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EM 306 – Statics FINAL EXAM Fall 2009 - Landis Name ___________________________________ EID ___________________________________ Unique Number __________________________ Instructions: Correctly drawn and labeled free body diagrams are required for all problems with equilibrium analyses. Show all of your work. Place a box around your final answers and include units. Do all of your work on separate sheets of paper. Nothing written directly on the test sheet will be graded. Problem 1. Determine the tension in the string and the resulting reactions at A and B required to maintain equilibrium. The angle θ is 30º. ( points) Problem 2. Determine (a) the location of the centroid, (b) Iyy , and (c) Iyy. The centroid of a semi-circle is located 4 R / 3! from its base, and the moments of inertia about axes passing through its centroid are I (^) y! y != " 8
8 9 " $ %&^ ' ()^ R^4 and I (^) x! x != " 8 R^4. (15 points)
EM 306 – Statics FINAL EXAM Fall 2009 - Landis Problem 3. The 12-lb disk A is at the center of the inclined surface. The tension in the string AB is 4 - lb. What minimum coefficient of friction between the disk and the surface is necessary to keep the disk from slipping? (25 points) Problem 4. When the crank AB is vertical, the beam CD is horizontal and the cable makes a 20 º angle with the horizontal. Determine the moment M required for equilibrium of the frame. (20 points) Problem 5. Determine the internal shear force and bending moment distributions for the beam. (20 points)
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