ABSTRACT
When a structural member is loaded, it deforms and, as it deforms, work is done. Figure 7.1a shows the load-deformation response of a bar of length L in axial tension. The shape of the curve depends on the size of the bar and the material from which it is made. The work done as an axial load PB is gradually applied to the bar is the area under the curve from P = 0 to P = PB shown as the shaded area OABC in Figure 7.1a. If the bar is subsequently unloaded, some of the energy associated with this work may be recovered. The unloading curve is represented by the dashed line from B to D. For the materials commonly used in structures, the unloading path BD is a straight line approximately parallel to the tangent to the curve at the origin (i.e. parallel to the line OA in Figure 7.1a). The area of the triangular region CBD represents the energy recovered during unloading and is called elastic strain energy Ue. The energy that is not recoverable during unloading has been used to cause inelastic deformation of the material (inelastic strain energy).
