48 Concrete Shear
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CONCRETE SHEAR
Page 48 - 1
TANK SUPPORT
48
At column 39 to 139 Seismic ENGINEERING with the SPREADSHEET Copyright 2006 American Society of Civil Engineers A
B
C
BEARING ON CONCRETE 4 ksi f'c 290 k_ult Punching 1 unitless ratio P_ult 290.0 k_ult f_brg Фbrg A 1 req'd
3.4 ksi_ult 0.7
A2
122 in2 452 in2
multiplier A req'd
2.00 61 in2
D
E
F
G
P_ult
290.0 k_ult
Ao
6786 in2
I
2
J
K
L
M
N
1
along this plane
convert circular column to equivalent square
452.4 in2 452 in² > 122 in²
188 in
H
Figure 48-1 Bearing area and edge distance
A_pl
1.00 unitless 36.0 in
21562345.xls
A 2 is measured
CIRCULAR PUNCHING SHEAR dia 24.00 in
βc d bo
y
ultimate strength of concrete SEISMIC ultimate load LRFD factor required 0.85 * f'c allowable bearing on concrete 11.0 in on a side minimum area of supporting surface not to exceed 2 ACI 10.17.1 A1/A2
Christy 7:14 08/31/09
1.0 * 290.0 ratio = 1 for circular column depth to tension reinforcing (dia + d)*pi bo * d 36.0 * 188
row 30 Critical Section Unloaded Area d/2 Face + d
Vc 33
αs
2575 k
02 ACI 11.12.2.1 (11-33) 6 * (4 * 1000)^0.5 /1000 * 188 * 36.0 where (2 + 4/βc ) = 6 factor (αs d /bo + 2) √ f'c bo d 02 ACI 11.12.2.1 (11-34) (40 * 36.0 /188.5 + 2) * (4 * 1000)^0.5 /1000 * 188 * 36.0
Vc 34
40 unitless 4137 k
Vc 35
1717 k
Ao 4 √ f'c 02 ACI 11.12.2.1 (11-35) 6,786 * 4 * (4 * 1000)^0.5 * 0.85 /1000
Vc min
1717 k
Use minimum Vc for punching shear.
Фv Vu
0.85 unitless
strength reduction factor Ф Vc minimum 1459 k ult OK 290.0 < 1,459 k ultimate allowed
Figure 48-2 Shear punching in plan view.
αs
40 for interior columns 30 for edge columns 20 for corner columns
d
Figure 48-3 Shear cone dimensions in elevation view.
row 60
STIRRUP REINFORCING b1 60.0 in
width of critical section
s fy
stirrup / tie spacing < d/2 or 24" stirrup / tie yield strength
Av
4.0 in 40 ksi 0 in2 =0.31*10
Page 48 - 2
sum of area for all vertical bars to resist shear Note: Calculation for Av is done in the input cell. The actual calculation is copied to an adjacent cell and parked with the [space bar] to show the math.
21562345.xls row 70
Vs
0.0 k
Vu
1459.2 k-ult
Av Fy d /s ACI 11.5.6.2 0.00 * 40 * 36.0 /4.0
d
Ф (Vc minimum + Vs)
0.85 * (1,717 + 0.0) OK 290.0 required < 1,459.2 k ultimate allowed
d/2 Figure 48-4 Shear reinforcing through the shear cone.
INCLINED BAR REINFORCING f'c 4 ksi Vu reqd 290.0 k ult d 36.0 in Vc 1716.7 k ult Фv 0.85 unitless b1 α fy Av
Vs
60.0 in 60.0 degrees 1.047 radians 60 ksi 9.6 in2
498.8 k
but not greater than: bw 72.0 in Vs
Vs use Vu
491.8 k
Per ACI Commentary R11.12.3 In slabs 10" and thinner, shear reinforcement should be enclosed stirrups with a longitudinal bar at each corner.
