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A structural steel rod has a radius of 1...

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)`.

Text Solution

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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 %`
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