Spreader beam (CHS strut) for a two-point lift 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

• ✓ Combined utilisation ≤ 1.0
• ✓ Section not slender in compression
• ✓ N* ≤ φNc

Method, formulas and assumptions

• Outside diameter = CHOOSE(1,168.3,219.1,273.1,323.9,406.4) = 168.3 mm
• Wall thickness = CHOOSE(1,6.4,6.4,9.3,9.5,12.7) = 6.4 mm
• Area = PI()*(168.3-6.4)*6.4 = 3255.2 mm²
• Second moment = PI()/64*(168.3^4-(168.3-2*6.4)^4) = 1.068e+7 mm⁴
• Radius of gyration = SQRT(1.068e+7/3255.2) = 57.285 mm
• Elastic modulus = 1.068e+7/(168.3/2) = 1.269e+5 mm³
• Self-weight = 3255.2*78.5/1000000 = 0.25553 kN/m
• Strut force N* = γ·DLF·W/(2tanα) = 1.5*1.25*200/(2*TAN(RADIANS(60))) = 108.25 kN
• Top sling tension (factored) = 1.5*1.25*200/(2*SIN(RADIANS(60))) = 216.51 kN
• Self-weight moment 1.2w·s²/8 = 1.2*0.25553*6^2/8 = 1.3799 kNm
• λn = (L/r)√(fy/250) = 6*1000/57.285*SQRT(350/250) = 123.93
• αa = 2100*(123.93-13.5)/(123.93^2-15.3*123.93+2050) = 14.949
• λ = λn + αa·αb = 123.93+14.949*(-0.5) = 116.45
• η = MAX(0,0.00326*(116.45-13.5)) = 0.33563
• ξ = ((116.45/90)^2+1+0.33563)/(2*(116.45/90)^2) = 0.89887
• αc = 0.89887*(1-SQRT(1-(90/(0.89887*116.45))^2)) = 0.43986
• φNc = 0.9αc·A·fy = 0.9*0.43986*3255.2*350/1000 = 451.02 kN
• φMs = 0.9fy·Z = 0.9*350*1.269e+5/1000000 = 39.987 kNm
• Check: d/t·(fy/250) (≤ 82 non-slender) = 168.3/6.4*350/250 = 36.816
• Limit: 1.0 = 1 = 1
• Limit: slenderness 82 = 82 = 82
• Interaction N*/φNc + M*/φMs = 108.25/451.02+1.3799/39.987 = 0.27453
• End fittings, padeyes and the sling/shackle WLL must be checked separately. A simple N/φNc + M/φMs sum is conservative compared with AS 4100 8.4 in-plane interaction.

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