Static analysis of Euler-Bernoulli beams

The chapter reviews fundamental theories, formulas, solution methods, and a set (toolbox) of MATLAB functions for static analysis of Euler–Bernoulli beams. The system requirements for the MATLAB toolbox—a PC with Win 98SE/NT/2000 and XP or Mac with OS 9.x and up, and the software MATLAB (version 5.x and up) installed on the computer. A fundamental problem in the static analysis of Euler-Bernoulli beams is stated as the given external loads and boundary disturbances that determines the beam response (displacement, rotation, bending moment, and shear force), which is governed by a given equation and boundary conditions. There are many solution methods available for the static analysis of Euler-Bernoulli beams. The chapter presents three analytical solution methods for the beam problem—method of singularity functions, the boundary value approach, and distributed transfer function method (DTFM). The MATLAB functions are developed based on the distributed transfer function method, which is an exact analytical modeling and solution method for many one-dimensional distributed systems including bars, shafts, strings, and beams.