# V. CSA S16-01 - Wide Flange Beam Interaction Ratio 3

## Reference

Handbook of Steel Construction, 9th Edition, H Markham, Ont.: Canadian Institute of Steel Construction, 2007. p4-115.

## Problem

Find the interaction ratio, beam, and column resistance.

## Given

• E = 200,000 MPa (STEEL)
• Fy = 345 MPa (ASTM A992)

Simply supported beam/column has a 3.7 m span, Ky is 1.0, Kz 1.0, Lu = 3.7 m

The factored axial load is 2,000 kN and end moments of 200 kN·m and 300 kN·m in the strong axis and 50 kN·m at each end in the weak axis.

Steel section is W310X129.

## Comparison

Table 1. CAN/CSA-S16 comparison
Interaction Ratio 0.990 0.990 none
Beam Resistance, Weak axis (kN·m) 308 307.7 negligible
Beam Resistance, Strong axis (kN·m) 671 670.7 negligible
Column Resistance (kN) 4,240 4,242 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 3.STD is typically installed with the program.

``````STAAD SPACE VERIFICATION CISC HANDBOOK 9th Edition PAGE 4-115
START JOB INFORMATION
ENGINEER DATE 14-Nov-18
JOB NAME Verification Example S16-01 : Compression + Bending(s)
JOB CLIENT Bentley Systems Inc
JOB REF CISC Hand Book [9th Edition] 4th Printing (Page 4-115)
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 W310X129
*
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
2 MX 50
1 MX 50
1 1.0 2 1.0 3 1.0
*
PERFORM ANALYSIS
*
*
*
UNIT MMS NEWTON
PARAMETER 1
TRACK 2 ALL
LY 3700 ALL
LZ 3700 ALL
SSY 0 ALL
SSZ 0 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        0.990         4
2000.00 C        -50.00         300.00        0.00
VERIFICATION CISC HANDBOOK 9TH EDITION PAGE 4-115        -- PAGE NO.    5
ALL UNITS ARE - KNS  MET  (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
MEMBER PROPERTIES (UNIT = CM)
-----------------------------
CROSS SECTION AREA =  1.65E+02   MEMBER LENGTH =  3.70E+02
IZ =  3.08E+04   SZ =  1.94E+03   PZ =  2.16E+03
IY =  1.00E+04   SY =  6.49E+02   PY =  9.91E+02
IX =  2.13E+02   CW =  2.21E+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 =  5.123E+03   CR2 =  4.242E+03   SECTION CLASS 1
CRZ =  4.892E+03   CTORFLX =  4.242E+03
TENSILE CAPACITY     =  5.008E+03   COMPRESSIVE CAPACITY =  4.242E+03
FACTORED MOMENT RESISTANCE : MRY =  3.077E+02   MRZ =  6.707E+02
MU =  2.638E+03
FACTORED SHEAR RESISTANCE  : VRY =  8.537E+02   VRZ =  1.731E+03
MISCELLANEOUS INFORMATION
--------------------------
NET SECTION FACTOR FOR TENSION =  1.000
KL/RY =   47.527   KL/RZ =   27.081   ALLOWABLE KL/R =  200.000
UNSUPPORTED LENGTH OF THE COMPRESSION FLANGE (M) =  3.700
OMEGA-1 (Y-AXIS) = 1.00   OMEGA-1 (Z-AXIS) = 1.00   OMEGA-2 = 1.00
SHEAR FORCE (KNS) : Y AXIS =  1.351E+02   Z AXIS =  2.703E+01
SLENDERNESS RATIO OF WEB (H/W) =  2.11E+01
```