Assume that a diaphyseal cross section carries a bending moment M. Let the cross section be circular with inner and outer diameter of 20 and 30 mm, respectively, and assume that the neutral axis (NA) passes through the centroid. Draw the cross section and write an equation for the normal stress?, as function of angular position ? Measured from the neutral axis. Assume that modeling adds or removes bone on the periosteal and endosteal surfaces at a rate proportional to the local longitudinal stress on the surface: M_F/R = -K?(?) where the opposition rate M_F / R is negative for tensile stress and positive for compressive stress and the rate of constant K is the same for each kind of modeling and each surface.
(a) Sketch a line adjacent to the original periosteal surface that would represent the circumference after some arbitrary period of time.
(b) Do the same for the endosteal surface. (Scale your sketch so that the maximum thickness of bone added is about half the original cortical thickness.)
(3) What happened to the bone's cross-sectional geometry? Would this change be advantageous in some way?