PROJECT SHEET NO.
1
PROJECT NO. PREPARED DATE 4/17/2013
CLIENT CHECKED DATE
PUNCHING SHEAR DESIGN TO ACI318-05
FOR INTERIOR COLUMNS
A. DESIGN INPUT
t = 450 mm THICKNESS OF SLAB
d = 377 mm EFFECTIVE DEPTH OF SLAB
cx = 500 mm WIDTH OF COLUMN IN X-DIRECTION
cy = 500 mm WIDTH OF COLUMN IN Y-DIRECTION
fy = 420 MPa YIELD STRENGTH OF REINFORCEMENT
fc' = 28 MPa CYLINDER STRENGTH OF CONCRETE
Pu = 1481 KN FACTORED POINT LOAD
Mux = 16 KN.m FACTORED MOMENT AT COLUMN ABOUT X-AXIS
Muy = 10.9 KN.m FACTORED MOMENT AT COLUMN ABOUT Y-AXIS
B. PARAMETERS
REFERENCES
fyt = 420 MPa MAXIMUM STRESS IN REINFORCEMENT SEC. 11.5.2
Ø = 0.75 STRENGTH REDUCTION FACTOR FOR SHEAR SEC. 9.3.2.3
β = 1.000 RATIO OF LONG SIDE TO SHORT SIDE OF COLUMN SEC. 11.12.2.1
αs = 40 FACTOR FOR INTERIOR COLUMNS SEC. 11.12.2.1
bx = cx + d = 877 mm x = bx / 2 = 438.5 mm
by = cy + d = 877 mm y = by / 2 = 438.5 mm
bo = 2 (bx + by) = 3508 mm LENGTH OF CRITICAL PERIMETER
TAKEN d/2 FROM COLUMN FACE
Ac = bod = 1,322.52 x103mm2 AREA OF CONCRETE RESISTING
SHEAR AT CRITICAL SECTION
CALCULATE NOMINAL SHEAR CAPACITY OF CONCRETE
TAKEN AS THE LEAST OF: SEC. 11.12.2.1
2 3,569.03 KN
VC 0.17 1 fc 'bo d
d
VC 0.083 s 2 fc 'bod 3,658.58 KN
bo
VC 0.33 fc 'bod 2,309.37 KN -- GOVERNS
Vc = 2,309.37 KN
FACTOR TO CALCULATE SHEAR DUE TO UNBALANCED MOMENT, gv: SEC. 11.12.6.1
SEC. 13.5.3.2
1 1
vx 1 0.400 vy 1 0.400 ACI 421.1R-99 SEC 3.2
2 by 2 bx
1 1
3 bx 3 by
PROPERTY OF ASSUMED CRITICAL SECTION ANALOGOUS TO POLAR MOMENT OF INERTIA, J:
b 3 b b 2 b d3
J x d y x y y 177,362.90 x106 mm4 SEC. R11.12.6.1
6 2 6 ACI 421.1R-99 SEC 3.2
b 3 b b 2 b d3
J y d x y x x 177,362.90 x106 mm4
6 2 6
, PROJECT 0 SHEET NO.
2
PROJECT NO. 0 PREPARED 0 DATE 4/17/2013
CLIENT 0 CHECKED DATE
C. DESIGN CHECKS
Pu vx Mux y vy Muy x 1.146 MPa SEC. R11.12.6.1
vu NET SHEAR STRESS IN CON-
Ac Jx Jy CRETE AT CRITICAL SECTION ACI 421.1R-99 SEC 3.2
Vc 1.310 MPa SHEAR CAPACITY OF CONCRETE
v c
bo d
(0.5 fc ') 1.984 MPa MAXIMUM ALLOWABLE SHEAR STRESS IN SECTION
CHECK IF DEPTH OF SECTION IS ADEQUATE:
Since vu < (0.5 fc ') DEPTH IS ADEQUATE! SEC. 11.12.3.2
CHECK IF PUNCHING SHEAR REINFORCEMENT IS REQUIRED:
Since vu < v c PUNCHING SHEAR REINFORCEMENT IS NOT REQUIRED! SEC. 11.5.7.1
D. DESIGN OF PUNCHING SHEAR REINFORCEMENT
Vn Vu and Vn Vc Vs SEC. 11.1.1
Vu v u Ac 1,516.182 KN
V 831.899 KN
Vs u 0.17 fc 'bod SEC. 11.12.3.1
Asv V
s 5.254 mm2/mm SEC. 11.5.7.2
s fyt d
Using 6 legs of T10 at 150 mm shear links, x 4 sides
Asv mm2/mm mm2/mm
12.566 > 5.254 REINFORCEMENT IS SUFFICIENT!
s
CHECK SPACING AND DIAMETER OF SHEAR REINFORCEMENT:
s = 150 mm < d/2 = 188.5 mm SPACING IS OK! SEC. 11.5.5.1
< 600 mm
d = 377 mm > 16(10mmØ) = 160 mm PROVIDED DIAMETER OF SEC. 11.12.3
REINFORCEMENT IS
ACCEPTABLE!
CHECK LOCATION WHERE PUNCHING SHEAR REINFORCEMENT IS NO LONGER REQUIRED:
DESIGN PROCEDURE AS
At L = 1813.1 mm from the face of the column, OUTLINED IN ACI 421.1R-99
SEC.3.4 AND APPENDIX B
bo = 12256.674 x = 2063.141 y = 2063.14086098181 mm Ac = 4,620.77 x103mm2
9 4
Jx = 10303.24 x10 mm Jy = 10303.239723068 x109 mm4
vu = 0.323 < v c.max 0.17 fc ' 0.675 MPa SHEAR REINFORCEMENT IS
NO LONGER REQUIRED!
