Definition of Shear Force and Bending Moment
Shear Force
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.
Sometimes, a crack is developed in a body from the parallel shear force acting in a different direction at another point of the body. Colinear forces are also termed as compressive forces.
Bending Moment
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.
FAQ: Shear Force and Bending Moment
What is Shear Force?
Shear force is the unbalanced vertical force acting on a section of a structural element. It is the force that pushes one part of the body in one direction while another part of the body is pushed in the opposite direction. Shear forces can cause cracks in a body when acting in different directions at different points.
What is Bending Moment?
The bending moment is the algebraic sum of all the moments of forces to the right or left of a section. It is the reaction induced in a structural element due to an external force or moment applied. In equilibrium, the moment created by external forces is balanced by the internal load-induced couple, known as the bending moment.
How is Shear Force defined in terms of Sign Convention?
Shear force at a section is considered positive when the left-hand portion tends to slide upward, or the right-hand portion tends to slide downward. Conversely, it is considered negative when the left-hand portion tends to slide downward, or the right-hand portion tends to slide upward.
How is Bending Moment defined in terms of Sign Convention?
A bending moment at a section is considered positive when it tends to bend the beam into a curvature with a concavity at the top or when the moments act clockwise to the left or anti-clockwise to the right. It is considered negative when it bends the beam into a curvature with convexity at the top or moments act anti-clockwise to the left or clockwise to the right. Positive bending moments are also termed as sagging moments, and negative bending moments are termed as hogging moments.
What is the Relationship between Loading, Shear Force, and Bending Moment?
- If there is a point load at a section on the beam, the shear force changes suddenly, but the bending moment remains constant.
- If there is no load between two points, the shear force does not change, but the bending moment changes linearly.
- If there is a uniformly distributed load between two points, the shear force changes linearly, and the bending moment changes parabolically.
- If there is a uniformly varying load between two points, the shear force changes parabolically, and the bending moment changes cubically.
- Where the shear force changes its sign, the bending moment is maximum. The point where the bending moment changes its sign is known as the point of contra flexure or inflection point.
What happens to the shear force and bending moment when there is a point load on the beam?
When there is a point load on the beam, the shear force changes suddenly, but the bending moment remains constant at that point.
How does the shear force behave when there is no load between two points?
When there is no load between two points, the shear force remains constant, and its graph is a horizontal line.
What is the behavior of the bending moment under a uniformly distributed load?
Under a uniformly distributed load, the bending moment changes according to the parabolic law, resulting in a parabolic graph.
How does the shear force change under a uniformly varying load?
Under a uniformly varying load, the shear force changes according to the parabolic law, resulting in a parabolic graph.
What is the point of contra flexure?
The point of contra flexure or inflection point is where the bending moment changes its sign. This point indicates where the bending moment transitions from positive to negative or vice versa.