−δl = Wl / 2EA;
if the same cylinder lies on the plane with its generators horizontal, its length is increased by an amount
δl = σWh′ / EA.
71. In recent years important results have been found by considering the effects produced in an elastic solid by forces applied at isolated points.
Taking the case of a single force F applied at a point in the interior, we may show that the stress at a distance r from the point consists of
(1) a radial pressure of amount
| 2 − σ | F | cos θ | , | ||
| 1 − σ | 4π | r² |
(2) tension in all directions at right angles to the radius of amount
| 1 − 2σ | F | cos θ | , | ||
| 2(1 − σ) | 4π | r² |
(3) shearing stress consisting of traction acting along the radius dr on the surface of the cone θ = const. and traction acting along the meridian dθ on the surface of the sphere r = const. of amount