Daniel Tian Li
PROJECT :
PAGE :
CLIENT :
DESIGN BY :
JOB NO. :
DATE :
REVIEW BY :
Design of Post-Tensioned Concrete Floor Based on ACI 318-05 1. DESIGN METHODS 1.1 BREAKDOWN TWO WAYS FLOOR INTO DESIGN STRIPS IN ONE DIRECTION AND ONE WAY SLABS IN OTHER DIRECTION. DESIGN STRIPS WORK AS CONTINUOUS BEAMS BY BANDED ALL TENDONS AT COLUMN. THE PERPENDICULAR DIRECTION LIKE MULTI-SPAN ONE WAY SLABS, USING DISTRIBUTED TENDONS. 1.2 SPECIFY TOTAL REQUIRED EFFECTIVE POST-TENSIONING FORCES AT BANDED TENDONS, ON STRUCTURAL DRAWINGS, AND UNIFORM FORCES IN DISTRIBUTED TENDONS. 1.3 WHEN TENDON LESS THAN 140 FT, STRESS AT ONE END. OTHERWISE STRESS AT BOTH ENDS. 1.4 THE VARIOUS LIVE LOADING CONDITIONS SHOULD BE CONSIDER BY INPUT LL ZERO AT SOME SPANS.
2. INPUT DATA & DESIGN SUMMARY CONCRETE STRENGTH
f'c
=
4.5
ksi
REBAR YIELD STRESS
fy
=
60
ksi
TENDON PROPERTIES
fpu
=
270
ksi
fpy
=
243
ksi
fse
= =
175
ksi
1/2
in
= = = = = # #
0.153
in2
8
in
30
ft
22
in
CONCRETE COST =
100
lb / ft2
22
in
TENDONS COST =
0.476
lb / ft2
REBARS COST =
0.349
lb / ft2
Mid of L2
Support
dia Aps SLAB THICKNESS
t
TRIBUTARY WIDTH IF BANDED AS DESIGN STRIPS COLUMN WIDTH
W c1
COLUMN DEPTH
c2
TOP BAR SIZE AT COLUMN BOTTOM CONTINUOUS BAR SIZE
Location
Mid of L1
Left
Support
THE DESIGN IS ADEQUATE.
5 4
Mid of LTyp
Mid of Ln-1
Support
Support
Mid Ln
Span (ft)
20
30
30
30
20
DL (psf)
120
120
120
120
120
LL (psf)
75
75
75
75
75
75%
75%
80%
75%
75%
Balanced DL (60%-80% suggested) dCGS (in, from bottom)
4
3.33
REQD EFFECTIVE PT (k / ft) Total if banded (kips) Tendons
2.5
2.5
7.5
2.5
25.92
7.5
3.33
24.30
4
22.31
669.4
729.0
777.6
729.0
669.4
1 / 2 in Dia @ 13 in o.c.
1 / 2 in Dia @ 12 in o.c.
1 / 2 in Dia @ 13 in o.c.
1 / 2 in Dia @ 14 in o.c.
26
28
30
28
26
7 # 5 , L = 3.03 ft
Bot Bars, Cont., E. Way
10 # 5 , L = 9.39 ft Not ReqD
Required column cap thk, (in)
7.5
24.30
1 / 2 in Dia @ 14 in o.c.
Total Number if banded Top Bars at Column
7.5
22.31
Right
Not ReqD
22 # 5 , L = 9.39 ft
# 4 @ 45in. o.c. Not ReqD
22 # 5 , L = 9.39 ft Not ReqD
Not ReqD
10 # 5 , L = 9.39 ft
# 4 @ 45in. o.c. Not ReqD
7 # 5 , L = 3.03 ft Not ReqD
Not ReqD
Not ReqD
3. DESIGN LOADS & SECTION FORCES Location MDL (ft-k / ft)
Left
Mid of L1
Support
Mid of L2
Support
Mid of LTyp
Support
Mid of Ln-1
Support
Mid Ln
Right
0.00
2.14
-7.72
5.01
-9.26
4.24
-9.26
5.01
-7.72
2.14
0.00
MLL (ft-k / ft)
0.00
1.34
-4.83
3.13
-5.78
2.65
-5.78
3.13
-4.83
1.34
0.00
0.00
-1.65
5.71
-3.66
7.23
-3.57
7.23
-3.66
5.71
-1.65
Balanced Load (psf, uplift)
-90
Balanced MBal (ft-k / ft) Required Effective PT (k / ft) Tendon Spacing (in) Primary MFe (ft-k / ft)
0.00
-90
0.00
-90
-90
22.31
24.30
25.92
24.30
14
13
12
13
-1.25
6.51 7.09
Secondary MSec (ft-k / ft)
-96
0.40
7.56 -3.04
7.09
1.38
0.62
-0.14
0.80
-3.24
0.33
0.33
22.31 14
7.56 7.09
0.00
6.51 -3.04
-1.25
0.00
0.40
0.00
Right
7.09
0.33
0.80
-0.14
0.62
1.38
4. CHECK SERVICE LOAD STRESSES Location
Left
Mid of L1
Support
Mid of L2
Support
Mid of LTyp
Support
Mid of Ln-1
Support
Mid Ln
A (in2 / ft)
96
96
96
96
96
96
96
96
96
96
96
S (in / ft)
128
128
128
128
128
128
128
128
128
128
128
F / A (ksi)
0.232
0.232
0.232
0.270
0.270
0.270
0.232
0.232
0.232
0.279
0.232
0.186
0.232
0.503
0.45 fc' =
2.025
-0.409
0.404
0.232
3
0.253 Check 125 psi < F /A < 275 psi M / S + F / A , (ksi)
0.232
[Satisfactory] 0.279
for load combination (DL + PT) 0.232
0.186
for load combination (DL + PT) Check ft < 7.5 (fc') M / S + F / A , (ksi) for load (DL + LL + PT)
and fc < 0.45 fc' 0.232
0.080 0.380
0.421 0.442
0.5
0.333
0.253
0.253
0.207
0.443
-0.462 0.674
-0.479
0.080 0.063
0.582
0.043 0.380
0.064
0.460 0.443
(ACI 318-05, 18.3.3 & 18.4.2a),
-0.409 -0.388
0.253
0.063 0.460
0.126
[Satisfactory] 0.404
0.253 (ADAPT suggestion)
0.043 0.064
- M / S + F / A , (ksi)
0.253
where
0.421 0.126 7.5 (fc')
0.5
-0.462 -0.479
0.674
0.442 =
-0.388
- M / S + F / A , (ksi)
0.232
for load (DL + LL + PT) Check ft < 7.5 (fc')0.5 and fc < 0.6 fc'
0.061
0.874 0.895 [Satisfactory]
1.002 -0.167
-0.042
0.985 (ACI 318-05, 18.3.3 & 18.4.2b),
1.002 0.985 where
0.874 -0.167
0.895
7.5 (fc')0.5 =
0.503
0.061
0.232
0.6 fc' =
2.700
(cont'd)
5. CALCULATE NON-PRESTRESSED REINFORCEMENT Location
Left
Max. Nc (k / ft), (ACI 318, 18.0)
