Question

The low strength concrete floor slab is integrated with a wide- flange A-36 steel beam using shear studs (not shown) to form the composite beam. (Figure 1) Part A If the allowable bending stress for the concrete is (Gallow)con = 10 MPa and allowable bending stress for steel is allow)st = 165 MPa, determine the maximum allowable internal moment M that can be applied to the beam. Express your answer with the appropriate units. Figure 1 of 1 H HÅ ? M= Value Units 100 mm Submit Request Answer 15 mm 400 mm Provide Feedback Next > 15 mm 15 mm 200 mm

Answer 1

Salem Transform the beam cross-section into that of steel 22.1 Econs Es+ = Ollos 200 bst Ollos xsm - 0.1105 m Location of centroid f transformed section: - у Eỹ A EA 0.0075 (0.016) (0-2) + 0-2 (0-36) (0.018) + 0.3925(0-015) (0-2) +0.45(0-1) Collos) 01015(0-2) + 0-37(0.015) + 0.015 (0-2) + ollollos) Is = 0.3222m Moment of Inertia ! - I = I (0-2) (0-015)3 + 0-2 (0-015) (0-3222-0.007512 + to Be (0-015) (0-37)3 + 0.01s (0-37)(0-3 222-0-2)? íz (0-2) (0-015)3 + 0-2 (0.015) (0-3925 - 6-3222)? (0-1105 760-193 + 0-1105(0-1) (0-45-0-3222)? +

647.938 106 mt Fiorst, consider the failure of steel: (Jallow)st Mest 165 x10 6 M (0.3222) 647-93x106 M = 331.77 N-m Now consider failure of concrete? (Gallow) conc M Ceon 10x106= Ollos کا M* (ous-0.3222) 647.93X166 ] M = 329.85 N-m Max. allowable internal moment - M.=329.85 N-m Ane