Solved Problems in Axial Deformation (206-211)

Problem 206
A steel rod having a cross-sectional area of 300 mm² and a length of 150 m is suspended vertically from one end. It supports a tensile load of 20 kN at the lower end. If the unit mass of steel is 7850 kg/m³ and E = 200 × 10³ MN/m², find the total elongation of the rod.

Solution 206

Problem 207
A steel wire 30 ft long, hanging vertically, supports a load of 500 lb. Neglecting the weight of the wire, determine the required diameter if the stress is not to exceed 20 ksi and the total elongation is not to exceed 0.20 in. Assume E = 29 × 10⁶ psi.

Solution 207

Problem 208
A steel tire, 10 mm thick, 80 mm wide, and 1500.0 mm inside diameter, is heated and shrunk onto a steel wheel 1500.5 mm in diameter. If the coefficient of static friction is 0.30, what torque is required to twist the tire relative to the wheel? Neglect the deformation of the wheel. Use E = 200 GPa.

Solution 208

Problem 209
An aluminum bar having a cross-sectional area of 0.5 in² carries the axial loads applied at the positions shown in Fig. P-209. Compute the total change in length of the bar if E = 10 × 10⁶ psi. Assume the bar is suitably braced to prevent lateral buckling.

Solution 209

Problem 210
Solve Prob. 209 if the points of application of the 6000-lb and the 4000-lb forces are interchanged.

Solution 210

Problem 211
A bronze bar is fastened between a steel bar and an aluminum bar as shown in Fig. P-211. Axial loads are applied at the positions indicated. Find the largest value of P that will not exceed an overall deformation of 3.0 mm, or the following stresses: 140 MPa in the steel, 120 MPa in the bronze, and 80 MPa in the aluminum. Assume that the assembly is suitably braced to prevent buckling. Use E_st = 200 GPa, E_al = 70 GPa, and E_br = 83 GPa.

Solution 211