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# Daily Concept Booster Mechanical Engineering: Shear Force and Bending Moment

## Shear Force and Bending Moment

### Shear Force

Shear force at any cross-section is the algebraic sum of all the transverse forces either from LHS or from RHS of the that cross-section.
Its sign at any cross-section is taken positive when the couple produced by it on either side of the cross-section is in clockwise direction and vice-versa.

### Bending Moment

The bending moment at any cross-section is the algebraic sum of all the moments and couples either from LHS or from RHS of the that cross-section.
A bending moment is called sagging at a cross-section, when it is acting in clockwise direction on LHS of that cross-section of the beam or when it is acting in anticlockwise direction on RHS of that cross-section of the beam and it is taken as positive. It has concavity upward.
A bending moment is called hogging at a cross-section, when it is acting in anticlockwise direction on LHS of that cross-section of the beam or when it is acting in clockwise direction on RHS of that cross-section of the beam and it is taken as negative. It has convexity upward.

## Relation between shear force (F), Bending Moment (M) and Rate of loading (W)

Let W be the load per unit length i.e., rate of loading
W=dF/dx
Rate of loading is also called as the rate of change of shear force.
And, rate of change of bending moment is called shear force
F=dM/dx
Some Important point
A point which is called contra-flexure or point of inflection at which bending moment changes its sign.
If degree of loading curve is n then the degree of shear force curve is n+1 and degree of bending moment curve is n+2

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