Question

(b) A hip implant in thigh bone may be modelled by concentric cylinder as illustrated in Figure Q5. The implant is a composite circular bar made of inner metallic core with a diameter of 1.0 cm and outer sleeve made of bone with a diameter of 2.5 cm. This structure now is subjected to axial compressive force F 3 kN and E(bone) 17 GPa core with a diameter or stpucture now is subj?cted to Figure Q5 Determine the axial stresses in the metallic core and the bone respectively when the following materials are selected for the core stainless steel (E = 193 GPa) Co-Cr alloy (E 214 GPa) titanium alloy (E 124 GPa) E denotes Young's modulus (15 marks) Based on the results obtained above, explain which material should be selected for the best stiffening effect and then propose at least two different methods that can further reduce the stress in the bone

Answer 1

Given that,

   d₁ = 2.5 cm

   d₂ = 1 cm

F = 3KN

E = 17 GPa

$\sigma$ _a = F / E x 3.14 x (d₁-d₂)² x 100

       = 3 x 10³ / 17 x 10³ x 3.14 x (25 - 10 )² x 10

       = 124.73 N /mm²

This is the normal condition,

Now, if E = 193 GPa

   $\sigma$ _a1 = F / E x 3.14 x (d₁-d₂)² x 100

         = 3 x 10³ / 193 x 10³ x 3.14 x ( 25 - 10 )² x 100

       = 109.8 N/mm²

$\sigma$ _a2 = F / E x 3.14 x (d₁-d₂)² x 100

        = 3 x 10³ / 214 x 10³ x 3.14 x ( 25 - 10 )² x 100

       = 99 N/mm²

   $\sigma$ _a3 = F / E x 3.14 x (d₁-d₂)² x 100

          = 3 x 10³ / 124 x 10³ x 3.14 x ( 25 - 10 )² x 100

          = 171 N/mm²

From all the above conditions, we can say that,

    Co - Cr alloy is the best suitable.