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 assumen 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,
`" "DeltaL=((F//A)L)/(Y)`
`" "=((3.18xx10^(8)"N m"^(-2))(1"m"))/(2xx10^(11)"N m"^(-2))`
`" "=1.59xx10^(-3)"m"`
`" "`=1.59 mm
The strain is given by
`"Strain"=DeltaL//L`
`" "=(1.59xx10^(-3)"m")//(1"m")`
`" "=1.59xx10^(-3)`
`" "` = 0.16%