Complete a study that investigates and compares the response of a) asimply-supported Bernoulli beam, b) a simply supported Timoshenko beam, and c) a simply supported two dimensional beam (constructed with surface elements). You are to construct and analyze the two-dimensional beam using STAAD Pro. All three beams must have identical geometry, material properties, and boundary conditions. Analyze the beams under a mid-span downward concentrated force. You are to study the similarities/differences in normal bending stress, xx, and vertical deflection at mid-span, , between both one-dimensional beam systems and the two-dimensional beam system. Derive analytical expressions for the mid-span deflection under a point load for the Bernoulli and Timoshenko beam systems, respectively (you may use
the Principal of Virtual Work). Plot the bending stress and mid-span deflection responses for the analytical beam solutions and STAAD output as a function of span to depth ratio (L/D) and compare the solutions using % relative error. At what span to depth ratio do the two solutions converge? You must submit a report that includes an Abstract, Introduction, Methods, Results, and Conclusions. Standard technical writing guidelines should be followed. The report should not contain more than 5 pages.