Software Verification

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Roderick Carson
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1 AISC Example 001 COMPOSITE GIRDER DESIGN EXAMPLE DESCRIPTION A typial bay of a omposite floor system is illstrated below. Selet an appropriate ASTM A992 W-shaped beam and determine the reqired nmber of ¾ in.-diameter steel headed std anhors. The beam will not be shored dring onstrtion. To ahieve a two-hor fire rating withot the appliation of spray applied fire protetion material to the omposite dek, 4 ½ in. of normal weight (145 lb/ft 3 ) onrete will be plaed above the top of the dek. The onrete has a speified ompressive strength, f = 4 ksi. GEOMETRY, PROPERTIES AND LOADING Member Properties W21x50 E = ksi Fy = 50 ksi Loading w = 800 plf (Dead Load) w = 250 plf (Constrtion) w = 100 plf (SDL) w = 1000 plf (Live Load) Geometry Span, L = 45 ft AISC Example 001-1

2 TECHNICAL FEATURES OF ETABS TESTED Composite beam design, inlding: Seletion of steel setion, amber and shear std distribtion Member bending apaities, at onstrtion and in servie Member defletions, at onstrtion and in servie RESULTS COMPARISON Independent reslts are referened from Example I.1 from the AISC Design Examples, Version Otpt Parameter ETABS Independent Perent Differene Pre-omposite M (k-ft) % Pre-omposite ΦbMn (k-ft) % Pre-omposite Defletion (in.) % Reqired Strength M (k-ft) % Fll Composite ΦbMn (k-ft) % Partial Composite ΦbMn (k-ft) % Shear Std Capaity Qn 17.2; ; % Shear Std Distribtion % Live Load Defletion (in.) % Reqired Strength V (kip) % ΦVn (k) % AISC Example 001-2

3 COMPUTER FILE: AISC EXAMPLE 001.EDB CONCLUSION The ETABS reslts show an aeptable omparison with the independent reslts. The live load defletion differs de to a differene in methodology. In the AISC example, the live load defletion is ompted based on a lower bond vale of the beam moment of inertia, whereas in ETABS, it is ompted based on the approximate vale of the beam moment of inertia derived from Eqation (C-I3-6) from the Commentary on the AISC Load and Resistane Fator Design Speifiation Seond Edition. AISC Example 001-3

4 HAND CALCULATION Properties: Materials: Setion: Dek: ASTM A572 Grade 50 Steel E = 29,000 ksi, Fy = 50 ksi, wsteel = 490 pf 4000 psi normal weight onrete E = 3,644 ksi, W21x50 f = 4 ksi, wonrete = 145 pf d = 20.8 in, bf = 6.53 in, tf = in, tw = 0.38 in, k = 1.04 in Asteel = 14.7 in 2, Ssteel = 94.6 in 3, Zsteel = 110 in 3, Isteel = 984 in 4 t =4 ½ in., hr = 3 in., sr =12 in., wr = 6 in. Shear Connetors: d = ¾ in, h =4 ½ in, F = 65 ksi Design for Pre-Composite Condition: Constrtion Reqired Flexral Strength: w D = + = 3 ( ) kip/ft w L = = kip/ft w = = 1.36 kip/ft M Moment Capaity: w L = = = kip-ft 8 8 Φ M =Φ Z F = ( ) 12 = kip-ft b n b s y AISC Example 001-4

5 Pre-Composite Defletion: ( 45 12) 4 n = = = 384EI , wL D 1.59 in. Camber = 0.8 n = = 2.07 in., whih is ronded down to 2 in. Design for Composite Flexral Strength: Reqired Flexral Strength: w = = 2.68 kip/ft M w L = = = kip-ft 8 8 Fll Composite Ation Available Flexral Strength: Effetive width of slab: ft b = 2 sides = 10.0 ft = ft 2 8 Resistane of steel in tension: C = Py = As Fy = = 735 kips ontrols Resistane of slab in ompression: ( ) A = b t = = 540 in C = 0.85 f ' A = = 1836 kips Depth of ompression blok within slab: C 735 a = = = 1.80 in b f ' ( ) Moment resistane of omposite beam for fll omposite ation: a 1.80 d1 = ( t + h r) = ( ) = 6.60 in. 2 d 20.8 /12 Φ Mn =Φ Py d1 + Py = / = kip-ft 2 2 AISC Example 001-5