width of critical section
row 90
angle of shear bars from the plane of beam/column reinforcing α > 30º stirrup / tie yield strength =0.6*12 sum of area for all bars to resist shear
longitudinal reinforcing
Av Fy sin α ACI 11.5.6.5 (11-17) 9.60 * 60 * sin 60.0 width of tributary beam 3 √ f'c bw d 3 * ( 4.00 * 1000)^0.5 * 72.0 * 36.00 /1000
d/2
d
491.8 k 1877.2 k-ult
Ф (Vc minimum + Vs)
0.85 * (1,717 + 491.8) OK 290.0 required < 1,877.2 k ultimate allowed
Figure 48-5 Inclined shear reinforcing. row 110
TORSION Torsion per ACI 11.6.3 Tu 1006286 in-lb/ft ult f'c
Page 48 - 3 =1174*1000*12 /14 ultimate torsional moment
4 ksi
Фtorsion
0.75 factor
Aoh
3456 in2
Acp
3456 in2
pcp
264 in
Column Strip 21562345.xls
row 120
36 For Nonprestressed members Torsional effects on bending and shear can be neglected when Tu Limit < Tu Tu Limit
row 130
Ф √ f'c (Acp2 / pcp) 2146025 in-lb ult TRUE logic OK Tu limit ≥ Tu required Torsion reinforcing not required
96
Figure 48-6 Beam torsion shear. Aoh
ρh
T1
0.007 unitless
0.013
=12*0.6/(24*42) ratio of horizontal shear reinforcing area to gross area of the vertical concrete section
0.000
torsion reinforcement, in2 Acp
area enclosed by the outside perimeter of the concrete cross section, in2
pcp
outside perimeter of the concrete cross section, in
(Vu / bw d)2 (290 /(72.0 * 36.0) )^2
T2
area enclosed by the centerline of the closed
(Tu ρh / 1.7 Aoh2)2 (1,006,286 * 0.007 /(1.7 * 3,456^2) )^2
T required
0.11 k-in ult
√(Vu /bw d)2 + (Tu ρh / 1.7 Aoh2)2
T provided
0.99 k-in ult
Фv ( Vc / bw d + 8 √ f'c ) 0.85 * (1,716.7 /(72.0 * 36.0) + 8 * (4 * 1000)^0.5 /1000)
row 150
row 160
BEAM SHEAR V beam ratio beam Vu req'd f'c d bw
Page 48 - 4 230.0 k 1 unitless 230.0 k_ult 4 ksi 36 in 96 in
=460/2 column punching divided by 2 sides fluid + DL seismic
depth to reinforcing width of beam or tributary slab
Vc
437.2 k
Ф Vu allow
0.85 unitless strength reduction factor 371.6 k_ult 0.85 * 437.2 TRUE logic OK 371.6 > 230.0 k_ult required
s fy
6.0 in 40 ksi
2 √ f'c bw * d ACI 11.3.1.1 2 * (4 * 1000)^0.5 * 36.0 * 96 /1000
stirrup / tie spacing < d/2 or 24" stirrup / tie yield strength
Av
0.00 in2 =0.2*12
sum of area for all bars to resist shear
Av req'd
0.72 in2
50 * bw * s /fy ACI 11.5.5.2 50 * 96 * 6.0 /40.00 /1000
Vs
Vu allow
0.0 k
371.6 k-ult
Av Fy d /s ACI 11.5.6.2 0.00 * 40 * 36.0 /6.0 Ф (Vc + Vs) 0.85 * (437.2 + 0)
FOR MEMBERS SUBJECT TO SHEAR AND FLEXURE As 7.2 in2 area of tension reinforcing =0.6*12 ρw 0.0021 unitless density of tension reinforcing Mu 1174.0 k-ft ult factored ultimate moment limit
7.1
21562345.xls Figure 48-7 Beam shear elevation. Bar 10M 15M 20M 25M 30M 35M 45M
Area 0.12 0.27 0.49 0.76 1.1 1.49 2.47
55M 0 3 4 5 6 7 8 9 10 11 14 18
3.68 0 0.11 0.20 0.31 0.44 0.6 0.79 1.00 1.27 1.56 2.25 4.00
