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STR2-47 - the slope and deflection expressions using the...

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ERCIYES UNIVERSITY ENGINEERING FACULTY DEPARTMENT OF MECHANICAL ENGINEERING STRENGTH OF MATERIALS – II, FINAL EXAM June 11, 2007 SM2-047 1. (30 points) An unequal-leg angle section has the dimensions shown in Figure. At this cross section the moment is M = 10 kN-m and is oriented parallel to the short leg of the angle. (a) Determine the orientation of the neutral axis of the cross section, and the show this orientation on a sketch. (b) Determine the maximum tensile stress and the maximum compressive stress on the cross section. (y- and z-axes are centroidal principal axes) 2. (30 points) (a) Prove that the shear center of an equal-leg angle is at the corner of the angle, and prove that the resultant of the shear flow in the legs of the angle is equal to the total shear force on the section. The shear force acts normal to the axis of symmetry of the cross section. Assume that (t « b). (b) Determine the maximum shear stress in the cross. 3. (30 points) For the beam and loading shown, determine (a)
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Unformatted text preview: the slope and deflection expressions using the singularity functions, (b) the reactions at both supports, (c) the bending moment at D. 4. (25 points) A torque is applied to gear A of a two-shaft system and is transmitted through gears at B and C to a fixed end at D. The shafts are made of steel (G = 80 GPa). Each shaft has a diameter d = 32 mm, and they are supported by frictionless bearings. If the torque applied to gear A is 400 N-m, and D is restrained, (a) determine the maximum shear stress in each shaft, and (b) determine the angle of rotation of the gear A relative to its no-load position. 5. (25 points) A hollow steel shaft is 0.9 m long and has the cross section shown. The steel is assumed to be elastoplastic with σ Y = 180 MPa and G = 77 GPa. Determine the applied torque and the corresponding angle of twist (a) at the onset of yield, (b) when the plastic zone is 10 mm deep. Prof. Dr. M. Kemal Apalak Problem 1 Problem 2 Problem 3 Problem 4 Problem 5...
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