University of Massachusetts - AmherstDepartment of Civil & Environmental EngineeringCEE 331: Structural Analysis

Homework #9: Due November 18You can use MASTAN to check your answers to 1 and 2.

Problem 1: Hibbeler 9-40

Problem 2: Hibbeler 9-50

Problem 3: Consider the cantilever beam shown, that has a square cross section withside lengths a, length l, and loaded by a distributed load q. The material has elasticmodulus E.

(a) Calculate the tip deflection of the cantilever in terms of a, q, E, and l. Use themethod of virtual work and consider bending and strain energy using a shape factorK = 1.2 for the shear part. You must calculate the cross sectional area and moment ofinertia in terms of a.(b) Calculate the ratio of the bending displacement to the shear displacement. Arrangeterms so that the ratio l/a appears in your expression.(c) Plot the ratio of bending to shear displacement as a function of l/a. Above whatspan to depth ratio would your engineering judgement tell you it would be acceptableto ignore shear deformation?

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