# Relationship between shear force diagram and bending moment

### Shear and moment diagram - Wikipedia

image source: Strength of Materials, Part I by Prof. Stephen P Timoshenko) The shearing force is the rate of change of Bending Moment in the considered. In the following diagram \displaystyle \delta x is the length of a small slice of a loaded beam at a distance x. The relationship between shear force and bending moment is.

The positive bending convention was chosen such that a positive shear force would tend to create a positive moment. Alternative drawing convention[ edit ] In structural engineering and in particular concrete design the positive moment is drawn on the tension side of the member.

This convention puts the positive moment below the beam described above.

### Shear Force and Bending Moment - Materials - Engineering Reference with Worked Examples

A convention of placing moment diagram on the tension side allows for frames to be dealt with more easily and clearly. Additionally placing the moment on the tension side of the member shows the general shape of the deformation and indicates on which side of a concrete member rebar should be placed, as concrete is weak in tension.

For a horizontal beam one way to perform this is at any point to "chop off" the right end of the beam. The example below includes a point load, a distributed load, and an applied moment.

The supports include both hinged supports and a fixed end support. The first drawing shows the beam with the applied forces and displacement constraints. Page Comments Introduction Shear Forces occurs when two parallel forces act out of alignment with each other.

**Relation Between Load, SF & BM - Strength of Materials**

For example, in a large boiler made from sections of sheet metal plate riveted together, there is an equal and opposite force exerted on the rivets, owing to the expansion and contraction of the plates. Bending Moments are rotational forces within the beam that cause bending.

## Shear Force and Bending Moment Diagrams

At any point within a beam, the Bending Moment is the sum of: Shearing Force The shearing force SF at any section of a beam represents the tendency for the portion of the beam on one side of the section to slide or shear laterally relative to the other portion.

The diagram shows a beam carrying loads. It is simply supported at two points where the reactions are. Assume that the beam is divided into two parts by a section XX.

The resultant of the loads and reaction acting on the left of AA is F vertically upwards, and since the whole beam is in equilibrium, the resultant force to the right of AA must be F downwards. F is called the Shearing Force at the section AA.

It may be defined as follows: Where forces are neither in the lateral or axial direction they must be resolved in the usual way and only the lateral components are used to calculate the shear force. Bending Moment and Shear Force Diagrams: The diagrams which illustrate the variations in B. F values along the length of the beam for any fixed loading conditions would be helpful to analyze the beam further.

- Shear Force and Bending Moment

If x dentotes the length of the beam, then F is function x i. Again M is a function x i. The construction of the shear force diagram and bending moment diagrams is greatly simplified if the relationship among load, shear force and bending moment is established.

Let us detach this portion of the beam and draw its free body diagram.