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`2.0xx 10 ^(11) Nm^(-2).`

Explanation

The rod is held by a clamp at one end and the force F is applied at the other end in parallel to the length of rod.
`therefore ` Stress on the rod.
Stress `= ("Force")/("Area")= F/A = (F)/(pi r ^(2))`
` = (100 xx 10 ^(3))/(3.14xx (10 xx 10 ^(-3)) ^(2))=0.318 xx 10 ^(5) +4 =3.18 xx 10 ^(8) Nm ^(-2)`
Now,` Y =("Stress")/("Strain" ) = ("Stress")/((Delta L)/(L))`
`therefore Delta L = ("Stress " xxL )/(Y)`
`=(3.18 xx 10 ^(8) xx 1 )/( 2 xx 10 ^(11))`
` = 1. 59 xx 10 ^(-3) m`
`= 1. 59 mm`
Strain`= (Delta L )/(L )= (1. 59 xx 10 ^(-3))/( 1)`
`= 1. 59 xx 10 ^(-3) = 1.59 xx 10 ^(-3) xx 100 %`
`~~ 0.159 % ~~ 0.16 %`