Compression member: PFC channel calculator

Inputs in the worked example

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Worked example — results

• ✓ N* ≤ φNc

Method, formulas and assumptions

• Area = 2*75*12+(200-2*12)*6 = 2856 mm²
• Ix = (75*200^3-(75-6)*(200-2*12)^3)/12 = 1.865e+7 mm⁴
• Centroid from web back = (2*75^2*12/2+(200-2*12)*6^2/2)/2856 = 24.744 mm
• Iy = 2*(12*75^3/12+75*12*(75/2-24.744)^2)+(200-2*12)*6^3/12+(200-2*12)*6*(24.744-6/2)^2 = 1.639e+6 mm⁴
• rx = SQRT(1.865e+7/2856) = 80.814 mm
• ry = SQRT(1.639e+6/2856) = 23.956 mm
• kf (web λey 45) = IF((200-2*12)/6*SQRT(300/250)<=45,1,(2*75*12+45*6^2/SQRT(300/250))/2856) = 1
• φNs = 0.9*1*2856*300/1000 = 771.12 kN
• λn = (le/r)√kf √(fy/250) = 4*1000/80.814*SQRT(1)*SQRT(300/250) = 54.221
• αa = 2100*(54.221-13.5)/(54.221^2-15.3*54.221+2050) = 20.555
• λ = λn + αa·αb = 54.221+20.555*0.5 = 64.498
• η = MAX(0,0.00326*(64.498-13.5)) = 0.16625
• ξ = ((64.498/90)^2+1+0.16625)/(2*(64.498/90)^2) = 1.6354
• Slenderness reduction αc = MIN(1,1.6354*(1-SQRT(1-(90/(1.6354*64.498))^2))) = 0.7825
• λn = (le/r)√kf √(fy/250) = 2*1000/23.956*SQRT(1)*SQRT(300/250) = 91.453
• αa = 2100*(91.453-13.5)/(91.453^2-15.3*91.453+2050) = 18.16
• λ = λn + αa·αb = 91.453+18.16*0.5 = 100.53
• η = MAX(0,0.00326*(100.53-13.5)) = 0.28373
• ξ = ((100.53/90)^2+1+0.28373)/(2*(100.53/90)^2) = 1.0144
• Slenderness reduction αc = MIN(1,1.0144*(1-SQRT(1-(90/(1.0144*100.53))^2))) = 0.53734
• φNc = MIN(0.7825,0.53734)*771.12 = 414.35 kN

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