| 1 − 2σ | F | sin θ | , | ||
| 2(1 − σ) | 4π | r² |
where θ is the angle between the radius vector r and the line of action of F. The line marked T in fig. 30 shows the direction of the tangential traction on the spherical surface.
| Fig. 30. |
| Fig. 31. |
Thus the lines of stress are in and perpendicular to the meridian plane, and the direction of one of those in the meridian plane is inclined to the radius vector r at an angle
| ½ tan−1 ( | 2 − 4σ | tan θ ). |
| 5 − 4σ |
The corresponding displacement at any point is compounded of a radial displacement of amount
| 1 + σ | F | cos θ | ||
| 2(1 − σ) | 4πE | r |
and a displacement parallel to the line of action of F of amount
| (3 − 4σ) (1 + σ) | F | 1 | . | ||
| 2(1 − σ) | 4πE | r |
The effects of forces applied at different points and in different directions can be obtained by summation, and the effect of continuously distributed forces can be obtained by integration.