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

Assume: \(E=100 \mathrm{GPa}\), small area of cross section \(=1 \mathrm{~cm}^{2}\), and large area of cross section \(=2 \mathrm{~cm}^{2}\).

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 \(\left[\mathbf{K}_{s}ight]\left\{\mathbf{Q}_{s}ight\}=\left\{\mathbf{F}_{s}ight\}\).

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

d. Determine the displacements and element forces.

Transcribed Image Text:

3. Element 1 5 kN 1 Element 2 1 m 1 m (2 2 kN