Question

A beam ABC is simply supported at A and B and has an overhang BC (see Fig.). The beam is loaded by two forces P and a clockwise couple of moment Pa that act through the arrangement shown. Draw the shear-force and bending-moment diagrams for beam ABC.

Answer 1

Given that,

A beam ABC is simply supported at A and B and has an overhang BC.

The reaction of top member will acts as the force be the beam  ABC.

We need to calculate the value of $R_{p}$ and $R_{Q}$

Using figure

$\sum{M_{p}}=0$

$Pa+Pa-R_{Q}2a=0$

$R_{Q}=\dfrac{2Pa}{2a}$

$R_{Q}=P$

For $R_{P}$

$R_{Q}+R_{P}=2P$

Put the value of $R_{Q}$

$P+R_{P}=2P$

$R_{p}=P$

We need to calculate the value of $R_{A}$ and $R_{B}$

Using figure

$\sum{M_{A}}=0$

$3Pa+Pa=R_{B}2a$

$R_{B}=\dfrac{4Pa}{2a}$

$R_{B}=2P$

For $R_{A}$

$R_{A}+R_{B}=2P$

Put the value of $R_{B}$

$R_{A}+2P=2P$

$R_{A}=0$

We need to draw a shear diagram

For diagram,

$V_{A}=0$

$V_{a}==0$

$V_{c}=P$

$V_{B_{left}}=P$

$V_{B_{right}}=-2P+P$

$V_{B_{right}}=P$

We need to draw a bending moment diagram

For diagram,

$M_{B}=-Pa$

Hence, This is required solution.

Answer 2

Answer:

Explanation:

A beam ABC is simply supported at A and B and has an overhang BC.

The reaction of top member will acts as the force be the beam ABC.

We need to calculate the value of and

Using figure

For

Put the value of

We need to calculate the value of and

Using figure

For

Put the value of

We need to draw a shear diagram

For diagram,

We need to draw a bending moment diagram

For diagram,

Hence, This is required solution.