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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

Table 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 CONNECT Edition\Samples\ Verification Models\09 Steel Design\Canada\S16 2001\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