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1 BS Examle-001 STEEL DESIGNES MANUAL SIXTH EDITION - DESIGN OF SIMPLY SUPPOTED COMPOSITE BEAM EXAMPLE DESCIPTION Deign a omoite floor ith beam at 3-m enter anning 12 m. The omoite lab i 130 mm dee. The floor i to reit an imoed load of 5.0 kn/m 2, artition loading of 1.0 kn/m 2 and a eiling load of 0.5 kn/m 2. The floor i to be un-roed during ontrution. GEOMETY, POPETIES AND LOADING Member Proertie UKB57x191x67 E = 205,000 MPa Fy = 355 MPa Loading = 6.67kN/m (Dead Load) = 1.5kN/m (Contrution) = 1.5kN/m (Suerimoed Load) = 18.00kN/m (Live Load) Geometry San, L = 12 m TECHNICAL FEATUES OF ETABS TESTED Comoite beam deign, inluding: Seletion of teel etion, amber and hear tud ditribution Member bending aaitie, at ontrution and in ervie Member defletion, at ontrution and in ervie BS Examle-001-1

2 ESULTS COMPAISON Indeendent reult are referened from the firt examle, Deign of Simly Suorted Comoite Beam, in Chater 21 of the Steel Contrution Intitute Steel Deigner Manual, Sixth Edition. Outut Parameter ETABS Indeendent Perent Differene Contrution Deign Moment (kn-m) % Contrution M (kn-m) % Contrution Defletion (mm) % Deign Moment (kn-m) % Full Comoite M (kn-m) % Partial Comoite M (kn-m) % Shear Stud Caaity Qn (kn) % Live Load Defletion (mm) % Alied Shear Fore Fv (kn) % Shear eitane Pv (kn) % COMPUTE FILE: BS EXAMPLE 001.EDB CONCLUSION The ETABS reult ho an exellent omarion ith the indeendent reult. BS Examle-001-2

3 HAND CALCULATION Proertie: Material: S355 Steel: E = 205,000 MPa, y = 355 MPa, γ = 7850 kg/m 3 Light-eight onrete: E = 2,855 MPa, fu = 30 MPa, γ = 1800 kg/m 3 Setion: UKB57x191x67 D = 53.6 mm, bf = mm, tf = 12.7 mm, t = 8.5 mm Ateel = 8,550 mm 2, Iteel = 29,380 m Dek: D =130 mm, D = 50 mm, r = 300 mm, br = 150 mm Shear Connetor: d = 19 mm, h = 95 mm, Fu = 50 MPa Loading: Self eight lab = 2.0 kn/m 2 Self eight beam = 0.67 kn/m Contrution load = 0.5 kn/m 2 Ceiling = 0.5 kn/m 2 Partition (live load) = 1.0 kn/m 2 Ouany (live load) = 5.0 kn/m 2 Deign for Pre-Comoite Condition: Contrution equired Flexural Strength: ult ontrution = ( ) 3.0 = 11.7 kn/m BS Examle-001-3

4 M L ult ontrution ult ontrution M = S P = = z y Pre-Comoite Defletion: kn-m 3 6 1, kn-m ontrution = = 6.67 kn/m 5 L , E I , , ontrution δ 29.9 mm Camber = 0.8 δ= 2 mm, hih i rounded don to 20 mm Deign for Comoite Flexural Strength: equired Flexural Strength: ult = ( ) 3.0 = 0.2 kn/m 2 2 ult L M ult 72.3 kn-m 8 8 Full Comoite Ation Available Flexural Strength: Effetive idth of lab: L 12,000 B e 3, 000 mm 3,000 mmm eitane of lab in omreion: = 0.5 f B ( D D ) = , = 3, 20 kn u e eitane of teel in tenion: P A = y = y = 8, = 3,035 kn ontrol Moment reitane of omoite beam for full omoite ation: ( D D) D M = + D for , = + = 2 3, , kn-m BS Examle-001 -

5 Partial Comoite Ation Available Flexural Strength: Aume 72% omoite ation the 75% aumed in the examle require more hear tud than an fit on the beam given it atual lear length. q = 0.72 = 2,189 kn Tenile eitane of eb: y = t D 2 t = = 1, 292 kn f A q >, the lati axi i in the teel flange, and ( D D) 2 D q ( q) tf M = + q D 2 2 f Shear Stud Strength: 2 ( 3,035 2,189) , = 3, , , ,035 1, 292 = kn-m Charateriti reitane of 19 mm-diameter tud in normal eight 30 MPa onrete: Qk = 100 kn from BS 5950: Part 3 Table 5 Adjuting for light-eight onrete: Q = 90 kn k edution fator for rofile hae ith rib erendiular to the beam and to tud er rib: ( h D ) 150 ( 95 50) br k = 0.6 = 0.6 = 1.62 but k 0.8 D D Deign trength: Q = k 0.8 Q = = 57.6 kn Shear Stud Ditribution: k The examle lae to ro of hear tud and omute the number of dek rib available for laing hear tud baed on the beam enter to enter an and the dek rib aing: 12 m / 300 mm = 0 BS Examle-001-5

6 Hoever, the number of dek rib available for laing hear tud mut be baed on the beam lear an, and ine the lear beam an i omehat le than the 12 m enter to enter an there are only 39 dek rib available. ETABS elet 72% omoite ation, hih i the highet ahievable and uffiient to meet the live load defletion riteria. ETABS atifie thi 72% omoite ation by laing one tud er dek rib along the entire length of the beam, lu a eond tud er rib in all the dek rib exet the mid-an rib ine thi i the loation of the beam zero moment and a tud in that rib ould not ontribute anything to the total reitane of the hear onnetor. The total reitane of the hear onnetor i: q = 2 19 Q = = 2,189 kn Live Load Defletion: The eond moment of area of the omoite etion, baed on elati roertie, I i given by: I r ( D ) ( r) 2 3 eff Ateel + D + D b D D = + + I 1+α 12 α A e 8,550 teel beff ( D D) 3,000 ( ) For light-eight onrete: α =10 α =25 l Proortion of total loading hih i long term: e teel dl dl live ρ l dl + dl + live α =α +ρ α α = = 18.1 I e l l , , = = = mm Live load defletion auming full omoite ation: 6 BS Examle-001-6

7 5 L ,000 live δ 6 38 E I , Adjut for artial omoite ation: live δ = = E I 5 L , , = 80.7 mm non-omoite referene defletion ( K ) δ artial =δ δ δ mm = = 33.2 mm Deign for Shear Strength: equired Shear Strength: ult L Fv 21. kn 2 2 Shear eitane of Steel Setion: P = y D t = = kn V BS Examle-001-7