Punching Shear(12Jan)

Punching Shear Page 1

Made Sheet No. DateZA 1 8-Apr-23

Check Rev. Date9-Apr-23

PROJECT TITLE: abcLOCATION: xyz

PUNCHING SHEAR CALCULATIONS AS PER ACI 318Material Properties Design Forces

Slab Thickness "h" 400 mm ### kN-m1500 mm 149.78 kN-m500 mm ### kN

Min. cover to centroid of rebar 50 mmMax. cover to centeroid of rebar 50 mmEffective depth "d = h - avg.cov 350 mm Input data only in yellow cells Compressive strength of concrete "fc' '' 35 MPa

420 MPa

Bending about x-axis1850 mm850 mm

0.4965400 mm

1.89E+06925 mm

9.64E+08925 mm

9.64E+081050.00 kN-m

Bending about y-axis850 mm

1850 mm0.311425 mm

6.49E+08425 mm

6.49E+08149.78 kN-m

Column strip -ve moment "Mux"Column Breadth "C1" Column strip -ve moment "Muy"Column Depth "C2" Factored shear force "Vu"

Yield strength of steel "fy"

b1 = c1 + d b2 = c2 + dγvx= 1 - 1/(1+2/3sqrt(b1/b2))bo = 2*b1+2* b2

Ac = 2(b1+b2)d mm2

Cx = b1/2Jx/Cx={b1d(b1+3b2)+d3}/3 mm3

C'x = b1-Cx

Jx/C'x = (Jx/Cx)(Cx/C'x ) mm3

Mux transformed = Mux

b1 = c2 + d b2 = c1 + dγvy= 1 - 1/(1+2/3sqrt(b1/b2))Cy = b1/2Jy/Cy={b1d(b1+3b2)+d3}/3 mm3

C'y = b1-Cy

Jy/C'y = (Jy/Cy)(Cy/C'y ) mm3

Muy transformed = Muy

Punching Shear Page 2

Made Sheet No. DateZA 2 8-Apr-23

Check Rev. Date9-Apr-23

PROJECT TITLE: abcLOCATION: xyz

PUNCHING SHEAR CALCULATIONS ACI 318

Check shear strength of slab without shear reinforcement0.299 MPa0.156 MPa1.236 MPa1.380 MPa1.380 MPa1.479 MPa1.257 MPa1.691 MPa

Permissible shear stress 1.257 MPa1.380 Not OK

Punching shear ratio ==================== 1.097

vu1 = Vu/Ac - γvxMux trans(C'x/Jx ) + γvy Muy trans (Cy/Jy)vu2 = Vu/Ac - γvxMux trans(C'x/Jx ) - γvy Muy trans (C'y/Jy)vu3 = Vu/Ac + γvxMux trans(Cx/Jx ) - γvy Muy trans (C'y/Jy)vu4 = Vu/Ac + γvxMux trans(Cx/Jx ) + γvy Muy trans (Cy/Jy)Hence v max

ΦVn = 0.33*Φsqrt(fc' )ΦVn = 0.17*Φ(1+2/βc)sqrt(fc' )ΦVn = 0.083*Φ(2+40d/bo)sqrt(fc' )

Punching Shear Page 3

document.xls 4/12

Made Sheet No. DateZA 1 8-Apr-23

Check Rev. Date9-Apr-23

PROJECT TITLE: abcLOCATION: xyz

PUNCHING SHEAR CALCULATIONS AS PER ACI 318Material Properties Design Forces

Slab Thickness "h" 400 mm 629.92 kN-m600 mm 0.00 kN-m600 mm 534.01 kN

Min. cover to centroid of rebar 40 mmMax. cover to centeroid of rebar 65 mmEffective depth "d = h - avg.cov 347.5 mm Input data only in yellow cells Edge distance "e" 0 mmCompressive strength of concrete "fc' '' 20 MPa

420 MPa

Bending about x-axis773.75 mm947.5 mm0.376

2495.00 mm8.67E+05

239.96 mm2.62E+08

533.79 mm1.18E+08

233.79 mm505.07 kN-m

Bending about y-axis947.5 mm

773.75 mm0.425

473.75 mm3.14E+08

473.75 mm3.14E+08

0.00 kN-m

Column strip -ve moment "Mux"Column Breadth "C1" Column strip -ve moment "Muy"Column Depth "C2" Factored shear force "Vu"

