Which one of the following statements is NOT correct regarding the relationships between bending moment, shear force and applied load ?

Explanation:

Shear Force:

Shear force at any section is the summation of all transverse loading, either to the left or to the right of any section.

Bending Moment:

The bending moment at any section is a resultant algebraic sum of moments caused by transverse forces either from the left or right of the section.

Relationship between bending moment, shear force, and loading:

The rate of change of shear force at any section is equal to the load intensity at that section.

$\frac{dV}{dx}=\omega \Rightarrow dV=\omega dx\Rightarrow V=\int \omega dx$

i.e. change of shear force between two sections is equal to the area under load intensity diagram between those two sections.

The rate of change of bending moment at any section is equal to shear force at that section.

$\frac{dM}{dx}=V\Rightarrow dM=Vdx\Rightarrow M=\int Vdx$

i.e. change of bending moment between two sections is equal to the area under the shear force diagram between those two sections.

Important Points

• The shear force and bending moment at free end is always zero.