Mid of L1
Mid of L2
Support
0.000
As (in2 / ft), (ACI 318, 18.9.3.2) Bottom Bars, Each Way
Support
Mid of LTyp
1.599
Support
0.134
Mid of Ln-1
Support
1.599
Mid Ln
Right
0.000
0.000
0.053
0.000
0.053
0.000
Not ReqD
# 4 @ 45in. o.c.
Not ReqD
# 4 @ 45in. o.c.
Not ReqD
Max. Acf (in2), (ACI 318, 18.0)
2880
2880
2880
2880
2880
2880
As' (in2), (ACI 318, 18.9.3.2)
2.160
2.160
2.160
2.160
2.160
2.160
7#5
7#5
7#5
7#5
7#5
7#5
3.03
9.39
9.39
9.39
9.39
3.03
Top Bars at Column L (ft), (ACI 318, 18.9.4.1)
6. CHECK FLEXURAL CAPACITY BY STRENGTH DESIGN METHOD Location
Left
Mid of L1
Support
Factored Mu (ft-k / ft)
0.00
5.11
-16.19
1.2 MDL + 1.6 MLL + 1.0 MSec dp (in)
Mid of L2
-15.61
11.64 5.50
Support
Mid of LTyp
Support
-20.03
9.67
-20.03
-20.50
Mid of Ln-1
-20.50
11.64 5.50
4.00
4.67
7.50
0.00273
0.00234
0.00146 0.00157
0.00214
0.00157
0.00157
0.00214
L / dp
60.00
51.39
40.00
65.45
48.00
65.45
48.00
65.45
fps (ksi)
185.64
186.56
190.44
188.24
185.88
188.24
0.131
0.131
rp
(ACI 318, 18.7.2, b & c)
191.62
Aps (in2 / ft) Actual Area
203.09
0.14
6.75
6.63 0.85
6.75
6.63
0.21
0.40
0.67 0.64
Actual As (in2 / ft) Top Bars at Column
0.153
Mid Ln
Right
-16.19
5.11
0.00
-15.61 7.50
4.67
4.00
0.00146
0.00234
0.00273
0.00157
203.09
40.00
51.39
60.00
190.44
186.56
185.64
0.131
0.131
191.62
0.153
0.131
0.141
0.14
0.14
6.75
6.63
6.75
6.63
6.75
6.63
0.55
0.85
0.67
0.40
0.21
0.88
0.88
0.65
0.64
0.000
0.018
0.000
0.018
0.000
Not ReqD
# 4 @ 136in. o.c.
Not ReqD
# 4 @ 136in. o.c.
Not ReqD
0.053
0.000
0.053
0.000
0.000
2.933
6.655
6.655
2.933
0.000
Not ReqD
10 # 5
22 # 5
22 # 5
10 # 5
Not ReqD
Actual As' (in ) 2
2.170
f Mn (ft-k / ft)
-9.23
8.21
Actual Capacity
3.100
6.820
-16.34
-21.62
-17.51
Check f Mn > Mu εpt, (ACI 318, 18.8.1)
0.65
0.000
Required As' (in2)
191.62
0.153 0.14
6.63
Required As (in / ft)
7.50 0.00170
0.141
d (in)
Bottom Bars, Each Way
5.50 0.00232
191.62
0.131
a (in) 2
7.50 0.00170
Support
12.68
11.14
-20.66
6.820
3.100
-21.62
-16.34
-20.66
12.68
2.170 8.21
-9.23
0.0262
0.0433
-17.51
[Satisfactory] 0.0433
0.0262
εc(dp - a / b1) / (a / b1)
0.0246
0.0188
0.0261
Check εpt > 0.005
0.0180
[Satisfactory]
0.0216
0.0181
0.0188
0.0246
0.0181
0.0180
0.0261
Support
Mid of Ln-1
Support
(ACI 318, 18.8.1)
7. CHECK PUNCHING SHEAR CAPACITY BY STRENGTH DESIGN METHOD Location RDL (k)
Left
Mid of L1
35.99
Support
Mid of L2
90.01
Support
Mid of LTyp
108.00
108.00
Mid Ln
90.01
Right 35.99
RLL (k)
22.49
56.26
67.50
67.50
56.26
22.49
RSec (k)
-26.99
-67.51
-83.70
-83.70
-67.51
-26.99
52.18
130.52
153.90
153.90
130.52
52.18
Vu =1.2 RDL + 1.6 RLL + 1.0 Rsec Required b0d, (ACI 318, 11-36)
228.48
565.70
655.06
655.06
565.70
228.48
Required d, (ACI 318, 11.0)
3.16
5.20
5.88
5.88
5.20
3.16
For f Vn < Vu, the required
0.00
0.00
0.00
0.00
0.00
0.00
Not ReqD
Not ReqD
Not ReqD
Not ReqD
Not ReqD
Not ReqD
column cap thickness, tcap (in)
8. CALCULATE COST FOR SLAB & CAP Location Concrete
Left
Mid of L1
Mid of L2
Support
Mid of LTyp
Support
Mid of Ln-1
Support
Mid Ln
Right
1.67
5.00
5.00
5.00
5.00
1.67
cap concrete
0.00
0.00
0.00
0.00
0.00
0.00
Total = length (ft)
Tendons
Support
cap dim (ft)
T / 30 ft TW