row 180
row 190
Vu d / Mu < 1.0
a b Vc
1.0 0.120 0.005 433.3 k
( 1.9 √f'c + 2500 ρw Vu d / Mu ) bw d ACI 11.3.2.1 1.9 * (4.0 * 1000)^0.5 /1000 2500 * 0.0021 * 1.0 /1000 (0.120 + 0.005) * 96.0 * 36.0
Vc limit
765.0 k
3.5 √ f'c bw * d
Vc
433.3 k
minimum( Vc limit, Vc )
Vu allow
Ф (Vc + Vs) 368.3 k-ult TRUE logic OK 368.3 > 230.0 k_ult required
row 200
ACI 11.3.2.1
row 210
PHOTOGRAPHS
Page 48 - 5
21562345.xls row 220
row 230
row 240
Figure 48-8 Weld stud application. row 250 Weld stud application requires a large generator. The welded end of the stud contains the weld material and flux. The white, porcelan ferrules contain the electric arc, flux, and weld material. After welding, the ferrule is broken off and discarded. You can visit the Nelson Weld Stud site at: http://www.nelsonstud.com row 260 For evaluation reports, go to the International Building Codes Evaluation Service website at: http://www.icbo.org/ICBO_ES/ On February 1, 2003, ICBO ES formally joined with the National Evaluation Service, BOCAI evaluation services, and SBCCI PST & ESI in the new ICC Evaluation Service, Inc. (ICC-ES). ICC-ES is a subsidiary of the International Code Council. The web site address will change in time.
Figure 48-9 The big, portable weld stud generator. row 270
Page 48 - 6 48
21562345.xls
Page 48 - 7
21562345.xls
Page 48 - 8
21562345.xls
Page 48 - 9
21562345.xls
Page 48 - 10
21562345.xls
Page 48 - 1
TANK SUPPORT
48
At column 39 to 139 Seismic ENGINEERING with the SPREADSHEET Copyright 2006 American Society of Civil Engineers A
B
C
BEARING ON CONCRETE 4 ksi f'c 290 k_ult Punching 1 unitless ratio P_ult 290.0 k_ult f_brg Фbrg A 1 req'd
3.4 ksi_ult 0.7
A2
122 in2 452 in2
multiplier A req'd
2.00 61 in2
D
E
F
G
P_ult
290.0 k_ult
Ao
6786 in2
I
2
J
K
L
M
N
1
along this plane
convert circular column to equivalent square
452.4 in2 452 in² > 122 in²
188 in
H
Figure 48-1 Bearing area and edge distance
A_pl
1.00 unitless 36.0 in
21562345.xls
A 2 is measured
CIRCULAR PUNCHING SHEAR dia 24.00 in
βc d bo
y
ultimate strength of concrete SEISMIC ultimate load LRFD factor required 0.85 * f'c allowable bearing on concrete 11.0 in on a side minimum area of supporting surface not to exceed 2 ACI 10.17.1 A1/A2
Christy 7:14 08/31/09
1.0 * 290.0 ratio = 1 for circular column depth to tension reinforcing (dia + d)*pi bo * d 36.0 * 188
row 30 Critical Section Unloaded Area d/2 Face + d
Vc 33
αs
2575 k
02 ACI 11.12.2.1 (11-33) 6 * (4 * 1000)^0.5 /1000 * 188 * 36.0 where (2 + 4/βc ) = 6 factor (αs d /bo + 2) √ f'c bo d 02 ACI 11.12.2.1 (11-34) (40 * 36.0 /188.5 + 2) * (4 * 1000)^0.5 /1000 * 188 * 36.0
Vc 34
40 unitless 4137 k
Vc 35
1717 k
Ao 4 √ f'c 02 ACI 11.12.2.1 (11-35) 6,786 * 4 * (4 * 1000)^0.5 * 0.85 /1000
Vc min
1717 k
Use minimum Vc for punching shear.
