Contents Eurocode 2 04 PT SL 001

User Manual: Eurocode 2-04 PT-SL-001

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EXAMPLE Eurocode 2-04 PT-SL-001 - 1
EXAMPLE Eurocode 2-04 PT-SL-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 SAFE. 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
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EXAMPLE Eurocode 2-04 PT-SL-001 - 2
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,
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, was added to the A-
Strip. The self weight and live loads have been 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 mid-span of the slab. Independent hand
calculations were compared with the SAFE results and summarized for verification
and validation of the SAFE 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 ν = 0
Dead load wd = self KN/m2
Live load wl = 4.788 KN/m2
TECHNICAL FEATURES OF SAFE TESTED
Calculation of the required flexural reinforcement
Check of slab stresses due to the application of dead, live, and post-tensioning
loads.
RESULTS COMPARISON
Table 1 shows the comparison of the SAFE total factored moments, required mild
steel reinforcing, and slab stresses with independent hand calculations.
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EXAMPLE Eurocode 2-04 PT-SL-001 - 3
Table 1 Comparison of Results
FEATURE TESTED INDEPENDENT
RESULTS SAFE
RESULTS DIFFERENCE
Mu (Ultimate) (kN-m) 166.41 166.41 0.00%
(D+PTI), MPa −5.057 −5.057 0.00%
(D+PTI), MPa 2.839 2.839 0.00%
(D+L+PTF), MPa −10.460 −10.465 0.05%
(D+L+PTF), MPa 8.402 8.407 0.06%
(D+0.5L+PTF(L)), MPa −7.817 −7.817 0.00%
(D+0.5L+PTF(L)), MPa 5.759 5.759 0.00%
Table 2 Comparison of Design Moments and Reinforcements
National Annex Method Design Moment
(kN-m)
Reinforcement Area
(sq-cm)
As+
CEN Default, Norway,
Slovenia and Sweden
SAFE 166.41 15.39
Calculated 166.41 15.36
Finland , Singapore and UK SAFE 166.41 15.89
Calculated 166.41 15.87
Denmark SAFE 166.41 15.96
Calculated 166.41 15.94
COMPUTER FILE: EUROCODE 2-04 PT-SL-001.FDB
CONCLUSION
The SAFE results show an acceptable comparison with the independent results.
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EXAMPLE Eurocode 2-04 PT-SL-001 - 4
HAND CALCULATIONS:
Design Parameters:
Mild Steel Reinforcing Post-Tensioning
f’c = 30MPa fpu = 1862 MPa
fy = 400MPa fpy = 1675 MPa
Stressing Loss = 186 MPa
Long-Term Loss = 94 MPa
fi = 1490 MPa
fe = 1210 MPa
γ
m, steel = 1.15
γ
m, concrete = 1.50
0.1
=
η
for fck ≤ 50 MPa
8.0=
λ
for fck ≤ 50 MPa
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 × 23.56 kN/m3 = 5.984 kN/m2 (D) × 1.35 = 8.078 kN/m2 (Du)
Live, = 4.788 kN/m2 (L) × 1.50 = 7.182 kN/m2 (Lu)
Total = 10.772 kN/m2 (D+L) = 15.260 kN/m2 (D+L)ult
ω
=10.772 kN/m2 × 0.914 m = 9.846 kN/m,
u
ω
= 15.260 kN/m2 × 0.914 m = 13.948 kN/m
Ultimate Moment,
2
1
8
U
wl
M=
=
( )
2
13.948 9.754 8×
= 165.9 kN-m
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EXAMPLE Eurocode 2-04 PT-SL-001 - 5
Ultimate Stress in strand,
7000 1 1.36

=+−


PU P
PS SE
CK
fA
ff d l
f bd
( )
( )
1862(198)
1210 7000(229) 1 1.36 9754
30(914) 229
1361MPa

=+−



=
Ultimate force in PT,
( )( )
,( ) 2 99 1361 1000 269.5 kN
ult PT P PS
F Af
= = =
CEN Default, Norway, Slovenia and Sweden:
Design moment M = 166.4122 kN-m
Compression block depth ratio:
cd
fbd
M
m
η
2
=
( )( )
( )
( )
2
166.4122 0.1736
0.914 0.229 1 30000 1.50
= =
Required area of mild steel reinforcing,
m21
1−
−=
ω
=
1 1 2(0.1736) 0.1920−− =
2
1(30 /1.5)(914)(229)
0.1920 2311mm
400 /1.15
cd
EquivTotal
yd
f bd
Af
η
ω
 
= = =
 
 

2
1361 2311mm
400 1.15

= +=


EquivTotal P S
AA A
2
1361
2311 198 1536 mm
400 /1.15

=−=


S
A
Finland, Singapore and UK:
Design moment M = 166.4122 kN-m
Compression block depth ratio:
cd
fbd
M
m
η
2
=
( )( ) ( )
( )
2
166.4122 0.2042
0.914 0.229 0.85 30000 1.50
= =
Required area of mild steel reinforcing,
m211 −−=
ω
=
1 1 2(0.2042) 0.23088−− =
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EXAMPLE Eurocode 2-04 PT-SL-001 - 6
2
0.85(30 /1.5)(914)(229)
0.23088 2362 mm
400 /1.15
cd
EquivTotal
yd
f bd
Af
η
ω
 
= = =
 
 

2
1361 2362 mm
400 1.15

= +=


EquivTotal P S
AA A
2
1361
2362 198 1587 mm
400 1.15

=−=


S
A
Denmark:
Design moment M = 166.4122 kN-m
Compression block depth ratio:
cd
fbd
M
m
η
2
=
( )( ) ( )
( )
2
166.4122 0.1678
0.914 0.229 1.0 30000 1.45
= =
Required area of mild steel reinforcing,
m
21
1−
−=
ω
=
1 1 2(0.1678) 0.1849−− =
2
1.0(30 /1.45)(914)(229)
0.1849 2402 mm
400 /1.20
cd
EquivTotal
yd
f bd
Af
η
ω
 
= = =
 
 

2
1361 2402 mm
400 1.2

= +=


EquivTotal P S
AA A
2
1361
2402 198 1594 mm
400 1.2

=−=


S
A
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=
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
F MM
fAS
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EXAMPLE Eurocode 2-04 PT-SL-001 - 7
where S = 0.00983m3
1.109 3.948 MPaf=−±
5.058(Comp)max, 2.839(Tension)max
f= −
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 431f. .
=−±
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
+
−−−
=±=±
D L PT
PTI
MM
F
fAS
1 029 6 788f. .=−±
7.817(Comp)max, 5.759(Tension)max
f= −

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