PROJECT CSA Axial-Flexure Resistance Calculation SECTION 1
TITLE Design Topics DATE #######
FILE File Name TIME 12:23 PM
Evaluates the axial-flexure resistance of a member
Factored Compressive Load Cf = 6000 [kN]
Factored Tensile Load Tf = 0 [kN]
Factored Tensile Resistance Tr = 1000 [kN]
Max. Factored Moment, x-axis Mfx = 3000 [kN-m]
Factored Larger End Moment, x Mfx_l = 3000 [kN-m]
Factored Smaller End Moment, x Mfx_s = -1500 [kN-m]
Max. Factored Moment, y-axis Mfy = 500 [kN-m]
Factored Larger End Moment, y Mfy_l = 500 [kN-m]
Factored Smaller End Moment, y Mfy_s = -500 [kN-m]
Load case, x-direction caseX = 1
Load case, y-direction caseY = 1
Member class class = 1
Member shape shape = 2
WWF wwf = FALSE
Gross Area Ag = 63400 [mm^2]
Effective Length Factor K = 1
Unsupported length wrt x-axis. L = 5000 [mm]
Depth of section d = 1118 [mm]
Clear depth of web bet. flange h = 1118 [mm]
Flange width b = 405 [mm]
Flange thickness t = 45 [mm]
Web thickness web = 25.9 [mm]
Moment of inertia, x-axis Ix = 1.29E+10 [mm^4]
Elastic section modulus, x-axis Sx = 23100000 [mm^3]
Plastic section modulus, x-axis Zx = 26600000 [mm^3]
Moment of inertia, y-axis Iy = 500000000 [mm^4]
Elastic section modulus, y-axis Sy = 2470000 [mm^3]
Plastic section modulus, y-axis Zy = 3870000 [mm^3]
Distance between web stiffeners a = 5000 [mm]
Load resistance factor phi = 0.9
Elastic modulus Est = 200000 [Mpa]
Yield strength Fy = 350 [Mpa]
Ultimate strength Fu = 450 [Mpa]
Shear modulus G = 77000 [Mpa]
St. venant torsion constant J = 3.10E+07 [mm^4]
Warping torsional constant Cw = 1.44E+14 [mm^6]
Web area Aw = d*web = 28956 [mm^2]
Flange area Af = 2*b*t = 36450 [mm^2]
kv = IF(a/h<1,4+5.34/(a/h)^2,5.34+4/(a/h)^2) = 5.54
KF = sqrt(kv/Fy) = 0.126
Fs_case FsCase = IF(h/web<=439*KF,1,IF(h/web<=502*KF,2,IF(h/web<=621*KF,3,4))) = 1
Inelastic buckling strength Fcri = 290*sqrt(Fy*kv)/(h/web) = 296 [Mpa]
Inelastic post-buckling strength Fti = (0.5*Fy-0.866*Fcri)*(1/sqrt(1+(a/h)^2)) = -17.7 [Mpa]
Elastic buckling strength Fcre = 180000*kv/(h/web)^2 = 535 [Mpa]
Elastic post-buckling strength Fte = (0.5*Fy-0.866*Fcre)*(1/sqrt(1+(a/h)^2)) = -62.9 [Mpa]
Fs1 = 0.66*Fy = 231 [Mpa]
Fs2 = Fcri = 296 [Mpa]
Fs3 = Fcri+Fti = 278 [Mpa]
Fs4 = Fcre+Fte = 472 [Mpa]
Ultimate shear stress Fs = index(Fs1:Fs4,FsCase,1) = 231 [Mpa]
Elastic shear resistance, y-dir. Vrey = phi*Aw*Fs/1e3 = 6020 [kN]
Elastic shear resistance, x-dir. Vrex = phi*Af*Fs/1e3 = 7578 [kN]
Plastic shear resistance, y-dir. Vrpy = 0.55*phi*web*d*Fy/1e3 = 5017 [kN]
Plastic shear resistance, x-dir. Vrpx = 0.55*phi*Af*Fy/1e3 = 6315 [kN]
End moment ratio, x-axis kx = Mfx_s/Mfx_l = -0.5
End moment ratio, y-axis ky = Mfy_s/Mfy_l = -1
Effective width beff = 200*t/sqrt(Fy) = 481 [mm]
Effective section modulus, x-axis Sex = 1/(6*d)*(beff*d^3-(beff-web)*(d-2*t)^3) = 26501147 [mm^3]
Plastic moment, x-axis Mpx = Zx*Fy/1e6 = 9310 [kN-m]
Yield moment, y-axis Myx = Sx*Fy/1e6 = 8085 [kN-m]
Plastic moment, x-axis Mpy = Zy*Fy/1e6 = 1355 [kN-m]