Фv Vu
0.85 unitless
strength reduction factor Ф Vc minimum 1459 k ult OK 290.0 < 1,459 k ultimate allowed
Figure 48-2 Shear punching in plan view.
αs
40 for interior columns 30 for edge columns 20 for corner columns
d
Figure 48-3 Shear cone dimensions in elevation view.
row 60
STIRRUP REINFORCING b1 60.0 in
width of critical section
s fy
stirrup / tie spacing < d/2 or 24" stirrup / tie yield strength
Av
4.0 in 40 ksi 0 in2 =0.31*10
Page 48 - 2
sum of area for all vertical bars to resist shear Note: Calculation for Av is done in the input cell. The actual calculation is copied to an adjacent cell and parked with the [space bar] to show the math.
21562345.xls row 70
Vs
0.0 k
Vu
1459.2 k-ult
Av Fy d /s ACI 11.5.6.2 0.00 * 40 * 36.0 /4.0
d
Ф (Vc minimum + Vs)
0.85 * (1,717 + 0.0) OK 290.0 required < 1,459.2 k ultimate allowed
d/2 Figure 48-4 Shear reinforcing through the shear cone.
INCLINED BAR REINFORCING f'c 4 ksi Vu reqd 290.0 k ult d 36.0 in Vc 1716.7 k ult Фv 0.85 unitless b1 α fy Av
Vs
60.0 in 60.0 degrees 1.047 radians 60 ksi 9.6 in2
498.8 k
but not greater than: bw 72.0 in Vs
Vs use Vu
491.8 k
Per ACI Commentary R11.12.3 In slabs 10" and thinner, shear reinforcement should be enclosed stirrups with a longitudinal bar at each corner.
width of critical section
row 90
angle of shear bars from the plane of beam/column reinforcing α > 30º stirrup / tie yield strength =0.6*12 sum of area for all bars to resist shear
longitudinal reinforcing
Av Fy sin α ACI 11.5.6.5 (11-17) 9.60 * 60 * sin 60.0 width of tributary beam 3 √ f'c bw d 3 * ( 4.00 * 1000)^0.5 * 72.0 * 36.00 /1000
d/2
d
491.8 k 1877.2 k-ult
Ф (Vc minimum + Vs)
0.85 * (1,717 + 491.8) OK 290.0 required < 1,877.2 k ultimate allowed
Figure 48-5 Inclined shear reinforcing. row 110
TORSION Torsion per ACI 11.6.3 Tu 1006286 in-lb/ft ult f'c
Page 48 - 3 =1174*1000*12 /14 ultimate torsional moment
4 ksi
Фtorsion
0.75 factor
Aoh
3456 in2
Acp
3456 in2
pcp
264 in
Column Strip 21562345.xls
row 120
36 For Nonprestressed members Torsional effects on bending and shear can be neglected when Tu Limit < Tu Tu Limit
row 130
Ф √ f'c (Acp2 / pcp) 2146025 in-lb ult TRUE logic OK Tu limit ≥ Tu required Torsion reinforcing not required
96
Figure 48-6 Beam torsion shear. Aoh
ρh
T1
0.007 unitless
0.013
=12*0.6/(24*42) ratio of horizontal shear reinforcing area to gross area of the vertical concrete section
0.000
torsion reinforcement, in2 Acp
area enclosed by the outside perimeter of the concrete cross section, in2
pcp
outside perimeter of the concrete cross section, in
(Vu / bw d)2 (290 /(72.0 * 36.0) )^2
T2
area enclosed by the centerline of the closed
(Tu ρh / 1.7 Aoh2)2 (1,006,286 * 0.007 /(1.7 * 3,456^2) )^2
T required
0.11 k-in ult
√(Vu /bw d)2 + (Tu ρh / 1.7 Aoh2)2
