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).

A structurual steel rod has a radius of 10 mm and a length of 1.0 m. A

1.	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).
Answer» Solution :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)/(pi r^(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 %`