# V.CSA S16-09 - 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\S16 2009\CSA S16-09 - Beam Shear Capacity.STD is typically installed with the program.

START JOB INFORMATION
ENGINEER DATE 17-Mar-19
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
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD.PRO CODE CHECKING - S16-09 (v1.1)
*******************************************
ALL UNITS ARE - KN   MET  (UNLESS OTHERWISE Noted)
-------------------- START OF DESIGN OUTPUT OF MEMBER      1 --------------------
*MEMBER NO:     1    CRITICAL RATIO:  1.803(FAIL)     LOAD:     1
LOCATION (MET): 0.00  CONDITION: Cl. 13.8
UNIT: KN MET
STRENGTH CHECKS:
CRITICAL RATIO:  1.803(FAIL)     LOAD CASE:     1  LOCATION (MET): 0.00  CONDITION: Cl. 13.8
DESIGN FORCES:   Fx:      0.00(T)    Fy:   254.22      Fz:      0.00
Mx:   0.00E+00      My:  0.00E+00     Mz:   5.40E+02
UNIT: CM
SECTION PROPERTIES:       AZZ:      55.594 AYY:      48.896 CW:    1340255.500
SZZ:    1806.818 SYY:     194.258
IZZ:   47700.008 IYY:    2030.000
UNIT: NEW MM
MATERIAL PROPERTIES:      FYLD:      350.000   FU:      450.000
ACTUAL MEMBER LENGTH(MET):    11.000
PARAMETERS:                  KZ:  1.000  KY:  1.000  NSF:  1.000  SLF:  1.000
SLENDERNESS:   ACTUAL SLENDERNESS RATIO:     250.172  LOAD:     1   LOC.(MET):   0.000
ALLOWABLE SLENDERNESS RATIO:  300.000
SECTION CLASS:
COMPRESSION:     Class 4
FLEXURE:         Class 2
FLANGE:          Class 2
WEB:             Class 1
UNIT: KN MET
TENSION:        FORCE:    CAPACITY:    RATIO:    CRITERIA:    LOAD CASE:   LOCATION(MET):
YIELDING:        0.000    3307.500      0.000    Cl. 13.2           1        0.000
RUPTURE:         0.000    3543.750      0.000    Cl. 13.2           1        0.000
STAAD SPACE                                              -- PAGE NO.    6
STAAD.PRO CODE CHECKING - (          S16-09)   v1.1
********************************************
ALL UNITS ARE - KN   MET  (UNLESS OTHERWISE Noted)
COMPRESSION:    FORCE:    CAPACITY:    RATIO:    CRITERIA:    LOAD CASE:   LOCATION(MET):
MAJOR:           0.000    2253.274      0.000    Cl. 13.3.5(a)      1        0.000
MINOR:           0.000     253.222      0.000    Cl. 13.3.5(a)      1        0.000
INTERMEDIATE:   Ag:(CM)     KL/r:     Fe:(N MM)        λ          n:
MAJOR:          89.688     51.609      759.622      0.679        1.340
MINOR:          89.688    250.172       32.328      3.290        1.340
FLEX TOR BUCK:  FORCE:    CAPACITY:    RATIO:    CRITERIA:    LOAD CASE:   LOCATION(MET):
0.000     854.388      0.000    Cl. 13.3.5(a)      1        0.000
INTERMEDIATE:   Fe:(N MM) λ            n:
125.187    1.672        1.340
SHEAR:          FORCE:    CAPACITY:    RATIO:    CRITERIA:    LOAD CASE:   LOCATION(MET):
MAJOR:        -538.417    1042.826      0.516    Cl. 13.4.1.1       1       11.000
MINOR:           0.000    1050.727      0.000    AISC G2-1          1        0.000
INTERMEDIATE:   Aw:(CM)    Kv:          Ka:       Fcri:(N MM)  Fcre:(N MM)  Fs:(N MM)
MAJOR:          48.896    5.349       0.048       237.748       345.654      231.000
MINOR:          55.594
UNIT: KN MET
YIELDING:       FORCE:    CAPACITY:    RATIO:    CRITERIA:    LOAD CASE:   LOCATION(MET):
MAJOR:       -5.40E+02    6.49E+02      0.832    Cl. 13.5(a)        1        0.000
MINOR:        0.00E+00    9.54E+01      0.000    Cl. 13.5(a)        1        0.000
INTERMEDIATE:   Mp:        Se:         My:
MAJOR:        7.21E+02    0.00E+00    0.00E+00
MINOR:        1.06E+02    0.00E+00    0.00E+00
UNIT: KN MET
LAT TOR BUCK:   FORCE:    CAPACITY:    RATIO:    CRITERIA:    LOAD CASE:   LOCATION(MET):
MAJOR:       -5.40E+02    2.99E+02      1.803    Cl. 13.6(a)(ii     1        0.000
INTERMEDIATE:  Iyc(CM):   w 2:     w 3:       b x:     Mu:     rt:     Myr:     Lu:     Lyr:
MAJOR:        0.00E+00  2.29   0.00     0.00   3.33E+02  0.00   0.00E+00  0.00   0.00
UNIT: KN MET
INTERACTION:                RATIO:    CRITERIA:    LOAD CASE:   LOCATION(MET):
FLEXURE AND AXIAL TENSION:
C/S STRENGTH:                0.832    Cl. 13.9.1         1       0.000
MEMBER STRENGTH:             1.803    Cl. 13.9.2         1       0.000
FLEXURE AND AXIAL COMPRESSION:
C/S STRENGTH:                0.707    Cl. 13.8.2         1       0.000
MEMBER STRENGTH:             0.707    Cl. 13.8.2         1       0.000
LTB STRENGTH:                1.533    Cl. 13.8.2         1       0.000
FLEX AND SHEAR:              1.422    Cl. 14.6(a)        1       0.000
BIAXIAL FLEX:                1.803    Cl. 13.8           1       0.000
STAAD SPACE                                              -- PAGE NO.    7
INTERMEDIATE:
FLEXURE AND AXIAL TENSION:
C/S STRENGTH:   Tf:   0.00E+00  Tr:   3.31E+03  Mfz:  -5.40E+02  Mrz:   6.49E+02
FLEXURE AND AXIAL COMPRESSION:
Cf:       Mfz:       Mfy:     Cr:     Mrz:     Mry:     b :    Cez:     Cey:    w 1z:  w 1y: U1z: U1y:
C/S STR: 0.00E+00 -5.40E+02  0.00E+00 2.83E+03 6.49E+02 9.54E+01 0.85 7.98E+03 3.39E+02 0.74 0.60 1.00 1.00
MEM STR: 0.00E+00 -5.40E+02  0.00E+00 2.53E+02 6.49E+02 9.54E+01 0.85 7.98E+03 3.39E+02 0.60 0.74 1.00 1.00
LTB STR: 0.00E+00 -5.40E+02  0.00E+00 2.53E+02 2.99E+02 9.54E+01 0.85 7.98E+03 3.39E+02 0.74 0.60 1.00 1.00
FLEX SHEAR:  Mfz:  -5.40E+02  Mrz:   2.99E+02  Vfy:   2.54E+02  Vry:   1.04E+03
BIAX FLEX:   Mfz:  -5.40E+02  Mrz:   2.99E+02  Mfy:   0.00E+00  Mry:   9.54E+01
-------------------- END OF DESIGN OUTPUT OF MEMBER      1 --------------------