Software Verification

PROGRAM NAME: SAFE

REVISION NO.: 0

EXAMPLE AS 3600-01 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 reinforcing strength 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.

Prestressing tendon, Ap

Mild Steel, As
229 mm

254 mm

25 mm
Length, L = 9754 mm 914 mm

Elevation Section

Figure 1 One-Way Slab

EXAMPLE AS 3600-01 PT-SL-001 - 1

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PROGRAM NAME: SAFE
REVISION NO.: 0

A 914-mm-wide design strip is centered along the length of the slab and is 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, 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
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 tendon), Ap = 198 mm2
Concrete unit weight, wc = 23.56 KN/m3
Concrete modulus of elasticity, Ec = 25000 N/mm3
Rebar 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

¾ Calculation of the required flexural reinforcement
¾ 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 the independent hand calculations.

EXAMPLE AS 3600-01 PT-SL-001 - 2

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PROGRAM NAME: SAFE
REVISION NO.: 0

Table 1 Comparison of Results

INDEPENDENT SAFE
FEATURE TESTED DIFFERENCE
RESULTS RESULTS
Factored moment,
156.12 156.14 0.01%
Mu (Ultimate) (kN-m)
Area of Mild Steel req’d,
16.55 16.59 0.24%
As (sq-cm)
Transfer Conc. Stress, top
−3.500 −3.498 0.06%
(0.8D+1.15PTI), MPa
Transfer Conc. Stress, bot
0.950 0.948 0.21%
(0.8D+1.15PTI), MPa
Normal Conc. Stress, top
−10.460 −10.465 0.10%
(D+L+PTF), MPa
Normal Conc. Stress, bot
8.402 8.407 0.05%
(D+L+PTF), MPa
Long-Term Conc. Stress,
−7.817 −7.817 0.00%
top (D+0.5L+PTF(L)), MPa
Long-Term Conc. Stress,
5.759 5.759 0.00%
bot (D+0.5L+PTF(L)), MPa

COMPUTER FILE: AS 3600-01 PT-SL-001.FDB

CONCLUSION
The SAFE results show a very close comparison with the independent results.

EXAMPLE AS 3600-01 PT-SL-001 - 3

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PROGRAM NAME: SAFE
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HAND CALCULATIONS:
Design Parameters:
Mild Steel Reinforcing Post-Tensioning
f’c = 30MPai fpu = 1862 MPa
fy = 400MPa fpy = 1675 MPa
Stressing Loss = 186 MPa
Long-Term Loss = 94 MPa
fi = 1490 MPa
fe = 1210 MPa
φ = 0.80
γ = [0.85 − 0.007( f 'c −28)]= 0.836
amax = γk u d = 0.836*0.4*229 = 76.5 mm

Prestressing tendon, Ap

Mild Steel, As
229 mm

254 mm

25 mm
Length, L = 9754 mm 914 mm

Elevation Section

Loads:
Dead, self-wt = 0.254 m x 23.56 kN/m3 = 5.984 kN/m2 (D) x 1.2 = 7.181 kN/m2 (Du)
Live, = 4.788 kN/m2 (L) x 1.5 = 7.182 kN/m2 (Lu)
Total = 10.772 kN/m2 (D+L) = 14.363 kN/m2 (D+L)ult

ω =10.772 kN/m2 x 0.914m = 9.846 kN/m, ωu = 14.363 kN/m2 x 0.914m = 13.128 kN/m

wl12
Ultimate Moment, M U = = 13.128 x (9.754)2/8 = 156.12 kN-m
8

EXAMPLE AS 3600-01 PT-SL-001 - 4

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f 'C bef d P
Ultimate Stress in strand, f PS = f SE + 70 +
300 AP
30(914)(229)
= 1210 + 70 +
300(198)
= 1386 MPa ≤ f SE + 200 = 1410 MPa

Ultimate force in PT, Fult , PT = AP ( f PS ) = 197.4(1386) /1000 = 273.60 kN

Total Ultimate force, Fult ,Total = 273.60 + 560.0 = 833.60 kN
2M*
Stress block depth, a = d − d 2 −
0.85 f 'c φ b
2(159.12)
= 0.229 − 0.2292 − = 40.90
0.85(30000)(0.80)(0.914)
Ultimate moment due to PT,
a 40.90
M ult , PT = Fult , PT (d − )φ = 273.60(229 − )(0.80) /1000 = 45.65 kN-m
2 2
Net ultimate moment, M net = M U − M ult , PT = 156.1 − 45.65 = 110.45 kN-m

Required area of mild steel reinforcing,

M net 110.45
AS = = (1e6) = 1655 mm 2
a 0.04090
φ f y (d − ) 0.80(400000)(0.229 − )
2 2

Check of Concrete Stresses at Midspan:

Initial Condition (Transfer), load combination (0.8D+1.15PTi) = 0.80D+0.0L+1.15PTI

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, M D = 5.984(0.914)(9.754) 2 / 8 = 65.04 kN-m
Moment due to PT, M PT = FPTI (sag) = 257.4(102 mm) /1000 = 26.25 kN-m
F M − M PT (1.15)(−257.4) (0.80)65.04 − (1.15)26.23
Stress in concrete, f = PTI ± D = ±
A S 0.254(0.914) 0.00983
where S=0.00983m3
f = −1.275 ± 2.225 MPa
f = −3.500(Comp) max, 0.950(Tension) max

EXAMPLE AS 3600-01 PT-SL-001 - 5

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PROGRAM NAME: SAFE
REVISION NO.: 0

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, M D = 5.984(0.914)(9.754) 2 / 8 = 65.04 kN-m
Moment due to live load, M L = 4.788(0.914)(9.754) 2 / 8 = 52.04 kN-m
Moment due to PT, M PT = FPTI (sag) = 238.9(102 mm) /1000 = 24.37 kN-m

Stress in concrete for (D+L+PTF),

F M − M PT −238.8 117.08 − 24.37
f = PTI ± D + L = ±
A S 0.254(0.914) 0.00983
f = −1.029 ± 9.431
f = −10.460(Comp) max, 8.402(Tension) max

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, M D = 5.984(0.914)(9.754) 2 / 8 = 65.04 kN-m
Moment due to dead load, M L = 4.788(0.914)(9.754) 2 / 8 = 52.04 kN-m
Moment due to PT, M PT = FPTI (sag) = 238.9(102 mm) /1000 = 24.37 kN-m

Stress in concrete for (D+0.5L+PTF(L)),

F M − M PT −238.9 91.06 − 24.33
f = PTI ± D + 0.5 L = ±
A S 0.254(0.914) 0.00983
f = −1.029 ± 6.788
f = −7.817(Comp) max, 5.759(Tension) max

EXAMPLE AS 3600-01 PT-SL-001 - 6