1
PROJECT NO. PREPARED DATE 4/17/2013
CLIENT CHECKED DATE
PUNCHING SHEAR DESIGN TO ACI318-05
FOR INTERIOR COLUMNS
A. DESIGN INPUT
t = 450 mm THICKNESS OF SLAB
d = 377 mm EFFECTIVE DEPTH OF SLAB
cx = 500 mm WIDTH OF COLUMN IN X-DIRECTION
cy = 500 mm WIDTH OF COLUMN IN Y-DIRECTION
fy = 420 MPa YIELD STRENGTH OF REINFORCEMENT
fc' = 28 MPa CYLINDER STRENGTH OF CONCRETE
Pu = 1481 KN FACTORED POINT LOAD
Mux = 16 KN.m FACTORED MOMENT AT COLUMN ABOUT X-AXIS
Muy = 10.9 KN.m FACTORED MOMENT AT COLUMN ABOUT Y-AXIS
B. PARAMETERS
REFERENCES
fyt = 420 MPa MAXIMUM STRESS IN REINFORCEMENT SEC. 11.5.2
Ø = 0.75 STRENGTH REDUCTION FACTOR FOR SHEAR SEC. 9.3.2.3
β = 1.000 RATIO OF LONG SIDE TO SHORT SIDE OF COLUMN SEC. 11.12.2.1
αs = 40 FACTOR FOR INTERIOR COLUMNS SEC. 11.12.2.1
bx = cx + d = 877 mm x = bx / 2 = 438.5 mm
by = cy + d = 877 mm y = by / 2 = 438.5 mm
bo = 2 (bx + by) = 3508 mm LENGTH OF CRITICAL PERIMETER
TAKEN d/2 FROM COLUMN FACE
Ac = bod = 1,322.52 x103mm2 AREA OF CONCRETE RESISTING
SHEAR AT CRITICAL SECTION
CALCULATE NOMINAL SHEAR CAPACITY OF CONCRETE
TAKEN AS THE LEAST OF: SEC. 11.12.2.1
2 3,569.03 KN
VC 0.17 1 fc 'bo d
d
VC 0.083 s 2 fc 'bod 3,658.58 KN
bo
VC 0.33 fc 'bod 2,309.37 KN -- GOVERNS
Vc = 2,309.37 KN
FACTOR TO CALCULATE SHEAR DUE TO UNBALANCED MOMENT, gv: SEC. 11.12.6.1
SEC. 13.5.3.2
1 1
vx 1 0.400 vy 1 0.400 ACI 421.1R-99 SEC 3.2
2 by 2 bx
1 1
3 bx 3 by
PROPERTY OF ASSUMED CRITICAL SECTION ANALOGOUS TO POLAR MOMENT OF INERTIA, J:
b 3 b b 2 b d3
J x d y x y y 177,362.90 x106 mm4 SEC. R11.12.6.1
6 2 6 ACI 421.1R-99 SEC 3.2
b 3 b b 2 b d3
J y d x y x x 177,362.90 x106 mm4
6 2 6
, PROJECT 0 SHEET NO.
2
PROJECT NO. 0 PREPARED 0 DATE 4/17/2013
CLIENT 0 CHECKED DATE
C. DESIGN CHECKS
Pu vx Mux y vy Muy x 1.146 MPa SEC. R11.12.6.1
vu NET SHEAR STRESS IN CON-
Ac Jx Jy CRETE AT CRITICAL SECTION ACI 421.1R-99 SEC 3.2
Vc 1.310 MPa SHEAR CAPACITY OF CONCRETE
v c
bo d
(0.5 fc ') 1.984 MPa MAXIMUM ALLOWABLE SHEAR STRESS IN SECTION
CHECK IF DEPTH OF SECTION IS ADEQUATE:
Since vu < (0.5 fc ') DEPTH IS ADEQUATE! SEC. 11.12.3.2
CHECK IF PUNCHING SHEAR REINFORCEMENT IS REQUIRED:
Since vu < v c PUNCHING SHEAR REINFORCEMENT IS NOT REQUIRED! SEC. 11.5.7.1
D. DESIGN OF PUNCHING SHEAR REINFORCEMENT
Vn Vu and Vn Vc Vs SEC. 11.1.1
Vu v u Ac 1,516.182 KN
V 831.899 KN
Vs u 0.17 fc 'bod SEC. 11.12.3.1
Asv V
s 5.254 mm2/mm SEC. 11.5.7.2
s fyt d
Using 6 legs of T10 at 150 mm shear links, x 4 sides
Asv mm2/mm mm2/mm
12.566 > 5.254 REINFORCEMENT IS SUFFICIENT!
s
CHECK SPACING AND DIAMETER OF SHEAR REINFORCEMENT:
s = 150 mm < d/2 = 188.5 mm SPACING IS OK! SEC. 11.5.5.1
< 600 mm
d = 377 mm > 16(10mmØ) = 160 mm PROVIDED DIAMETER OF SEC. 11.12.3
REINFORCEMENT IS
ACCEPTABLE!
CHECK LOCATION WHERE PUNCHING SHEAR REINFORCEMENT IS NO LONGER REQUIRED:
DESIGN PROCEDURE AS
At L = 1813.1 mm from the face of the column, OUTLINED IN ACI 421.1R-99
SEC.3.4 AND APPENDIX B
bo = 12256.674 x = 2063.141 y = 2063.14086098181 mm Ac = 4,620.77 x103mm2
9 4
Jx = 10303.24 x10 mm Jy = 10303.239723068 x109 mm4
vu = 0.323 < v c.max 0.17 fc ' 0.675 MPa SHEAR REINFORCEMENT IS
NO LONGER REQUIRED!
