A structurual steel rod has a radius of 10 mm and a length of 1.0 m. A 100 kN force stretches it along its length. Calculate (a) stress, (b) elongation, and (c ) strain on the rod. Young's modulus. Of structural steel is `2.0xx10^(11)" N "^(-2)`.

Explanation

We assume that the rod is held by clamp at one end, and the force F is applied at the other end, parallel to the length of the rod. Then the stress on the rod is given by
Stress ` = F/A = (F )/(pir^2) = (100 xx 10^3)/(3.14 xx (10^(-2))^2)`
` = 3.18 xx 10^8 Nm^(-2)`
The elongation `Delta L = ((F//A)L)/(Y) = ((3.18 xx 10^8)(1))/(2 xx 10^11)`
` = 1.59 xx 10^(-3) m = 1.59 mm`
The strain is given by , strain ` = Delta L//L`
` = (1.59 xx 10^(-3))/(1) = 1.59 xx 10^(-3) = 0.16%`