T provided
0.99 k-in ult
Фv ( Vc / bw d + 8 √ f'c ) 0.85 * (1,716.7 /(72.0 * 36.0) + 8 * (4 * 1000)^0.5 /1000)
row 150
row 160
BEAM SHEAR V beam ratio beam Vu req'd f'c d bw
Page 48 - 4 230.0 k 1 unitless 230.0 k_ult 4 ksi 36 in 96 in
=460/2 column punching divided by 2 sides fluid + DL seismic
depth to reinforcing width of beam or tributary slab
Vc
437.2 k
Ф Vu allow
0.85 unitless strength reduction factor 371.6 k_ult 0.85 * 437.2 TRUE logic OK 371.6 > 230.0 k_ult required
s fy
6.0 in 40 ksi
2 √ f'c bw * d ACI 11.3.1.1 2 * (4 * 1000)^0.5 * 36.0 * 96 /1000
stirrup / tie spacing < d/2 or 24" stirrup / tie yield strength
Av
0.00 in2 =0.2*12
sum of area for all bars to resist shear
Av req'd
0.72 in2
50 * bw * s /fy ACI 11.5.5.2 50 * 96 * 6.0 /40.00 /1000
Vs
Vu allow
0.0 k
371.6 k-ult
Av Fy d /s ACI 11.5.6.2 0.00 * 40 * 36.0 /6.0 Ф (Vc + Vs) 0.85 * (437.2 + 0)
FOR MEMBERS SUBJECT TO SHEAR AND FLEXURE As 7.2 in2 area of tension reinforcing =0.6*12 ρw 0.0021 unitless density of tension reinforcing Mu 1174.0 k-ft ult factored ultimate moment limit
7.1
21562345.xls Figure 48-7 Beam shear elevation. Bar 10M 15M 20M 25M 30M 35M 45M
Area 0.12 0.27 0.49 0.76 1.1 1.49 2.47
55M 0 3 4 5 6 7 8 9 10 11 14 18
3.68 0 0.11 0.20 0.31 0.44 0.6 0.79 1.00 1.27 1.56 2.25 4.00
row 180
row 190
Vu d / Mu < 1.0
a b Vc
1.0 0.120 0.005 433.3 k
( 1.9 √f'c + 2500 ρw Vu d / Mu ) bw d ACI 11.3.2.1 1.9 * (4.0 * 1000)^0.5 /1000 2500 * 0.0021 * 1.0 /1000 (0.120 + 0.005) * 96.0 * 36.0
Vc limit
765.0 k
3.5 √ f'c bw * d
Vc
433.3 k
minimum( Vc limit, Vc )
Vu allow
Ф (Vc + Vs) 368.3 k-ult TRUE logic OK 368.3 > 230.0 k_ult required
row 200
ACI 11.3.2.1
row 210
PHOTOGRAPHS
Page 48 - 5
21562345.xls row 220
row 230
row 240
Figure 48-8 Weld stud application. row 250 Weld stud application requires a large generator. The welded end of the stud contains the weld material and flux. The white, porcelan ferrules contain the electric arc, flux, and weld material. After welding, the ferrule is broken off and discarded. You can visit the Nelson Weld Stud site at: http://www.nelsonstud.com row 260 For evaluation reports, go to the International Building Codes Evaluation Service website at: http://www.icbo.org/ICBO_ES/ On February 1, 2003, ICBO ES formally joined with the National Evaluation Service, BOCAI evaluation services, and SBCCI PST & ESI in the new ICC Evaluation Service, Inc. (ICC-ES). ICC-ES is a subsidiary of the International Code Council. The web site address will change in time.
Figure 48-9 The big, portable weld stud generator. row 270
Page 48 - 6 48
21562345.xls
Page 48 - 7
21562345.xls
Page 48 - 8
21562345.xls
Page 48 - 9
21562345.xls
Page 48 - 10
21562345.xls
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