As 3600 01 pt sl 001

As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001 As 3600 01 pt sl 001

Software Verification PROGRAM NAME: REVISION NO.: SAFE 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 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 AS 3600-01 PT-SL-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE 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, Effective depth, T, h = d = Clear span, Concrete strength, Yield strength of steel, Prestressing, ultimate Prestressing, effective Area of prestress (single tendon), Concrete unit weight, Concrete modulus of elasticity, Rebar modulus of elasticity, Poisson’s ratio, L f 'c fy fpu fe Ap wc Ec Es ν = = = = = = = = = = Dead load, Live load, wd wl = = 254 mm 229 mm 9754 30 400 1862 1210 198 23.56 25000 200,000 mm MPa MPa MPa MPa mm2 KN/m3 N/mm3 N/mm3 self KN/m2 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 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 - Software Verification PROGRAM NAME: REVISION NO.: SAFE Table Comparison of Results FEATURE TESTED INDEPENDENT RESULTS SAFE RESULTS DIFFERENCE 156.12 156.14 0.01% 16.55 16.59 0.24% −3.500 −3.498 0.06% 0.950 0.948 0.21% −10.460 −10.465 0.10% 8.402 8.407 0.05% −7.817 −7.817 0.00% 5.759 5.759 0.00% Factored moment, Mu (Ultimate) (kN-m) Area of Mild Steel req’d, As (sq-cm) Transfer Conc Stress, top (0.8D+1.15PTI), MPa Transfer Conc Stress, bot (0.8D+1.15PTI), 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 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 - Software Verification PROGRAM NAME: REVISION NO.: SAFE HAND CALCULATIONS: Design Parameters: Mild Steel Reinforcing f’c = 30MPai fy = 400MPa Post-Tensioning fpu = fpy = Stressing Loss = Long-Term Loss = fi = fe = 1862 MPa 1675 MPa 186 MPa 94 MPa 1490 MPa 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 Elevation 914 mm 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 Ultimate Moment, M U = EXAMPLE AS 3600-01 PT-SL-001 - wl12 = 13.128 x (9.754)2/8 = 156.12 kN-m Software Verification PROGRAM NAME: REVISION NO.: Ultimate Stress in strand, f PS = f SE + 70 + SAFE f 'C bef d P 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 Stress block depth, a = d − d − 2M* 0.85 f 'c φ b = 0.229 − 0.2292 − 2(159.12) = 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 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 = (1e6) = 1655 mm AS = 0.04090 a ) φ f y (d − ) 0.80(400000)(0.229 − 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) / = 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 - Software Verification PROGRAM NAME: REVISION NO.: SAFE 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 dead 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 AS 3600-01 PT-SL-001 -