(Solved): 1.25 Figure \( 1.81 \) shows a three-stepped bar fixed at one end and subjected to an axial force ...

1.25 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 ( \( \left.i=1,2,3\right) \). b. Find the equivalent spring constant (or stiffness) of the stepped bar, \( k_{\text {eq }} \), in the axial direction so that \( F=k_{\text {eq }} x \). c. Indicate whether the steps behave as series or parallel springs. FIGURE 1.81 A stepped bar subjected to axial force.