Beam design for W18x50 grade A992

≔Ω 1.67 ≔ϕ 0.9

≔Fy 50 ≔E 29000 ≔D 18 ≔tf 0.570 ≔Sx 88.93

≔Zx 1013

≔Cw 30406

≔c 1.0 ≔J 1.244

≔Iy 40.14

≔ry 1.65

≔Lb 0 ≔Cb 1.0 ≔h0 =−D tf 17.43

Yielding per AISC F2.1

≔Mp =⋅Fy Zx 420.833 ⋅

Lateral Torsional Buckling per F2.2

≔Lp =⋅⋅1.76 ry

‾‾‾―E

Fy

5.828 ≔rts =‾‾‾‾‾‾‾

―――‾‾‾‾‾⋅Iy Cw

Sx

1.982

≔Lr =⋅⋅⋅1.95 rts ―――E

⋅0.7 Fy

‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾

+――⋅J c

⋅Sx h0

‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾

+⎛⎜⎝――

⋅J c

⋅Sx h0

⎞⎟⎠

2

⋅6.76⎛⎜⎝―――

⋅0.7 Fy

E

⎞⎟⎠

2

16.957

≔Fcr ⎛⎝Lb⎞⎠ ⋅――――⋅⋅Cb

2E

⎛⎜⎝―Lb

rts

⎞⎟⎠

2

‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾+1 ⋅⋅0.078 ――

⋅J c

⋅Sx h0

⎛⎜⎝―Lb

rts

⎞⎟⎠

2

≔Mn =‖‖‖‖‖‖‖‖‖‖‖

|||||||||

|

|

|

if ≤Lb Lp

‖‖ return ⋅Fy Zx

|||

|

if ≤<Lp Lb Lr

‖‖‖‖

return min⎛⎜⎝

,⋅Cb

⎛⎜⎝

−Mp ⋅⎛⎝ −Mp ⋅⋅0.7 Fy Sx⎞⎠ ―――−Lb Lp

−Lr Lp

⎞⎟⎠

Mp

⎞⎟⎠

|

|

if ≥Lb Lr

‖‖ return min ⎛⎝ ,⋅Fcr ⎛⎝Lb⎞⎠ Sx Mp⎞⎠

420.833 ⋅

LRFD: ASD:

=⋅ϕ Mn 378.75 ⋅ =――Mn

Ω251.996 ⋅