# Ph.D. Preliminary Qualifying Examination. Cover Page. Thermodynamic. January 17, 2013 (Thursday) 9:30 am 12:30 noon Room 2145 Engineering Building

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1 GENERAL INSTRUCTIONS: COLLEGE OF ENGINEERING MECHANICAL ENGINEERING Ph.D. Preliminary Qualifying Examination Cover Page Thermodynamic January 17, 2013 (Thursday) 9:30 am 12:30 noon Room 2145 Engineering Building This examination contains five problems. You are required to select and solve four of the five problems. Clearly indicate the problems you wish to be graded. If you attempt solving all of them without indicating which four of your choice, the worst four problems will be considered. Note that Problem 1 is mandatory. Do all your work on the provided sheets of paper. If you need extra sheets, please request them from the proctor. When you are finished with the test, return the exam plus any additional sheets to the proctor. For identification purposes, please fill out the following information in ink. Be sure to print and sign your name. This cover page will be separated from the rest of the exam before the exam is graded. Write your student number on all exam pages. Do not write your name on any of the other exam pages. Name (print) Signature Student Number

2 Solid Mechanics January 17,2013 This is one of five problems. You are required to work four of the five problems, and Problem #1 is Mandatory. Clearly indicate which problems you are choosing. Show all work on the exam sheets and write your student personal identification (PID) number on each sheet. Do not write your name on any sheet. #1 The arrangement shown for the rigid bar has a simple support and is suspended by two bars made of brass and steel. The bars are fixed at both ends. Find (a) the vertical deflection of point D and (b) the forces in the brass and steel bars. The cross sectional areas of the brass and steel bars are 50 cm 2 and 25 cm 2, respectively. The elastic moduli for bras and steel are 97 GPa and 207 GPa, respectively. Brass 0.3 m Steel 0.5 m 0.25 m 0.25 m Rigid Bar D 100 N

3 Solid Mechanics January 17,2013 This is one of five problems. You are required to work four of the five problems, and Problem #1 is Mandatory. Clearly indicate which problems you are choosing. Show all work on the exam sheets and write your student personal identification (PID) number on each sheet. Do not write your name on any sheet. 2. The wall crane supports a load of 700lb. Determine the horizontal and vertical components of reactions at the pins A and D. Also, what is the force in the cable at the winch W. The jib ABC has weight of 100 lb and member BD has weight of 40 lb. Each member is uniform and has a center of gravity at its center. (Must draw free body diagram of each component before starting calculations.)

4 Solid Mechanics January 17,2013 This is one of five problems. You are required to work four of the five problems, and Problem #1 is Mandatory. Clearly indicate which problems you are choosing. Show all work on the exam sheets and write your student personal identification (PID) number on each sheet. Do not write your name on any sheet. 4. Determine the normal force, shear force, and moment at sections passing through E and F. Member BC is pinned at B and there is a smooth slot C (allowing horizontal motion). (Must draw free body diagram for each section, calculate support reactions, reactions at B and C)

5 Solid Mechanics January 17,2013 This is one of five problems. You are required to work four of the five problems, and Problem #1 is Mandatory. Clearly indicate which problems you are choosing. Show all work on the exam sheets and write your student personal identification (PID) number on each sheet. Do not write your name on any sheet. 5. The pipe assembly supports the vertical loads as shown. Determine the components of reactions at the ball and socket joint A and the tension in the supporting cables BC and BD. (Must draw free body diagram before starting calculations.)

6 Solid Mechanics January 21, 2009 This is one of five problems. You are required to work four of the five problems. Clearly indicate which problems you are choosing. Show all work on the exam sheets and write your student personal identification (PID) number on each sheet. Do not write your name on any sheet. #3 Draw the shear and bending moment diagrams for the following beam with the shown distributed load, one concentrated load and two unknown reactions R A and R B : 1kN/m 1.5 kn R A 2m 2m 1m 1m Show all your work with magnitude of shear and bending moment and identify the location where shear vanishes, and the location where maximum bending moment occurs. R B

7 Solid Mechanics January 21, 2009 This is one of five problems. You are required to work four of the five problems. Clearly indicate which problems you are choosing. Show all work on the exam sheets and write your student personal identification (PID) number on each sheet. Do not write your name on any sheet. #4 In the structure shown below members ABC, BDE and CD are assumed to be solid rigid members. The structure is pinned to the ground at A and supported by a roller at E. For this structure: A. Draw the Free Body Diagram for member BE showing all support forces and loads. B. Determine the values of all the support forces acting on BE. C. Draw the diagrams for the bending moment and shear force distributions along member BE. Unless otherwise indicated, all joints and support points are assumed to be pinned or hinged joints.

8 Solid Mechanics January 21, 2009 This is one of five problems. You are required to work four of the five problems. Clearly indicate which problems you are choosing. Show all work on the exam sheets and write your student personal identification (PID) number on each sheet. Do not write your name on any sheet. #5. An element in a structural material is stressed as shown below. The values of shear, compression and tension are 100, 600 and 600 MPa, respectively. Find (a) the principal stresses and angle of the plane on which it occurs, and (b) the maximum shear stress and the angle of the plane on which it occurs.

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