Question

A steel bar 2 m long is fixed between two supports. If the temperature of the bar is raised by 18"C, find the stress in the bar if the supports are rigid.

Answer 1

Given:

A steel bar 2 m long is fixed between two supports. If the temperature of the bar is raised by 18°C.

To Find:

Find the stress in the bar if the supports are rigid.

Solution:

We know that value of linear thermal expansion coefficient and young's modulus of elasticity of steel material:

$\mathbf{\textrm{Linear thrermal expansion coefficient}\ = \alpha = 13\times 10^{-6} \ \ \dfrac{1}{^{\circ}C}}$

$\mathbf{\textrm{Modulus of elasicity}\ = E = 200\times 10^{9} \ \ \dfrac{N}{m^{2}}}$

$\mathbf{\textrm{Increase in temperature}\ =\Delta T= 18^{\circ}C}$

Due to increase in temperature of bar, there are increase in length of bar. But it is resisted by rigid wall, so there are stress produce in steel bar:

Nature of stress in bar is compressive stress:

Since stress is produce due to change in length, so it is called thermal compressive stress:

Value of thermal compressive stress in gives as:

$\mathbf{\textrm{Stress in bar}\ =\sigma =E\times \alpha \times \Delta T}$

$\mathbf{\textrm{Stress in bar}\ =\sigma =200\times 10^{9}\times 13\times 10^{-6} \times 18}$

$\mathbf{\textrm{Stress in bar}\ =\sigma =46800000 \ \dfrac{N}{m^{2}}}$

Means thermal stress produce in steel bar is 46800000 Pa.