2250 2100 1670 1570 1280 1190 923 801 485 446 303 270 228 217 147 123 64.7 57.5

7.31 5.56 5.1 10.2 8.55 5.46 14.2 12.8 12 11.1 10.3 7.79 6.95 6.6 4.63 4.39 2.41 2.01 9.67 2.48 1.77 1.43 1.43 1 258 240 199 187 175 165 155 128 119 103 89 64.7 59.4 50.6 45.1 38.1 36.2 29.4 24.6 16.2 14.4

2.49 2.47 2.43 2.17 2.13 1.72 4.96 4.86 4.56 4.58 4.57 3.83 3.82 3.85 3.11 3.1 2.36 2.34 2.08 1.64 1.67 1.68 1.68 1.28 9.43 9.71 9.01 9.21 9.47 7.71 7.89 7.62 7.83 6.7 7.07 5.75 5.95 4.55 4.76 4.72 4.83 3.78 4.07 3.09 3.26

17.3 12.5 10.0 9.50 7.70 7.50 5.70 117 102 89.0 73.0 84.0 74.0 63.0 53.0 57.0 42.0 36.0

4.97 4.64 4.61 4.77 4.54 4.83 4.48 9.25 10.5 11.9 14.4 8.97 10.0 11.8 13.8 9.05 12.0 9.16

9.67 19.4 16.8 8.33 14.1 5.38 11.0 14.2 16.2 18.5 22.6 14.2 16.1 18.9 22.3 13.9 18.9 14.2

26.2 22 12.3 6.76 6.05 2.91 2.5 1220 1050 904 729 650 569 472 393 294 210 119

8.74 7.34 4.9 3.38 3.03 1.94 1.67 172 150 131 107 106 93.8 79.1 66.7 58.8 43.4 29.8

2.28 2.45 2.05 1.56 1.64 1.15 1.23 5.96 5.92 5.88 5.84 5.14 5.11 5.06 5.03 4.18 4.13 3.36

nd AISC 13th Edition Manual (Dec. 2005) Zx 1620 1410 1270 1100 2760 2320 1960 1800 1680 1640 1460 1330 1250 1120 964 869 1710 1430 1410 1270 1190 1130 1010 906 774 693 598 3650 2910 2330 2130 1910 1710 1550 1410 1280 1190 1100 1030 963 1040 936 833

Iy 1200 1040 923 796 2520 2040 1690 1540 1420 1380 1220 1090 1040 926 796 695 803 644 640 562 521 493 444 390 331 283 229 4200 3230 2490 2250 1990 1750 1570 1420 1300 1200 1090 1010 940 528 468 411

Sy 150 132 117 101 302 249 208 191 177 173 153 138 132 101 88.2 130 106 105 93.5 87.1 82.6 74.6 66.1 56 47.9 38.8 467 367 289 263 235 208 188 171 156 144 132 123 114 86.5 77.2 67.5

ry 3.49 3.49 3.47 3.43 3.8 3.72 3.65 3.64 3.6 3.6 3.58 3.54 3.58 3.55 3.54 3.45 2.64 2.57 2.58 2.55 2.52 2.52 2.54 2.51 2.49 2.4 2.29 4.22 4.1 4 3.96 3.92 3.88 3.85 3.83 3.82 3.8 3.76 3.74 3.71 2.65 2.62 2.58

Zy 236 205 182 157 481 394 328 300 277 270 239 215 204 182 156 137 212 172 170 150 140 132 118 105 88.3 76 62.2 743 581 454 412 368 325 293 265 241 223 204 190 176 137 122 107

rts 4.24 4.21 4.17 4.13 4.63 4.50 4.41 4.37 4.34 4.33 4.28 4.23 4.25 4.21 4.18 4.12 3.30 3.21 3.21 3.16 3.13 3.12 3.11 3.07 3.04 2.98 2.89 5.14 4.96 4.80 4.74 4.69 4.61 4.58 4.53 4.53 4.50 4.46 4.42 4.40 3.25 3.21 3.18

q3222

767 718 668 624 581 509 1560 1420 1270 1160 1040 940 857 773 629 559 514 467 415 1450 1320 1190 1060 943 847 751 675 607 500 437 408 378 346 312 283 1890 1240 1130 1030 936 852 772 711 631 570

375 347 320 295 270 225 1620 1460 1290 1160 1040 933 840 749 310 273 246 218 187 1550 1390 1240 1100 959 855 757 673 598 227 196 181 164 146 128 115 2110 1310 1180 1050 953 859 769 704 619 555

61.9 57.6 53.2 49.1 45.1 37.7 200 181 161 146 131 118 106 95.2 53.9 47.2 42.7 37.9 32.6 198 179 162 144 127 114 100 89.5 79.8 43.3 37.2 34.4 31.3 27.9 24.5 22.1 277 179 162 146 133 120 108 100 88.1 78.8

2.56 2.55 2.53 2.5 2.47 2.38 3.77 3.74 3.71 3.68 3.66 3.62 3.59 3.56 2.5 2.47 2.43 2.39 2.32 3.67 3.64 3.6 3.58 3.53 3.51 3.49 3.46 3.42 2.28 2.25 2.23 2.19 2.15 2.1 2.09 3.65 3.48 3.45 3.41 3.39 3.36 3.33 3.32 3.29 3.25

97.7 90.7 83.8 77.3 70.9 59.7 312 282 250 226 202 182 164 147 84.4 73.9 66.9 59.5 51.3 310 279 252 223 196 175 155 138 123 68 58.4 54 49.2 43.9 38.6 34.7 437 279 252 227 206 187 168 154 136 122

3.15 3.13 3.11 3.08 3.06 2.99 4.49 4.44 4.39 4.35 4.31 4.29 4.25 4.21 3.03 3.01 2.98 2.94 2.89 4.37 4.32 4.27 4.22 4.16 4.13 4.10 4.07 4.03 2.77 2.75 2.73 2.70 2.66 2.62 2.60 4.41 4.14 4.09 4.04 4.00 3.96 3.92 3.89 3.85 3.83

515 464 395 343 305 278 244 1130 1020 922 835 744 675 606 559 511 468 418 370 327 289 280 254 224 200 177 153 134 530 476 432 373 333 307 279 253 221 196 172 160 144 126 107 129 110

497 443 184 159 139 124 106 1160 1030 919 823 724 651 578 530 479 443 391 340 297 259 119 109 94.4 82.5 70.4 34.5 29.1 542 483 435 376 333 305 274 248 92.9 81.4 70.6 64.7 57.5 48.4 38.7 30.6 24.9

70.9 63.5 36.8 31.5 27.8 24.8 21.2 170 152 137 124 110 99.4 88.8 81.8 74.3 68.4 60.5 53 46.5 40.7 26.5 24 20.9 18.4 15.7 9.8 8.3 86.1 77.2 70 60.1 53.5 49.2 44.5 40.3 22.1 19.5 17 15.7 14 11.8 9.52 9.35 7.64

3.23 3.2 2.21 2.18 2.15 2.12 2.07 3.27 3.23 3.2 3.17 3.14 3.11 3.08 3.07 3.04 3.05 3.01 2.97 2.94 2.91 1.99 1.98 1.95 1.92 1.87 1.38 1.34 3.02 3 2.99 2.95 2.93 2.92 2.9 2.89 1.84 1.83 1.81 1.8 1.77 1.73 1.66 1.35 1.3

109 97.7 57.6 49.3 43.4 38.8 33.2 267 238 214 193 171 154 137 126 115 105 93.2 81.5 71.4 62.4 41.5 37.5 32.6 28.6 24.5 15.7 13.3 133 119 108 92.6 82.3 75.6 68.2 61.7 34.7 30.5 26.6 24.4 21.7 18.4 14.9 14.8 12.2

3.79 3.76 2.66 2.64 2.62 2.59 2.54 3.92 3.86 3.81 3.76 3.71 3.67 3.62 3.60 3.57 3.57 3.53 3.49 3.46 3.42 2.40 2.40 2.37 2.34 2.30 1.75 1.71 3.55 3.51 3.48 3.45 3.42 3.40 3.37 3.35 2.24 2.21 2.19 2.17 2.15 2.11 2.05 1.68 1.64

95.4 754 676 611 549 490 442 398 356 322 290 262 230 211 186 163 146 133 123 112 101 90.7 78.4 66.5 198 175 150 130 105 92 82.3 73 64 54 44.2 1660 1480 1320 1180 1050 936 869 801 736 672

20.7 795 704 628 558 493 440 391 347 311 278 253 220 201 175 152 60.3 54.8 50.1 44.9 40.1 22.5 19.1 15.3 186 163 138 119 43.1 37.2 32.8 28.9 24.5 12.4 9.59 4720 4170 3680 3250 2880 2560 2360 2170 1990 1810

6.37 132 118 107 95.8 85.3 76.8 68.8 61.4 55.5 49.9 44.9 39.4 36.1 31.6 27.6 15.8 14.4 13.3 11.9 10.7 7.43 6.35 5.12 35.7 31.4 26.9 23.2 12.1 10.5 9.34 8.25 7 4.49 3.49 527 472 423 378 339 304 283 262 241 221

1.26 2.95 2.91 2.88 2.85 2.82 2.79 2.76 2.74 2.72 2.7 2.69 2.66 2.65 2.63 2.61 1.7 1.69 1.68 1.67 1.65 1.29 1.27 1.22 2.51 2.49 2.47 2.46 1.6 1.59 1.57 1.57 1.52 1.17 1.12 4.69 4.62 4.55 4.49 4.43 4.38 4.34 4.31 4.27 4.24

10.2 207 185 166 149 132 119 106 94.8 85.4 76.7 69.1 60.5 55.3 48.4 42.2 24.7 22.5 20.6 18.5 16.6 11.7 10 8.06 54.9 48.1 41.1 35.5 18.9 16.3 14.5 12.7 10.8 7.03 5.48 816 730 652 583 522 468 434 402 370 338

1.60 3.53 3.47 3.42 3.37 3.32 3.28 3.24 3.20 3.17 3.13 3.13 3.10 3.08 3.05 3.02 2.05 2.03 2.02 2.00 1.98 1.58 1.56 1.52 2.92 2.88 2.85 2.82 1.92 1.89 1.88 1.86 1.83 1.42 1.38 5.68 5.57 5.46 5.36 5.26 5.17 5.11 5.06 5.00 4.94

603 542 487 436 390 355 320 287 260 234 212 192 173 157 139 126 115 102 87.1 78.4 69.6 61.5 54.6 47.3 40.2 33.2 603 537 481 428 386 348 311 275 243 214 186 164 147 132 119 108 96.8 86.4 77.9

1610 1440 1290 1150 1030 931 838 748 677 548 495 447 402 362 148 134 121 107 57.7 51.4 45.2 26.7 23.3 19.6 8.91 7 1190 1050 937 828 742 664 589 517 454 398 345 301 270 241 216 195 174 107 95.8

199 179 161 145 130 119 107 96.2 87.3 74.5 67.5 61.2 55.2 49.9 29.3 26.6 24.2 21.5 14.3 12.8 11.3 7.88 6.91 5.82 3.55 2.8 177 159 143 127 115 104 93 82.3 72.8 64.2 56 49.3 44.4 39.7 35.8 32.4 29.1 21.4 19.2

4.2 4.17 4.13 4.1 4.07 4.05 4.02 4 3.98 3.76 3.74 3.73 3.71 3.7 2.48 2.48 2.46 2.45 1.92 1.91 1.89 1.55 1.53 1.49 1.08 1.04 3.47 3.42 3.38 3.34 3.31 3.28 3.25 3.22 3.19 3.16 3.13 3.11 3.09 3.07 3.05 3.04 3.02 2.51 2.48

304 274 246 221 198 180 163 146 133 113 102 92.7 83.6 75.6 44.8 40.5 36.9 32.8 22 19.6 17.3 12.1 10.6 8.99 5.54 4.39 274 244 220 196 177 159 143 126 111 98 85.4 75.1 67.5 60.4 54.3 49.2 44.1 32.5 29.1

4.87 4.81 4.75 4.69 4.64 4.59 4.55 4.51 4.47 4.23 4.20 4.17 4.14 4.11 2.85 2.82 2.80 2.78 2.22 2.20 2.18 1.82 1.80 1.77 1.31 1.27 4.13 4.05 4.00 3.93 3.87 3.82 3.76 3.71 3.66 3.61 3.56 3.52 3.49 3.46 3.43 3.40 3.38 2.82 2.79

71.9 64.2 57 51.2 43.1 37.2 29.3 24.7 20.1 17.4 147 130 113 97.6 85.3 74.6 66.6 60.4 54.9 46.8 38.8 36.6 31.3 26 21.6 18.7 16 12.6 70.1 59.8 49 39.8 34.7 30.4 27.2 23.1 20.4 17 13.6 11.4 8.87 18.9 15 10.8 11.7

56.3 50 44.1 24.5 20.3 17.3 4.66 3.76 2.82 2.36 236 207 179 154 134 116 103 93.4 53.4 45 36.6 16.7 14.1 11.4 4.29 3.56 2.89 2.18 88.6 75.1 60.9 49.1 42.6 37.1 21.7 18.3 9.77 7.97 3.41 2.73 2.09 17.1 13.3 9.32 4.43

13.9 12.4 11 7.47 6.24 5.34 2.31 1.88 1.41 1.19 45.3 40 34.8 30.1 26.4 23 20.6 18.7 13.3 11.3 9.2 5.75 4.89 3.97 2.14 1.78 1.45 1.1 21.4 18.3 15 12.2 10.6 9.27 6.63 5.63 3.71 3.04 1.7 1.37 1.06 5.61 4.41 3.11 2.2

1.96 1.95 1.94 1.54 1.52 1.51 0.848 0.822 0.773 0.753 2.68 2.65 2.63 2.6 2.59 2.57 2.56 2.54 2.01 1.98 1.94 1.37 1.36 1.33 0.874 0.845 0.81 0.785 2.12 2.1 2.08 2.04 2.03 2.02 1.62 1.61 1.26 1.23 0.876 0.843 0.841 1.52 1.5 1.45 0.967

21.3 19 16.8 11.5 9.56 8.17 3.66 2.98 2.26 1.9 69.2 61 53.1 45.9 40.1 35 31.3 28.3 20.3 17.2 14 8.84 7.5 6.1 3.35 2.8 2.3 1.74 32.7 27.9 22.9 18.5 16.1 14.1 10.1 8.57 5.69 4.66 2.67 2.15 1.66 8.56 6.72 4.75 3.39

2.25 2.23 2.21 1.79 1.77 1.75 1.04 1.02 0.982 0.962 3.07 3.03 2.99 2.95 2.91 2.88 2.86 2.84 2.27 2.24 2.20 1.60 1.58 1.55 1.06 1.04 1.01 0.983 2.43 2.39 2.35 2.31 2.28 2.26 1.84 1.82 1.46 1.43 1.06 1.03 1.01 1.74 1.70 1.66 1.13

8.3 6.23 5.73 11.6 9.63 6.28 16.5 15 14.3 13.2 12.2 9.22 8.2 7.77 5.43 5.15 2.8 2.33 11.1 2.74 2 1.6 1.6 1.12 306 279 239 222 204 198 183 152 139 124 104 77 69.2 60.9 52.7 44.6 41.8 35.4 28.3 19.2 16.5

2.99 2.2 1.99 9.13 7.51 3.86 2.01 1.51 1.09 1.01 1.03 0.672 0.593 0.562 0.376 0.352 0.18 0.173 8.7 1.47 0.325 0.248 0.248 0.248 83 76.8 47.4 44.7 42 49.9 46.6 29.5 27.5 24 20.7 15.6 14.3 15.6 13.5 9.84 9.33 8.3 6.73 4.27 3.69

1.5 1.11 1.01 3.63 3 1.9 1.07 0.864 0.709 0.661 0.636 0.5 0.441 0.418 0.329 0.308 0.195 0.173 3.48 0.771 0.289 0.221 0.221 0.221 20.6 19.5 13.1 12.5 12 13.9 13.2 9.25 8.78 7.69 6.91 5.53 5.19 5.69 5.13 3.88 3.73 3.36 2.89 2.05 1.84

0.918 0.905 0.89 1.28 1.26 1 0.744 0.667 0.559 0.564 0.592 0.503 0.5 0.503 0.443 0.439 0.372 0.398 1.25 0.915 0.506 0.496 0.496 0.521 1.53 1.57 1.27 1.3 1.34 1.33 1.36 1.16 1.19 1.08 1.14 1.03 1.06 1.03 1.06 0.98 1 0.899 0.95 0.795 0.827

2.32 1.72 1.56 5.53 4.58 2.92 1.68 1.37 1.15 1.07 1.02 0.809 0.711 0.67 0.529 0.495 0.311 0.273 5.33 1.18 0.453 0.346 0.346 0.344 36.3 33.4 24 22.4 20.8 24.9 23.1 16.7 15.4 14.3 12.1 10 9.08 10.3 8.86 6.8 6.44 6.19 4.99 3.67 3.18

1.08 1.06 1.05 1.45 1.43 1.16 0.933 0.852 0.731 0.732 0.768 0.650 0.646 0.646 0.563 0.560 0.467 0.499 1.44 1.04 0.593 0.580 0.580 0.597 1.94 1.93 1.66 1.66 1.67 1.71 1.71 1.49 1.49 1.42 1.42 1.32 1.31 1.32 1.30 1.22 1.21 1.16 1.14 0.999 0.985

10.5 8.45 5.66 4.04 3.5 2.35 1.94 194 169 146 118 120 105 88.3 74 66.5 48.3 33.6

2.29 1.8 1.19 0.887 0.748 0.578 0.447 443 380 326 261 213 186 153 127 101 71.7 40.3

1.28 1.08 0.795 0.635 0.562 0.461 0.383 59.5 51.4 44.3 35.8 34.6 30.4 25.3 21.1 19.7 14.2 9.88

0.673 0.702 0.638 0.564 0.576 0.513 0.518 3.59 3.56 3.53 3.49 2.94 2.92 2.88 2.86 2.45 2.41 1.95

2.35 1.86 1.37 1.13 0.97 0.821 0.656 91.4 78.8 67.7 54.6 53.2 46.6 38.7 32.2 30.3 21.8 15.2

0.859 0.831 0.754 0.698 0.676 0.638 0.605 4.15 4.10 4.05 4.00 3.41 3.38 3.33 3.29 2.84 2.77 2.26

ho 42.3 42.0 41.9 41.7 39.8 39.3 38.9 38.8 38.6 38.5 38.4 38.2 38.1 38.0 37.8 37.6 39.1 38.7 38.7 38.5 38.4 38.3 38.1 38.0 37.8 37.6 37.4 38.3 37.5 36.9 36.7 36.4 36.2 36.0 35.8 35.7 35.5 35.4 35.3 35.2 35.7 35.6 35.3

J 74.7 50.9 37.3 24.9 445 277 177 142 116 109 79.4 61.2 51.5 38.1 24.8 18.3 172 105 103 76.6 65 56.1 41.3 30.4 19.3 14 9.36 1060 593 327 258 194 142 109 84.3 64.3 52.7 41.6 34.7 28.7 52.9 39.6 28

Cw 535000 461000 405000 346000 997000 789000 638000 579000 528000 513000 448000 399000 379000 334000 284000 246000 306000 241000 239000 208000 192000 181000 161000 141000 118000 99700 80000 1540000 1130000 846000 754000 661000 575000 509000 456000 412000 378000 342000 316000 292000 168000 148000 128000

Wno 168 166 165 165 166 161 158 156 155 154 153 151 151 150 149 149 121 118 117 115 115 114 113 112 112 111 110 172 165 159 157 154 152 150 149 148 147 147 146 145 109 108 108

Sw 1180 1040 928 793 2240 1830 1510 1380 1280 1240 1100 982 940 841 719 628 946 766 754 668 622 589 530 468 395 336 270 3320 2560 1990 1800 1600 1410 1270 1150 1040 960 873 812 756 576 512 446

Qf 278 248 223 192 479 403 341 318 295 289 259 234 225 203 175 153 270 226 225 203 190 182 166 148 126 107 86.7 641 518 419 383 347 311 282 259 235 219 200 187 175 174 157 136

35.2 35.2 35.1 35.0 34.9 34.8 33.7 33.5 33.3 33.1 33.0 32.8 32.7 32.5 32.6 32.4 32.3 32.2 32.1 30.8 30.6 30.4 30.2 30.0 29.8 29.6 29.5 29.4 29.5 29.3 29.2 29.2 29.1 29.0 28.9 29.0 27.9 27.7 27.5 27.4 27.2 27.1 26.9 26.8 26.6

22.2 18.5 15.1 12.4 10.1 7 148 115 84.4 65.1 48.7 36.2 27.8 20.8 17.7 12.4 9.7 7.37 5.3 173 134 103 75.2 54.1 40.3 28.4 21 15.6 14.5 9.72 7.99 6.43 4.99 3.77 2.84 496 170 131 101 79.5 61.6 47 37.6 27.1 20.1

116000 107000 98500 90200 82200 68100 459000 408000 357000 319000 281000 251000 224000 198000 82400 71700 64400 56600 48300 366000 324000 287000 250000 215000 190000 166000 146000 129000 49400 42100 38600 34900 30900 26800 24000 443000 255000 226000 199000 178000 159000 141000 128000 111000 98400

107 106 105 105 105 104 137 135 133 131 130 130 129 128 93.7 94.1 93 92.7 92.5 120 118 117 115 114 112 112 111 110 77.5 76.9 76.8 76.5 76.2 76.2 75.1 111 103 101 99 98.5 97.3 96.2 94.8 93.7 93.8

407 378 349 321 294 245 1260 1130 1010 904 807 726 647 577 329 289 257 228 197 1140 1030 922 816 714 637 556 494 441 240 202 188 171 152 134 119 1500 935 842 745 685 616 550 501 439 393

126 118 109 101 93.1 77.9 287 262 235 214 193 173 156 140 108 94.3 84.6 75.3 65.1 267 244 222 199 176 159 140 125 113 85.8 72.4 67.5 61.5 54.9 48.5 43.7 342 231 211 190 176 160 145 134 119 106

26.5 26.4 26.5 26.4 26.3 26.2 26.1 25.3 25.0 24.9 24.6 24.5 24.3 24.1 24.0 23.9 23.8 23.7 23.5 23.4 23.3 23.6 23.4 23.3 23.2 23.1 23.2 23.1 21.4 21.2 21.1 20.9 20.8 20.7 20.6 20.6 20.7 20.6 20.5 20.4 20.4 20.3 20.2 20.4 20.3

15.1 11.3 11.1 7.33 5.28 4.03 2.81 201 152 117 90.5 66.6 51.3 38.3 30.8 23.9 18.5 13.4 9.5 6.72 4.72 7.07 5.26 3.7 2.68 1.87 1.71 1.18 40.9 30.7 23.6 15.4 11.3 8.98 6.83 5.21 6.03 4.34 3.02 2.45 1.83 1.24 0.803 1.77 1.14

87300 77200 32500 27600 24000 21300 17900 186000 161000 142000 125000 108000 96100 84100 76300 68400 62600 54600 47100 40800 35200 16600 15000 12800 11100 9430 4620 3870 62000 54400 48500 41100 36000 32700 29200 26200 9940 8630 7410 6760 5960 4980 3950 3190 2570

92.8 92.5 66.3 66.6 65.7 65.4 65.2 86.6 84.4 83.1 81.8 80.6 79.5 78.4 78.1 76.9 77.3 76.1 75.9 75 74.7 52.9 53.1 52.6 52.2 51.8 40.7 40.5 67.3 66.3 65.5 65.5 64.4 64.3 63.4 63.3 43.5 43 42.5 42.2 42 41.7 41 33.5 33.1

351 316 182 156 136 122 104 807 707 635 569 502 450 400 371 333 306 268 235 204 179 117 105 91.3 79.8 68 42.2 35.8 346 307 276 235 206 191 171 156 85.2 75 65.2 59.8 53.2 44.7 35.9 35.8 28.9

95.5 86.3 68.4 58.4 51.7 46.3 39.8 209 188 172 156 140 127 115 107 97.1 89.2 78.8 69.5 61 53.9 48.7 43.8 38.4 33.8 28.9 22.5 19.3 102 91.6 83.7 71 62.8 58.7 53 48.6 37.7 33.7 29.7 27.4 24.6 20.8 16.9 20.5 16.7

20.2 19.6 19.4 19.2 19.0 18.8 18.6 18.5 18.3 18.2 18.1 17.9 17.8 17.7 17.6 17.5 17.7 17.6 17.5 17.5 17.4 17.5 17.4 17.3 16.0 15.9 15.8 15.7 15.7 15.6 15.6 15.5 15.4 15.4 15.3 17.5 17.1 16.8 16.4 16.1 15.8 15.6 15.4 15.3 15.1

0.77 176 134 103 78.7 58.6 44.7 33.8 25.2 19.2 14.5 10.6 7.48 5.86 4.1 2.83 3.49 2.73 2.17 1.66 1.24 1.22 0.81 0.506 7.73 5.45 3.57 2.39 2.22 1.52 1.11 0.794 0.545 0.461 0.262 1450 1120 869 669 514 395 331 273 222 178

2110 76200 65900 57600 50100 43400 38000 33300 29000 25700 22700 20300 17400 15800 13600 11700 4700 4240 3850 3430 3040 1720 1440 1140 11900 10200 8590 7300 2660 2270 1990 1730 1460 739 565 362000 305000 258000 219000 187000 160000 144000 129000 116000 103000

32.9 58.7 57.7 56.6 55.5 54.5 53.6 52.5 51.6 50.9 50.7 50.7 49.7 49.2 48.9 48.2 33.8 33.5 33.1 32.9 32.7 26.5 26.1 25.9 41.6 41.4 40.5 39.9 27.9 27.7 27.3 27.1 27 21.4 21.1 78.3 75.6 72.8 70.4 68.4 66.3 65.4 64.1 62.9 61.6

24.1 482 429 384 343 302 270 238 210 188 170 152 131 119 105 90.1 52.3 47.7 43.5 39 34.9 24.3 20.7 16.5 107 94.2 79.3 67.6 35.5 30.8 27.2 24 20.3 13 10 1720 1510 1320 1160 1020 894 830 758 690 624

14 140 127 116 106 94.6 86 76.9 69 62.8 57.2 50.6 44.3 40.7 36 31.5 25.6 23.6 21.7 19.6 17.7 15.1 13 10.5 38.7 34.4 29.4 25.5 18.8 16.5 14.7 13.1 11.1 8.94 6.95 318 287 258 232 209 187 176 163 150 138

14.9 14.7 14.5 14.3 14.2 14.0 13.9 13.8 13.7 13.6 13.5 13.5 13.4 13.3 13.5 13.4 13.3 13.2 13.3 13.2 13.1 13.6 13.5 13.5 13.5 13.4 13.9 13.6 13.4 13.2 13.0 12.8 12.6 12.5 12.3 12.2 12.0 11.9 11.8 11.7 11.6 11.6 11.5 11.6 11.5

136 104 79.1 59.5 44.6 34.8 26.5 19.7 15.2 12.3 9.37 7.12 5.37 4.06 5.07 3.87 3.01 2.19 1.94 1.45 1.05 0.798 0.569 0.38 0.358 0.208 243 185 143 108 83.8 64.7 48.8 35.6 25.8 18.5 12.9 9.13 6.85 5.1 3.84 2.93 2.18 2.1 1.58

89100 77700 67800 59000 51500 45900 40500 35600 31700 25500 22700 20200 18000 16000 6710 5990 5380 4710 2540 2240 1950 1230 1070 887 405 314 57000 48600 42000 35800 31200 27200 23600 20100 17200 14700 12400 10700 9410 8270 7330 6540 5780 3570 3160

60.1 58.9 58 56.8 55.9 55.2 54.5 53.9 53.1 50.2 49.8 49.1 49 48.2 33.9 33.9 33.2 33.1 26.7 26.5 26.3 23 22.9 22.6 17 16.7 46.4 44.8 44 42.7 42 41 40.2 39.2 38.4 37.7 36.9 36.3 36 35.4 35.3 34.9 34.5 28.9 28.8

550 491 439 388 344 312 280 250 224 190 172 154 139 124 73.3 67.1 59.8 53.4 35.5 31.7 27.9 20 17.6 14.6 8.95 7 460 401 356 313 281 249 222 193 168 146 126 110 98.8 86.6 78.5 70.1 62.6 46.2 41.4

124 112 102 91.1 81.7 75 67.6 61 55.4 49.5 45 40.7 36.9 33.2 27.6 25.4 22.9 20.6 16.8 15.1 13.4 11.3 10 8.34 6.76 5.34 119 107 96 85.8 78.3 70.6 64.1 56.5 50.1 44.1 38.6 34.2 30.9 27.4 24.9 22.5 20.2 17.8 16

11.6 11.5 11.4 12.0 11.9 11.8 11.9 11.8 11.7 11.7 10.1 10.0 9.85 9.73 9.63 9.54 9.48 9.42 9.48 9.39 9.30 10.0 9.89 9.81 9.85 9.78 9.72 9.66 8.07 7.94 7.82 7.69 7.63 7.57 7.60 7.53 7.88 7.81 7.80 7.74 7.69 5.93 5.84 5.73 5.88

1.71 1.26 0.906 0.741 0.457 0.3 0.293 0.18 0.103 0.0704 15.1 10.9 7.53 5.11 3.56 2.48 1.82 1.39 1.51 0.976 0.583 0.622 0.402 0.239 0.233 0.156 0.104 0.0547 5.05 3.33 1.96 1.12 0.769 0.536 0.537 0.346 0.282 0.172 0.137 0.0871 0.0426 0.461 0.24 0.101 0.223

1880 1650 1440 879 720 607 164 131 96.9 80.4 6020 5150 4330 3630 3100 2640 2320 2070 1200 992 791 414 345 275 104 85.1 68.3 50.9 1440 1180 931 726 619 530 312 259 152 122 51.8 40.8 30.9 150 113 76.5 38.2

23.4 23.2 22.8 19.6 19.3 19.2 12 11.9 11.7 11.6 26.4 25.7 25.3 24.8 24.3 24 23.7 23.6 19 18.8 18.5 14.5 14.2 14.1 9.85 9.79 9.73 9.56 16.7 16.3 15.8 15.5 15.3 15.1 12.4 12.2 10.4 10.3 7.81 7.74 7.57 9.01 8.78 8.58 5.92

30.2 26.8 23.5 16.8 13.9 11.8 5.12 4.17 3.09 2.59 85.8 74.1 64.4 55 47.3 41.3 36.5 33 23.6 19.9 16 10.7 9.03 7.32 3.91 3.24 2.63 1.99 32.3 27.2 22 17.5 15.2 13.2 9.44 7.95 5.47 4.44 2.47 1.97 1.53 6.23 4.82 3.34 2.42

14.3 12.8 11.3 9.75 8.17 7.03 4.76 3.91 2.93 2.48 30.6 26.9 23.5 20.5 17.9 15.7 14 12.8 11.3 9.55 7.75 7.02 5.98 4.88 3.65 3.04 2.48 1.91 14.5 12.4 10.3 8.3 7.28 6.35 5.52 4.71 3.96 3.23 2.31 1.86 1.48 3.88 3.07 2.15 2.24

5.75 5.69 5.64 4.72 4.65 3.82 12.3 12.3 11.8 11.8 11.8 9.81 9.81 9.81 7.81 7.81 5.81 5.75 4.56 3.56 3.81 3.88 3.88 2.88 23.4 23.4 23.1 23.1 23.1 19.4 19.4 19.2 19.2 17.3 17.3 14.4 14.4 11.3 11.3 11.5 11.5 9.51 9.51 7.58 7.58

0.0903 0.0405 0.0333 0.316 0.192 0.151 0.0493 0.0414 0.05 0.0393 0.0292 0.0314 0.0224 0.0187 0.0184 0.0156 0.0099 0.0053 0.313 0.0184 0.0147 0.0082 0.0082 0.0079 12.8 10.1 7.59 6.05 4.89 8.4 6.65 4.59 3.58 4.1 2.33 2.12 1.54 2.77 1.69 1.05 0.878 1.29 0.603 0.55 0.335

24.7 17.7 15.8 50.9 40.6 14 76 57.1 37.7 35 35.9 16.1 14.2 13.5 5.73 5.38 1.53 1.45 45.7 4.87 1.19 0.93 0.93 0.511 11400 10500 6350 5980 5620 4690 4370 2720 2530 1800 1550 805 737 501 433 323 306 188 152 61.2 52.9

5.75 5.6 5.55 5.94 5.81 3.87 11.5 10.8 9.04 9.05 9.6 6.59 6.57 6.6 4.45 4.46 2.68 2.9 5.73 3.46 2.15 2.18 2.18 1.61 47.1 46.1 41.9 41.2 40.5 34.9 34.2 30.7 30 27 26 20.3 19.8 15.5 14.9 14.5 14.3 11.8 11.1 7.9 7.58

1.61 1.19 1.06 3.21 2.62 1.36 2.46 1.99 1.56 1.46 1.4 0.91 0.8 0.77 0.48 0.45 0.21 0.19 2.98 0.53 0.21 0.16 0.16 0.12 103 98.8 66 63.8 61.6 57.8 55.5 38.9 37.3 29.2 26.9 17.8 16.9 14 12.9 10 9.74 7.13 6.34 3.5 3.22

1.52 1.15 1.03 2.42 1.99 1.24 2.51 2.17 1.92 1.8 1.65 1.28 1.13 1.09 0.79 0.74 0.43 0.36 2.23 0.53 0.35 0.27 0.27 0.2 46.2 46.2 32.7 32.7 32.7 28.5 28.5 21.9 21.9 16.6 16.6 11.4 11.4 8.95 8.95 7.24 7.24 5.08 5.08 3 3

5.64 5.64 4.67 3.71 3.71 2.74 2.74 13.41 13.31 13.22 13.11 11.60 11.52 11.43 11.35 9.43 9.28 7.58

0.371 0.167 0.114 0.12 0.0732 0.0896 0.0433 8.02 5.39 3.59 2.01 4.24 2.98 1.83 1.12 1.97 0.813 0.77

18.2 14.3 6.52 3.05 2.57 1.08 0.838 19900 16800 14200 11200 7140 6160 5000 4080 2240 1540 578

5.03 4.7 3.51 2.59 2.47 1.72 1.6 49.9 49.2 48.5 47.8 35.6 35.2 34.6 34.2 24.1 23.4 15.4

1.61 1.41 0.859 0.531 0.481 0.28 0.242 149 128 110 88 75 65.5 54.1 44.7 34.8 24.7 14

1.57 1.57 1.06 0.671 0.671 0.385 0.385 38 33 28.6 23.3 23.1 20.4 17.1 14.3 12.9 9.41 6.5

Qw 805 701 630 547 1370 1150 969 891 829 808 720 652 614 551 473 427 848 706 695 622 587 555 495 442 376 336 288 1820 1450 1160 1060 950 847 767 698 635 591 543 509 476 516 464 412

Shape C15X50 C15X40 C15X33.9 C12X30 C12X25 C12X20.7 C10X30 C10X25 C10X20 C10X15.3 C9X20 C9X15 C9X13.4 C8X18.7 C8X13.7 C8X11.5 C7X14.7 C7X12.2 C7X9.8 C6X13 C6X10.5 C6X8.2 C5X9 C5X6.7 C4X7.2 C4X5.4 C4X4.5 C3X6 C3X5 C3X4.1 C3X3.5 MC18X58 MC18X51.9 MC18X45.8 MC18X42.7 MC13X50 MC13X40 MC13X35 MC13X31.8 MC12X50 MC12X45 MC12X40 MC12X35

A 14.7 11.8 10 8.81 7.34 6.08 8.81 7.34 5.87 4.48 5.87 4.41 3.94 5.51 4.04 3.37 4.33 3.6 2.87 3.81 3.08 2.39 2.64 1.97 2.13 1.58 1.38 1.76 1.47 1.2 1.09 17.1 15.3 13.5 12.6 14.7 11.8 10.3 9.35 14.7 13.2 11.8 10.3

d 15 15 15 12 12 12 10 10 10 10 9 9 9 8 8 8 7 7 7 6 6 6 5 5 4 4 4 3 3 3 3 18 18 18 18 13 13 13 13 12 12 12 12

tw 0.716 0.52 0.4 0.51 0.387 0.282 0.673 0.526 0.379 0.24 0.448 0.285 0.233 0.487 0.303 0.22 0.419 0.314 0.21 0.437 0.314 0.2 0.325 0.19 0.321 0.184 0.125 0.356 0.258 0.17 0.132 0.7 0.6 0.5 0.45 0.787 0.56 0.447 0.375 0.835 0.71 0.59 0.465

379 355 330 308 287 251 778 707 632 573 515 467 423 382 311 278 253 230 205 722 655 593 529 469 421 372 335 301 248 215 202 187 170 154 139 943 621 563 508 466 424 384 351 312 282

MC12X31 MC12X10.6 MC10X41.1 MC10X33.6 MC10X28.5 MC10X25 MC10X22 MC10X8.4 MC10X6.5 MC9X25.4 MC9X23.9 MC8X22.8 MC8X21.4 MC8X20 MC8X18.7 MC8X8.5 MC7X22.7 MC7X19.1 MC6X18 MC6X15.3 MC6X16.3 MC6X15.1 MC6X12

MC6x7 MC6x6.5 MC4x13.8 MC3x7.1

9.12 3.1 12.1 9.87 8.37 7.35 6.45 2.46 1.95 7.47 7.02 6.7 6.28 5.88 5.5 2.5 6.67 5.61 5.29 4.49 4.79 4.44 3.53 2.09 1.95 4.03 2.11

12 12 10 10 10 10 10 10 10 9 9 8 8 8 8 8 7 7 6 6 6 6 6 6 6 4 3

0.37 0.19 0.796 0.575 0.425 0.38 0.29 0.17 0.152 0.45 0.4 0.427 0.375 0.4 0.353 0.179 0.503 0.352 0.379 0.34 0.375 0.316 0.31 0.179 0.155 0.5 0.312

254 229 195 170 151 137 121 568 506 459 416 370 336 302 280 254 233 207 184 163 144 139 126 111 98.9 87 75.3 66.1 264 237 215 186 164 153 138 126 109 96.8 85 78.7 71.2 61.8 52.3 63.4 53.9

46.8 375 339 306 276 246 222 198 177 160 146 131 114 105 92.4 80.6 72.4 66.3 60.6 55.3 49.9 44.9 38.6 32.7 98.5 87.3 74.4 64.1 52 45.6 40.6 36 31.6 26.6 21.6 829 739 657 585 522 466 435 401 367 335

300 269 243 216 194 177 159 143 129 116 105 94.8 86.1 77.1 68.2 62.2 56 50.2 42.5 38.3 34 30.3 26.9 23.1 19.7 16.1 301 267 240 213 193 173 156 136 121 106 92.4 81 73 64.9 58.9 53.2 47.5 42.4 38.3

35.4 31.7 27.8 25.4 21.3 18.3 14.4 12.2 9.82 8.49 73.5 64.2 55.9 48.4 42.1 36.8 32.8 29.8 27 23 18.9 18.2 15.4 12.9 10.6 9.14 7.83 6.14 34.8 29.7 24.2 19.7 17.1 15 13.4 11.3 10.1 8.37 6.64 5.55 4.29 9.39 7.38 5.32 5.77

4.08 3.04 2.78 5.73 4.74 3.09 8.06 7.36 7.02 6.48 5.98 4.52 4.01 3.8 2.66 2.52 1.37 1.14 5.45 1.3 0.93 0.73 0.73 0.5 153 139 119 110 101 98.3 91.1 75.6 69.1 61.9 51.8 38.2 34.3 30.3 26.2 22.2 20.8 17.6 14 9.53 8.17

