Definition of bending moment, shear force and Sign conventions
Definition:
Shear force: The force which tends to shear off the section and is obtained as the algebraic sum of all forces including the reactions acting normally 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 the left side or right side of the support is known as the 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 a 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 a 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 a 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 a sagging bending moment. | The moment about the point which produces convexity above the centre line is called a hogging bending moment. |
 |  |
It is also termed a positive bending moment | It is also termed a negative bending moment |
The top fibres of the beam are subjected to compression. | The top fibres of the beam are subjected to tension. |
The bottom fibres of the beam are subjected to tension. | The bottom fibres of the beam are subjected to compression. |
Sign conventions for bending moments
Direction | Positive BM | Negative BM |
Left side | Clockwise | Anti Clockwise |
Right side | Anti Clockwise | Clockwise |
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