Csa a23 3 04 pt sl 001

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Software Verification PROGRAM NAME: REVISION NO.: SAFE EXAMPLE CSA 23.3-04 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 Prestressing tendon, Ap Mild Steel, As 229 mm 254 mm 25 mm Length, L = 9754 mm 914 mm Section Elevation Figure One-Way Slab EXAMPLE CSA 23.3-04 PT-SL-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE 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 were added to the slab The loads and posttensioning 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 SAFE results and summarized for verification and validation of the SAFE results GEOMETRY, PROPERTIES AND LOADING Thickness Effective depth Clear span T, h = d = L = 254 229 9754 mm mm mm 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 ν = = = = = = = = = 30 400 1862 1210 198 23.56 25000 200,000 MPa MPa MPa MPa mm2 KN/m3 N/mm3 N/mm3 Dead load Live load wd wl = = self 4.788 KN/m2 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 EXAMPLE CSA 23.3-04 PT-SL-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE RESULTS COMPARISON Table shows the comparison of the SAFE total factored moments, required mild steel reinforcing, and slab stresses with the independent hand calculations Table 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 Long-Term Conc Stress, top (D+0.5L+PTF(L)), MPa Long-Term Conc Stress, bot (D+0.5L+PTF(L)), MPa INDEPENDENT RESULTS SAFE RESULTS DIFFERENCE 159.4 159.4 0.00% 16.25 16.32 0.43% −5.058 −5.057 0.02% 2.839 2.839 0.00% −10.460 −10.465 0.05% 8.402 8.407 0.06% −7.817 −7.817 0.00% 5.759 5.759 0.00% COMPUTER FILE: CSA A23.3-04 PT-SL-001.FDB CONCLUSION The SAFE results show an exact comparison with the independent results EXAMPLE CSA 23.3-04 PT-SL-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE HAND CALCULATIONS: Design Parameters: Mild Steel Reinforcing fcu = 30MPa fy = 400MPa Post-Tensioning fpu = 1862 MPa fpy = 1675 MPa Stressing Loss = 186 MPa Long-Term Loss = 94 MPa fi = 1490 MPa fe = 1210 MPa φc = 0.65 , φS = 0.85 α1 = 0.85 – 0.0015f'c ≥ 0.67 = 0.805 β1 = 0.97 – 0.0025f'c ≥ 0.67 = 0.895 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 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) = 14.662 kN/m2 (D+L)ult Total = 10.772 kN/m2 (D+L) ω =10.772 kN/m2 x 0.914m = 9.846 kN/m, ωu = 16.039 kN/m2 x 0.914m = 13.401 kN/m Ultimate Moment, M U = EXAMPLE CSA 23.3-04 PT-SL-001 - wl12 = 13.401 x (9.754)2/8 = 159.42 kN-m Software Verification PROGRAM NAME: REVISION NO.: Ultimate Stress in strand, f pb = f pe + cy = SAFE 8000 ( d p − cy ) lo φ p Ap f pr + φs As f y 0.9(197)(1347) + 0.85(1625)(400) = = 61.66 mm α1φc f 'c β1b 0.805(0.65)(30.0)(0.895)(914) f pb = 1210 + 8000 ( 229 − 61.66 ) = 1347 MPa 9754 Depth of the compression block, a, is given as: Stress block depth, a = d − d − 2M * α f 'c φc b = 0.229 − 0.2292 − 2(159.42) = 55.18 0.805(30000)(0.65)(0.914) Ultimate force in PT, Fult , PT = AP ( f PS ) = 197(1347) /1000 = 265.9 kN Ultimate moment due to PT, a 55.18 M ult , PT = Fult , PT (d − )φ = 265.9(0.229 − )(0.85) = 45.52 kN-m 2 Net Moment to be resisted by As, M NET = MU − M PT = 159.42 − 45.52 = 113.90 kN-m The area of tensile steel reinforcement is then given by: As = M NET 113.90 = (1e6) = 1625 mm 55.18 0.87 f y z 0.87(400)(229 − ) 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) / = 65.04 kN-m EXAMPLE CSA 23.3-04 PT-SL-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE Moment due to PT, M PT = FPTI (sag) = 257.4(102 mm) /1000 = 26.25 kN-m F M − M PT −257.4 65.04 − 26.23 Stress in concrete, 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 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) / = 65.04 kN-m Moment due to live load, M L = 4.788(0.914)(9.754) / = 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) / = 65.04 kN-m Moment due to live load, M L = 4.788(0.914)(9.754) / = 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)), M − M PT F −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 CSA 23.3-04 PT-SL-001 -