Total =
854.2
T / 30 ft TW
0.00
198.08
Total =
625.5
20.01 44.71
Rebars
179395
Average =
30.02 10.89
30.02 , (ACI 318 App. E) 435.77
0.00
T / 30 ft TW
100
lb / ft2
30.02 Average =
0.476
435.77
10.89
Average =
0.349
20.01 lb / ft2 , (AISC Manual 2nd page 7-15) 198.08
0.00
44.71
lb / ft2
Note: 1. The column moments are negligible for gravity punching design. Lateral loads, seismic and wind, should be supported by shear walls. Using equivalent frames to support lateral loads is not suggested. 2. By inspection, the deflections of slab do not govern PT concrete floor design. Otherwise, using PT concrete floor is inadequate for larger live load. (ACI 318, 9.5.4.1) 3. The secondary moments are very important concept of PT floor design. Based on this concept, PT floor design are always continuous beams design and one way slabs design. So using two ways finite element analysis to design PT floor is inadequate. Technical References: 1. "Design of Post-Tensioned Slabs Using Unbounded Tendons, Third Edition", The Post-Tensioning Institute, 2004. 2. "Design, Construction and Maintenance of Cast-in-Place Post-Tensioned Concrete Parking Structures, First Edition", The Post-Tensioning Institute, 2001. 3. Bijan O. Aalami & Allan Bommer, "Design Fundamentals of Post-Tensioned Concrete Floors, First Edition", The Post-Tensioning Institute, 1999.
Daniel Tian Li
PROJECT :
PAGE :
CLIENT :
DESIGN BY :
JOB NO. :
DATE :
REVIEW BY :
Design of Post-Tensioned Concrete Floor Based on ACI 318-05 1. DESIGN METHODS 1.1 BREAKDOWN TWO WAYS FLOOR INTO DESIGN STRIPS IN ONE DIRECTION AND ONE WAY SLABS IN OTHER DIRECTION. DESIGN STRIPS WORK AS CONTINUOUS BEAMS BY BANDED ALL TENDONS AT COLUMN. THE PERPENDICULAR DIRECTION LIKE MULTI-SPAN ONE WAY SLABS, USING DISTRIBUTED TENDONS. 1.2 SPECIFY TOTAL REQUIRED EFFECTIVE POST-TENSIONING FORCES AT BANDED TENDONS, ON STRUCTURAL DRAWINGS, AND UNIFORM FORCES IN DISTRIBUTED TENDONS. 1.3 WHEN TENDON LESS THAN 140 FT, STRESS AT ONE END. OTHERWISE STRESS AT BOTH ENDS. 1.4 THE VARIOUS LIVE LOADING CONDITIONS SHOULD BE CONSIDER BY INPUT LL ZERO AT SOME SPANS.
2. INPUT DATA & DESIGN SUMMARY CONCRETE STRENGTH
f'c
=
5
ksi
REBAR YIELD STRESS
fy
=
60
ksi
TENDON PROPERTIES
fpu
=
270
ksi
fpy
=
243
ksi
fse
= =
175
ksi
1/2
in
= = = = = # #
0.153
in2
8
in
30
ft
22
in
CONCRETE COST =
100
lb / ft2
22
in
TENDONS COST =
0.484
lb / ft2
REBARS COST =
0.289
lb / ft2
Mid of L2
Support
dia Aps SLAB THICKNESS
t
TRIBUTARY WIDTH IF BANDED AS DESIGN STRIPS COLUMN WIDTH
W c1
COLUMN DEPTH
c2
TOP BAR SIZE AT COLUMN BOTTOM CONTINUOUS BAR SIZE
Location
Mid of L1
Left
Support
THE DESIGN IS ADEQUATE.
5 4
Mid of L3
Mid L4
Support
Span (ft)
20
30
30
20
DL (psf)
120
120
120
120
LL (psf)
75
75
75
75
75%
80%
80%
75%
Balanced DL (60%-80% suggested) dCGS (in, from bottom)
4
3.33
REQD EFFECTIVE PT (k / ft) Total if banded (kips) Tendons
2.5
2.5
7.5
3.33
25.92
4
22.31
669.4
777.6
777.6
669.4
1 / 2 in Dia @ 12 in o.c.
1 / 2 in Dia @ 12 in o.c.
1 / 2 in Dia @ 14 in o.c.
26
30
30
26
7 # 5 , L = 3.03 ft
Bot Bars, Cont., E. Way Required column cap thk, (in)
7.5
25.92
1 / 2 in Dia @ 14 in o.c.
