The figure below shows a rigidly connected, uniform frame with built$-$in supports.

From the Structures Data Sheet we know that the rotational stiffness of a beam element is

proportional to $E\frac{\text{I}}{L}.$

$($a$)$ Use this fact to work out the elastic moments in the frame members at $\text{'}a\text{'}.$ Explain

your reasoning.

$($b$)$ Sketch a free$-$body diagram of joint $\text{'}a\text{'}$ showing all of the moments $($applied and

elastic$)$ acting on it$.$