Contents AISC 360 10 Example 002
User Manual: AISC-360-10 Example 002
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Software Verification PROGRAM NAME: REVISION NO.: ETABS 3 AISC-360-10 Example 002 COMPOSITE GIRDER DESIGN EXAMPLE DESCRIPTION The design is checked for the composite girder shown below. The deck is 3 in. deep with 4 ½″ normal weight (145 pcf) concrete cover with a compressive strength of 4 ksi. The girder will not be shored during construction. The applied loads are the weight of the structure, a 25 psf construction live load, a 10 psf superimposed dead load and a 100 psf non-reducible service line load. GEOMETRY, PROPERTIES AND LOADING Member Properties W24x76 E = 29000 ksi Fy = 50 ksi Loading P = 36K (Dead Load) P = 4.5K (SDL) P = 45K (Live Load) Geometry Span, L = 45 ft AISC-360-10 Example 002 - 1 Software Verification PROGRAM NAME: REVISION NO.: ETABS 3 TECHNICAL FEATURES OF ETABS TESTED Composite beam design, including: Selection of steel section, camber and shear stud distribution Member bending capacities, at construction and in service Member deflections, at construction and in service RESULTS COMPARISON Independent results are referenced from Example I.2 from the AISC Design Examples, Version 14.0. ETABS Independent Percent Difference Pre-composite Mu (k-ft) 622.3 622.3 0.00% Pre-composite ΦbMn (k-ft) 677.2 677.2 0.00% 1.0 1.0 0.00% Required Strength Mu (k-ft) 1216.3 1216.3 0.00% Full Composite ΦbMn (k-ft) 1480.1 1480.1 0.00% Partial Composite ΦbMn (k-ft) 1267.3 1267.3 0.00% Shear Stud Capacity Qn 21.54 21.54 0.00% Shear Stud Distribution 26, 3, 26 26, 3, 26 0.00% Live Load Deflection (in.) 0.63 0.55 12.7% Required Strength Vu (kip) 122.0 122.0 0.00% ΦVn (k) 315.5 315.5 0.00% Output Parameter Pre-composite Deflection (in.) AISC-360-10 Example 002 - 2 Software Verification PROGRAM NAME: REVISION NO.: ETABS 3 COMPUTER FILE: AISC-360-10 EXAMPLE 002.EDB CONCLUSION The ETABS results show an acceptable comparison with the independent results. The live load deflection differs more markedly because of a difference in methodology. In the AISC example, the live load deflection is computed based on a lower bound value of the beam moment of inertia, whereas in ETABS, it is computed based on the approximate value of the beam moment of inertia derived from Equation (C-I3-6) from the Commentary on the AISC Load and Resistance Factor Design Specification – Second Edition. AISC-360-10 Example 002 - 3 Software Verification PROGRAM NAME: REVISION NO.: ETABS 3 HAND CALCULATION Properties: Materials: ASTM A572 Grade 50 Steel E = 29,000 ksi, Fy = 50 ksi, wsteel = 490 pcf 4000 psi normal weight concrete Ec = 3,644 ksi, f c′ = 4 ksi, wconcrete = 145 pcf Section: W24x76 d = 23.9 in, bf = 8.99 in, tf = 0.68 in, tw = 0.44 in Asteel = 22.4 in2, Isteel = 2100 in4 Deck: tc =4 ½ in., hr = 3 in., sr =12 in., wr = 6 in. Shear Connectors: d = ¾ in, h =4 ½ in, Fu = 65 ksi Design for Pre-Composite Condition: Construction Required Flexural Strength: 22.4 w A = = 76.2 plf •w = sq .ft . • 490 pcf steel steel 144 PD = 36 kips [(45 ft)(10 ft)(75 psf ) + (50 plf )(45 ft)] (0.001 kip / lb) = PL = ft)(10 ft)(25 psf )] (0.001 kip/lb) [(45 11.25 kips 1.2 wL2 L + (1.2 PD + 1.6 PL ) 8 3 2 76.2 • 30 30 = 1.2 + (1.2 • 36 +1.6 • 11.25 = 622.3 kip-ft ) 8 3 Mu = AISC-360-10 Example 002 - 4 Software Verification PROGRAM NAME: REVISION NO.: ETABS 3 Moment Capacity: Lb = 10 ft Lp = 6.78 ft Lr = 19.5 ft ΦbBF = 22.6 kips ΦbMpx = 750 kip-ft Cb = 1.0 Φ b M= Cb Φ b M px − Φ b BF ( Lb − L p ) n = 1.0 750 − 22.6 • (10 − 6.78 ) = 677.2 kip-ft Pre-Composite Deflection: 0.0762 • 3604 PD L 5wD L 36.0 • 360 12 ∆ = + = + = 1.0 nc 28 EI 384 EI 28 • 29, 000 • 2,100 384 • 29, 000 • 2,100 3 4 3 5• = 0.8 • ∆ nc = 0.8 in. which is rounded down to ¾ in. Camber Design for Composite Flexural Strength: Required Flexural Strength: 40.5 kips P = [ (45 ft)(10 ft)(75 +10psf ) + (50 plf)(45 ft)] (0.001 kip/lb) = D P L = ft)(10 ft)(100 psf ) ] (0.001 kip/lb) [ (45 45 kips 1.2 wL2 L + (1.2 PD + 1.6 PL ) 8 3 2 1.2 • 76.22 • 30 30 1216.3 kip-ft = + (1.2 • 40.5 +1.6 = • 45) 8 3 Mu = Full Composite Action Available Flexural Strength: Effective width of slab: = b eff 30.0 ft = 7.5 = ft 90 in. 8 AISC-360-10 Example 002 - 5 Software Verification PROGRAM NAME: REVISION NO.: ETABS 3 Resistance of steel in tension: C = Py = As • Fy = 22.4 • 50 = 1,120 kips controls Resistance of slab in compression Ac = beff • tc + (beff 2) • hr = (7.5 • 12) • 4.5 + 2 7.5 • 12 • 3= 540 in 2 C= 0.85 • f 'c A= 0.85 • 4 • 540 = 1836 kips c Depth of compression block within slab: = a C 1,120 = = 3.66 in. 0.85 • beff • f 'c 0.85 • (7.5 • 12) • 4 Moment resistance of composite beam for full composite action: d1 = (tc + hr ) − 3.66 a = (4.5 + 3) − = 5.67 in. 2 2 d ΦM = Φ C • d + P • n 1 y 2 23.9 12 = 0.9 • 1,120 • 5.67 / 12 + 1,120 • 1480.1 kip-ft = 2 Partial Composite Action Available Flexural Strength: Assume 50% composite action: C = 0.5 • Py = 560 kips Depth of compression block within slab = a C 560 = = 1.83 in. 0.85 • beff • f 'c 0.85 • (7.5 • 12) • 4 d1 = (tc + hr ) − a 1.83 = (4.5 + 3) − = 6.58 in. 2 2 Depth of compression block within steel section flange = x Py − C 1,120 − 560 = = 0.623 in. 2 • b f • Fy 2 • 8.99 • 50 = d 2 x= / 2 0.311 in. AISC-360-10 Example 002 - 6 Software Verification PROGRAM NAME: REVISION NO.: ETABS 3 M n =C • (d1 + d 2 ) + Py • (d3 − d 2 ) 23.9 = 560 • (6.58 + 0.312) + 1,120 • − 0.312 12 =1, 408 kip-ft 2 ΦM n = 0.9 M n = 0.9 • 1, 408 = 1, 267.3 kip-ft Shear Stud Strength: = Qn 0.5 Asa f 'c Ec ≤ Rg R p Asa Fu 0.442 in 2 Asa = πd sa 2 4 = π(0.75) 2 4 = f c ' = 4 ksi 1.5 1.5 = E w= f c ' 145 = 4 3, 490 ksi c Rg = 1.0 Studs welded directly to the steel shape with the slab haunch Rp = 0.75 Studs welded directly to the steel shape Fu = 65 ksi Qn = 0.5 • 0.4422 4 • 3, 490 ≤ 1.0 • 0.75 • 0.4422 • 65 = 26.1 kips ≥ 21.54 kips controls Shear Stud Distribution: n= = ΣQn Qn 560 = 26 studs from each end to nearest concentrated load point 21.54 Add 3 studs between load points to satisfy maximum stud spacing requirement. Live Load Deflection: Modulus of elasticity ratio: = n E= / Ec 29, 000 / 3, = 644 8.0 AISC-360-10 Example 002 - 7 Software Verification PROGRAM NAME: REVISION NO.: ETABS 3 Transformed elastic moment of inertia assuming full composite action: Transformed Area A (in2) Moment Arm from Centroid y (in.) Ay (in.3) Ay2 (in,4) I0 (in.4) Slab 50.9 17.2 875 15,055 86 Deck ribs 17.0 13.45 228 3,069 13 W21x50 22.4 0 0 0 2,100 1,103 18,124 2,199 Element 89.5 I x =I 0 + Ay 2 =2,199 + 18,124 =20,323 in.4 = y 1, 092 = 12.2 in. 89.5 2 I tr = I x − A • y = 20,323 − 90.3 • 12.22 = 6,831 in 4 Effective moment of inertia assuming partial composite action: I equiv = I s + ΣQn Py ( I tr − I s ) = 2,100 + 0.5 ( 6,831 − 2,100 ) = 5, 446 in 4 I eff = 0.75 • I equiv = 0.75 • 5, 446 = 4, 084 in 4 = ∆ LL PL L3 45.0 • (30 • 12)3 = = 0.633 in. 28EI eff 28 • 29,000 • 4,084 Design for Shear Strength: Required Shear Strength: Pu = 1.2 • PD + 1.6 • PL = 1.2 • 40.5 + 1.6 • 45 = 120.6 kip = Vu 1.2 • w • L 1.2 • 0.076 • 30 120.6 121.2 kip-ft = + Pu += 2 2 Available Shear Strength: ΦVn = Φ • 0.6 • d • tw • Fy = 1.0 • 0.6 • 23.9 • 0.44 • 50 = 315.5 kips AISC-360-10 Example 002 - 8
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