Quantum mechanics

Beam (structure)

Engineering

Statically indeterminate

Differential equation

Bending

Virtual work

Algebraic equation

Physics

Finite element method

Nonlinear system

Mathematics

Truss

Mathematical analysis

Structural engineering

Finite difference

Cantilever

Journal of the Structural Division

Deflections of regular trusses formed from repeated modules (panels) are analyzed using finite-difference calculus. The expressions used are in general algebraic form allowing for arbitrary stiffnesses of the bars forming the basic panel and arbitrary panel width and panel depth. Solutions for simply supported and cantilever trusses under the action of point loads, uniform loads and linearly varying loads are given in terms of polynomials. It is shown that by using Taylor's expansion the finite-difference equations reduce approximately to the differential equation for the bending and shear of an analogous beam. The degree of accuracy is related directly to the fineness of the trusses. Analogous beam solutions are compared with the given solutions showing that the analogy is satisfactory.

Behavior of Howe, Pratt, and Warren Trusses