Chapter 1, Problem 17E

A stepped bar is clamped at one end and subjected to concentrated forces as shown.

Assume: $E=\text{1}00\text{GPa}$, small area of cross section $={\text{1cm}}^{\text{2}},$ and large area of cross section $={\text{2m}}^{\text{2}}.$

a. Write the element stiffness matrices of elements 1 and 2 showing the row addresses.

b. Assemble the above element stiffness matrices to obtain the following structural level equations in the form $\left[K_s\right]\left\{Q_s\right\}=\left\{F_s\right\}$.

c. Delete the rows and columns corresponding to zero DOFs to obtain the global equations in the form of $\left[K\right]\left\{Q\right\}=\left\{F\right\}$.

d. Determine the displacements and element forces.