Sample Mech 260 Final 28Dec2010

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University of British Columbia
Mechanical Engineering
MECH 260
Farrokh Sassani

THE UNIVERSITY OF BRITISH COLUMBIA Department of Mechanical Engineering Sessional Examination - December 2010 Mech 260 - Introduction to Mechanics of Materials - Sections 101& 102 Instructors: C. W. de Silva (102) and F. Sassani (101) Time: 2.5 hours Closed book/notes. One 8.5”x11” fact sheet (double-sided) This question paper prepared by student is allowed contains 3 pages Non-programmable non-graphing calculators allowed. Alternatively, you may use only the “arithmetic mode” of a programmable calculator. No communication devices are allowed. Draw a box around your answers and clearly indicate units. For each question, 1 bonus point will be given for orderly and neat presentation. Question 1 (Total points: 20) The carriage arm of a machine is made of rigid metal parts and a synthetic rubber attachment piece, as shown in Figure 1. Note: All the components except the rubber attachment piece are assumed rigid. One side of the rubber piece is firmly glued to a rigid wall of the machine. The other side is firmly glued to the top end of the carriage arm. The metal arm is made of two pieces joined using a single bolt and nut, in double shear arrangement, as shown. When a vertical load P is applied to the free end of the carriage arm, it moves vertically through 2 mm. The dimensions of the rubber attachment piece are 50mm40mm  20mm as shown. The shear modulus of the rubber attachment piece isG  0.5MPa . (a) Determine the value of the load P in newtons . (12 points) (b) If the diameter of the bolt id 10mm, determine the average shear stress in the X-section of the bolt. (8 points) 40mm 20 mm Synthetic Rubber Attachment Piece 50 mm 20 mm 50 mm Rigid Wall 10 mm Double Shear Bolt Joint and Nut (in double shear) Load P Load P Figure 1 (a): Perspective View. Figure 1 (b): Front View. ____________________________________________________________________________________________________ Mech 260 (sections 101and 102) - December 2010 examination Page 1 of 3 Question 2 (Total points: 25) At a temperature of 5°C, a 3-mm gap exists between two polymer bars and a rigid wall as shown in Figure 2. Bar (1) is 50 mm wide and 20 mm thick [E = 800 1Pa; α = 140 × 11 /°C]. -6 -6 Bar (2) is 75 mm wide and 25 mm thick [E = 2.72GPa; α = 67 × 20 /°C]. The supporting wall at C i
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