Question 6.2: Design of a Suspension Rod An aluminum rod is to withstand a......
Design of a Suspension Rod
An aluminum rod is to withstand an applied force of 45,000 pounds. The engineering stress strain curve for the aluminum alloy to be used is shown in Figure 6-5. To ensure safety, the maximum allowable stress on the rod is limited to 25,000 psi, which is below the yield strength of the aluminum. The rod must be at least 150 in. long but must deform elastically no more than 0.25 in. when the force is applied. Design an appropriate rod.
From the definition of engineering strain,
e=\frac{\Delta l}{l_{0}}For a rod that is 150 in. long, the strain that corresponds to an extension of 0.25 in. is
e=\frac{0.25 \ in.}{150 \ in.}=0.00167According to Figure 6-5, this strain is purely elastic, and the corresponding stress value is approximately 17,000 psi, which is below the 25,000 psi limit. We use the definition of engineering stress to calculate the required cross-sectional area of the rod:
S=\frac{F}{A_{0}}Note that the stress must not exceed 17,000 psi, or consequently, the deflection will be greater than 0.25 in. Rearranging,
A_{0}=\frac{F}{S}=\frac{45,000 \ lb}{17,000 \ psi}=2.65 \ in.^2The rod can be produced in various shapes, provided that the cross-sectional area is 2.65 in.² For a round cross section, the minimum diameter to ensure that the stress is not too high is
A_{0}=\frac{\pi d^2}{4}=2.65 \ in.^2 or d=1.84 in.
Thus, one possible design that meets all of the specified criteria is a suspension rod that is 150 in. long with a diameter of 1.84 in.