Figure 1.81 shows a three-stepped bar fixed at one end and subjected to an axial force \(F\) at the other end. The length of step \(i\) is \(l_{i}\) and its cross sectional area is \(A_{i}, i=1,2,3\). All the steps are made of the same material with Young's modulus \(E_{i}=E, i=1,2,3\).

a. Find the spring constant (or stiffness) \(k_{i}\) of step \(i\) in the axial direction \((i=1,2,3)\).

b. Find the equivalent spring constant (or stiffness) of the stepped bar, \(k_{\mathrm{eq}}\), in the axial direction so that \(F=k_{\mathrm{eq}} x\).

c. Indicate whether the steps behave as series or parallel springs.

Transcribed Image Text:

+ FIGURE 1.81 A stepped bar subjected to axial force. x F