A beam is a long, slender structural member generally subjected to transverse loading that produces significant bending effects as opposed to twisting or axial effects. A continuous beam can be modelled by employing 2-node beam elements. To derive equations of a beam element, it is important to briefly review classical beam theory.
Figure 6.25 (a) Beam subjected to transverse loading, (b) Beam theory sign conventions
Consider the simply supported beam shown in Figure 6.25. The beam is of length L with axial co-ordinate x and transverse local co-ordinate y.
In Figure 6.25, fy(x) = transverse loading, ...