Software Verification

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1 EC 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 to uniform loading. Choose a UKB457x191x74 in S 355 steel. GEOMETRY, PROPERTIES AND LOADING EC Example-001-1

2 Member Properties UKB457x191x74 E = 05,000 MPa fy = 355 MPa Loading w = 8.43kN/m (Dead Load) w =.5kN/m (Constrution) w = 1.5kN/m (Superimposed Load) w = 15.00kN/m (Live Load) Geometry Span, L = 1 m Beam spaing, b =3 m TECHNICAL FEATURES OF ETABS TESTED Composite beam design, inluding: Seletion of steel setion, amber and shear stud distribution Member bending apaities, at onstrution and in servie Member defletions, at onstrution and in servie RESULTS COMPARISON Independent results are referened from the first example, Design of Simply Supported Composite Beam, in Chapter of the Steel Constrution Institute Steel Designer s Manual, Seventh Edition. Output Parameter ETABS Independent Perent Differene Constrution MEd (kn-m) % Constrution Ma,pl,Rd (kn-m) % Constrution Defletion (mm) % Design Moment (kn-m) % Full Composite Mp (kn-m) % Partial Composite M (kn-m) % Shear Stud Capaity PRd Input 5.0 NA Shear Stud Distribution % Live Load Defletion (mm) % EC Example-001 -

3 Output Parameter ETABS Independent Perent Differene Required Strength VEd (kn) % Vpl,Rd (kn) % COMPUTER FILE: EC EXAMPLE 001.EDB CONCLUSION The ETABS results show an aeptable omparison with the independent results. The shear stud apaity Pr was entered as an overwrite, sine it is ontrolled by the dek profile geometry and the exat geometry of the example, whih assumes a dek profile with a rib depth of 60 mm, a depth above profile of 60 mm and a total depth of 130 mm, annot be modeled in ETABS, sine in ETABS, only the rib depth and depth above profile an be speified. EC Example-001-3

4 HAND CALCULATION Properties: Materials: Setion: Dek: S 355 Steel: E = 10,000 MPa, fy = 355 MPa, partial safety fator γa = 1.0 Normal weight onrete lass C5/30: Em = 30,500 MPa, fu = 30 MPa, density w = 4 kn/m 3 UKB457x191x74 ha = 457 mm, bf = mm, tf = 14.5 mm, tw = 9 mm, Aa = 9,460 mm, Iay = 33,319 m 4, Wpl = 1,653 m 3 Slab depth hs =130 mm, depth above profile h = 60 mm, Dek profile height hp = 60 mm, hd = hp + 10 mm for re-entrant stiffener, sr = 300 mm, b0 = 150 mm Shear Connetors: Loadings: d = 19 mm, h = 95 mm, Fu = 450 MPa Self weight slab, deking, reinforement =.567 kn/m Self weight beam = 0.73 kn/m Constrution load = 0.75 kn/m Ceiling = 0.5 kn/m Partitions (live load) = 1.0 kn/m Oupany (live load) = 4.0 kn/m EC Example-001-4

5 Design for Pre-Composite Condition: Constrution Required Flexural Strength: w fatored onstrution = 1.5 ( ) = kn/m M Ed Moment Capaity: wfatored onstrution L = = = 50.4 kn-m 8 8 M W f 3 6 a, pl, Rd = pl d = 1, = 587 kn-m Pre-Composite Defletion: w onstrution = = 8.43 kn/m 5 w L , onstrution δ= = = E Iay ,000 33, mm Camber = 0.8 δ= 6 mm, whih is rounded down to 5 mm Design for Composite Flexural Strength: Required Flexural Strength: w fatored = ( ) 3.0 = kn/m wfatored L M Ed = = = 68.4 kn-m 8 8 Full Composite Ation Available Flexural Strength: Effetive width of slab: L 1 b eff = = = 3 m 8 8 Resistane of slab in ompression: 0.85 fk 3 R = beff h = 0.85 (5 /1.5) 3, =,550 kn ontrols γ Resistane of steel setion in tension: R = f A = = s yd a , ,358 kn EC Example-001-5

6 Depth of ompression blok within steel setion flange: Rs R 3,358,50 x = = = 6 mm b f f yd d = x/ = 0.73 in. The plasti axis is in the steel flange and the moment resistane for full omposite ation is: h h h ( Rs R ) t f Ma, pl, RD = Rs d +R hs - R (3,358,550) 14.5 = 3, , = kn-m Partial Composite Ation Available Flexural Strength: Assume 77.5% omposite ation: R q = R = ,358 = 1,976 kn Tensile Resistane of web: s f R = t D t p = = 3 w w ( f ) y 8.5 ( ) , 9 kn As Rq > Rw, the plasti axis is in the steel flange, and h Rq h ( Rs Rq) t f M = Rs + Rq hs R Rf , (3,358 1,976) 14.5 = 3, , , = 971. kn-m Resistane of Shear Connetor: Resistane of shear onnetor in solid slab: d h 95 PRd = 0.9 α d fk Em γv 0.8 fu π γv with α =1.0 for = > 4 4 d α k m γ v = , = 73 kn d f E ontrols EC Example-001-6

7 d 19 v 0.8 f u π γ = π 1.5 = 81.7 kn 4 4 Redution fator for deking perpendiular to beam assuming two studs per rib: 0.7 k ( 0 ) ( ) 1 t = b hp hs hp 0.75 per EN Table 6. n r = ( ) 1 = P = = 5 kn Rd Total resistane with two studs per rib and 19 ribs from the support to the mid-span: R = 19 5 = 1,976 kn q Live Load Defletion: The seond moment of area of the omposite setion, based on elasti properties, I is given by: I 3 Aa ( h+ hp + h) beff h = + + I 4 (1 + n r) 1 n Aa 9, 460 r = = = 0.05 b h 3, eff n = modular ratio = 10 for normal weight onrete subjet to variable loads I 3 9, 460 ( ) 3, = , ( ) 1 10 = ( ) 10 = mm ay w L 5 15 (1, 000) δ = = = 19.1 mm 4 4 live live E I , EC Example-001-7

8 Design for Shear Strength: Required Shear Strength: V Ed wfatored L = = = 09.5 kn Shear Resistane of Steel Setion: = = 843 kn 3 10 V pl, Rd 3 EC Example-001-8

Software Verification

Software Verification AISC-360-10 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