Solved: A bar in tension has a circular cross section and

Chapter 4, Problem 4-5

(choose chapter or problem)

A bar in tension has a circular cross section and includes a tapered portion of length l, as shown.

(a) For the tapered portion, use Eq. (4-3) in the form of \(\delta=\int_0^l[F /(A E)] d x\) to show that

                                                     \(\delta=\frac{4}{\pi} \frac{F l}{d_1 d_2 E}\)

(b) Determine the elongation of each portion if \(d_1=0.5 \mathrm{in}, d_2=0.75 \mathrm{in}, l=l_1=l_2=2.0 \mathrm{in}\), E = 30 Mpsi, and F = 1000 lbf.