Page 301 - Introduction to Continuum Mechanics

The Elastic Solid 285

Example 5.18.1

Consider a thick-wall cylinder subjected to the action of external pressure p 0 only. If the
outer radius is much much larger than the inner radius. What is the stress field?
Solution. From Eqs. (5.18.3), we have

When b is much much larger than a, these become

5.19 Pure Bending of a Curved Beam

Fig. 5.17 shows a curved beam whose boundary surfaces are given by r = a,r = b,
0 = ±a and z = ±h/2. The boundary surface r = a ,r - b and z — ±h/2 are traction-free.
Assuming the dimension h is very small compared with the other dimensions., we wish to obtain
a plane stress solution for this curved beam under the action of equal and opposite bending
couples acting on the faces 6 = ±a.