Resting on a fixed horizontal base, a steel rod is clamped at both of its ends. At 20^ C , the rod is in an unstrained state. Determine the longitudinal strain developed in the rod when the temperature increases to 50^ C . The coefficient of linear expansion for steel is 1.2 10⁻⁵ ^ C⁻¹ .

Step-by-step solution

Given: Initial temperature, T₁ = 20^ C Final temperature, T₂ = 50^ C Change in temperature, T = 50^ C - 20^ C = 30^ C Coefficient of linear expansion, = 1.2 10⁻⁵ ^ C⁻¹ If the rod were free to expand, the increase in length would be L = L T . Since the rod is clamped at both ends, it cannot expand. The rigid supports exert a compressive force to maintain the original length. The longitudinal (mechanical) strain developed in the rod is given by: Strain = - L L = - T Substituting the given values: Strain = -(1.2 10⁻⁵)