Question

1. A symmetrically loaded triangular beam is shown in Figure 4.7(2) with 1 =32MPa. Compute M.. d600 1000 1000 8 N35 7 1000 Figure 4.7(2) Cross-section details of a triangular beam Note: all dimensions are in mm. 2. Given a beam section bxD-450mmx950mm, M*=1500kNm, =32MPa, fo=500MPa and the maximum aggregate size=20mm. Design and detail the section. Use N28 bars for the main reinforcement and R10 bars for stirrups. Exposure classifi-cation A2 applies.

Answer 1

solution Given that fe = 32 MPa Symmetrically loaded triangular beam 0.85€ Tec d=600 1000 1000 6N 36 .T 1000 لمفه in mm 1-0.003 2 0.85 $0.904 (3.-28) a 0.85 assume B = 0.8.5 -0.05 - 0.82 С a fc A = 0.85*32*10.8200 10.906dna) C = 10.54 dine? T = fy Agr = 500 X6120 306610 N neutral axis CET 10.32 dra = 306x10" dna 538.3 mm =C x leverarm = 10.54 X 538.3 x 538.3% (538-3-(3 *0.87 $0.827*538.3) 8.3) = 7.37 % LOS N-mm 737 KN-M

Strength reduction factor As Ag 6120 = 0.014 _ x1000x866 for 0.014 $ = 0.9 Therefore, Ultimate moment Mu= N - 737 *0.9 = 663.6 kNm (2) Solution : Given that : DX D = uso mm x 9.50 mm cuse d =900 mm Mh y = 1500 kN-m te = '32 MPa -500 MPa 9 20 mm maximum aggrigate size R 10 bars for stirrups N28 bars Take coven = 25 mm 0.133 fek bel? = (0.133X32)450 (960)2 ·limit = 1551,3 ) Kom MulM limit Hence Single Reinforce de section M = 0.89 fy Ast (d-0.4280) 1500710 = 0.87X 500 X Ast (900 -0.42 80,46 16x900)

Ast = 4T 48.9 mm2 Area of N 28 bar = 615.8 mm? Hence hist. No. of bars = Ą 4748.१ 6.15.8 = 7.71 8 bars Therefore, 8. no with Ast=49.60 mm2 of bars
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Answer 2

Transcribed image text: for No. 13 (No. 4) stirrups 3.11. For the beam with the triangular cross section shown in Fig. P3.11, determine (a) the balanced reinforcement ratio and (b) the maximum reinforcement ratio if e,-0.005. The dimensions of the triangle are such that the width of the triangle equals the distance from the apex. Thus, the width at the effective depth b equals the effective depth d. Express the reinforcement ratio p in terms of b and d. Draw the strain distribution, and stress distribution, and define your notation. FIGURE P3.11

Answer 3

Transcribed image text: for No. 13 (No. 4) stirrups 3.11. For the beam with the triangular cross section shown in Fig. P3.11, determine (a) the balanced reinforcement ratio and (b) the maximum reinforcement ratio if e,-0.005. The dimensions of the triangle are such that the width of the triangle equals the distance from the apex. Thus, the width at the effective depth b equals the effective depth d. Express the reinforcement ratio p in terms of b and d. Draw the strain distribution, and stress distribution, and define your notation. FIGURE P3.11