18.9 : Deformation of Member under Multiple Loadings

When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.

In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an element of length is expressed, and the total deformation of the member is calculated by integrating this expression over the entire length of the member.

In scenarios where one end of the rod is fixed, the deformation is equal to the displacement of its free end. However, when both ends of a rod move, the deformation is measured by the relative displacement of one end concerning the other. Consider a system of three elastic bars connected by a rigid pin. If a load is applied at one point, each bar will deform. For the bars attached to fixed supports, the common deformation is measured by the displacement of a specific point. For the bar where both ends move, deformation is measured by the difference between the displacements of the two points.