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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 a clamp at one end the formce 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^(02))^(2)m^(2))=3.18xx10^(8)Nm^(-2)`
The elongation, `DeltaL=((FlA)L)/(Y)=(3.18xx10^(8)Nm^(-2)xx1m)/(2xx10^(11)Nm^(-2))`
`=1.59xx10^(-3)m=1.59mm`
The strain is given by
`"Strain"=(DeltaL)/(L)=((1.59xx10^(-3)m))/(1m)=1.59xx10^(-3)=0.16%`
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