Total Number if banded Top Bars at Column
7.5
22.31
Right
9 # 5 , L = 9.39 ft Not ReqD
Not ReqD
22 # 5 , L = 9.39 ft Not ReqD
Not ReqD
9 # 5 , L = 9.39 ft
# 4 @ 378in. o.c. Not ReqD
7 # 5 , L = 3.03 ft Not ReqD
Not ReqD
Not ReqD
3. DESIGN LOADS & SECTION FORCES Location MDL (ft-k / ft)
Left
Mid of L1
Support
Mid of L2
Support
Mid of L3
Support
Mid L4
Right
0.00
2.21
-7.59
4.85
-9.71
4.85
-7.59
2.21
0.00
MLL (ft-k / ft)
0.00
1.38
-4.74
3.03
-6.07
3.03
-4.74
1.38
0.00
0.00
-1.54
5.93
-3.92
7.84
-3.92
5.93
-1.54
Balanced Load (psf, uplift) Balanced MBal (ft-k / ft)
-90
Required Effective PT (k / ft) Tendon Spacing (in)
-96
-96
22.31
25.92
25.92
14
12
12
Primary MFe (ft-k / ft)
0.00
-1.25
Secondary MSec (ft-k / ft)
0.00
0.29
6.51 7.56
7.56 -3.24
0.58
-3.24
7.56 -0.28
1.63
0.68
-0.28
-90
22.31 14 7.56 6.51
0.68
0.00
-1.25
0.00
0.58
0.29
0.00
Right
1.63
4. CHECK SERVICE LOAD STRESSES Location
Left
Mid of L1
Support
Mid of L2
Support
Mid of L3
Support
Mid L4
A (in2 / ft)
96
96
96
96
96
96
96
96
96
S (in / ft)
128
128
128
128
128
128
128
128
128
F / A (ksi)
0.232
0.232
0.232
0.270
0.270
0.270 0.232
0.232
0.295
0.232
3
0.270 Check 125 psi < F /A < 275 psi M / S + F / A , (ksi)
0.232
[Satisfactory] 0.295
for load combination (DL + PT)
- M / S + F / A , (ksi)
0.170
for load combination (DL + PT)
M / S + F / A , (ksi) for load (DL + LL + PT)
0.232
0.095 0.358
0.388 0.426
Check ft < 7.5 (fc')0.5 and fc < 0.45 fc'
0.182
0.358 0.182
0.445
-0.474 0.642
-0.474
0.114 0.077 0.426 0.388
(ACI 318-05, 18.3.3 & 18.4.2a),
-0.368 -0.330
0.232
0.095 0.445
[Satisfactory] 0.425
0.270 (ADAPT suggestion)
0.077 0.114
0.232
0.270
0.642
where
0.170
0.232
0.45 fc' =
0.530
0.425
0.232
-0.330 -0.368
0.45 fc' =
2.250
- M / S + F / A , (ksi)
0.232
for load (DL + LL + PT) Check ft < 7.5 (fc')0.5 and fc < 0.6 fc'
0.040
0.833 0.870 [Satisfactory]
1.014 -0.102
-0.102
1.014 (ACI 318-05, 18.3.3 & 18.4.2b),
0.870 0.833 where
0.040
0.232
7.5 (fc')0.5 =
0.530
0.6 fc' =
3.000
(cont'd)
5. CALCULATE NON-PRESTRESSED REINFORCEMENT Location
Left
Max. Nc (k / ft), (ACI 318, 18.0)
Mid of L1
Mid of L2
Support
0.000
As (in2 / ft), (ACI 318, 18.9.3.2) Bottom Bars, Each Way
Mid of L3
Support
0.672
Support
0.672
Mid L4
Right
0.000
0.000
0.000
0.000
0.000
Not ReqD
Not ReqD
Not ReqD
Not ReqD
Max. Acf (in2), (ACI 318, 18.0)
2880
2880
2880
2880
2880
As' (in2), (ACI 318, 18.9.3.2)
2.160
2.160
2.160
2.160
2.160
7#5
7#5
7#5
7#5
7#5
3.03
9.39
9.39
9.39
3.03
Top Bars at Column L (ft), (ACI 318, 18.9.4.1)
6. CHECK FLEXURAL CAPACITY BY STRENGTH DESIGN METHOD Location
Left
Mid of L1
Support
Factored Mu (ft-k / ft)
0.00
5.14
-16.12
1.2 MDL + 1.6 MLL + 1.0 MSec dp (in)
Mid of L2
-15.06
11.35 5.50
Support
Mid of L3
Support
Mid L4
Right
-21.63
11.35
-15.06
5.14
0.00
4.67
4.00
-21.63
-16.12
4.00
4.67
7.50
0.00273
0.00234
0.00146 0.00170
0.00232
0.00170
0.00146
0.00234
0.00273
L / dp
60.00
51.39
40.00
65.45
48.00
65.45
40.00
51.39
60.00
fps (ksi)
186.25
187.27
191.59
189.22
186.60
189.22 187.27
186.25
0.131
0.131
0.153
0.15
0.15
0.131
0.131
0.131
d (in)
6.63
6.75
6.63
6.75
6.63
6.75
6.63
6.75
6.63
a (in)
0.19
0.36
0.60
0.83
0.57
0.54 0.36
0.19
rp
(ACI 318, 18.7.2, b & c)