Yield strength of steel "fy"

b1 = c1 + d/2+e b2 = c2 + dγvx= 1 - 1/(1+2/3sqrt(b1/b2))bo = 2*b1+ b2

Ac =( 2b1+b2)d mm2

Cx = b21/(2b1+b2)Jx/Cx={2b21d(b1+2b2)+d3(2b1+b2)}/6b1 mm3

C'x = b1-Cx

Jx/C'x = (Jx/Cx)(Cx/C'x) mm3

ax

Mux transformed = Mux - ax*Vu

b1 = c2 + d b2 = c1 + d/2+eγvy= 1 - 1/(1+2/3sqrt(b1/b2))Cy = b1/2Jy/Cy={b1d(b1+6b2)+d3}/6 mm3

C'y = b1-Cy

Jy/C'y = (Jy/Cy)(Cy/C'y ) mm3

Muy transformed = Muy

document.xls 5/12

Made Sheet No. DateZA 2 8-Apr-23

Check Rev. Date9-Apr-23

PROJECT TITLE: abcLOCATION: xyz

PUNCHING SHEAR CALCULATIONS ACI 318

Check shear strength of slab without shear reinforcement1.341 MPa1.341 MPa-0.998 MPa-0.998 MPa1.341 MPa1.107 MPa1.711 MPa1.720 MPa

Permissible shear stress 1.107 MPa1.341 Not OK

Punching shear ratio ==================== 1.212

vu1 = Vu/Ac + γvxMux trans(Cx/Jx ) + γvy Muy trans (Cy/Jy)vu2 = Vu/Ac + γvxMux trans(Cx/Jx ) - γvy Muy trans (C'y/Jy)vu3 = Vu/Ac - γvxMux trans(C'x/Jx ) - γvy Muy trans (C'y/Jy)vu4 = Vu/Ac - γvxMux trans(C'x/Jx ) + γvy Muy trans (Cy/Jy)Hence v max

ΦVn = 0.33*Φsqrt(fc' )ΦVn = 0.17*Φ(1+2/βc)sqrt(fc' )ΦVn = 0.083*Φ(2+30d/bo)sqrt(fc' )

document.xls 6/12

document.xls 7/12

Made Sheet No. DateZA 1 8-Apr-23

Check Rev. Date9-Apr-23

PROJECT TITLE: abcLOCATION: xyz

PUNCHING SHEAR CALCULATIONS AS PER ACI 318Material Properties Design Forces

Slab Thickness "h" 400 mm 0.00 kN-m600 mm 452.05 kN-m600 mm 595.95 kN

Min. cover to centroid of rebar 40 mmMax. cover to centeroid of rebar 65 mmEffective depth "d = h - avg.cov 347.5 mm Input data only in yellow cells Edge distance "e" 0 mmCompressive strength of concrete "fc' '' 20 MPa

420 MPa

Bending about x-axis947.5 mm

773.75 mm0.425

473.75 mm3.14E+08

473.75 mm3.14E+08

0.00 kN-m

Bending about y-axis773.75 mm947.5 mm0.376

2495.000 mm8.67E+05

239.96 mm2.62E+08

533.79 mm1.18E+08

233.79 mm312.72 kN-m

Column strip -ve moment "Mux"Column Breadth "C1" Column strip -ve moment "Muy"Column Depth "C2" Factored shear force "Vu"

Yield strength of steel "fy"

b1 = c1 + db2 = c2 + d/2+eγvx= 1 - 1/(1+2/3sqrt(b1/b2))Cx = b1/2Jx/Cx={b1d(b1+6b2)+d3/6 mm3

C'x = b1-Cx

Jx/C'x = (Jx/Cx)(Cx/C'x) mm3

Mux transformed = Mux

b1 = c2 + d/2+eb2 = c1 + dγvy= 1 - 1/(1+2/3sqrt(b1/b2))bo = 2*b1+ b2

Ac =( 2b1+b2)d mm2

Cy = b21/(2b1+b2)Jy/Cy={2b21d(b1+2b2)+d3(2b1+b2)}/6b1 mm3

C'y = b1-Cy

Jy/C'y = (Jy/Cy)(Cy/C'y ) mm3

ay

Muy transformed = Muy - ay*Vu

document.xls 8/12

Made Sheet No. DateZA 2 8-Apr-23

Check Rev. Date9-Apr-23

PROJECT TITLE: abcLOCATION: xyz

PUNCHING SHEAR CALCULATIONS ACI 318

Check shear strength of slab without shear reinforcement1.137 MPa-0.312 MPa-0.312 MPa1.137 MPa1.137 MPa1.107 MPa1.711 MPa1.720 MPa