5.23 4.18 2.79 1.99 1.73 1.16 0.961 96.3 83.3 71.9 58.3 59 51.9 43.3 36.2 32.8 23.7 16.6

C and MC Section Prope bf 3.72 3.52 3.4 3.17 3.05 2.94 3.03 2.89 2.74 2.6 2.65 2.49 2.43 2.53 2.34 2.26 2.3 2.19 2.09 2.16 2.03 1.92 1.89 1.75 1.72 1.58 1.58 1.6 1.5 1.41 1.37 4.2 4.1 4 3.95 4.41 4.19 4.07 4 4.14 4.01 3.89 3.77

tf 0.65 0.65 0.65 0.501 0.501 0.501 0.436 0.436 0.436 0.436 0.413 0.413 0.413 0.39 0.39 0.39 0.366 0.366 0.366 0.343 0.343 0.343 0.32 0.32 0.296 0.296 0.296 0.273 0.273 0.273 0.273 0.625 0.625 0.625 0.625 0.61 0.61 0.61 0.61 0.7 0.7 0.7 0.7

k 1.4375 1.4375 1.4375 1.125 1.125 1.125 1 1 1 1 1 1 1 0.9375 0.9375 0.9375 0.875 0.875 0.875 0.8125 0.8125 0.8125 0.75 0.75 0.75 0.75 0.75 0.6875 0.6875 0.6875 0.6875 1.4375 1.4375 1.4375 1.4375 1.4375 1.4375 1.4375 1.4375 1.3125 1.3125 1.3125 1.3125

T 12.125 12.125 12.125 9.75 9.75 9.75 8 8 8 8 7 7 7 6.125 6.125 6.125 5.25 5.25 5.25 4.375 4.375 4.375 3.5 3.5 2.5 2.5 2.5 1.625 1.625 1.625 1.625 15.125 15.125 15.125 15.125 10.125 10.125 10.125 10.125 9.375 9.375 9.375 9.375

gage 2.25 2 2 1.75 1.75 1.75 1.75 1.75 1.5 1.5 1.5 1.375 1.375 1.5 1.375 1.375 1.25 1.25 1.25 1.375 1.125 1.125 1.125 --1 ------------2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5

rts 1.17 1.15 1.13 1.01 1.00 0.983 0.925 0.911 0.894 0.869 0.848 0.824 0.813 0.800 0.774 0.756 0.738 0.721 0.698 0.689 0.669 0.643 0.617 0.584 0.563 0.528 0.524 0.519 0.495 0.469 0.455 1.35 1.35 1.34 1.34 1.41 1.38 1.35 1.34 1.37 1.35 1.33 1.30

3.67 1.5 4.32 4.1 3.95 3.41 3.32 1.5 1.17 3.5 3.45 3.5 3.45 3.03 2.98 1.87 3.6 3.45 3.5 3.5 3 2.94 2.5 1.88 1.85 2.5 1.94

0.7 0.309 0.575 0.575 0.575 0.575 0.575 0.28 0.202 0.55 0.55 0.525 0.525 0.5 0.5 0.311 0.5 0.5 0.475 0.385 0.475 0.475 0.375 0.291 0.291 0.5 0.351

1.3125 0.75 1.3125 1.3125 1.3125 1.3125 1.3125 0.75 0.5625 1.25 1.25 1.1875 1.1875 1.125 1.125 0.8125 1.125 1.125 1.0625 0.875 1.0625 1.0625 0.875 0.75 0.75 1 0.8125

9.375 10.500 7.375 7.375 7.375 7.375 7.375 8.5 8.875 6.5 6.5 5.625 5.625 5.75 5.75 6.375 4.75 4.75 3.875 4.25 3.875 3.875 4.25 4.5 4.5 2 1.375

2.25 --2.5 2.5 2.5 2 2 ----2 2 2 2 2 2 1.125 2 2 2 2 1.75 1.75 1.5 ---------

1.28 0.477 1.44 1.40 1.36 1.17 1.14 0.486 0.364 1.20 1.18 1.20 1.18 1.03 1.02 0.624 1.23 1.18 1.20 1.20 1.03 1.01 0.856 0.638 0.630 0.852 0.657

C and MC Section Properties from AISC Version 13.0 CD Database (Dec. 2005) and AISC 13th Edition Manual (Dec. 20 ho 14.4 14.4 14.4 11.5 11.5 11.5 9.56 9.56 9.56 9.56 8.59 8.59 8.59 7.61 7.61 7.61 6.63 6.63 6.63 5.66 5.66 5.66 4.68 4.68 3.70 3.70 3.70 2.73 2.73 2.73 2.73 17.4 17.4 17.4 17.4 12.4 12.4 12.4 12.4 11.3 11.3 11.3 11.3

wt./ft. 50 40 33.9 30 25 20.7 30 25 20 15.3 20 15 13.4 18.7 13.7 11.5 14.7 12.2 9.8 13 10.5 8.2 9 6.7 7.2 5.4 4.5 6 5 4.1 3.5 58 51.9 45.8 42.7 50 40 35 31.8 50 45 40 35

eo 0.583 0.767 0.896 0.618 0.746 0.87 0.368 0.494 0.636 0.796 0.515 0.681 0.742 0.431 0.604 0.697 0.441 0.538 0.647 0.38 0.486 0.599 0.427 0.552 0.386 0.501 0.587 0.322 0.392 0.461 0.493 0.695 0.797 0.909 0.969 0.815 1.03 1.16 1.24 0.741 0.844 0.952 1.07

Ix 404 348 315 162 144 129 103 91.1 78.9 67.3 60.9 51 47.8 43.9 36.1 32.5 27.2 24.2 21.2 17.3 15.1 13.1 8.89 7.48 4.58 3.85 3.65 2.07 1.85 1.65 1.57 675 627 578 554 314 273 252 239 269 251 234 216

Sx 53.8 46.5 42 27 24 21.5 20.7 18.2 15.8 13.5 13.5 11.3 10.6 11 9.02 8.14 7.78 6.92 6.07 5.78 5.04 4.35 3.56 2.99 2.29 1.92 1.83 1.38 1.23 1.1 1.04 75 69.6 64.2 61.5 48.3 41.9 38.8 36.7 44.9 41.9 39 36

rx 5.24 5.45 5.62 4.29 4.43 4.61 3.42 3.52 3.66 3.87 3.22 3.4 3.49 2.82 2.99 3.11 2.51 2.6 2.72 2.13 2.22 2.34 1.83 1.95 1.47 1.56 1.63 1.08 1.12 1.17 1.2 6.29 6.41 6.55 6.64 4.62 4.82 4.95 5.05 4.28 4.36 4.46 4.59

11.3 11.7 9.43 9.43 9.43 9.43 9.43 9.72 9.80 8.45 8.45 7.48 7.48 7.50 7.50 7.69 6.50 6.50 5.53 5.62 5.53 5.53 5.63 5.71 5.71 3.50 2.65

31 10.6 41.1 33.6 28.5 25 22 8.4 6.5 25.4 23.9 22.8 21.4 20 18.7 8.5 22.7 19.1 18 15.3 16.3 15.1 12 7 6.5 13.8 7.1

1.17 0.284 0.864 1.06 1.21 1.03 1.12 0.332 0.182 0.986 1.04 1.04 1.09 0.843 0.889 0.542 1.01 1.15 1.17 1.16 0.93 0.982 0.725 0.583 0.612 0.643 0.574

202 55.3 157 139 126 110 102 31.9 22.9 87.9 84.9 63.8 61.5 54.4 52.4 23.3 47.4 43.1 29.7 25.3 26 24.9 18.7 11.4 11 8.85 2.72

33.7 9.22 31.5 27.8 25.3 22 20.5 6.39 4.59 19.5 18.9 15.9 15.4 13.6 13.1 5.82 13.5 12.3 9.89 8.44 8.66 8.3 6.24 3.81 3.66 4.43 1.81

4.71 4.22 3.61 3.75 3.89 3.87 3.99 3.61 3.43 3.43 3.48 3.09 3.13 3.04 3.09 3.05 2.67 2.77 2.37 2.38 2.33 2.37 2.3 2.34 2.38 1.48 1.14

th Edition Manual (Dec. 2005) Zx 68.5 57.5 50.8 33.8 29.4 25.6 26.7 23.1 19.4 15.9 16.9 13.6 12.6 13.9 11 9.63 9.75 8.46 7.19 7.29 6.18 5.16 4.39 3.55 2.84 2.29 2.12 1.74 1.52 1.32 1.24 95.4 87.3 79.2 75.1 60.8 51.2 46.5 43.4 56.5 52 47.7 43.2

Iy 11 9.17 8.07 5.12 4.45 3.86 3.93 3.34 2.8 2.27 2.41 1.91 1.75 1.97 1.52 1.31 1.37 1.16 0.957 1.05 0.86 0.687 0.624 0.47 0.425 0.312 0.289 0.3 0.241 0.191 0.169 17.6 16.3 14.9 14.3 16.4 13.7 12.3 11.4 17.4 15.8 14.2 12.6

Sy 3.77 3.34 3.09 2.05 1.87 1.72 1.65 1.47 1.31 1.15 1.17 1.01 0.954 1.01 0.848 0.775 0.772 0.696 0.617 0.638 0.561 0.488 0.444 0.372 0.337 0.277 0.265 0.263 0.228 0.196 0.182 5.28 5.02 4.77 4.64 4.77 4.24 3.97 3.79 5.64 5.3 4.98 4.64

ry 0.865 0.883 0.901 0.762 0.779 0.797 0.668 0.675 0.69 0.711 0.64 0.659 0.666 0.598 0.613 0.623 0.561 0.568 0.578 0.524 0.529 0.536 0.486 0.489 0.447 0.444 0.457 0.413 0.405 0.398 0.394 1.02 1.03 1.05 1.07 1.06 1.08 1.09 1.1 1.09 1.09 1.1 1.11

x(bar) 0.799 0.778 0.788 0.674 0.674 0.698 0.649 0.617 0.606 0.634 0.583 0.586 0.601 0.565 0.554 0.572 0.532 0.525 0.541 0.514 0.5 0.512 0.478 0.484 0.459 0.457 0.493 0.455 0.439 0.437 0.443 0.862 0.858 0.866 0.877 0.974 0.963 0.98 1 1.05 1.04 1.04 1.05

Zy 8.14 6.84 6.19 4.32 3.82 3.47 3.78 3.18 2.7 2.34 2.46 2.04 1.94 2.17 1.73 1.57 1.63 1.42 1.26 1.35 1.14 0.987 0.913 0.757 0.695 0.565 0.531 0.543 0.464 0.399 0.364 10.7 9.86 9.14 8.82 10.2 8.66 8.04 7.69 10.9 10.1 9.31 8.62

39.7 11.6 39.3 33.7 30 26.2 23.9 7.92 5.9 23.5 22.5 19.1 18.2 16.4 15.6 6.95 16.4 14.5 11.7 9.91 10.4 9.83 7.47 4.5 4.28 5.53 2.24

11.3 0.378 15.7 13.1 11.3 7.25 6.4 0.326 0.133 7.57 7.14 7.01 6.58 4.42 4.15 0.624 7.24 6.06 5.88 4.91 3.77 3.46 1.85 0.603 0.565 2.13 0.666

4.37 0.307 4.85 4.35 3.99 2.96 2.75 0.268 0.137 2.99 2.89 2.81 2.71 2.02 1.95 0.431 2.83 2.55 2.47 2.01 1.82 1.73 1.03 0.439 0.422 1.29 0.518

1.11 0.349 1.14 1.15 1.16 0.993 0.997 0.364 0.262 1.01 1.01 1.02 1.02 0.867 0.868 0.5 1.04 1.04 1.05 1.05 0.887 0.883 0.724 0.537 0.539 0.727 0.562

1.08 0.269 1.09 1.09 1.12 0.953 0.99 0.284 0.194 0.97 0.981 1.01 1.02 0.84 0.849 0.428 1.04 1.08 1.12 1.05 0.927 0.94 0.704 0.501 0.513 0.849 0.653

8.15 0.635 9.49 8.28 7.59 5.65 5.29 0.548 0.284 5.7 5.51 5.37 5.18 3.86 3.72 0.875 5.38 4.85 4.68 3.85 3.47 3.3 1.97 0.865 0.836 2.4 0.998

xp 0.49 0.392 0.332 0.367 0.306 0.253 0.441 0.367 0.294 0.224 0.326 0.245 0.219 0.344 0.252 0.211 0.309 0.257 0.205 0.318 0.256 0.199 0.264 0.215 0.266 0.231 0.321 0.294 0.245 0.262 0.296 0.474 0.424 0.374 0.349 0.566 0.452 0.396 0.36 0.613 0.55 0.49 0.428

J 2.65 1.45 1.01 0.861 0.538 0.369 1.22 0.687 0.368 0.209 0.427 0.208 0.168 0.434 0.186 0.13 0.267 0.161 0.0996 0.237 0.128 0.0736 0.109 0.0549 0.0817 0.0399 0.0322 0.0725 0.0425 0.0269 0.0226 2.81 2.03 1.45 1.23 2.96 1.55 1.13 0.937 3.23 2.33 1.69 1.24

Cw 492 410 358 151 130 112 79.5 68.3 56.9 45.5 39.4 31 28.2 25.1 19.2 16.5 13.1 11.2 9.15 7.19 5.91 4.7 2.93 2.22 1.24 0.921 0.871 0.462 0.379 0.307 0.276 1070 985 897 852 558 462 412 380 411 373 336 297

ro(bar) 5.49 5.71 5.94 4.54 4.72 4.93 3.63 3.76 3.93 4.19 3.46 3.69 3.79 3.05 3.26 3.41 2.75 2.86 3.02 2.37 2.48 2.65 2.1 2.26 1.75 1.88 2.01 1.4 1.45 1.53 1.57 6.56 6.7 6.87 6.97 5.07 5.32 5.5 5.64 4.77 4.88 5.01 5.18

H 0.937 0.927 0.92 0.919 0.909 0.899 0.921 0.912 0.9 0.884 0.899 0.882 0.875 0.894 0.874 0.862 0.875 0.862 0.845 0.858 0.842 0.824 0.815 0.79 0.767 0.742 0.71 0.69 0.673 0.655 0.646 0.944 0.939 0.933 0.93 0.875 0.859 0.849 0.842 0.859 0.851 0.842 0.831

0.425 0.129 0.604 0.494 0.419 0.367 0.467 0.123 0.0975 0.415 0.39 0.419 0.452 0.367 0.344 0.156 0.477 0.579 0.644 0.511 0.465 0.543 0.294 0.174 0.191 0.508 0.414

1 0.0596 2.26 1.2 0.791 0.638 0.51 0.0413 0.0191 0.691 0.599 0.572 0.495 0.441 0.38 0.0587 0.625 0.407 0.379 0.223 0.336 0.285 0.155 0.0464 0.0412 0.373 0.0928

267 11.7 269 224 193 124 110 7 2.76 104 98 75.2 70.8 47.8 45 8.21 58.3 49.3 34.6 30 22.1 20.5 11.3 4 3.75 4.84 0.915

5.34 4.27 4.26 4.47 4.68 4.46 4.62 3.68 3.46 4.08 4.15 3.84 3.91 3.58 3.65 3.24 3.53 3.7 3.46 3.41 3.11 3.18 2.8 2.63 2.68 2.23 1.76

0.822 0.983 0.79 0.77 0.752 0.803 0.791 0.972 0.988 0.77 0.763 0.715 0.707 0.779 0.773 0.91 0.659 0.638 0.563 0.579 0.643 0.634 0.74 0.83 0.824 0.55 0.516

Shape

WT22X167.5 WT22X145 WT22X131 WT22X115 WT20X296.5 WT20X251.5 WT20X215.5 WT20X198.5 WT20X186 WT20X181 WT20X162 WT20X148.5 WT20X138.5 WT20X124.5 WT20X107.5 WT20X99.5 WT20X196 WT20X165.5 WT20X163.5 WT20X147 WT20X139 WT20X132 WT20X117.5 WT20X105.5 WT20X91.5 WT20X83.5 WT20X74.5 WT18X400 WT18X326 WT18X264.5 WT18X243.5 WT18X220.5 WT18X197.5 WT18X180.5 WT18X165 WT18X151 WT18X141 WT18X131 WT18X123.5 WT18X116 WT18X128 WT18X115.5 WT18X105

A 49.2 42.7 38.4 33.8 87.2 73.9 63.4 58.4 54.6 53.3 47.7 43.7 40.7 36.7 31.7 29.2 57.6 48.7 48.0 43.1 41.0 38.8 34.5 31.0 26.7 24.6 21.9 118 96.1 77.8 71.7 64.9 58.2 53.0 48.5 44.4 41.5 38.5 36.3 34.5 37.7 34.1 30.9

d 22.0 21.8 21.7 21.5 21.5 21.0 20.6 20.5 20.3 20.3 20.1 19.9 19.8 19.7 19.5 19.3 20.8 20.4 20.4 20.2 20.1 20.0 19.8 19.7 19.5 19.3 19.1 21.0 20.2 19.6 19.7 19.1 18.9 18.7 18.5 18.4 18.3 18.1 18.0 18.6 18.7 18.6 18.3

tw 1.03 0.865 0.785 0.710 1.79 1.54 1.34 1.22 1.16 1.12 1.00 0.930 0.830 0.750 0.650 0.650 1.42 1.22 1.18 1.06 1.03 0.960 0.830 0.750 0.650 0.650 0.630 2.38 1.97 1.61 1.50 1.36 1.22 1.12 1.02 0.945 0.885 0.840 0.800 0.870 0.960 0.870 0.830

bf 15.9 15.8 15.8 15.8 16.7 16.4 16.2 16.1 16.1 16.0 15.9 15.8 15.8 15.8 15.8 15.8 12.4 12.2 12.1 12.0 12.0 11.9 11.9 11.8 11.8 11.8 11.8 18.0 17.6 17.2 17.1 17.0 16.8 16.7 16.6 16.7 16.6 16.6 16.5 12.1 12.2 12.1 12.2

WT18X97 WT18X91 WT18X85 WT18X80 WT18X75 WT18X67.5 WT16.5X193.5 WT16.5X177 WT16.5X159 WT16.5X145.5 WT16.5X131.5 WT16.5X120.5 WT16.5X110.5 WT16.5X100.5 WT16.5X84.5 WT16.5X76 WT16.5X70.5 WT16.5X65 WT16.5X59 WT15X195.5 WT15X178.5 WT15X163 WT15X146 WT15X130.5 WT15X117.5 WT15X105.5 WT15X95.5 WT15X86.5 WT15X74 WT15X66 WT15X62 WT15X58 WT15X54 WT15X49.5 WT15X45 WT13.5X269.5 WT13.5X184 WT13.5X168 WT13.5X153.5 WT13.5X140.5 WT13.5X129 WT13.5X117.5 WT13.5X108.5 WT13.5X97 WT13.5X89

28.5 26.8 25.0 23.5 22.1 19.9 57.0 52.1 46.8 42.8 38.7 35.5 32.6 29.6 24.8 22.4 20.8 19.2 17.3 57.6 52.5 47.9 42.9 38.4 34.6 31.1 28.1 25.5 21.7 19.4 18.2 17.1 15.9 14.5 13.2 79.3 54.2 49.5 45.2 41.4 38.0 34.7 32.0 28.6 26.2

18.2 18.2 18.1 18.0 17.9 17.8 18.0 17.8 17.6 17.4 17.3 17.1 17.0 16.8 16.9 16.7 16.7 16.5 16.4 16.6 16.4 16.2 16.0 15.8 15.7 15.5 15.3 15.2 15.3 15.2 15.1 15.0 14.9 14.8 14.8 16.3 15.2 15.0 14.8 14.6 14.5 14.3 14.2 14.1 13.9

0.765 0.725 0.680 0.650 0.625 0.600 1.26 1.16 1.04 0.960 0.870 0.830 0.775 0.715 0.670 0.635 0.605 0.580 0.550 1.36 1.24 1.14 1.02 0.930 0.830 0.775 0.710 0.655 0.650 0.615 0.585 0.565 0.545 0.520 0.470 1.97 1.38 1.26 1.16 1.06 0.980 0.910 0.830 0.750 0.725

12.1 12.1 12.0 12.0 12.0 12.0 16.2 16.1 16.0 15.9 15.8 15.9 15.8 15.7 11.5 11.6 11.5 11.5 11.5 15.6 15.5 15.4 15.3 15.2 15.1 15.1 15.0 15.0 10.5 10.5 10.5 10.5 10.5 10.5 10.4 15.3 14.7 14.6 14.4 14.4 14.3 14.2 14.1 14.0 14.1

WT13.5X80.5 WT13.5X73 WT13.5X64.5 WT13.5X57 WT13.5X51 WT13.5X47 WT13.5X42 WT12X185 WT12X167.5 WT12X153 WT12X139.5 WT12X125 WT12X114.5 WT12X103.5 WT12X96 WT12X88 WT12X81 WT12X73 WT12X65.5 WT12X58.5 WT12X52 WT12X51.5 WT12X47 WT12X42 WT12X38 WT12X34 WT12X31 WT12X27.5 WT10.5X100.5 WT10.5X91 WT10.5X83 WT10.5X73.5 WT10.5X66 WT10.5X61 WT10.5X55.5 WT10.5X50.5 WT10.5X46.5 WT10.5X41.5 WT10.5X36.5 WT10.5X34 WT10.5X31 WT10.5X27.5 WT10.5X24 WT10.5X28.5 WT10.5X25

23.8 21.6 18.9 16.8 15.0 13.8 12.4 54.4 49.2 44.9 41.0 36.8 33.6 30.4 28.1 25.8 23.9 21.5 19.3 17.2 15.3 15.1 13.8 12.4 11.2 10.0 9.11 8.10 29.6 26.8 24.4 21.6 19.4 17.9 16.3 14.9 13.7 12.2 10.7 10.0 9.13 8.10 7.07 8.37 7.36

13.8 13.7 13.8 13.6 13.5 13.5 13.4 14.0 13.8 13.6 13.4 13.2 13.0 12.9 12.7 12.6 12.5 12.4 12.2 12.1 12.0 12.3 12.2 12.1 12.0 11.9 11.9 11.8 11.5 11.4 11.2 11.0 10.9 10.8 10.8 10.7 10.8 10.7 10.6 10.6 10.5 10.4 10.3 10.5 10.4

0.660 0.605 0.610 0.570 0.515 0.490 0.460 1.52 1.38 1.26 1.16 1.04 0.960 0.870 0.810 0.750 0.705 0.650 0.605 0.550 0.500 0.550 0.515 0.470 0.440 0.415 0.430 0.395 0.910 0.830 0.750 0.720 0.650 0.600 0.550 0.500 0.580 0.515 0.455 0.430 0.400 0.375 0.350 0.405 0.380

14.0 14.0 10.0 10.1 10.0 10.0 10.0 13.7 13.5 13.4 13.3 13.2 13.1 13.0 13.0 12.9 13.0 12.9 12.9 12.8 12.8 9.00 9.07 9.02 8.99 8.97 7.04 7.01 12.6 12.5 12.4 12.5 12.4 12.4 12.3 12.3 8.42 8.36 8.30 8.27 8.24 8.22 8.14 6.56 6.53

WT10.5X22 WT9X155.5 WT9X141.5 WT9X129 WT9X117 WT9X105.5 WT9X96 WT9X87.5 WT9X79 WT9X71.5 WT9X65 WT9X59.5 WT9X53 WT9X48.5 WT9X43 WT9X38 WT9X35.5 WT9X32.5 WT9X30 WT9X27.5 WT9X25 WT9X23 WT9X20 WT9X17.5 WT8X50 WT8X44.5 WT8X38.5 WT8X33.5 WT8X28.5 WT8X25 WT8X22.5 WT8X20 WT8X18 WT8X15.5 WT8X13 WT7X365 WT7X332.5 WT7X302.5 WT7X275 WT7X250 WT7X227.5 WT7X213 WT7X199 WT7X185 WT7X171

6.49 45.8 41.6 37.9 34.4 31.1 28.2 25.7 23.2 21.0 19.1 17.5 15.6 14.3 12.7 11.2 10.4 9.55 8.82 8.10 7.33 6.77 5.88 5.15 14.7 13.1 11.3 9.84 8.39 7.37 6.63 5.89 5.29 4.56 3.84 107 97.8 88.9 80.9 73.5 66.9 62.6 58.5 54.4 50.3

10.3 11.2 10.9 10.7 10.5 10.3 10.2 10.0 9.86 9.75 9.63 9.49 9.37 9.30 9.20 9.11 9.24 9.18 9.12 9.06 9.00 9.03 8.95 8.85 8.49 8.38 8.26 8.17 8.22 8.13 8.07 8.01 7.93 7.94 7.85 11.2 10.8 10.5 10.1 9.80 9.51 9.34 9.15 8.96 8.77

0.350 1.52 1.40 1.28 1.16 1.06 0.960 0.890 0.810 0.730 0.670 0.655 0.590 0.535 0.480 0.425 0.495 0.450 0.415 0.390 0.355 0.360 0.315 0.300 0.585 0.525 0.455 0.395 0.430 0.380 0.345 0.305 0.295 0.275 0.250 3.07 2.83 2.60 2.38 2.19 2.02 1.88 1.77 1.66 1.54

6.50 12.0 11.9 11.8 11.7 11.6 11.5 11.4 11.3 11.2 11.2 11.3 11.2 11.1 11.1 11.0 7.64 7.59 7.56 7.53 7.50 6.06 6.02 6.00 10.4 10.4 10.3 10.2 7.12 7.07 7.04 7.00 6.99 5.53 5.50 17.9 17.7 17.4 17.2 17.0 16.8 16.7 16.6 16.5 16.4

WT7X155.5 WT7X141.5 WT7X128.5 WT7X116.5 WT7X105.5 WT7X96.5 WT7X88 WT7X79.5 WT7X72.5 WT7X66 WT7X60 WT7X54.5 WT7X49.5 WT7X45 WT7X41 WT7X37 WT7X34 WT7X30.5 WT7X26.5 WT7X24 WT7X21.5 WT7X19 WT7X17 WT7X15 WT7X13 WT7X11 WT6X168 WT6X152.5 WT6X139.5 WT6X126 WT6X115 WT6X105 WT6X95 WT6X85 WT6X76 WT6X68 WT6X60 WT6X53 WT6X48 WT6X43.5 WT6X39.5 WT6X36 WT6X32.5 WT6X29 WT6X26.5

45.7 41.6 37.8 34.2 31.0 28.4 25.9 23.4 21.3 19.4 17.7 16.0 14.6 13.2 12.0 10.9 10.0 8.96 7.80 7.07 6.31 5.58 5.00 4.42 3.85 3.25 49.4 44.8 41.0 37.0 33.9 30.9 27.9 25.0 22.4 20.0 17.6 15.6 14.1 12.8 11.6 10.6 9.54 8.52 7.78

8.56 8.37 8.19 8.02 7.86 7.74 7.61 7.49 7.39 7.33 7.24 7.16 7.08 7.01 7.16 7.09 7.02 6.95 6.96 6.90 6.83 7.05 6.99 6.92 6.96 6.87 8.41 8.16 7.93 7.71 7.53 7.36 7.19 7.02 6.86 6.71 6.56 6.45 6.36 6.27 6.19 6.13 6.06 6.10 6.03

1.41 1.29 1.18 1.07 0.980 0.890 0.830 0.745 0.680 0.645 0.590 0.525 0.485 0.440 0.510 0.450 0.415 0.375 0.370 0.340 0.305 0.310 0.285 0.270 0.255 0.230 1.78 1.63 1.53 1.40 1.29 1.18 1.06 0.960 0.870 0.790 0.710 0.610 0.550 0.515 0.470 0.430 0.390 0.360 0.345

16.2 16.1 16.0 15.9 15.8 15.7 15.7 15.6 15.5 14.7 14.7 14.6 14.6 14.5 10.1 10.1 10.0 10.0 8.06 8.03 8.00 6.77 6.75 6.73 5.03 5.00 13.4 13.2 13.1 13.0 12.9 12.8 12.7 12.6 12.5 12.4 12.3 12.2 12.2 12.1 12.1 12.0 12.0 10.0 10.0

WT6X25 WT6X22.5 WT6X20 WT6X17.5 WT6X15 WT6X13 WT6X11 WT6X9.5 WT6X8 WT6X7 WT5X56 WT5X50 WT5X44 WT5X38.5 WT5X34 WT5X30 WT5X27 WT5X24.5 WT5X22.5 WT5X19.5 WT5X16.5 WT5X15 WT5X13 WT5X11 WT5X9.5 WT5X8.5 WT5X7.5 WT5X6 WT4X33.5 WT4X29 WT4X24 WT4X20 WT4X17.5 WT4X15.5 WT4X14 WT4X12 WT4X10.5 WT4X9 WT4X7.5 WT4X6.5 WT4X5 WT3X12.5 WT3X10 WT3X7.5 WT3X8

7.30 6.56 5.84 5.17 4.40 3.82 3.24 2.79 2.36 2.08 16.5 14.7 12.9 11.3 10.0 8.82 7.91 7.21 6.63 5.73 4.85 4.42 3.81 3.24 2.81 2.50 2.21 1.77 9.84 8.54 7.05 5.87 5.14 4.56 4.12 3.54 3.08 2.63 2.22 1.92 1.48 3.67 2.94 2.21 2.37

6.10 6.03 5.97 6.25 6.17 6.11 6.16 6.08 6.00 5.96 5.68 5.55 5.42 5.30 5.20 5.11 5.05 4.99 5.05 4.96 4.87 5.24 5.17 5.09 5.12 5.06 5.00 4.94 4.50 4.38 4.25 4.13 4.06 4.00 4.03 3.97 4.14 4.07 4.06 4.00 3.95 3.19 3.10 3.00 3.14

0.370 0.335 0.295 0.300 0.260 0.230 0.260 0.235 0.220 0.200 0.755 0.680 0.605 0.530 0.470 0.420 0.370 0.340 0.350 0.315 0.290 0.300 0.260 0.240 0.250 0.240 0.230 0.190 0.570 0.510 0.400 0.360 0.310 0.285 0.285 0.245 0.250 0.230 0.245 0.230 0.170 0.320 0.260 0.230 0.260

8.08 8.05 8.01 6.56 6.52 6.49 4.03 4.01 3.99 3.97 10.4 10.3 10.3 10.2 10.1 10.1 10.0 10.0 8.02 7.99 7.96 5.81 5.77 5.75 4.02 4.01 4.00 3.96 8.28 8.22 8.11 8.07 8.02 8.00 6.54 6.50 5.27 5.25 4.02 4.00 3.94 6.08 6.02 5.99 4.03

WT3X6 WT3X4.5 WT3X4.25 WT2.5X9.5 WT2.5X8 WT2X6.5 MT6.25X6.2 MT6.25X5.9 MT6X5.9 MT6X5.4 MT6X5 MT5X4.5 MT5X4 MT5X3.75 MT4X3.25 MT4X3.1 MT3X2.2 MT3X1.85 MT2.5X9.45 MT2X3 ST12X60.5 ST12X53 ST12X50 ST12X45 ST12X40 ST10X48 ST10X43 ST10X37.5 ST10X33 ST9X35 ST9X27.35 ST7.5X25 ST7.5X21.45 ST6X25 ST6X20.4 ST6X17.5 ST6X15.9 ST5X17.5 ST5X12.7 ST4X11.5 ST4X9.2 ST3X8.6 ST3X6.25 ST2.5X5 ST2X4.75

1.78 1.34 1.26 2.78 2.35 1.91 1.80 1.69 1.72 1.58 1.46 1.32 1.17 1.10 0.953 0.904 0.643 0.540 2.76 0.855 17.8 15.6 14.7 13.2 11.7 14.1 12.7 11.0 9.69 10.3 8.02 7.34 6.30 7.32 5.96 5.12 4.65 5.14 3.73 3.38 2.70 2.53 1.83 1.47 1.39

3.02 2.95 2.92 2.58 2.51 2.08 6.27 6.25 6.00 5.99 5.99 5.00 4.98 5.00 4.00 4.00 3.00 2.96 2.50 1.90 12.3 12.3 12.0 12.0 12.0 10.2 10.2 10.0 10.0 9.00 9.00 7.50 7.50 6.00 6.00 6.00 6.00 5.00 5.00 4.00 4.00 3.00 3.00 2.50 2.00

0.230 0.170 0.170 0.270 0.240 0.280 0.155 0.155 0.177 0.160 0.149 0.157 0.141 0.130 0.135 0.129 0.114 0.0980 0.316 0.130 0.800 0.620 0.745 0.625 0.500 0.800 0.660 0.635 0.505 0.711 0.461 0.550 0.411 0.687 0.462 0.428 0.350 0.594 0.311 0.441 0.271 0.465 0.232 0.214 0.326

4.00 3.94 3.94 5.03 5.00 4.06 3.75 3.50 3.07 3.07 3.25 2.69 2.69 2.69 2.28 2.28 1.84 2.00 5.00 3.80 8.05 7.87 7.25 7.13 7.00 7.20 7.06 6.39 6.26 6.25 6.00 5.64 5.50 5.48 5.25 5.08 5.00 4.94 4.66 4.17 4.00 3.57 3.33 3.00 2.80

ST2X3.85 ST1.5X3.75 ST1.5X2.85

1.13 1.10 0.830

2.00 1.50 1.50

0.193 0.349 0.170

2.66 2.51 2.33

WT, MT, and ST Section Properties from AISC tf 1.77 1.58 1.42 1.22 3.23 2.76 2.36 2.20 2.05 2.01 1.81 1.65 1.58 1.42 1.22 1.07 2.52 2.13 2.13 1.93 1.81 1.73 1.58 1.42 1.20 1.03 0.830 4.29 3.54 2.91 2.68 2.44 2.20 2.01 1.85 1.68 1.57 1.44 1.35 1.57 1.73 1.57 1.36

k(des) 2.56 2.37 2.21 2.01 4.41 3.94 3.54 3.38 3.23 3.19 2.99 2.83 2.76 2.60 2.40 2.25 3.70 3.31 3.31 3.11 2.99 2.91 2.76 2.60 2.40 2.21 2.01 5.24 4.49 3.86 3.63 3.39 3.15 2.96 2.80 2.63 2.52 2.39 2.30 2.32 2.48 2.32 2.11

k(det) 2.625 2.4375 2.25 2.0625 4.5 4 3.625 3.5 3.3125 3.25 3.0625 2.9375 2.875 2.6875 2.5 2.3125 3.8125 3.375 3.375 3.1875 3.0625 3 2.875 2.6875 2.5 2.3125 2.125 5.5625 4.8125 4.1875 4 3.6875 3.4375 3.25 3.125 2.9375 2.8125 2.6875 2.625 2.4375 2.625 2.4375 2.3125

gage 5.5 5.5 5.5 5.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 5.5 5.5 7.5 5.5

wt./ft. 167.5 145 131 115 296.5 251.5 215.5 198.5 186 181 162 148.5 138.5 124.5 107.5 99.5 196 265.5 163.5 147 139 132 117.5 105.5 91.5 83.5 74.5 400 326 264.5 243.5 220.5 197.5 180.5 165 151 141 131 123.5 116 128 115.5 105

bf/(2*tf) 4.50 5.02 5.57 6.45 2.58 2.98 3.44 3.66 3.93 3.99 4.40 4.80 5.03 5.55 6.45 7.39 2.45 2.86 2.85 3.11 3.31 3.45 3.77 4.17 4.92 5.76 7.11 2.10 2.48 2.96 3.19 3.48 3.83 4.16 4.49 4.96 5.29 5.75 6.11 6.54 3.53 3.86 4.48

1.26 1.18 1.10 1.02 0.940 0.790 2.28 2.09 1.89 1.73 1.57 1.40 1.28 1.15 1.22 1.06 0.960 0.855 0.740 2.44 2.24 2.05 1.85 1.65 1.50 1.32 1.19 1.07 1.18 1.00 0.930 0.850 0.760 0.670 0.610 3.54 2.48 2.28 2.09 1.93 1.77 1.61 1.50 1.34 1.19

2.01 1.93 1.85 1.77 1.69 1.54 3.07 2.88 2.68 2.52 2.36 2.19 2.06 1.94 1.92 1.76 1.66 1.56 1.44 3.23 3.03 2.84 2.64 2.44 2.29 2.10 1.97 1.85 1.83 1.65 1.58 1.50 1.41 1.32 1.26 4.33 3.27 3.07 2.88 2.72 2.56 2.40 2.29 2.13 1.98

2.1875 2.125 2 1.9375 1.875 1.6875 3.1875 2.9375 2.75 2.625 2.4375 2.25 2.125 2 2.125 1.9375 1.8125 1.75 1.625 3.375 3.125 2.9375 2.75 2.5625 2.375 2.25 2.0625 2 2.0625 1.875 1.8125 1.75 1.6875 1.5625 1.5 4.4375 3.375 3.1875 3 2.8125 2.6875 2.5 2.375 2.25 2.0625

5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5

97 91 85 80 75 67.5 194 177 159 145.5 131.5 120.5 110.5 100.5 84.5 76 70.5 65 59 195.5 178.5 163 146 130.5 117.5 105.5 95.5 86.5 74 66 62 58 54 49.5 45 269.5 184 168 153.5 140.5 129 117.5 108.5 97 89

4.81 5.12 5.47 5.88 6.37 7.56 3.55 3.85 4.23 4.60 5.03 5.66 6.20 6.85 4.71 5.48 6.01 6.73 7.76 3.19 3.45 3.75 4.12 4.59 5.02 5.74 6.35 7.40 4.44 5.27 5.65 6.17 6.89 7.80 8.52 2.15 2.96 3.19 3.46 3.72 4.03 4.41 4.71 5.24 5.92

1.08 0.975 1.10 0.930 0.830 0.745 0.640 2.72 2.48 2.28 2.09 1.89 1.73 1.57 1.46 1.34 1.22 1.09 0.960 0.850 0.750 0.980 0.875 0.770 0.680 0.585 0.590 0.505 1.63 1.48 1.36 1.15 1.04 0.960 0.875 0.800 0.930 0.835 0.740 0.685 0.615 0.522 0.430 0.650 0.535

1.87 1.76 1.70 1.53 1.43 1.34 1.24 3.22 2.98 2.78 2.59 2.39 2.23 2.07 1.96 1.84 1.72 1.59 1.46 1.35 1.25 1.48 1.38 1.27 1.18 1.09 1.19 1.01 2.13 1.98 1.86 1.65 1.54 1.46 1.38 1.30 1.43 1.34 1.24 1.19 1.12 1.02 0.930 1.15 1.04

2 1.875 2 1.8125 1.75 1.625 1.5625 3.625 3.375 3.1875 3 2.8125 2.625 2.5 2.375 2.25 2.125 2 1.875 1.75 1.625 1.875 1.75 1.6875 1.5625 1.5 1.5 1.4375 2.5 2.375 2.25 2 1.9375 1.8125 1.75 1.6875 1.625 1.5 1.4375 1.375 1.3125 1.1875 1.125 1.3125 1.25

5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 3.5 3.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 3.5 3.5

80.5 73 64.5 57 51 47 42 185 167.5 153 139.5 125 114.5 103.5 96 88 81 73 65.5 58.5 52 51.5 47 42 38 34 31 27.5 100.5 91 83 73.5 66 61 55.5 50.5 46.5 41.5 36.5 34 31 27.5 24 28.5 25

6.49 7.16 4.55 5.41 6.03 6.70 7.78 2.51 2.73 2.94 3.18 3.49 3.79 4.14 4.43 4.81 5.31 5.92 6.70 7.53 8.50 4.59 5.18 5.86 6.61 7.66 5.97 6.94 3.86 4.22 4.57 5.44 6.01 6.45 7.05 7.68 4.53 5.00 5.60 6.04 6.70 7.87 9.47 5.04 6.10

