Q.1
a) The cable BC carries a tension of 750 N. Write this tension as a force T acting on point B in terms of the unit vectors i, j, and k. The elbow at A forms a right angle.
b) For the right-angle pipe OAB of part (a). Replace the 750-N tensile force which the cable exerts on point B by a force-couple system at point O.
Q.II
a) The smooth homogeneous sphere rests in the 1200 frictionless groove and bears against the end plate, which is normal to the direction of the groove. Determine the angle θ, measured from the horizontal, for which the reaction on each side of the groove equals the force supported by the end plate.
b) If a force F = 15 N is required to release the spring loaded clamps, what are the normal reactions at A and B if F = 0?
Q.III
Determine the compression force C exerted on the can for an applied force P = 50 N when the can crusher is in the position shown. Note that there are two links AB and two links AOD, with one pair of linkages on each side of the stationary portion of the crusher. Also, in B is on the vertical centerline of the can. Finally, note that small square projections E of the moving jaw move in recessed slots of the fixed frame.
Q.IV
The magnitude of force P is slowly increased. Does the homogeneous box of mass m slip or tip first? State the value of P which would cause each occurrence. Neglect any effect of the size of the small feet.
Q.V
Calculate the horizontal force P on the light 100 wedge necessary to initiate movement of the 40-kg cylinder. The coefficient of static friction for both pairs of contacting surfaces is 0.25. Also determine the friction force FB at point B. (Caution: Check carefully your assumption of where slipping occurs.)
Q.VI
a) Aspherical fiberglass buoy used in an underwater experiment is anchored in shallow water by a chain [see part (a) of the figure]. Because the buoy is positioned just below the surface of the water, it is not expected to collapse from the water pressure. The chain is attached to the buoy by a shackle and pin [see part (b) of the figure]. The diameter of the pin is 0.5 in. and the thickness of the shackle is 0.25 in. The buoy has a diameter of 60 in. and weighs 1800 lb on land (not including the weight of the chain). (a) Determine the average shear stress τaver in the pin. (b) Determine the average bearing stress σb between the pin and the shackle.
b) A hollow steel cylinder is compressed by a force P (see figure). The cylinder has inner diameter d1 = 3.9 in., outer diameter d2 = 4.5 in., and modulus of elasticity E = 30,000 ksi. When the force P increases from zero to 40 k, the outer diameter of the cylinder increases by 455 x10-6 in.
(a) Determine the increase in the inner diameter.
(b) Determine the increase in the wall thickness.
(c) Determine Poisson's ratio for the steel.
Q.VII
a) A steel rod of diameter 15 mm is held snugly (but without any initial stresses) between rigid walls by the arrangement shown in the figure. Calculate the temperature drop ΔT (degrees Celsius) at which the average shear stress in the 12-mm diameter bolt becomes 45 MPa. (For the steel rod, use α = 12 x 10-6/°C and E = 200 GPa.)
Q.VIII
Figure shows a hand crank with static vertical load applied to the handle.
a) Copy the drawing and mark on it the location of highest bending stress. Make a three-dimensional Mohr circle representation of the stresses at this point. (Neglect stress concentration.)
(b) Mark on the drawing the location of highest combined torsional and transverse shear stress. Make a three-dimensional Mohr circle representation of the stresses at this point, again neglecting stress concentration.
Q.IX
The beam AC is simply supported at A and C and subject to the uniformly distributed load of 300 N/m plus the couple of magnitude 2700 N ⋅ m as shown in figure. Write equations for shearing force and bending moment and make sketches of these equations.
