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V. CSA S16-01 - Wide Flange Beam Interaction Ratio 2

Reference

Handbook of Steel Construction, 9th Edition, H Markham, Ont.: Canadian Institute of Steel Construction, 2007.. p.4-114

Problem

Find the interaction ratio, beam and column resistance.

Given

  • E = 200,000 MPa (STEEL).
  • Fy = 300 MPa   CSA G40.21-M

Simply supported beam/column has a 3.7 m span, Ky is 1.0, Kz 1.0. Factored axial load is 2000 kN and end moments of 200 kN·m and 300 kN·m.

Steel section is W310X118

Comparison

Table 1. Comparison of results
Criteria Reference STAAD.Pro Difference
Interaction Ratio 0.940 0.941 negligible
Beam Resistance (kN·m) 606 605.5 negligible
Column Resistance (kN) 3,850 3,849 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 2.STD is typically installed with the program.

STAAD SPACE VERIFICATION CISC HANDBOOK 9th Edition PAGE 4-114
START JOB INFORMATION
ENGINEER DATE 14-Nov-18
JOB NAME Verification Example S16-01 : Compression + Major Bending
JOB CLIENT Bentley Systems Inc
JOB REF CISC Hand Book [9th Edition] 4th Printing (Page 4-114)
JOB NO CISC
JOB REV 1.0
JOB PART 1
END JOB INFORMATION
*
*
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 3.7 0;
*
MEMBER INCIDENCES
1 1 2;
*
MEMBER PROPERTY CANADIAN
1 TABLE ST W310X118
*
SUPPORTS
1 PINNED
2 FIXED BUT FY MX MY MZ
*
*
UNIT MMS NEWTON
DEFINE MATERIAL START
ISOTROPIC STEEL_ASTM_A992
E 200000
POISSON 0.3
DENSITY 7.68191e-05
ALPHA 6.5e-06
DAMP 0.03
G 76902.7
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
*
CONSTANTS
MATERIAL STEEL_ASTM_A992 ALL
*
*
UNIT METER KN
LOAD 1 AXIAL
JOINT LOAD
2 FY -2000
LOAD 2 BENDING MAJOR
JOINT LOAD
2 MZ 200
1 MZ 300
LOAD 3 LOADTYPE None  TITLE AXIAL+BENDINGMAJOR
REPEAT LOAD
1 1.0 2 1.0 
*
PERFORM ANALYSIS
*
LOAD LIST 3
*
*
UNIT MMS NEWTON
PARAMETER 1
CODE CANADIAN 2001
TRACK 2 ALL
LY 3700 ALL
LZ 3700 ALL
CMZ 0.4 ALL
FYLD 345 ALL
CHECK CODE ALL
*
STEEL MEMBER TAKE OFF ALL
FINISH

STAAD Output

                       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   W310X118                 (CANADIAN SECTIONS)
                           PASS     CSA-13.8.2C        0.941         3
                     2000.00 C          0.00         300.00        0.00
      VERIFICATION CISC HANDBOOK 9TH EDITION PAGE 4-114        -- 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 =  1.50E+02   MEMBER LENGTH =  3.70E+02
   IZ =  2.75E+04   SZ =  1.75E+03   PZ =  1.95E+03
   IY =  9.02E+03   SY =  5.88E+02   PY =  8.93E+02
   IX =  1.60E+02   CW =  1.97E+06
   MATERIAL PROPERTIES (UNIT = MPA)
   --------------------------------
   FYLD = 345.0   FU = 396.7   E =  2.00E+05   G =  7.69E+04
   SECTION CAPACITIES (UNIT - KN,M)
   ---------------------------------
   CR1 =  4.658E+03   CR2 =  3.849E+03   SECTION CLASS 2
   CRZ =  4.443E+03   CTORFLX =  3.849E+03
   TENSILE CAPACITY     =  4.553E+03   COMPRESSIVE CAPACITY =  3.849E+03
   FACTORED MOMENT RESISTANCE : MRY =  2.773E+02   MRZ =  6.055E+02
                                 MU =  2.300E+03
   FACTORED SHEAR RESISTANCE  : VRY =  7.657E+02   VRZ =  1.571E+03
   MISCELLANEOUS INFORMATION
   --------------------------
   NET SECTION FACTOR FOR TENSION =  1.000
   KL/RY =   47.714   KL/RZ =   27.326   ALLOWABLE KL/R =  200.000
   UNSUPPORTED LENGTH OF THE COMPRESSION FLANGE (M) =  3.700
   OMEGA-1 (Y-AXIS) = 1.00   OMEGA-1 (Z-AXIS) = 0.40   OMEGA-2 = 1.00
   SHEAR FORCE (KNS) : Y AXIS =  1.351E+02   Z AXIS =  0.000E+00
   SLENDERNESS RATIO OF WEB (H/W) =  2.32E+01