A structural 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 2.0 `xx` `10^(11)` N `"m"^(-2)`.

Explanation

We assume that the rod is held by a 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))`
`=(100xx10^(3)N)/(3.14xx(10^(-2)m)^(2))`
`=3.18xx10^(8)" N m"^(-2)`
The elongation,
`Delta=((F//A)L)/(Y)`
`=((3.18xx10^(8)" N m"^(-2))(1m))/(2xx10^(11)"N m"^(-2))`
`=1.59xx10^(-3)` m
`=1.59` mm
The strain is given by
Str ain `=DeltaL//L`
`(1.59xx10^(-3)m)//(1m)`
`=1.59xx10^(-3)`
`=0.16%`