Punching Shear Check for Slabs - ACI 318-08

PUNCHING SHEAR CHECK FOR SLABS - ACI 318 - 08

Column - C6 - Grid A - 4 Roof

1.0 Material Properties Specified compressive strength of concrete

f'c  38MPa

Square root of specified compressive strength of concrete

SR1  SR 

f'c MPa

MPa

8.3MPa if SR1  8.3MPa SR1 otherwise

Specified yield strength for transverse reinforcement

SR1  6  MPa

SR  6  MPa

fyt  460MPa

2.0 Structural Input Column shorter plan dimension

c1  800mm

Column longer plan dimension

c2  800mm

Slab thickness

D  280mm

Cover to reinforcement in slabs

cs  30mm

Bar dia in slab

d b  16mm

Factored shear force

Vu  956kN

Factored moment

M ux  3kN m M uy  207.4kN m

 

3.0 Check for punching shear Strength reduction factor for shear calculations Refer 9.3.2.3

ϕ  0.75

c2 Ratio of long side to short side of column β  c1 Refer 11.11.2.1(a), Modification factor Refer 8.6.1

β1

λ  1

For normal weight concrete

Effective depth of slab

db d  D  cs  2

d  242  mm

Constant for computing nominal shear strength - Refer 11.11.2.1(b)

αs  40 columntype  "Interior"

40 for interior columns 30 for edge columns 20 for corner columns

3.1 Check at critical section A at a distance of d/2 from column face b 1 

c1  d if ( columntype = "Interior" )  ( columntype = "Edge short" ) d

c1 

otherwise

2

b 1  1.042 m b 2 

c2  d if ( columntype = "Interior" )  ( columntype = "Edge long" ) d

c2 

otherwise

2

b 2  1.042 m



 if (columntype = "Interior" ) b1  2b2 if (columntype = "Edge short" ) 2b1  b2 if (columntype = "Edge long" ) b1  b2 if ( columntype = "Corner" )

b oA 

Perimeter of critical section A

2 b1  b2

b oA  4.168 m 1

Fraction for calculating unbalanced moment about x axis transfered by flexure Refer 13.5.3.1 & Eq 13-1

γfx 

Fraction for calculating unbalanced moment about x axis transfered by eccentricity of shear Refer 13.5.3.1 & Eq 13-1

γvx  1  γfx

Fraction for calculating unbalanced moment about y axis transfered by flexure Refer 13.5.3.1 & Eq 13-1

γfy 

Fraction for calculating unbalanced moment about y axis transfered by eccentricity of shear Refer 13.5.3.1 & Eq 13-1 Area of concrete assumed at critical section

2

1

3



γfx  0.6

b1 b2

γvx  0.4

1 2

1

3



γfy  0.6

b2 b1

γvy  1  γfy

γvy  0.4

Ac  b oA d

Ac  1.009 m

Property analogous to polar moment of inertia divided by half length of critical section. Refer R11.11.7.2 Jfactorx 

2





3



3

b1 d b1  3 b2  d

if ( columntype = "Interior" )

3



b1 d b1  6 b2  d

if ( columntype = "Edge short" )

6



2



3



2b 1  d  b 1  2  b 2  d  2  b 1  b 2 6 b1 2





3



b1  d b1  4 b2  d  b1  b2 6 b1





if ( columntype = "Edge long" )

if ( columntype = "Corner" )

8

3

Jfactorx  3.551  10  mm Jfactory 





3



3

b2 d b2  3 b1  d

if ( columntype = "Interior" )

3



b2 d b2  6 b1  d

if ( columntype = "Edge short" )

6



2



3



2b 2  d  b 2  2  b 1  d  2  b 2  b 1





2

6 b1  b2







3

b2  d b2  4 b1  d  b2  b1



6  2b 2  b 1







if ( columntype = "Edge long" )

if ( columntype = "Corner" ) 8

3

Jfactory  3.551  10  mm Max factored shear stress

Vu

v u 

b oA d

1 1  γvx M ux  γvy M uy Jfactorx Jfactory v u  1.18 MPa

Nominal shear strength provided by concrete Eq 11-31

v c1A  ϕ 0.17  1 

Eq 11-32

v c2A  ϕ 0.083   αs





2

  λ SR

β

 2  λ SR

d b oA



Eq 11-33

v c3A  ϕ 0.33 λ SR

Refer 11.11.2.1

v c  min v c1A v c2A v c3A

Refer 11.4.7

v c2A  1.66 MPa v c3A  1.53 MPa



ShearreinforcementA 

v c1A  2.36 MPa



v c  1.53 MPa

"Reqd" if v u  v c "Not reqd" otherwise ShearreinforcementA  "Not reqd

3.0 Design of punching shear reinforcement Refer 11.11.7.2

v cmax  0.17 SR  1.048  MPa

Nominal shear strength provided by shear reinforcement

v s 

vu ϕ





 min v c v cmax

Maximum limit of nominal shear strength v smax  0.66 SR resisted by shear reinforcement Assumed spacing of bars

sd  100mm

Number of branches

Nb 

v s  0.532  MPa v smax  4.069  MPa

4 if ( columntype = "Interior" ) 3 if columntype = "Edge short"  columntype = "Edge long" 2 if ( columntype = "Corner" )

Nb  4

Number of legs

n  2

Area of shear reinf. required/m of critical AreqA  perimeter Refer 11.4.7.2



AreqA 4

d req 

Provided dia of shear reinforcement

d prov  16mm

d req  8.757  mm

Nb  n  π

v u  b oA d

Provide T16 @ 100mm c/c

0.17 ϕ d  SR

Di 

2

AreqA  482  mm

fyt

Rebar dia of shear reinforcement

Distance upto which links should be extended from the face of column



min v s v smax  b oA sd



 2  c1  2  c2

if ( columntype = "Interior" )

4 2 v u  b oA d 0.17 ϕ d  SR



 c1  2  c2

 if ( columntype = "Edge short" )

2 2 v u  b oA d 0.17 ϕ d  SR



 2  c1  c2

0.17 ϕ d  SR



 c1  c2 2

 if ( columntype = "Edge long" )

2 2 v u  b oA d



 if ( columntype = "Corner" ) Di  545  mm

4.0 Spacing restrictions - Refer Sec 11.11.3.3

  d

Max distance between column face and first line of stirrup legs

d 1 

Max spacing between adjacent stirrup legs in the first line of shear reinf

d 2  2  d

Max spacing between successive lines of shear reinf that surround the column

d 3 

2

d 2

d 1  121  mm d 2  484  mm d 3  121  mm