Contents Eurocode 2 04 PT SL 001
User Manual: Eurocode 2-04 PT-SL-001
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Software Verification PROGRAM NAME: REVISION NO.: SAFE 0 EXAMPLE Eurocode 2-04 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 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 Eurocode 2-04 PT-SL-001 - 1 Software Verification PROGRAM NAME: REVISION NO.: SAFE 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, was added to the AStrip. The self weight and live loads have been 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 mid-span 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 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 f pu fe Ap wc Ec Es ν = = = = = = = = = 30 400 1862 1210 198 23.56 25000 200,000 0 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 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 SAFE total factored moments, required mild steel reinforcing, and slab stresses with independent hand calculations. EXAMPLE Eurocode 2-04 PT-SL-001 - 2 Software Verification PROGRAM NAME: REVISION NO.: SAFE 0 Table 1 Comparison of Results INDEPENDENT RESULTS SAFE RESULTS DIFFERENCE Factored moment, Mu (Ultimate) (kN-m) 166.41 166.41 0.00% Transfer Conc. Stress, top (D+PTI), MPa −5.057 −5.057 0.00% Transfer Conc. Stress, bot (D+PTI), MPa 2.839 2.839 0.00% Normal Conc. Stress, top (D+L+PTF), MPa −10.460 −10.465 0.05% Normal Conc. Stress, bot (D+L+PTF), MPa 8.402 8.407 0.06% Long-Term Conc. Stress, top (D+0.5L+PTF(L)), MPa −7.817 −7.817 0.00% Long-Term Conc. Stress, bot (D+0.5L+PTF(L)), MPa 5.759 5.759 0.00% FEATURE TESTED Table 2 Comparison of Design Moments and Reinforcements Reinforcement Area (sq-cm) National Annex CEN Default, Norway, Slovenia and Sweden Method Design Moment (kN-m) As + SAFE 166.41 15.39 Calculated 166.41 15.36 SAFE 166.41 15.89 Calculated 166.41 15.87 SAFE 166.41 15.96 Calculated 166.41 15.94 Finland , Singapore and UK Denmark COMPUTER FILE: EUROCODE 2-04 PT-SL-001.FDB CONCLUSION The SAFE results show an acceptable comparison with the independent results. EXAMPLE Eurocode 2-04 PT-SL-001 - 3 Software Verification PROGRAM NAME: REVISION NO.: SAFE 0 HAND CALCULATIONS: Design Parameters: Mild Steel Reinforcing f’c = 30MPa fy = 400MPa Post-Tensioning f pu = 1862 MPa f py = 1675 MPa Stressing Loss = 186 MPa Long-Term Loss = 94 MPa f i = 1490 MPa f e = 1210 MPa γm, steel = 1.15 γm, concrete = 1.50 η = 1.0 for fck ≤ 50 MPa λ = 0.8 for fck ≤ 50 MPa 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) × 1.35 = 8.078 kN/m2 (D u ) Live, = 4.788 kN/m2 (L) × 1.50 = 7.182 kN/m2 (Lu ) Total = 10.772 kN/m2 (D+L) = 15.260 kN/m2 (D+L)ult ω =10.772 kN/m2 × 0.914 m = 9.846 kN/m, ωu = 15.260 kN/m2 × 0.914 m = 13.948 kN/m wl12 2 Ultimate Moment, M U = = 13.948 × ( 9.754 ) 8 = 165.9 kN-m 8 EXAMPLE Eurocode 2-04 PT-SL-001 - 4 Software Verification PROGRAM NAME: REVISION NO.: SAFE 0 f A Ultimate Stress in strand, f PS = f SE + 7000d 1 − 1.36 PU P l fCK bd 1862(198) ( 1210 + 7000(229) 1 − 1.36 = 9754 ) 30(914) ( 229 ) = 