Contents AISC 360 05 Example 001
User Manual: AISC-360-05 Example 001
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Software Verification PROGRAM NAME: REVISION NO.: ETABS 3 AISC-360-05 Example 001 COMPOSITE GIRDER DESIGN EXAMPLE DESCRIPTION A series of 45-ft. span composite beams at 10 ft. o/c carry the loads shown below. The beams are ASTM A992 and are unshored during construction. The concrete has a specified compressive strength, fc′ = 4 ksi. Design a typical floor beam with 3-in., 18-gage composite deck and 4 ½ in. normal weight concrete above the deck, for fire protection and mass. Select an appropriate beam and determine the required number of ¾ in.-diameter shear studs. GEOMETRY, PROPERTIES AND LOADING Member Properties W21x55 E = 29000 ksi Fy = 50 ksi Loading w = 830 plf (Dead Load) w = 200 plf (Construction) w = 100 plf (SDL) w = 1000 plf (Live Load) Geometry Span, L = 45 ft AISC-360-05 Example 001 - 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.1 from the AISC Design Examples, Version 13.0. ETABS Independent Percent Difference Pre-composite Mu (k-ft) 333.15 333.15 0.00% Pre-composite ΦbMn (k-ft) 472.5 472.5 0.00% 2.3 2.3 0.00% Required Strength Mu (k-ft) 687.5 687.5 0.00% Full Composite ΦbMn (k-ft) 1027.1 1027.1 0.00% Partial Composite ΦbMn (k-ft) 770.3 770.3 0.00 % Shear Stud Capacity Qn 17.2 17.2 0.00 % Shear Stud Distribution 35 34 2.9% Live Load Deflection (in.) 1.35 1.30 3.70% Required Strength Vu (kip) 61.1 61.1 0.00% ΦVn (k) 234 234 0.00% Output Parameter Pre-composite Deflection (in.) AISC-360-05 Example 001 - 2 Software Verification PROGRAM NAME: REVISION NO.: ETABS 3 COMPUTER FILE: AISC-360-05 EXAMPLE 001.EDB CONCLUSION The ETABS results show an acceptable comparison with the independent results. The live load deflection differs due to 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-360-05 Example 001 - 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, fc′ = 4 ksi, wconcrete = 145 pcf Section: W21x55 d = 20.8 in, bf = 8.22 in, tf = 0.522 in, tw = 0.38 in, h = 18.75 in., rfillet = 0.5 in. Asteel = 16.2 in2, Ssteel = 109.6 in3, Zsteel = 126 in3, Isteel = 1140 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: wD =(10 • 77.5 + 55.125) • 10−3 =0.830125 kip/ft wL = 10 • 20 • 10−3 = 0.200 kip/ft wu = 1.2 • 0.830125 + 1.6 • 0.200 = 1.31615 kip/ft wu • L2 1.31615 • 452 = Mu = = 333.15 kip-ft 8 8 Moment Capacity: Φ b M n =Φ b • Z s • Fy =( 0.9 • 126 • 50 ) 12 =472.5 kip-ft AISC-360-05 Example 001 - 4 Software Verification PROGRAM NAME: REVISION NO.: ETABS 3 Pre-Composite Deflection: 0.830 4 • ( 45 • 12 ) 5wD L 12 = ∆ nc = = 2.31 in. 384 EI 384 • 29, 000 • 1,140 4 5• Design for Composite Flexural Strength: Required Flexural Strength: wu = 1.2 • 0.830 + 1.2 • 0.100 + 1.6 • 1 = 2.71 kip/ft wu • L2 2.68 • 452 Mu = = = 687.5 kip-ft 8 8 Full Composite Action Available Flexural Strength: Effective width of slab: 10.0 45.0 ft beff = • 2 sides =10.0 ft ≤ =11.25 ft 2 8 Resistance of steel in tension: C = Py = As • Fy = 16.2 • 50 = 810 kips controls Resistance of slab in compression: Ac = beff • tc = (10 • 12 ) • 4.5 = 540 in 2 C= 0.85 • f 'c A= 0.85 • 4 • 540 = 1836 kips c Depth of compression block within slab: = a C 810 = = 1.99 in. 0.85 • beff • f 'c 0.85 • (10 • 12 ) • 4 Moment resistance of composite beam for full composite action: d1 = (tc + hr ) − 2.00 a = (4.5 + 3) − = 6.51 in. 2 2 d 20.8 / 12 ΦM n = Φ Py • d1 + Py • = 0.9 810 • 6.51 / 12 + 810 • 1027.1 kip-ft = 2 2 AISC-360-05 Example 001 - 5 Software Verification PROGRAM NAME: REVISION NO.: ETABS 3 Partial Composite Action Available Flexural Strength: Assume 36.1% composite action: C= 0.361 • P= 0.361 • 810= 292.4 kips y Depth of compression block within concrete slab: C 292.4 = = 0.72 in. 0.85 • beff • f 'c 0.85 • (10 • 12 ) • 4 = a ( tc + hr ) − d1 = a = 2 ( 4.5 + 3) − 0.72 = 7.14 in. 2 Compression force within steel section: (P y − C ) 2 =( 810 − 292.4 ) 2 =258.8 kips Tensile resistance of one flange: Fflange = b f • t f • Fy = 8.22 • 0.522 • 50 = 214.5 kip Tensile resistance of web: Fweb = T • tw • Fy = 18.75 • 0.375 • 50 = 351.75 kips Tensile resistance of one fillet area: Ffillet= (P − 2• F y flange − Fweb ) 2= (810 − 2 • 214.5 − 351.2 ) 2= 14.6 kips Compression force in web: Cweb =( Py − C ) / 2 − Fflange − Ffillet =258.8 − 214.5 − 14.6 =29.7 kips Depth of compression block in web: x= Cweb 29.7 • T= • 18.76= 1.584 in. Fweb 351.75 Location of centroid of steel compression force measured from top of steel section: d2 0.5 • t f • Fflange + ( t f + 0.5 • rfillet ) • Ffillet + ( t f + rfillet + 0.5 • x ) • C web = ( Py − C ) / 2 0.5 • 0.522 • 214.5 + ( 0.522 + 0.5 • 0.5) • 14.6 + ( 0.522 + 0.5 + 0.5 • 1.58) • 29.7 = 0.467 in. 258.8 AISC-360-05 Example 001 - 6 Software Verification PROGRAM NAME: REVISION NO.: ETABS 3 Moment resistance of composite beam for partial composite action: ΦM n = Φ C • ( d1 + d 2 ) + Py • ( d 3 − d 2 ) 20.8 12 770.3 kip-ft = 0.9 292.4 • ( 7.14 + 0.467 ) + 810 • − 0.467 = 2 Shear Stud Strength: From AISC Manual Table 3.21 assuming one shear stud per rib placed in the weak position, the strength of ¾ in.-diameter shear studs in normal weight concrete with f c′ = 4 ksi and deck oriented perpendicular to the beam is: Qn = 17.2 kips Shear Stud Distribution: = n ΣQn 292.4 = = 17 from each end to mid-span, rounded up to 35 total 17.2 Qn Live Load Deflection: Modulus of elasticity ratio: n E= Ec 29, 000 3,= = 644 8.0 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 67.9 15.65 1,062 16,620 115 W21x50 16.2 0 0 0 1,140 1,062 16,620 1,255 Element 84.1 I x =I 0 + Ay 2 = 1, 255 + 16,620 = 17,874 in.4 = y 1, 062 = 12.6 in. 84.1 2 I tr = I x − A • y = 17,874 − 82.6 • 12.62 = 4, 458 in 4 AISC-360-05 Example 001 - 7 Software Verification PROGRAM NAME: REVISION NO.: ETABS 3 Effective moment inertia assuming partial composite action: I equiv = I s + ΣQn Py ( I tr − I s ) = 1,140 + 0.361 ( 4, 458 − 1,140 ) = 3,133 in 4 I eff = 0.75 • I equiv = 0.75 • 3,133 = 2,350 in 4 5 • (1 12 ) • ( 30 • 12 ) 5wL L4 = ∆ LL = = 1.35 in. 384 EI eff 384 • 29, 000 • 2,350 4 Design for Shear Strength: Required Shear Strength: wu = 1.2 • 0.830 + 1.2 • 0.100 + 1.6 • 1 = 2.71 kip/ft wu • L 2.71 • 45 = = 61.1 kip-ft Vu = 2 2 Available Shear Strength: 1.0 • 0.6 • 20.8 • 0.375 • 50 = 234 kips ΦVn = Φ • 0.6 • d • t w • Fy = AISC-360-05 Example 001 - 8
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