Definition of bending moment , shear force and Sign conventions

Definition:

Shear force: The force which tend to shear off the section and is obtained as the algebraic sum of all forces including the reactions acting normal to the axis of the beam either to the left or right of the beam.

Sign convention

Positive Shear Force

 Negative Shear Force

Sign convention for shear force in brief

Direction	Positive SF	Negative SF
Left side	Upward force	Downward force
Right side	Downward force	Upward force

Bending moment: The algebraic sum of all the moments of the forces and reactions in a beam towards either left side or right side of the support is known as bending moment.

Types of bending moment:

Sagging bending moment: The moment about the point which produces convexity below the centre line is called as sagging bending moment. It is also called as positive bending moment.

Consider the simply supported beam with central concentrated load “F”. The moment due to the force F produces a deflection in the downward direction which in turn results in the formation of sagging bending moment.

Hogging bending moment: The moment about the point which produces convexity above the centre line is called as hogging bending moment. It is also called as negative bending moment.

Consider the simply supported beam with central concentrated load “F”. The moment due to the force F produces a deflection in the upward direction which in turn results in the formation of hogging bending moment.

Differences between sagging and hogging bending moment

Sagging bending moment	Hogging bending moment
The moment about the point which produces convexity below the centre line is called as sagging bending moment.	The moment about the point which produces convexity above the centre line is called as hogging bending moment.
It is also termed as positive bending moment	It is also termed as negative bending moment
Top fibres of beam are subjected to compression.	Top fibers of beam are subjected to tension.
Bottom fibers of beam are subjected to tension.	Bottom fibers of beam are subjected to compression.

Sign conventions for bending moments

Direction	Positive BM	Negative BM
Left side	Clock wise	Anti Clock wise
Right side	Anti Clock wise	Clock wise