Question

Rod BD is made of steel (E = 29 × 106 psi) and is used to brace the axially compressed member ABC. The maximum force that can be developed in member BD is 0.02P. If the stress must not exceed 18 ksi and the maximum change in length of BD must not exceed 0.001 times the length of ABC, determine the smallest-diameter rod that can be used for member BD. Take P = 148 kips.

Answer 1

0.429 in

Step-by-step explanation:

F =0.02P= (0.02)(130) =2.6 kips =2.6 *10^3 lb

maximum stress upper limit = 18 ksi =18 *10^3 psi

A = F/ρ = 2.6 *10^3/18 *10^3 = 0.144 in2

Deformation, δ =(0.001)(144) =0.144 in

δ = FL/AE ⇒ A = FL/δE

A= 2.6 *10^3 * 54/(29 × 10^6 *0.144)

=0.03362 in

The larger area is used

A= πd^2/4 ⇒ d = √(4A/π) = √(4 *0.144/π)

=0.429 in