Step 1

(a)

Draw a free body diagram of the beam.

Here, ${A_x}$ is the horizontal force acting at point $A$, ${A_y}$ is the vertical force acting at point $A$, and $T$ is the tension developed in the cable $B$.

 
Step 2

(b)

Draw a free body diagram of the beam.

Here, ${A_x}$ is the horizontal force acting at point $A$, ${A_y}$ is the vertical force acting at point $A$, and ${B_x}$ is the horizontal force acting at point $B$.

 
Step 3

(c)

The length of the beam is $L = {\rm{6}}\;{\rm{m}}$.

The variable distributed load is $w = 400\;{\rm{N/m}}$.

We will find the net load acting on the beam.

\[P = \frac{1}{2} \times L \times w\]

Substitute the given value in the above equation.

\[\begin{array}{c} P = \frac{1}{2} \times \left( {6\;{\rm{m}}} \right) \times \left( {{\rm{400}}\;{\rm{N/m}}} \right)\\ = \left( {3\;{\rm{m}}} \right) \times \left( {{\rm{400}}\;{\rm{N/m}}} \right)\\ = {\rm{1200}}\;{\rm{N}} \end{array}\]

Draw a free body diagram of the beam.

Here, ${A_y}$ is the vertical force acting at point $A$, ${B_y}$ is the vertical force acting at point $B$, and ${B_x}$ is the horizontal force acting at point $B$.

 
Step 4

(d)

Draw a free body diagram of the beam.

Here, ${A_x}$ is the horizontal force acting at point $A$, ${A_y}$ is the vertical force acting at point $A$, and $N$ is the normal force acting at point $B$.

 
Step 5

(e)

The length of the beam $AB$ is $L = 4\;{\rm{m}}$.

The variable distributed load is $w = 200\;{\rm{N/m}}$.

We will find the net load acting on the beam.

\[P = \frac{1}{2} \times L \times w\]

Substitute the given value in the above equation.

\[\begin{array}{c} P = \frac{1}{2} \times \left( {4\;{\rm{m}}} \right) \times \left( {{\rm{200}}\;{\rm{N/m}}} \right)\\ = \left( {2\;{\rm{m}}} \right) \times \left( {{\rm{200}}\;{\rm{N/m}}} \right)\\ = 4{\rm{00}}\;{\rm{N}} \end{array}\]

Draw a free body diagram of the beam.

Here, ${A_x}$ is the horizontal force acting at point $A$, ${M_A}$ is the moment developed at point $A$, and ${B_y}$ is the vertical force acting at point $B$.

 
Step 6

(f)

Draw a free body diagram of the beam.

Here, ${C_x}$ is the horizontal force acting at point $C$, ${C_y}$ is the vertical force acting at point $C$, and ${B_y}$ is the normal force acting at point $B$.