Permissible shear stress 1.107 MPa1.137 Not OK

Punching shear ratio ==================== 1.027

vu1 = Vu/Ac + γvxMux trans(Cx/Jx ) + γvy Muy trans (Cy/Jy)vu2 = Vu/Ac + γvxMux trans(Cx/Jx ) - γvy Muy trans (C'y/Jy)vu3 = Vu/Ac - γvxMux trans(C'x/Jx ) - γvy Muy trans (C'y/Jy)vu4 = Vu/Ac - γvxMux trans(C'x/Jx ) + γvy Muy trans (Cy/Jy)Hence v max

ΦVn = 0.33*Φsqrt(fc' )ΦVn = 0.17*Φ(1+2/βc)sqrt(fc' )ΦVn = 0.083*Φ(2+30d/bo)sqrt(fc' )

document.xls 9/12

document.xls 10/12

Made Sheet No. DateZA 1 8-Apr-23

Check Rev. Date9-Apr-23

PROJECT TITLE: abcLOCATION: xyz

PUNCHING SHEAR CALCULATIONS AS PER ACI 318Material Properties Design Forces

Slab Thickness "h" 400 mm 222.00 kN-m600 mm 129.40 kN-m600 mm 240.00 kN

Min. cover to centroid of rebar 40 mmMax. cover to centeroid of rebar 65 mmEffective depth "d = h - avg.cov 347.5 mm Input data only in yellow cells

150 mm150 mm

Compressive strength of concrete "fc' '' 20 MPa420 MPa

Bending about x-axis923.75 mm923.75 mm0.400

1847.50 mm6.42E+05

230.94 mm2.61E+08

692.81 mm8.70E+07

242.81 mm163.73 kN-m

Bending about y-axis923.75 mm923.75 mm0.400

230.94 mm2.61E+08

692.81 mm8.70E+07

242.81 mm71.13 kN-m

Column strip -ve moment "Mux"Column Breadth "C1" Column strip -ve moment "Muy"Column Depth "C2" Factored shear force "Vu"

Edge distance "ex"Edge distance "ey"

Yield strength of steel "fy"

b1 = c1 + d/2+ex b2 = c2 + d/2+ey

γvx= 1 - 1/(1+2/3sqrt(b1/b2))bo = b1+ b2

Ac =( b1+b2)d mm2

Cx = b21/(2b1+b2)Jx/Cx={b21d(b1+4b2)+d3(b1+b2)}/6b1 mm3

C'x = b1-Cx

Jx/C'x = (Jx/Cx)(Cx/C'x) mm3

ax

Mux transformed = Mux - ax*Vu

b1 = c2 + d/2+ey

b2 = c1 + d/2+ex

γvy= 1 - 1/(1+2/3sqrt(b1/b2))Cy = b21/2(b1+b2)Jy/Cy={b21d(b1+4b2)+d3(b1+b2)}/6b1 mm3

C'y = b1-Cy

Jy/C'y = (Jy/Cy)(Cy/C'y ) mm3

ay

Muy transformed = Muy - ay*Vu

document.xls 11/12

Made Sheet No. DateZA 2 8-Apr-23

Check Rev. Date9-Apr-23

PROJECT TITLE: abcLOCATION: xyz

PUNCHING SHEAR CALCULATIONS ACI 318

Check shear strength of slab without shear reinforcement0.734 MPa0.298 MPa-0.270 MPa0.734 MPa1.107 MPa1.711 MPa1.604 MPa

Permissible shear stress 1.107 MPa0.734 OK

Punching shear ratio ==================== 0.663

vu1 = Vu/Ac + γvxMux trans(Cx/Jx ) + γvy Muy trans (Cy/Jy)vu2 = Vu/Ac + γvxMux trans(Cx/Jx ) - γvy Muy trans (C'y/Jy)vu4 = Vu/Ac - γvxMux trans(C'x/Jx ) + γvy Muy trans (Cy/Jy)Hence v max

ΦVn = 0.33*Φsqrt(fc' )ΦVn = 0.17*Φ(1+2/βc)sqrt(fc' )ΦVn = 0.083*Φ(2+20d/bo)sqrt(fc' )

document.xls 12/12