Question

A uniform steel rod of 5 mm² 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 10^1ON/m²)

Answer 1

Given that α _steel = 12 x 10^-6 /°C, γ _steel = 20 x 10¹⁰ N/m²

Area of cross-section of the rod, A = 5 mm² = 5 × 10⁻⁶ m

Change in temperature (ΔT), (T₂ − T₁) = 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 10¹⁰ x 12 x 10^-6 x 25 x 5 x 10^-6

      = 300 N

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

Strain = α_steelΔT

          = 12 x 10^-6 x 25

          = 3 x 10^-4