Mechanics of Materials (I) November 1, 2000
Mid-term Exam 1
1. A plate of length L and width b is subjected to a uniform tensile stress s at the ends. The material has modulus of elasticity E and Poisson’s ratio n. (a) Before the stress was applied, the slope of the diagonal line OA was b/L. What is the slope when the stress s is acting? (b) What is the unit change in area OBAC of the face of the plate? (c) What is the unit change in cross-sectional area? (20%)
2. Two blocks of rubber with E = 4.55 ksi and n = 0.3 are bonded to rigid supports and to a plate AB. The dimension of each block is . Knowing that c = 4 in. and P = 10 kips, determine the smallest allowable dimensions a and b of the blocks if the shearing stress in the rubber is not to exceed 200 psi and the displacement of the plate is to be at least 3/16 in. (15%)
3. A semicircular rigid plate ACBD of weight W = 500 N and radius R = 1m is supported at points A, B and D by three identical wires. Point C is at the center of the circular arc ADB and radius CD is perpendicular to diameter AB. Each wire has modulus of elasticity E = 210 GPa, diameter d = 2 mm, and length L = 1.2 m. A downward load P = 3W is placed on radius CD at point p, distance x from point C. What should be the distance x so that the line CD on the plate will have a slope of 0.1o under the combined action of the force P and the weight W? (20%)
Mechanics of Materials (I) Mid-term Exam 1
November 1, 2000
4. The bimetallic thermal control shown in the figure is made of a brass (length Lb = 0.75 in. and cross-sectional area Ab = 0.1 in.2) and a magnesium bar brass (length Lm = 1.3 in. and cross-sectional area Am = 0.2 in.2). There is a gap d = 0.005 in. between their free ends at room temperature. Calculate the following quantities: (a) the temperature increase DT (above room temperature) at which the two bars come into contact, and (b) the stress s in the magnesium bar when the temperature increase DT is 300 oF. Use the following material properties: ab = 10´10-6/oF, am = 14.5´10-6/ oF, Eb = 15´106 psi, and Em = 6.5´106 psi. (15%)
5. A prismatic bar is subjected to an axial force that produces normal stresses on a certain inclined plane as shown. (i) Determine the angle q (). (ii) Determine the stresses acting on all faces of a stress element oriented at q = 60o and show the stresses and their directions on a sketch of the element. (15%)
6. The truss ABCD supports a vertical load P at joint D. All bars of the truss have axial rigidity EA. (i) Determine the strain energy U of the entire truss. (ii) Use the strain energy to calculate the vertical displacement dd of joint D. (15%)