SHS / RHS beam: bending & shear calculator

Inputs in the worked example

The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.

Worked example — results

• ✓ Bending
• ✓ Shear
• ✓ Deflection

Method, formulas and assumptions

• Ix = (100*200^3-(100-2*6)*(200-2*6)^3)/12 = 1.794e+7 mm⁴
• Zx = 2*1.794e+7/200 = 1.794e+5 mm³
• Sx = 100*200^2/4-(100-2*6)*(200-2*6)^2/4 = 2.224e+5 mm³
• Flange λe (b − 2t)/t √(fy/250) = (100-2*6)/6*SQRT(350/250) = 17.354
• Web λe = (200-2*6)/6*SQRT(350/250) = 37.074
• Ze (compact λf ≤ 30, λw ≤ 82; linear to λy 40/115) = IF(AND(17.354<=30,37.074<=82),MIN(2.224e+5,1.5*1.794e+5),IF(AND(17.354<=40,37.074<=115),1.794e+5+MIN((40-17.354)/10,(115-37.074)/33,1)*(MIN(2.224e+5,1.5*1.794e+5)-1.794e+5),1.794e+5*MIN(40/17.354,1))) = 2.224e+5 mm³
• φMs = 0.9*350*2.224e+5/1E6 = 70.066 kNm
• M* = wL²/8 = 12*5^2/8 = 37.5 kNm
• φVu = 0.9·0.6 fy·2(d − 2t)t = 0.9*0.6*350*2*(200-2*6)*6/1000 = 426.38 kN
• V* = 12*5/2 = 30 kN
• Deflection = 5*8*(5*1000)^4/(384*200000*1.794e+7) = 18.146 mm
• L/250 = 5*1000/250 = 20 mm

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