Midterm 2 with Solution - Introductory Solid Mechanics | TAM 251, Exams of Applied Solid Mechanics

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TAM 251. Midterm II. Wed 27 April 2011 NAME: DISCUSSION SECTION # This is a close-book, close-note exam. You have 45 minutes to complete it. Answer the questions in the space provided. THE REVERSE SIDE OF THE PAGES WILL NOT BE GRADED; use them for scratch calculations if you wish. The value of each and every question (“a”, “b”, “c”, et cetera) is the same: 4 points. PLEASE BOX YOUR ANSWERS! PROBLEM 1 Consider a simply supported beam of Young’s modulus £, moment of inertia J, and length L. Moments M4 ad Mg are applied respectively at c = 0 and x = L, as indicated in the figure. a is the small angle of rotation at z = 0, and @ is the small angle of rotation at z = L. ————- x Ay OS Ms i - (; 1 6, (a) Mark the reactions on the figure, then invoke equilibrium to solve for them. WU z >] ec fee fe) ghz0 » Bl-Re- Baro *7 (By> Mertl - El a aes Zhe >) Ay 4 Dy 0 4) [Ay - (Nox Ma) | - {| (b) Draw a suitable free-body diagram and use it to obtain an expression for the bending moment M(x) and an expression for the shear force V(x). Check that the relation between M() and V(z) is satisfied. Ma \ fo> \4 a=W 2»