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MECH 101 Final Exam

1. Select one most accurate answer in each of the following questions. (4% each) 1-(i) What cannot be transmitted through a hinge joint of a beam?
the axial force, (b) the transverse force, (c) the inertia force, (d) the bending moment, (e) the bending deflection.

1-(ii) The animation of the logo linked to the MECH101 course website represents

the growth of a Mohrs circle, (b) the evolution of stress distribution in elastic-plastic torsion, (c) the build up of pressure in a pressure vessel, (d) change of normal stress distribution during bending, (e) meaningless.

1-(iii) The fact that the neutral plane must pass through the centroid of the cross-section is because of the equilibrium of

the axial force, (b) the shear force, (c) the inertia force, (d) the bending moment, (e) the reaction force.

1-(iv) A solid cube is dropped from the surface of the sea toward the bottom of the sea. During this travel, the Mohrs circle of the stress state of this solid cube should be

a circle becoming larger and larger, (b) a circle becoming smaller and smaller, (c) a rotating circle, (d) a point moving toward the right hand side on the x-axis, (e) a point moving toward the left hand side on the x-axis.

1-(v) The eigen vector of a column buckling problem is the

critical load, (b) bifurcation point, (c) mode shape, (d) buckling amplitude, (e) slenderness ratio.

2. The two shafts shown below are made of A-3. The box beam is constructed from four boards that are 36 steel. Each has a diameter of 25 mm and fastened together using nails spaced along the beam they are connected using the gears fixed to every 50 mm. If each nail can resist a shear force of 250 their ends. Their other ends are attached to N, determine the greatest shear force V that can be fixed supports at A and B. They are also applied to the beam without causing failure of the nails. supported by journal bearings at C and D, (15%) which allow free rotation of the shafts along their axes. If the maximum allowable twisting angle of shaft AE is 2 deg., what will be the maximum torque TE that can be

Spring 2008
4. A wood pipe having an inner diameter of 1 m is bound together using steel hoops having a cross-sectional area of 125 mm2. If the allowable stress for the hoops is sallow = 85 MPa, determine their maximum spacing s along the section of pipe so that the pipe can resist an internal gauge pressure of 0.028 MPa. Assume each hoop supports the pressure loading acting along the length s of the pipe. (15%)
5. Due to the applied loading, the element at point A on the solid cylinder in the figure below is subjected to the state of stress shown. Draw the corresponding Mohrs circle and then determine the principal stresses and maximum shear stress acting at this point. The angle between the maximum shear orientation and the longitudinal axis of the cylinder must be specified as well. (15%)

6. EI is