Shear Force and Bending Moment
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.
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
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
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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