0.450 2.74 2.50 2.30 2.11 1.91 1.75 1.59 1.44 1.32 1.20 1.06 0.940 0.870 0.770 0.680 0.810 0.750 0.695 0.630 0.570 0.605 0.525 0.425 0.985 0.875 0.760 0.665 0.715 0.630 0.565 0.505 0.430 0.440 0.345 4.91 4.52 4.16 3.82 3.50 3.21 3.04 2.85 2.66 2.47

0.950 3.24 3.00 2.70 2.51 2.31 2.15 1.99 1.84 1.72 1.60 1.46 1.34 1.27 1.17 1.08 1.21 1.15 1.10 1.03 0.972 1.01 0.927 0.827 1.39 1.58 1.47 1.37 1.12 1.03 0.967 0.907 0.832 0.842 0.747 5.51 5.12 4.76 4.42 4.10 3.81 3.63 3.44 3.26 3.07

1.125 3.4375 0.1875 3 2.75 0.5625 2.4375 2.4375 2.375 2.1875 2.0625 1.9375 1.8125 1.75 1.625 1.5625 1.5 1.4375 1.375 1.3125 1.25 1.25 1.1875 1.125 1.875 1.75 1.625 1.5625 1.375 1.3125 1.25 1.1875 1.125 1.125 1.0625 6.1875 5.8125 5.4375 5.125 4.8125 4.5 4.3125 4.125 3.9375 3.75

3.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 5.5 5.5 5.5 5.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5

22 155.5 141.5 129 117 105.5 97 87.5 79 71.5 65 59.5 53 48.5 43 38 35.5 32.5 30 27.5 25 23 20 17.5 50 44.5 38.5 33.5 28.5 25 22.5 20 18 15.5 13 365 332.5 302.5 275 250 227.5 213 199 185 171

7.22 2.19 2.38 2.56 2.76 3.02 3.27 3.58 3.92 4.25 4.65 5.31 5.96 6.41 7.20 8.11 4.71 5.06 5.44 5.98 6.57 5.01 5.73 7.06 5.29 5.92 6.77 7.70 4.98 5.61 6.23 6.93 8.12 6.28 7.97 1.82 1.95 2.09 2.25 2.43 2.62 2.75 2.92 3.10 3.31

2.26 2.07 1.89 1.72 1.56 1.44 1.31 1.19 1.09 1.03 0.940 0.860 0.780 0.710 0.855 0.785 0.720 0.645 0.660 0.595 0.530 0.515 0.455 0.385 0.420 0.335 2.96 2.71 2.47 2.25 2.07 1.90 1.74 1.56 1.40 1.25 1.11 0.990 0.900 0.810 0.735 0.670 0.605 0.640 0.575

2.86 2.67 2.49 2.32 2.16 2.04 1.91 1.79 1.69 1.63 1.54 1.46 1.38 1.31 1.45 1.38 1.31 1.24 1.25 1.19 1.12 0.915 0.855 0.785 0.820 0.735 3.55 3.30 3.07 2.85 2.67 2.50 2.33 2.16 2.00 1.85 1.70 1.59 1.50 1.41 1.33 1.27 1.20 1.24 1.17

3.5625 3.375 3.1875 3 2.875 2.75 2.625 2.5 2.375 2.3125 2.25 2.1875 2.0625 2 1.6875 1.625 1.5625 1.5 1.5 1.4375 1.375 1.25 1.1875 1.125 1.125 1.0625 3.875 3.625 3.375 3.125 2.9375 2.8125 2.625 2.4375 2.3125 2.125 2 1.875 1.8125 1.6875 1.625 1.5625 1.5 1.5 1.375

7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 3.5 3.5 3.5 2.75 2.75 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5

155.5 141.5 128.5 116.5 105.5 96.5 88 79.5 72.5 66 60 54.5 49.5 45 41 37 34 30.5 26.5 24 21.5 19 17 15 13 11 168 152.5 139.5 126 115 105 95 85 76 68 60 53 48 43.5 39.5 36 32.5 29 26.5

3.59 3.89 4.23 4.62 5.06 5.45 5.97 6.54 7.11 7.15 7.80 8.49 9.34 10.2 5.92 6.41 6.97 7.75 6.11 6.75 7.54 6.57 7.41 8.74 5.98 7.46 2.26 2.45 2.66 2.89 3.11 3.37 3.65 4.03 4.46 4.96 5.57 6.17 6.76 7.48 8.22 8.99 9.92 7.82 8.69

0.640 0.575 0.515 0.520 0.440 0.380 0.425 0.350 0.265 0.225 1.25 1.12 0.990 0.870 0.770 0.680 0.615 0.560 0.620 0.530 0.435 0.510 0.440 0.360 0.395 0.330 0.270 0.210 0.935 0.810 0.685 0.560 0.495 0.435 0.465 0.400 0.400 0.330 0.315 0.255 0.205 0.455 0.365 0.260 0.405

1.14 1.08 1.02 0.820 0.740 0.680 0.725 0.650 0.565 0.525 1.75 1.62 1.49 1.37 1.27 1.18 1.12 1.06 1.12 1.03 0.935 0.810 0.740 0.660 0.695 0.630 0.570 0.510 1.33 1.20 1.08 0.954 0.889 0.829 0.859 0.794 0.700 0.630 0.615 0.555 0.505 0.705 0.664 0.559 0.655

1.5 1.375 1.375 1.1875 1.125 1.0625 0.9375 0.875 0.8125 0.75 1.9375 1.8125 1.6875 1.5625 1.4375 1.375 1.3125 1.25 1.3125 1.1875 1.125 1.125 1.0625 0.9375 0.9375 0.875 0.8125 0.75 1.625 1.5 1.375 1.25 1.1875 1.125 0.9375 0.875 0.875 0.8125 0.8125 0.75 0.6875 0.9375 0.875 0.75 0.875

5.5 5.5 5.5 3.5 3.5 3.5 2.25 2.25 2.25 2.25 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 2.75 2.75 2.75 2.25 2.25 2.25 2.25 5.5 5.5 5.5 5.5 5.5 5.5 3.5 3.5 2.75 2.75 2.25 2.25 2.25 3.5 3.5 3.5 2.25

25 22.5 20 17.5 15 13 11 9.5 8 7 56 50 44 38.5 34 30 27 24.5 22.5 19.5 16.5 15 13 11 9.5 8.5 7.5 6 33.5 29 24 20 17.5 15.5 14 12 10.5 9 7.5 6.5 5 12.5 10 7.5 8

6.31 7.00 7.77 6.31 7.41 8.54 4.74 5.72 7.53 8.82 4.17 4.62 5.18 5.86 6.58 7.41 8.15 8.93 6.47 7.53 9.15 5.70 6.56 7.99 5.09 6.08 7.41 9.43 4.43 5.07 5.92 7.21 8.10 9.19 7.03 8.12 6.59 7.95 6.37 7.84 9.61 6.68 8.25 11.5 4.98

0.280 0.215 0.195 0.430 0.360 0.345 0.228 0.211 0.225 0.210 0.180 0.206 0.182 0.173 0.189 0.177 0.171 0.129 0.416 0.160 1.09 1.09 0.870 0.870 0.870 0.920 0.920 0.795 0.795 0.691 0.691 0.622 0.622 0.659 0.659 0.544 0.544 0.491 0.491 0.425 0.425 0.359 0.359 0.326 0.293

0.530 0.465 0.444 0.730 0.660 0.595 0.563 0.563 0.563 0.563 0.500 0.563 0.563 0.438 0.563 0.438 0.375 0.313 0.813 0.500 2.00 2.00 1.75 1.75 1.75 1.75 1.75 1.63 1.63 1.50 1.50 1.38 1.38 1.44 1.44 1.19 1.19 1.13 1.13 1.00 1.00 0.813 0.813 0.750 0.750

0.75 0.6875 0.6875 0.8125 0.75 0.75 0.5625 0.5625 0.5625 0.5625 0.5 0.5625 0.5625 0.4375 0.5625 0.4375 0.375 0.3125 0.8125 0.5 2 2 1.75 1.75 1.75 1.75 1.75 1.625 1.625 1.5 1.5 1.375 1.375 1.4375 1.4375 1.1875 1.1875 1.125 1.125 1 1 0.8125 0.8125 0.75 0.75

2.25 2.25 2.25 2.75 2.75 2.25 ------------------------2.75 --4 4 4 4 4 4 4 3.5 3.5 3.5 3.5 3.5 3.5 3 3 3 3 2.75 2.75 2.25 2.25 ---------

6 4.5 4.25 9.5 8 6.5 6.2 5.9 5.9 5.4 5 4.5 4 3.75 3.25 3.1 2.2 1.85 9.45 3 60.5 53 50 45 40 48 43 37.5 33 35 27.35 25 21.45 25 20.4 17.5 15.9 17.5 12.7 11.5 9.2 8.6 6.25 5 4.75

7.14 9.16 10.1 5.85 6.94 5.88 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.293 0.260 0.260

0.750 0.625 0.625

0.75 0.625 0.625

-------

3.85 3.75 2.85

0.00 0.00 0.00

ction Properties from AISC Version 13.0 CD Database (Dec. 2005) and AISC 13th Edition Manual (Dec. 2005) d/tw 21.5 25.2 27.6 30.2 12.0 13.7 15.4 16.8 17.5 18.1 20.1 21.4 23.9 26.3 30.0 29.7 14.7 16.7 17.3 19.1 19.6 20.8 23.9 26.2 30.0 29.7 30.3 8.94 10.4 12.4 13.1 14.3 15.7 17.0 18.5 19.8 21.0 21.9 22.9 24.0 19.5 21.3 22.1

Ix 2170 1830 1640 1440 3310 2730 2290 2070 1930 1870 1650 1500 1360 1210 1030 988 2270 1880 1840 1630 1550 1450 1260 1120 955 899 815 4090 3160 2440 2220 1980 1740 1570 1410 1280 1190 1110 1040 978 1210 1080 985

Sx 131 111 99.4 88.6 209 174 148 134 126 122 108 98.9 88.6 79.4 68.0 66.5 153 128 125 111 106 99.2 85.7 76.7 65.7 63.7 59.7 264 208 164 150 134 119 107 97.0 88.8 82.6 77.5 73.3 69.1 87.4 78.5 73.1

rx 6.63 6.54 6.53 6.53 6.16 6.07 6.01 5.96 5.95 5.92 5.88 5.87 5.78 5.75 5.71 5.81 6.27 6.21 6.19 6.14 6.14 6.11 6.04 6.01 5.98 6.05 6.10 5.89 5.74 5.60 5.57 5.52 5.47 5.43 5.39 5.37 5.36 5.36 5.36 5.36 5.66 5.63 5.65

y(bar) 5.53 5.26 5.19 5.17 5.66 5.38 5.18 5.03 4.98 4.91 4.77 4.71 4.50 4.41 4.28 4.47 5.94 5.74 5.66 5.51 5.51 5.41 5.17 5.08 4.97 5.19 5.45 5.80 5.35 4.96 4.84 4.69 4.53 4.42 4.30 4.22 4.16 4.14 4.12 4.10 4.92 4.82 4.87

Zx 234 196 176 157 379 314 266 240 225 217 192 176 157 140 120 117 275 231 224 199 191 178 153 137 117 115 108 491 383 298 272 242 213 192 173 158 146 137 129 122 156 140 131

23.8 25.1 26.6 27.7 28.7 29.6 14.3 15.3 16.9 18.1 19.8 20.6 21.9 23.6 25.2 26.4 27.5 28.5 29.9 12.2 13.2 14.2 15.7 17.0 18.9 20.0 21.6 23.2 23.6 24.6 25.8 26.6 27.4 28.5 31.4 8.25 11.0 11.9 12.8 13.8 14.8 15.7 17.1 18.7 19.2

901 845 786 740 698 637 1460 1320 1160 1060 943 872 799 725 649 592 552 513 469 1220 1090 981 861 765 674 610 549 497 466 421 396 373 349 322 290 1530 939 839 753 677 613 556 502 444 414

67.0 63.1 58.9 55.8 53.1 49.7 107 96.8 85.8 78.3 70.2 65.8 60.8 55.5 51.1 47.4 44.7 42.1 39.2 96.9 87.2 78.8 69.6 62.4 55.1 50.5 45.7 41.7 40.6 37.4 35.3 33.7 32.0 30.0 27.1 128 81.7 73.4 66.4 59.9 54.7 50.0 45.2 40.3 38.2

5.62 5.62 5.61 5.61 5.62 5.66 5.07 5.03 4.99 4.96 4.93 4.96 4.95 4.95 5.12 5.14 5.15 5.18 5.20 4.61 4.56 4.52 4.48 4.46 4.41 4.43 4.42 4.42 4.63 4.66 4.66 4.67 4.69 4.71 4.69 4.39 4.16 4.12 4.08 4.04 4.02 4.00 3.96 3.94 3.97

4.80 4.77 4.73 4.74 4.78 4.96 4.27 4.15 4.02 3.93 3.83 3.84 3.81 3.77 4.21 4.26 4.29 4.36 4.47 4.00 3.87 3.76 3.62 3.54 3.41 3.39 3.34 3.31 3.84 3.90 3.90 3.94 4.01 4.09 4.04 4.34 3.71 3.58 3.47 3.35 3.27 3.20 3.10 3.02 3.04

120 113 105 100 95.5 90.1 193 174 154 140 125 116 107 97.8 90.8 84.5 79.8 75.6 70.8 177 159 143 125 112 98.2 89.5 80.8 73.5 72.2 66.8 63.1 60.4 57.7 54.4 49.0 242 151 135 121 109 98.9 89.9 81.1 71.8 67.7

20.9 22.6 22.6 23.9 26.3 27.5 29.0 9.21 10.0 10.8 11.5 12.7 13.6 14.8 15.7 16.8 17.7 19.0 20.2 22.1 24.1 22.3 23.6 25.6 27.2 28.6 27.6 29.8 12.7 13.7 15.0 15.3 16.8 18.1 19.6 21.4 18.6 20.8 23.3 24.6 26.2 27.7 29.5 26.0 27.4

372 336 323 289 258 239 216 779 686 611 546 478 431 382 350 319 293 264 238 212 189 204 186 166 151 137 131 117 285 253 226 204 181 166 150 135 144 127 110 103 93.8 84.4 74.9 90.4 80.3

34.4 31.2 31.0 28.3 25.3 23.8 21.9 74.7 66.3 59.4 53.6 47.2 42.9 38.3 35.2 32.2 29.9 27.2 24.8 22.3 20.0 22.0 20.3 18.3 16.9 15.6 15.6 14.1 31.9 28.5 25.5 23.7 21.1 19.3 17.5 15.8 17.9 15.7 13.8 12.9 11.9 10.9 9.90 11.8 10.7

3.95 3.95 4.13 4.15 4.14 4.16 4.18 3.78 3.73 3.69 3.65 3.61 3.58 3.55 3.53 3.51 3.50 3.50 3.52 3.51 3.51 3.67 3.67 3.67 3.68 3.70 3.79 3.80 3.10 3.07 3.04 3.08 3.06 3.04 3.03 3.01 3.25 3.22 3.21 3.20 3.21 3.23 3.26 3.29 3.30

2.98 2.94 3.39 3.42 3.37 3.41 3.48 3.57 3.42 3.29 3.18 3.05 2.96 2.87 2.80 2.74 2.70 2.66 2.65 2.62 2.59 3.01 2.99 2.97 3.00 3.06 3.46 3.50 2.57 2.48 2.39 2.39 2.33 2.28 2.23 2.18 2.74 2.66 2.60 2.59 2.58 2.64 2.74 2.85 2.93

60.8 55.0 55.1 50.4 45.0 42.4 39.2 140 123 110 98.8 86.5 78.1 69.3 63.5 57.8 53.3 48.2 43.9 39.2 35.1 39.2 36.1 32.5 30.1 27.9 28.4 25.6 58.6 52.1 46.3 42.4 37.6 34.3 31.0 27.9 31.8 28.0 24.4 22.9 21.1 19.4 17.8 21.2 19.4

29.5 7.34 7.80 8.38 9.08 9.75 10.6 11.3 12.2 13.3 14.4 14.5 15.9 17.4 19.2 21.4 18.7 20.4 22.0 23.2 25.3 25.1 28.4 29.5 14.5 16.0 18.2 20.7 19.1 21.4 23.4 26.2 26.9 28.9 31.4 3.65 3.82 4.03 4.25 4.47 4.72 4.98 5.17 5.41 5.69

71.1 383 337 298 261 229 202 181 160 142 127 119 104 93.8 82.4 71.8 78.2 70.7 64.7 59.5 53.5 52.1 44.8 40.1 76.8 67.2 56.9 48.6 48.7 42.3 37.8 33.1 30.6 27.5 23.5 739 622 524 442 375 321 287 257 229 203

9.68 46.6 41.5 37.0 32.7 29.1 25.8 23.4 20.8 18.5 16.7 15.9 14.1 12.7 11.2 9.83 11.2 10.1 9.29 8.63 7.79 7.77 6.73 6.21 11.4 10.1 8.59 7.36 7.77 6.78 6.10 5.35 5.05 4.64 4.09 95.4 82.1 70.6 60.9 52.7 45.9 41.4 37.6 33.9 30.4

3.31 2.89 2.85 2.80 2.75 2.72 2.68 2.66 2.63 2.60 2.58 2.60 2.59 2.56 2.55 2.54 2.74 2.72 2.71 2.71 2.70 2.77 2.76 2.79 2.28 2.27 2.24 2.22 2.41 2.40 2.39 2.37 2.41 2.45 2.47 2.62 2.52 2.43 2.34 2.26 2.19 2.14 2.10 2.05 2.01

2.98 2.93 2.80 2.68 2.55 2.44 2.34 2.26 2.17 2.09 2.02 2.03 1.97 1.91 1.86 1.80 2.26 2.20 2.16 2.16 2.12 2.33 2.29 2.39 1.76 1.70 1.63 1.56 1.94 1.89 1.86 1.81 1.88 2.02 2.09 3.47 3.25 3.05 2.85 2.67 2.51 2.40 2.30 2.19 2.09

17.6 90.6 80.2 71.0 62.4 55.0 48.5 43.6 38.5 34.0 30.5 28.7 25.2 22.6 19.9 17.3 20.0 18.0 16.5 15.3 13.8 13.9 12.0 11.2 20.7 18.1 15.3 13.0 13.8 12.0 10.8 9.43 8.93 8.27 7.36 211 182 157 136 117 102 91.7 82.9 74.4 66.2

6.07 6.49 6.97 7.50 8.02 8.70 9.17 10.1 10.9 11.4 12.3 13.6 14.6 15.9 14.0 15.7 16.9 18.5 18.8 20.3 22.4 22.7 24.5 25.6 27.3 29.9 4.74 5.02 5.18 5.52 5.86 6.23 6.78 7.31 7.88 8.49 9.24 10.6 11.6 12.2 13.2 14.2 15.5 16.9 17.5

176 153 133 116 102 89.8 80.5 70.2 62.5 57.8 51.7 45.3 40.9 36.5 41.2 36.0 32.6 28.9 27.6 24.9 21.9 23.3 20.9 19.0 17.3 14.8 190 162 141 121 106 92.1 79.0 67.8 58.5 50.6 43.4 36.3 32.0 28.9 25.8 23.2 20.6 19.1 17.7

26.7 23.5 20.7 18.2 16.2 14.4 13.0 11.4 10.2 9.57 8.61 7.56 6.88 6.16 7.14 6.25 5.69 5.07 4.94 4.49 3.98 4.22 3.83 3.55 3.31 2.91 31.2 27.0 24.1 20.9 18.5 16.4 14.2 12.3 10.8 9.46 8.22 6.92 6.12 5.60 5.03 4.54 4.06 3.76 3.54

1.96 1.92 1.88 1.84 1.81 1.78 1.76 1.73 1.71 1.73 1.71 1.68 1.67 1.66 1.85 1.82 1.81 1.80 1.88 1.88 1.86 2.04 2.04 2.07 2.12 2.14 1.96 1.90 1.86 1.81 1.77 1.73 1.68 1.65 1.62 1.59 1.57 1.53 1.51 1.50 1.49 1.48 1.47 1.50 1.51

1.97 1.86 1.75 1.65 1.57 1.49 1.43 1.35 1.29 1.29 1.24 1.17 1.14 1.09 1.39 1.32 1.29 1.25 1.38 1.35 1.31 1.54 1.53 1.58 1.72 1.76 2.31 2.16 2.05 1.92 1.82 1.72 1.62 1.52 1.43 1.35 1.28 1.19 1.13 1.10 1.06 1.02 0.985 1.03 1.02

57.7 50.4 43.9 38.2 33.4 29.4 26.3 22.8 20.2 18.6 16.5 14.4 12.9 11.5 13.2 11.5 10.4 9.15 8.87 8.00 7.05 7.45 6.74 6.25 5.89 5.20 68.4 59.1 51.9 44.8 39.4 34.5 29.8 25.6 22.0 19.0 16.2 13.6 11.9 10.7 9.49 8.48 7.50 6.97 6.46

16.5 18.0 20.2 20.8 23.7 26.6 23.7 25.9 27.3 29.8 7.52 8.16 8.96 10.0 11.1 12.2 13.6 14.7 14.4 15.7 16.8 17.5 19.9 21.2 20.5 21.1 21.7 26.0 7.89 8.58 10.6 11.5 13.1 14.0 14.1 16.2 16.6 17.7 16.6 17.4 23.2 10.0 11.9 13.0 12.1

18.7 16.6 14.4 16.0 13.5 11.7 11.7 10.1 8.70 7.67 28.6 24.5 20.8 17.4 14.9 12.9 11.1 10.0 10.2 8.84 7.71 9.28 7.86 6.88 6.68 6.06 5.45 4.35 10.9 9.12 6.85 5.73 4.82 4.28 4.23 3.53 3.90 3.41 3.28 2.89 2.15 2.29 1.76 1.41 1.69

3.79 3.39 2.95 3.23 2.75 2.40 2.59 2.28 2.04 1.83 6.40 5.56 4.77 4.05 3.49 3.04 2.64 2.39 2.47 2.16 1.93 2.24 1.91 1.72 1.74 1.62 1.50 1.22 3.05 2.61 1.97 1.69 1.43 1.28 1.28 1.08 1.18 1.05 1.07 0.974 0.717 0.886 0.693 0.577 0.685

1.60 1.59 1.57 1.76 1.75 1.75 1.90 1.90 1.92 1.92 1.32 1.29 1.27 1.24 1.22 1.21 1.19 1.18 1.24 1.24 1.26 1.45 1.44 1.46 1.54 1.56 1.57 1.57 1.05 1.03 0.986 0.988 0.968 0.969 1.01 0.999 1.12 1.14 1.22 1.23 1.20 0.789 0.774 0.797 0.844

1.17 1.13 1.09 1.30 1.27 1.25 1.63 1.65 1.74 1.76 1.21 1.13 1.06 0.990 0.932 0.884 0.836 0.807 0.907 0.876 0.869 1.10 1.06 1.07 1.28 1.32 1.37 1.36 0.936 0.874 0.777 0.735 0.688 0.668 0.734 0.695 0.831 0.834 0.998 1.03 0.953 0.610 0.560 0.558 0.676

6.88 6.10 5.28 5.71 4.83 4.20 4.63 4.11 3.72 3.32 13.4 11.4 9.65 8.06 6.85 5.87 5.05 4.52 4.65 3.99 3.48 4.01 3.39 3.02 3.10 2.90 2.71 2.20 6.29 5.25 3.94 3.25 2.71 2.39 2.38 1.98 2.11 1.86 1.91 1.74 1.27 1.68 1.29 1.03 1.25

13.1 17.4 17.1 9.54 10.4 7.43 40.4 40.3 33.9 37.4 40.2 31.8 35.3 38.4 29.6 31.0 26.3 30.2 7.91 14.6 15.3 19.8 16.1 19.2 24.0 12.7 15.4 15.7 19.8 12.7 19.5 13.6 18.2 8.73 13.0 14.0 17.1 8.42 16.1 9.07 14.8 6.45 12.9 11.7 6.13

1.32 0.950 0.905 1.01 0.845 0.526 7.29 6.94 6.61 6.03 5.62 3.47 3.08 2.91 1.57 1.50 0.579 0.483 1.05 0.208 259 216 215 190 162 143 124 109 92.9 84.5 62.3 40.5 32.9 25.1 18.9 17.2 14.8 12.5 7.79 5.00 3.49 2.12 1.26 0.671 0.462

0.564 0.408 0.397 0.485 0.413 0.321 1.61 1.57 1.61 1.46 1.36 1.00 0.894 0.836 0.558 0.533 0.268 0.226 0.528 0.133 30.1 24.1 26.3 22.6 18.6 20.3 17.2 15.8 12.9 14.0 9.60 7.72 5.99 6.04 4.27 3.95 3.30 3.62 2.05 1.76 1.14 1.02 0.547 0.348 0.319

0.862 0.842 0.848 0.604 0.599 0.524 2.01 2.03 1.96 1.95 1.96 1.62 1.62 1.63 1.29 1.29 0.949 0.945 0.617 0.493 3.82 3.72 3.83 3.79 3.72 3.18 3.13 3.15 3.10 2.87 2.79 2.35 2.29 1.85 1.78 1.83 1.78 1.56 1.45 1.22 1.14 0.915 0.831 0.677 0.575

0.677 0.623 0.637 0.487 0.458 0.440 1.74 1.84 1.89 1.86 1.86 1.54 1.52 1.51 1.18 1.18 0.841 0.827 0.512 0.341 3.63 3.28 3.84 3.60 3.30 3.13 2.91 3.07 2.81 2.94 2.51 2.25 2.01 1.84 1.58 1.65 1.51 1.56 1.20 1.15 0.942 0.915 0.692 0.570 0.553

1.01 0.720 0.700 0.970 0.801 0.616 2.92 2.86 2.89 2.63 2.45 1.81 1.61 1.51 1.01 0.967 0.483 0.409 1.03 0.241 54.5 43.3 47.5 41.1 33.6 36.9 31.1 28.6 23.4 25.1 17.3 14.0 10.8 11.0 7.71 7.12 5.94 6.58 3.70 3.19 2.07 1.85 1.01 0.650 0.592

10.4 4.30 8.82

0.307 0.200 0.114

0.198 0.187 0.0970

0.522 0.426 0.370

0.448 0.432 0.329

0.381 0.351 0.196

nual (Dec. 2005) yp 1.54 1.35 1.22 1.07 2.61 2.25 1.95 1.81 1.70 1.66 1.50 1.38 1.29 1.16 1.01 0.929 2.33 2.00 1.98 1.80 1.71 1.63 1.45 1.31 1.13 1.10 1.72 3.28 2.73 2.26 2.10 1.91 1.73 1.59 1.46 1.33 1.25 1.16 1.10 1.03 1.54 1.40 1.27

Iy 600 521 462 398 1260 1020 843 771 709 691 609 546 522 463 398 347 401 322 320 281 261 246 222 195 165 141 114 2100 1610 1240 1120 997 877 786 711 648 599 545 507 470 264 234 206

Sy 75.2 65.9 58.6 50.5 151 124 104 95.7 88.3 86.3 76.6 69.0 65.9 58.8 50.5 44.1 64.9 52.9 52.7 46.7 43.5 41.3 37.3 33.0 28.0 23.9 19.4 234 184 145 131 117 104 94.0 85.5 77.8 72.2 65.8 61.4 57.0 43.2 38.6 33.8

ry 3.49 3.49 3.47 3.43 3.80 3.72 3.65 3.63 3.60 3.60 3.57 3.54 3.58 3.55 3.54 3.45 2.64 2.57 2.58 2.55 2.52 2.52 2.54 2.51 2.49 2.40 2.29 4.22 4.10 4.00 3.96 3.92 3.88 3.85 3.83 3.82 3.80 3.76 3.74 3.71 2.65 2.62 2.58

Zy 118 102 90.9 78.3 240 197 164 150 138 135 119 107 102 90.8 77.8 68.2 106 85.7 85.0 75.0 69.9 66.0 59.0 52.1 44.0 37.8 30.9 371 290 227 206 184 162 146 132 120 112 102 94.8 88.0 68.5 60.9 53.4

Qs(50) 0.822 0.629 0.526 0.438 1.00 1.00 1.00 1.00 1.00 0.993 0.893 0.825 0.699 0.580 0.445 0.452 1.00 1.00 1.00 0.945 0.918 0.855 0.699 0.581 0.445 0.454 0.435 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.974 0.909 0.848 0.799 0.749 0.694 0.922 0.829 0.791

1.18 1.11 1.04 0.980 0.923 1.23 1.76 1.62 1.46 1.35 1.23 1.12 1.03 0.940 1.08 0.967 0.901 0.832 0.862 1.85 1.70 1.56 1.41 1.27 1.15 1.03 0.935 0.851 1.04 0.921 0.867 0.815 0.757 0.912 0.835 2.60 1.85 1.70 1.56 1.44 1.33 1.22 1.13 1.02 0.932

187 174 160 147 135 113 810 729 645 581 517 466 420 375 155 136 123 109 93.5 774 693 622 549 480 427 378 336 299 114 98.0 90.4 82.1 73.0 63.9 57.3 1060 655 587 527 477 430 384 352 309 278

30.9 28.8 26.6 24.6 22.5 18.9 100 90.6 80.7 73.1 65.5 58.8 53.2 47.6 27.0 23.6 21.3 18.9 16.3 99.2 89.6 81.0 71.9 63.3 56.8 50.1 44.7 39.9 21.7 18.6 17.2 15.6 13.9 12.2 11.0 138 89.3 80.8 72.9 66.4 60.2 54.2 49.9 44.1 39.4

2.56 2.55 2.53 2.50 2.47 2.38 3.77 3.74 3.71 3.68 3.65 3.62 3.59 3.56 2.50 2.47 2.43 2.38 2.32 3.67 3.64 3.60 3.58 3.53 3.51 3.49 3.46 3.42 2.28 2.25 2.23 2.19 2.15 2.10 2.09 3.65 3.48 3.45 3.41 3.39 3.36 3.33 3.32 3.29 3.25

48.8 45.3 41.8 38.6 35.4 29.8 156 141 125 113 101 90.8 82.1 73.3 42.1 36.9 33.4 29.7 25.6 155 140 126 111 97.9 87.5 77.2 68.9 61.4 33.9 29.2 27.0 24.6 21.9 19.3 17.3 218 140 126 113 103 93.3 83.8 77.0 67.8 60.8

0.702 0.637 0.566 0.521 0.486 0.456 1.00 1.00 1.00 0.991 0.905 0.867 0.801 0.717 0.628 0.575 0.528 0.492 0.448 1.00 1.00 1.00 1.00 1.00 0.955 0.899 0.816 0.733 0.715 0.662 0.602 0.567 0.534 0.492 0.405 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.961 0.938

0.849 0.772 0.945 0.832 0.750 0.692 0.621 1.99 1.82 1.67 1.54 1.39 1.28 1.17 1.09 1.00 0.921 0.833 0.750 0.672 0.600 0.841 0.764 0.685 0.622 0.560 1.28 1.53 1.18 1.07 0.983 0.864 0.780 0.724 0.662 0.605 0.812 0.728 0.647 0.606 0.554 0.493 0.459 0.638 0.771

248 222 92.2 79.3 69.6 62.0 52.8 581 513 460 412 362 326 289 265 240 221 195 170 149 130 59.7 54.5 47.2 41.3 35.2 17.2 14.5 271 241 217 188 166 152 137 124 46.4 40.7 35.3 32.4 28.7 24.2 19.4 15.3 12.5

35.4 31.7 18.4 15.8 13.9 12.4 10.6 85.1 75.9 68.6 61.9 54.9 49.7 44.4 40.9 37.2 34.2 30.3 26.5 23.2 20.3 13.3 12.0 10.5 9.18 7.85 4.90 4.15 43.1 38.6 35.0 30.0 26.7 24.6 22.2 20.2 11.0 9.74 8.51 7.83 6.97 5.89 4.76 4.67 3.82

3.23 3.20 2.21 2.18 2.15 2.12 2.07 3.27 3.23 3.20 3.17 3.14 3.11 3.08 3.07 3.04 3.05 3.01 2.97 2.94 2.91 1.99 1.98 1.95 1.92 1.87 1.38 1.34 3.02 3.00 2.99 2.95 2.93 2.91 2.90 2.89 1.84 1.83 1.81 1.80 1.77 1.73 1.66 1.35 1.30

54.5 48.8 28.8 24.6 21.7 19.4 16.6 133 119 107 96.3 85.2 77.0 68.6 63.1 57.3 52.6 46.6 40.7 35.7 31.2 20.7 18.7 16.3 14.3 12.3 7.85 6.65 66.5 59.5 53.9 46.3 41.1 37.8 34.1 30.8 17.3 15.2 13.3 12.2 10.9 9.18 7.44 7.40 6.08

0.851 0.764 0.763 0.698 0.578 0.530 0.475 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.946 0.885 0.793 0.692 0.781 0.715 0.609 0.541 0.489 0.525 0.449 1.00 1.00 1.00 1.00 1.00 0.995 0.919 0.828 0.966 0.856 0.728 0.666 0.581 0.520 0.461 0.592 0.532

1.06 1.91 1.75 1.61 1.48 1.34 1.23 1.13 1.02 0.937 0.856 0.778 0.695 0.640 0.570 0.505 0.683 0.629 0.583 0.538 0.489 0.558 0.489 0.450 0.706 0.631 0.549 0.481 0.589 0.521 0.471 0.421 0.378 0.413 0.372 3.00 2.77 2.55 2.35 2.16 1.99 1.88 1.76 1.65 1.54

10.3 398 352 314 279 246 220 196 174 156 139 126 110 100 87.6 76.2 30.1 27.4 25.0 22.5 20.0 11.3 9.55 7.67 93.1 81.3 69.2 59.5 21.6 18.6 16.4 14.4 12.2 6.20 4.79 2360 2080 1840 1630 1440 1280 1180 1090 994 903

3.18 66.2 59.2 53.4 47.9 42.7 38.4 34.4 30.7 27.7 24.9 22.5 19.7 18.0 15.8 13.8 7.89 7.22 6.63 5.97 5.35 3.71 3.17 2.56 17.9 15.7 13.4 11.6 6.06 5.26 4.67 4.12 3.50 2.24 1.74 264 236 211 189 169 152 141 131 121 110

1.26 2.95 2.91 2.88 2.85 2.82 2.79 2.76 2.74 2.72 2.70 2.69 2.66 2.65 2.63 2.61 1.70 1.69 1.68 1.67 1.65 1.29 1.27 1.22 2.51 2.49 2.47 2.46 1.60 1.59 1.57 1.56 1.52 1.17 1.12 4.69 4.62 4.55 4.49 4.43 4.38 4.34 4.31 4.27 4.24

5.07 104 92.5 83.1 74.4 66.1 59.4 53.1 47.4 42.7 38.3 34.5 30.2 27.6 24.2 21.1 12.3 11.2 10.3 9.26 8.28 5.84 4.97 4.02 27.4 24.0 20.5 17.7 9.42 8.15 7.22 6.36 5.42 3.51 2.73 408 365 326 292 261 234 217 201 185 169

0.459 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.939 0.825 0.965 0.877 0.797 0.734 0.623 0.636 0.495 0.460 1.00 1.00 0.990 0.863 0.942 0.826 0.726 0.581 0.554 0.480 0.406 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

1.41 1.29 1.18 1.08 0.980 0.903 0.827 0.751 0.688 0.658 0.602 0.548 0.500 0.456 0.593 0.541 0.498 0.448 0.484 0.440 0.395 0.412 0.371 0.329 0.383 0.325 1.84 1.69 1.56 1.42 1.31 1.21 1.10 0.994 0.896 0.805 0.716 0.637 0.580 0.527 0.480 0.439 0.398 0.426 0.389

807 722 645 576 513 466 419 374 338 274 247 223 201 181 74.1 66.9 60.7 53.7 28.8 25.7 22.6 13.3 11.6 9.79 4.45 3.50 593 525 469 414 371 332 295 259 227 199 172 151 135 120 108 97.5 87.2 53.5 47.9

99.4 89.7 80.7 72.5 65.0 59.3 53.5 48.1 43.7 37.2 33.7 30.6 27.6 25.0 14.6 13.3 12.1 10.7 7.15 6.40 5.65 3.94 3.45 2.91 1.77 1.40 88.6 79.3 71.3 63.6 57.5 51.9 46.5 41.2 36.4 32.1 28.0 24.7 22.2 19.9 17.9 16.2 14.5 10.7 9.58

4.20 4.17 4.13 4.10 4.07 4.05 4.02 4.00 3.98 3.76 3.74 3.73 3.71 3.70 2.48 2.48 2.46 2.45 1.92 1.91 1.89 1.55 1.53 1.49 1.08 1.04 3.47 3.42 3.38 3.34 3.31 3.28 3.25 3.22 3.19 3.16 3.13 3.11 3.09 3.07 3.05 3.04 3.02 2.51 2.48

152 137 123 110 98.9 90.1 81.3 73.0 66.2 56.5 51.2 46.3 41.8 37.8 22.4 20.2 18.4 16.4 11.0 9.80 8.64 6.07 5.32 4.49 2.76 2.19 137 122 110 97.9 88.4 79.7 71.2 62.9 55.6 48.9 42.7 37.5 33.7 30.2 27.1 24.6 22.0 16.2 14.5

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.972 0.957 0.883 0.776 0.758 0.668 0.609 0.538 0.448 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.452 0.408 0.365 0.394 0.337 0.295 0.402 0.348 0.639 0.760 0.791 0.711 0.631 0.555 0.493 0.438 0.395 0.361 0.413 0.359 0.305 0.380 0.330 0.282 0.349 0.311 0.305 0.322 0.594 0.520 0.435 0.364 0.321 0.285 0.315 0.272 0.292 0.251 0.276 0.240 0.188 0.302 0.244 0.185 0.294

28.2 25.0 22.0 12.2 10.2 8.66 2.33 1.88 1.41 1.18 118 103 89.3 76.8 66.7 58.1 51.7 46.7 26.7 22.5 18.3 8.35 7.05 5.71 2.15 1.78 1.45 1.09 44.3 37.5 30.5 24.5 21.3 18.5 10.8 9.14 4.88 3.98 1.70 1.36 1.05 8.53 6.64 4.66 2.21

6.97 6.21 5.50 3.73 3.12 2.67 1.15 0.939 0.706 0.593 22.6 20.0 17.4 15.1 13.2 11.5 10.3 9.34 6.65 5.64 4.60 2.87 2.44 1.99 1.07 0.887 0.723 0.551 10.7 9.13 7.51 6.08 5.31 4.64 3.31 2.81 1.85 1.52 0.849 0.682 0.531 2.81 2.21 1.56 1.10

1.96 1.95 1.94 1.54 1.52 1.51 0.847 0.821 0.773 0.753 2.67 2.65 2.63 2.60 2.58 2.57 2.56 2.54 2.01 1.98 1.94 1.37 1.36 1.33 0.874 0.844 0.810 0.785 2.12 2.10 2.08 2.04 2.03 2.02 1.62 1.61 1.26 1.23 0.876 0.843 0.840 1.52 1.50 1.45 0.966

10.6 9.47 8.38 5.73 4.78 4.08 1.83 1.49 1.13 0.947 34.6 30.5 26.5 22.9 20.0 17.5 15.6 14.1 10.1 8.57 7.00 4.41 3.75 3.05 1.67 1.40 1.15 0.869 16.3 13.9 11.4 9.24 8.05 7.03 5.04 4.28 2.84 2.33 1.33 1.07 0.826 4.28 3.36 2.37 1.69

1.00 0.998 0.885 0.855 0.708 0.567 0.711 0.598 0.539 0.451 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.904 0.837 0.873 0.843 0.810 0.593 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.735 1.00 1.00 1.00 1.00

