Bs 8110 97 pt sl 001

Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001 Bs 8110 97 pt sl 001

Software Verification PROGRAM NAME: REVISION NO.: SAFE EXAMPLE BS 8110-97 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 BS 8110-97 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, was added to the AStrip 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 = 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 = = = = = = = = = Dead load Live load wd wl = = 254 mm 229 mm 9754 mm 30 400 1862 1210 198 23.56 25000 200,000 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 BS 8110-97 PT-SL-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE Table Comparison of Results FEATURE TESTED INDEPENDENT RESULTS SAFE RESULTS DIFFERENCE 174.4 174.4 0.00% 19.65 19.79 0.71% −5.058 −5.057 0.02% 2.839 2.847 0.28% −10.460 −10.465 50% 8.402 8.407 0.06% 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 COMPUTER FILE: BS 8110-97 PT-SL-001.FDB CONCLUSION The SAFE results show a very close comparison with the independent results EXAMPLE BS 8110-97 PT-SL-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE HAND CALCULATIONS: Design Parameters: Mild Steel Reinforcing fcu = 30 MPa fy = 400 MPa Post-Tensioning fpu = 1862 MPa fpy = 1675 MPa Stressing Loss = 186 MPa Long-Term Loss = 94 MPa fi = 1490 MPa fe = 1210 MPa γm, steel = 1.15 γm, concrete = 1.50 Prestressing tendon, Ap Mild Steel, As 229 mm 254 mm 25 mm Length, L = 9754 mm 914 mm Section Elevation Loads: Dead, self-wt = 0.254 m x 23.56 kN/m3 = 5.984 kN/m2 (D) x 1.4 = 8.378 kN/m2 (Du) Live, = 4.788 kN/m2 (L) x 1.6 = 7.661 kN/m2 (Lu) Total = 10.772 kN/m2 (D+L) = 16.039 kN/m2 (D+L)ult ω =10.772 kN/m2 x 0.914m = 9.846 kN/m, ωu = 16.039 kN/m2 x 0.914m = 14.659 kN/m wl12 = 14.659 x (9.754)2/8 = 174.4 kN-m f pu Ap ⎞ 7000 ⎛ Ultimate Stress in strand, f pb = f pe + ⎜1 − 1.7 ⎟ l/d ⎝ f cu bd ⎠ Ultimate Moment, M U = = 1210 + ⎛ 7000 1862(198) ⎞ ⎜1 − 1.7 ⎟ 9.754 / 0.229 ⎝ 30(914)(229) ⎠ = 1358 MPa ≤ 0.7 f pu = 1303 MPa EXAMPLE BS 8110-97 PT-SL-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE K factor used to determine the effective depth is given as: 174.4 M = = 0.1213 < 0.156 K= 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 ) = 197.4(1303) /1000 = 257.2 KN Ultimate moment due to PT, M ult , PT = Fult , PT ( z ) / γ = 257.2(0.192) /1.15 = 43.00 kN-m Net Moment to be resisted by As, M NET = MU − M PT = 174.4 − 43.00 = 131.40 kN-m The area of tensile steel reinforcement is then given by: As = M NET 131.4 = (1e6) = 1965 mm 0.87 f y z 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) / = 65.04 kN-m Moment due to PT, M PT = FPTI (sag) = 257.4(102mm) /1000 = 26.25 kN-m F M − M PT −257.4 65.04 − 26.23 Stress in concrete, f = PTI ± D = ± 0.254(0.914) 0.00983 A S 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 EXAMPLE BS 8110-97 PT-SL-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE Stress in concrete for (D+L+PTF), F M − M PT −238.8 117.08 − 24.37 = ± f = PTI ± D + L 0.254(0.914) 0.00983 A S f = −1.029 ± 9.431 f = −10.460(Comp) max, 8.402(Tension) max EXAMPLE BS 8110-97 PT-SL-001 -