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V. CSA S16-01 - Wide Flange Beam Interaction Ratio 1

Reference

CAN/CSA-S16.1-94, National Standard of Canada, Limit States Design of Steel Structures. The Canadian Standards Association, 1994 with CISC (Canadian Institute of Steel Construction) handbook. CISC Example 1 page 5-91.

Problem

Find the interaction ratio, beam resistance and beam deflection.

Given

  • E = 200000 MPa (STEEL)
  • Fy = 300 Mpa  CSA G40.21-M

Simply supported beam has a 8.0 m span; Ky is 1.0, Kz 1.0, unsupported length 1.0 m

Allowable Live Load deflection, L/300 = 8000/300 = 27 mm

Factored Uniform Load IS 7 kN/m DEAD, 15 kN/m LIVE.

Steel section is W410X54

Comparison

表 1. Comparison of results
Criteria Reference STAAD.Pro Difference
Interaction Ratio 0.88 0.882 negligible
Beam Resistance (kN·m) 284 283.5 negligible
Beam Deflection (mm) 21 21.39 negligible

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\Canada\CSA S16-01 - Wide Flange Beam Interaction Ratio 1.STD is typically installed with the program.

STAAD SPACE VERIFICATION CISC 1994 HANDBOOK EXAMPLE PAGE 5-91
START JOB INFORMATION
ENGINEER DATE 21-Sep-18
END JOB INFORMATION
* CISC EXAMPLE 1 PAGE 5-91, LIMIT STATES DESIGN, CSA-S16.1-94
* SIMPLY SUPPORTED BEAM WITH UNIFORM LOAD
* LIVE LOAD DEFLECTION OF L/300
UNIT MMS KN
JOINT COORDINATES
1 0 0 0; 2 8000 0 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY CANADIAN
1 TABLE ST W410X54
UNIT METER KN
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 1.99947e+08
POISSON 0.3
END DEFINE MATERIAL
UNIT MMS KN
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 PINNED
2 FIXED BUT MY MZ
UNIT METER KN
LOAD 1 DEAD
MEMBER LOAD
1 UNI GY -7
LOAD 2 LIVE
MEMBER LOAD
1 UNI GY -15
LOAD COMB 3 1.25DL + 1.5 LL
1 1.25 2 1.5 
PERFORM ANALYSIS
LOAD LIST 2
PRINT SECTION DISPL
LOAD LIST 3
PARAMETER 1
CODE CANADIAN 2001
TRACK 2 ALL
UNL 1 ALL
FYLD 300000 ALL
BEAM 1 ALL
CHECK CODE ALL
STEEL TAKE OFF ALL
FINISH

STAAD Output

     MEMBER SECTION DISPLACEMENTS
     ----------------------------
     UNITS ARE - CM  
     MEMB  LOAD     GLOBAL X,Y,Z DISPL FROM START TO END JOINTS AT 1/12TH PTS
       1     2       0.0000    0.0000    0.0000    0.0000   -0.5623    0.0000
                     0.0000   -1.0822    0.0000    0.0000   -1.5237    0.0000
                     0.0000   -1.8590    0.0000    0.0000   -2.0681    0.0000
                     0.0000   -2.1392    0.0000    0.0000   -2.0681    0.0000 
                     0.0000   -1.8590    0.0000    0.0000   -1.5237    0.0000
                     0.0000   -1.0822    0.0000    0.0000   -0.5623    0.0000
                     0.0000    0.0000    0.0000
     MAX LOCAL  DISP =    2.13916   AT     400.00  LOAD    2   L/DISP=    373
         ************ END OF SECT DISPL RESULTS ***********
    39. LOAD LIST 3
    40. PARAMETER 1
    41. CODE CANADIAN 2001
    42. TRACK 2 ALL
    43. UNL 1 ALL
    44. FYLD 300000 ALL
    45. BEAM 1 ALL
    46. CHECK CODE ALL
 STEEL DESIGN    
      VERIFICATION CISC 1994 HANDBOOK EXAMPLE PAGE 5-91        -- PAGE NO.    4 
                       STAAD.PRO CODE CHECKING - (CAN/CSA-S16-01  ) V2.1           
                       ********************************************
 ALL UNITS ARE - KNS  MET  (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       1 ST   W410X54                  (CANADIAN SECTIONS)
                           PASS     CSA-13.8.2+        0.882         3 
                        0.00 C          0.00        -250.00        4.00
      VERIFICATION CISC 1994 HANDBOOK EXAMPLE PAGE 5-91        -- PAGE NO.    5 
 ALL UNITS ARE - KNS  MET  (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
   MEMBER PROPERTIES (UNIT = CM)
   -----------------------------
   CROSS SECTION AREA =  6.81E+01   MEMBER LENGTH =  8.00E+02
   IZ =  1.86E+04   SZ =  9.23E+02   PZ =  1.05E+03
   IY =  1.01E+03   SY =  1.14E+02   PY =  1.77E+02
   IX =  2.26E+01   CW =  3.88E+05
   MATERIAL PROPERTIES (UNIT = MPA)
   --------------------------------
   FYLD = 300.0   FU = 345.0   E =  2.00E+05   G =  7.69E+04
   SECTION CAPACITIES (UNIT - KN,M)
   ---------------------------------
   CR1 =  1.839E+03   CR2 =  2.646E+02   SECTION CLASS 1
   CRZ =  1.556E+03   CTORFLX =  2.646E+02
   TENSILE CAPACITY     =  1.797E+03   COMPRESSIVE CAPACITY =  2.646E+02
   FACTORED MOMENT RESISTANCE : MRY =  4.779E+01   MRZ =  2.835E+02 
                                 MU =  3.952E+03
   FACTORED SHEAR RESISTANCE  : VRY =  5.386E+02   VRZ =  4.604E+02
   MISCELLANEOUS INFORMATION
   --------------------------
   NET SECTION FACTOR FOR TENSION =  1.000
   KL/RY =  207.732   KL/RZ =   48.407   ALLOWABLE KL/R =  300.000
   UNSUPPORTED LENGTH OF THE COMPRESSION FLANGE (M) =  1.000
   OMEGA-1 (Y-AXIS) = 1.00   OMEGA-1 (Z-AXIS) = 1.00   OMEGA-2 = 1.00
   SHEAR FORCE (KNS) : Y AXIS =  0.000E+00   Z AXIS =  0.000E+00
   SLENDERNESS RATIO OF WEB (H/W) =  5.08E+01
    47. STEEL TAKE OFF ALL
      VERIFICATION CISC 1994 HANDBOOK EXAMPLE PAGE 5-91        -- PAGE NO.    6 
 STEEL TAKE OFF  
   STEEL TAKE-OFF
   --------------
      PROFILE                 LENGTH(METE)      WEIGHT(KN  )
   In Steel Takeoff the density of steel is assumed for members with no density.
   ST  W410X54                      8.00             4.185
                                          ----------------
                                    TOTAL =          4.185