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Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are Y₁ and Y₂. The combination behaves as a single wire then Young's modulus is:

1. Y = 2Y₁Y₂ / 3(Y₁ + Y₂)
2. Y = 2Y₁Y₂ / (Y₁ + Y₂)
3. Y = Y₁Y₂ / 2(Y₁ + Y₂)
4. Y = Y₁Y₂ / (Y₁ + Y₂)

Correct answer: Y = 2Y₁Y₂ / (Y₁ + Y₂)

Solution

Two equal wires in series each have stiffness Y_i*A/L; the combination (length 2L) has stiffness Y*A/(2L). Adding compliances: 2/Y = 1/Y1 + 1/Y2, giving Y = 2*Y1*Y2/(Y1 + Y2).

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