## What is a Bending Moment?

In general, we can define the bending moment as the reaction induced when a certain amount of load or force is applied to an element which makes it bend.

In mechanics, bending moment is said to be the reactionary stress which is introduced in any element when any kind of external force is applied to the element which causes it to bend. This concept is quite useful in structural engineering because it can help in knowing where and what amount of bending will occur when forces are applied to it. One of the simplest elements which is subjected to bending is known as the beam. We can also understand this by taking an example of the beam which is simply supported, from both the ends. These ends are supposed to react only for the shear loads. Bending leads to failure when the stress generated by the force becomes equal to or becomes more than the ultimate strength of the system or an element.

Beams can also be fixed from one end while the other end can be supported simply, Such a type of beam can be called a cantilever beam. This type of beam is completely fixed from one end while the other end is not fixed. While the fact is that, the beam supports are not absolutely fixed or absolutely rotating free. A beam is supposed to break due to the shear forces before the failure. And if it is not constrained, it will start rotating around a pivot point due to bending force.

The reactionary loads occurring internally in the area of cross section of the element can be taken as a resultant force and as a resultant couple. In the condition of equilibrium, the external moments and external forces are supposed to be balanced with the couple loads. This resultant of internal couple is considered as the bending moment while the resultant of internal force is considered as the shear force, if it is in the same direction as in the direction of the plane of element, and if the force is perpendicular to the plane of the element then it is said to be normal force.

The bending moment at some cross section through any element is described as the total of all the moments in respect to that section, which are acting to that one of the sides of that section.

The moments and the forces on both the sides of the cross section are supposed to be equal in all circumstances so that it will counteract each other and so that it can help in maintaining the state of balanced equilibrium.

## Types of Bending Moment

### Negative Bending Moment

When the clockwise bending moments are taken to be negative in nature then this is called negative bending moment and the phenomena which occurs within an element is called hogging.

### Positive Bending Moment

When the clockwise bending moments are taken to be positive in nature then this is said to have a positive bending moment and the phenomenon which occurs within the element is called sagging.

### Zero Bending Moment

The point of conversion from hogging to sagging or from sagging to hogging is called zero bending moment and this is known as the point of contra flexure.

Moments and force can be calculated by the product of the force with distance. They generally have the unit as Newton-meters (N.m). The concept of bending moment is to be taken care while designing or while building any structure.

**Different Types of Beams **

**Simply supported beam** - It is one of the simplest types of structures. It only has two supports, one at both the ends. One of which is pinned while the other one is a roller support. This setup prohibits the movement of the beam from any of the ends while leaving it to rotate freely. And with the help of roller support it allows the movement in axial direction while the horizontal movement is restricted by the other end which is supported.

**Fixed beam** - It is the type of beam which is supported from both the ends. Both the ends are fixed rigidly in a way that it leads to the slope at both the ends to be zero. The ends are fixed in a way so that there is no rotation of the beam taking place.

**Overhanging beam** - If the side portion of the beam is longer than the support, such types of beams are called overhanging beams. Overhanging can take place on one side of support or on both the sides.

**Continuous beam** - To increase structural integrity, beams are developed in a way that they are continuous over the supports. In the event of a section failure, a continuous beam helps in providing an alternate load path. These are generally preferred in developing buildings and bridges in seismically prone areas. It is a structure that is statically indeterminate.

**Cantilever beam** - It is the type of beam whose one end extends past the point of support which is free to move in the vertical direction when the vertical load is given between the end which is free and the support.

**Types of Bending Stress **

**Pure bending stress** - It is the stress condition in which a bending moment is provided to the beam in the absence of any kind of shear, axial or torsional force.

**Simple bending stress **- When the bending occurs due to the internal or external loads, such type of stress is known as simple bending stress. This type of stress helps in producing both the normal as well as shear force stress.

## Limitations Related to Bending Moment

In the tool’s holder test, which is done for stiffness damping and the capability for supporting the bending moment loads, a static load is provided with the help of a hydraulic cylinder on the right-hand side and the deflection is being calculated with the help of capacitance gauges. The bending moment is found critical in machine tool spindles as it causes the tool to differentiate from the tool holder or the tool holder to be differentiated from the spindle. When a mechanical structure bends as a result of an applied moment, a bending moment exists.

## Context and Applications:** **

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

- B.Sc. Physics
- M.Sc. Physics

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