MEC 2403/MAE 2401
Problem Set2
Q1. An 80-m-long wire of 5-mm diameter is made of a steel with E = 200 GPa and an ultimate tensile strength of 400 MPa. If a factor of safety of 3.2 is desired, determine (a) the largest allowable tension in the wire, (b) the corresponding elongation of the wire.
Q2. Two gage marks are placed exactly 250 mm apart on a 12-mm-diameter aluminum rod. Knowing that, with an axial load of 6000 N acting on the rod, the distance between the gage marks is 250.18 mm, determine the modulus of elasticity of the aluminum used in the rod.
Q3. A square yellow-brass bar must not stretch more than 2.5 mm when it is subjected to a tensile load. Knowing that E = 105 GPa and that the allowable tensile strength is 180 MPa, determine (a) the maximum allowable length of the bar , (b) the required dimensions of the cross section if the tensile load is 40 kN.
Q4. The 4-mm-diameter cable BC is made of a steel with E = 200 GPa. Knowing that the maximum stress in the cable must not exceed 190 MPa and that the elongation of the cable must not exceed 6 mm, find the maximum load P that can be applied as shown .
Q5 . The brass tube AB(E =105GPa) has a cross-sectional area of 140 mm2 and is fitted with a plug at A. The tube is attached at B to a rigid plate that is itself attached at C to the bottom of an aluminum cylinder (E =72GPa) with a cross-sectional area of 250 mm2. The cylinder is then hung from a support at D. In order to close the cylinder, the plug must move down through 1 mm . Determine the force P that must be applied to the cylinder.
Q6. A 250-mm-long aluminum tube (E =70 GPa) of 36-mm outer diameter and 28-mm inner diameter can be closed at both ends by means of single-threaded screw-on covers of 1.5-mm pitch. With one cover screwed on tight, a solid brass rod (E =105 GPa) of 25-mm diameter is placed inside the tube and the second cover is screwed on . Since the rod is slightly longer than the tube, it is observed that the cover must be forced against the rod by rotating it one-quarter of a turn before it can be tightly closed. Determine (a) the average normal stress in the tube and in the rod, (b) the deformations of the tube and of the rod.
Q7. Members AB and BC are made of steel (E = 200 GPa) with crosssectional areas of 516 mm2 and 412 mm2 , respectively. For the loading shown, determine the elongation of (a) member AB , (b) member BC.
Q8 Determine the deflection of the apex A of a homogenous circular cone of height h, density ρ , and modulus of elasticity E, due to its own weight.
Q9. A homogenous cable of length L and uniform. cross section is suspended from one end (a) Denoting by ρ the density (mass per unit volume) of the cable and by E its modulus of elasticity, determine the elongation of the cable due to its own weight. (b) Show that the same elongation would be obtained if the cable were horizontal and if a force equal to half of its weight were applied at each end.
Q10. Compressive centric forces of 160 kN are applied at both ends of the assembly shown by means of rigid plates. Knowing that 200 GPa s E = and 70 GPa, aE = determine (a) the normal stresses in the steel core and the aluminum shell, (b) the deformation of the assembly.
Q11. Knowing that a 0.5-mm gap exists when the temperature is 24°C, determine (a) the temperature at which the normal stress in the aluminum bar will be equal to -75 MPa, (b) the corresponding exact length of the aluminum bar.