A bar with a crack at its centre buckles as a result of temperature rise of 32^(0)C. If the fixed distance L_(0) is 3.77m and the coefficient of linear expansion of the bar is 25xx10-6//0C find the rise x of the centre.

A bar with a crack at its centre buckles as a result of temperature ri

1.	A bar with a crack at its centre buckles as a result of temperature rise of 32^(0)C. If the fixed distance L_(0) is 3.77m and the coefficient of linear expansion of the bar is 25xx10-6//0C find the rise x of the centre.
Answer» Solution :Consider one half of the bar, its initial length `l_(0)=(L_(0))/(2)` Its length after increase in temperature`DELTAT , l=l_(0) (1+alpha DeltaT)` By Pythogoras theorem `X^(2)=l^(2)-l_(0)^(2)` `= l_(0)^(2)(1+2alphaDeltaT-1) or x=l_(0) sqrt(2alpha DeltaT)` `=(3.77)/(2) sqrt(2(25xx10^(-6) XX 32))=7.5xx10^(-2)m`