189.22
Aps (in2 / ft) Actual Area
200.98
0.131
Bottom Bars, Each Way Actual As (in2 / ft) Required As' (in2) Top Bars at Column
7.50 0.00170
189.22
191.59
0.58
0.153
0.83
0.153
0.60
0.000
0.000
0.006
0.000
Not ReqD
Not ReqD
# 4 @ 378in. o.c.
Not ReqD
0.000
0.000
0.006
0.000
0.000
2.683
6.705
2.683
0.000
Not ReqD
9#5
22 # 5
9#5
Not ReqD
2.790
2.170
Actual As' (in ) 2
2.170
f Mn (ft-k / ft)
-9.28
8.27
Actual Capacity
2.790
6.820
-16.22
-21.74
-18.36
Check f Mn > Mu εpt, (ACI 318, 18.8.1)
5.50 0.00232
0.153
0.54 Required As (in2 / ft)
7.50 0.00170
12.02
11.35
-21.74
-18.36 -16.22
8.27
-9.28
0.0271
0.0284
0.0469
Support
Mid L4
[Satisfactory] 0.0469
0.0284
εc(dp - a / b1) / (a / b1)
0.0271
0.0187
0.0302
Check εpt > 0.005
0.0199
[Satisfactory]
0.0203
0.0187
0.0302
(ACI 318, 18.8.1)
7. CHECK PUNCHING SHEAR CAPACITY BY STRENGTH DESIGN METHOD Location RDL (k)
Left
Mid of L1
35.99
Support
Mid of L2
90.01
Support
Mid of L3
108.00
Right
90.01
35.99
RLL (k)
22.49
56.26
67.50
56.26
22.49
RSec (k)
-26.99
-70.21
-86.40
-70.21
-26.99
52.18
127.81
151.21
127.81
52.18
Vu =1.2 RDL + 1.6 RLL + 1.0 Rsec Required b0d, (ACI 318, 11-36)
219.34
527.85
613.74
527.85
219.34
Required d, (ACI 318, 11.0)
3.04
4.90
5.57
4.90
3.04
For f Vn < Vu, the required
0.00
0.00
0.00
0.00
0.00
Not ReqD
Not ReqD
Not ReqD
Not ReqD
Not ReqD
column cap thickness, tcap (in)
8. CALCULATE COST FOR SLAB & CAP Location Concrete
Left
Mid of L1
Mid of L2
Support
Mid of LTyp
Support
1.67
5.00
5.00
5.00
cap concrete
0.00
0.00
0.00
0.00
Total = length (ft)
Tendons
Support
cap dim (ft)
T / 30 ft TW
Total =
670.1
T / 30 ft TW
0.00
178.27
Total =
400.5
20.01 44.71
Rebars
138572
Average =
30.02 0.00
30.02 , (ACI 318 App. E) 435.77
1.30
T / 30 ft TW
Mid of Ln-1
Right 5.00 0.00
100
lb / ft2
20.01 Average =
0.484
178.27
0.00
Average =
0.289
lb / ft2 , (AISC Manual 2nd page 7-15) 44.71 lb / ft2
Note: 1. The column moments are negligible for gravity punching design. Lateral loads, seismic and wind, should be supported by shear walls. Using equivalent frames to support lateral loads is not suggested. 2. By inspection, the deflections of slab do not govern PT concrete floor design. Otherwise, using PT concrete floor is inadequate for larger live load. (ACI 318, 9.5.4.1) 3. The secondary moments are very important concept of PT floor design. Based on this concept, PT floor design are always continuous beams design and one way slabs design. So using two ways finite element analysis to design PT floor is inadequate. Technical References: 1. "Design of Post-Tensioned Slabs Using Unbounded Tendons, Third Edition", The Post-Tensioning Institute, 2004. 2. "Design, Construction and Maintenance of Cast-in-Place Post-Tensioned Concrete Parking Structures, First Edition", The Post-Tensioning Institute, 2001. 3. Bijan O. Aalami & Allan Bommer, "Design Fundamentals of Post-Tensioned Concrete Floors, First Edition", The Post-Tensioning Institute, 1999.
Daniel Tian Li
PROJECT :
PAGE :
CLIENT :
DESIGN BY :
JOB NO. :
DATE :
REVIEW BY :
Design of Post-Tensioned Concrete Floor Based on ACI 318-05 1. DESIGN METHODS 1.1 BREAKDOWN TWO WAYS FLOOR INTO DESIGN STRIPS IN ONE DIRECTION AND ONE WAY SLABS IN OTHER DIRECTION. DESIGN STRIPS WORK AS CONTINUOUS BEAMS BY BANDED ALL TENDONS AT COLUMN. THE PERPENDICULAR DIRECTION LIKE MULTI-SPAN ONE WAY SLABS, USING DISTRIBUTED TENDONS. 1.2 SPECIFY TOTAL REQUIRED EFFECTIVE POST-TENSIONING FORCES AT BANDED TENDONS, ON STRUCTURAL DRAWINGS, AND UNIFORM FORCES IN DISTRIBUTED TENDONS. 1.3 WHEN TENDON LESS THAN 140 FT, STRESS AT ONE END. OTHERWISE STRESS AT BOTH ENDS. 1.4 THE VARIOUS LIVE LOADING CONDITIONS SHOULD BE CONSIDER BY INPUT LL ZERO AT SOME SPANS.
2. INPUT DATA & DESIGN SUMMARY CONCRETE STRENGTH
f'c
=
5
ksi
REBAR YIELD STRESS
fy
=
60
ksi
TENDON PROPERTIES
fpu
=
270
ksi
fpy
=
243
ksi
fse
= =
175
ksi
1/2
in
= = = = = # #
0.153
in2
8
in
30
ft
22
in
CONCRETE COST =
100
lb / ft2
22
in
TENDONS COST =
0.468
lb / ft2
REBARS COST =
0.321
lb / ft2
Mid of L2
Support
dia Aps SLAB THICKNESS
t
TRIBUTARY WIDTH IF BANDED AS DESIGN STRIPS COLUMN WIDTH
W c1
COLUMN DEPTH
c2
TOP BAR SIZE AT COLUMN BOTTOM CONTINUOUS BAR SIZE
Location
Mid of L1
Left
Support
THE DESIGN IS ADEQUATE.
5 4
Mid of L3
Span (ft)
20
30
20
DL (psf)
120
120
120
LL (psf)
75
75
75
75%
80%
75%
Balanced DL (60%-80% suggested) dCGS (in, from bottom)
4
3.33
REQD EFFECTIVE PT (k / ft) Total if banded (kips) Tendons
2.5
3.33
4
22.31
669.4
777.6
669.4
1 / 2 in Dia @ 12 in o.c.
1 / 2 in Dia @ 14 in o.c.
26
30
26
7 # 5 , L = 3.03 ft
Bot Bars, Cont., E. Way
15 # 5 , L = 9.39 ft Not ReqD
Required column cap thk, (in)
7.5
25.92
1 / 2 in Dia @ 14 in o.c.
