ACI 318 14 PT SL Example 001
User Manual: ACI 318-14 PT-SL Example 001
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Software Verification PROGRAM NAME: REVISION NO.: ETABS 0 ACI 318-14 PT-SL EXAMPLE 001 Design Verification of Post-Tensioned Slab using the ACI 318-14 code 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 10 inches thick by 36 inches wide and spans 32 feet, as shown in shown in Figure 1. A 36-inch-wide design strip was centered along the length of the slab and was defined as an A-Strip. B-strips were placed at each end of the span perpendicular to the Strip-A (the B-Strips are necessary to define the tendon profile). A tendon, with two strands having an area of 0.153 square inches each, was added to the AStrip. The self weight and live loads were added to the slab. The loads and posttensioning forces are shown below. 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 ETABS results and summarized for verification and validation of the ETABS results. Loads: Dead = self weight, Live = 100psf ACI 318-14 PT-SL EXAMPLE 001 - 1 Software Verification PROGRAM NAME: REVISION NO.: ETABS 0 Figure 1 One-Way Slab GEOMETRY, PROPERTIES AND LOADING Thickness, Effective depth, Clear span, Concrete strength, Yield strength of steel, Prestressing, ultimate T, h d L f 'C fy = = = = = f pu = Prestressing, effective fe Area of Prestress (single strand), AP Concrete unit weight, wc Modulus of elasticity, Ec Modulus of elasticity, Es Poisson’s ratio, Dead load, wd Live load, wl 10 9 384 4,000 60,000 in in in psi psi 270,000 psi = 175,500 psi = = = = = = = 0.153 0.150 3,600 29,000 0 self 100 sq in pcf ksi ksi psf psf 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. ACI 318-14 PT-SL EXAMPLE 001 - 2 Software Verification PROGRAM NAME: REVISION NO.: ETABS 0 RESULTS COMPARISON The ETABS total factored moments, required mild steel reinforcing and slab stresses are compared to the independent hand calculations in Table 1. Table 1 Comparison of Results FEATURE TESTED INDEPENDENT RESULTS ETABS RESULTS DIFFERENCE 1429.0 1428.3 -0.05% 2.21 2.21 0.00% 0.734 0.735 0.14% 0.414 0.414 0.00% 1.518 1.519 0.07% 1.220 1.221 0.08% 1.134 1.135 0.09% 0.836 0.837 0.12% Factored moment, Mu (Ultimate) (k-in) Area of Mild Steel req’d, As (sq-in) Transfer Conc. Stress, top (D+PTI), ksi Transfer Conc. Stress, bot (D+PTI), ksi Normal Conc. Stress, top (D+L+PTF), ksi Normal Conc. Stress, bot (D+L+PTF), ksi Long-Term Conc. Stress, top (D+0.5L+PTF(L)), ksi Long-Term Conc. Stress, bot (D+0.5L+PTF(L)), ksi COMPUTER FILE: ACI 318-14 PT-SL EX001.EDB CONCLUSION The ETABS results show an acceptable comparison with the independent results. ACI 318-14 PT-SL EXAMPLE 001 - 3 Software Verification ETABS 0 PROGRAM NAME: REVISION NO.: CALCULATIONS: Design Parameters: =0.9 Mild Steel Reinforcing fc = 4000 psi fy = 60,000 psi Post-Tensioning fj Stressing Loss Long-Term Loss fi fe = 216.0 ksi = 27.0 ksi = 13.5 ksi = 189.0 ksi = 175.5 ksi Loads: Dead, self-wt = 10 / 12 ft 0.150 kcf = 0.125 ksf (D) 1.2 = 0.150 ksf (Du) Live, 0.100 ksf (L) 1.6 = 0.160 ksf (Lu) Total =0.225 ksf (D+L) 0.310 ksf (D+L)ult =0.225 ksf 3 ft = 