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PROJECT CSA Axial-Flexure Resistance Calculation SECTION 1 TITLE Design Topics DATE ####### FILE File Name TIME 12:23 PM DESCRIPTION Evaluates the axial-flexure resistance of a member INPUT 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] CALCULATION 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. Engineering Calculation Template Manual INTRODUCTION 1. This template provides necessary macros to build up engineering calculations for quick re-calc and clear presentation. 2. Key functions: - set up formulae - retrieve maximum 'efficiency' value - set up border for printing - page setup for printing HOW TO USE [0] Save the file 'template_mg123.xls' with another appropriate name. Ensure this file (mg123.xls) is put in the same directory as your newly saved file. [1] Use the styles as in sheet 'sample' to fill in title, logo, etc. [2] Define variables, equations, units. [3] Use macro 'formatted' to calculate the defined formulae. Bring up a list of macro by ALT-F8. SHEET STRUCTURE Ranges: Column A: section descriptions Column B: variable/formula description Column C: variable name, to be referenced in formulae Column D, F: equal sign Column E: formulae Column G: variable values or formula results Column H: units or efficiency evaluation Sheet/project description: cells A1:H7 Maximum efficiency: cell I1 number of rows used: cell J1 calculation contents: from row 8 MACRO DESCRIPTIONS formatted validate and calculate all the variables and formulae. All variable referenced in the formulae have to be defined in the same sheet. The name of variable cannot duplicate the 'reserved words' of Excel, such as SIN, SQRT. getEfficiency most engineering calculations end up with some 'efficiency' or 'sufficiency' evaluations, i.e. calculations by 'load/capacity'. If many sufficiency/efficiency calculations are formatted as that in sheet 'sample', this macro will pick up the maximum (the limit value) of them and display it in cell i1. pageSetup This macro sets up margins and footers. SetPrintBorders This macro sets up borders for printing. So far it is quite slow and needs improvement. setWidth Adjust column widths so that it looks like that in sheet 'sample'. CREDITS This template is first created by Mr. Michael Gedig using the ideas from Dr. S. F. Stiemer's and Mr. David S.K. "auto123.wks". Mr. Ye Zhou got his hands on it and further improved it a bit.