Chapter 16, Problem 29P

Mechanical/Aerospace Engineering

Roller bearings are subject to fatigue failure caused by large contact loads F (Fig. P16.29).

The problem of finding the location of the maximum stress along the x axis can be shown to be equivalent to maximizing the function

$f\left(x\right)=\frac{0.4}{\sqrt{1+x^2}}-\sqrt{1+x^2}\left(1-\frac{0.4}{1+x^2}\right)+x$

Find the x that maximizes $f\left(x\right)$.

FIGURE P16.29

Roller bearings.