Question

The beam shown below is made from steel with a modulus of elasticity of 10,000 ksi. The section is a rectangular beam that is 15" tall and 7" wide. The length of the beam is 30 ft. (a) Identify the individual load cases from the beam tables that should be applied. Draw the deflected 2) shape for each case and clearly show or mark locations where deflection or slope are zero. (b) Evaluate the deflection of the beam at A in inch. [Ans.to check va 0.926 in upward] (c) Evaluate the slope of the beam at B in radians. Ans. to check θв -0.00514 rad] (d) Calculate the deflection halfway between B and C in inch. [Ans.to check v0.289 in downward] 5 k/ft L/2 L/2

Answer 1

" E = 10000 Ksi L = 30 ff = 360 inch b = 7"" wide h = 15"" height (c) shape at B = -wl^3/24 EI = w(l/2)^3/24 EF I = bh^3/12 = 7 times 15^3/12 = 1968 implies 5 inch = -5 times (780)^3/24 times 10000 times 1968.75 times 12 = -.00514 Rad Also (down) (b) deflection of beam at A = theta_B times l/2 = 0.0514 times 180 = 0.926 inch (upward) (d) deflection in middle = 5/384 times wl^4/EI = 5/384 times 5 times 180^4/12 times 10000 times 1968.75 = 0.209 inch (downward) (a) slope at between B & C will be zero. And at B and C deflection is zero."