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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

Calculate Equivalent Concentrated Load

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.

R 1 = w f L 2 + M 1 M 2 L = 40.17 × 11.0 2 + 540 185 11.0 = 253.2  kN

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
Criteria Reference STAAD.Pro Difference
Vr (kN) 1,043 1,042.826 negligible

STAAD.Pro Input File

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.

STAAD SPACE
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
MEMBER PROPERTY CANADIAN
1 TABLE ST W530X82
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 ENFORCED BUT FX MY MZ
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
JOINT LOAD
1 MZ 540
2 MZ -185
MEMBER LOAD
1 UNI GY -40.033
1 CON GY -352.27 10.945
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT SUPPORT REACTION ALL
PARAMETER 1
CODE CANADIAN 2009
FYLD 350000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD.Pro Output

                       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      
  SECTION: ST   W530X82                 (CANADIAN SECTIONS)
  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 --------------------