Yield moment, y-axis Myy = Sy*Fy/1e6 = 865 [kN-m]
Lat. Supported Mrx, Class 1 sMrx1 = phi*Mpx = 8379 [kN-m]
Lat. Supported Mrx, Class 2 sMrx2 = phi*Mpx = 8379 [kN-m]
Lat. Supported Mrx, Class 3 sMrx3 = phi*Myx = 7277 [kN-m]
Lat. Supported Mrx, Class 4 sMrx4 = phi*Sex*Fy/1e6 = 8348 [kN-m]
Laterally supported bending, x sMrx = index(sMrx1:sMrx4,class,1) = 8379 [kN-m]
Effective section modulus, y-axis Sey = 1/(6*beff)*(2*t*beff^3+(d-2*t)*web^3) = 3477616 [mm^3]
Lat. Supported Mry, Class 1 sMry1 = phi*Mpy = 1219 [kN-m]
Lat. Supported Mry, Class 2 sMry2 = phi*Mpy = 1219 [kN-m]
Lat. Supported Mry, Class 3 sMry3 = phi*Myy = 778 [kN-m]
Lat. Supported Mry, Class 4 sMry4 = phi*Sey*Fy/1e6 = 1095 [kN-m]
Laterally supported bending, y sMry = index(sMry1:sMry4,class,1) = 1219 [kN-m]
Mmax between lateral support? M_l = IF(Mfx>Mfx_l,true,false) = FALSE
w = 1.75+1.05*kx+0.3*kx^2 = 1.3
Inflence of moment distribution w2 = IF(M_l,1,IF(w<=2.5,w,2.5)) = 1.3
Critical elastic moment Mu = w2*PI()/L*sqrt(Est*Iy*G*J+(PI()*Est/L)^2*Iy*Cw)/1e6 = 30296 [kN-m]
Length category length = IF((Mu>0.67*Mpx),1,2) = 1
Lat. Unsupported Mrx,mid, Cl.1,2 uMrxi12 = 1.15*phi*Mpx*(1-0.28*Mpx/Mu) = 8807 [kN-m]
Lat. Unsupported Mrx,mid, Cl.3,4 uMrxi34 = 1.15*phi*Myx*(1-0.28*Myx/Mu) = 7743 [kN-m]
Lat. Unsupported Mrx, mid-length uMrxi = IF(class<=2,uMrxi12,uMrxi34) = 8807 [kN-m]
Lat. Unsupported Mrx,long, All Cl. uMrxl = phi*Mu = 27266 [kN-m]
Lat. Unsupported Mrx uMrx = min(IF(length=1,uMrxi,uMrxl),sMrx) = 8379 [kN-m]
Lat. Unsupported Mry uMry = sMry = 1219 [kN-m]
Bi-axial bending check, x-axis sbib = Mfx/sMrx+Mfy/sMry = 0.77 O.K.
Bi-axial bending check, y-axis ubib = Mfx/uMrx+Mfy/uMry = 0.77 O.K.
n = IF(wwf,2.24,1.34) = 1.34
Compressive Resistance, l=0 Cr0 = phi*Ag*Fy/1000 = 19971 [kN]
ry = sqrt(Iy/Ag) = 88.8 [mm]
Lambda lam = K*L/ry*sqrt(Fy/(PI()^2*Est)) = 0.750
Compressive Resistance Cr = phi*Ag*Fy*(1+lam^(2*n))^(-1/n)/1000 = 15041 [kN]
w1x = if(caseX=1,IF((.6-.4*kx)>=.4,.6-.4*kx,.4),IF(caseX=2,1,0.85)) = 0.8
w1y = if(caseY=1,IF((.6-.4*ky)>=.4,.6-.4*ky,.4),IF(caseY=2,1,0.85)) = 1
Euler buckling strength, x-axis Cex = PI()^2*Est*Ix/L^2/1000 = 1018543 [kN]
Euler buckling strength, y-axis Cey = PI()^2*Est*Iy/L^2/1000 = 39478 [kN]
U1x = w1x/(1-Cf/Cex) = 0.80
U1x_ = IF(U1x<1,1,U1x) = 1
U1y = w1y/(1-Cf/Cey) = 1.18
Modifier for Class 1 I-shapes I1 = IF(shape =2,0.85,1) = 0.85
Modifier for Class 1 I-shapes I2 = IF(shape =2,0.6,1) = 0.6
Cross-sectional strength cross = Cf/Cr0+I1*Mfx/sMrx+I2*Mfy/sMry = 0.85 O.K.
Overall member strength overall = Cf/Cr+I1*U1x*Mfx/sMrx+I2*U1y*Mfy/sMry = 0.93 O.K.
Lat. torsional buckling strength lateral = Cf/Cr+I1*U1x_*Mfx/uMrx+I2*U1y*Mfy/sMry = 0.99 O.K.
Bending & tension ba = Tf/Tr+Mfx/sMrx+Mfy/sMry = 0.77 O.K.
bb12 = (-Tf*Zx/(sMrx*Ag))-Tf*Zy/(sMry*Ag)+Mfx/sMrx+Mfy/sMry = 0.77
bb34 = (-Tf*Sx/(uMrx*Ag))-Tf*Sy/(uMry*Ag)+Mfx/uMrx+Mfy/uMry = 0.77
Bending & tension bb = IF(class<=2,bb12,bb34) = 0.77 O.K.
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