Beam Column for Z Section: (Reference: AISI S100-2007)
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Given:
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Section Information
Inside bend radius of arc: R = 4.763 mm  
Depth of web: A' = 114 mm  
width of flange: B' = 56 mm  
Thickness: t = 1.524 mm  
width of lips: C' = 15.24 mm  
Lip bend angle: f = 90^o  
Radius of arc centerline: r = R + t / 2 = 4.763 + 1.524 / 2 =5.525 mm
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Member Information
Bending coefficient: C_b = 1   
unSupported length about axis X: L_x = 1270 mm  
unSupported length about axis Y: L_y = 1270 mm  
torsional unSupported length: L_t = 1270 mm  
Effective length factor about X: K_x = 1   
Effective length factor about Y: K_y = 1   
Yield strength of steel: F_y =350 MPa  
Moment coefficient about axis X: C_mx = 0.85   
Moment coefficient about axis Y: C_my = 1   
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Loading
Factored compressive load: P_f = 18 kN  
Factored moment about axis X: M_fx = 1 kN.m  
Factored moment about axis Y: M_fy = 0.8 kN.m  
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Results:
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Area of cross section: A_g = 367.1 mm²  
moment of inertia about axis X: I_x = 765000 mm⁴  
moment of inertia about axis Y: I_y = 273000 mm⁴  
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r_x = (I_x / A_g)^0.5 = (7.65e+05 / 367.1)^0.5 =45.65 mm
r_y = (I_y / A_g)^0.5 = (2.73e+05 / 367.1)^0.5 =27.27 mm
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Slendness Ratio
Slendness ratio about axis X: K_x. L_x/ r_x = 1.0 x 1,270.0 / 45.65 =27.8 
Slendness ratio about axis Y: K_y. L_y/ r_y = 1.0 x 1,270.0 / 27.27 =46.6 
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Axial Compressive Strength P_r
P_r = f_c . A_e . F_n = 54.5 kN, for detail, see: cfzaxial.aspx  
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Axial Compressive Strength P_r0
P_r0 = f_c . A_g . F_y = 0.8 x 367.1 x 350.0 /1,000 =102.8 kN, Eq. C4.1-1
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Magnification Factors a_x, a_y
P_ex = p² . E . I_x / (K_x . L_x)² = 3.14² x 2.03e+05 x 7.65e+05 x 10^-3 / (1.0 x 1,270.0)² =950.3 kN, Eq. C5.2.2-6
P_ey = p² . E . I_y / (K_y . L_y)² = 3.14² x 2.03e+05 x 2.73e+05 x 10^-3 / (1.0 x 1,270.0)² =339.1 kN, Eq. C5.2.2-7
a_x = 1 - P_f / P_ex = 1 - 18.0 / 950.3 =0.98 Eq. C5.2.2-4
a_y = 1 - P_f / P_ey = 1 - 18.0 / 339.1 =0.95 Eq. C5.2.2-5
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Flexural Strength
M_rx = 3.6 kN.m, for detail, see: cfzflex.aspx  
M_ry = 1.6 kN.m, for detail, see: cfzflex.aspx  
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Combined Compressive Axial Load and Bending
P_f / P_r + C_mx . M_fx / (M_rx . a_x) + C_my . M_fy / (M_ry . a_y) = 18.0 / 54.5 + 0.85 x 1.0 / (3.6 x 0.98) + 1.0 x 0.8 / (1.6 x 0.95) =1.1 Eq. C5.2.2-1 
P_f / P_r0 + M_fx / M_rx + M_fy / M_ry = 18.0 / 102.8 + 1.0 / 3.6 + 0.8 / 1.6 =0.95 Eq. C5.2.2-2