0.675 klf, Ultimate Moment, M U u = 0.310 ksf 3ft = 0.930 klf wl12 = 0.310 klf 322/8 = 119.0 k-ft = 1429.0 k-in 8 ACI 318-14 PT-SL EXAMPLE 001 - 4 Software Verification PROGRAM NAME: REVISION NO.: ETABS 0 f'c (span-to-depth ratio > 35) 300 P 4, 000 175,500 10, 000 300 0.000944 199, 624 psi 205,500 psi Ultimate Stress in strand, f PS f SE 10000 Ultimate force in PT, Fult , PT AP f PS 2 0.153199.62 61.08 kips Ultimate force in RC, Fult , RC As f y 2.00(assumed) 60.0 120.0 kips Total Ultimate force, Fult ,Total 61.08 120.0 181.08 kips Stress block depth, a Fult ,Total 0.85 f ' cb 181.08 1.48 in 0.85 4 36 a 1.48 Ultimate moment due to PT, M ult , PT Fult , PT d 61.08 9 0.9 454.1 k-in 2 2 Net ultimate moment, M net M U M ult , PT 1429.0 454.1 974.9 k-in Required area of mild steel reinforcing, AS M net 974.9 2.18 in 2 a 1.48 f y d 0.9 60 9 2 2 Note: The required area of mild steel reinforcing was calculated from an assumed amount of steel. Since the assumed value and the calculated value are not the same a second iteration can be performed. The second iteration changes the depth of the stress block and the calculated area of steel value. Upon completion of the second iteration the area of steel was found to be 2.21in2 ACI 318-14 PT-SL EXAMPLE 001 - 5 Software Verification PROGRAM NAME: REVISION NO.: ETABS 0 Check of Concrete Stresses at Mid-Span: Initial Condition (Transfer), load combination (D + L + PTi) = 1.0D + 1.0PTI The stress in the tendon at transfer = jacking stress stressing losses = 216.0 27.0 = 189.0 ksi The force in the tendon at transfer, = 189.0 2 0.153 57.83 kips 2 Moment due to dead load, M D 0.125 3 32 8 48.0 k-ft 576 k-in Moment due to PT, M PT FPTI (sag) 57.83 4 in 231.3 k-in F M M PT 57.83 576.0 231.3 Stress in concrete, f PTI D , where S = 600 in3 A S 10 36 600 f 0.161 0.5745 f = -0.735(Comp)max, 0.414(Tension)max Normal Condition, load combinations: (D + L + PTF) = 1.0D + 1.0L + 1.0PTF Tendon stress at normal = jacking stressing long-term = 216.0 27.0 13.5 = 175.5 ksi The force in tendon at Normal, = 175.5 2 0.153 53.70 kips 2 Moment due to dead load, M D 0.125 3 32 8 48.0 k-ft 576 k-in Moment due to dead load, M L 0.100 3 32 8 38.4 k-ft 461 k-in 2 Moment due to PT, M PT FPTI (sag) 53.70 4 in 214.8 k-in FPTI M D L M PT 53.70 1037.0 214.8 10 36 600 A S f 0.149 1.727 0.358 f 1.518(Comp) max,1.220(Tension) max Stress in concrete for (D + L+ PTF), f Long-Term Condition, load combinations: (D + 0.5L + PTF(L)) = 1.0D + 0.5L + 1.0PTF Tendon stress at normal = jacking stressing long-term = 216.0 27.0 13.5 = 175.5 ksi The force in tendon at Normal, = 175.5 2 0.153 53.70 kips 2 Moment due to dead load, M D 0.125 3 32 8 48.0 k-ft 576 k-in Moment due to dead load, M L 0.100 3 32 8 38.4 k-ft 460 k-in 2 Moment due to PT, ACI 318-14 PT-SL EXAMPLE 001 - 6 M PT FPTI (sag) 53.70 4 in 214.8 k-in Software Verification PROGRAM NAME: REVISION NO.: ETABS 0 Stress in concrete for (D + 0.5L + PTF(L)), M M PT 53.70 806.0 214.8 F f PTI D 0.5 L A S 10 36 600 f 0.149 0.985 f 1.134(Comp) max, 0.836(Tension) max ACI 318-14 PT-SL EXAMPLE 001 - 7
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