Total Number if banded Top Bars at Column
7.5
22.31
Right
Not ReqD
15 # 5 , L = 9.39 ft
# 4 @ 58in. o.c. Not ReqD
7 # 5 , L = 3.03 ft Not ReqD
Not ReqD
Not ReqD
3. DESIGN LOADS & SECTION FORCES Location MDL (ft-k / ft)
Left
Mid of L1
Support
Mid of L2
Support
Mid of L3
Right
0.00
1.96
-8.08
5.42
-8.08
1.96
0.00
MLL (ft-k / ft)
0.00
1.23
-5.05
3.39
-5.05
1.23
0.00
0.00
-1.32
6.37
-4.43
6.37
-1.32
Balanced Load (psf, uplift)
-90
Balanced MBal (ft-k / ft) Required Effective PT (k / ft) Tendon Spacing (in) Primary MFe (ft-k / ft)
0.00
-96
22.31
25.92
14
12
-1.25
6.51 7.56
Secondary MSec (ft-k / ft)
0.00
0.07
-90
22.31 14 6.51
-3.24
0.14
0.00
-1.25
0.00
0.07
0.00
Right
7.56 0.14
1.19
1.19
1.19
4. CHECK SERVICE LOAD STRESSES Location
Left
Mid of L1
Support
Mid of L2
Support
Mid of L3
A (in2 / ft)
96
96
96
96
96
96
96
S (in / ft)
128
128
128
128
128
128
128
F / A (ksi)
0.232
0.232
0.232
0.232
0.232
0.232
0.293
0.232
0.172
0.232
3
0.270 Check 125 psi < F /A < 275 psi M / S + F / A , (ksi)
0.232
[Satisfactory] 0.293
for load combination (DL + PT) 0.232
0.172
for load combination (DL + PT) Check ft < 7.5 (fc') M / S + F / A , (ksi) for load (DL + LL + PT)
and fc < 0.45 fc' 0.232
0.072 0.363
0.393 0.430
0.5
0.430 (ACI 318-05, 18.3.3 & 18.4.2a),
-0.401 -0.363
0.110 0.393
0.177
[Satisfactory] 0.408
0.270 (ADAPT suggestion)
0.072 0.110
- M / S + F / A , (ksi)
0.270
-0.401 0.681
-0.363
0.408
where 0.232
0.45 fc' =
0.530
0.45 fc' =
2.250
- M / S + F / A , (ksi)
0.232
for load (DL + LL + PT) Check ft < 7.5 (fc')0.5 and fc < 0.6 fc'
0.057
0.866 0.903 [Satisfactory]
0.866 -0.141
0.057
0.232
0.903 (ACI 318-05, 18.3.3 & 18.4.2b),
where
7.5 (fc')0.5 =
0.530
0.6 fc' =
3.000
(cont'd)
5. CALCULATE NON-PRESTRESSED REINFORCEMENT Location
Left
Max. Nc (k / ft), (ACI 318, 18.0)
Mid of L1
Mid of L2
Support
0.000
As (in2 / ft), (ACI 318, 18.9.3.2) Bottom Bars, Each Way
Support
Mid of L3
1.158
Right
0.000
0.000
0.000
0.000
Not ReqD
Not ReqD
Not ReqD
Max. Acf (in2), (ACI 318, 18.0)
2880
2880
2880
2880
As' (in2), (ACI 318, 18.9.3.2)
2.160
2.160
2.160
2.160
7#5
7#5
7#5
7#5
3.03
9.39
9.39
3.03
Top Bars at Column L (ft), (ACI 318, 18.9.4.1)
6. CHECK FLEXURAL CAPACITY BY STRENGTH DESIGN METHOD Location
Left
Mid of L1
Support
Factored Mu (ft-k / ft)
0.00
4.39
-17.63
1.2 MDL + 1.6 MLL + 1.0 MSec dp (in)
Mid of L2
-16.58
13.12 5.50
4.00
4.67
7.50
0.00273
0.00234
0.00146 0.00170
0.00232
L / dp
60.00
51.39
40.00
65.45
fps (ksi)
186.25
187.27
191.59
0.131
0.131
rp
(ACI 318, 18.7.2, b & c)
