Assignment 1 ENS 3190/5113 Mechanics of Solids Semester

Assignment 1 ENS 3190/5113 Mechanics of Solids Semester 2 2012 Due: 4:30PM Thursday 13 Sept 2012 Value: 10% of the final mark Question 1 (Total mark for Q 1 is 21 out of 57.5): Before the 400kN load is applied the rigid platform rests on two steel bars each with a cross-sectional area of 1400 mm2 as shown below. The cross sectional area of the aluminium bar is 2800 mm2. A) Compute the normal stress in the aluminium bar after the load is applied. Use Es=200 GPa and Eal=70 GPa and neglect the weight of the structure. B) Repeat your calculations assuming that there is no gap between the aluminium bar and the platform. C) What is the minimum gap for which the stress in the aluminium bar will be zero. D) Using the results from A to C draw a graph and show the relationship between the gap and stress in the aluminium bar. E) Prove if the relationship between the normal stress in the aluminium bar and gap is linear or of a higher degree. Question 2 (Total mark for Q 2 is 20 out of 57.5): A shaft carries a distributed torque of intensity (torque per unit length) t=tb(x/L). Determine: A) Determine the maximum shear stress in the shaft; B) Determine the angle of twist of the shaft at B; C) Draw a diagram showing how the shear stress on the outer surface of the shaft varies between A and B ie along the shaft. Use L = 1.5 m; d=25 mm; tb=200 N.m/m and G=80 GPa. Question 3 (Total mark for Q 3 is 16.5 out of 57.5): Draw the load and bending moment diagrams that correspond to the given shear force diagrams below.
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