A bar in tension has a circular cross section and includes a conical portion of length l , as Shown, the task is to find the spring rate of the entire bar. Equation (4–4) is useful for the outer portions of diameters d1 and d2, but a new relation must be derived for the tapered section. If α is the apex half-angle, as shown, show that the spring rate of the tapered portion of the shaft is
Answer to relevant QuestionsWhen a hoisting cable is long, the weight of the cable itself contributes to the elongation. If a cable has a weight per unit length of w, a length of l , and a load P attached to the free end, show that the cable elongation ...Using the results of Prob. 4–9, determine the end contraction of the uniformly loaded simply supported beam of appendix Table A–9–7. Assume the left support cannot deflect in the x direction, whereas the right support ...Using superposition, determine the maximum deflection of the beam shown in the figure. The material is carbon steel.For the shaft shown in the figure, let a1 = 4 in, b1 = 12 in, a2 = 10 in, F1 = 100 lbf, F2 = 300 lbf, and E = 30 Mpsi. The shaft is to be sized so that the maximum slope at either bearing A or bearing B does not exceed 0.001 ...Solve Prob. 4–12 using singularity functions. Use statics to determine the reactions.
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