CSA A23.3 04 PT SL Example 001
User Manual: CSA A23.3-04 PT-SL Example 001
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CSA 23.3-04 PT-SL EXAMPLE 001 - 1
CSA 23.3-04 PT-SL EXAMPLE 001
Post-Tensioned Slab Design
PROBLEM DESCRIPTION
The purpose of this example is to verify the slab stresses and the required area of
mild steel strength reinforcing for a post-tensioned slab.
A one-way simply supported slab is modeled in ETABS. The modeled slab is 254
mm thick by 914 mm wide and spans 9754 mm as shown in shown in Figure 1.
Length, L = 9754 mm
Elevation Section
Prestressing tendon, Ap
Mild Steel, As
914 mm 25 mm
229 mm
254 mm
Length, L = 9754 mm
Elevation Section
Prestressing tendon, Ap
Mild Steel, As
914 mm 25 mm
229 mm
254 mm
Figure 1 One-Way Slab
A 254-mm-wide design strip is centered along the length of the slab and has been
defined as an A-Strip. B-strips have been placed at each end of the span
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CSA 23.3-04 PT-SL EXAMPLE 001 - 2
perpendicular to Strip-A (the B-Strips are necessary to define the tendon profile).
A tendon with two strands, each having an area of 99 mm2, has been added to the
A-Strip. The self weight and live loads were added to the slab. The loads and post-
tensioning forces are as follows:
Loads: Dead = self weight, Live = 4.788 KN/m2
The total factored strip moments, required area of mild steel reinforcement, and
slab stresses are reported at the midspan of the slab. Independent hand calculations
have been compared with the ETABS results and summarized for verification and
validation of the ETABS results.
GEOMETRY, PROPERTIES AND LOADING
Thickness T, h = 254 mm
Effective depth d = 229 mm
Clear span L = 9754 mm
Concrete strength f 'c = 30 MPa
Yield strength of steel fy = 400 MPa
Prestressing, ultimate fpu = 1862 MPa
Prestressing, effective fe = 1210 MPa
Area of Prestress (single strand) Ap = 198 mm2
Concrete unit weight wc = 23.56 KN/m3
Modulus of elasticity Ec = 25000 N/mm3
Modulus of elasticity Es = 200,000 N/mm3
Poisson’s ratio = 0
Dead load wd = self KN/m2
Live load wl = 4.788 KN/m2
TECHNICAL FEATURES OF ETABS TESTED
Calculation of the required flexural reinforcement
Check of slab stresses due to the application of dead, live, and post-tensioning
loads.
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RESULTS COMPARISON
Table 1 shows the comparison of the ETABS total factored moments, required
mild steel reinforcing, and slab stresses with the independent hand calculations.
Table 1 Comparison of Results
FEATURE TESTED INDEPENDENT
RESULTS ETABS
RESULTS DIFFERENCE
Factored moment,
Mu (Ultimate) (kN-m) 159.4 159.4 0.00%
Area of Mild Steel req’d,
As (sq-cm) 16.25 16.33 0.49%
Transfer Conc. Stress, top
(D+PTI), MPa 5.058 5.057 -0.02%
Transfer Conc. Stress, bot
(D+PTI), MPa 2.839 2.839 0.00%
Normal Conc. Stress, top
(D+L+PTF), MPa 10.460 10.467 0.07%
Normal Conc. Stress, bot
(D+L+PTF), MPa 8.402 8.409 0.08%
Long-Term Conc. Stress,
top (D+0.5L+PTF(L)), MPa 7.817 7.818 0.01%
Long-Term Conc. Stress,
bot (D+0.5L+PTF(L)), MPa 5.759 5.760 0.02%
COMPUTER FILE: CSA A23.3-04 PT-SL EX001.EDB
CONCLUSION
The ETABS results show an exact comparison with the independent results.
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HAND CALCULATIONS:
Design Parameters:
Mild Steel Reinforcing Post-Tensioning
fcu = 30MPa fpu = 1862 MPa
fy = 400MPa fpy = 1675 MPa
Stressing Loss = 186 MPa
Long-Term Loss = 94 MPa
fi = 1490 MPa
fe = 1210 MPa
065
c.
, 0 85
S.
