A rod of cortical bone (Young's modulus 20 GPa) and a rod of Ti-6Al-4V (Young's modulus 110 GPa) with the same cross-sectional area are joined in parallel and together carry a tensile load along their length. If both have the same strain, which value is closest to the fraction of the total load carried by the bone?

Answer: C. About 15%

Because the strain ε is the same, each stress is proportional to the Young's modulus (σ = Eε), and since the cross-sectional areas are also equal, the loads are in the ratio 20 : 110. The bone's share is 20/(20 + 110) ≈ 0.154, about 15%. The implant takes over about 85% of the load that the bone alone used to carry, so the stimulus to the bone falls sharply and stress shielding occurs. About 85% is the share carried by the implant, and about 18% takes the modulus ratio 20/110 directly as the share. Switching to a β titanium alloy with a Young's modulus of about 55 GPa raises the bone's share to 20/75 ≈ 27%. The real shapes of bone and stem are complicated, but the idea that the difference in Young's modulus decides the load sharing is the same.