243 Final 2007

DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING MAE 243: Mechanics of Materials Fall 2006, Final Exam

Name:______________,____________ Section:_________

PROBLEM (1): An elastomeric bearing pad consisting of two steel plates bonded to a chloroprene elastomer (an artificial rubber) is subjected to a shear force V during a static loading test (see figure). The pad has dimension a=150mm and b=250mm, and the elastomer has thickness t=50mm. When the force V equals 12 kN, the top plate is found to have displaced laterally 8.0mm with respect to the bottom plate. What is the shear modulus of elasticity G of the chloroprene?

DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING MAE 243: Mechanics of Materials Fall 2006, Final Exam

Name:______________,____________ Section:_________

PROBLEM (2): A bar of circular cross section having two different diameters d and 2d is shown in the figure. The length of each segment of the bar is L/2 and the modulus of elasticity of the material is E. Calculate the strain energy if the load P = 27 kN, the length L = 600 mm, the diameter d = 40 mm, and the material is brass with E = 105 GPa.

DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING MAE 243: Mechanics of Materials Fall 2006, Final Exam

Name:______________,____________ Section:_________

PROBLEM (3): A plastic bar of diameter d = 50 mm is to be twisted by torque T until the angle of rotation between the ends of the bar is 50. If the allowable shear strain in the plastic is 0.013 rad, what is the minimum permissible length of the bar?

DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING MAE 243: Mechanics of Materials Fall 2006, Final Exam

Name:______________,____________ Section:_________

PROBLEM (4): A simple beam AB shown in the figure supports a concentrated load of 4000 lb (4.0 k) and a segment of uniform load of 2000 lb/ft (2.0 k/ft). Draw and label the shear-force and bendingmoment diagram for this beam. (Key points should be marked on the sketchs. Full credit will be given for sketchs with accurate labels on maxima, minima and intercepts. A bonus point will be awarded for determining the equations of any non-linear segments).

DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING MAE 243: Mechanics of Materials Fall 2006, Final Exam

Name:______________,____________ Section:_________

PROBLEM (5): A cantilever beam of length L = 6 ft supports a uniform load of intensity q = 200 lb/ft and a concentrated load P = 2500 lb. Calculate the required section modulus S (= I/c) if σallow = 15,000 psi.

DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING MAE 243: Mechanics of Materials Fall 2006, Final Exam

Name:______________,____________ Section:_________

PROBLEM (6): An element in biaxial stress is subjected to the normal stresses shown in the figure. (i) Determine the maximum in-plane shear stress, associated normal stresses and the orientation of the element. You should sketch and label your element.

DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING MAE 243: Mechanics of Materials Fall 2006, Final Exam

Name:______________,____________ Section:_________

PROBLEM (7): A post is supported by a pole of hollow circular cross section, as shown in the figure. The outer and inner diameters of the pole are 10.0 in. and 8.0 in., respectively. The pole is 40 ft high and weights 3800 lb. the sign has dimensions 6 ft x 3 ft and weighs 400 lb. Note that its center of gravity is 41 in. from the axis of the pole. The wind pressure against the sign is 30 lb/ft2.

(a) Determine the stresses acting on a stress element at point A, which is on the outer surface of the pole at the “front” of the pole, that is, the part of the pole nearest to the viewer. (b) Determine the maximum tensile, compressive, and shear stresses at point A.

DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING MAE 243: Mechanics of Materials Fall 2006, Final Exam

Name:______________,____________ Section:_________

PROBLEM (8): A gold microbeam attached to a silicon wafer behaves like a cantilever beam subjected to a uniform load (see figure). The beam has length L=27.5 µm and rectangular cross section of width b=4.0 µm and thickness t=0.88 µm. The total load on the beam is 17.2 µN. If the deflection at the end of the beam is 2.46 µm what is the modulus of elasticity Eg of the gold alloy? The moment for such a beam is given by M =

− qL2 qx 2 + qLx − 2 2