0.222 0.170 0.160 0.276 0.235 0.236 0.372 0.808 1.13 1.05 1.08 0.808 0.809 0.759 0.472 0.497 0.190 0.174 0.276 0.112 1.26 1.02 2.16 1.42 0.909 1.35 0.972 1.34 0.841 1.78 0.737 0.826 0.605 0.758 0.577 0.543 0.480 0.673 0.403 0.439 0.336 0.394 0.271 0.239 0.250

1.50 1.10 0.995 4.56 3.75 1.93 1.00 0.756 0.543 0.506 0.517 0.336 0.296 0.281 0.188 0.176 0.0897 0.0863 4.35 0.732 41.5 38.4 23.7 22.3 21.0 25.0 23.3 14.8 13.7 12.0 10.4 7.79 7.13 7.79 6.74 4.92 4.66 4.15 3.36 2.13 1.84 1.14 0.901 0.597 0.444

0.748 0.557 0.505 1.81 1.50 0.950 0.536 0.432 0.354 0.330 0.318 0.250 0.220 0.209 0.165 0.154 0.0973 0.0863 1.74 0.385 10.3 9.76 6.55 6.27 6.00 6.93 6.59 4.62 4.39 3.84 3.45 2.76 2.59 2.84 2.57 1.94 1.87 1.68 1.44 1.02 0.922 0.642 0.541 0.398 0.317

0.918 0.905 0.890 1.28 1.26 1.00 0.746 0.669 0.561 0.566 0.594 0.505 0.502 0.505 0.444 0.441 0.374 0.400 1.26 0.926 1.53 1.57 1.27 1.30 1.34 1.33 1.36 1.16 1.19 1.08 1.14 1.03 1.06 1.03 1.06 0.980 1.00 0.899 0.950 0.795 0.827 0.673 0.702 0.638 0.564

1.16 0.856 0.778 2.76 2.28 1.46 0.839 0.684 0.575 0.532 0.509 0.403 0.354 0.334 0.264 0.247 0.155 0.136 2.66 0.588 18.1 16.7 12.0 11.2 10.4 12.5 11.6 8.36 7.70 7.17 6.06 4.99 4.54 5.16 4.43 3.40 3.22 3.10 2.49 1.84 1.59 1.17 0.930 0.686 0.565

1.00 1.00 1.00 1.00 1.00 1.00 0.340 0.342 0.483 0.397 0.344 0.548 0.446 0.376 0.633 0.578 0.779 0.609 1.00 1.00 1.00 1.00 1.00 1.00 0.878 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.204 0.219 0.171

0.374 0.289 0.223

0.281 0.230 0.192

0.576 0.513 0.518

0.485 0.411 0.328

1.00 1.00 1.00

J 37.2 25.4 18.6 12.4 221 138 88.2 70.6 57.7 54.2 39.6 30.5 25.7 19.0 12.4 9.12 85.4 52.5 51.4 38.2 32.4 27.9 20.6 15.2 9.65 6.99 4.66 525 295 163 128 96.6 70.7 54.1 42.0 32.1 26.3 20.8 17.3 14.3 26.4 19.7 13.9

Cw 438 275 200 139 2340 1400 881 677 558 511 362 279 218 158 101 83.5 796 484 449 322 282 233 156 113 71.2 62.9 51.9 5810 3070 1600 1250 914 652 491 372 285 231 185 155 129 205 151 119

ro(bar) 8.82 8.66 8.64 8.67 8.29 8.17 8.09 8.01 8.00 7.96 7.89 7.88 7.75 7.70 7.66 7.82 8.26 8.19 8.13 8.06 8.08 8.02 7.88 7.84 7.81 8.01 8.23 8.11 7.91 7.72 7.68 7.60 7.54 7.49 7.43 7.41 7.38 7.39 7.39 7.39 7.45 7.40 7.49

H 0.723 0.733 0.731 0.723 0.762 0.760 0.756 0.760 0.756 0.759 0.760 0.756 0.770 0.770 0.771 0.746 0.679 0.674 0.680 0.681 0.675 0.679 0.691 0.690 0.688 0.659 0.626 0.797 0.795 0.794 0.792 0.792 0.792 0.792 0.793 0.792 0.791 0.785 0.783 0.780 0.703 0.703 0.687

11.1 9.20 7.51 6.17 5.04 3.48 73.9 57.1 42.1 32.5 24.3 18.0 13.9 10.4 8.81 6.16 4.84 3.67 2.64 86.3 66.6 51.2 37.5 26.9 20.1 14.1 10.5 7.78 7.24 4.85 3.98 3.21 2.49 1.88 1.41 247 84.5 65.4 50.5 39.6 30.7 23.4 18.8 13.5 10.0

92.7 77.6 63.2 53.6 46.0 37.3 615 468 335 256 188 146 113 84.9 55.4 43.0 35.4 29.3 23.4 636 478 361 257 184 133 96.4 71.2 53.0 37.6 28.5 23.9 20.5 17.3 14.3 10.5 1740 532 401 304 232 178 135 105 74.3 57.7

7.45 7.45 7.44 7.46 7.50 7.65 7.05 7.00 6.93 6.90 6.86 6.90 6.89 6.88 6.74 6.82 6.86 6.93 7.02 6.51 6.45 6.40 6.33 6.30 6.24 6.27 6.25 6.24 6.10 6.19 6.20 6.24 6.31 6.38 6.35 6.26 5.96 5.90 5.85 5.79 5.76 5.73 5.68 5.64 5.69

0.688 0.685 0.684 0.678 0.670 0.644 0.803 0.803 0.804 0.802 0.802 0.792 0.788 0.784 0.715 0.700 0.691 0.677 0.659 0.817 0.818 0.817 0.819 0.815 0.818 0.809 0.807 0.802 0.716 0.698 0.694 0.683 0.668 0.653 0.654 0.831 0.828 0.829 0.828 0.830 0.828 0.825 0.828 0.827 0.815

7.53 5.62 5.55 3.65 2.63 2.01 1.40 100 75.6 58.4 45.1 33.2 25.5 19.1 15.3 11.9 9.22 6.70 4.74 3.35 2.35 3.53 2.62 1.84 1.34 0.932 0.850 0.588 20.4 15.3 11.8 7.69 5.62 4.47 3.40 2.60 3.01 2.16 1.51 1.22 0.913 0.617 0.400 0.884 0.570

42.7 31.7 24.0 17.5 12.6 10.2 7.79 553 405 305 230 165 125 91.3 72.5 55.8 43.8 31.9 23.1 16.4 11.6 12.3 9.57 6.90 5.30 4.08 3.92 2.93 85.4 63.0 47.3 32.5 23.4 18.4 13.8 10.4 9.33 6.50 4.42 3.62 2.78 2.08 1.52 2.50 1.89

5.66 5.64 5.48 5.54 5.53 5.57 5.63 5.47 5.40 5.34 5.28 5.22 5.19 5.14 5.11 5.09 5.09 5.08 5.09 5.08 5.07 4.88 4.89 4.90 4.93 4.99 5.13 5.17 4.67 4.64 4.59 4.63 4.60 4.58 4.56 4.53 4.37 4.33 4.30 4.30 4.31 4.37 4.44 4.36 4.44

0.814 0.812 0.732 0.716 0.713 0.702 0.685 0.837 0.837 0.837 0.837 0.838 0.836 0.836 0.836 0.835 0.832 0.827 0.818 0.814 0.809 0.733 0.727 0.720 0.709 0.691 0.619 0.606 0.859 0.859 0.861 0.846 0.845 0.846 0.845 0.846 0.730 0.732 0.732 0.728 0.721 0.703 0.676 0.665 0.640

0.383 87.2 66.5 51.1 39.1 29.1 22.3 16.8 12.5 9.58 7.23 5.30 3.73 2.92 2.04 1.41 1.74 1.36 1.08 0.830 0.619 0.609 0.404 0.252 3.85 2.72 1.78 1.19 1.10 0.760 0.555 0.396 0.272 0.230 0.130 714 555 430 331 254 196 164 135 110 88.3

1.40 339 251 189 140 102 75.7 56.5 41.2 30.7 22.8 17.4 12.1 9.29 6.42 4.37 3.96 3.01 2.35 1.84 1.36 1.20 0.788 0.598 10.4 7.19 4.61 3.01 1.99 1.34 0.974 0.673 0.516 0.366 0.243 5250 3920 2930 2180 1620 1210 991 801 640 502

4.49 4.41 4.36 4.30 4.23 4.19 4.13 4.10 4.06 4.02 4.00 4.03 4.00 3.97 3.95 3.93 3.72 3.69 3.67 3.68 3.66 3.67 3.65 3.74 3.63 3.60 3.57 3.54 3.30 3.28 3.27 3.24 3.30 3.26 3.32 5.47 5.35 5.24 5.15 5.06 4.98 4.92 4.87 4.82 4.77

0.623 0.875 0.873 0.874 0.875 0.874 0.875 0.872 0.872 0.874 0.873 0.862 0.860 0.863 0.861 0.861 0.752 0.755 0.756 0.749 0.748 0.695 0.693 0.662 0.878 0.877 0.877 0.879 0.770 0.769 0.767 0.769 0.745 0.695 0.667 0.966 0.966 0.966 0.966 0.967 0.967 0.968 0.968 0.968 0.968

67.5 51.8 39.3 29.6 22.2 17.3 13.2 9.84 7.56 6.13 4.67 3.55 2.68 2.03 2.53 1.93 1.50 1.09 0.967 0.723 0.522 0.398 0.284 0.190 0.179 0.104 120 92.0 70.9 53.5 41.6 32.1 24.3 17.7 12.8 9.21 6.42 4.55 3.42 2.54 1.91 1.46 1.09 1.05 0.788

375 281 209 154 113 87.2 65.2 47.9 36.3 26.6 20.0 15.0 11.1 8.31 5.63 4.19 3.21 2.29 1.46 1.07 0.751 0.554 0.400 0.287 0.207 0.134 481 356 267 195 148 112 82.1 58.3 41.3 28.9 19.7 13.6 10.1 7.34 5.43 4.07 2.97 2.08 1.53

4.71 4.66 4.61 4.57 4.52 4.49 4.46 4.43 4.40 4.21 4.19 4.16 4.14 4.12 3.24 3.21 3.19 3.17 2.89 2.87 2.86 2.86 2.87 2.90 2.82 2.86 4.07 4.00 3.94 3.88 3.83 3.79 3.73 3.69 3.65 3.61 3.57 3.53 3.51 3.49 3.47 3.45 3.43 3.00 3.00

0.969 0.969 0.969 0.970 0.970 0.971 0.970 0.971 0.971 0.966 0.966 0.968 0.967 0.968 0.912 0.916 0.916 0.915 0.868 0.866 0.865 0.799 0.792 0.772 0.712 0.689 0.958 0.959 0.958 0.958 0.958 0.958 0.960 0.960 0.960 0.959 0.959 0.961 0.962 0.960 0.960 0.960 0.960 0.944 0.939

0.855 0.627 0.452 0.369 0.228 0.150 0.146 0.0899 0.0511 0.0350 7.50 5.41 3.75 2.55 1.78 1.23 0.909 0.693 0.753 0.487 0.291 0.310 0.201 0.119 0.116 0.0776 0.0518 0.0272 2.51 1.66 0.977 0.558 0.384 0.267 0.268 0.173 0.141 0.0855 0.0679 0.0433 0.0212 0.229 0.120 0.0504 0.111

1.23 0.885 0.620 0.437 0.267 0.174 0.137 0.0934 0.0678 0.0493 16.9 11.9 8.02 5.31 3.62 2.46 1.78 1.33 0.981 0.616 0.356 0.273 0.173 0.107 0.0796 0.0610 0.0475 0.0255 3.56 2.28 1.30 0.715 0.480 0.327 0.230 0.144 0.0916 0.0562 0.0382 0.0269 0.0114 0.171 0.0858 0.0342 0.0426

2.67 2.66 2.63 2.56 2.54 2.54 2.52 2.54 2.62 2.64 3.04 3.00 2.97 2.94 2.91 2.89 2.87 2.85 2.43 2.42 2.40 2.17 2.15 2.16 2.08 2.11 2.16 2.16 2.41 2.38 2.34 2.32 2.30 2.28 1.98 1.96 1.80 1.80 1.72 1.74 1.70 1.76 1.73 1.71 1.37

0.899 0.898 0.901 0.834 0.830 0.827 0.683 0.665 0.624 0.611 0.963 0.964 0.964 0.964 0.965 0.964 0.966 0.966 0.940 0.936 0.927 0.849 0.848 0.830 0.729 0.703 0.672 0.661 0.962 0.961 0.966 0.961 0.963 0.961 0.935 0.936 0.877 0.863 0.760 0.733 0.749 0.953 0.953 0.937 0.880

0.0449 0.0202 0.0166 0.157 0.0958 0.0750 0.0246 0.0206 0.0249 0.0196 0.0145 0.0156 0.0112 0.00932 0.00917 0.00778 0.00494 0.00265 0.156 0.00919 6.38 5.05 3.76 3.01 2.44 4.16 3.30 2.28 1.78 2.02 1.16 1.05 0.765 1.36 0.842 0.524 0.438 0.633 0.300 0.271 0.167 0.181 0.0830 0.0568 0.0590

0.0178 0.00736 0.00620 0.0775 0.0453 0.0233 0.0284 0.0268 0.0337 0.0250 0.0202 0.0138 0.00989 0.00792 0.00463 0.00403 0.00124 0.000754 0.0732 0.00193 27.5 15.0 19.5 12.1 6.94 15.0 9.17 7.21 4.02 7.03 2.26 2.02 0.995 1.97 0.787 0.556 0.364 0.725 0.173 0.168 0.0642 0.0772 0.0197 0.0100 0.00995

1.37 1.34 1.34 1.44 1.43 1.16 2.69 2.75 2.71 2.69 2.71 2.22 2.22 2.22 1.74 1.75 1.27 1.28 1.43 1.08 5.14 4.88 5.28 5.11 4.88 4.36 4.21 4.29 4.10 4.02 3.71 3.22 3.04 2.60 2.42 2.49 2.39 2.23 1.98 1.73 1.58 1.35 1.20 1.02 0.903

0.846 0.852 0.839 0.964 0.962 0.947 0.634 0.602 0.567 0.574 0.572 0.585 0.583 0.588 0.612 0.608 0.646 0.644 0.955 0.942 0.640 0.686 0.584 0.615 0.656 0.625 0.659 0.613 0.654 0.582 0.660 0.635 0.689 0.662 0.732 0.695 0.731 0.653 0.767 0.704 0.788 0.705 0.819 0.839 0.797

0.0364 0.0432 0.0216

0.00457 0.00496 0.00189

0.834 0.732 0.667

0.869 0.830 0.911

Shape

L8X8X1-1/8 L8X8X1 L8X8X7/8 L8X8X3/4 L8X8X5/8 L8X8X9/16 L8X8X1/2 L8X6X1 L8X6X7/8 L8X6X3/4 L8X6X5/8 L8X6X9/16 L8X6X1/2 L8X6X7/16 L8X4X1 L8X4X7/8 L8X4X3/4 L8X4X5/8 L8X4X9/16 L8X4X1/2 L8X4X7/16 L7X4X3/4 L7X4X5/8 L7X4X1/2 L7X4X7/16 L7X4X3/8 L6X6X1 L6X6X7/8 L6X6X3/4 L6X6X5/8 L6X6X9/16 L6X6X1/2 L6X6X7/16 L6X6X3/8 L6X6X5/16 L6X4X7/8 L6X4X3/4 L6X4X5/8 L6X4X9/16 L6X4X1/2 L6X4X7/16 L6X4X3/8 L6X4X5/16

A 16.7 15.0 13.2 11.4 9.61 8.68 7.75 13.0 11.5 9.94 8.36 7.56 6.75 5.93 11.0 9.73 8.44 7.11 6.43 5.75 5.06 7.69 6.48 5.25 4.62 3.98 11.0 9.75 8.46 7.13 6.45 5.77 5.08 4.38 3.67 7.98 6.94 5.86 5.31 4.75 4.18 3.61 3.03

d 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 7.00 7.00 7.00 7.00 7.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00

b 8.00 8.00 8.00 8.00 8.00 8.00 8.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00

t 1.125 1 0.875 0.75 0.625 0.5625 0.5 1 0.875 0.75 0.625 0.5625 0.5 0.4375 1 0.875 0.75 0.625 0.5625 0.5 0.4375 0.75 0.625 0.5 0.4375 0.375 1 0.875 0.75 0.625 0.5625 0.5 0.4375 0.375 0.3125 0.875 0.75 0.625 0.5625 0.5 0.4375 0.375 0.3125

L6X3-1/2X1/2 L6X3-1/2X3/8 L6X3-1/2X5/16 L5X5X7/8 L5X5X3/4 L5X5X5/8 L5X5X1/2 L5X5X7/16 L5X5X3/8 L5X5X5/16 L5X3-1/2X3/4 L5X3-1/2X5/8 L5X3-1/2X1/2 L5X3-1/2X3/8 L5X3-1/2X5/16 L5X3-1/2X1/4 L5X3X1/2 L5X3X7/16 L5X3X3/8 L5X3X5/16 L5X3X1/4 L4X4X3/4 L4X4X5/8 L4X4X1/2 L4X4X7/16 L4X4X3/8 L4X4X5/16 L4X4X1/4 L4X3-1/2X1/2 L4X3-1/2X3/8 L4X3-1/2X5/16 L4X3-1/2X1/4 L4X3X5/8 L4X3X1/2 L4X3X3/8 L4X3X5/16 L4X3X1/4 L3-1/2X3-1/2X1/2 L3-1/2X3-1/2X7/16 L3-1/2X3-1/2X3/8 L3-1/2X3-1/2X5/16 L3-1/2X3-1/2X1/4 L3-1/2X3X1/2 L3-1/2X3X7/16 L3-1/2X3X3/8

4.50 3.42 2.87 7.98 6.94 5.86 4.75 4.18 3.61 3.03 5.81 4.92 4.00 3.05 2.56 2.06 3.75 3.31 2.86 2.40 1.94 5.44 4.61 3.75 3.31 2.86 2.40 1.94 3.50 2.67 2.25 1.81 3.89 3.25 2.48 2.09 1.69 3.25 2.87 2.48 2.09 1.69 3.00 2.65 2.30

6.00 6.00 6.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50

3.50 3.50 3.50 5.00 5.00 5.00 5.00 5.00 5.00 5.00 3.50 3.50 3.50 3.50 3.50 3.50 3.00 3.00 3.00 3.00 3.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 3.50 3.50 3.50 3.50 3.00 3.00 3.00 3.00 3.00 3.50 3.50 3.50 3.50 3.50 3.00 3.00 3.00

0.5 0.375 0.3125 0.875 0.75 0.625 0.5 0.4375 0.375 0.3125 0.75 0.625 0.5 0.375 0.3125 0.25 0.5 0.4375 0.375 0.3125 0.25 0.75 0.625 0.5 0.4375 0.375 0.3125 0.25 0.5 0.375 0.3125 0.25 0.625 0.5 0.375 0.3125 0.25 0.5 0.4375 0.375 0.3125 0.25 0.5 0.4375 0.375

L3-1/2X3X5/16 L3-1/2X3X1/4 L3-1/2X2-1/2X1/2 L3-1/2X2-1/2X3/8 L3-1/2X2-1/2X5/16 L3-1/2X2-1/2X1/4 L3X3X1/2 L3X3X7/16 L3X3X3/8 L3X3X5/16 L3X3X1/4 L3X3X3/16 L3X2-1/2X1/2 L3X2-1/2X7/16 L3X2-1/2X3/8 L3X2-1/2X5/16 L3X2-1/2X1/4 L3X2-1/2X3/16 L3X2X1/2 L3X2X3/8 L3X2X5/16 L3X2X1/4 L3X2X3/16 L2-1/2X2-1/2X1/2 L2-1/2X2-1/2X3/8 L2-1/2X2-1/2X5/16 L2-1/2X2-1/2X1/4 L2-1/2X2-1/2X3/16 L2-1/2X2X3/8 L2-1/2X2X5/16 L2-1/2X2X1/4 L2-1/2X2X3/16 L2-1/2X1-1/2X1/4 L2-1/2X1-1/2X3/16 L2X2X3/8 L2X2X5/16 L2X2X1/4 L2X2X3/16 L2X2X1/8

1.93 1.56 2.75 2.11 1.78 1.44 2.75 2.43 2.11 1.78 1.44 1.09 2.50 2.21 1.92 1.67 1.31 0.996 2.25 1.73 1.46 1.19 0.902 2.25 1.73 1.46 1.19 0.900 1.55 1.31 1.06 0.809 0.938 0.715 1.36 1.15 0.938 0.715 0.484

3.50 3.50 3.50 3.50 3.50 3.50 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.00 2.00 2.00 2.00 2.00

3.00 3.00 2.50 2.50 2.50 2.50 3.00 3.00 3.00 3.00 3.00 3.00 2.50 2.50 2.50 2.50 2.50 2.50 2.00 2.00 2.00 2.00 2.00 2.50 2.50 2.50 2.50 2.50 2.00 2.00 2.00 2.00 1.50 1.50 2.00 2.00 2.00 2.00 2.00

0.3125 0.25 0.5 0.375 0.3125 0.25 0.5 0.4375 0.375 0.3125 0.25 0.1875 0.5 0.4375 0.375 0.3125 0.25 0.1875 0.5 0.375 0.3125 0.25 0.1875 0.5 0.375 0.3125 0.25 0.1875 0.375 0.3125 0.25 0.1875 0.25 0.1875 0.375 0.3125 0.25 0.1875 0.125

Single Angle Section Proper k 1.75 1.625 1.5 1.375 1.25 1.1875 1.125 1.5 1.375 1.25 1.125 1.0625 1 0.9375 1.5 1.375 1.25 1.125 1.0625 1 0.9375 1.25 1.125 1 0.9375 0.875 1.5 1.375 1.25 1.125 1.0625 1 0.9375 0.875 0.8125 1.375 1.25 1.125 1.0625 1 0.9375 0.875 0.8125

wt./ft. 56.9 51.0 45.0 38.9 32.7 29.6 26.4 44.2 39.1 33.8 28.5 25.7 23.0 20.2 37.4 33.1 28.7 24.2 21.9 19.6 17.2 26.2 22.1 17.9 15.7 13.6 37.4 33.1 28.7 24.2 21.9 19.6 17.2 14.9 12.4 27.2 23.6 20.0 18.1 16.2 14.3 12.3 10.3

eo 1.05 0.943 0.832 0.720 0.606 0.548 0.490 0.816 0.721 0.624 0.526 0.476 0.425 0.374 0.691 0.612 0.531 0.448 0.405 0.363 0.320 0.550 0.464 0.376 0.331 0.286 0.918 0.813 0.705 0.594 0.538 0.481 0.423 0.365 0.306 0.665 0.578 0.488 0.442 0.396 0.349 0.301 0.252

Ix 98.1 89.1 79.7 69.9 59.6 54.2 48.8 80.9 72.4 63.5 54.2 49.4 44.4 39.3 69.7 62.6 55.0 47.0 42.9 38.6 34.2 37.8 32.4 26.6 23.6 20.5 35.4 31.9 28.1 24.1 22.0 19.9 17.6 15.4 13.0 27.7 24.5 21.0 19.2 17.3 15.4 13.4 11.4

Sx 17.5 15.8 14.0 12.2 10.3 9.33 8.36 15.1 13.4 11.7 9.86 8.94 8.01 7.06 14.0 12.5 10.9 9.20 8.34 7.48 6.59 8.39 7.12 5.79 5.11 4.42 8.55 7.61 6.64 5.64 5.12 4.59 4.06 3.51 2.95 7.13 6.23 5.29 4.81 4.31 3.81 3.30 2.77

rx 2.41 2.43 2.45 2.46 2.48 2.49 2.49 2.49 2.50 2.52 2.54 2.55 2.55 2.56 2.51 2.53 2.55 2.56 2.57 2.58 2.59 2.21 2.23 2.25 2.26 2.27 1.79 1.81 1.82 1.84 1.85 1.86 1.86 1.87 1.88 1.86 1.88 1.89 1.90 1.91 1.92 1.93 1.94

1 0.875 0.8125 1.375 1.25 1.125 1 0.9375 0.875 0.8125 1.1875 1.0625 0.9375 0.8125 0.75 0.6875 0.9375 0.875 0.8125 0.75 0.6875 1.125 1 0.875 0.8125 0.75 0.6875 0.625 0.875 0.75 0.6875 0.625 1 0.875 0.75 0.6875 0.625 0.875 0.8125 0.75 0.6875 0.625 0.875 0.8125 0.75

15.3 11.7 9.80 27.2 23.6 20.0 16.2 14.3 12.3 10.3 19.8 16.8 13.6 10.4 8.70 7.00 12.8 11.3 9.80 8.20 6.60 18.5 15.7 12.8 11.3 9.80 8.20 6.60 11.9 9.10 7.70 6.20 13.6 11.1 8.50 7.20 5.80 11.1 9.80 8.50 7.20 5.80 10.2 9.10 7.90

0.376 0.287 0.241 0.802 0.698 0.590 0.479 0.422 0.365 0.307 0.582 0.493 0.400 0.305 0.256 0.207 0.375 0.331 0.286 0.241 0.194 0.679 0.576 0.468 0.413 0.357 0.300 0.242 0.438 0.334 0.281 0.227 0.498 0.407 0.311 0.262 0.211 0.466 0.412 0.357 0.301 0.243 0.431 0.382 0.331

16.6 12.9 10.9 17.8 15.7 13.6 11.3 10.0 8.76 7.44 13.9 12.0 10.0 7.75 6.58 5.36 9.43 8.41 7.35 6.24 5.09 7.62 6.62 5.52 4.93 4.32 3.67 3.00 5.30 4.15 3.53 2.89 6.01 5.02 3.94 3.36 2.75 3.63 3.25 2.86 2.44 2.00 3.45 3.10 2.73

4.23 3.23 2.72 5.16 4.52 3.85 3.15 2.78 2.41 2.04 4.26 3.63 2.97 2.28 1.92 1.55 2.89 2.56 2.22 1.87 1.51 2.79 2.38 1.96 1.73 1.50 1.27 1.03 1.92 1.48 1.25 1.01 2.28 1.87 1.44 1.22 0.988 1.48 1.32 1.15 0.969 0.787 1.45 1.29 1.12

1.92 1.93 1.94 1.49 1.50 1.52 1.53 1.54 1.55 1.56 1.55 1.56 1.58 1.59 1.60 1.61 1.58 1.59 1.60 1.61 1.62 1.18 1.20 1.21 1.22 1.23 1.24 1.25 1.23 1.25 1.25 1.26 1.23 1.24 1.26 1.27 1.27 1.05 1.06 1.07 1.08 1.09 1.07 1.08 1.09

0.6875 0.625 0.875 0.75 0.6875 0.625 0.875 0.8125 0.75 0.6875 0.625 0.5625 0.875 0.8125 0.75 0.6875 0.625 0.5625 0.8125 0.6875 0.625 0.5625 0.5 0.75 0.625 0.5625 0.5 0.4375 0.625 0.5625 0.5 0.4375 0.5 0.4375 0.625 0.5625 0.5 0.4375 0.375

6.60 5.40 9.40 7.20 6.10 4.90 9.40 8.30 7.20 6.10 4.90 3.71 8.50 7.60 6.60 5.60 4.50 3.39 7.70 5.90 5.00 4.10 3.07 7.70 5.90 5.00 4.10 3.07 5.30 4.50 3.62 2.75 3.22 2.47 4.70 3.92 3.19 2.44 1.65

0.279 0.226 0.395 0.303 0.256 0.207 0.458 0.405 0.351 0.296 0.239 0.181 0.418 0.370 0.321 0.271 0.220 0.167 0.377 0.291 0.247 0.200 0.153 0.450 0.347 0.293 0.237 0.180 0.311 0.264 0.214 0.164 0.189 0.145 0.342 0.290 0.236 0.180 0.123

2.33 1.92 3.24 2.56 2.20 1.81 2.20 1.98 1.75 1.50 1.23 0.948 2.07 1.87 1.65 1.41 1.16 0.899 1.92 1.54 1.32 1.09 0.847 1.22 0.972 0.837 0.692 0.535 0.914 0.790 0.656 0.511 0.594 0.464 0.476 0.414 0.346 0.271 0.189

0.951 0.773 1.41 1.09 0.925 0.753 1.06 0.946 0.825 0.699 0.569 0.433 1.03 0.921 0.803 0.681 0.555 0.423 1.00 0.779 0.662 0.541 0.414 0.716 0.558 0.474 0.387 0.295 0.546 0.465 0.381 0.293 0.364 0.280 0.348 0.298 0.244 0.188 0.129

1.09 1.10 1.08 1.10 1.11 1.12 0.895 0.903 0.910 0.918 0.926 0.933 0.910 0.917 0.924 0.932 0.940 0.947 0.922 0.937 0.945 0.953 0.961 0.735 0.749 0.756 0.764 0.771 0.766 0.774 0.782 0.790 0.792 0.801 0.591 0.598 0.605 0.612 0.620

ngle Angle Section Properties from AISC Version 13.0 CD Database (Dec. 2005) and AISC 13th Edition Manual (Dec. 20 y(bar) 2.40 2.36 2.31 2.26 2.21 2.19 2.17 2.65 2.60 2.55 2.50 2.48 2.46 2.43 3.03 2.99 2.94 2.89 2.86 2.84 2.81 2.50 2.45 2.40 2.38 2.35 1.86 1.81 1.77 1.72 1.70 1.67 1.65 1.62 1.60 2.12 2.07 2.03 2.00 1.98 1.95 1.93 1.90

Zx 31.6 28.5 25.3 22.0 18.6 16.8 15.1 27.3 24.3 21.1 17.9 16.2 14.6 12.9 24.3 21.7 18.9 16.1 14.6 13.1 11.6 14.8 12.5 10.2 9.03 7.81 15.4 13.7 11.9 10.1 9.18 8.22 7.25 6.27 5.26 12.7 11.1 9.44 8.59 7.71 6.81 5.89 4.96

yp 1.05 0.943 0.832 0.720 0.606 0.548 0.490 1.47 1.41 1.34 1.27 1.23 1.20 1.16 2.47 2.41 2.34 2.27 2.23 2.20 2.16 1.87 1.80 1.74 1.70 1.67 0.918 0.813 0.705 0.594 0.538 0.481 0.423 0.365 0.306 1.44 1.38 1.31 1.28 1.25 1.22 1.19 1.16

Iy 98.1 89.1 79.7 69.9 59.6 54.2 48.8 38.8 34.9 30.8 26.4 24.1 21.7 19.3 11.6 10.5 9.37 8.11 7.44 6.75 6.03 9.00 7.79 6.48 5.79 5.06 35.4 31.9 28.1 24.1 22.0 19.9 17.6 15.4 13.0 9.70 8.63 7.48 6.86 6.22 5.56 4.86 4.13

Sy 17.5 15.8 14.0 12.2 10.3 9.33 8.36 8.92 7.94 6.92 5.88 5.34 4.79 4.23 3.94 3.51 3.07 2.62 2.38 2.15 1.90 3.01 2.56 2.10 1.86 1.61 8.55 7.61 6.64 5.64 5.12 4.59 4.06 3.51 2.95 3.37 2.95 2.52 2.29 2.06 1.83 1.58 1.34

ry 2.41 2.43 2.45 2.46 2.48 2.49 2.49 1.72 1.74 1.75 1.77 1.78 1.79 1.80 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.08 1.10 1.11 1.12 1.12 1.79 1.81 1.82 1.84 1.85 1.86 1.86 1.87 1.88 1.10 1.12 1.13 1.14 1.14 1.15 1.16 1.17

2.07 2.02 2.00 1.56 1.52 1.47 1.42 1.40 1.37 1.35 1.74 1.69 1.65 1.60 1.57 1.55 1.74 1.72 1.69 1.67 1.64 1.27 1.22 1.18 1.15 1.13 1.11 1.08 1.24 1.20 1.17 1.14 1.37 1.32 1.27 1.25 1.22 1.05 1.03 1.00 0.979 0.954 1.12 1.09 1.07

7.49 5.74 4.84 9.31 8.14 6.93 5.66 5.00 4.33 3.65 7.60 6.50 5.33 4.09 3.45 2.78 5.12 4.53 3.93 3.32 2.68 5.02 4.28 3.50 3.10 2.69 2.26 1.82 3.46 2.66 2.24 1.81 4.08 3.36 2.60 2.19 1.77 2.66 2.36 2.06 1.74 1.41 2.61 2.32 2.03

1.48 1.41 1.38 0.802 0.698 0.590 0.479 0.422 0.365 0.307 1.12 1.06 0.997 0.933 0.901 0.868 1.25 1.21 1.18 1.15 1.12 0.679 0.576 0.468 0.413 0.357 0.300 0.242 0.497 0.433 0.401 0.368 0.810 0.747 0.683 0.651 0.618 0.466 0.412 0.357 0.301 0.243 0.480 0.446 0.411

4.24 3.33 2.84 17.8 15.7 13.6 11.3 10.0 8.76 7.44 5.52 4.80 4.02 3.15 2.69 2.20 2.55 2.29 2.01 1.72 1.41 7.62 6.62 5.52 4.93 4.32 3.67 3.00 3.76 2.96 2.52 2.07 2.85 2.40 1.89 1.62 1.33 3.63 3.25 2.86 2.44 2.00 2.32 2.09 1.84

1.59 1.22 1.03 5.16 4.52 3.85 3.15 2.78 2.41 2.04 2.20 1.88 1.55 1.19 1.01 0.816 1.13 1.00 0.874 0.739 0.600 2.79 2.38 1.96 1.73 1.50 1.27 1.03 1.50 1.16 0.980 0.794 1.34 1.10 0.851 0.721 0.585 1.48 1.32 1.15 0.969 0.787 1.09 0.971 0.847

0.968 0.984 0.991 1.49 1.50 1.52 1.53 1.54 1.55 1.56 0.974 0.987 1.00 1.02 1.02 1.03 0.824 0.831 0.838 0.846 0.853 1.18 1.20 1.21 1.22 1.23 1.24 1.25 1.04 1.05 1.06 1.07 0.845 0.858 0.873 0.880 0.887 1.05 1.06 1.07 1.08 1.09 0.877 0.885 0.892

1.05 1.02 1.20 1.15 1.13 1.10 0.929 0.907 0.884 0.860 0.836 0.812 0.995 0.972 0.949 0.925 0.900 0.874 1.08 1.03 1.01 0.980 0.952 0.803 0.758 0.735 0.711 0.687 0.826 0.803 0.779 0.754 0.866 0.839 0.632 0.609 0.586 0.561 0.534

1.72 1.39 2.52 1.96 1.67 1.36 1.91 1.70 1.48 1.26 1.02 0.774 1.86 1.66 1.45 1.23 1.00 0.761 1.78 1.39 1.19 0.969 0.743 1.29 1.01 0.853 0.695 0.529 0.982 0.839 0.688 0.529 0.644 0.497 0.629 0.537 0.440 0.338 0.230

0.375 0.336 0.736 0.668 0.633 0.596 0.458 0.405 0.351 0.296 0.239 0.181 0.494 0.462 0.430 0.397 0.363 0.328 0.736 0.668 0.633 0.596 0.556 0.450 0.347 0.293 0.237 0.180 0.425 0.391 0.356 0.318 0.606 0.568 0.342 0.290 0.236 0.180 0.123

1.58 1.30 1.36 1.09 0.937 0.775 2.20 1.98 1.75 1.50 1.23 0.948 1.29 1.17 1.03 0.888 0.734 0.568 0.667 0.539 0.467 0.390 0.305 1.22 0.972 0.837 0.692 0.535 0.513 0.446 0.372 0.292 0.160 0.126 0.476 0.414 0.346 0.271 0.189

0.718 0.585 0.756 0.589 0.501 0.410 1.06 0.946 0.825 0.699 0.569 0.433 0.736 0.656 0.573 0.487 0.397 0.303 0.470 0.368 0.314 0.258 0.198 0.716 0.558 0.474 0.387 0.295 0.361 0.309 0.253 0.195 0.142 0.110 0.348 0.298 0.244 0.188 0.129

0.900 0.908 0.701 0.716 0.723 0.731 0.895 0.903 0.910 0.918 0.926 0.933 0.718 0.724 0.731 0.739 0.746 0.753 0.543 0.555 0.562 0.569 0.577 0.735 0.749 0.756 0.764 0.771 0.574 0.581 0.589 0.597 0.411 0.418 0.591 0.598 0.605 0.612 0.620

h Edition Manual (Dec. 2005) x(bar) 2.40 2.36 2.31 2.26 2.21 2.19 2.17 1.65 1.60 1.56 1.51 1.49 1.46 1.44 1.04 0.997 0.949 0.902 0.878 0.854 0.829 1.00 0.958 0.910 0.886 0.861 1.86 1.81 1.77 1.72 1.70 1.67 1.65 1.62 1.60 1.12 1.07 1.03 1.00 0.981 0.957 0.933 0.908

Zy 31.6 28.5 25.3 22.0 18.6 16.8 15.1 16.2 14.4 12.5 10.5 9.52 8.52 7.50 7.73 6.77 5.82 4.86 4.39 3.91 3.42 5.60 4.69 3.77 3.31 2.84 15.4 13.7 11.9 10.1 9.17 8.22 7.25 6.26 5.26 6.26 5.42 4.56 4.13 3.69 3.24 2.79 2.33

xp 1.05 0.943 0.832 0.720 0.606 0.548 0.490 0.816 0.721 0.624 0.526 0.476 0.425 0.374 0.691 0.612 0.531 0.448 0.405 0.363 0.320 0.550 0.464 0.376 0.331 0.286 0.918 0.813 0.705 0.594 0.538 0.481 0.423 0.365 0.306 0.665 0.578 0.488 0.442 0.396 0.349 0.301 0.252

Iz 40.9 36.8 32.7 28.5 24.2 22 19.7 21.3 18.9 16.5 14.1 12.8 11.5 10.2 7.87 7.01 6.13 5.24 4.79 4.32 3.84 5.64 4.8 3.95 3.5 3.05 15 13.3 11.6 9.83 8.94 8.04 7.11 6.17 5.2 5.82 5.08 4.32 3.94 3.55 3.14 2.73 2.31

Sz 7.23 6.51 5.78 5.04 4.27 3.88 3.49 4.84 4.31 3.78 3.22 2.94 2.64 2.35 2.15 1.93 1.7 1.47 1.34 1.22 1.09 1.71 1.47 1.21 1.08 0.942 3.53 3.13 2.73 2.32 2.11 1.89 1.68 1.45 1.23 1.9 1.66 1.42 1.3 1.17 1.04 0.908 0.769

rz 1.56 1.56 1.57 1.57 1.58 1.58 1.59 1.28 1.28 1.29 1.29 1.30 1.30 1.31 0.844 0.846 0.850 0.856 0.859 0.863 0.867 0.855 0.860 0.866 0.869 0.873 1.17 1.17 1.17 1.17 1.18 1.18 1.18 1.19 1.19 0.854 0.856 0.859 0.861 0.864 0.867 0.870 0.874

0.829 0.781 0.756 1.56 1.52 1.47 1.42 1.40 1.37 1.35 0.993 0.947 0.901 0.854 0.829 0.804 0.746 0.722 0.698 0.673 0.648 1.27 1.22 1.18 1.15 1.13 1.11 1.08 0.994 0.947 0.923 0.897 0.867 0.822 0.775 0.750 0.725 1.05 1.03 1.00 0.979 0.954 0.869 0.846 0.823

