Definition of Shear Force and Bending Moment
Shear force is the unbalanced vertical force which is acting on to the right or left of the section.It’s also termed as aligned forces pushing one part of the body in the specific direction, and the other part of the body is another direction.
Bending moment is the algebraic sum of all the moment of forces, according to the right or left of the section. It’s the reaction which is induced in a structural element due to external force or moment is applied.
In the equilibrium position, the moment which is created by external forces is balanced by the couple induced by the internal load; this internal couple is called a bending moment.
What Is Shear Force : Sign Convention of Shear Force:
Shear force is an unbalanced vertical force, so it tends to slide one portion of the beam upward or downward with respect to the other.
Shear force at a section is considered as positive when the left-hand portion tends to slide upward, or the right-hand portion tends to slide downward.
Same as a shear force at a section is negative when the left-hand portion tends to slide downward, or the right-hand portion tends to slide upward.
What Is Bending Moment : Sign Convention for Bending Moment:
We considered bending moment at a section is positive when it tends to bend the beam at a point to a curvature having a concavity at the top or when the moments are acting clockwise direction to the left or anti-clockwise direction to the right.
On the other hand, we considered bending moment at a section is negative when it tends to bend the beam at a point to a curvature having convexity at the top or moments are taken anti-clockwise direction to the left or clockwise direction to the right.
Sometimes the positive bending moment is termed as sagging moment, and the negative bending moment is termed as a hogging moment.
Relation Between Loading, Shear Force & Bending Moment:
The following relations are essential for loading, shear force and bending moment relation-
If there is a point load at a section on the beam, then the shear force suddenly changes(i.e. the shear force line is vertical). But the bending moment remains the same.
If there is no load between two points, then the shear force does not change (I.e. shear force line is horizontal) but the bending moment changes linearly (I.e. bending moment line is an inclined straight line).
If there is a uniformly distributed load between two points, then the shear force changes linearly (I.e. shear line is an inclined straight line). But the bending moment changes according to the parabolic law(i.e. bending moment line will be parabola).
If there us a uniformly varying load between two points then the shear force changes according to the parabolic law(i.e. shear force line will be parabola) but the bending moment changes according to the cubic law.
Where shear force changes, it’s sign there bending moment is maximum.
Where bending moment changes, it’s a sign that point is known as the point of contra flexure or inflation point.