SS CP 65 1999 PT SL Example 001
User Manual: SS CP 65-1999 PT-SL Example 001
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Software Verification PROGRAM NAME: REVISION NO.: ETABS 0 SS CP 65-99 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. Prestressing tendon, Ap Mild Steel, As 229 mm 254 mm 25 mm Length, L = 9754 mm 914 mm Section Elevation Figure 1 One-Way Slab SS CP 65-99 PT-SL EXAMPLE 001 - 1 Software Verification PROGRAM NAME: REVISION NO.: ETABS 0 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, has been 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: Live = 4.788 kN/m2 Dead = self weight, 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 are compared with the ETABS results and summarized for verification and validation of the ETABS results. GEOMETRY, PROPERTIES AND LOADING Thickness Effective depth Clear span T, h = d = L = Concrete strength Yield strength of steel Prestressing, ultimate Prestressing, effective Area of Prestress (single strand) Concrete unit weight Modulus of elasticity Modulus of elasticity Poisson’s ratio f 'c fy fpu fe Ap wc Ec Es Dead load Live load wd = wl = 254 229 9754 = 30 = 400 = 1862 = 1210 = 198 = 23.56 = 25000 = 200,000 = 0 self 4.788 mm mm mm MPa MPa MPa MPa mm2 kN/m3 N/mm3 N/mm3 kN/m2 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 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. SS CP 65-99 PT-SL EXAMPLE 001 - 2 Software Verification PROGRAM NAME: REVISION NO.: ETABS 0 Table 1 Comparison of Results FEATURE TESTED Factored moment, Mu (Ultimate) (kN-m) Area of Mild Steel req’d, As (sq-cm) Transfer Conc. Stress, top (D+PTI), MPa Transfer Conc. Stress, bot (D+PTI), MPa Normal Conc. Stress, top (D+L+PTF), MPa Normal Conc. Stress, bot (D+L+PTF), MPa INDEPENDENT RESULTS ETABS RESULTS DIFFERENCE 174.4 174.4 0.00% 19.65 19.80 0.76% 5.058 5.057 -0.02% 2.839 2.839 0.00% 10.460 10.467 0.07% 8.402 8.409 0.08% COMPUTER FILE: SS CP 65-1999 PT-SL EX001.EDB CONCLUSION The ETABS results show an acceptable comparison with the independent results. SS CP 65-99 PT-SL EXAMPLE 001 - 3 Software Verification PROGRAM NAME: REVISION NO.: ETABS 0 HAND CALCULATIONS: Design Parameters: Mild Steel Reinforcing f’c = 30MPa fy = 400MPa m, steel = 1.15 Post-Tensioning fpu = 1862 MPa fpy = 1675 MPa Stressing Loss = 186 MPa Long-Term Loss = 94 MPa fi = 1490 MPa fe = 1210 MPa m, concrete = 1.50 Prestressing tendon, Ap Mild Steel, As 229 mm 254 mm 25 mm Length, L = 9754 mm Elevation 914 mm Section Loads: Dead, self-wt = 0.254 m 23.56 kN/m3 = 5.984 kN/m2 (D) 1.4 = 8.378 kN/m2 (Du) Live, = 4.788 kN/m2 (L) 1.6 = 7.661 kN/m2 (Lu) Total = 10.772 kN/m2 (D+L) = 16.039 kN/m2 (D+L)ult =10.772 kN/m2 0.914 m = 9.846 kN/m, u = 16.039 kN/m2 0.914 m = 14.659 kN/m wl12 Ultimate Moment, M U = 14.659 (9.754)2/8 = 174.4 kN-m 8 SS CP 65-99 PT-SL EXAMPLE 001 - 4 Software Verification PROGRAM NAME: REVISION NO.: ETABS 0 f pu Ap 7000 1 1.7 l/d f cu bd 7000 1862(198) 1210 1 1.7 9754 / 229 30(914)(229) Ultimate Stress in strand, f pb f pe 1358 MPa 0.7 f pu 1303 MPa K factor used to determine the effective depth is given as: 174.4 M K 0.1213 < 0.156 = 2 f cu bd 30000(0.914)(0.229) 2 K 0.95d = 192.2 mm z d 0.5 0.25 0.9 Ultimate force in PT, Fult , PT AP ( f PS ) 2 99 1303 1000 258.0 kN Ultimate moment due to PT, M ult , PT Fult , PT ( z ) / 258.0 0.192 1.15 43.12 kN-m Net Moment to be resisted by As, M NET MU M PT 174.4 43.12 131.28 kN-m The area of tensile steel reinforcement is then given by: M NET 131.28 1e6 1965 mm 2 As = 0.87 f y z X 0.87 400 192 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, M D 5.984 0.914 9.754 8 65.04 kN-m 2 Moment due to PT, Stress in concrete, M PT FPTI (sag) 257.4 102 mm 1000 26.25 kN-m F M M PT 257.4 65.04 26.23 f PTI D A S 0.254 0.914 0.00983 where S = 0.00983m3 f 1.109 3.948 MPa f 5.058(Comp) max, 2.839(Tension) max SS CP 65-99 PT-SL EXAMPLE 001 - 5 Software Verification PROGRAM NAME: REVISION NO.: ETABS 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 8 65.04 kN-m 2 Moment due to live load, M L 4.788 0.914 9.754 8 52.04 kN-m 2 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 SS CP 65-99 PT-SL EXAMPLE 001 - 6
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