Stress and strain, maximum applied force before permanent deformation/breakage

[wolfpack11]

Compute the maximum longitudinal force that may be supported by a bone before breaking, given that the compressive stress at which bone breaks is 2.00e8 N/m^2. Treat the bone as a solid cylinder of radius 1.55 cm. The attempt at a solution
I tried using the equation Max Torque = pi/4 * (r^3) * max stress. Plugged in 0.0155 m for "r" and 2.00e8 N/m^2 for max stress, got 585 N*m for torque, then divided again by 0.0155 m to get the Force (377000 N). This answer wasn't accepted into webassign. What am i missing in the problem solving?

 

[PhanthomJay]

You are calculating max torque or moment due to bending stresses, but the problem is asking, perhaps not too clearly, for max axial (longitudinal) load based on allowable axial stress. Instead of using bending stress = M/S, try using axial stress = P/A.

 

[wolfpack11]

Ok. If P is the compressive force, and A is the cross-sectional area that the force is applied to, I would think that A= ∏*r^2 for the surface of the cylinder. Then, multiplying A by the maximum stress 2e8 N*m^2 would yield P?

 

[PhanthomJay]

Yes.

 

[Nickie]

Your approach seems correct, but there may be an error in your conversion of units. The maximum longitudinal force that a bone can support before breaking should be in units of Newtons (N), not Newton-meters (N*m). Make sure to double check your units and conversions to ensure that your final answer is in the correct units. Additionally, it may be helpful to round your final answer to the appropriate number of significant figures.