Question

Part A- Answer all questions (Total Marks for Part A: 120) Part A- Question 1 (Total Marks for Part A - Question 1: 24) A 140mm thick concrete slab is supported by a series of parallel 460UB82.1 steel beams at 2400mm centres. Assume there is sufficient bond between the steel beam and the concrete slab to enable the materials to act together as a composite unit Assume for steel E 200 GPa ? 280 MPa for concrete E-25 GPa ? = 25 MPa a) Draw the stress diagram for the transformed section (transform into steel), and the stress diagram for the composite section. On the diagrams show the stresses at the top and bottom of the steel beam and at the top and bottom of the concrete slab, and thus show that the maximum stresses for the materials have not been exceeded. (18 marks) b) Calculate the Melastic (maximum elastic moment) for the composite beam (6 marks) Data for 460UB82.1 A-10500 mm D 460 mm I 372*106 mm4 ly- 18.6*10' mm1 140 mm 460 mm

Answer 1

Transformed steel section Modular ratio = E_s/E_c = 200 GPa/25 GPa = 8 centroid y^bar = A_1 y_1 + A_2 y_2/A_1 + A_2 A_1 = 10500 A_2 = 2400/8 times 140 = 42000mm^2 y_1 = 230 y_2 = 460 + 140/2 \r\n y^bar = 10500 times 230 + 42000 times 530/10500 + 42000 = 470 mm from bottom Transformed steel section Consider The Stress at the extreme bottom of the transformed section be 280 MPa Now stress at top of transformed steel section sigma_top/130 = 280/470 sigma_top = 77.4468 MPa \r\n Now stress at junction sigma_j/10 = 280/470 sigma_j = 5.95745 MPa Now when it comes to concrete, The stress at junction is 5.95745/8 = 0.74468 MPa Now stress in extreme top in concrete = 77.4468/8 = 9.68 MPa Actual stress distribution of section \r\n (I)_transformed steel section = 300 times 140^3/12 + 300 times 140 times (130 - 70)^2 + 372 times 10^6 + 10500 times (470 - 230)^2 = 68.6 times 10^6