Optional Midterm

Optional Midterm - MAE 131A/SE110A – Fall 2009 Optional...

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Unformatted text preview: MAE 131A/SE110A – Fall 2009 Optional Mid‐term Tuesday November 3, 2009 Time: 3:35 to 4:55 Problem 1 (6 points) The two wooden members (A & B) shown (right Fig.), which support a 16‐kN load, are joined by plywood splices fully glued on the surfaces in contact. The ultimate A shearing stress in the glue is 2.5MPa and the clearance between the members is 6 mm. [To receive full credit, you must draw a free­body diagram for each piece and B carefully show all the forces acting on that piece.] (a) (2 points) Find the minimum thickness of each of the two wooden members (A & B) if the normal stress in either one should not exceed 15MPa. (b) (2 points) Find the average axial stress in the upper and lower plywood splices if each is 5mm thick. (c) (2 points) Determine the required length L of each splice if a factor of safety of 2.75 is to be achieved. Problem 2 (6 points) Compressive centric forces of 40 kips are applied at both ends of the assembly shown by means of rigid plates. Knowing that Es = 29 × 106 psi (for steel) and Ea = 10 × 106 psi (for aluminum), determine: (a) (2 points) the normal (axial) strain, (b) (2 points) the normal (axial) stress in the steel core and in the aluminum shell, and (c) (2 points) the deformation (total shortening) of the assembly. Problem 3 (6 points) Knowing that the internal diameter of the hollow shaft shown is d = 0.9 in., determine: (a) (2 points) the maximum shearing stress caused by a torque of magnitude T = 9 kip ⋅ in., (b) (2 points) the corresponding minimum shear stress, and (c) (2 points) the total rotation of the left end relative to the fixed right end; the shear modulus of the shaft is 11× 106 psi and its length is 9 in. 1 Problem 4 (7 points) Consider a box beam of 5mm wall thickness (right Fig.), 80mm subjected to a bending moment of Mz = 10kN‐m. The two y dashed lines are the z‐ and y‐axes of the beam, passing trough the centroid of its cross section. (a) (2 points): Find the area moment of inertial, Iz, z z about the horizontal (dashed) z‐axis and the 100mm corresponding section modulus, Sz, the area moment of inertial, Iy, about the vertical (dashed) y‐ axis and the corresponding section modulus, Sy, and the polar moment of inertia about the centriod of the cross section. (b) (1.5 points): Find the maximum normal stress that this beam is carrying. (c) (1.5 points): Find the maximum tensile strain in the beam if it elastic modulus is 65GPa. (d) (2 points): If in addition to Mz = 10kN‐m, the beam is carrying a bending moment My = 5kN‐m about its y axis, find the orientation of the neutral axis relative to the z‐axis, and calculate the normal stress produced by these two moments at the upper right corner of the beam. 2 ...
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