On Galileo’s Tallest Column

Figure 3

Stress fields and the corresponding body. (a) . (b) . (c) Von Mises stress . The origin of coordinates is up in the centre of the figures, and there the stress tensor is null. In (a), the three curves that define the body—from the stress field and satisfying the Von Mises criterion—are drawn. The red curve is , that is, the stress-free surface of the body. The pale blue curve is ; the body cannot extend beyond. The pale rose curve is ; the support line cannot extend beyond. The three curves intersect in a unique point. The support can be the horizontal line for this point; in this way, it can be assured that the stress at the support does not exceed the allowable stress. The insurmountable size of the body is the absolute value of the ordinate of the intersection point, in this example.

(a)

(b)

(c)