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.
(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 50mm40mm 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
Wall 10 mm
(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
Bar (2) is 75 mm wide and 25 mm thick [E = 2.72GPa; α = 67 × 20 /°C]. The supporting wall at C i