To solve the problem of finding the clockwise rotational deformation at point $D$ in the given frame, we will need to analyze the frame using structural analysis techniques such as moment-area methods or using energy methods like the virtual work principle. Since axial deformations are neglected, we focus on bending moments and their contribution to rotational deformation.

Steps to Analyze the Problem:

1. Structure Overview:

   • The frame consists of a horizontal member $AB$ with length $L$, and a vertical member $CD$ with length $L/2$.
   • A load $P$ acts horizontally at point $D$, which will cause both the horizontal beam $AB$ and the vertical column $CD$ to deform.

2. Fixed Support at $A$:

   • The frame is fixed at point $A$, meaning no translations or rotations occur at this point.

3. Pin Support at $C$ and Roller at $B$:

   • The support at $C$ is a pin, and the support at $B$ is a roller. These allow rotations but prevent vertical displacements.

4. Moments and Deformation:

   • The applied force $P$ at point $D$ induces a moment at the base $A$, as well as moments along the members $AB$ and $CD$.

5. Assumptions:

   • Neglect axial deformations.
   • $EI$ (flexural rigidity) is constant for all members.

Solution Approach:

To compute the rotational deformation at point $D$, we typically follow these steps:

1. Calculate the Moment Distribution:

   • For horizontal member $AB$:
     • Since $P$ applies a moment at point $D$, calculate the bending moment caused by this force along both $AB$ and $CD$.
   • For vertical member $CD$:
     • Consider the moment transferred from member $AB$ to member $CD$.

2. Apply Virtual Work (Rotation):

   • Use the virtual work method to determine the rotational deformation at point $D$. The total rotational deformation is obtained by integrating the bending moments over the length of each member.
   • The virtual work equation for rotation at a point $D$ is given by: $\theta_D = \frac{1}{EI} \int_0^L M(x) \cdot M'(x) \, dx$ where $M(x)$ is the moment distribution due to the applied load $P$, and $M'(x)$ is the moment distribution due to a unit load applied at point $D$ for rotation.

3. Result:

   • Once the moments are calculated and integrated, you will get the total rotational deformation at point $D$.