Bimetallic (Composite) Beam of Brass and Steel: Effect of uniform temperature rise on internal forces and deformation

Introduction:A composite (bimetallic) beam made of brass and steel experiences internal restraint when temperature changes. Because brass has a higher coefficient of thermal expansion than steel, a uniform temperature rise creates incompatible free expansions, leading to self-equilibrating internal forces and bending. This question checks understanding of thermal strain compatibility and induced internal actions.

Given Data / Assumptions:

• Two equal strips: one brass, one steel, perfectly bonded.
• Uniform temperature increase across the beam.
• Material properties: alpha_brass > alpha_steel; linear elastic range.

Concept / Approach:Free thermal strain = alpha * delta_T. Since alpha_brass > alpha_steel, brass wants to elongate more. Bonding enforces equal overall extension at the interface, inducing tension in the less-expanding material (steel) and compression in the more-expanding material (brass). The force couple generated by these equal and opposite forces produces curvature (bending) of the composite strip.

Step-by-Step Solution:Step 1: Identify mismatch in free thermal strains: brass larger than steel.Step 2: Compatibility requires equal actual extension, so internal forces arise.Step 3: Steel is pulled (tension) to match brass; brass is pushed (compression) to match steel.Step 4: These opposite forces at different layers form a couple, causing bending (curvature).Step 5: Therefore all statements hold simultaneously.

Verification / Alternative check:Classical bimetallic strip behavior (used in thermostats) confirms curvature toward the material with the lower expansion (steel side becomes concave).

Why Other Options Are Wrong:a–d: Each is individually correct, but the question seeks the combined effect; the comprehensive option is correct.

Common Pitfalls:Assuming equal expansions because strips are equal in size; forgetting that perfect bonding enforces compatibility; thinking temperature rise only changes length without causing internal forces.

Final Answer:All the above.