Which of the following is the correct relation of shearing force (F) and bending moment (M) at a section?

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:

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 load intensity at that section.

\(\frac{{dF}}{{dx}} = \omega \Rightarrow dF = \omega dx \Rightarrow F = \smallint \omega dx\)

i.e. Change of shear force between two sections is equal to the area under the 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.

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\(\frac{{dM}}{{dx}} = F \Rightarrow dM = Fdx \Rightarrow M = \smallint Fdx\)

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

The presence of a concentrated couple leads to sudden rise or fall of the Bending moment diagram depending upon the sign and direction of the couple.