2.88 2.18 1.82 9.30 8.14 6.92 5.66 5.00 4.33 3.65 4.07 3.43 2.79 2.12 1.77 1.42 2.08 1.82 1.57 1.31 1.05 5.01 4.28 3.50 3.10 2.68 2.26 1.82 2.69 2.06 1.74 1.40 2.45 1.99 1.52 1.28 1.03 2.66 2.36 2.05 1.74 1.41 1.97 1.75 1.52

0.376 0.287 0.241 0.802 0.698 0.590 0.479 0.422 0.365 0.307 0.582 0.493 0.400 0.305 0.256 0.207 0.375 0.331 0.286 0.241 0.194 0.679 0.576 0.468 0.413 0.357 0.300 0.242 0.438 0.334 0.281 0.227 0.498 0.407 0.311 0.262 0.211 0.466 0.412 0.357 0.301 0.243 0.431 0.382 0.331

2.58 2 1.7 7.56 6.59 5.61 4.6 4.08 3.55 3.01 3.22 2.74 2.25 1.74 1.47 1.19 1.55 1.37 1.2 1.01 0.825 3.25 2.76 2.25 2 1.73 1.46 1.18 1.8 1.38 1.17 0.95 1.59 1.3 1.01 0.851 0.691 1.51 1.34 1.17 0.989 0.807 1.15 1.03 0.895

0.914 0.714 0.609 2.14 1.86 1.59 1.3 1.15 1 0.85 1.22 1.05 0.862 0.67 0.569 0.463 0.645 0.575 0.503 0.428 0.35 1.15 0.975 0.797 0.706 0.613 0.517 0.419 0.719 0.555 0.47 0.382 0.72 0.592 0.46 0.39 0.318 0.609 0.54 0.471 0.4 0.326 0.537 0.478 0.418

0.756 0.763 0.767 0.971 0.972 0.975 0.980 0.983 0.986 0.990 0.744 0.746 0.750 0.755 0.758 0.761 0.642 0.644 0.646 0.649 0.652 0.774 0.774 0.776 0.777 0.779 0.781 0.783 0.716 0.719 0.721 0.723 0.631 0.633 0.636 0.638 0.639 0.679 0.681 0.683 0.685 0.688 0.618 0.620 0.622

0.798 0.773 0.701 0.655 0.632 0.607 0.929 0.907 0.884 0.860 0.836 0.812 0.746 0.724 0.701 0.677 0.653 0.627 0.580 0.535 0.511 0.487 0.462 0.803 0.758 0.735 0.711 0.687 0.578 0.555 0.532 0.508 0.372 0.347 0.632 0.609 0.586 0.561 0.534

1.28 1.04 1.39 1.07 0.900 0.728 1.91 1.70 1.48 1.25 1.02 0.774 1.34 1.19 1.03 0.873 0.707 0.536 0.887 0.679 0.572 0.463 0.351 1.29 1.00 0.853 0.694 0.528 0.657 0.557 0.454 0.347 0.261 0.198 0.628 0.536 0.440 0.338 0.230

0.279 0.226 0.395 0.303 0.256 0.207 0.458 0.405 0.351 0.296 0.239 0.181 0.418 0.370 0.321 0.271 0.220 0.167 0.377 0.291 0.247 0.200 0.153 0.450 0.347 0.293 0.237 0.180 0.311 0.264 0.214 0.164 0.189 0.145 0.342 0.290 0.236 0.180 0.123

0.761 0.623 0.782 0.608 0.518 0.425 0.924 0.819 0.712 0.603 0.491 0.374 0.666 0.591 0.514 0.437 0.356 0.272 0.409 0.318 0.271 0.223 0.173 0.521 0.4 0.339 0.275 0.21 0.273 0.233 0.191 0.149 0.0975 0.076 0.203 0.173 0.141 0.109 0.0751

0.356 0.292 0.42 0.329 0.281 0.232 0.436 0.386 0.336 0.284 0.231 0.176 0.37 0.329 0.287 0.244 0.199 0.153 0.266 0.209 0.179 0.149 0.116 0.295 0.226 0.192 0.156 0.119 0.189 0.161 0.133 0.104 0.0818 0.0644 0.144 0.122 0.1 0.0771 0.0531

0.624 0.628 0.532 0.535 0.538 0.541 0.580 0.580 0.581 0.583 0.585 0.586 0.516 0.516 0.517 0.518 0.520 0.521 0.425 0.426 0.428 0.431 0.435 0.481 0.481 0.481 0.482 0.482 0.419 0.420 0.423 0.426 0.321 0.324 0.386 0.386 0.387 0.389 0.391

TAN  1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.542 0.546 0.550 0.554 0.556 0.557 0.559 0.247 0.252 0.257 0.262 0.264 0.266 0.268 0.324 0.329 0.334 0.337 0.339 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.421 0.428 0.435 0.438 0.440 0.443 0.446 0.449

Qs(36) 1.00 1.00 1.00 1.00 0.997 0.959 0.912 1.00 1.00 1.00 0.997 0.959 0.912 0.850 1.00 1.00 1.00 0.997 0.959 0.912 0.850 1.00 1.00 0.965 0.912 0.840 1.00 1.00 1.00 1.00 1.00 1.00 0.973 0.912 0.826 1.00 1.00 1.00 1.00 1.00 0.973 0.912 0.826

J 7.13 5.08 3.46 2.21 1.30 0.961 0.683 4.34 2.96 1.90 1.12 0.823 0.584 0.396 3.68 2.51 1.61 0.955 0.704 0.501 0.340 1.47 0.868 0.456 0.310 0.198 3.68 2.51 1.61 0.955 0.704 0.501 0.340 0.218 0.129 2.03 1.31 0.775 0.572 0.407 0.276 0.177 0.104

Cw 32.5 23.4 16.1 10.4 6.16 4.55 3.23 16.3 11.3 7.28 4.33 3.20 2.28 1.55 12.9 8.89 5.75 3.42 2.53 1.80 1.22 3.97 2.37 1.25 0.851 0.544 9.24 6.41 4.17 2.50 1.85 1.32 0.899 0.575 0.338 4.04 2.64 1.59 1.18 0.843 0.575 0.369 0.217

ro(bar) 4.29 4.32 4.36 4.39 4.42 4.43 4.45 3.88 3.92 3.95 3.98 3.99 4.01 4.02 3.75 3.78 3.80 3.83 3.84 3.86 3.87 3.31 3.34 3.37 3.38 3.40 3.18 3.21 3.24 3.28 3.29 3.31 3.32 3.34 3.35 2.82 2.85 2.88 2.90 2.91 2.93 2.94 2.96

H 0.630 0.630 0.630 0.630 0.630 0.630 0.630 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.640 0.630 0.630 0.630 0.630 0.630 0.630 0.630 0.630 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.343 0.349 0.352 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.464 0.472 0.479 0.485 0.489 0.491 0.357 0.361 0.364 0.368 0.371 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.750 0.755 0.757 0.759 0.534 0.542 0.551 0.554 0.558 1.00 1.00 1.00 1.00 1.00 0.713 0.717 0.720

1.00 0.912 0.826 1.00 1.00 1.00 1.00 1.00 0.983 0.912 1.00 1.00 1.00 0.983 0.912 0.804 1.00 1.00 0.983 0.912 0.804 1.00 1.00 1.00 1.00 1.00 0.997 0.912 1.00 1.00 0.997 0.912 1.00 1.00 1.00 0.997 0.912 1.00 1.00 1.00 1.00 0.965 1.00 1.00 1.00

0.386 0.168 0.0990 2.07 1.33 0.792 0.417 0.284 0.183 0.108 1.09 0.651 0.343 0.150 0.0883 0.0464 0.322 0.220 0.141 0.0832 0.0438 1.02 0.610 0.322 0.220 0.141 0.0832 0.0438 0.301 0.132 0.0782 0.0412 0.529 0.281 0.123 0.0731 0.0386 0.281 0.192 0.123 0.0731 0.0386 0.260 0.178 0.114

0.779 0.341 0.201 3.53 2.32 1.40 0.744 0.508 0.327 0.193 1.52 0.918 0.491 0.217 0.128 0.0670 0.444 0.304 0.196 0.116 0.0606 1.12 0.680 0.366 0.252 0.162 0.0963 0.0505 0.302 0.134 0.0798 0.0419 0.472 0.255 0.114 0.0676 0.0356 0.238 0.164 0.106 0.0634 0.0334 0.191 0.132 0.0858

2.88 2.90 2.92 2.64 2.67 2.70 2.73 2.74 2.76 2.77 2.36 2.39 2.42 2.45 2.47 2.48 2.38 2.39 2.41 2.42 2.43 2.10 2.13 2.16 2.18 2.19 2.21 2.22 2.03 2.06 2.08 2.09 1.91 1.94 1.97 1.98 1.99 1.87 1.89 1.90 1.92 1.93 1.75 1.76 1.78

0.00 0.00 0.00 0.640 0.630 0.630 0.630 0.630 0.630 0.630 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.640 0.630 0.630 0.630 0.630 0.630 0.630 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.630 0.630 0.630 0.630 0.630 0.00 0.00 0.00

0.722 0.725 0.485 0.495 0.500 0.504 1.00 1.00 1.00 1.00 1.00 1.00 0.666 0.671 0.675 0.679 0.683 0.687 0.413 0.426 0.432 0.437 0.442 1.00 1.00 1.00 1.00 1.00 0.612 0.618 0.624 0.628 0.354 0.360 1.00 1.00 1.00 1.00 1.00

1.00 0.965 1.00 1.00 1.00 0.965 1.00 1.00 1.00 1.00 1.00 0.912 1.00 1.00 1.00 1.00 1.00 0.912 1.00 1.00 1.00 1.00 0.912 1.00 1.00 1.00 1.00 0.983 1.00 1.00 1.00 0.983 1.00 0.983 1.00 1.00 1.00 1.00 0.912

0.0680 0.0360 0.234 0.103 0.0611 0.0322 0.230 0.157 0.101 0.0597 0.0313 0.0136 0.213 0.146 0.0943 0.0560 0.0296 0.0130 0.192 0.0855 0.0510 0.0270 0.0119 0.188 0.0833 0.0495 0.0261 0.0114 0.0746 0.0444 0.0235 0.0103 0.0209 0.00921 0.0658 0.0393 0.0209 0.00921 0.00293

0.0512 0.0270 0.159 0.0714 0.0426 0.0225 0.144 0.100 0.0652 0.0390 0.0206 0.00899 0.112 0.0777 0.0507 0.0304 0.0161 0.00705 0.0908 0.0413 0.0248 0.0132 0.00576 0.0791 0.0362 0.0218 0.0116 0.00510 0.0268 0.0162 0.00868 0.00382 0.00694 0.00306 0.0174 0.0106 0.00572 0.00254 0.000789

1.79 1.80 1.66 1.69 1.71 1.72 1.59 1.60 1.62 1.64 1.65 1.67 1.46 1.48 1.49 1.51 1.52 1.54 1.39 1.42 1.43 1.45 1.46 1.30 1.33 1.35 1.36 1.38 1.22 1.23 1.25 1.26 1.19 1.20 1.05 1.06 1.08 1.09 1.10

0.00 0.00 0.00 0.00 0.00 0.00 0.630 0.630 0.630 0.630 0.630 0.630 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.640 0.630 0.630 0.630 0.630 0.00 0.00 0.00 0.00 0.00 0.00 0.640 0.640 0.630 0.630 0.630

Shape 2L8X8X1-1/8 2L8X8X1 2L8X8X7/8 2L8X8X3/4 2L8X8X5/8 2L8X8X9/16 2L8X8X1/2 2L6X6X1 2L6X6X7/8 2L6X6X3/4 2L6X6X5/8 2L6X6X9/16 2L6X6X1/2 2L6X6X7/16 2L6X6X3/8 2L6X6X5/16 2L5X5X7/8 2L5X5X3/4 2L5X5X5/8 2L5X5X1/2 2L5X5X7/16 2L5X5X3/8 2L5X5X5/16 2L4X4X3/4 2L4X4X5/8 2L4X4X1/2 2L4X4X7/16 2L4X4X3/8 2L4X4X5/16 2L4X4X1/4 2L3-1/2X3-1/2X1/2 2L3-1/2X3-1/2X7/16 2L3-1/2X3-1/2X3/8 2L3-1/2X3-1/2X5/16 2L3-1/2X3-1/2X1/4 2L3X3X1/2 2L3X3X7/16 2L3X3X3/8 2L3X3X5/16 2L3X3X1/4 2L3X3X3/16 2L2-1/2X2-1/2X1/2 2L2-1/2X2-1/2X3/8

A 33.6 30.2 26.6 23 19.4 17.5 15.7 22 19.5 16.9 14.3 12.9 11.5 10.2 8.76 7.34 16 14 11.8 9.58 8.44 7.3 6.13 10.9 9.21 7.49 6.61 5.71 4.8 3.87 6.53 5.77 5 4.21 3.41 5.5 4.86 4.22 3.55 2.87 2.18 4.5 3.47

d 8 8 8 8 8 8 8 6 6 6 6 6 6 6 6 6 5 5 5 5 5 5 5 4 4 4 4 4 4 4 3.5 3.5 3.5 3.5 3.5 3 3 3 3 3 3 2.5 2.5

b 8 8 8 8 8 8 8 6 6 6 6 6 6 6 6 6 5 5 5 5 5 5 5 4 4 4 4 4 4 4 3.5 3.5 3.5 3.5 3.5 3 3 3 3 3 3 2.5 2.5

2L2-1/2X2-1/2X5/16 2L2-1/2X2-1/2X1/4 2L2-1/2X2-1/2X3/16 2L2X2X3/8 2L2X2X5/16 2L2X2X1/4 2L2X2X3/16 2L2X2X1/8 2L8X6X1LLBB 2L8X6X7/8LLBB 2L8X6X3/4LLBB 2L8X6X5/8LLBB 2L8X6X9/16LLBB 2L8X6X1/2LLBB 2L8X6X7/16LLBB 2L8X4X1LLBB 2L8X4X7/8LLBB 2L8X4X3/4LLBB 2L8X4X5/8LLBB 2L8X4X9/16LLBB 2L8X4X1/2LLBB 2L8X4X7/16LLBB 2L7X4X3/4LLBB 2L7X4X5/8LLBB 2L7X4X1/2LLBB 2L7X4X7/16LLBB 2L7X4X3/8LLBB 2L6X4X7/8LLBB 2L6X4X3/4LLBB 2L6X4X5/8LLBB 2L6X4X9/16LLBB 2L6X4X1/2LLBB 2L6X4X7/16LLBB 2L6X4X3/8LLBB 2L6X4X5/16LLBB 2L6X3-1/2X1/2LLBB 2L6X3-1/2X3/8LLBB 2L6X3-1/2X5/16LLBB 2L5X3-1/2X3/4LLBB 2L5X3-1/2X5/8LLBB 2L5X3-1/2X1/2LLBB 2L5X3-1/2X3/8LLBB 2L5X3-1/2X5/16LLBB 2L5X3-1/2X1/4LLBB 2L5X3X1/2LLBB

2.93 2.37 1.8 2.73 2.32 1.89 1.44 0.982 26.1 23.1 20 16.8 15.2 13.6 12 22.1 19.6 17 14.3 13 11.6 10.2 15.4 13 10.5 9.27 8 16 13.9 11.7 10.6 9.5 8.36 7.22 6.05 9.04 6.88 5.78 11.6 9.85 8.01 6.1 5.12 4.13 7.51

2.5 2.5 2.5 2 2 2 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6 6 5 5 5 5 5 5 5

2.5 2.5 2.5 2 2 2 2 2 6 6 6 6 6 6 6 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3

2L5X3X7/16LLBB 2L5X3X3/8LLBB 2L5X3X5/16LLBB 2L5X3X1/4LLBB 2L4X3-1/2X1/2LLBB 2L4X3-1/2X3/8LLBB 2L4X3-1/2X5/16LLBB 2L4X3-1/2X1/4LLBB 2L4X3X5/8LLBB 2L4X3X1/2LLBB 2L4X3X3/8LLBB 2L4X3X5/16LLBB 2L4X3X1/4LLBB 2L3-1/2X3X1/2LLBB 2L3-1/2X3X7/16LLBB 2L3-1/2X3X3/8LLBB 2L3-1/2X3X5/16LLBB 2L3-1/2X3X1/4LLBB 2L3-1/2X2-1/2X1/2LLBB 2L3-1/2X2-1/2X3/8LLBB 2L3-1/2X2-1/2X5/16LLBB 2L3-1/2X2-1/2X1/4LLBB 2L3X2-1/2X1/2LLBB 2L3X2-1/2X7/16LLBB 2L3X2-1/2X3/8LLBB 2L3X2-1/2X5/16LLBB 2L3X2-1/2X1/4LLBB 2L3X2-1/2X3/16LLBB 2L3X2X1/2LLBB 2L3X2X3/8LLBB 2L3X2X5/16LLBB 2L3X2X1/4LLBB 2L3X2X3/16LLBB 2L2-1/2X2X3/8LLBB 2L2-1/2X2X5/16LLBB 2L2-1/2X2X1/4LLBB 2L2-1/2X2X3/16LLBB 2L8X6X1SLBB 2L8X6X7/8SLBB 2L8X6X3/4SLBB 2L8X6X5/8SLBB 2L8X6X9/16SLBB 2L8X6X1/2SLBB 2L8X6X7/16SLBB 2L8X4X1SLBB

6.62 5.73 4.81 3.88 7.01 5.35 4.5 3.63 7.98 6.51 4.98 4.19 3.38 6.04 5.34 4.63 3.91 3.16 5.53 4.25 3.58 2.9 5.01 4.44 3.86 3.25 2.64 2 4.53 3.5 2.96 2.4 1.83 3.11 2.64 2.14 1.64 26.1 23.1 20 16.8 15.2 13.6 12 22.1

5 5 5 5 4 4 4 4 4 4 4 4 4 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3 3 3 3 3 3 3 3 3 3 3 2.5 2.5 2.5 2.5 6 6 6 6 6 6 6 4

3 3 3 3 3.5 3.5 3.5 3.5 3 3 3 3 3 3 3 3 3 3 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2 2 2 2 2 2 2 2 2 8 8 8 8 8 8 8 8

2L8X4X7/8SLBB 2L8X4X3/4SLBB 2L8X4X5/8SLBB 2L8X4X9/16SLBB 2L8X4X1/2SLBB 2L8X4X7/16SLBB 2L7X4X3/4SLBB 2L7X4X5/8SLBB 2L7X4X1/2SLBB 2L7X4X7/16SLBB 2L7X4X3/8SLBB 2L6X4X7/8SLBB 2L6X4X3/4SLBB 2L6X4X5/8SLBB 2L6X4X9/16SLBB 2L6X4X1/2SLBB 2L6X4X7/16SLBB 2L6X4X3/8SLBB 2L6X4X5/16SLBB 2L6X3-1/2X1/2SLBB 2L6X3-1/2X3/8SLBB 2L6X3-1/2X5/16SLBB 2L5X3-1/2X3/4SLBB 2L5X3-1/2X5/8SLBB 2L5X3-1/2X1/2SLBB 2L5X3-1/2X3/8SLBB 2L5X3-1/2X5/16SLBB 2L5X3-1/2X1/4SLBB 2L5X3X1/2SLBB 2L5X3X7/16SLBB 2L5X3X3/8SLBB 2L5X3X5/16SLBB 2L5X3X1/4SLBB 2L4X3-1/2X1/2SLBB 2L4X3-1/2X3/8SLBB 2L4X3-1/2X5/16SLBB 2L4X3-1/2X1/4SLBB 2L4X3X5/8SLBB 2L4X3X1/2SLBB 2L4X3X3/8SLBB 2L4X3X5/16SLBB 2L4X3X1/4SLBB 2L3-1/2X3X1/2SLBB 2L3-1/2X3X7/16SLBB 2L3-1/2X3X3/8SLBB

19.6 17 14.3 13 11.6 10.2 15.4 13 10.5 9.27 8 16 13.9 11.7 10.6 9.5 8.36 7.22 6.05 9.04 6.88 5.78 11.6 9.85 8.01 6.1 5.12 4.13 7.51 6.62 5.73 4.81 3.88 7.01 5.35 4.5 3.63 7.98 6.51 4.98 4.19 3.38 6.04 5.34 4.63

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3 3 3 3 3 3.5 3.5 3.5 3.5 3 3 3 3 3 3 3 3

8 8 8 8 8 8 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6 6 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 3.5 3.5 3.5

2L3-1/2X3X5/16SLBB 2L3-1/2X3X1/4SLBB 2L3-1/2X2-1/2X1/2SLBB 2L3-1/2X2-1/2X3/8SLBB 2L3-1/2X2-1/2X5/16SLBB 2L3-1/2X2-1/2X1/4SLBB 2L3X2-1/2X1/2SLBB 2L3X2-1/2X7/16SLBB 2L3X2-1/2X3/8SLBB 2L3X2-1/2X5/16SLBB 2L3X2-1/2X1/4SLBB 2L3X2-1/2X3/16SLBB 2L3X2X1/2SLBB 2L3X2X3/8SLBB 2L3X2X5/16SLBB 2L3X2X1/4SLBB 2L3X2X3/16SLBB 2L2-1/2X2X3/8SLBB 2L2-1/2X2X5/16SLBB 2L2-1/2X2X1/4SLBB 2L2-1/2X2X3/16SLBB

3.91 3.16 5.53 4.25 3.58 2.9 5.01 4.44 3.86 3.25 2.64 2 4.53 3.5 2.96 2.4 1.83 3.11 2.64 2.14 1.64

3 3 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2 2 2 2 2 2 2 2 2

3.5 3.5 3.5 3.5 3.5 3.5 3 3 3 3 3 3 3 3 3 3 3 2.5 2.5 2.5 2.5

Double Angle Section Properties from AISC Version 13.0 CD Da t 1.125 1 0.875 0.75 0.625 0.5625 0.5 1 0.875 0.75 0.625 0.5625 0.5 0.4375 0.375 0.3125 0.875 0.75 0.625 0.5 0.4375 0.375 0.3125 0.75 0.625 0.5 0.4375 0.375 0.3125 0.25 0.5 0.4375 0.375 0.3125 0.25 0.5 0.4375 0.375 0.3125 0.25 0.1875 0.5 0.375

wt./ft. 114 103 90.6 78.4 66 59.7 53.3 75 66.4 57.6 48.5 43.9 39.3 34.6 29.8 25 54.6 47.5 40.1 32.6 28.7 24.8 20.9 37 31.3 25.5 22.5 19.4 16.3 13.2 22.2 19.6 17 14.3 11.6 18.7 16.6 14.3 12.1 9.77 7.41 15.3 11.8

Ix 196 178 159 140 119 108 97.6 70.8 63.8 56.2 48.2 44.1 39.7 35.2 30.7 26 35.6 31.5 27.2 22.5 20.1 17.5 14.9 15.2 13.2 11 9.86 8.64 7.35 6 7.26 6.51 5.72 4.89 4 4.4 3.96 3.5 2.99 2.46 1.9 2.44 1.94

Sx 35 31.6 28 24.4 20.6 18.7 16.7 17.1 15.2 13.3 11.3 10.2 9.18 8.11 7.01 5.9 10.3 9.04 7.7 6.29 5.57 4.83 4.07 5.58 4.77 3.91 3.47 3.01 2.54 2.05 2.96 2.63 2.29 1.94 1.57 2.13 1.89 1.65 1.4 1.14 0.867 1.43 1.12

rx 2.41 2.43 2.45 2.46 2.48 2.49 2.49 1.79 1.81 1.82 1.84 1.85 1.86 1.86 1.87 1.88 1.49 1.5 1.52 1.53 1.54 1.55 1.56 1.18 1.2 1.21 1.22 1.23 1.24 1.25 1.05 1.06 1.07 1.08 1.09 0.895 0.903 0.91 0.918 0.926 0.933 0.735 0.749

y(bar) 2.4 2.36 2.31 2.26 2.21 2.19 2.17 1.86 1.81 1.77 1.72 1.7 1.67 1.65 1.62 1.6 1.56 1.52 1.47 1.42 1.4 1.37 1.35 1.27 1.22 1.18 1.15 1.13 1.11 1.08 1.05 1.03 1 0.979 0.954 0.929 0.907 0.884 0.86 0.836 0.812 0.803 0.758

0.3125 0.25 0.1875 0.375 0.3125 0.25 0.1875 0.125 1 0.875 0.75 0.625 0.5625 0.5 0.4375 1 0.875 0.75 0.625 0.5625 0.5 0.4375 0.75 0.625 0.5 0.4375 0.375 0.875 0.75 0.625 0.5625 0.5 0.4375 0.375 0.3125 0.5 0.375 0.3125 0.75 0.625 0.5 0.375 0.3125 0.25 0.5

10 8.07 6.13 9.3 7.89 6.43 4.91 3.34 88.8 78.5 68 57.3 51.8 46.3 40.7 75.2 66.6 57.8 48.7 44.1 39.5 34.8 52.4 44.2 35.8 31.5 27.2 54.3 47.2 39.9 36.1 32.3 28.5 24.6 20.6 30.7 23.4 19.7 39.6 33.5 27.2 20.8 17.4 14.1 25.5

1.67 1.38 1.07 0.952 0.828 0.691 0.541 0.378 162 145 127 108 98.7 88.8 78.7 139 125 110 94.1 85.7 77.2 68.5 75.6 64.7 53.3 47.3 41.1 55.4 48.9 42 38.4 34.7 30.8 26.8 22.7 33.2 25.7 21.8 27.8 24 19.9 15.5 13.2 10.7 18.9

0.949 0.773 0.59 0.696 0.595 0.489 0.376 0.257 30.2 26.8 23.3 19.7 17.9 16 14.1 28.1 25 21.7 18.4 16.7 15 13.2 16.8 14.2 11.6 10.2 8.83 14.3 12.5 10.6 9.61 8.63 7.62 6.59 5.55 8.45 6.47 5.45 8.52 7.26 5.94 4.56 3.84 3.1 5.79

0.756 0.764 0.771 0.591 0.598 0.605 0.612 0.62 2.49 2.5 2.52 2.54 2.55 2.55 2.56 2.51 2.53 2.55 2.56 2.57 2.58 2.59 2.21 2.23 2.25 2.26 2.27 1.86 1.88 1.89 1.9 1.91 1.92 1.93 1.94 1.92 1.93 1.94 1.55 1.56 1.58 1.59 1.6 1.61 1.58

0.735 0.711 0.687 0.632 0.609 0.586 0.561 0.534 2.65 2.6 2.55 2.5 2.48 2.46 2.43 3.03 2.99 2.94 2.89 2.86 2.84 2.81 2.5 2.45 2.4 2.38 2.35 2.12 2.07 2.03 2 1.98 1.95 1.93 1.9 2.07 2.02 2 1.74 1.69 1.65 1.6 1.57 1.55 1.74

0.4375 0.375 0.3125 0.25 0.5 0.375 0.3125 0.25 0.625 0.5 0.375 0.3125 0.25 0.5 0.4375 0.375 0.3125 0.25 0.5 0.375 0.3125 0.25 0.5 0.4375 0.375 0.3125 0.25 0.1875 0.5 0.375 0.3125 0.25 0.1875 0.375 0.3125 0.25 0.1875 1 0.875 0.75 0.625 0.5625 0.5 0.4375 1

22.5 19.5 16.4 13.2 23.8 18.2 15.3 12.4 27.1 22.1 16.9 14.2 11.5 20.6 18.2 15.8 13.3 10.8 18.8 14.5 12.2 9.88 17.1 15.1 13.1 11.1 8.97 6.82 15.4 11.9 10.1 8.18 6.24 10.6 8.97 7.3 5.57 88.8 78.5 68 57.3 51.8 46.3 40.7 75.2

16.8 14.7 12.5 10.2 10.6 8.3 7.07 5.78 12 10 7.88 6.72 5.49 6.91 6.2 5.45 4.67 3.84 6.48 5.13 4.39 3.61 4.15 3.73 3.3 2.83 2.33 1.8 3.85 3.07 2.64 2.18 1.69 1.83 1.58 1.31 1.02 77.6 69.8 61.5 52.8 48.2 43.5 38.6 23.3

5.12 4.44 3.74 3.03 3.84 2.96 2.5 2.02 4.56 3.75 2.89 2.44 1.98 2.9 2.58 2.24 1.9 1.55 2.82 2.18 1.85 1.51 2.07 1.84 1.61 1.36 1.11 0.846 2 1.56 1.32 1.08 0.828 1.09 0.931 0.762 0.585 17.8 15.9 13.8 11.8 10.7 9.58 8.46 7.87

1.59 1.6 1.61 1.62 1.23 1.25 1.25 1.26 1.23 1.24 1.26 1.27 1.27 1.07 1.08 1.09 1.09 1.1 1.08 1.1 1.11 1.12 0.91 0.917 0.924 0.932 0.94 0.947 0.922 0.937 0.945 0.953 0.961 0.766 0.774 0.782 0.79 1.72 1.74 1.75 1.77 1.78 1.79 1.8 1.03

1.72 1.69 1.67 1.64 1.24 1.2 1.17 1.14 1.37 1.32 1.27 1.25 1.22 1.12 1.09 1.07 1.05 1.02 1.2 1.15 1.13 1.1 0.995 0.972 0.949 0.925 0.9 0.874 1.08 1.03 1.01 0.98 0.952 0.826 0.803 0.779 0.754 1.65 1.6 1.56 1.51 1.49 1.46 1.44 1.04

0.875 0.75 0.625 0.5625 0.5 0.4375 0.75 0.625 0.5 0.4375 0.375 0.875 0.75 0.625 0.5625 0.5 0.4375 0.375 0.3125 0.5 0.375 0.3125 0.75 0.625 0.5 0.375 0.3125 0.25 0.5 0.4375 0.375 0.3125 0.25 0.5 0.375 0.3125 0.25 0.625 0.5 0.375 0.3125 0.25 0.5 0.4375 0.375

66.6 57.8 48.7 44.1 39.5 34.8 52.4 44.2 35.8 31.5 27.2 54.3 47.2 39.9 36.1 32.3 28.5 24.6 20.6 30.7 23.4 19.7 39.6 33.5 27.2 20.8 17.4 14.1 25.5 22.5 19.5 16.4 13.2 23.8 18.2 15.3 12.4 27.1 22.1 16.9 14.2 11.5 20.6 18.2 15.8

21.1 18.7 16.2 14.9 13.5 12.1 18 15.6 13 11.6 10.1 19.4 17.3 15 13.7 12.4 11.1 9.72 8.26 8.47 6.65 5.68 11 9.6 8.04 6.31 5.38 4.4 5.1 4.58 4.02 3.44 2.82 7.53 5.92 5.05 4.13 5.7 4.79 3.79 3.24 2.66 4.65 4.18 3.69

7.02 6.14 5.23 4.77 4.29 3.81 6.01 5.12 4.2 3.72 3.22 6.74 5.9 5.03 4.58 4.12 3.65 3.17 2.67 3.17 2.45 2.07 4.4 3.76 3.09 2.38 2.01 1.63 2.26 2.01 1.75 1.48 1.2 3 2.32 1.96 1.59 2.67 2.2 1.7 1.44 1.17 2.18 1.94 1.69

1.04 1.05 1.06 1.07 1.08 1.09 1.08 1.1 1.11 1.12 1.12 1.1 1.12 1.13 1.14 1.14 1.15 1.16 1.17 0.968 0.984 0.991 0.974 0.987 1 1.02 1.02 1.03 0.824 0.831 0.838 0.846 0.853 1.04 1.05 1.06 1.07 0.845 0.858 0.873 0.88 0.887 0.877 0.885 0.892

0.997 0.949 0.902 0.878 0.854 0.829 1 0.958 0.91 0.886 0.861 1.12 1.07 1.03 1 0.981 0.957 0.933 0.908 0.829 0.781 0.756 0.993 0.947 0.901 0.854 0.829 0.804 0.746 0.722 0.698 0.673 0.648 0.994 0.947 0.923 0.897 0.867 0.822 0.775 0.75 0.725 0.869 0.846 0.823

0.3125 0.25 0.5 0.375 0.3125 0.25 0.5 0.4375 0.375 0.3125 0.25 0.1875 0.5 0.375 0.3125 0.25 0.1875 0.375 0.3125 0.25 0.1875

13.3 10.8 18.8 14.5 12.2 9.88 17.1 15.1 13.1 11.1 8.97 6.82 15.4 11.9 10.1 8.18 6.24 10.6 8.97 7.3 5.57

3.16 2.61 2.72 2.17 1.87 1.55 2.58 2.33 2.06 1.78 1.47 1.14 1.33 1.08 0.935 0.779 0.61 1.03 0.891 0.744 0.583

1.44 1.17 1.51 1.18 1 0.819 1.47 1.31 1.15 0.974 0.794 0.606 0.94 0.736 0.628 0.515 0.396 0.722 0.617 0.507 0.391

0.9 0.908 0.701 0.716 0.723 0.731 0.718 0.724 0.731 0.739 0.746 0.753 0.543 0.555 0.562 0.569 0.577 0.574 0.581 0.589 0.597

0.798 0.773 0.701 0.655 0.632 0.607 0.746 0.724 0.701 0.677 0.653 0.627 0.58 0.535 0.511 0.487 0.462 0.578 0.555 0.532 0.508

m AISC Version 13.0 CD Database (Dec. 2005) and AISC 13th Edition Manual (Dec. 2005) Zx 63.2 57 50.5 43.9 37.1 33.7 30.1 30.8 27.4 23.9 20.2 18.4 16.4 14.5 12.5 10.5 18.6 16.3 13.9 11.3 10 8.67 7.3 10 8.56 7.01 6.2 5.37 4.52 3.65 5.33 4.73 4.11 3.47 2.82 3.83 3.4 2.97 2.51 2.04 1.55 2.59 2.01

yp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

ry(0) 3.41 3.39 3.36 3.34 3.32 3.31 3.3 2.58 2.56 2.54 2.52 2.51 2.5 2.49 2.48 2.47 2.16 2.13 2.11 2.09 2.08 2.07 2.06 1.73 1.71 1.69 1.68 1.67 1.66 1.65 1.49 1.48 1.47 1.46 1.44 1.29 1.28 1.27 1.26 1.25 1.24 1.09 1.07

ry(3/8) 3.54 3.52 3.5 3.47 3.45 3.44 3.43 2.72 2.7 2.67 2.65 2.64 2.63 2.62 2.6 2.59 2.3 2.27 2.25 2.22 2.21 2.2 2.19 1.88 1.85 1.83 1.81 1.8 1.79 1.78 1.63 1.61 1.6 1.59 1.57 1.43 1.42 1.41 1.39 1.38 1.37 1.23 1.21

ry(3/4) 3.68 3.66 3.63 3.61 3.58 3.57 3.56 2.86 2.84 2.81 2.79 2.78 2.76 2.75 2.74 2.72 2.44 2.41 2.39 2.36 2.35 2.34 2.32 2.03 2 1.97 1.96 1.94 1.93 1.91 1.77 1.76 1.74 1.73 1.72 1.58 1.57 1.55 1.54 1.52 1.51 1.39 1.36

ro(bar)(0) 4.56 4.56 4.56 4.56 4.56 4.56 4.56 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 2.85 2.85 2.85 2.85 2.85 2.84 2.84 2.28 2.28 2.28 2.28 2.28 2.28 2.28 1.99 1.99 1.99 1.99 1.99 1.71 1.71 1.71 1.71 1.71 1.71 1.43 1.42

1.71 1.39 1.06 1.26 1.07 0.88 0.676 0.46 54.5 48.5 42.3 35.8 32.5 29.1 25.7 48.6 43.4 37.9 32.2 29.2 26.2 23.2 29.5 25.1 20.4 18.1 15.6 25.3 22.2 18.9 17.2 15.4 13.6 11.8 9.91 15 11.5 9.68 15.2 13 10.7 8.18 6.89 5.57 10.2

0 0 0 0 0 0 0 0 1.47 1.41 1.34 1.27 1.23 1.2 1.16 2.47 2.41 2.34 2.27 2.23 2.2 2.16 1.87 1.8 1.74 1.7 1.67 1.44 1.38 1.31 1.28 1.25 1.22 1.19 1.16 1.48 1.41 1.38 1.12 1.06 1 0.93 0.9 0.87 1.25

1.05 1.04 1.03 0.865 0.853 0.842 0.831 0.818 2.39 2.37 2.35 2.33 2.32 2.31 2.3 1.46 1.44 1.42 1.39 1.38 1.38 1.37 1.48 1.45 1.44 1.43 1.42 1.57 1.55 1.53 1.52 1.51 1.5 1.49 1.48 1.27 1.26 1.25 1.39 1.37 1.35 1.33 1.32 1.31 1.11

1.19 1.18 1.17 1.01 0.996 0.982 0.967 0.951 2.52 2.5 2.47 2.45 2.44 2.43 2.42 1.6 1.57 1.55 1.52 1.51 1.5 1.49 1.61 1.58 1.56 1.55 1.54 1.71 1.68 1.66 1.65 1.64 1.62 1.61 1.6 1.4 1.38 1.37 1.53 1.5 1.48 1.46 1.44 1.43 1.24

1.34 1.33 1.31 1.17 1.15 1.14 1.12 1.1 2.66 2.63 2.61 2.59 2.58 2.56 2.55 1.75 1.72 1.69 1.66 1.65 1.63 1.62 1.75 1.73 1.7 1.68 1.67 1.86 1.83 1.8 1.79 1.77 1.76 1.75 1.74 1.54 1.52 1.5 1.68 1.65 1.62 1.59 1.58 1.57 1.39

1.42 1.42 1.42 1.14 1.14 1.13 1.13 1.13 4.06 4.07 4.07 4.08 4.09 4.09 4.09 3.86 3.87 3.88 3.89 3.9 3.9 3.91 3.41 3.42 3.43 3.43 3.44 2.96 2.97 2.98 2.98 2.99 2.99 2.99 3 2.94 2.95 2.95 2.49 2.49 2.5 2.51 2.51 2.52 2.44

9.07 7.87 6.63 5.37 6.91 5.32 4.49 3.63 8.16 6.73 5.19 4.38 3.55 5.23 4.65 4.05 3.43 2.79 5.05 3.93 3.33 2.72 3.72 3.31 2.89 2.46 2 1.52 3.55 2.78 2.37 1.94 1.49 1.96 1.68 1.38 1.06 32.4 28.7 24.9 21 19 17 15 15.5

1.21 1.18 1.15 1.12 0.5 0.43 0.4 0.37 0.81 0.75 0.68 0.65 0.62 0.48 0.45 0.41 0.38 0.34 0.74 0.67 0.63 0.6 0.49 0.46 0.43 0.4 0.36 0.33 0.74 0.67 0.63 0.6 0.56 0.43 0.39 0.36 0.32 0.82 0.72 0.62 0.53 0.48 0.43 0.37 0.69

1.1 1.09 1.08 1.07 1.44 1.42 1.4 1.39 1.21 1.19 1.17 1.16 1.15 1.23 1.22 1.21 1.2 1.19 0.992 0.97 0.96 0.95 1.04 1.02 1.01 1 0.991 0.98 0.795 0.771 0.76 0.749 0.739 0.815 0.804 0.794 0.784 3.63 3.61 3.59 3.57 3.55 3.54 3.53 3.94

1.23 1.22 1.21 1.19 1.57 1.55 1.53 1.52 1.35 1.32 1.3 1.29 1.27 1.37 1.36 1.35 1.33 1.32 1.13 1.11 1.09 1.08 1.18 1.16 1.15 1.14 1.12 1.11 0.94 0.911 0.897 0.883 0.869 0.957 0.943 0.93 0.916 3.77 3.75 3.72 3.7 3.69 3.68 3.66 4.08

1.38 1.36 1.35 1.33 1.72 1.69 1.68 1.66 1.5 1.47 1.44 1.43 1.41 1.52 1.51 1.49 1.48 1.46 1.28 1.25 1.24 1.22 1.33 1.32 1.3 1.29 1.27 1.25 1.1 1.07 1.05 1.03 1.02 1.11 1.1 1.08 1.07 3.91 3.89 3.86 3.84 3.83 3.81 3.8 4.23

