# 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

Steel section is W410X54

## Comparison

Table 1. Comparison of results
Interaction Ratio 0.88 0.882 negligible
Beam Resistance (kN·m) 284 283.5 negligible
Beam Deflection (mm) 21 21.39 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 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;
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
1 UNI GY -7
1 UNI GY -15
LOAD COMB 3 1.25DL + 1.5 LL
1 1.25 2 1.5
PERFORM ANALYSIS
PRINT SECTION DISPL
PARAMETER 1
TRACK 2 ALL
UNL 1 ALL
FYLD 300000 ALL
BEAM 1 ALL
CHECK CODE ALL
STEEL TAKE OFF ALL
FINISH
``````

```     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 ***********
40. PARAMETER 1
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)
FX            MY             MZ       LOCATION
=======================================================================
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)
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
```