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A steel rod of cross-sectional areaIm^(2...

A steel rod of cross-sectional area`Im^(2)` is acted upon by forces shown in the fig. Determine the total elongation of the bar. (Take `Y=2.0xxK=8.33xx10^(-11)N//n^(2))`

Text Solution

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The action of forces on each part of rod is shown in fig.

We know that the extension due to external force F is given by `Deltal_(AB)=(Fl)/(AY)`
`Deltal_(AB)=((60xx10^(3))xx1.5)/(1xx2xx10^(11))=4.5xx10^(-7)m`
`Deltal_(BC)=((70xx10^(3))xx1)/(1xx2xx10^(11))=3.5xx10^(-7)m and Deltal_(CD)=((50xx10^(3))xx2)/(1xx2xx10^(11))=5.0xx10^(-7)m`
The total extension `Delta=Delta_(AB)+Delta_(BC)+Delta_(CD)`
`=4.5xx10^(-7)+3.5xx10^(-7)+5.0xx10^(-7)=13xx10^(-7)m`
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