2.45 2.45 2.46 2.46 2.14 2.14 2.14 2.14 2.02 2.02 2.03 2.03 2.03 1.85 1.85 1.85 1.85 1.85 1.75 1.75 1.76 1.76 1.57 1.57 1.57 1.57 1.57 1.57 1.47 1.48 1.48 1.48 1.49 1.29 1.29 1.29 1.29 4.18 4.17 4.17 4.16 4.15 4.15 4.15 4.11

13.5 11.6 9.73 8.77 7.81 6.85 11.2 9.38 7.54 6.61 5.68 12.5 10.8 9.13 8.26 7.38 6.49 5.58 4.67 5.77 4.36 3.65 8.13 6.87 5.57 4.23 3.55 2.85 4.15 3.65 3.14 2.62 2.1 5.39 4.13 3.48 2.8 4.9 3.99 3.04 2.56 2.06 3.94 3.49 3.04

0.61 0.53 0.45 0.41 0.36 0.32 0.55 0.46 0.38 0.33 0.29 0.67 0.58 0.49 0.44 0.4 0.35 0.3 0.25 0.38 0.29 0.24 0.58 0.49 0.4 0.31 0.26 0.21 0.38 0.33 0.29 0.24 0.19 0.44 0.33 0.28 0.23 0.5 0.41 0.31 0.26 0.21 0.43 0.38 0.33

3.91 3.89 3.86 3.85 3.83 3.82 3.34 3.31 3.29 3.28 3.26 2.82 2.8 2.77 2.76 2.75 2.74 2.73 2.72 2.82 2.8 2.78 2.33 2.3 2.28 2.26 2.25 2.23 2.35 2.34 2.33 2.32 2.3 1.75 1.73 1.72 1.7 1.84 1.81 1.79 1.78 1.76 1.55 1.54 1.52

4.06 4.03 4 3.99 3.97 3.96 3.48 3.46 3.43 3.42 3.4 2.96 2.94 2.91 2.9 2.89 2.88 2.86 2.85 2.96 2.94 2.92 2.47 2.45 2.42 2.39 2.38 2.37 2.5 2.48 2.47 2.46 2.44 1.89 1.86 1.85 1.83 1.98 1.95 1.93 1.91 1.9 1.69 1.67 1.66

4.21 4.18 4.15 4.13 4.12 4.1 3.63 3.6 3.57 3.56 3.54 3.11 3.08 3.06 3.04 3.03 3.02 3 2.99 3.11 3.08 3.06 2.62 2.59 2.57 2.54 2.52 2.51 2.64 2.63 2.62 2.6 2.58 2.03 2 1.99 1.97 2.13 2.1 2.07 2.06 2.04 1.84 1.82 1.81

4.09 4.07 4.05 4.04 4.03 4.02 3.57 3.55 3.53 3.53 3.52 3.1 3.09 3.08 3.07 3.07 3.06 3.06 3.05 3.04 3.02 3.02 2.6 2.59 2.58 2.56 2.56 2.55 2.54 2.54 2.53 2.52 2.51 2.16 2.16 2.16 2.15 2.1 2.09 2.08 2.07 2.06 1.88 1.88 1.88

2.56 2.08 2.78 2.13 1.8 1.46 2.68 2.38 2.07 1.75 1.41 1.07 1.77 1.36 1.14 0.926 0.703 1.31 1.11 0.909 0.695

0.28 0.23 0.4 0.3 0.26 0.21 0.42 0.37 0.32 0.27 0.22 0.17 0.38 0.29 0.25 0.2 0.15 0.31 0.26 0.21 0.16

1.51 1.5 1.62 1.59 1.58 1.57 1.35 1.34 1.32 1.31 1.3 1.29 1.42 1.39 1.38 1.37 1.35 1.13 1.12 1.1 1.09

1.65 1.63 1.76 1.73 1.72 1.7 1.49 1.48 1.46 1.45 1.44 1.42 1.56 1.54 1.52 1.51 1.49 1.27 1.26 1.24 1.23

1.79 1.78 1.91 1.88 1.87 1.85 1.64 1.63 1.61 1.6 1.58 1.57 1.72 1.69 1.67 1.66 1.64 1.42 1.41 1.39 1.38

1.87 1.87 1.82 1.81 1.8 1.8 1.61 1.6 1.6 1.59 1.59 1.58 1.55 1.54 1.53 1.52 1.52 1.32 1.32 1.32 1.31

ro(bar)(3/8) 4.66 4.66 4.66 4.66 4.66 4.65 4.65 3.53 3.53 3.52 3.52 3.52 3.52 3.52 3.51 3.51 2.96 2.95 2.95 2.94 2.94 2.94 2.94 2.39 2.39 2.38 2.38 2.38 2.37 2.37 2.1 2.09 2.09 2.09 2.08 1.82 1.82 1.81 1.81 1.81 1.8 1.54 1.53

ro(bar)(3/4) 4.77 4.77 4.76 4.76 4.76 4.75 4.75 3.64 3.63 3.63 3.62 3.62 3.62 3.62 3.61 3.61 3.07 3.06 3.06 3.05 3.05 3.04 3.04 2.51 2.5 2.49 2.49 2.49 2.48 2.48 2.21 2.21 2.2 2.2 2.19 1.94 1.94 1.93 1.93 1.92 1.91 1.67 1.65

H(0) 0.837 0.834 0.831 0.829 0.826 0.825 0.824 0.843 0.839 0.835 0.831 0.829 0.827 0.826 0.824 0.823 0.845 0.84 0.835 0.83 0.828 0.826 0.825 0.847 0.841 0.834 0.832 0.829 0.826 0.824 0.838 0.835 0.832 0.829 0.826 0.842 0.838 0.834 0.83 0.827 0.823 0.85 0.839

H(3/8) 0.844 0.841 0.838 0.836 0.833 0.832 0.831 0.852 0.848 0.844 0.84 0.838 0.836 0.835 0.833 0.832 0.856 0.851 0.846 0.842 0.839 0.838 0.836 0.861 0.854 0.848 0.846 0.843 0.84 0.838 0.854 0.851 0.848 0.845 0.842 0.861 0.857 0.853 0.849 0.845 0.842 0.871 0.861

H(3/4) 0.851 0.848 0.845 0.843 0.84 0.839 0.837 0.861 0.857 0.853 0.849 0.847 0.846 0.844 0.842 0.841 0.866 0.861 0.857 0.852 0.85 0.848 0.847 0.874 0.868 0.862 0.859 0.856 0.854 0.851 0.869 0.866 0.863 0.86 0.857 0.878 0.874 0.87 0.866 0.863 0.859 0.89 0.881

Qs(0) 1 1 1 1 1 1 0.998 1 1 1 1 1 1 1 0.998 0.914 1 1 1 1 1 1 0.998 1 1 1 1 1 1 0.998 1 1 1 1 1 1 1 1 1 1 0.998 1 1

1.53 1.52 1.52 1.25 1.25 1.24 1.24 1.23 4.14 4.14 4.15 4.16 4.16 4.16 4.16 3.91 3.92 3.93 3.94 3.94 3.95 3.95 3.47 3.47 3.48 3.49 3.49 3.04 3.04 3.05 3.05 3.05 3.06 3.06 3.06 2.99 3 3 2.57 2.57 2.58 2.58 2.58 2.58 2.51

1.65 1.64 1.63 1.38 1.37 1.37 1.36 1.35 4.23 4.23 4.23 4.24 4.24 4.24 4.24 3.97 3.98 3.99 3.99 4 4 4 3.53 3.54 3.55 3.55 3.55 3.12 3.12 3.13 3.13 3.13 3.13 3.13 3.13 3.06 3.07 3.07 2.66 2.66 2.66 2.66 2.66 2.66 2.58

0.834 0.829 0.825 0.847 0.841 0.835 0.83 0.826 0.721 0.718 0.714 0.712 0.71 0.709 0.708 0.568 0.566 0.564 0.562 0.562 0.561 0.561 0.611 0.608 0.606 0.605 0.605 0.678 0.673 0.669 0.667 0.665 0.663 0.662 0.661 0.615 0.613 0.612 0.699 0.693 0.688 0.683 0.682 0.68 0.628

0.856 0.852 0.847 0.874 0.868 0.862 0.857 0.853 0.732 0.728 0.725 0.722 0.72 0.719 0.718 0.58 0.577 0.575 0.573 0.572 0.571 0.571 0.624 0.621 0.618 0.617 0.616 0.694 0.688 0.684 0.682 0.679 0.678 0.676 0.674 0.63 0.627 0.625 0.717 0.711 0.705 0.7 0.698 0.696 0.646

0.876 0.872 0.868 0.897 0.891 0.886 0.882 0.877 0.742 0.739 0.735 0.732 0.731 0.729 0.728 0.594 0.59 0.587 0.585 0.584 0.583 0.582 0.639 0.635 0.632 0.63 0.629 0.71 0.705 0.7 0.697 0.695 0.693 0.691 0.689 0.646 0.642 0.641 0.736 0.73 0.724 0.718 0.716 0.714 0.667

1 1 1 1 1 1 1 0.998 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

2.51 2.51 2.52 2.52 2.23 2.23 2.23 2.22 2.11 2.11 2.11 2.11 2.11 1.94 1.94 1.94 1.94 1.94 1.83 1.83 1.83 1.83 1.66 1.66 1.66 1.66 1.66 1.65 1.55 1.55 1.56 1.56 1.55 1.38 1.38 1.38 1.38 4.3 4.29 4.28 4.27 4.27 4.26 4.26 4.25

2.58 2.59 2.59 2.59 2.33 2.33 2.33 2.32 2.21 2.2 2.2 2.2 2.2 2.05 2.05 2.05 2.04 2.04 1.93 1.93 1.92 1.92 1.78 1.77 1.77 1.76 1.76 1.75 1.66 1.65 1.65 1.65 1.64 1.49 1.49 1.49 1.48 4.43 4.42 4.4 4.39 4.39 4.38 4.38 4.39

0.626 0.624 0.623 0.622 0.784 0.778 0.775 0.773 0.728 0.721 0.715 0.712 0.71 0.78 0.776 0.773 0.77 0.767 0.706 0.698 0.695 0.693 0.774 0.769 0.764 0.76 0.756 0.753 0.684 0.675 0.671 0.668 0.666 0.754 0.748 0.744 0.74 0.924 0.922 0.919 0.917 0.916 0.915 0.913 0.983

0.644 0.642 0.64 0.638 0.802 0.795 0.792 0.79 0.75 0.743 0.736 0.733 0.73 0.801 0.797 0.794 0.79 0.787 0.732 0.724 0.72 0.717 0.8 0.795 0.79 0.785 0.781 0.778 0.717 0.707 0.702 0.698 0.695 0.786 0.781 0.775 0.771 0.929 0.926 0.924 0.921 0.92 0.919 0.918 0.984

0.664 0.661 0.659 0.657 0.819 0.813 0.81 0.807 0.773 0.765 0.757 0.754 0.751 0.822 0.818 0.814 0.811 0.807 0.759 0.75 0.746 0.742 0.824 0.819 0.815 0.81 0.806 0.802 0.751 0.739 0.734 0.73 0.726 0.817 0.812 0.806 0.801 0.933 0.93 0.928 0.926 0.924 0.923 0.922 0.985

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.998 0.938 1

4.22 4.2 4.18 4.17 4.16 4.15 3.7 3.68 3.66 3.66 3.65 3.23 3.22 3.21 3.2 3.19 3.19 3.18 3.17 3.17 3.15 3.14 2.73 2.71 2.7 2.69 2.68 2.67 2.68 2.67 2.66 2.65 2.64 2.28 2.27 2.26 2.26 2.22 2.21 2.2 2.19 2.18 2 1.99 1.99

4.37 4.35 4.32 4.31 4.3 4.29 3.84 3.82 3.8 3.79 3.78 3.37 3.35 3.34 3.33 3.32 3.31 3.31 3.3 3.31 3.29 3.28 2.86 2.85 2.83 2.81 2.81 2.8 2.81 2.8 2.79 2.78 2.77 2.4 2.39 2.38 2.37 2.36 2.34 2.32 2.32 2.31 2.13 2.12 2.11

0.981 0.98 0.979 0.978 0.978 0.977 0.969 0.967 0.965 0.964 0.963 0.952 0.949 0.946 0.945 0.943 0.942 0.94 0.939 0.964 0.962 0.96 0.943 0.94 0.936 0.933 0.931 0.929 0.962 0.961 0.959 0.958 0.957 0.882 0.876 0.874 0.871 0.93 0.925 0.92 0.918 0.915 0.892 0.889 0.885

0.982 0.981 0.98 0.98 0.979 0.978 0.971 0.969 0.968 0.967 0.966 0.956 0.953 0.95 0.949 0.948 0.946 0.945 0.944 0.967 0.965 0.964 0.949 0.945 0.942 0.938 0.937 0.935 0.966 0.964 0.963 0.962 0.961 0.893 0.888 0.885 0.883 0.938 0.933 0.928 0.926 0.924 0.904 0.901 0.898

0.984 0.983 0.981 0.981 0.98 0.98 0.973 0.971 0.97 0.969 0.968 0.959 0.957 0.954 0.953 0.952 0.95 0.949 0.948 0.969 0.967 0.966 0.953 0.95 0.947 0.944 0.942 0.941 0.969 0.968 0.967 0.965 0.964 0.904 0.899 0.896 0.894 0.945 0.94 0.936 0.934 0.932 0.915 0.912 0.91

1 1 1 1 0.998 0.938 1 1 1 0.998 0.928 1 1 1 1 1 1 0.998 0.914 1 0.998 0.914 1 1 1 1 0.998 0.894 1 1 1 0.998 0.894 1 1 1 0.998 1 1 1 1 0.998 1 1 1

1.98 1.98 1.95 1.93 1.92 1.92 1.73 1.72 1.72 1.71 1.7 1.7 1.69 1.67 1.66 1.65 1.64 1.45 1.44 1.43 1.43

2.11 2.1 2.08 2.07 2.06 2.05 1.86 1.85 1.85 1.84 1.83 1.82 1.83 1.81 1.8 1.79 1.78 1.59 1.58 1.57 1.56

0.883 0.88 0.938 0.933 0.93 0.928 0.905 0.901 0.897 0.893 0.89 0.887 0.955 0.949 0.946 0.944 0.941 0.913 0.909 0.904 0.901

0.895 0.893 0.946 0.941 0.939 0.937 0.918 0.914 0.911 0.907 0.904 0.901 0.962 0.957 0.954 0.952 0.95 0.927 0.923 0.92 0.916

0.907 0.905 0.953 0.949 0.947 0.944 0.929 0.926 0.923 0.92 0.917 0.914 0.968 0.963 0.961 0.959 0.957 0.939 0.936 0.933 0.929

1 1 1 1 1 1 1 1 1 1 1 0.998 1 1 1 1 0.998 1 1 1 1

Qs(s) 1 1 1 1 0.997 0.959 0.912 1 1 1 1 1 1 0.973 0.912 0.826 1 1 1 1 1 0.983 0.912 1 1 1 1 1 0.997 0.912 1 1 1 1 0.965 1 1 1 1 1 0.912 1 1

Shape

HSS20X12X5/8 HSS20X12X1/2 HSS20X12X3/8 HSS20X12X5/16 HSS20X8X5/8 HSS20X8X1/2 HSS20X8X3/8 HSS20X8X5/16 HSS20X4X1/2 HSS20X4X3/8 HSS20X4X5/16 HSS20X4X1/4 HSS18X6X5/8 HSS18X6X1/2 HSS18X6X3/8 HSS18X6X5/16 HSS18X6X1/4 HSS16X16X5/8 HSS16X16X1/2 HSS16X16X3/8 HSS16X16X5/16 HSS16X12X5/8 HSS16X12X1/2 HSS16X12X3/8 HSS16X12X5/16 HSS16X8X5/8 HSS16X8X1/2 HSS16X8X3/8 HSS16X8X5/16 HSS16X8X1/4 HSS16X4X5/8 HSS16X4X1/2 HSS16X4X3/8 HSS16X4X5/16 HSS16X4X1/4 HSS16X4X3/16 HSS14X14X5/8 HSS14X14X1/2 HSS14X14X3/8 HSS14X14X5/16 HSS14X10X5/8 HSS14X10X1/2 HSS14X10X3/8

A 35.0 28.3 21.5 18.1 30.3 24.6 18.7 15.7 20.9 16.0 13.4 10.8 25.7 20.9 16.0 13.4 10.8 35.0 28.3 21.5 18.1 30.3 24.6 18.7 15.7 25.7 20.9 16.0 13.4 10.8 21.0 17.2 13.2 11.1 8.96 6.76 30.3 24.6 18.7 15.7 25.7 20.9 16.0

h 20 20 20 20 20 20 20 20 20 20 20 20 18 18 18 18 18 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 14 14 14 14 14 14 14 14

1 1 0.983 1 1 1 1 0.912 1 1 1 0.997 0.959 0.912 0.85 1 1 1 0.997 0.959 0.912 0.85 1 1 0.965 0.912 0.84 1 1 1 1 1 0.973 0.912 0.826 1 0.912 0.826 1 1 1 0.983 0.912 0.804 1

HSS14X10X5/16 HSS14X10X1/4 HSS14X6X5/8 HSS14X6X1/2 HSS14X6X3/8 HSS14X6X5/16 HSS14X6X1/4 HSS14X6X3/16 HSS14X4X5/8 HSS14X4X1/2 HSS14X4X3/8 HSS14X4X5/16 HSS14X4X1/4 HSS14X4X3/16 HSS12X12X5/8 HSS12X12X1/2 HSS12X12X3/8 HSS12X12X5/16 HSS12X12X1/4 HSS12X12X3/16 HSS12X10X1/2 HSS12X10X3/8 HSS12X10X5/16 HSS12X10X1/4 HSS12X8X5/8 HSS12X8X1/2 HSS12X8X3/8 HSS12X8X5/16 HSS12X8X1/4 HSS12X8X3/16 HSS12X6X5/8 HSS12X6X1/2 HSS12X6X3/8 HSS12X6X5/16 HSS12X6X1/4 HSS12X6X3/16 HSS12X4X5/8 HSS12X4X1/2 HSS12X4X3/8 HSS12X4X5/16 HSS12X4X1/4 HSS12X4X3/16 HSS12X3-1/2X3/8 HSS12X3-1/2X5/16 HSS12X3X5/16

13.4 10.8 21.0 17.2 13.2 11.1 8.96 6.76 18.7 15.3 11.8 9.92 8.03 6.06 25.7 20.9 16.0 13.4 10.8 8.15 19.0 14.6 12.2 9.90 21.0 17.2 13.2 11.1 8.96 6.76 18.7 15.3 11.8 9.92 8.03 6.06 16.4 13.5 10.4 8.76 7.10 5.37 10.0 8.46 8.17

14 14 14 14 14 14 14 14 14 14 14 14 14 14 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12

1 0.983 0.912 0.804 1 1 0.997 0.912 1 1 1 0.997 0.912 1 1 1 1 0.965 1 1 1 0.965 1 1 1 1 1 0.912 1 1 1 1 0.912 1 1 1 0.983 1 1 1 0.997 0.959 0.912 0.85 1

HSS12X3X1/4 HSS12X3X3/16 HSS12X2X5/16 HSS12X2X1/4 HSS12X2X3/16 HSS10X10X5/8 HSS10X10X1/2 HSS10X10X3/8 HSS10X10X5/16 HSS10X10X1/4 HSS10X10X3/16 HSS10X8X5/8 HSS10X8X1/2 HSS10X8X3/8 HSS10X8X5/16 HSS10X8X1/4 HSS10X8X3/16 HSS10X6X5/8 HSS10X6X1/2 HSS10X6X3/8 HSS10X6X5/16 HSS10X6X1/4 HSS10X6X3/16 HSS10X5X3/8 HSS10X5X5/16 HSS10X5X1/4 HSS10X5X3/16 HSS10X4X5/8 HSS10X4X1/2 HSS10X4X3/8 HSS10X4X5/16 HSS10X4X1/4 HSS10X4X3/16 HSS10X4X1/8 HSS10X3-1/2X1/2 HSS10X3-1/2X3/8 HSS10X3-1/2X5/16 HSS10X3-1/2X1/4 HSS10X3-1/2X3/16 HSS10X3-1/2X1/8 HSS10X3X3/8 HSS10X3X5/16 HSS10X3X1/4 HSS10X3X3/16 HSS10X3X1/8

6.63 5.02 7.59 6.17 4.67 21.0 17.2 13.2 11.1 8.96 6.76 18.7 15.3 11.8 9.92 8.03 6.06 16.4 13.5 10.4 8.76 7.10 5.37 9.67 8.17 6.63 5.02 14.0 11.6 8.97 7.59 6.17 4.67 3.16 11.1 8.62 7.30 5.93 4.50 3.04 8.27 7.01 5.70 4.32 2.93

12 12 12 12 12 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

1 1 0.997 0.959 0.912 0.85 1 1 0.965 0.912 0.84 1 1 1 1 1 0.973 0.912 0.826 1 0.912 0.826 1 1 1 0.983 0.912 0.804 1 1 0.983 0.912 0.804 1 1 0.997 0.912 1 1 1 0.997 0.912 1 1 1

HSS10X2X3/8 HSS10X2X5/16 HSS10X2X1/4 HSS10X2X3/16 HSS10X2X1/8 HSS9X9X5/8 HSS9X9X1/2 HSS9X9X3/8 HSS9X9X5/16 HSS9X9X1/4 HSS9X9X3/16 HSS9X9X1/8 HSS9X7X5/8 HSS9X7X1/2 HSS9X7X3/8 HSS9X7X5/16 HSS9X7X1/4 HSS9X7X3/16 HSS9X5X5/8 HSS9X5X1/2 HSS9X5X3/8 HSS9X5X5/16 HSS9X5X1/4 HSS9X5X3/16 HSS9X3X1/2 HSS9X3X3/8 HSS9X3X5/16 HSS9X3X1/4 HSS9X3X3/16 HSS8X8X5/8 HSS8X8X1/2 HSS8X8X3/8 HSS8X8X5/16 HSS8X8X1/4 HSS8X8X3/16 HSS8X8X1/8 HSS8X6X5/8 HSS8X6X1/2 HSS8X6X3/8 HSS8X6X5/16 HSS8X6X1/4 HSS8X6X3/16 HSS8X4X5/8 HSS8X4X1/2 HSS8X4X3/8

7.58 6.43 5.24 3.98 2.70 18.7 15.3 11.8 9.92 8.03 6.06 4.09 16.4 13.5 10.4 8.76 7.10 5.37 14.0 11.6 8.97 7.59 6.17 4.67 9.74 7.58 6.43 5.24 3.98 16.4 13.5 10.4 8.76 7.10 5.37 3.62 14.0 11.6 8.97 7.59 6.17 4.67 11.7 9.74 7.58

10 10 10 10 10 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

1 0.965 1 1 1 0.965 1 1 1 1 1 0.912 1 1 1 1 0.912 1 1 1 0.983

HSS8X4X5/16 HSS8X4X1/4 HSS8X4X3/16 HSS8X4X1/8 HSS8X3X1/2 HSS8X3X3/8 HSS8X3X5/16 HSS8X3X1/4 HSS8X3X3/16 HSS8X3X1/8 HSS8X2X3/8 HSS8X2X5/16 HSS8X2X1/4 HSS8X2X3/16 HSS8X2X1/8 HSS7X7X5/8 HSS7X7X1/2 HSS7X7X3/8 HSS7X7X5/16 HSS7X7X1/4 HSS7X7X3/16 HSS7X7X1/8 HSS7X5X1/2 HSS7X5X3/8 HSS7X5X5/16 HSS7X5X1/4 HSS7X5X3/16 HSS7X5X1/8 HSS7X4X1/2 HSS7X4X3/8 HSS7X4X5/16 HSS7X4X1/4 HSS7X4X3/16 HSS7X4X1/8 HSS7X3X1/2 HSS7X3X3/8 HSS7X3X5/16 HSS7X3X1/4 HSS7X3X3/16 HSS7X3X1/8 HSS7X2X1/4 HSS7X2X3/16 HSS7X2X1/8

HSS6X6X5/8 HSS6X6X1/2

6.43 5.24 3.98 2.70 8.81 6.88 5.85 4.77 3.63 2.46 6.18 5.26 4.30 3.28 2.23 14.0 11.6 8.97 7.59 6.17 4.67 3.16 9.74 7.58 6.43 5.24 3.98 2.70 8.81 6.88 5.85 4.77 3.63 2.46 7.88 6.18 5.26 4.30 3.28 2.23 3.84 2.93 2.00 11.7 9.74

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 6

HSS6X6X3/8 HSS6X6X5/16 HSS6X6X1/4 HSS6X6X3/16 HSS6X6X1/8 HSS6X5X1/2 HSS6X5X3/8 HSS6X5X5/16 HSS6X5X1/4 HSS6X5X3/16 HSS6X5X1/8 HSS6X4X1/2 HSS6X4X3/8 HSS6X4X5/16 HSS6X4X1/4 HSS6X4X3/16 HSS6X4X1/8 HSS6X3X1/2 HSS6X3X3/8 HSS6X3X5/16 HSS6X3X1/4 HSS6X3X3/16 HSS6X3X1/8 HSS6X2X3/8 HSS6X2X5/16 HSS6X2X1/4 HSS6X2X3/16 HSS6X2X1/8 HSS5-1/2X5-1/2X3/8 HSS5-1/2X5-1/2X5/16 HSS5-1/2X5-1/2X1/4 HSS5-1/2X5-1/2X3/16 HSS5-1/2X5-1/2X1/8 HSS5X5X1/2 HSS5X5X3/8 HSS5X5X5/16 HSS5X5X1/4 HSS5X5X3/16 HSS5X5X1/8 HSS5X4X1/2 HSS5X4X3/8 HSS5X4X5/16 HSS5X4X1/4 HSS5X4X3/16 HSS5X4X1/8

7.58 6.43 5.24 3.98 2.70 8.81 6.88 5.85 4.77 3.63 2.46 7.88 6.18 5.26 4.30 3.28 2.23 6.95 5.48 4.68 3.84 2.93 2.00 4.78 4.10 3.37 2.58 1.77 6.88 5.85 4.77 3.63 2.46 7.88 6.18 5.26 4.30 3.28 2.23 6.95 5.48 4.68 3.84 2.93 2.00

6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 5.5 5.5 5.5 5.5 5.5 5 5 5 5 5 5 5 5 5 5 5 5

HSS5X3X1/2 HSS5X3X3/8 HSS5X3X5/16 HSS5X3X1/4 HSS5X3X3/16 HSS5X3X1/8 HSS5X2-1/2X1/4 HSS5X2-1/2X3/16 HSS5X2-1/2X1/8 HSS5X2X3/8 HSS5X2X5/16 HSS5X2X1/4 HSS5X2X3/16 HSS5X2X1/8 HSS4-1/2X4-1/2X1/2 HSS4-1/2X4-1/2X3/8 HSS4-1/2X4-1/2X5/16 HSS4-1/2X4-1/2X1/4 HSS4-1/2X4-1/2X3/16 HSS4-1/2X4-1/2X1/8 HSS4X4X1/2 HSS4X4X3/8 HSS4X4X5/16 HSS4X4X1/4 HSS4X4X3/16 HSS4X4X1/8 HSS4X3X3/8 HSS4X3X5/16 HSS4X3X1/4 HSS4X3X3/16 HSS4X3X1/8 HSS4X2-1/2X3/8 HSS4X2-1/2X5/16 HSS4X2-1/2X1/4 HSS4X2-1/2X3/16 HSS4X2-1/2X1/8 HSS4X2X3/8 HSS4X2X5/16 HSS4X2X1/4 HSS4X2X3/16 HSS4X2X1/8 HSS3-1/2X2-1/2X3/8 HSS3-1/2X2-1/2X5/16 HSS3-1/2X2-1/2X1/4 HSS3-1/2X2-1/2X3/16

6.02 4.78 4.10 3.37 2.58 1.77 3.14 2.41 1.65 4.09 3.52 2.91 2.24 1.54 6.95 5.48 4.68 3.84 2.93 2.00 6.02 4.78 4.10 3.37 2.58 1.77 4.09 3.52 2.91 2.24 1.54 3.74 3.23 2.67 2.06 1.42 3.39 2.94 2.44 1.89 1.30 3.39 2.94 2.44 1.89

5 5 5 5 5 5 5 5 5 5 5 5 5 5 4.5 4.5 4.5 4.5 4.5 4.5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3.5 3.5 3.5 3.5

HSS3-1/2X2-1/2X1/8

HSS3-1/2X3-1/2X3/8 HSS3-1/2X3-1/2X5/16 HSS3-1/2X3-1/2X1/4 HSS3-1/2X3-1/2X3/16 HSS3-1/2X3-1/2X1/8 HSS3-1/2X2X1/4 HSS3-1/2X2X3/16 HSS3-1/2X2X1/8 HSS3-1/2X1-1/2X1/4 HSS3-1/2X1-1/2X3/16 HSS3-1/2X1-1/2X1/8 HSS3X3X3/8 HSS3X3X5/16 HSS3X3X1/4 HSS3X3X3/16 HSS3X3X1/8 HSS3X2-1/2X5/16 HSS3X2-1/2X1/4 HSS3X2-1/2X3/16 HSS3X2-1/2X1/8 HSS3X2X5/16 HSS3X2X1/4 HSS3X2X3/16 HSS3X2X1/8 HSS3X1-1/2X1/4 HSS3X1-1/2X3/16 HSS3X1-1/2X1/8 HSS3X1X3/16 HSS3X1X1/8 HSS2-1/2X2-1/2X5/16 HSS2-1/2X2-1/2X1/4 HSS2-1/2X2-1/2X3/16 HSS2-1/2X2-1/2X1/8 HSS2-1/2X2X1/4 HSS2-1/2X2X3/16 HSS2-1/2X2X1/8 HSS2-1/2X1-1/2X1/4 HSS2-1/2X1-1/2X3/16 HSS2-1/2X1-1/2X1/8 HSS2-1/2X1X3/16 HSS2-1/2X1X1/8 HSS2-1/4X2-1/4X1/4 HSS2-1/4X2-1/4X3/16 HSS2-1/4X2-1/4X1/8

1.3 4.09 3.52 2.91 2.24 1.54 2.21 1.71 1.19 1.97 1.54 1.07 3.39 2.94 2.44 1.89 1.30 2.64 2.21 1.71 1.19 2.35 1.97 1.54 1.07 1.74 1.37 0.956 1.19 0.840 2.35 1.97 1.54 1.07 1.74 1.37 0.956 1.51 1.19 0.840 1.02 0.724 1.74 1.37 0.956

3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.25 2.25 2.25

HSS2-1/4X2X3/16 HSS2-1/4X2X1/8 HSS2X2X1/4 HSS2X2X3/16 HSS2X2X1/8 HSS2X1-1/2X3/16 HSS2X1-1/2X1/8

HSS2X1X3/16 HSS2X1X1/8

1.28 0.898 1.51 1.19 0.840 1.02 0.724 0.845 0.608

2.25 2.25 2 2 2 2 2 2 2

Rectangular HSS (Tube) Section Properties from AISC Vers b 12 12 12 12 8 8 8 8 4 4 4 4 6 6 6 6 6 16 16 16 16 12 12 12 12 8 8 8 8 8 4 4 4 4 4 4 14 14 14 14 10 10 10

t(nom) 0.625 0.5 0.375 0.3125 0.625 0.5 0.375 0.3125 0.5 0.375 0.3125 0.25 0.625 0.5 0.375 0.3125 0.25 0.625 0.5 0.375 0.3125 0.625 0.5 0.375 0.3125 0.3125 0.5 0.375 0.3125 0.25 0.625 0.5 0.375 0.3125 0.25 0.1875 0.625 0.5 0.375 0.3125 0.625 0.5 0.375

t(des) 0.581 0.465 0.349 0.291 0.581 0.465 0.349 0.291 0.465 0.349 0.291 0.233 0.581 0.465 0.349 0.291 0.233 0.581 0.465 0.349 0.291 0.581 0.465 0.349 0.291 0.581 0.465 0.349 0.291 0.233 0.581 0.465 0.349 0.291 0.233 0.174 0.581 0.465 0.349 0.291 0.581 0.465 0.349

wt./ft. 127 103 78.4 65.8 110 89.6 68.3 57.3 75.9 58.1 48.9 39.5 93.1 75.9 58.1 48.9 39.5 127 103 78.4 65.8 110 89.6 68.3 57.4 93.1 75.9 58.1 48.9 39.5 76.1 62.3 47.9 40.3 32.7 24.7 110 89.6 68.2 57.3 93.1 75.9 58.1

b/t 17.7 22.8 31.4 38.2 10.8 14.2 19.9 24.5 5.60 8.46 10.7 14.2 7.33 9.90 14.2 17.6 22.8 24.5 31.4 42.8 52.0 17.7 22.8 31.4 38.2 10.8 14.2 19.9 24.5 31.3 3.88 5.60 8.46 10.7 14.2 20.0 21.1 27.1 37.1 45.1 14.2 18.5 25.7

h/t 31.4 40.0 54.3 65.7 31.4 40.0 54.3 65.7 40.0 54.3 65.7 82.8 28.0 35.7 48.6 58.9 74.3 24.5 31.4 42.8 52.0 24.5 31.4 42.8 52.0 24.5 31.4 42.8 52.0 65.7 24.5 31.4 42.8 52.0 65.7 89.0 21.1 27.1 37.1 45.1 21.1 27.1 37.1

10 10 10 6 6 6 6 6 4 4 4 4 4 4 12 12 12 12 12 12 10 10 10 10 8 8 8 8 8 8 6 6 6 6 6 6 4 4 4 4 4 4 3.5 3.5 3

0.3125 0.25 0.625 0.5 0.375 0.3125 0.25 0.1875 0.625 0.5 0.375 0.3125 0.25 0.1875 0.625 0.5 0.375 0.3125 0.25 0.1875 0.5 0.375 0.3125 0.25 0.625 0.5 0.375 0.3125 0.25 0.1878 0.625 0.5 0.375 0.3125 0.25 0.1875 0.625 0.5 0.375 0.3125 0.25 0.1875 0.375 0.3125 0.3125

0.291 0.233 0.581 0.465 0.349 0.291 0.233 0.174 0.581 0.465 0.349 0.291 0.233 0.174 0.581 0.465 0.349 0.291 0.233 0.174 0.465 0.349 0.291 0.233 0.581 0.465 0.349 0.291 0.233 0.174 0.581 0.465 0.349 0.291 0.233 0.174 0.581 0.465 0.349 0.291 0.233 0.174 0.349 0.291 0.291

48.9 39.5 76.1 62.3 47.9 40.3 32.7 24.7 67.6 55.5 42.7 36.1 29.2 22.1 93.1 75.9 58.0 48.8 39.4 29.8 69.1 52.9 44.6 36.0 76.1 62.3 47.8 40.4 32.6 24.8 67.6 55.5 42.7 36.1 29.2 22.2 59.1 48.7 37.6 31.8 25.8 19.7 36.3 30.8 29.7

31.4 39.9 7.33 9.90 14.2 17.6 22.8 31.5 3.88 5.60 8.46 10.7 14.2 20.0 17.7 22.8 31.4 38.2 48.5 66.0 18.5 25.7 31.4 39.9 10.8 14.2 19.9 24.5 31.3 43.0 7.33 9.90 14.2 17.6 22.8 31.5 3.88 5.60 8.46 10.7 14.2 20.0 7.03 9.03 7.31

45.1 57.1 21.1 27.1 37.1 45.1 57.1 77.5 21.1 27.1 37.1 45.1 57.1 77.5 17.7 22.8 31.4 38.2 48.5 66.0 22.8 31.4 38.2 48.5 17.7 22.8 31.4 38.2 48.5 66.0 17.7 22.8 31.4 38.2 48.5 66.0 17.7 22.8 31.4 38.2 48.5 66.0 31.4 38.2 38.2

3 3 2 2 2 10 10 10 10 10 10 8 8 8 8 8 8 6 6 6 6 6 6 5 5 5 5 4 4 4 4 4 4 4 3.5 3.5 3.5 3.5 3.5 3.5 3 3 3 3 3

0.25 0.1875 0.3125 0.25 0.1875 0.625 0.5 0.375 0.3125 0.25 0.1875 0.625 0.5 0.375 0.3125 0.25 0.1875 0.625 0.5 0.375 0.3125 0.25 0.1875 0.375 0.3125 0.25 0.1875 0.625 0.5 0.375 0.3125 0.25 0.1875 0.125 0.5 0.375 0.3125 0.25 0.1875 0.125 0.375 0.3125 0.25 0.1875 0.125

0.233 0.174 0.291 0.233 0.174 0.581 0.465 0.349 0.291 0.233 0.174 0.581 0.465 0.349 0.291 0.233 0.174 0.581 0.465 0.349 0.291 0.233 0.174 0.349 0.291 0.233 0.174 0.581 0.465 0.349 0.291 0.233 0.174 0.116 0.465 0.349 0.291 0.233 0.174 0.116 0.349 0.291 0.233 0.174 0.116

24.1 18.4 27.6 22.4 17.1 76.1 62.3 47.8 40.3 32.6 24.7 67.6 55.5 42.7 36.1 29.2 22.2 59.1 48.7 37.6 31.8 25.8 19.7 35.1 29.7 24.1 18.4 50.6 41.9 32.5 27.6 22.4 17.1 11.6 40.2 31.2 26.5 21.5 16.5 11.1 30.0 25.4 20.7 15.8 10.7

9.88 14.2 3.87 5.58 8.49 14.2 18.5 25.7 31.4 39.9 54.5 10.8 14.2 19.9 24.5 31.3 43.0 7.33 9.90 14.2 17.6 22.8 31.5 11.3 14.2 18.5 25.7 3.88 5.60 8.46 10.7 14.2 20.0 31.5 4.53 7.03 9.03 12.0 17.1 27.2 5.60 7.31 9.88 14.2 22.9

48.5 66.0 38.2 48.5 66.0 14.2 18.5 25.7 31.4 39.9 54.5 14.2 18.5 25.7 31.4 39.9 54.5 14.2 18.5 25.7 31.4 39.9 54.5 25.7 31.4 39.9 54.5 14.2 18.5 25.7 31.4 39.9 54.5 83.2 18.5 25.7 31.4 39.9 54.5 83.2 25.7 31.4 39.9 54.5 83.2

2 2 2 2 2 9 9 9 9 9 9 9 7 7 7 7 7 7 5 5 5 5 5 5 3 3 3 3 3 8 8 8 8 8 8 8 6 6 6 6 6 6 4 4 4

0.375 0.3125 0.25 0.1875 0.125 0.625 0.5 0.375 0.3125 0.25 0.1875 0.125 0.625 0.5 0.375 0.3125 0.25 0.1875 0.625 0.5 0.375 0.3125 0.25 0.1875 0.5 0.375 0.3125 0.25 0.1875 0.625 0.5 0.375 0.3125 0.25 0.1875 0.125 0.625 0.5 0.375 0.3125 0.25 0.1875 0.625 0.5 0.375

0.349 0.291 0.233 0.174 0.116 0.581 0.465 0.349 0.291 0.233 0.174 0.116 0.581 0.465 0.349 0.291 0.233 0.174 0.581 0.465 0.349 0.291 0.233 0.174 0.465 0.349 0.291 0.233 0.174 0.581 0.465 0.349 0.291 0.233 0.174 0.116 0.581 0.465 0.349 0.291 0.233 0.174 0.581 0.465 0.349

