A uniform steel rod of 5 mm^{2} cross section is heated from 0°C to 25°C. Calculate the force which must be exerted to prevent it from expanding. Also calculate strain.

(α for steel = 12 ^{x} 10^{-6}/°C and γ for steel = 20 x 10^{1O}N/m^{2})

#### Solution

Given that α_{ steel} = 12 x 10^{-6} /°C, γ_{ steel} = 20 x 10^{10} N/m^{2}

Area of cross-section of the rod, A = 5 mm^{2} = 5 × 10^{−6} m

Change in temperature (ΔT), (T_{2} − T_{1}) = 25°C

Force exerted by the rod due to heating = Thermal stress × Area

Thermal stress = γ x Strain

= γ_{steel} x α_{steel} x ΔT

Therefore, the force exerted by the rod due to heating is

= γ_{steel} x α_{steel} x ΔT x A

= 20 x 10^{10} x 12 x 10^{-6} x 25 x 5 x 10^{-6}

= 300 N

`"Strain" = "Change in length"/ "Original length"= alphaDelta"T"`

**Strain = α _{steel}ΔT**

** = 12 x 10 ^{-6} x 25**

** = 3 x 10 ^{-4}**