6 Partial Composite Ation Available Flexral Strength: Assme 50.9% omposite ation: C = P y = kips Depth of ompression blok within onrete slab: C a = 0.92 in b f ' = = a ( ) ( ) ( ) 0.92 d in. 1 = t h + r 2 = + 2 = Compressive fore in steel setion: Py C = = kips Steel setion flange ltimate ompressive fore: Cflange = bf tf Fy = = kips Steel setion web (exlding fillet areas) ltimate ompressive fore: C = ( d 2 k) t F = ( ) = kips web w y Steel setion fillet ltimate ompressive fore: C fillet Py (2 Cflange + Cweb) 735 ( ) = = = 14.5 kips Assming a retanglar fillet area, the distane from the bottom of the top flange to the netral axis of the omposite setion is: ( Py C)/2 C flange x = (k t f ) C fillet = ( ) = 0.20 in AISC Example 001-6

7 Distane from the entroid of the ompressive fore in the steel setion to the top of the steel setion: d 2 Cflange tf /2 + ((P y C)/2 Cflange) ( tf + x/2) = ( P C)/2 y / 2 + ( ) ( / 2) = = in Moment resistane of omposite beam for partial omposite ation: ( ) ( ) Φ Mn =Φ C d + d + P d d Shear Std Strength: 1 2 y = ( ) = kip-ft 2 From AISC Manal Table 3.21, assming the shear stds are plaed in the weak position, the strength of ¾ in.-diameter shear stds in normal weight onrete with f = 4 ksi and dek oriented perpendilar to the beam is: Q = 17.2 kips for one shear std per dek flte n Q = 14.6 kips for two shear stds per dek flte n Shear Std Distribtion: There are at most 22 dek fltes along eah half of the lear span of the beam. ETABS only onts the stds in the first 21 dek fltes as the 22 nd flte is potentially too lose to the point of zero moment for any std loated in it to be etive. With two shear stds in the first flte, 20 in the next in the next twenty fltes, and one shear std in the 22 nd flte, in eah half of the beam, there is a total of 46 shear stds on the beam, and the total fore provided by the shear stds in eah half span is: Σ = = kip Q n AISC Example 001-7

8 Live Load Defletion: Modls of elastiity ratio: n= EE = 29,000 3,644 = 8.0 Transformed elasti moment of inertia assming fll omposite ation: Element Transformed Area A (in 2 ) Moment Arm from Centroid y (in.) Ay (in. 3 ) Ay 2 (in, 4 ) I0 (in. 4 ) Slab ,062 16, W21x ,062 16,620 1,099 I x = I0 + Ay = 1, , 620 = 17, 719 in. 1,062 y = = 12.9 in I = I A y = 17, = 4, 058 in tr x 2 4 Effetive moment inertia assming partial omposite ation: Ieqiv = Is + ΣQn / Py ( Itr Is) = (4, ) = 3,176 in 4 I = 0.75 I = ,176 = 2,382 in eqiv wL L 5 (1/12) (30 12) LL = = = 1.34 in. 384EI , 000 2, 382 Design for Shear Strength: Reqired Shear Strength: w = = 2.68 kip/ft V w L = = = 60.3 kip-ft AISC Example 001-8

9 Available Shear Strength: Φ V =Φ 0.6 d t F = = kips n w y AISC Example 001-9

Software Verification

Software Verification EC-4-004 Example-001 STEEL DESIGNERS MANUAL SEVENTH EDITION - DESIGN OF SIMPLY SUPPORTED COMPOSITE BEAM EXAMPLE DESCRIPTION Consider an internal seondary omposite beam of 1-m span between olumns and subjet