Abstract

Graphostatics is interpreted here in the broader sense, as statics in which geometry plays a part. A stress function defines stresses or forces by its values or derivatives. If a stress function associated with points of a horizontal plane is represented by elevations above this plane, a stress surface is obtained. The geometry of such surfaces has useful applications. Ordinarily, the stress functions are introduced through the differential equations of equilibrium, and thereafter one may derive the geometry of the stress surfaces. Instead, one may define the stress surfaces by some of their geometrical properties, and afterward derive the differential equations. This scheme offers advantages in economy of thought, and is used here. The following stress functions are considered: (A) Two stress functions for transverse shears in slabs. (B) Prandtl’s stress function for torsion. (C) Timoshenko’s stress function for the bending of beams. (D) The deflection of an elastic slab as stress function for the moments, shears, and reactions. (E) Airy’s function for a plane state of stresses in a slice. Discussions of the following subjects are added: (F) The analogy of slabs and slices. (G) Elastic weights for deformations of slices found as reactions in slabs. (H) Influence surfaces for moments and shears in slabs determined as Airy’s surfaces for slices.

This content is only available via PDF.
You do not currently have access to this content.