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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.

				
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posted:11/16/2011
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