Question

Consider the shear force diagram as shown below:


Consider the following statements:

1. There exist a $UDL$ over span $AC$ having intensity $0.8kN/m$

2. There exist an upward concentrated load of magnitude $7kN$ at pint ${}^{\prime }{D}^{\prime }$.

3. There exist a concentrated couple of magnitude $10kN-m$ acting in clockwise direction somewhere in span AE.

4. There exist a concentrated couple of magnitude $10kN-m$ acting in counter-clockwise direction at point ${}^{\prime }{B}^{\prime }$.

Which of the following statements can be inferred from the given SFD?

• A. $1$ & $4$ only
• B. $2$ & $3$ only
• C. $2$ only
• D. $3$ only

Answer 1

The correct option is D $3$ only

For the given $SFD$


The loading diagram is:


Now, check the equilibrium of structure
$+\uparrow \sum F=0$
$\sum F=7-2\times 5-4+7$
$\sum F=0$ OK
Also,



$\sum M_A=2\times 5\times \frac{5}{2}+4\times 7-7\times 9$

$\Rightarrow \sum M_A=-10kN-m$

i.e., there exist an unbalanced anticlockwise moment of magnitude $10kN-m$ in the beam and to satisfy the equilibrium of structure, there must exist a clockwise concentrated couple anywhere on the span.
Hence, only statement 3 can be inferred for given SFD