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 to uniform loading. Choose a UKB457x191x74 in S 355 steel. GEOMETRY, PROPERTIES AND LOADING EC-4-004 Example-001-1
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) 50.4 50.4 0.00% Constrution Ma,pl,Rd (kn-m) 587 587 0.00% Constrution Defletion (mm) 3.5 3.5 0.00% Design Moment (kn-m) 68.4 68.4 0.01% Full Composite Mp (kn-m) 100 100 0.00% Partial Composite M (kn-m) 971. 971. 0.00% Shear Stud Capaity PRd Input 5.0 NA Shear Stud Distribution 77 76 1.3% Live Load Defletion (mm) 19.3 19.1 1.03% EC-4-004 Example-001 -
Output Parameter ETABS Independent Perent Differene Required Strength VEd (kn) 09.5 09.5 0.00% Vpl,Rd (kn) 843 843 0.00% COMPUTER FILE: EC-4-004 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-4-004 Example-001-3
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 = 190.4 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-4-004 Example-001-4
Design for Pre-Composite Condition: Constrution Required Flexural Strength: w fatored onstrution = 1.5 (.567 3.0 + 0.73) + 1.5 0.75 3.0 = 13.91 kn/m M Ed Moment Capaity: wfatored onstrution L 13.91 1 = = = 50.4 kn-m 8 8 M W f 3 6 a, pl, Rd = pl d = 1,653 10 355 10 = 587 kn-m Pre-Composite Defletion: w onstrution =.567 3.0 + 0.73 = 8.43 kn/m 5 w L 5 8.43 1,000 4 4 onstrution δ= = = 4 384 E Iay 384 10,000 33,319 10 3.5 mm Camber = 0.8 δ= 6 mm, whih is rounded down to 5 mm Design for Composite Flexural Strength: Required Flexural Strength: w fatored = 1.5 0.73 + (1.5.567 + 1.5 0.5 + 1.5 1+ 1.5 4.0) 3.0 = 34.91 kn/m wfatored L 34.91 1 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, 000 60 10 =,550 kn ontrols γ Resistane of steel setion in tension: R = f A = = s yd a 3 355 9, 460 10 3,358 kn EC-4-004 Example-001-5
Depth of ompression blok within steel setion flange: Rs R 3,358,50 x = = = 6 mm b f 190.4 355 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 4 453.6 60 (3,358,550) 14.5 = 3,358 10 +,550 130 10 10 980 4 = 100.0 kn-m Partial Composite Ation Available Flexural Strength: Assume 77.5% omposite ation: R q = 0.775 R = 0.775 3,358 = 1,976 kn Tensile Resistane of web: s f 3 3 3 R = t D t p = = 3 w w ( f ) y 8.5 (453.6 1.7) 355 10 1, 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 4 453.6 1,976 60 (3,358 1,976) 14.5 = 3,358 10 + 1,976 130 10 10, 50 980 4 = 971. kn-m Resistane of Shear Connetor: Resistane of shear onnetor in solid slab: 3 3 3 d h 95 PRd = 0.9 α d fk Em γv 0.8 fu π γv with α =1.0 for = > 4 4 d 19 3 0.9 α k m γ v = 0.9 1.0 19 5 30,500 10 1.5 = 73 kn d f E ontrols EC-4-004 Example-001-6
d 19 v 0.8 f u π γ =0.8 450 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 1994-1-1 Table 6. n r 0.7 150 = ( 95 60 ) 1 = 0.7 0.75 60 P = 0.7 73 = 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, 000 60 eff n = modular ratio = 10 for normal weight onrete subjet to variable loads I 3 9, 460 (457 + 70 + 60) 3, 000 60 = + + 33,30 10 4 (1 + 10 0.05) 1 10 = (6.69 + 0.05 + 3.33) 10 = 10.08 10 mm ay 8 8 4 5 w L 5 15 (1, 000) δ = = = 19.1 mm 4 4 live live 8 384 E I 384 10, 000 10.08 10 4 EC-4-004 Example-001-7
Design for Shear Strength: Required Shear Strength: V Ed wfatored L 34.91 1 = = = 09.5 kn Shear Resistane of Steel Setion: 457 9.0 355 = = 843 kn 3 10 V pl, Rd 3 EC-4-004 Example-001-8