V. CSA S16-01 - Beam Shear Capacity

Reference

Kulak, G.L. and G.Y. Grondin. 2010. Limit States Design in Structural Steel. 9th Edition. Markham, ON:CISC. Example 5.3

Problem

The W530x82 beam has a maximum shear force, v = 540 kN due to factored loads.

L = 11.0 m

The material used is G40.21 350W steel (Fy = 350 MPa) (FYLD)

Calculations

Evaluate the slenderness effects of the beam web:

$h w = 528 − 2 ( 13.3 ) 9.5 = 52.8 ⁢ < 439 k v F y = 439 5.34 350 = 54.2$

Therefore the shear capacity is calculated as:

Vr = ϕ×Aw×Fy = 0.9×528×9.5×350 = 1,043 kN

The given end moments and assumed distributed loads (which was determined to given an equivalent mid-span moment of the given example) do not result in a shear force of 540 kN. Therefore, an additional concentrated load is added near the first support.

P = 540 kN - 253.2 kN = 287 kN

The STAAD.Pro will have this load applied at 1 mm away from the left support.

Comparison

Table 1. Comparison of results
Vr (kN) 1,043 1,042.826 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Canada\CSA S16-01 - Beam Shear Capacity.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 25-June-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 11 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.92
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH FY 350000 FU 450000 RY 1.5 RT 1.2
G 7.692e+07
END DEFINE MATERIAL
1 TABLE ST W530X82
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 ENFORCED BUT FX MY MZ
1 MZ 540
2 MZ -185
1 UNI GY -40.033
1 CON GY -352.27 10.945
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT SUPPORT REACTION ALL
PARAMETER 1
FYLD 350000 ALL
FU 450000 ALL
SHE 1 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


                       STAAD.PRO CODE CHECKING - (CAN/CSA-S16-01  ) V2.1
********************************************
ALL UNITS ARE - KNS  MET  (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
*     1 ST   W530X82                  (CANADIAN SECTIONS)
FAIL     CSA-13.8.2+        4.092         1
0.00 C          0.00         540.00        0.00
STAAD SPACE                                              -- PAGE NO.    6
ALL UNITS ARE - KNS  MET  (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
MEMBER PROPERTIES (UNIT = CM)
-----------------------------
CROSS SECTION AREA =  1.05E+02   MEMBER LENGTH =  1.10E+03
IZ =  4.77E+04   SZ =  1.81E+03   PZ =  2.06E+03
IY =  2.03E+03   SY =  1.94E+02   PY =  3.03E+02
IX =  5.18E+01   CW =  1.34E+06
MATERIAL PROPERTIES (UNIT = MPA)
--------------------------------
FYLD = 350.0   FU = 450.0   E =  2.05E+05   G =  7.88E+04
SECTION CAPACITIES (UNIT - KN,M)
---------------------------------
CR1 =  3.308E+03   CR2 =  2.965E+02   SECTION CLASS 2
CRZ =  2.638E+03   CTORFLX =  2.965E+02
TENSILE CAPACITY     =  3.308E+03   COMPRESSIVE CAPACITY =  2.965E+02
FACTORED MOMENT RESISTANCE : MRY =  9.545E+01   MRZ =  1.319E+02
MU =  1.466E+02
FACTORED SHEAR RESISTANCE  : VRY =  1.043E+03   VRZ =  7.705E+02
MISCELLANEOUS INFORMATION
--------------------------
NET SECTION FACTOR FOR TENSION =  1.000
KL/RY =  250.172   KL/RZ =   51.609   ALLOWABLE KL/R =  300.000
UNSUPPORTED LENGTH OF THE COMPRESSION FLANGE (M) = 11.000
OMEGA-1 (Y-AXIS) = 1.00   OMEGA-1 (Z-AXIS) = 1.00   OMEGA-2 = 1.00
SHEAR FORCE (KNS) : Y AXIS =  2.542E+02   Z AXIS =  0.000E+00
SLENDERNESS RATIO OF WEB (H/W) =  5.28E+01