189.22
Aps (in2 / ft) Actual Area
0.00170
200.98
40.00
51.39
60.00
191.59
187.27
186.25
0.131
0.131
189.22 0.131
6.75
6.63
0.66
0.33
0.19
0.66 0.61
0.65
0.61
0.000
0.041
0.000
Not ReqD
# 4 @ 58in. o.c.
Not ReqD
0.000
0.041
0.000
0.000
4.367
4.367
0.000
Not ReqD
15 # 5
15 # 5
Not ReqD
Actual As' (in ) 2
2.170
f Mn (ft-k / ft)
-9.28
8.30
Actual Capacity
4.650
4.650
-17.90
-17.90
-20.03
Check f Mn > Mu εpt, (ACI 318, 18.8.1)
4.00 0.00273
6.63
6.63
0.33
Top Bars at Column
4.67 0.00234
6.75
6.75
Actual As (in2 / ft)
7.50 0.00146
0.15
0.19
Required As' (in2)
0.00
0.15
6.63
Required As (in / ft)
Right
4.39
0.153
d (in)
Bottom Bars, Each Way
Mid of L3
-17.63 -16.58
0.131
a (in) 2
Support
13.13
2.170 8.30
-9.28
0.0314
0.0469
-20.03
[Satisfactory] 0.0469
0.0314
εc(dp - a / b1) / (a / b1)
0.0241
0.0241
0.0267
Check εpt > 0.005
0.0173
[Satisfactory]
0.0267 (ACI 318, 18.8.1)
7. CHECK PUNCHING SHEAR CAPACITY BY STRENGTH DESIGN METHOD Location RDL (k)
Left
Mid of L1
35.99
Support
Mid of L2
90.01
Support
Mid of L3
90.01
Right 35.99
RLL (k)
22.49
56.26
56.26
22.49
RSec (k)
-26.99
-70.21
-70.21
-26.99
52.18
127.82
127.82
52.18
Vu =1.2 RDL + 1.6 RLL + 1.0 Rsec Required b0d, (ACI 318, 11-36)
219.34
527.86
527.86
219.34
Required d, (ACI 318, 11.0)
3.04
4.90
4.90
3.04
For f Vn < Vu, the required
0.00
0.00
0.00
0.00
Not ReqD
Not ReqD
Not ReqD
Not ReqD
column cap thickness, tcap (in)
8. CALCULATE COST FOR SLAB & CAP Location Concrete
Left
Mid of L1
Mid of L2
Support
1.67
5.00
5.00
cap concrete
0.00
0.00
0.00
Total = length (ft)
Tendons
Support
cap dim (ft)
20.01 44.71
Rebars
97749
Mid of LTyp
Total =
457.8
0.00
297.12
Total =
313.9
5.00 0.00
T / 30 ft TW 30.02 T / 30 ft TW 8.45
Right
Average =
100
lb / ft2
Average =
0.468
lb / ft2 , (AISC Manual 2nd page 7-15)
0.321
lb / ft2
20.01 , (ACI 318 App. E) 297.12
0.00
T / 30 ft TW
44.71 Average =
Note: 1. The column moments are negligible for gravity punching design. Lateral loads, seismic and wind, should be supported by shear walls. Using equivalent frames to support lateral loads is not suggested. 2. By inspection, the deflections of slab do not govern PT concrete floor design. Otherwise, using PT concrete floor is inadequate for larger live load. (ACI 318, 9.5.4.1) 3. The secondary moments are very important concept of PT floor design. Based on this concept, PT floor design are always continuous beams design and one way slabs design. So using two ways finite element analysis to design PT floor is inadequate. Technical References: 1. "Design of Post-Tensioned Slabs Using Unbounded Tendons, Third Edition", The Post-Tensioning Institute, 2004. 2. "Design, Construction and Maintenance of Cast-in-Place Post-Tensioned Concrete Parking Structures, First Edition", The Post-Tensioning Institute, 2001. 3. Bijan O. Aalami & Allan Bommer, "Design Fundamentals of Post-Tensioned Concrete Floors, First Edition", The Post-Tensioning Institute, 1999.
Daniel Tian Li
PROJECT :
PAGE :
CLIENT :
DESIGN BY :
JOB NO. :
DATE :
REVIEW BY :
Design of Post-Tensioned Concrete Floor Based on ACI 318-05 1. DESIGN METHODS 1.1 BREAKDOWN TWO WAYS FLOOR INTO DESIGN STRIPS IN ONE DIRECTION AND ONE WAY SLABS IN OTHER DIRECTION. DESIGN STRIPS WORK AS CONTINUOUS BEAMS BY BANDED ALL TENDONS AT COLUMN. THE PERPENDICULAR DIRECTION LIKE MULTI-SPAN ONE WAY SLABS, USING DISTRIBUTED TENDONS. 1.2 SPECIFY TOTAL REQUIRED EFFECTIVE POST-TENSIONING FORCES AT BANDED TENDONS, ON STRUCTURAL DRAWINGS, AND UNIFORM FORCES IN DISTRIBUTED TENDONS. 1.3 WHEN TENDON LESS THAN 140 FT, STRESS AT ONE END. OTHERWISE STRESS AT BOTH ENDS. 1.4 THE VARIOUS LIVE LOADING CONDITIONS SHOULD BE CONSIDER BY INPUT LL ZERO AT SOME SPANS.
2. INPUT DATA & DESIGN SUMMARY CONCRETE STRENGTH
f'c
=
5
ski
REBAR YIELD STRESS
fy
=
60
ski
TENDON PROPERTIES
fpu
=
270
ski
fpy
=
243
ski
fse
= =
175
ski
1/2
in
= = = = = # #
0.153
in2
8
in
30
ft
22
in
CONCRETE COST =
100
lb / ft2
22
in
TENDONS COST =
0.431
lb / ft2
REARS COST =
0.157
lb / ft2
Mid L2
Right
dia Aps SLAB THICKNESS
t
TRIBUTARY WIDTH IF BANDED AS DESIGN STRIPS COLUMN WIDTH
W c1
COLUMN DEPTH
c2
TOP BAR SIZE AT COLUMN BOTTOM CONTINUOUS BAR SIZE
Location
Mid of L1
Left
Support
5 4
Span (ft)
20
20
DL (psf)
120
120
LL (psf)
75
75
75%
75%
Balanced DL (60%-80% suggested) dCGS (in, from bottom)
4
3.33
REQD EFFECTIVE PT (k / ft) Total if banded (kips) Tendons
3.33
669.4
669.4 1 / 2 in Dia @ 14 in o.c.
26
26
7 # 5 , L = 3.03 ft
Bot Bars, Cont., E. Way Required column cap thk, (in)
4
22.31
1 / 2 in Dia @ 14 in o.c.
Total Number if banded Top Bars at Column
7.5
22.31
7 # 5 , L = 6.06 ft
# 4 @ 73in. o.c. Not ReqD
THE DESIGN IS INADEQUATE, SEE BELOW.
