Question

Problem 2. A concrete beam is reinforced by three steel rebars placed as shown. The modulus of elasticity is 3x106 psi for concrete and 29x106 psi for steel. Find the tensile stress in rebars and maximum compressive stress in concrete under an external bending moment of (a) 80 kip.in and (b) 240 kip.in. Given the compressive strength of concrete fe' = 3 ksi and yield stress of rebars fy = 60 ksi, discuss the state of crack in concrete and yield in rebars for each of the two cases. 16 in. 7-in. diameter (#7) 2 in. | 8 in. Based on the solution obtained, draw (a) strain and (b) stress diagram at the beam cross section for Stages 1 and 2. The diagrams must include the corresponding values at the top and bottom of the section further to the steel rebar level.

Answer 1

DELTA PONO Determine the area of the stool Ai= n(2 d² & in diameter 16 in 2in 8 in = 3 x 2 ( 7 ) ² = wgowan: 1-792 in2 Determine moment of inertia I-bd3 8X16 12 12 = 2730 667 in y Determine the distance from Na to the sted reinfarcement top fibre. Since the beam is rectangular beam, the NA lies at the centre of the depth NA = b = 16 = 8 in. 2 2 Determine the com.rossive and Jemeile flere dances a compressive = A, fy - 1.742 X 60 85 Fc (b) (185) (3) (8). a compressive = 5.12 in. C sensite = a = 5:12 [fc = 3 KSC, 8=-85] Jensile = 6 • 023 in Determine the tensile and combossive stresses a. when M = 80 kip.in TE= Mx a I OCESOX 103 x 5:12 2730.667 10o = 149.99 Ulinzi at = MXG I of = gox 103 x 6.023 2730.667 lot=176-455 ib/in?

DELTA PO NO when M= 240 Kikin M = oc oc = MX a. Moc I = 240x10²x5.12 2730.667 orc = 449.99 lbl in 2 ota MXC =240x103 x 6°023 2730.667 lot = 529.365 (blin . a. when M = 8 okup in. 16 SS blin” lo 149.9961192 b. When M= 240 Kip in 529.365 (blin? 449.99 lb/in?