MAAE 2202 A. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work.

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1 It is most beneficial to you to write this mock final exam UNDER EXAM CONDITIONS. This means: Complete the exam in 3 hours. Work on your own. Keep your textbook closed. Attempt every question. After the time limit, go back over your work with a different colour or on a separate piece of paper and try to do the questions you are unsure of. Record your ideas in the margins to remind yourself of what you were thinking when you take it up at PASS. The purpose of this mock exam is to give you practice answering questions in a timed setting and to help you to gauge which aspects of the course content you know well and which are in need of further development and review. Use this mock exam as a learning tool in preparing for the actual exam. Please note: Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work. Often, there is not enough time to review the entire exam in the PASS workshop. Decide which questions you most want to review the Facilitator may ask students to vote on which questions they want to discuss in detail. Facilitators do not bring copies of the mock exam to the session. Please print out and complete the exam before you attend. Facilitators do not produce or distribute an answer key for mock exams. Facilitators help students to work together to compare and assess the answers they have. If you are not able to attend the PASS workshop, you can work alone or with others in the class. Good Luck writing the Mock Exam!! Date and location of mock exam take-up: Saturday, December 16, :30 PM 8:30 PM in ME 3380

2 Question 1: MAAE 2202 A Multiple Choice Questions (Answer will be only one among A to D for each sub-question) (1) The mechanism below is pinned at points A, B, C, and D. To determine the internal reactions at plane a-a, which of the following FBDs is correct? a. b. c. d.

3 (2) Which of the following beams is not under symmetric beam bending? a. b. c. d. (3) A beam is held in place by rigid walls on both ends as shown. As temperature increases, a pressure force p is applied in the y-direction to prevent deformation in the y-direction. Which stresses and strains are present in the beam? a. ε " 0, ε & 0, σ " = 0, σ & = 0 b. ε " = 0, ε & = 0, σ " 0, σ & 0 c. ε " 0, ε & = 0, σ " 0, σ & = 0 d. ε " = 0, ε & 0, σ " = 0, σ & 0 (4) Which of the following statements is incorrect with regards to symmetric beam bending? a. Maximum bending stress occurs at the neutral plane b. Shear stress is zero at the outer surfaces of the beam c. Force is always applied perpendicular to the neutral axis d. Positive bending moment induces tensile stress on the bottom surface of a beam (5) What is the shear stress acting at point B in the following structure? a. 6.2 MPa b. 3.2 Pa c. 1.6 MPa d. 3.2 MPa

4 (6) Struts A and B are identical except for their end constraints. A is pin-pinned and B is fixedfree. Which of the following statements are correct? a. Strut A can take 2 times more load than strut B b. Strut A can take 2 times less load than strut B c. Strut A can take 4 times more load than strut B d. Strut A can take 4 times less load than strut B (7) Which of the following is true about buckling analysis of real struts? a. A strut cannot fail if the applied load is less than the critical buckling load b. A column with a low slenderness ratio will yield rather than buckle c. For rectangular beams, buckling will always occur in the plane where the 2 nd moment of area is smallest d. A strut will buckle if the applied load is less than the critical buckling load (8) Which of the following statements apply to the following shaft? a. T * = T + b. τ *- = τ -. c. τ -. = τ.+ d. θ.- + θ -* = θ.+ (9) What is the maximum amount of tensile stress a material can support before failure? a. Proportion limit b. Yield strength c. Tensile strength d. Fracture strength (10) Which of the following statements about volumetric strain is correct? a. Volume is conserved for a solid body under three-dimensional stress. b. Volumetric strain is the sum of the deformations in each axial direction. c. Volumetric strain is associated with shear strains. d. Volumetric strain can be calculated using the bulk modulus for a body under hydrostatic stress.

5 (11) Which shear force and bending moment diagrams are correct for the following beam? a. b. c. d. (12) A bar consists of a circular steel core surrounded by a brass tube and an aluminum tube with rigid plates at each end, as shown below. If load P is applied on the end plates, which statement is incorrect about the following system? a. It is statically indeterminate. b. The aluminum, brass, and steel components will experience the same vertical deformation. c. The aluminum, brass, and steel components will experience the same load. d. The system can be solved using force equilibrium and deformation compatibility.

