# Force and moment relationship

### Shear Force and Bending Moment Diagrams - Wikiversity

If we take this section out of the beam we must add the forces and moments that were previously exerted by the material in order to maintain equilibrium. relationship is known as Hooke's law and can be expressed as an equation k. F δ = where the measure both force vectors, and torque or moment vectors. The construction of the shear force diagram and bending moment diagrams is greatly simplified if the relationship among load, shear force and bending moment.

Basic shear diagram[ edit ] What if there is more than one force, as shown in the diagram below, what would the shear force diagram look like then?

The way you go about this is by figuring out the shear force at points A,B,C,E as there is an external force acting at these points. The way you work out the shear force at any point, is by covering either with your hand or a piece of papereverything to right of that point, and simply adding up the external forces.

Then plot the point on the shear force diagram. For illustration purposes, this is done for point D: BUT - slight complication - there's a force acting at point B, are you going to include it? The answer is both yes and no. You need to take 2 measurements. If you don't understand why, leave a message on the discussion section of this page its at the topI will elaborate on the explanation: Notice how nothing exciting happens at point D, which is why you wouldn't normally analyse the shear force at that point.

For clarity, when doing these diagrams it is recommended you move you paper from left to right, and hence analyse points A,B, C, and E, in that order. You can also do this procedure covering the left side instead of the right, your diagram will be "upside down" though.

## Shear and moment diagram

Both diagrams are correct. Basic bending moment diagram[ edit ] Bending moment refers to the internal moment that causes something to bend. Hence bending moment is shown on a bending moment diagram. The same case from before will be used here: To work out the bending moment at any point, cover with a piece of paper everything to the right of that point, and take moments about that point.

## Shear Force and Bending Moment Diagrams

I will take clockwise moments to be positive. To illustrate, I shall work out the bending moment at point C: This is because the 40N force at point C exerts no moment about point C, either way. Repeating the procedure for points A,B and E, and joining all the points: Normally you would expect the diagram to start and end at zero, in this case it doesn't. This is my fault, and it happened because I accidentally chose my forces such that there is a moment disequilibrium.

It also means that if you're covering the left side as opposed to the right, you will get a completely different diagram. Upon inspection, the forces are unbalanced, so it is immediately expected that the diagram will most likely not be balanced.

Point moments[ edit ] Point moments are something that you may not have come across before. Below, a point moment of 20Nm is exerted at point C.

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

Work out the reaction of A and D: So how does a point moment affect the shear force and bending moment diagrams? It has absolutely no effect on the shear force diagram. You can just ignore point C when drawing the shear force diagram. The supports include both hinged supports and a fixed end support. The first drawing shows the beam with the applied forces and displacement constraints. The second drawing is the loading diagram with the reaction values given without the calculations shown or what most people call a free body diagram.

The third drawing is the shear force diagram and the fourth drawing is the bending moment diagram.

For the bending moment diagram the normal sign convention was used. Below the moment diagram are the stepwise functions for the shear force and bending moment with the functions expanded to show the effects of each load on the shear and bending functions. The example is illustrated using United States customary units. Compute the reaction forces and moments[ edit ] Free-body diagram of whole beam The first step obtaining the bending moment and shear force equations is to determine the reaction forces.

This is done using a free body diagram of the entire beam. The beam has three reaction forces, Ra, Rb at the two supports and Rc at the clamped end. The clamped end also has a reaction couple Mc. These four quantities have to be determined using two equations, the balance of forces in the beam and the balance of moments in the beam.

- Shear Force and Bending Moment

Four unknowns cannot be found given two independent equations in these unknown variables and hence the beam is statically indeterminate. One way of solving this problem is to use the principle of linear superposition and break the problem up into the superposition of a number of statically determinate problems.