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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
β1
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