27.4 23.3 19.0 14.5 9.85 67.6 55.5 42.7 36.0 29.2 22.2 15.0 59.1 48.7 37.6 31.8 25.8 19.7 50.6 41.9 32.5 27.6 22.4 17.1 35.1 27.4 23.3 19.0 14.5 59.1 48.7 37.6 31.8 25.8 19.6 13.3 50.6 41.9 32.5 27.6 22.4 17.1 42.1 35.1 27.4

2.73 3.87 5.58 8.49 14.2 12.5 16.4 22.8 27.9 35.6 48.7 74.6 9.05 12.1 17.1 21.1 27.0 37.2 5.61 7.75 11.3 14.2 18.5 25.7 3.45 5.60 7.31 9.88 14.2 10.8 14.2 19.9 24.5 31.3 43.0 66.0 7.33 9.90 14.2 17.6 22.8 31.5 3.88 5.60 8.46

25.7 31.4 39.9 54.5 83.2 12.5 16.4 22.8 27.9 35.6 48.7 74.6 12.5 16.4 22.8 27.9 35.6 48.7 12.5 16.4 22.8 27.9 35.6 48.7 16.4 22.8 27.9 35.6 48.7 10.8 14.2 19.9 24.5 31.3 43.0 66.0 10.8 14.2 19.9 24.5 31.3 43.0 10.8 14.2 19.9

4 4 4 4 3 3 3 3 3 3 2 2 2 2 2 7 7 7 7 7 7 7 5 5 5 5 5 5 4 4 4 4 4 4 3 3 3 3 3 3 2 2 2 6 6

0.3125 0.25 0.1875 0.125 0.5 0.375 0.3125 0.25 0.1875 0.125 0.375 0.3125 0.25 0.1875 0.125 0.625 0.5 0.375 0.3125 0.25 0.1875 0.125 0.5 0.375 0.3125 0.25 0.1875 0.125 0.5 0.375 0.3125 0.25 0.1875 0.125 0.5 0.375 0.3125 0.25 0.1875 0.125 0.25 0.1875 0.125 0.625 0.5

0.291 0.233 0.174 0.116 0.465 0.349 0.291 0.233 0.174 0.116 0.349 0.291 0.233 0.174 0.116 0.581 0.465 0.349 0.291 0.233 0.174 0.116 0.465 0.349 0.291 0.233 0.174 0.116 0.465 0.349 0.291 0.233 0.174 0.116 0.465 0.349 0.291 0.233 0.174 0.116 0.233 0.174 0.116 0.581 0.465

23.3 19.0 14.5 9.85 31.7 24.9 21.2 17.3 13.3 9.00 22.3 19.1 15.6 12.0 8.15 50.6 41.9 32.5 27.5 22.4 17.1 11.6 35.1 27.4 23.3 19.0 14.5 9.85 31.7 24.9 21.2 17.3 13.3 9.00 28.3 22.3 19.1 15.6 12.0 8.15 13.9 10.7 7.30 42.1 35.1

10.7 14.2 20.0 31.5 3.45 5.60 7.31 9.88 14.2 22.9 2.73 3.87 5.58 8.49 14.2 9.05 12.1 17.1 21.1 27.0 37.2 57.3 7.75 11.3 14.2 18.5 25.7 40.1 5.60 8.46 10.7 14.2 20.0 31.5 3.45 5.60 7.31 9.88 14.2 22.9 5.58 8.49 14.2 7.33 9.90

24.5 31.3 43.0 66.0 14.2 19.9 24.5 31.3 43.0 66.0 19.9 24.5 31.3 43.0 66.0 9.05 12.1 17.1 21.1 27.0 37.2 57.3 12.1 17.1 21.1 27.0 37.2 57.3 12.1 17.1 21.1 27.0 37.2 57.3 12.1 17.1 21.1 27.0 37.2 57.3 27.0 37.2 57.3 7.33 9.90

6 6 6 6 6 5 5 5 5 5 5 4 4 4 4 4 4 3 3 3 3 3 3 2 2 2 2 2 5.5 5.5 5.5 5.5 5.5 5 5 5 5 5 5 4 4 4 4 4 4

0.375 0.3125 0.25 0.1875 0.125 0.5 0.375 0.3125 0.25 0.1875 0.125 0.5 0.375 0.3125 0.25 0.1875 0.125 0.5 0.375 0.3125 0.25 0.1875 0.125 0.375 0.3125 0.25 0.1875 0.125 0.375 0.3125 0.25 0.1875 0.125 0.5 0.375 0.3125 0.25 0.1875 0.125 0.5 0.375 0.3125 0.25 0.1875 0.125

0.349 0.291 0.233 0.174 0.116 0.465 0.349 0.291 0.233 0.174 0.116 0.465 0.349 0.291 0.233 0.174 0.116 0.465 0.349 0.291 0.233 0.174 0.116 0.349 0.291 0.233 0.174 0.116 0.349 0.291 0.233 0.174 0.116 0.465 0.349 0.291 0.233 0.174 0.116 0.465 0.349 0.291 0.233 0.174 0.116

27.4 23.3 19.0 14.5 9.85 31.7 24.9 21.2 17.3 13.3 9.00 28.3 22.3 19.1 15.6 12.0 8.15 24.9 19.7 16.9 13.9 10.7 7.30 17.2 14.8 12.2 9.43 6.45 24.9 21.2 17.3 13.2 9.00 28.3 22.3 19.0 15.6 12.0 8.15 24.9 19.7 16.9 13.9 10.7 7.30

14.2 17.6 22.8 31.5 48.7 7.75 11.3 14.2 18.5 25.7 40.1 5.60 8.46 10.7 14.2 20.0 31.5 3.45 5.60 7.31 9.88 14.2 22.9 2.73 3.87 5.58 8.49 14.2 12.8 15.9 20.6 28.6 44.4 7.75 11.3 14.2 18.5 25.7 40.1 5.60 8.46 10.7 14.2 20.0 31.5

14.2 17.6 22.8 31.5 48.7 9.90 14.2 17.6 22.8 31.5 48.7 9.90 14.2 17.6 22.8 31.5 48.7 9.90 14.2 17.6 22.8 31.5 48.7 14.2 17.6 22.8 31.5 48.7 12.8 15.9 20.6 28.6 44.4 7.75 11.3 14.2 18.5 25.7 40.1 7.75 11.3 14.2 18.5 25.7 40.1

3 3 3 3 3 3 2.5 2.5 2.5 2 2 2 2 2 4.5 4.5 4.5 4.5 4.5 4.5 4 4 4 4 4 4 3 3 3 3 3 2.5 2.5 2.5 2.5 2.5 2 2 2 2 2 2.5 2.5 2.5 2.5

0.5 0.375 0.3125 0.25 0.1875 0.125 0.25 0.1875 0.125 0.375 0.3125 0.25 0.1875 0.125 0.5 0.375 0.3125 0.25 0.1875 0.125 0.5 0.375 0.3125 0.25 0.1875 0.125 0.375 0.3125 0.25 0.1875 0.125 0.375 0.3125 0.25 0.1875 0.125 0.375 0.3125 0.25 0.1875 0.125 0.375 0.3125 0.25 0.1875

0.465 0.349 0.291 0.233 0.174 0.116 0.233 0.174 0.116 0.349 0.291 0.233 0.174 0.116 0.465 0.349 0.291 0.233 0.174 0.116 0.465 0.349 0.291 0.233 0.174 0.116 0.349 0.291 0.233 0.174 0.116 0.349 0.291 0.233 0.174 0.116 0.349 0.291 0.233 0.174 0.116 0.349 0.291 0.233 0.174

21.5 17.2 14.8 12.2 9.43 6.45 11.3 8.79 6.02 14.6 12.7 10.5 8.15 5.60 24.9 19.7 16.9 13.9 10.7 7.30 21.5 17.2 14.8 12.2 9.40 6.45 14.6 12.7 10.5 8.15 5.60 13.4 11.6 9.63 7.51 5.17 12.1 10.5 8.78 6.87 4.75 12.09 10.54 8.78 6.87

3.45 5.60 7.31 9.88 14.2 22.9 7.73 11.4 18.6 2.73 3.87 5.58 8.49 14.2 6.68 9.89 12.5 16.3 22.9 35.8 5.60 8.46 10.7 14.2 20.0 31.5 5.60 7.31 9.88 14.2 22.9 4.16 5.59 7.73 11.4 18.6 2.73 3.87 5.58 8.49 14.2 4.16 5.59 7.73 11.4

7.75 11.3 14.2 18.5 25.7 40.1 18.5 25.7 40.1 11.3 14.2 18.5 25.7 40.1 6.68 9.89 12.5 16.3 22.9 35.8 5.60 8.46 10.7 14.2 20.0 31.5 8.46 10.7 14.2 20.0 31.5 8.46 10.7 14.2 20.0 31.5 8.46 10.7 14.2 20.0 31.5 7.03 9.03 12 17.1

2.5 3.5 3.5 3.5 3.5 3.5 2 2 2 1.5 1.5 1.5 3 3 3 3 3 2.5 2.5 2.5 2.5 2 2 2 2 1.5 1.5 1.5 1 1 2.5 2.5 2.5 2.5 2 2 2 1.5 1.5 1.5 1 1 2.25 2.25 2.25

0.125 0.375 0.3125 0.25 0.1875 0.125 0.25 0.1875 0.125 0.25 0.1875 0.125 0.375 0.3125 0.25 0.1875 0.125 0.3125 0.25 0.1875 0.125 0.3125 0.25 0.1875 0.125 0.25 0.1875 125 0.1875 0.125 0.3125 0.25 0.1875 0.125 0.25 0.1875 0.125 0.25 0.1875 0.125 0.1875 0.125 0.25 0.1875 0.125

0.116 0.349 0.291 0.233 0.174 0.116 0.233 0.174 0.116 0.233 0.174 0.116 0.349 0.291 0.233 0.174 0.116 0.291 0.233 0.174 0.116 0.291 0.233 0.174 0.116 0.233 0.174 0.116 0.174 0.116 0.291 0.233 0.174 0.116 0.233 0.174 0.116 0.233 0.174 0.116 0.174 0.116 0.233 0.174 0.116

4.75 14.6 12.7 10.5 8.13 5.60 7.93 6.23 4.32 7.08 5.59 3.90 12.1 10.5 8.78 6.85 4.75 9.47 7.93 6.23 4.32 8.41 7.08 5.59 3.90 6.23 4.95 3.47 4.31 3.04 8.40 7.08 5.57 3.90 6.23 4.95 3.47 5.38 4.31 3.04 3.67 2.62 6.23 4.94 3.47

18.6 7.03 9.03 12.0 17.1 27.2 5.58 8.49 14.2 3.44 5.62 9.93 5.60 7.31 9.88 14.2 22.9 5.59 7.73 11.4 18.6 3.87 5.58 8.49 14.2 3.44 5.62 9.93 2.75 5.62 5.59 7.73 11.4 18.6 5.58 8.49 14.2 3.44 5.62 9.93 2.75 5.62 6.66 9.93 16.4

27.2 7.03 9.03 12.0 17.1 27.2 12.0 17.1 27.2 12.0 17.1 27.2 5.60 7.31 9.88 14.2 22.9 7.31 9.88 14.2 22.9 7.31 9.88 14.2 22.9 9.88 14.2 22.9 14.2 22.9 5.59 7.73 11.4 18.6 7.73 11.4 18.6 7.73 11.4 18.6 11.4 18.6 6.66 9.93 16.4

2.25 2.25 2 2 2 1.5 2 1 1

0.1875 0.125 0.25 0.1875 0.125 0.1875 0.125 0.1875 0.125

0.174 0.116 0.233 0.174 0.116 0.174 0.116 0.174 0.116

4.63 3.26 5.38 4.30 3.04 3.67 2.62 3.03 2.19

8.49 14.2 5.58 8.49 14.2 5.62 9.93 2.75 5.62

9.93 16.4 5.58 8.49 14.2 8.49 14.2 8.49 14.2

Properties from AISC Version 13.0 CD Database (Dec. 2005) and AISC 13th Edition Manual (Dec. 2005) Ix 1880 1550 1200 1010 1440 1190 926 786 838 657 560 458 923 770 602 513 419 1370 1130 873 739 1090 904 702 595 815 679 531 451 368 539 455 360 308 253 193 897 743 577 490 687 573 447

Sx 188 155 120 101 144 119 92.6 78.6 83.8 65.7 56.0 45.8 103 85.6 66.9 57.0 46.5 171 141 109 92.3 136 113 87.7 74.4 102 84.9 66.3 56.4 46.1 67.3 56.9 45.0 38.5 31.6 24.2 128 106 82.5 69.9 98.2 81.8 63.9

rx 7.33 7.39 7.45 7.48 6.89 6.96 7.03 7.07 6.33 6.42 6.46 6.50 6.00 6.07 6.15 6.18 6.22 6.25 6.31 6.37 6.39 6.00 6.06 6.12 6.15 5.64 5.70 5.77 5.80 5.83 5.06 5.15 5.23 5.27 5.31 5.35 5.44 5.49 5.55 5.58 5.17 5.23 5.29

Zx 230 188 144 122 185 152 117 98.6 115 89.3 75.6 61.5 135 112 86.4 73.1 59.4 200 164 126 106 165 135 104 87.7 129 106 82.1 69.4 56.4 92.9 77.3 60.2 51.1 41.7 31.7 151 124 95.4 80.5 120 98.8 76.3

Iy 851 705 547 464 338 283 222 189 58.7 47.6 41.2 34.3 158 134 106 91.3 75.1 1370 1130 873 739 700 581 452 384 274 230 181 155 127 54.1 47.0 38.3 33.2 27.7 21.5 897 743 577 490 407 341 267

Sy 142 117 91.1 77.3 84.6 70.8 55.6 47.4 29.3 23.8 20.6 17.1 52.7 44.6 35.5 30.4 25.0 171 141 109 92.3 117 96.8 75.3 64.0 68.6 57.6 45.3 38.7 31.7 27.0 23.5 19.1 16.6 13.8 10.8 128 106 82.5 69.9 81.5 68.1 53.4

380 310 478 402 317 271 222 170 373 317 252 216 178 137 548 457 357 304 248 189 395 310 264 216 397 333 262 224 184 140 321 271 215 184 151 116 245 210 168 144 119 91.8 156 134 124

54.3 44.3 68.3 57.4 45.3 38.7 31.7 24.3 53.3 45.3 36.0 30.9 25.4 19.5 91.4 76.2 59.5 50.7 41.4 31.5 65.9 51.6 44.0 36.0 66.1 55.6 43.7 37.4 30.6 23.4 53.4 45.2 35.9 30.7 25.2 19.4 40.8 34.9 28.0 24.1 19.9 15.3 26.0 22.4 20.7

5.32 5.35 4.77 4.84 4.91 4.94 4.98 5.01 4.47 4.55 4.63 4.67 4.71 4.74 4.62 4.68 4.73 4.76 4.79 4.82 4.56 4.61 4.64 4.67 4.34 4.41 4.47 4.50 4.53 4.56 4.14 4.21 4.28 4.31 4.34 4.38 3.87 3.95 4.02 4.06 4.10 4.13 3.94 3.98 3.90

64.6 52.4 88.7 73.6 57.3 48.6 39.6 30.1 73.1 61.0 47.8 40.6 33.2 25.3 109 89.6 69.2 58.6 47.6 36.0 78.8 61.1 51.7 42.1 82.1 68.1 53.0 44.9 36.6 27.8 68.8 57.4 44.8 38.1 31.1 23.7 55.5 46.7 36.7 31.3 25.6 19.6 34.7 29.6 27.9

227 186 124 105 84.1 72.3 59.6 45.9 47.2 41.2 33.6 29.2 24.4 19.0 548 457 357 304 248 189 298 234 200 164 210 178 140 120 98.8 75.7 107 91.1 72.9 62.8 51.9 40.0 40.4 35.3 28.9 25.2 21.0 16.4 21.3 18.6 13.1

45.5 37.2 41.2 35.1 28.0 24.1 19.9 15.3 23.6 20.6 16.8 14.6 12.2 9.48 91.4 76.2 59.5 50.7 41.4 31.5 59.7 46.9 40.0 32.7 52.5 44.4 35.1 30.1 24.7 18.9 35.5 30.4 24.3 20.9 17.3 13.3 20.2 17.7 14.5 12.6 10.5 8.20 12.2 10.6 8.73

103 79.6 104 86.9 67.4 304 256 202 172 141 108 253 214 169 145 119 91.4 201 171 137 118 96.9 74.6 120 104 85.8 66.2 149 129 104 90.1 74.7 57.8 39.8 118 96.1 83.2 69.1 53.6 37.0 88.0 76.3 63.6 49.4 34.2

17.2 13.3 17.4 14.5 11.2 60.8 51.2 40.4 34.5 28.3 21.6 50.5 42.7 33.9 29.0 23.8 18.3 40.2 34.3 27.4 23.5 19.4 14.9 24.1 20.8 17.2 13.2 29.9 25.8 20.8 18.0 14.9 11.6 7.97 23.7 19.2 16.6 13.8 10.7 7.40 17.6 15.3 12.7 9.87 6.83

3.94 3.98 3.71 3.75 3.80 3.80 3.86 3.92 3.94 3.97 4.00 3.68 3.73 3.79 3.82 3.85 3.88 3.50 3.57 3.63 3.66 3.69 3.73 3.53 3.56 3.60 3.63 3.26 3.34 3.41 3.44 3.48 3.52 3.55 3.26 3.34 3.38 3.41 3.45 3.49 3.26 3.30 3.34 3.38 3.42

22.9 17.5 24.5 20.1 15.5 73.2 60.7 47.2 40.1 32.7 24.8 62.2 51.9 40.5 34.4 28.1 21.4 51.3 43.0 33.8 28.8 23.6 18.0 30.4 26.0 21.3 16.3 40.3 34.1 27.0 23.1 19.0 14.6 10.0 31.9 25.3 21.7 17.9 13.7 9.37 23.7 20.3 16.7 12.8 8.80

11.1 8.72 5.10 4.41 3.55 304 256 202 172 141 108 178 151 120 103 84.7 65.1 89.4 76.8 61.8 53.3 44.1 34.1 40.6 35.2 29.3 22.7 33.5 29.5 24.3 21.2 17.7 13.9 9.65 21.4 17.8 15.6 13.1 10.3 7.22 12.4 11.0 9.28 7.33 5.16

7.38 5.81 5.10 4.41 3.55 60.8 51.2 40.4 34.5 28.3 21.6 44.5 37.8 30.0 25.7 21.2 16.3 29.8 25.6 20.6 17.8 14.7 11.4 16.2 14.1 11.7 9.09 16.8 14.7 12.1 10.6 8.87 6.93 4.83 12.2 10.2 8.92 7.51 5.89 4.12 8.28 7.30 6.19 4.89 3.44

71.7 62.6 52.5 41.0 28.5 216 183 145 124 102 78.2 53.5 174 149 119 102 84.1 64.7 133 115 92.5 79.8 66.1 51.1 80.8 66.3 57.7 48.2 37.6 146 125 100 85.6 70.7 54.4 37.4 114 98.2 79.1 68.3 56.6 43.7 82.0 71.8 58.7

14.3 12.5 10.5 8.19 5.70 47.9 40.6 32.2 27.6 22.7 17.4 11.9 38.7 33.0 26.4 22.6 18.7 14.4 29.6 25.5 20.5 17.7 14.7 11.4 18.0 14.7 12.8 10.7 8.35 36.5 31.2 24.9 21.4 17.7 13.6 9.34 28.5 24.6 19.8 17.1 14.2 10.9 20.5 17.9 14.7

3.08 3.12 3.17 3.21 3.25 3.40 3.45 3.51 3.54 3.56 3.59 3.62 3.26 3.32 3.38 3.41 3.44 3.47 3.08 3.14 3.21 3.24 3.27 3.31 2.88 2.96 3.00 3.04 3.07 2.99 3.04 3.10 3.13 3.15 3.18 3.21 2.85 2.91 2.97 3.00 3.03 3.06 2.64 2.71 2.78

20.3 17.5 14.4 11.1 7.65 58.1 48.4 37.8 32.1 26.2 20.0 13.6 48.3 40.5 31.8 27.1 22.2 16.9 38.5 32.5 25.7 22.0 18.1 13.8 24.6 19.7 16.9 14.0 10.8 44.7 37.5 29.4 25.1 20.5 15.7 10.7 36.1 30.5 24.1 20.6 16.9 13.0 27.4 23.5 18.8

4.70 4.24 3.67 2.97 2.14 216 183 145 124 102 78.2 53.5 117 100 80.4 69.2 57.2 44.1 52.0 45.2 36.8 32.0 26.6 20.7 13.2 11.2 9.88 8.38 6.64 146 125 100 85.6 70.7 54.4 37.4 72.3 62.5 50.6 43.8 36.4 28.2 26.6 23.6 19.6

4.70 4.24 3.67 2.97 2.14 47.9 40.6 32.2 27.6 22.7 17.4 11.9 33.5 28.7 23.0 19.8 16.3 12.6 20.8 18.1 14.7 12.8 10.6 8.28 8.81 7.45 6.59 5.59 4.42 36.5 31.2 24.9 21.4 17.7 13.6 9.34 24.1 20.8 16.9 14.6 12.1 9.39 13.3 11.8 9.80

51.0 42.5 33.1 22.9 58.6 48.5 42.4 35.5 27.8 19.3 38.2 33.7 28.5 22.4 15.7 93.4 80.5 65.0 56.1 46.5 36.0 24.8 60.6 49.5 43.0 35.9 27.9 19.3 50.7 41.8 36.5 30.5 23.8 16.6 40.7 34.1 29.9 25.2 19.8 13.8 19.8 15.7 11.1 55.2 48.3

12.8 10.6 8.27 5.73 14.6 12.1 10.6 8.88 6.94 4.83 9.56 8.43 7.12 5.61 3.93 26.7 23.0 18.6 16.0 13.3 10.3 7.09 17.3 14.1 12.3 10.2 7.96 5.52 14.5 11.9 10.4 8.72 6.81 4.73 11.6 9.73 8.54 7.19 5.65 3.95 5.67 4.49 3.16 18.4 16.1

2.82 2.85 2.88 2.92 2.58 2.65 2.69 2.73 2.77 2.80 2.49 2.53 2.57 2.61 2.65 2.58 2.63 2.69 2.72 2.75 2.77 2.80 2.50 2.56 2.59 2.62 2.65 2.68 2.40 2.46 2.50 2.53 2.56 2.59 2.27 2.35 2.38 2.42 2.45 2.49 2.27 2.31 2.35 2.17 2.23

16.1 13.3 10.2 7.02 20.0 16.1 13.9 11.5 8.87 6.11 13.4 11.6 9.68 7.51 5.19 33.1 27.9 22.1 18.9 15.5 11.9 8.13 21.9 17.5 15.0 12.4 9.52 6.53 18.8 15.1 13.1 10.8 8.33 5.73 15.8 12.8 11.1 9.22 7.14 4.93 7.64 5.95 4.13 23.2 19.8

17.2 14.4 11.3 7.90 11.7 10.0 8.81 7.49 5.94 4.20 3.73 3.38 2.94 2.39 1.72 93.4 80.5 65.0 56.1 46.5 36.0 24.8 35.6 29.3 25.5 21.3 16.6 11.6 20.7 17.3 15.2 12.8 10.0 7.03 10.2 8.71 7.74 6.60 5.24 3.71 2.58 2.10 1.52 55.2 48.3

8.58 7.21 5.65 3.95 7.81 6.63 5.87 4.99 3.96 2.80 3.73 3.38 2.94 2.39 1.72 26.7 23.0 18.6 16.0 13.3 10.3 7.09 14.2 11.7 10.2 8.53 6.65 4.63 10.4 8.63 7.58 6.38 5.02 3.51 6.80 5.81 5.16 4.40 3.50 2.48 2.58 2.10 1.52 18.4 16.1

39.5 34.3 28.6 22.3 15.5 41.1 33.9 29.6 24.7 19.3 13.4 34.0 28.3 24.8 20.9 16.4 11.4 26.8 22.7 20.1 17.0 13.4 9.43 17.1 15.3 13.1 10.5 7.42 29.7 25.9 21.7 17.0 11.8 26.0 21.7 19.0 16.0 12.6 8.80 21.2 17.9 15.8 13.4 10.6 7.42

13.2 11.4 9.54 7.42 5.15 13.7 11.3 9.85 8.25 6.44 4.48 11.3 9.43 8.27 6.96 5.46 3.81 8.95 7.57 6.69 5.66 4.47 3.14 5.71 5.11 4.37 3.49 2.47 10.8 9.43 7.90 6.17 4.30 10.4 8.68 7.62 6.41 5.03 3.52 8.49 7.17 6.32 5.35 4.22 2.97

2.28 2.31 2.34 2.37 2.39 2.16 2.22 2.25 2.28 2.31 2.34 2.08 2.14 2.17 2.20 2.23 2.26 1.97 2.04 2.07 2.10 2.14 2.17 1.89 1.93 1.97 2.01 2.05 2.08 2.11 2.13 2.16 2.19 1.82 1.87 1.90 1.93 1.96 1.99 1.75 1.81 1.84 1.87 1.90 1.93

15.8 13.6 11.2 8.63 5.92 17.2 13.8 11.9 9.87 7.62 5.24 14.6 11.9 10.3 8.53 6.60 4.56 12.1 9.90 8.61 7.19 5.59 3.87 7.93 6.95 5.84 4.58 3.19 13.1 11.3 9.32 7.19 4.95 13.1 10.6 9.16 7.61 5.89 4.07 10.9 8.96 7.79 6.49 5.05 3.50

39.5 34.3 28.6 22.3 15.5 30.8 25.5 22.3 18.7 14.6 10.2 17.8 14.9 13.2 11.1 8.76 6.15 8.69 7.48 6.67 5.70 4.55 3.23 2.77 2.52 2.21 1.80 1.31 29.7 25.9 21.7 17.0 11.8 26.0 21.7 19.0 16.0 12.6 8.80 14.9 12.6 11.1 9.46 7.48 5.27

13.2 11.4 9.54 7.42 5.15 12.3 10.2 8.91 7.47 5.84 4.07 8.89 7.47 6.58 5.56 4.38 3.08 5.79 4.99 4.45 3.80 3.03 2.15 2.77 2.52 2.21 1.80 1.31 10.8 9.43 7.90 6.17 4.30 10.4 8.68 7.62 6.41 5.03 3.52 7.43 6.30 5.57 4.73 3.74 2.64

16.4 14.1 12.6 10.7 8.53 6.03 9.40 7.51 5.34 10.4 9.35 8.08 6.50 4.65 18.1 15.3 13.5 11.4 9.02 6.35 11.9 10.3 9.14 7.80 6.21 4.40 7.93 7.14 6.15 4.93 3.52 6.77 6.13 5.32 4.30 3.09 5.60 5.13 4.49 3.66 2.65 4.75 4.34 3.79 3.09

6.57 5.65 5.03 4.29 3.41 2.41 3.76 3.01 2.14 4.14 3.74 3.23 2.60 1.86 8.03 6.79 6.00 5.08 4.01 2.82 5.97 5.13 4.57 3.90 3.10 2.20 3.97 3.57 3.07 2.47 1.76 3.38 3.07 2.66 2.15 1.54 2.80 2.56 2.25 1.83 1.32 2.72 2.48 2.17 1.76

1.65 1.72 1.75 1.78 1.82 1.85 1.73 1.77 1.80 1.59 1.63 1.67 1.70 1.74 1.61 1.67 1.70 1.73 1.75 1.78 1.41 1.47 1.49 1.52 1.55 1.58 1.39 1.42 1.45 1.49 1.52 1.35 1.38 1.41 1.44 1.47 1.29 1.32 1.36 1.39 1.43 1.18 1.22 1.25 1.28

8.83 7.34 6.42 5.38 4.21 2.93 4.83 3.79 2.65 5.71 5.05 4.27 3.37 2.37 10.2 8.36 7.27 6.06 4.71 3.27 7.70 6.39 5.59 4.69 3.67 2.56 5.12 4.51 3.81 3.00 2.11 4.48 3.97 3.38 2.67 1.88 3.84 3.43 2.94 2.34 1.66 3.59 3.2 2.74 2.18

7.18 6.25 5.60 4.81 3.85 2.75 3.13 2.53 1.82 2.28 2.10 1.84 1.51 1.10 18.1 15.3 13.5 11.4 9.02 6.35 11.9 10.3 9.14 7.80 6.21 4.40 5.01 4.52 3.91 3.16 2.27 3.17 2.89 2.53 2.06 1.49 1.80 1.67 1.48 1.22 0.898 2.77 2.54 2.23 1.82

4.78 4.16 3.73 3.21 2.57 1.83 2.50 2.03 1.46 2.28 2.10 1.84 1.51 1.10 8.03 6.79 6.00 5.08 4.01 2.82 5.97 5.13 4.57 3.90 3.10 2.20 3.34 3.02 2.61 2.10 1.51 2.54 2.32 2.02 1.65 1.19 1.80 1.67 1.48 1.22 0.898 2.21 2.03 1.78 1.46

2.23 6.49 5.84 5.04 4.05 2.90 3.17 2.61 1.90 2.55 2.12 1.57 3.78 3.45 3.02 2.46 1.78 2.92 2.57 2.11 1.54 2.38 2.13 1.77 1.30 1.68 1.42 1.06 1.07 0.817 1.82 1.63 1.35 0.998 1.33 1.12 0.833 1.03 0.882 0.668 0.646 0.503 1.13 0.953 0.712

1.28 3.71 3.34 2.88 2.31 1.66 1.81 1.49 1.09 1.46 1.21 0.896 2.52 2.30 2.01 1.64 1.19 1.94 1.72 1.41 1.03 1.59 1.42 1.18 0.867 1.12 0.945 0.706 0.713 0.545 1.46 1.30 1.08 0.799 1.06 0.894 0.667 0.822 0.705 0.535 0.517 0.403 1.01 0.847 0.633

1.31 1.26 1.29 1.32 1.35 1.37 1.20 1.23 1.27 1.14 1.17 1.21 1.06 1.08 1.11 1.14 1.17 1.05 1.08 1.11 1.14 1.01 1.04 1.07 1.10 0.982 1.02 1.05 0.947 0.987 0.880 0.908 0.937 0.965 0.874 0.904 0.934 0.826 0.860 0.892 0.796 0.834 0.806 0.835 0.863

1.54 4.69 4.14 3.50 2.76 1.93 2.36 1.89 1.34 1.98 1.60 1.15 3.25 2.90 2.48 1.97 1.40 2.51 2.16 1.73 1.23 2.11 1.83 1.48 1.06 1.51 1.24 0.895 0.989 0.728 1.88 1.63 1.32 0.947 1.37 1.12 0.809 1.11 0.915 0.671 0.713 0.532 1.28 1.04 0.755

1.33 6.49 5.84 5.04 4.05 2.90 1.30 1.08 0.795 0.638 0.544 0.411 3.78 3.45 3.02 2.46 1.78 2.18 1.93 1.59 1.16 1.24 1.11 0.932 0.692 0.543 0.467 0.355 0.173 0.138 1.82 1.63 1.35 0.998 0.930 0.786 0.589 0.449 0.390 0.300 0.143 0.115 1.13 0.953 0.712

1.06 3.71 3.34 2.88 2.31 1.66 1.30 1.08 0.795 0.851 0.725 0.548 2.52 2.30 2.01 1.64 1.19 1.74 1.54 1.27 0.931 1.24 1.11 0.932 0.692 0.725 0.622 0.474 0.345 0.276 1.46 1.30 1.08 0.799 0.930 0.786 0.589 0.599 0.520 0.399 0.285 0.230 1.01 0.847 0.633

0.859 0.646 0.747 0.641 0.486 0.495 0.383 0.350 0.280

0.764 0.574 0.747 0.641 0.486 0.495 0.383 0.350 0.280

0.819 0.848 0.704 0.733 0.761 0.697 0.728 0.643 0.679

0.952 0.693 0.964 0.797 0.584 0.639 0.475 0.480 0.366

0.713 0.538 0.747 0.641 0.486 0.313 0.244 0.112 0.0922

0.713 0.538 0.747 0.641 0.486 0.417 0.325 0.225 0.184

Dec. 2005) ry 4.93 4.99 5.04 5.07 3.34 3.39 3.44 3.47 1.68 1.73 1.75 1.78 2.48 2.53 2.58 2.61 2.63 6.25 6.31 6.37 6.39 4.80 4.86 4.91 4.94 3.27 3.32 3.37 3.40 3.42 1.60 1.65 1.71 1.73 1.76 1.78 5.44 5.49 5.55 5.58 3.98 4.04 4.09

Zy 162 132 102 85.8 96.4 79.5 61.5 52.0 34.0 26.8 22.9 18.7 61.0 50.7 39.5 33.5 27.3 200 164 126 106 135 111 85.5 72.2 79.2 65.5 50.8 43.0 35.0 32.5 27.4 21.7 18.5 15.2 11.7 151 124 95.4 80.5 95.1 78.5 60.7

h(flat) 17.1875 17.75 18.3125 18.625 17.1875 17.75 18.3125 18.625 17.75 18.3125 18.625 18.875 15.1875 15.75 16.3125 16.5625 16.875 13.1875 13.75 14.3125 14.625 13.1875 13.75 14.3125 14.625 13.1875 13.75 14.3125 14.625 14.875 13.1875 13.75 14.3125 14.625 14.875 15.1875 11.1875 11.75 12.3125 12.625 11.1875 11.75 12.3125

b(flat) 9.1875 9.75 10.3125 10.625 5.1875 5.75 6.3125 6.625 --2.3125 2.625 2.875 3.1875 3.75 4.3125 4.5625 4.875 13.1875 13.75 14.3125 14.625 9.1875 9.75 10.3125 10.625 5.1875 5.75 6.3125 6.625 6.875 ----2.3125 2.625 2.875 3.1875 11.1875 11.75 12.3125 12.625 7.1875 7.75 8.3125

J 1890 1540 1180 997 916 757 586 496 195 156 134 111 462 387 302 257 210 2170 1770 1350 1140 1370 1120 862 727 681 563 436 369 300 174 150 120 103 85.2 65.5 1430 1170 900 759 832 685 528

C 257 209 160 134 167 137 105 88.3 63.8 49.9 42.4 34.7 109 89.9 69.5 58.7 47.7 276 224 171 144 204 166 127 107 132 108 83.4 70.4 57.0 60.5 50.7 39.7 33.8 27.6 21.1 208 170 130 109 146 120 91.8

4.12 4.14 2.43 2.48 2.53 2.55 2.58 2.61 1.59 1.64 1.69 1.72 1.74 1.77 4.62 4.68 4.73 4.76 4.79 4.82 3.96 4.01 4.04 4.07 3.16 3.21 3.27 3.29 3.32 3.35 2.39 2.44 2.49 2.52 2.54 2.57 1.57 1.62 1.67 1.70 1.72 1.75 1.46 1.48 1.27

51.4 41.8 48.4 40.4 31.6 26.9 22.0 16.7 28.5 24.1 19.1 16.4 13.5 10.3 109 89.6 69.2 58.6 47.6 36.0 69.6 54.0 45.7 37.2 61.9 51.5 40.1 34.1 27.8 21.1 42.1 35.2 27.7 23.6 19.3 14.7 24.5 20.9 16.6 14.2 11.7 9.00 14.0 12.1 10.0

12.5625 12.875 11.1875 11.75 12.3125 12.5625 12.875 13.1875 11.25 11.75 12.25 12.625 12.875 13.125 9.1875 9.75 10.3125 10.625 10.875 11.1875 9.75 10.3125 10.5625 10.875 9.1875 9.75 10.3125 10.5625 10.875 11.125 9.1875 9.75 10.3125 10.5625 10.875 11.1875 9.1875 9.75 10.3125 10.625 10.875 11.1875 10.3125 10.625 10.625

8.5625 8.875 3.1875 3.75 4.3125 4.5625 4.875 5.1875 ----2.25 2.625 2.875 3.125 9.1875 9.75 10.3125 10.625 10.875 11.1875 7.75 8.3125 8.5625 8.875 5.1875 5.75 6.3125 6.5625 6.875 7.125 3.1875 3.75 4.3125 4.5625 4.875 5.1875 ----2.3125 2.625 2.875 3.1875 -------

446 362 334 279 219 186 152 116 148 127 102 87.7 72.4 55.8 885 728 561 474 384 290 545 421 356 289 454 377 293 248 202 153 271 227 178 152 124 94.6 122 105 84.1 72.4 59.8 46.1 64.7 56.0 41.3

77.4 62.6 83.7 69.3 53.7 45.5 36.9 28.0 52.6 44.1 34.6 29.5 24.1 18.4 151 123 94.6 79.7 64.5 48.6 102 78.3 66.1 53.5 97.7 80.4 62.1 52.4 42.5 32.2 71.1 59.0 45.8 38.8 31.6 24.0 44.6 37.5 29.5 25.2 20.6 15.7 25.5 21.8 18.4

1.29 1.32 0.820 0.845 0.872 3.80 3.86 3.92 3.94 3.97 4.00 3.09 3.14 3.19 3.22 3.25 3.28 2.34 2.39 2.44 2.47 2.49 2.52 2.05 2.07 2.10 2.13 1.54 1.59 1.64 1.67 1.70 1.72 1.75 1.39 1.44 1.46 1.49 1.51 1.54 1.22 1.25 1.28 1.30 1.33

8.28 6.40 6.05 5.08 3.97 73.2 60.7 47.2 40.1 32.7 24.8 53.3 44.5 34.8 29.6 24.2 18.4 35.8 30.1 23.7 20.2 16.6 12.7 18.7 16.0 13.2 10.1 20.6 17.6 14.0 12.1 10.0 7.66 5.26 14.7 11.8 10.2 8.45 6.52 4.48 9.73 8.42 6.99 5.41 3.74

10.875 11.1875 10.625 10.875 11.1875 7.1875 7.75 8.3125 8.625 8.875 9.1875 7.1875 7.75 8.3125 8.625 8.875 9.1875 7.1875 7.75 8.3125 8.625 8.875 9.1875 8.3125 8.625 8.875 9.1875 7.1875 7.75 8.3125 8.625 8.875 9.1875 9.4375 7.75 8.3125 8.625 8.875 9.1875 9.4375 8.3125 8.625 8.875 9.1875 9.4375

--2.1875 ------7.1875 7.75 8.3125 8.625 8.875 9.1875 5.1875 5.75 6.3125 6.625 6.875 7.1875 3.1875 3.75 4.3125 4.625 4.875 5.1875 3.3125 3.625 3.875 4.1875 ----2.3125 2.625 2.875 3.1875 3.4375 --------2.6875 2.9375 ------2.1875 2.4375

34.5 26.8 17.6 15.1 12.0 498 412 320 271 220 167 346 288 224 190 155 118 209 176 139 118 96.7 73.8 100 86.0 70.7 54.1 95.7 82.6 66.5 57.3 47.4 36.5 25.1 63.2 51.5 44.6 37.0 28.6 19.8 37.8 33.0 27.6 21.5 14.9

15.1 11.6 11.6 9.64 7.49 102 84.2 64.8 54.8 44.4 33.6 80.4 66.4 51.4 43.5 35.3 26.7 58.6 48.7 37.9 32.2 26.2 19.9 31.2 26.5 21.6 16.5 36.7 31.0 24.4 20.9 17.1 13.1 8.90 26.5 21.1 18.0 14.8 11.4 7.75 17.7 15.2 12.5 9.64 6.61

0.787 0.812 0.838 0.864 0.890 3.40 3.45 3.51 3.54 3.56 3.59 3.62 2.68 2.73 2.78 2.81 2.84 2.87 1.92 1.97 2.03 2.05 2.08 2.10 1.17 1.21 1.24 1.27 1.29 2.99 3.04 3.10 3.13 3.15 3.18 3.21 2.27 2.32 2.38 2.40 2.43 2.46 1.51 1.56 1.61

