What is Shear Force And Bending Moment?
Table of Contents
1. What are shear force and bending moment?
Shear Force:- Shear force is defined as "net vertical force or imbalanced vertical force on either side of the section" at any segment of a beam. All vertical elements on the left or right side of the section are added together algebraically to form this value. Shear force has the effect of cutting the member at a section, similar to how scissors would cut a page.
Positive shear force is defined as the total of the vertical forces acting downward on the right side and upward on the left. In other words, shear that is positive clockwise. And in opposition to these, a negative shear force is defined as the sum of the vertical forces acting upward on the right side of the section and downward on the left side of the section or counterclockwise.
Bending Moment: The "bending moment" is the force that has a tendency to bend the beam in the plane of the applied load. In other words, the "net or unbalanced moment attributable to all forces on each side of the section" is what constitutes a bending moment at any segment of a beam. It is the algebraic sum of all moments brought by by all forces acting on the section's right or left side. A bending moment causes the element to bend.
2.Sign Conversion Using shear force and bending moments.
Shear force: The "bending moment" is the force that has a tendency to bend the beam in the plane of the applied load. In other words, the "net or unbalanced moment attributable to all forces on each side of the section" is what constitutes a bending moment at any segment of a beam. It is the algebraic sum of all moments brought by by all forces acting on the section's right or left side. A bending moment causes the element to bend.
Bending Moment: Positive bending moments are those where the sum of moments on the right side is counterclockwise and the sum of moments on the left side is clockwise. Another name for it is a sagging bending moment. The top surfaces will be compressed, while the bottom surfaces will be tensioned. A negative bending moment is the opposite of this, i.e., the sum of moments on the right side is clockwise and on the left side is anticlockwise. An alternative name for it is a "hogging" bending moment. Both the top and bottom surfaces will experience tension as a result.
Positive Bending Moment:
Negative Bending Moment:
3. Diagram of shear force and bending moment.
•It can be seen that the shear force is constant from the equation for shear force at X. In other words, the shear force magnitude at any location between A and B remains P regardless of x. Similar to how bending moment is directly proportional to distance, it can be shown from the equation of bending moment at x.
Case-1
Point load: Consider a cantilever beam AB of length L with fixed support at A and B at its free end and subjected to a vertical downward point load "P" at point B. At fixed end "A," there are three reactions, one vertical, one horizontal, and one moment. These reactions can be calculated by using conditions of equilibrium.
Case-2
Cantilever beam
Uniform Distribution Load: Consider a cantilever beam AB of length L with fixed support at A and B at the free end and subjected to a uniformly distributed load. At fixed end "A," there are three reactions, one vertical, one horizontal, and one moment. These reactions can be calculated by using conditions of equilibrium.
Case-3
Consider a cantilever beam AB of length L with end A fixed and end B free and subjected to a clockwise couple M at end B.E equilibrium conditions can be used to find reaction at support.
Case-4
Consider a cantilever beam AB with A end fixed and B end free that is subjected to a vertically downward uniformly varying load with zero intensity at the free end and unit length at the fixed end.
4.Useful tips for shear force and bending moment.
• The configuration of the shear force lines always determines the slope of the bending moment. The variations in shear force values also influence changes in slope (sagging or hogging).
• Maximum moment occurs when shear force intersects the BMD axis.
• BM is at its lowest while SF is at its highest, and vice versa.
• SFD and BMD always have zero starting and stopping values (unless at the point where there is a moment or couple)
• When a moment or couple is acting: clockwise (down direction) (+), anticlockwise (up direction) (-).
1. What are shear force and bending moment?
Shear Force:- Shear force is defined as "net vertical force or imbalanced vertical force on either side of the section" at any segment of a beam. All vertical elements on the left or right side of the section are added together algebraically to form this value. Shear force has the effect of cutting the member at a section, similar to how scissors would cut a page.
Positive shear force is defined as the total of the vertical forces acting downward on the right side and upward on the left. In other words, shear that is positive clockwise. And in opposition to these, a negative shear force is defined as the sum of the vertical forces acting upward on the right side of the section and downward on the left side of the section or counterclockwise.
Bending Moment: The "bending moment" is the force that has a tendency to bend the beam in the plane of the applied load. In other words, the "net or unbalanced moment attributable to all forces on each side of the section" is what constitutes a bending moment at any segment of a beam. It is the algebraic sum of all moments brought by by all forces acting on the section's right or left side. A bending moment causes the element to bend.
2.Sign Conversion Using shear force and bending moments.
Shear force: The "bending moment" is the force that has a tendency to bend the beam in the plane of the applied load. In other words, the "net or unbalanced moment attributable to all forces on each side of the section" is what constitutes a bending moment at any segment of a beam. It is the algebraic sum of all moments brought by by all forces acting on the section's right or left side. A bending moment causes the element to bend.
Bending Moment: Positive bending moments are those where the sum of moments on the right side is counterclockwise and the sum of moments on the left side is clockwise. Another name for it is a sagging bending moment. The top surfaces will be compressed, while the bottom surfaces will be tensioned. A negative bending moment is the opposite of this, i.e., the sum of moments on the right side is clockwise and on the left side is anticlockwise. An alternative name for it is a "hogging" bending moment. Both the top and bottom surfaces will experience tension as a result.
Positive Bending Moment:
Negative Bending Moment:
3. Diagram of shear force and bending moment.
•It can be seen that the shear force is constant from the equation for shear force at X. In other words, the shear force magnitude at any location between A and B remains P regardless of x. Similar to how bending moment is directly proportional to distance, it can be shown from the equation of bending moment at x.
Case-1
Point load: Consider a cantilever beam AB of length L with fixed support at A and B at its free end and subjected to a vertical downward point load "P" at point B. At fixed end "A," there are three reactions, one vertical, one horizontal, and one moment. These reactions can be calculated by using conditions of equilibrium.
Case-2
Cantilever beam
Uniform Distribution Load: Consider a cantilever beam AB of length L with fixed support at A and B at the free end and subjected to a uniformly distributed load. At fixed end "A," there are three reactions, one vertical, one horizontal, and one moment. These reactions can be calculated by using conditions of equilibrium.
Case-3
Consider a cantilever beam AB of length L with end A fixed and end B free and subjected to a clockwise couple M at end B.E equilibrium conditions can be used to find reaction at support.
Case-4
Consider a cantilever beam AB with A end fixed and B end free that is subjected to a vertically downward uniformly varying load with zero intensity at the free end and unit length at the fixed end.
4.Useful tips for shear force and bending moment.
• The configuration of the shear force lines always determines the slope of the bending moment. The variations in shear force values also influence changes in slope (sagging or hogging).
• Maximum moment occurs when shear force intersects the BMD axis.
• BM is at its lowest while SF is at its highest, and vice versa.
• SFD and BMD always have zero starting and stopping values (unless at the point where there is a moment or couple)
• When a moment or couple is acting: clockwise (down direction) (+), anticlockwise (up direction) (-).
Comments
Post a Comment