1 = 0.85 – 0.0015f'c 0.67 = 0.805
1 = 0.97 – 0.0025f'c 0.67 = 0.895
Length, L = 9754 mm
Elevation Section
Prestressing tendon, Ap
Mild Steel, As
914 mm 25 mm
229 mm
254 mm
Length, L = 9754 mm
Elevation Section
Prestressing tendon, Ap
Mild Steel, As
914 mm 25 mm
229 mm
254 mm
Loads:
Dead, self-wt = 0.254 m x 23.56 kN/m3 = 5.984 kN/m2 (D) x 1.25 = 7.480 kN/m2 (Du)
Live, = 4.788 kN/m2 (L) x 1.50 = 7.182 kN/m2 (Lu)
Total = 10.772 kN/m2 (D+L) = 14.662 kN/m2 (D+L)ult
=10.772 kN/m2 x 0.914m = 9.846 kN/m,
u
= 16.039 kN/m2 x 0.914m = 13.401 kN/m
Ultimate Moment, 2
1
8
U
wl
M= 13.401 x (9.754)2/8 = 159.42 kN-m
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CSA 23.3-04 PT-SL EXAMPLE 001 - 5
Ultimate Stress in strand,
8000
pb pe p y
o
f
fdc
l
11
0.9 197 1347 0.85 1625 400 61.66 mm
' 0.805 0.65 30.0 0.895 914
pppr ssy
y
cc
Af Af
cfb
8000
1210 229 61.66 1347 MPa
9754
pb
f
Depth of the compression block, a, is given as:
Stress block depth,
*
2
1cc
2M
ad d
f
'b
22 159.42
0.229 0.229 55.18
0.805 30000 0.65 0.914
Ultimate force in PT,
,( ) 197 1347 1000 265.9 kN
ult PT P PS
FAf
Ultimate moment due to PT,
,,
55.18
265.9 0.229 0.85 45.52 kN-m
22
ult PT ult PT
a
MFd
Net Moment to be resisted by As, NET U PT
M
MM
159.42 45.52 113.90 kN-m
The area of tensile steel reinforcement is then given by:
0.87
NET
s
y
M
A
f
z
=
2
113.90 1 6 1625 mm
55.18
0.87 400 229 2
e
Check of Concrete Stresses at Midspan:
Initial Condition (Transfer), load combination (D+PTi) = 1.0D+0.0L+1.0PTI
Tendon stress at transfer = jacking stress stressing losses = 1490 186 = 1304 MPa
The force in the tendon at transfer, =
1304 197.4 1000 257.4 kN
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Moment due to dead load,
2
5.984 0.914 9.754 8 65.04 kN-m
D
M
Moment due to PT,
(sag) 257.4 102 mm 1000 26.25 kN-m
PT PTI
MF
Stress in concrete, 257.4 65.04 26.23
0.254(0.914) 0.00983
PTI D PT
FMM
fAS
where S = 0.00983m3
1.109 3.948 MPaf
5.058(Comp)max, 2.839(Tension)maxf
Normal Condition, load combinations: (D+L+PTF) = 1.0D+1.0L+1.0PTF
Tendon stress at normal = jacking stressing long-term = 1490 186 94 = 1210 MPa
The force in tendon at normal, =
1210 197.4 1000 238.9 kN
Moment due to dead load,
2
5.984 0.914 9.754 8 65.04 kN-m
D
M
Moment due to live load,
2
4.788 0.914 9.754 8 52.04 kN-m
L
M
Moment due to PT,
(sag) 238.9 102 mm 1000 24.37 kN-m
PT PTI
MF
Stress in concrete for (D+L+PTF),
238.8 117.08 24.37
0.254 0.914 0.00983
PTI D L PT
FM M
fAS
1 029 9 431
f
..
10.460(Comp)max, 8.402(Tension)maxf
Long-Term Condition, load combinations: (D+0.5L+PTF(L)) = 1.0D+0.5L+1.0PTF
Tendon stress at normal = jacking stressing long-term = 1490 186 94 = 1210 MPa
The force in tendon at normal, =
1210 197.4 1000 238.9 kN
Moment due to dead load,
2
5.984 0.914 9.754 8 65.04 kN-m
D
M
Moment due to live load,
2
4.788 0.914 9.754 8 52.04 kN-m
L
M
Moment due to PT,
(sag) 238.9 102 mm 1000 24.37 kN-m
PT PTI
MF
Stress in concrete for (D+0.5L+PTF(L)),
0.5 238.9 91.06 24.33
0.254 0.914 0.00983
DL PT
PTI MM
F
fAS
1 029 6 788
f
..
7.817(Comp)max, 5.759(Tension)maxf
