# 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
Interaction Ratio 0.940 0.941 negligible
Beam Resistance (kN·m) 606 605.5 negligible
Column Resistance (kN) 3,850 3,849 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Canada\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;
*
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
2 FY -2000
2 MZ 200
1 MZ 300
1 1.0 2 1.0
*
PERFORM ANALYSIS
*
*
*
UNIT MMS NEWTON
PARAMETER 1
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.PRO CODE CHECKING - (CAN/CSA-S16-01  ) V2.1
********************************************
ALL UNITS ARE - KNS  MET  (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
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)
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
```