6 (13) What is the shear stress at the center of the stepped shaft at point A, given that the diameter of the shaft at point A is 10 in.? a. 0 psi b psi c psi d psi (14) Which of the following is the proper Macaulay s step function for the following beam? a. M = R * [x] 5[x] 8 2[x 0.5] ; b. M = R * [x] 5[x] 8 + 5[x 0.5] 8 2[x 0.5] ; c. M = R * x + 5[x] 8 5[x 0.5] 8 + 2[x 0.5] ; d. M = R * [x] 5[x] 8 + 5[x 0.5] 8 2 (15) A pinned beam is supported by two identical aluminum rods, as shown below. If a load P is applied downwards at point B, which statement is incorrect about the following system? a. It is statically indeterminate. b. The system can be solved using superposition method c. The deflection of point B is 5 times greater than that at point A. d. The stress in the rod at point A is not equal to the stress in the rod at point B. (16) A solid shaft and a hollow shaft made from the same material have the same outer diameter and the same length. If they are subjected to the same torque load, which of the following statements is true? a. Solid shaft has a smaller maximum shear stress and a smaller maximum twisting angle. b. Solid shaft has a greater maximum shear stress and a greater maximum twisting angle. c. Solid shaft has a greater maximum shear stress but a smaller maximum twisting angle. d. Solid shaft has a smaller maximum shear stress but a greater maximum twisting angle.

7 (17) A frictional belt system has a coefficient of friction of 0.3 and a contact angle of 135. What mass will not keep the following system in static equilibrium? a kg b kg c. 500 kg d kg (18) The following simply-supported beam is subjected to a point load as shown below. If its cross-section is a square, which of the following statements is incorrect? a. The slopes at the two supports are unequal. b. The slopes at the two supports have opposite signs. c. The deflection of the beam at the supports are zero. d. The maximum deflection occurs at the loading point. (19) For the given cantilever beam, which of the following statements is incorrect? a. Shear stress is zero everywhere within the beam. b. The bending stress at point 1 is greater than the bending stress at point 2. c. Tensile bending stress occurs at the top of the beam. d. Bending stress is non-uniform across the cross-section of the beam.

8 (20) Which of the following diagrams best represent the deflection of the following cantilever beam? a. b. c. d.

9 Question 2: MAAE 2202 A A rigid member ABC is supported by a steel pin-ended column at point B and connected to a flexible belt and pulley mechanism with a coefficient of friction of 0.2 at point A. Column BD has a Young s modulus of 207 GPa and a hollow cross-section as shown below. The other end of the flexible belt is attached to a motorized drum with a diameter of 0.50 m. a. What is the maximum torque T that the drum can apply before buckling occurs in column BD? b. With the maximum torque T applied, is column BD safe from yielding? Assume that steel has a yield strength of 250 MPa. c. With the maximum torque T applied, determine the deformation of column BD. Cross Section of Column BD

10 Question 3: MAAE 2202 A A cylinder and rod is made of brass and aluminum, respectively. The cylinder has a diameter of 80 mm and wall thickness of 3 mm, and the rod has a diameter of 20 mm. The end plates are assumed to be rigid. Brass has a Young s modulus of 100 GPa, a Poisson s ratio of 0.34, and a coefficient of thermal expansion of 18 x 10-6 / C. Aluminum has a Young s modulus of 70 GPa, a Poisson s ratio of 0.33, and a coefficient of thermal expansion of 22 x 10-6 / C. The space between the cylinder and the rod is filled with a fluid exerting 10 MPa of pressure. a. Determine the axial stresses in the cylinder and the rod at room temperature (20 C) b. Under the same conditions as part A, the system is heated to 100 C. Determine the new axial stresses in the cylinder and rod.

11 Question 4: MAAE 2202 A A solid steel shaft ABC is fixed to a wall at A and is linked to a hollow steel shaft DE through a gear system, as shown. Shaft ABC has a diameter of 1 in., while shaft DE has an outer diameter of 1 in. and an inner diameter of 0.5 in. The gears and C and D have radii of 1 ft. and 0.5 ft., respectively. Both shafts have a shear modulus of 11 psi. a. Determine the maximum allowable torque T so that the angle of twist at point E with respect to point A is less than 0.1. b. While torque T is applied, determine the maximum shear stress in the system.

12 Question 5: MAAE 2202 A A simply supported beam with a square cross-section with side length b is subjected to the loading conditions seen below. a. Draw the shear force and bending moment diagrams b. If the maximum allowable bending stress in the beam is 275 MPa, determine the value of b. c. Using the value of b calculated in part B, determine the maximum shear stress in the beam. Cross Section of Beam

13 Question 6: MAAE 2202 A A steel T-beam with a Young s modulus of 207 GPa and a cross-section shown below is constrained between two rigid walls and subjected to the given loading condition. a. Determine the reactions at both walls. b. Determine the deflection at the center of the beam. Cross Section of Beam