7 # 5 , L = 3.33 ft
# 4 @ 73in. o.c. Not ReqD
Not ReqD
3. DESIGN LOADS & SECTION FORCES Location MDL (ft-k / ft)
Left
Mid of L1
Support
Mid L2
Right
0.00
3.50
-5.00
3.50
0.00
MLL (ft-k / ft)
0.00
2.19
-3.13
2.19
0.00
0.00
-2.63
3.75
-2.63
Balanced Load (psf, uplift) Balanced MBal (ft-k / ft)
-90
Required Effective PT (k / ft)
-90
22.31
Tendon Spacing (in)
22.31
14
Primary MFe (ft-k / ft)
0.00
-1.25
Secondary MSec (ft-k / ft)
0.00
1.38
0.00
14 6.51 6.51
-1.25
0.00
2.76
1.38
0.00
Right
2.76
4. CHECK SERVICE LOAD STRESSES Location
Left
Mid of L1
Support
Mid L2
A (in2 / ft)
96
96
96
96
96
S (in / ft)
128
128
128
128
128
F / A (ksi)
0.232
0.232
0.232 0.232
0.232
3
0.232 Check 125 psi < F /A < 275 psi M / S + F / A , (ksi)
[Satisfactory]
0.232
0.314
0.115
0.232
0.150
0.350
for load combination (DL + PT)
- M / S + F / A , (ksi)
0.115
for load combination (DL + PT)
0.350
Check ft < 7.5 (fc')0.5 and fc < 0.45 fc' M / S + F / A , (ksi) for load (DL + LL + PT)
0.232
(ADAPT suggestion)
0.314 0.150
[Satisfactory] 0.520
0.232 0.232 (ACI 318-05, 18.3.3 & 18.4.2a),
-0.178 -0.178
0.520
0.232
where
0.45 fc' =
0.530
0.45 fc' =
2.250
- M / S + F / A , (ksi)
0.232
for load (DL + LL + PT) Check ft < 7.5 (fc')0.5 and fc < 0.6 fc'
-0.055
0.643 0.643 [Satisfactory]
-0.055
0.232 (ACI 318-05, 18.3.3 & 18.4.2b),
where
7.5 (fc')0.5 =
0.530
0.6 fc' =
3.000
(cont'd)
5. CALCULATE NON-PRESTRESSED REINFORCEMENT Location
Left
Max. Nc (k / ft), (ACI 318, 18.0)
Mid of L1
Mid L2
Support
0.250
As (in2 / ft), (ACI 318, 18.9.3.2) Bottom Bars, Each Way
Right
0.250
0.000
0.000
Not ReqD
Not ReqD
Max. Acf (in2), (ACI 318, 18.0)
2880
2880
2880
As' (in2), (ACI 318, 18.9.3.2)
2.160
2.160
2.160
7#5
7#5
7#5
3.03
6.06
3.33
Top Bars at Column L (ft), (ACI 318, 18.9.4.1)
6. CHECK FLEXURAL CAPACITY BY STRENGTH DESIGN METHOD Location
Left
Mid of L1
Support
Mid L2
Right
Factored Mu (ft-k / ft)
0.00
9.08
-8.24
9.08
0.00
4.67
4.00
1.2 MDL + 1.6 MLL + 1.0 MSec
-8.24
dp (in)
4.00
4.67
7.50
0.00273
0.00234
0.00146 0.00146
0.00234
0.00273
L / dp
60.00
51.39
32.00
51.39
60.00
fps (ksi)
186.25
187.27
214.46 187.27
186.25
0.131
0.131
0.131
0.131
0.131
d (in)
6.63
6.75
6.63
6.75
6.63
a (in)
0.19
0.52
0.26 0.52
0.19
rp
(ACI 318, 18.7.2, b & c)
191.59
Aps (in2 / ft) Actual Area
0.131
0.27 Required As (in2 / ft) Bottom Bars, Each Way Actual As (in2 / ft)
0.033
# 4 @ 73in. o.c.
# 4 @ 73in. o.c.
0.033
Required As' (in2) Top Bars at Column
0.033
0.000
0.000
Not ReqD
0#5
Not ReqD
2.170
2.170
Actual As' (in ) 2
2.170
f Mn (ft-k / ft)
-9.28
9.08
Actual Capacity
-17.66 -16.00
9.08
-9.28
[Unsatisfactory]
Check f Mn > Mu εpt, (ACI 318, 18.8.1)
0.033
0.000
0.0469
0.0186
εc(dp - a / b1) / (a / b1)
0.0669 0.0648
Check εpt > 0.005
0.0186
[Satisfactory]
0.0469 (ACI 318, 18.8.1)
7. CHECK PUNCHING SHEAR CAPACITY BY STRENGTH DESIGN METHOD Location RDL (k)
Left
Mid of L1
35.99
Support
Mid L2
72.02
Right 35.99
RLL (k)
22.50
45.01
22.50
RSec (k)
-26.99
-54.01
-26.99
52.19
104.42
52.19
Vu =1.2 RDL + 1.6 RLL + 1.0 Rsec Required b0d, (ACI 318, 11-36)
219.36
438.91
219.36
Required d, (ACI 318, 11.0)
3.04
4.19
3.04
For f Vn < Vu, the required
0.00
0.00
0.00
Not ReqD
Not ReqD
Not ReqD
column cap thickness, tcap (in)
8. CALCULATE COST FOR SLAB & CAP Location Concrete
Left
Mid of L1
1.67
5.00
cap concrete
0.00
0.00 Total =
length (ft)
Tendons
Support
cap dim (ft)
20.01 44.71
Rebars
56926
Mid of L2
Right 5.00 0.00
T / 30 ft TW
Average =
100
Average =
0.431
lb / ft2 , (AISC Manual 2nd page 7-15)
Average =
0.157
lb / ft2
lb / ft2
20.01
Total =
245.4
6.71
89.43
Total =
89.3
T / 30 ft TW 6.71
, (ACI 318 App. E) 49.23
T / 30 ft TW
Note: 1. The column moments are negligible for gravity punching design. Lateral loads, seismic and wind, should be supported by shear walls. Using equivalent frames to support lateral loads is not suggested. 2. By inspection, the deflections of slab do not govern PT concrete floor design. Otherwise, using PT concrete floor is inadequate for larger live load. (ACI 318, 9.5.4.1) 3. The secondary moments are very important concept of PT floor design. Based on this concept, PT floor design are always continuous beams design and one way slabs design. So using two ways finite element analysis to design PT floor is inadequate. Technical References: 1. "Design of Post-Tensioned Slabs Using Unbounded Tendons, Third Edition", The Post-Tensioning Institute, 2004. 2. "Design, Construction and Maintenance of Cast-in-Place Post-Tensioned Concrete Parking Structures, First Edition", The Post-Tensioning Institute, 2001. 3. Bijan O. Aalami & Allan Bommer, "Design Fundamentals of Post-Tensioned Concrete Floors, First Edition", The Post-Tensioning Institute, 1999.