1361 MPa ) 1000 269.5 kN Fult , PT A= 2 ( 99 )(1361= Ultimate force in PT,= P ( f PS ) CEN Default, Norway, Slovenia and Sweden: Design moment M = 166.4122 kN-m M Compression block depth ratio: m = 2 bd ηf cd 166.4122 = = 0.1736 ( 0.914 )( 0.229 )2 (1) ( 30000 1.50 ) Required area of mild steel reinforcing, ω = 1 − 1 − 2m = 1 − 1 − 2(0.1736) = 0.1920 η f bd 1(30 /1.5)(914)(229) 2 = = AEquivTotal ω= cd 0.1920 2311 mm 400 /1.15 f yd 1361 2 = = AEquivTotal AP + AS 2311 mm 400 1.15 1361 2311 − 198 1536 mm 2 AS = = 400 /1.15 Finland, Singapore and UK: Design moment M = 166.4122 kN-m Compression block depth ratio: m = M bd 2ηf cd 166.4122 = 0.2042 ( 0.914 )( 0.229 )2 ( 0.85 ) ( 30000 1.50 ) Required area of mild steel reinforcing, ω = 1 − 1 − 2m = 1 − 1 − 2(0.2042) = 0.23088 = EXAMPLE Eurocode 2-04 PT-SL-001 - 5 Software Verification SAFE 0 PROGRAM NAME: REVISION NO.: η f cd bd 0.85(30 /1.5)(914)(229) 2 = = AEquivTotal ω= 0.23088 2362 mm 400 /1.15 f yd 1361 2 = = AEquivTotal AP + AS 2362 mm 400 1.15 1361 2362 − 198 1587 mm 2 AS = = 400 1.15 Denmark: Design moment M = 166.4122 kN-m Compression block depth ratio: m = M bd 2ηf cd 166.4122 = 0.1678 ( 0.914 )( 0.229 )2 (1.0 ) ( 30000 1.45 ) Required area of mild steel reinforcing, ω = 1 − 1 − 2m = 1 − 1 − 2(0.1678) = 0.1849 = η f cd bd 1.0(30 /1.45)(914)(229) 2 = = AEquivTotal ω= 0.1849 2402 mm 400 /1.20 f yd 1361 2 = = AEquivTotal AP + AS 2402 mm 400 1.2 1361 2402 − 198 1594 mm 2 AS = = 400 1.2 Check of Concrete Stresses at Midspan: Initial Condition (Transfer), load combination (D+PT i ) = 1.0D+0.0L+1.0PT I 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 ( 0.914 )( 9.754 ) 8 65.04 kN-m Moment= due to dead load, M D 5.984 = 2 = M PT F= 257.4 (102 mm = ) 1000 26.25 kN-m PTI (sag) FPTI M D − M PT −257.4 65.04 − 26.23 Stress in concrete, f = ± = ± 0.254 ( 0.914 ) 0.00983 A S Moment due to PT, EXAMPLE Eurocode 2-04 PT-SL-001 - 6 Software Verification PROGRAM NAME: REVISION NO.: SAFE 0 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+PT F ) = 1.0D+1.0L+1.0PT F 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 ( 0.914 )( 9.754 ) 8 65.04 kN-m Moment due to dead load M D 5.984 = = 2 ( 0.914 )( 9.754 ) 8 52.04 kN-m Moment due to live load M L 4.788 = = 2 Moment due to PT, M PT F= = = 238.9 (102 mm ) 1000 24.37 kN-m PTI (sag) Stress in concrete for (D+L+PT F ), FPTI M D + L − M PT −238.8 117.08 − 24.37 f = ± = ± 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+PT F(L) ) = 1.0D+0.5L+1.0PT F 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 ( 0.914 )( 9.754 )2 8 65.04 kN-m Moment= due to dead load, M D 5.984 = ( 0.914 )( 9.754 ) 8 52.04 kN-m Moment= due to live load, M L 4.788 = 2 Moment due to PT, = M PT F= 238.9 (102 mm = ) 1000 24.37 kN-m PTI (sag) Stress in concrete for (D+0.5L+PT F(L) ), FPTI M D + 0.5 L − M PT −238.9 91.06 − 24.33 f = ± = ± A S 0.254 ( 0.914 ) 0.00983 f = −1.029 ± 6.788 f = −7.817(Comp) max, 5.759(Tension) max EXAMPLE Eurocode 2-04 PT-SL-001 - 7
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