Question

3) In many beam design problems deflection is a limiting criteria. Assume there is a rectangular, simply supported beam, and the width (b) of the beam is fixed by other design considerations; determine the difference in height (h) required for an aluminum beam compared to a steel beam if the deflection is to remain the same. Assume a Modulus of Elasticity of 29 x 10s psi for steel, and 10 x 10s psi for aluminum. Work Neatly! You must show all of your work! (15 points) The equation for the deflection of the beam is 6= W (2x)348EI For a rectangular cross-section, the moment of inertia is: | = 1 bh12 4) Calculate the required compressive strength (fer) for a concrete mix design if fc 5000 psi and data indicate a standard deviation of 550 psi based on 35 tests for a similar mix.Work Neatly! You must show all of your work! (15 points)

Answer 1

"1, det h be Therefore height of aluminum beam 2 ""h "" "" "" steel beam 3 width of beam in same = b 4 span of beam in same = l aluminum beam = bh^3/12: I steel beam = b times (h_1)^3/12 E_alu = 10 times 10^6 psi, E steel = 29 times 10^6 psi. delta aluminum beam = delta steel beam p times l^3 times 12/48 times 10 times 10^6 times bh^3 = p times l^3 times 12/29 times 10^6 times b times r_1^3 times 48 1/480 times 10 times r^3 = 1/29 times 10^6 times 18 times h^3_1 1/10h^3 = 1/29 h^3_1 1/10h^3 = 1/29h^3_1 h^3/h^3_1 = 29/10 = 2.9 h/h_1 = 1.426: h = 1.426h_1 h - h_1 = 1.426h_1- h_1 = 0.426h_1"