Studies have shown that the fibula suffers spiral fractures

Studies have shown that the fibula suffers spiral fractures when the angle of twist is 35.7 degree. Assume the fibula has an outer diameter of 1.4 cm and a length of 34 cm. What is the maximum shear strain in the fibula under these circumstances?

Solution

Data Given

Angle of twist in radians(Theta) = 35.7 x 3.14/180 = 0.623 radians

Outer diameter(D) = 1.4cm = 0.014m

Outer Radius = D/2 = 0.007m

Length(L) = 34 cm = 0.34m

Torsion equation

Shear modulus of elasticity(G) = 3.3 Gpa = 3.3N/m^2

T/J = Fs/R = (G x Theta)/L

Fs = (G x Theta x R)/L

=(3.3 x 0.623 x 0.007)/0.34

= 0.0423 N/m^2

Shear stress/Shear strain = Shear modulus of rigidity

Shear strain = Shear stress/ Shear modulus of rigidy

= 0.0423/3.3

= 0.013