1. Consider a beam of length L, cross-sectional area A, area moment I, Youngís modulus E and Poissonís ratio n. Let it be loaded by a uniform load P N/m on its upper surface. Find the shear, moment and deflection as a function of position on the beam, and the approximate stress in the beam, if

(a) the left end is clamped and the right pinned

(b) both ends are pinned

both ends are clamped

Use ordinary beam theory. Comment, if you can, on the approximations involved. What conflicts are there between your solutions and the general equations of elasticity?

2. Repeat for a beam in the form of a circular arc of total angle Q (¾ ¼) pinned at each end (case (b) only) and subject to a uniform load perpendicular to the beam. Let the properties of the beam be the same as those of the beam in problem 1. Let R denote the radius of curvature: RQ = L. Does the solution to this problem approach that of problem 1 as R --> *?