In the cantilever beam tutorial, we considered the case when a bar is subjected to a transverse load. We solved this case using the Euler-Bernoulli beam theory which assumes that transverse loads can only cause any point on the midline to move in the transverse direction. We denoted this transverse displacement as uy.
Now consider the case when a bar is subjected to a transverse load as well as an axial load. The transverse load causes a transverse displacement uy of the midline as before. In addition, the axial load causes an elongation or contraction of the midline (as in a truss model). We can denote this axial displacement as ux. The total displacement of any point on the midline is calculated as a superposition of these transverse and axial displacements.
In this problem, each member experiences both transverse and axial loads. So ux and uy are non-zero. The axial displacement has a simple linear variation along the midline as in a truss model.