5.76 5.06 4.26 3.34 2.33 58.1 48.4 37.8 32.1 26.2 20.0 13.6 40.5 34.0 26.7 22.8 18.7 14.3 25.3 21.5 17.1 14.6 12.0 9.25 10.8 8.80 7.63 6.35 4.92 44.7 37.5 29.4 25.1 20.5 15.7 10.7 29.5 24.9 19.8 16.9 13.9 10.7 16.6 14.3 11.5

8.3125 8.625 8.875 9.1875 9.4375 6.1875 6.75 7.3125 7.625 7.875 8.1875 8.4375 6.1875 6.75 7.3125 7.625 7.875 8.1875 6.1875 6.75 7.3125 7.625 7.875 8.1875 6.75 7.3125 7.625 7.875 8.1875 5.1875 5.75 6.3125 6.625 6.875 7.1875 7.4375 5.1875 5.75 6.3125 6.625 6.875 7.1875 5.1875 5.75 6.3125

----------6.1875 6.75 7.3125 7.625 7.875 8.1875 8.4375 4.1875 4.75 5.3125 5.625 5.875 6.1875 2.1875 2.75 3.3125 3.625 3.875 4.1875 --------2.1875 5.1875 5.75 6.3125 6.625 6.875 7.1875 7.4375 3.1875 3.75 4.3125 4.625 4.875 5.1875 ----2.3125

15.9 14.2 12.2 9.74 6.90 356 296 231 196 159 121 82.0 235 197 154 131 107 81.7 128 109 86.9 74.4 61.2 46.9 40.0 33.1 28.9 24.2 18.9 244 204 160 136 111 84.5 57.3 150 127 100 85.8 70.3 53.7 70.3 61.1 49.3

11.0 9.56 7.99 6.22 4.31 81.6 67.4 52.1 44.0 35.8 27.1 18.3 62.0 51.5 40.0 33.9 27.6 20.9 42.5 35.6 27.9 23.8 19.4 14.8 19.7 15.8 13.6 11.3 8.66 63.2 52.4 40.7 34.5 28.1 21.3 14.4 46.0 38.4 30.0 25.5 20.8 15.8 28.7 24.4 19.3

1.63 1.66 1.69 1.71 1.15 1.20 1.23 1.25 1.28 1.31 0.777 0.802 0.827 0.853 0.879 2.58 2.63 2.69 2.72 2.75 2.77 2.80 1.91 1.97 1.99 2.02 2.05 2.07 1.53 1.58 1.61 1.64 1.66 1.69 1.14 1.19 1.21 1.24 1.26 1.29 0.819 0.845 0.871 2.17 2.23

9.91 8.20 6.33 4.36 9.64 7.88 6.84 5.70 4.43 3.07 4.61 4.06 3.43 2.70 1.90 33.1 27.9 22.1 18.9 15.5 11.9 8.13 17.3 13.8 11.9 9.83 7.57 5.20 12.6 10.2 8.83 7.33 5.67 3.91 8.46 6.95 6.05 5.06 3.94 2.73 3.02 2.39 1.68 23.2 19.8

6.625 6.875 7.1875 7.4375 5.75 6.3125 6.625 6.875 7.1875 7.4375 6.3125 6.625 6.875 7.1875 7.4375 4.1875 4.75 5.3125 5.625 5.875 6.1875 6.4375 4.75 5.3125 5.625 5.875 6.1875 6.4375 4.75 5.3125 5.625 5.875 6.125 6.4375 4.75 5.3125 5.625 5.875 6.1875 6.4375 5.875 6.1875 6.4375 3.1875 3.75

2.625 2.875 3.1875 3.4375 --------2.1875 2.4375 ----------4.1875 4.75 5.3125 5.625 5.875 6.1875 6.4375 2.75 3.3125 3.625 3.875 4.1875 4.4375 --2.3125 2.625 2.875 3.125 3.4375 --------2.1875 2.4375 ------3.1875 3.75

42.6 35.3 27.2 18.7 34.3 28.5 24.9 20.8 16.2 11.3 12.1 10.9 9.36 7.48 5.30 158 133 105 89.7 73.5 56.1 38.2 75.8 60.6 52.1 42.9 32.9 22.5 50.5 41.0 35.4 29.3 22.7 15.6 28.6 23.9 20.9 17.5 13.7 9.48 7.95 6.35 4.51 94.9 81.1

16.5 13.6 10.4 7.10 17.4 14.0 12.1 10.0 7.68 5.27 8.65 7.57 6.35 4.95 3.44 47.1 39.3 30.7 26.1 21.3 16.2 11.0 27.2 21.4 18.3 15.0 11.4 7.79 21.1 16.8 14.4 11.8 9.07 6.20 15.0 12.1 10.5 8.68 6.69 4.60 5.52 4.32 3.00 33.4 28.1

2.28 2.31 2.34 2.37 2.39 1.87 1.92 1.95 1.98 2.01 2.03 1.50 1.55 1.58 1.61 1.63 1.66 1.12 1.17 1.19 1.22 1.25 1.27 0.760 0.785 0.810 0.836 0.861 2.08 2.11 2.13 2.16 2.19 1.82 1.87 1.90 1.93 1.96 1.99 1.46 1.52 1.54 1.57 1.60 1.62

15.8 13.6 11.2 8.63 5.92 15.2 12.2 10.5 8.72 6.73 4.63 11.0 8.94 7.75 6.45 5.00 3.46 7.28 6.03 5.27 4.41 3.45 2.40 3.46 3.07 2.61 2.07 1.46 13.1 11.3 9.32 7.19 4.95 13.1 10.6 9.16 7.61 5.89 4.07 9.35 7.67 6.67 5.57 4.34 3.01

4.3125 4.625 4.875 5.1875 5.4375 3.75 4.3125 4.625 4.875 5.1875 5.4375 3.75 4.3125 4.625 4.875 5.1875 5.4375 3.75 4.3125 4.625 4.875 5.1875 5.4375 4.3125 4.625 4.875 5.1875 5.4375 3.8125 4.125 4.375 4.6875 4.9375 2.75 3.3125 3.625 3.875 4.1875 4.4375 2.75 3.3125 3.625 3.875 4.1875 4.4375

4.3125 4.625 4.875 5.1875 5.4375 2.75 3.3125 3.625 3.875 4.1875 4.4375 --2.3125 2.625 2.875 3.1875 3.4375 --------2.1875 2.4375 ----------3.8125 4.125 4.375 4.6875 4.9375 2.75 3.3125 3.625 3.875 4.1875 4.4375 --2.3125 2.625 2.875 3.1875 3.4375

64.6 55.4 45.6 35.0 23.9 59.8 48.1 41.4 34.2 26.3 18.0 40.3 32.8 28.4 23.6 18.2 12.6 23.1 19.3 16.9 14.2 11.1 7.73 8.42 7.60 6.55 5.24 3.72 49.0 42.2 34.8 26.7 18.3 44.6 36.1 31.2 25.8 19.9 13.7 30.3 24.9 21.7 18.0 14.0 9.66

22.1 18.9 15.4 11.8 8.03 23.0 18.2 15.6 12.8 9.76 6.66 17.8 14.2 12.2 10.1 7.74 5.30 12.7 10.3 8.91 7.39 5.71 3.93 6.35 5.58 4.70 3.68 2.57 18.4 15.7 12.9 9.85 6.72 18.7 14.9 12.8 10.5 8.08 5.53 14.5 11.7 10.1 8.32 6.41 4.39

1.09 1.14 1.17 1.19 1.22 1.25 0.999 1.02 1.05 0.748 0.772 0.797 0.823 0.848 1.61 1.67 1.70 1.73 1.75 1.78 1.41 1.47 1.49 1.52 1.55 1.58 1.11 1.13 1.16 1.19 1.21 0.922 0.947 0.973 0.999 1.03 0.729 0.754 0.779 0.804 0.830 0.904 0.93 0.956 0.983

6.10 5.10 4.48 3.77 2.96 2.07 2.95 2.33 1.64 2.88 2.57 2.20 1.75 1.24 10.2 8.36 7.27 6.06 4.71 3.27 7.70 6.39 5.59 4.69 3.67 2.56 4.18 3.69 3.12 2.46 1.73 3.20 2.85 2.43 1.93 1.36 2.31 2.08 1.79 1.43 1.02 2.82 2.52 2.16 1.72

2.75 3.3125 3.625 3.875 4.1875 4.4375 3.875 4.1875 4.4375 3.3125 3.625 3.875 4.1875 4.4375 2.25 2.8125 3.125 3.375 3.6875 3.9375 --2.3125 2.625 2.875 3.1875 3.4375 2.3125 2.625 2.875 3.1875 3.4375 2.3125 2.625 2.875 3.125 3.4375 2.3125 2.625 2.875 3.1875 3.4375 --2.125 2.375 2.6875

--------2.1875 2.4375 ----------------2.25 2.8125 3.125 3.375 3.6875 3.9375 --2.3125 2.625 2.875 3.1875 3.4375 ---------------------------------------

17.6 14.9 13.1 11.0 8.64 6.02 7.93 6.26 4.40 6.61 5.99 5.17 4.15 2.95 31.3 25.7 22.3 18.5 14.4 9.92 21.0 17.5 15.3 12.8 10.0 6.91 10.6 9.41 7.96 6.26 4.38 7.57 6.77 5.78 4.59 3.23 4.83 4.40 3.82 3.08 2.20 6.16 5.53 4.75 3.78

10.3 8.44 7.33 6.10 4.73 3.26 4.99 3.89 2.70 5.20 4.59 3.88 3.05 2.13 14.8 11.9 10.2 8.44 6.49 4.45 11.2 9.14 7.91 6.56 5.07 3.49 6.59 5.75 4.81 3.74 2.59 5.32 4.67 3.93 3.08 2.14 4.04 3.59 3.05 2.41 1.69 4.57 4.03 3.4 2.67

1.01 1.26 1.29 1.32 1.35 1.37 0.766 0.792 0.818 0.569 0.594 0.619 1.06 1.08 1.11 1.14 1.17 0.908 0.935 0.963 0.990 0.725 0.751 0.778 0.804 0.559 0.584 0.610 0.380 0.405 0.880 0.908 0.937 0.965 0.731 0.758 0.785 0.546 0.572 0.597 0.374 0.399 0.806 0.835 0.863

1.22 4.69 4.14 3.50 2.76 1.93 1.58 1.27 0.912 1.06 0.867 0.630 3.25 2.90 2.48 1.97 1.40 2.20 1.90 1.52 1.09 1.58 1.38 1.12 0.803 0.911 0.752 0.550 0.432 0.325 1.88 1.63 1.32 0.947 1.17 0.956 0.694 0.764 0.636 0.469 0.360 0.274 1.28 1.04 0.755

2.9375 --2.125 2.375 2.6875 2.9375 2.375 2.6875 2.9375 2.375 2.6875 2.9375 ------2.1875 2.4375 ----2.1875 2.4375 ----2.1875 2.4375 1.875 2.1875 2.4375 2.1875 2.4375 -------------------------------

----2.125 2.375 2.6875 2.9375 ------------------2.1875 2.4375 ---------------------------------------------------------

2.67 11.2 9.89 8.35 6.56 4.58 3.16 2.55 1.83 1.79 1.49 1.09 6.64 5.94 5.08 4.03 2.84 4.34 3.74 3.00 2.13 2.87 2.52 2.05 1.47 1.44 1.21 0.886 0.526 0.408 3.20 2.79 2.25 1.61 1.90 1.55 1.12 1.10 0.929 0.687 0.412 0.322 1.96 1.60 1.15

1.87 6.77 5.90 4.92 3.83 2.65 2.64 2.09 1.47 1.88 1.51 1.08 4.74 4.18 3.52 2.76 1.92 3.39 2.87 2.27 1.59 2.60 2.23 1.78 1.25 1.58 1.28 0.920 0.792 0.585 2.74 2.35 1.86 1.31 1.82 1.46 1.04 1.29 1.05 0.759 0.648 0.483 1.85 1.48 1.05

0.747 0.774 0.704 0.733 0.761 0.554 0.581 0.365 0.390

0.877 0.639 0.964 0.797 0.584 0.521 0.389 0.288 0.223

-------------------

-------------------

1.32 0.957 1.31 1.09 0.796 0.664 0.496 0.301 0.238

1.30 0.927 1.41 1.14 0.817 0.822 0.599 0.505 0.380

Round HSS and Pipe Section A(surf) 5.17 5.2 5.23 5.25 4.5 4.53 4.57 4.58 3.87 3.9 3.92 3.93 3.83 3.87 3.9 3.92 3.93 5.17 5.2 5.23 5.25 4.5 4.53 4.57 4.58 3.83 3.87 3.9 3.92 3.93 3.17 3.2 3.23 3.25 3.27 3.28 4.5 4.53 4.57 4.58 3.83 3.87 3.9

Shape

HSS20X0.500 HSS20X0.375 HSS18X0.500 HSS18X0.375 HSS16X0.625 HSS16X0.500 HSS16X0.438 HSS16X0.375 HSS16X0.312 HSS16X0.250 HSS14X0.625 HSS14X0.500 HSS14X0.375 HSS14X0.312 HSS14X0.250 HSS12.750X0.500 HSS12.750X0.375 HSS12.750X0.250 HSS10.750X0.500 HSS10.750X0.375 HSS10.750X0.250 HSS10X0.625 HSS10X0.500 HSS10X0.375 HSS10X0.312 HSS10X0.250 HSS10X0.188 HSS9.625X0.500 HSS9.625X0.375 HSS9.625X0.312 HSS9.625X0.250 HSS9.625X0.188 HSS8.625X0.625 HSS8.625X0.500 HSS8.625X0.375 HSS8.625X0.322 HSS8.625X0.250 HSS8.625X0.188 HSS7.625X0.375 HSS7.625X0.328 HSS7.500X0.500 HSS7.500X0.375 HSS7.500X0.312

A 28.5 21.5 25.6 19.4 28.1 22.7 19.9 17.2 14.4 11.5 24.5 19.8 15 12.5 10.1 17.9 13.6 9.16 15 11.4 7.7 17.2 13.9 10.6 8.88 7.15 5.37 13.4 10.2 8.53 6.87 5.17 14.7 11.9 9.07 7.85 6.14 4.62 7.98 7.01 10.3 7.84 6.59

OD 20 20 18 18 16 16 16 16 16 16 14 14 14 14 14 12.75 12.75 12.75 10.75 10.75 10.75 10 10 10 10 10 10 9.625 9.625 9.625 9.625 9.625 8.625 8.625 8.625 8.625 8.625 8.625 8.625 8.625 7.5 7.5 7.5

3.92 3.93 3.17 3.2 3.23 3.25 3.27 3.28 2.83 2.87 2.9 2.92 2.93 2.95 3.83 3.87 3.9 3.92 3.93 3.95 3.53 3.57 3.58 3.6 3.17 3.2 3.23 3.25 3.27 3.28 2.83 2.87 2.9 2.92 2.93 2.95 2.5 2.53 2.57 2.58 2.6 2.62 2.48 2.5 2.42

HSS7.500X0.250 HSS7.500X0.188 HSS7X0.500 HSS7X0.375 HSS7X0.312 HSS7X0.250 HSS7X0.188 HSS7X0.125 HSS6.875X0.500 HSS6.875X0.375 HSS6.875X0.312 HSS6.875X0.250 HSS6.875X0.188 HSS6.625X0.500 HSS6.625X0.432 HSS6.625X0.375 HSS6.625X0.312 HSS6.625X0.280 HSS6.625X0.250 HSS6.625X0.188 HSS6.625X0.125 HSS6X0.500 HSS6X0.375 HSS6X0.312 HSS6X0.280 HSS6X0.250 HSS6X0.188 HSS6X0.125 HSS5.563X0.500 HSS5.563X0.375 HSS5.563X0.258 HSS5.563X0.188 HSS5.563X0.134 HSS5.500X0.500 HSS5.500X0.375 HSS5.500X0.258 HSS5X0.500 HSS5X0.375 HSS5X0.312 HSS5X0.258 HSS5X0.250 HSS5X0.188 HSS5X0.125 HSS4.500X0.375 HSS4.500X0.337

5.32 4 9.55 7.29 6.13 4.95 3.73 2.51 9.36 7.16 6.02 4.86 3.66 9 7.86 6.88 5.79 5.2 4.68 3.53 2.37 8.09 6.2 5.22 4.69 4.22 3.18 2.14 7.45 5.72 4.01 2.95 2.12 7.36 5.65 3.97 6.62 5.1 4.3 3.59 3.49 2.64 1.78 4.55 4.12

7.5 7.5 7 7 7 7 7 7 6.875 6.875 6.875 6.875 6.875 6.625 6.625 6.625 6.625 6.625 6.625 6.625 6.625 6 6 6 6 6 6 6 5.563 5.563 5.563 5.563 5.563 5.5 5.5 5.5 5 5 5 5 5 5 5 4.5 4.5

2.43 2.45 2.25 2.27 2.28 3.17 3.2 3.23 3.25 3.27 3.28 2.83 2.87 2.9 2.92 2.93 2.95 2.5 2.53 2.57 2.58 2.6 2.62 2.4 2.42 2.43 2.45 2.17 2.2 2.23 2.25 2.27 2.28 2.3 2.12 2.15 2.17 2.18 2.2 2.22 2.07 2.08 2.1 2.12 2.13

HSS4.500X0.237 HSS4.500X0.188 HSS4.500X0.125 HSS4X0.313 HSS4X0.250 HSS4X0.237 HSS4X0.226 HSS4X0.220 HSS4X0.188 HSS4X0.125 HSS3.500X0.313 HSS3.500X0.300 HSS3.500X0.250 HSS3.500X0.216 HSS3.500X0.203 HSS3.500X0.188 HSS3.500X0.125 HSS3X0.250 HSS3X0.216 HSS3X0.203 HSS3X0.188 HSS3X0.152 HSS3X0.134 HSS3X0.125 HSS2.875X0.250 HSS2.875X0.203 HSS2.875X0.188 HSS2.875X0.125 HSS2.500X0.250 HSS2.500X0.188 HSS2.500X0.125 HSS2.375X0.250 HSS2.375X0.218 HSS2.375X0.188 HSS2.375X0.154 HSS2.375X0.125 HSS1.900X0.188 HSS1.900X0.145 HSS1.900X0.120 HSS1.660X0.140 Pipe1/2STD Pipe3/4STD Pipe1STD Pipe1-1/4STD Pipe1-1/2STD

2.96 2.36 1.6 3.39 2.76 2.61 2.5 2.44 2.09 1.42 2.93 2.82 2.39 2.08 1.97 1.82 1.23 2.03 1.77 1.67 1.54 1.27 1.12 1.05 1.93 1.59 1.48 1.01 1.66 1.27 0.869 1.57 1.39 1.2 1 0.823 0.943 0.749 0.624 0.625 0.23 0.31 0.46 0.62 0.75

4.5 4.5 4.5 4 4 4 4 4 4 4 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3 3 3 3 3 3 3 2.875 2.875 2.875 2.875 2.5 2.5 2.5 2.375 2.375 2.375 2.375 2.375 1.9 1.9 1.9 1.66 0.84 1.05 1.315 1.66 1.9

1.9 1.92 1.93 1.95 1.97 2.83 2.87 2.9 2.92 2.93 2.95 2.97 2.5 2.53 2.57 2.58 2.6 2.62 2.17 2.2 2.23 2.25 2.27 2.28 1.87 1.9 1.92 1.93 1.95 2.5 2.53 2.57 2.58 2.6 2.62 2.63 2.17 2.2 2.23 2.25 2.27 2.28 1.83 1.87 1.9

Pipe2STD Pipe2-1/2STD Pipe3STD Pipe3-1/2STD Pipe4STD Pipe5STD Pipe6STD Pipe8STD Pipe10STD Pipe12STD Pipe1/2XS Pipe3/4XS Pipe1XS Pipe1-1/4XS Pipe1-1/2XS Pipe2XS Pipe2-1/2XS Pipe3XS Pipe3-1/2XS Pipe4XS Pipe5XS Pipe6XS Pipe8XS Pipe10XS Pipe12XS Pipe2XXS Pipe2-1/2XXS Pipe3XXS Pipe4XXS Pipe5XXS Pipe6XXS Pipe8XXS

1 1.59 2.08 2.51 2.97 4.03 5.22 7.85 11.1 13.6 0.3 0.41 0.6 0.83 1 1.39 2.11 2.83 3.44 4.14 5.72 7.88 11.9 15 17.9 2.51 3.81 5.16 7.64 10.7 14.7 20

2.375 2.875 3.5 4 4.5 5.563 6.625 8.625 10.75 12.75 0.84 1.05 1.315 1.66 1.9 2.375 2.875 3.5 4 4.5 5.563 6.625 8.625 10.75 12.75 2.375 2.875 3.5 4.5 5.563 6.625 8.625

1.92 1.93 1.95 1.97 1.7 1.73 1.75 1.77 1.78 1.8 1.57 1.58 1.6 1.62 1.63 2.17 2.2 2.23 2.25 2.27 2.28 2.3 1.87 1.9 1.92 1.93 1.95 1.97 1.7 1.73 1.75 1.77 1.78 1.8 1.53 1.57 1.58 1.6 1.62 1.63 1.43 1.45 1.47 1.83 1.87

1.9 1.92 1.93 1.95 1.97 1.7 1.73 1.75 1.77 1.78 1.8 1.53 1.57 1.58 1.6 1.62 1.63 1.37 1.4 1.42 1.43 1.45 1.47 1.23 1.25 1.27 1.28 1.3 1.73 1.75 1.77 1.78 1.8 1.53 1.57 1.58 1.6 1.62 1.63 1.37 1.4 1.42 1.43 1.45 1.47

1.2 1.23 1.25 1.27 1.28 1.3 1.18 1.2 1.22 1.07 1.08 1.1 1.12 1.13 1.37 1.4 1.42 1.43 1.45 1.47 1.2 1.23 1.25 1.27 1.28 1.3 1.07 1.08 1.1 1.12 1.13 0.983 1 1.02 1.03 1.05 0.9 0.917 0.933 0.95 0.967 0.900 0.917 0.933 0.950

0.967 1.07 1.08 1.1 1.12 1.13 0.85 0.867 0.883 0.767 0.784 0.8 0.9 0.917 0.933 0.95 0.967 0.833 0.85 0.867 0.883 0.75 0.767 0.784 0.8 0.683 0.7 0.717 0.617 0.633 0.75 0.767 0.784 0.8 0.683 0.7 0.717 0.6 0.617 0.633 0.534 0.55 0.683 0.7 0.717

0.659 0.675 0.6 0.617 0.633 0.534 0.55 0.45 0.467

Round HSS and Pipe Section Properties from AISC Version 13.0 CD Database (Dec. 2005) and AISC 13th Edition Manua ID 19.07 19.302 17.07 17.302 14.838 15.07 15.186 15.302 15.418 15.534 12.838 13.07 13.302 13.418 13.534 11.82 12.052 12.284 9.82 10.052 10.284 8.838 9.07 9.302 9.418 9.534 9.652 8.695 8.927 9.043 9.159 9.277 7.463 7.695 7.927 8.025 8.159 8.277 7.927 8.015 6.57 6.802 6.918

t(nom) 0.5 0.375 0.5 0.375 0.625 0.5 0.4375 0.375 0.3125 0.25 0.625 0.5 0.375 0.3125 0.25 0.5 0.375 0.25 0.5 0.375 0.25 0.625 0.5 0.375 0.3125 0.25 0.1875 0.5 0.375 0.3125 0.25 0.1875 0.625 0.5 0.375 0.3125 0.25 0.188 0.375 0.328 0.5 0.375 0.3125

t(des) 0.465 0.349 0.465 0.349 0.581 0.465 0.407 0.349 0.291 0.233 0.581 0.465 0.349 0.291 0.233 0.465 0.349 0.233 0.465 0.349 0.233 0.581 0.465 0.349 0.291 0.233 0.174 0.465 0.349 0.291 0.233 0.174 0.581 0.465 0.349 0.3 0.233 0.174 0.349 0.305 0.465 0.349 0.291

wt./ft. 104.00 78.67 93.54 70.66 103.00 82.85 72.87 62.64 52.32 42.09 89.36 72.16 54.62 45.65 36.75 65.48 49.61 33.41 54.79 41.59 28.06 62.64 50.78 38.58 32.31 26.06 19.72 48.77 37.08 31.06 25.06 18.97 53.45 43.43 33.07 28.58 22.38 16.96 29.06 25.59 37.42 28.56 23.97

d/t 43 57.3 38.7 51.6 27.5 34.4 39.3 45.8 55 68.7 24.1 30.1 40.1 48.1 60.1 27.4 36.5 54.7 23.1 30.8 46.1 17.2 21.5 28.7 34.4 42.9 57.5 20.7 27.6 33.1 41.3 55.3 14.8 18.5 24.7 28.8 37 49.6 21.8 25 16.1 21.5 25.8

I 1360 1040 985 754 838 685 606 526 443 359 552 453 349 295 239 339 262 180 199 154 106 191 159 123 105 85.3 64.8 141 110 93 75.9 57.7 119 100 77.8 68.1 54.1 41.3 52.9 47.1 63.9 50.2 42.9

7.034 7.152 6.07 6.302 6.418 6.534 6.652 6.768 5.945 6.177 6.293 6.409 6.527 5.695 5.821 5.927 6.043 6.105 6.159 6.277 6.393 5.07 5.302 5.418 5.48 5.534 5.652 5.768 4.633 4.865 5.083 5.215 5.315 4.57 4.802 5.02 4.07 4.302 4.418 4.52 4.534 4.652 4.768 3.802 3.874

0.25 0.1875 0.5 0.375 0.3125 0.25 0.1875 0.125 0.5 0.375 0.3125 0.25 0.1875 0.5 0.4375 0.375 0.3125 0.28 0.25 0.1875 0.125 0.5 0.375 0.3125 0.28 0.25 0.1875 0.125 0.5 0.375 0.258 0.1875 0.134 0.5 0.375 0.258 0.5 0.375 0.3125 0.258 0.25 0.1875 0.125 0.375 0.337

0.233 0.174 0.465 0.349 0.291 0.233 0.174 0.116 0.465 0.349 0.291 0.233 0.174 0.465 0.402 0.349 0.291 0.26 0.233 0.174 0.116 0.465 0.349 0.291 0.26 0.233 0.174 0.116 0.465 0.349 0.24 0.174 0.124 0.465 0.349 0.24 0.465 0.349 0.291 0.24 0.233 0.174 0.116 0.349 0.313

19.38 14.70 34.74 26.56 22.31 18.04 13.69 9.19 34.07 26.06 21.89 17.71 13.44 32.74 28.60 25.06 21.06 18.99 17.04 12.94 8.69 29.40 22.55 18.97 17.12 15.37 11.68 7.85 27.06 20.80 14.63 10.80 7.78 26.73 20.55 14.46 24.05 18.54 15.64 13.08 12.69 9.67 6.51 16.54 15.00

32.2 43.1 15.1 20.1 24.1 30 40.2 60.3 14.8 19.7 23.6 29.5 39.5 14.2 16.5 19 22.8 25.5 28.4 38.1 57.1 12.9 17.2 20.6 23.1 25.8 34.5 51.7 12 15.9 23.2 32 44.9 11.8 15.8 22.9 10.8 14.3 17.2 20.8 21.5 28.7 43.1 12.9 14.4

35.2 26.9 51.2 40.4 34.6 28.4 21.7 14.9 48.3 38.2 32.7 26.8 20.6 42.9 38.2 34 29.1 26.4 23.9 18.4 12.6 31.2 24.8 21.3 19.3 17.6 13.5 9.28 24.4 19.5 14.2 10.7 7.84 23.5 18.8 13.7 17.2 13.9 12 10.2 9.94 7.69 5.31 9.87 9.07

4.06 4.152 4.268 3.418 3.534 3.56 3.58 3.59 3.652 3.768 2.918 2.942 3.034 3.098 3.122 3.152 3.268 2.534 2.598 2.622 2.652 2.718 2.752 2.768 2.409 2.497 2.527 2.643 2.034 2.152 2.268 1.909 1.969 2.027 2.089 2.143 1.552 1.63 1.678 1.4 0.622 0.824 1.049 1.38 1.61

0.237 0.1875 0.125 0.3125 0.25 0.237 0.226 0.22 0.1875 0.125 0.313 0.3 0.25 0.216 0.203 0.01875 0.125 0.25 0.216 0.203 0.1875 0.152 0.134 0.125 0.25 0.203 0.1875 0.125 0.25 0.1875 0.125 0.25 0.218 0.1875 0.154 0.125 0.1875 0.145 0.12 0.14 0.109 0.113 0.133 0.14 0.145

0.22 0.174 0.116 0.291 0.233 0.22 0.21 0.205 0.174 0.116 0.291 0.279 0.233 0.201 0.189 0.174 0.116 0.233 0.201 0.189 0.174 0.141 0.124 0.116 0.233 0.189 0.174 0.116 0.233 0.174 0.116 0.233 0.203 0.174 0.143 0.116 0.174 0.135 0.111 0.13 0.101 0.105 0.124 0.13 0.135

10.80 8.67 5.85 12.34 10.00 9.53 9.12 8.89 7.66 5.18 10.66 10.26 8.69 7.58 7.15 6.66 4.51 7.35 6.43 6.07 5.65 4.63 4.11 3.84 7.02 5.80 5.40 3.67 6.01 4.65 3.17 5.68 5.03 4.40 3.66 3.01 3.44 2.72 2.28 2.27 0.85 1.13 1.68 2.27 2.72

20.5 25.9 38.8 13.7 17.2 18.2 19 19.5 23 34.5 12 12.5 15 17.4 18.5 20.1 30.2 12.9 14.9 15.9 17.2 21.3 24.2 25.9 12.3 15.2 16.5 24.8 10.7 14.4 21.6 10.2 11.7 13.6 16.6 20.5 10.9 14.1 17.1 12.8 8.32 10 10.6 12.8 14.1

6.79 5.54 3.84 5.87 4.91 4.68 4.5 4.41 3.83 2.67 3.81 3.69 3.21 2.84 2.7 2.52 1.77 1.95 1.74 1.66 1.55 1.3 1.16 1.09 1.7 1.45 1.35 0.958 1.08 0.865 0.619 0.91 0.824 0.733 0.627 0.527 0.355 0.293 0.251 0.184 0.016 0.035 0.083 0.184 0.293

2.067 2.469 3.068 3.548 4.026 5.047 6.065 7.981 10 12 0.546 0.742 0.957 1.278 1.5 1.939 2.323 2.9 3.364 3.826 4.813 5.761 7.625 9.75 11.75 1.503 1.771 2.3 3.152 4.063 4.897 6.875

0.154 0.203 0.216 0.226 0.237 0.258 0.28 0.322 0.365 0.375 0.147 0.154 0.179 0.191 0.2 0.218 0.276 0.3 0.318 0.337 0.375 0.432 0.5 0.5 0.5 0.436 0.552 0.6 0.674 0.75 0.864 0.875

0.143 0.189 0.201 0.211 0.221 0.241 0.261 0.3 0.34 0.349 0.137 0.143 0.166 0.178 0.186 0.204 0.257 0.28 0.296 0.315 0.349 0.403 0.465 0.465 0.465 0.406 0.514 0.559 0.628 0.699 0.805 0.816

3.66 5.80 7.58 9.12 10.80 14.60 19.00 28.60 40.50 49.60 1.09 1.48 2.17 3.00 3.63 5.03 7.67 10.30 12.50 15.00 20.80 28.60 43.40 54.80 65.50 9.04 13.70 18.60 27.60 38.60 53.20 72.50

16.6 15.2 17.4 19 20.4 23.1 25.4 28.8 31.6 36.5 6.13 7.34 7.92 9.33 10.2 11.6 11.2 12.5 13.5 14.3 15.9 16.4 18.5 23.1 27.4 5.85 5.59 6.26 7.17 7.96 8.23 10.6

0.627 1.45 2.85 4.52 6.82 14.3 26.5 68.1 151 262 0.019 0.043 0.101 0.231 0.372 0.827 1.83 3.7 5.94 9.12 19.5 38.3 100 199 339 1.27 2.78 5.79 14.7 32.2 63.5 154

d AISC 13th Edition Manual (Dec. 2005) S 136 104 109 83.8 105 85.7 75.8 65.7 55.4 44.8 78.9 64.8 49.8 42.1 34.1 53.2 41 28.2 37 28.7 19.8 38.3 31.7 24.7 20.9 17.1 13 29.2 22.8 19.3 15.8 12 27.7 23.1 18 15.8 12.5 9.57 13.9 12.3 17 13.4 11.4

r 6.91 6.95 6.2 6.24 5.46 5.49 5.51 5.53 5.55 5.58 4.75 4.79 4.83 4.85 4.87 4.35 4.39 4.43 3.64 3.68 3.72 3.34 3.38 3.41 3.43 3.45 3.47 3.24 3.28 3.3 3.32 3.34 2.85 2.89 2.93 2.95 2.97 2.99 2.58 2.59 2.49 2.53 2.55

Z 177 135 143 109 138 112 99 85.5 71.8 57.9 105 85.2 65.1 54.7 44.2 70.2 53.7 36.5 49.2 37.8 25.8 51.6 42.3 32.5 27.4 22.2 16.8 39 30 25.4 20.6 15.5 37.7 31 23.9 20.8 16.4 12.4 18.5 16.4 23 17.9 15.1

J 2720 2080 1970 1510 1680 1370 1210 1050 886 717 1100 907 698 589 478 678 523 359 398 309 213 383 317 247 209 171 130 281 219 186 152 115 239 199 156 136 108 82.5 106 94.1 128 100 85.8

C 272 208 219 168 209 171 152 131 111 89.7 158 130 100 84.2 68.2 106 82.1 56.3 74.1 57.4 39.6 76.6 63.5 49.3 41.9 34.1 25.9 58.5 45.5 38.7 31.5 24 55.4 46.2 36.1 31.6 25.1 19.1 27.8 24.7 34.1 26.8 22.9

9.37 7.17 14.6 11.6 9.88 8.11 6.21 4.25 14.1 11.1 9.51 7.81 5.99 13 11.5 10.3 8.79 7.96 7.22 5.54 3.79 10.4 8.28 7.11 6.45 5.86 4.51 3.09 8.77 7.02 5.12 3.85 2.82 8.55 6.84 5 6.88 5.55 4.79 4.08 3.97 3.08 2.12 4.39 4.03

2.57 2.59 2.32 2.35 2.37 2.39 2.41 2.43 2.27 2.31 2.33 2.35 2.37 2.18 2.2 2.22 2.24 2.25 2.26 2.28 2.3 1.96 2 2.02 2.03 2.04 2.06 2.08 1.81 1.85 1.88 1.91 1.92 1.79 1.83 1.86 1.61 1.65 1.67 1.69 1.69 1.71 1.73 1.47 1.48

12.3 9.34 19.9 15.5 13.1 10.7 8.11 5.5 19.1 14.9 12.6 10.3 7.81 17.7 15.6 13.8 11.7 10.5 9.52 7.24 4.92 14.3 11.2 9.49 8.57 7.75 5.91 4.02 12.1 9.5 6.8 5.05 3.67 11.8 9.27 6.64 9.6 7.56 6.46 5.44 5.3 4.05 2.77 6.03 5.5

70.3 53.8 102 80.9 69.1 56.8 43.5 29.7 96.7 76.4 65.4 53.7 41.1 85.9 76.4 68 58.2 52.7 47.9 36.7 25.1 62.4 49.7 42.6 38.7 35.2 27 18.6 48.8 39 28.5 21.4 15.7 47 37.6 27.5 34.4 27.7 24 20.4 19.9 15.4 10.6 19.7 18.1

18.7 14.3 29.3 23.1 19.8 16.2 12.4 8.49 28.1 22.2 19 15.6 12 25.9 23.1 20.5 17.6 15.9 14.4 11.1 7.59 20.8 16.6 14.2 12.9 11.7 9.02 6.19 17.5 14 10.2 7.7 5.64 17.1 13.7 10 13.8 11.1 9.58 8.15 7.95 6.15 4.25 8.78 8.06

3.02 2.46 1.71 2.93 2.45 2.34 2.25 2.21 1.92 1.34 2.18 2.11 1.83 1.63 1.54 1.44 1.01 1.3 1.16 1.1 1.03 0.865 0.774 0.73 1.18 1.01 0.941 0.667 0.862 0.692 0.495 0.766 0.694 0.617 0.528 0.443 0.374 0.309 0.264 0.222 0.0388 0.0671 0.126 0.222 0.309

1.52 1.53 1.55 1.32 1.33 1.34 1.34 1.34 1.35 1.37 1.14 1.14 1.16 1.17 1.17 1.18 1.2 0.982 0.992 0.996 1 1.01 1.02 1.02 0.938 0.952 0.957 0.976 0.806 0.825 0.844 0.762 0.771 0.781 0.791 0.8 0.613 0.626 0.634 0.543 0.264 0.336 0.423 0.543 0.626

4.03 3.26 2.23 4.01 3.31 3.15 3.02 2.96 2.55 1.75 3 2.9 2.49 2.19 2.07 1.93 1.33 1.79 1.58 1.5 1.39 1.15 1.03 0.965 1.63 1.37 1.27 0.884 1.2 0.943 0.66 1.07 0.96 0.845 0.713 0.592 0.52 0.421 0.356 0.305 0.0555 0.0942 0.177 0.305 0.421

13.6 11.1 7.68 11.7 9.82 9.36 9.01 8.83 7.67 5.34 7.61 7.38 6.41 5.69 5.41 5.04 3.53 3.9 3.48 3.31 3.1 2.59 2.32 2.19 3.4 2.89 2.7 1.92 2.15 1.73 1.24 1.82 1.65 1.47 1.25 1.05 0.71 0.586 0.501 0.368 0.032 0.07 0.166 0.368 0.586

6.04 4.93 3.41 5.87 4.91 4.68 4.5 4.41 3.83 2.67 4.35 4.22 3.66 3.25 3.09 2.88 2.02 2.6 2.32 2.21 2.06 1.73 1.55 1.46 2.37 2.01 1.88 1.33 1.72 1.38 0.99 1.53 1.39 1.23 1.06 0.887 0.747 0.617 0.527 0.444 -----------

0.528 1.01 1.63 2.26 3.03 5.14 7.99 15.8 28.1 41 0.0462 0.0818 0.154 0.278 0.392 0.696 1.27 2.11 2.97 4.05 7.02 11.6 23.1 37 53.2 1.07 1.94 3.31 6.53 11.6 19.2 35.8

0.791 0.952 1.17 1.34 1.51 1.88 2.25 2.95 3.68 4.39 0.253 0.325 0.41 0.528 0.61 0.771 0.93 1.14 1.31 1.48 1.85 2.2 2.89 3.64 4.35 0.711 0.854 1.06 1.39 1.74 2.08 2.78

0.713 1.37 2.19 3.03 4.05 6.83 10.6 20.8 36.9 53.7 0.0686 0.119 0.221 0.393 0.549 0.964 1.77 2.91 4.07 5.53 9.5 15.6 31 49.2 70.2 1.6 2.91 4.89 9.5 16.7 27.4 49.9

1.25 2.89 5.69 9.04 13.6 28.6 52.9 136 302 523 0.038 0.086 0.202 0.462 0.744 1.65 3.66 7.4 11.9 18.2 39 76.6 199 398 678 2.54 5.56 11.6 29.4 64.4 127 308

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Plates t 0.1250 0.1875 0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.6875 0.7500 0.8125 0.8750 0.9375 1.0000 1.1250 1.2500 1.3750 1.5000 1.6250 1.7500 1.8750 2.0000 2.1250 2.2500 2.3750 2.5000 2.6250 2.7500 2.8750 3.0000