# Calculating the shear and moment diagrams of a beam with a hinge

• Engineering
• DS5555
In summary, the conversation discusses the change in the value of the applied moment at a pin point from right to left and whether it is always zero. The participant also mentions a counter clockwise moment of 1 and an area of 3/4wa^2 on a graph, leading to a curve with a highpoint at the intersection on the shear graph.
DS5555
Homework Statement
I am given a beam fixed to the wall at the left hand of the beam and supported by a pin on the righthand side. The pin is 3a long, and going from left to right there is a hinge at measure a into the beam, a distributed force w from a to 2a, and a moment of wa^2 being applied at the pin support. I have drawn out the shear moment diagram but I am struggling to understand how to draw the moment diagram, as the numbers from my shear force diagram don't seem to match the last segment of the moment diagram and I am confused on how to
Relevant Equations
M' = V
area = V'

Welcome, DS5555!

What makes the value of the moment applied to the pin point change from right to left?

Thank you! Happy to be here. I had read previously that the moment at the pin would be zero. Is this not true? For my thinking from the right side of the beam to the pin point, I see that I have a counter clockwise moment of 1 (assuming that the units are in wa^2 for simplification of the graph. My graph has the error of some of the values there being written with wa^2 instead of without) so I have to be at the end at positive 1. I then see that I have an area of 3/4wa^2, so In order to reach 1 I have to start at 1/4, and so then I draw a curve with the highpoint being at where the intersection is on my shear graph.

## 1. How do I determine the reactions at the hinge?

The reactions at the hinge can be determined by taking the sum of the forces and moments acting on the beam at the hinge. This can be done by drawing a free body diagram and using the equations of equilibrium.

## 2. What is the difference between shear and moment?

Shear is the force that acts parallel to the cross-section of the beam, while moment is the force that causes rotation around a point. Shear and moment are related to each other and are important factors in determining the strength and stability of a beam.

## 3. How do I calculate the shear and moment diagrams?

The shear and moment diagrams can be calculated by using the equations of equilibrium and the properties of the beam. The process involves finding the reactions at the supports, determining the internal forces and moments at different points along the beam, and plotting them on a diagram.

## 4. What is the significance of a hinge in a beam?

A hinge is a point of zero moment, meaning that it does not resist bending or cause any rotation in the beam. It is often used in structural designs to provide flexibility and allow for movement in the beam, such as in trusses or cantilever beams.

## 5. How does the location of the hinge affect the shear and moment diagrams?

The location of the hinge can significantly affect the shear and moment diagrams. If the hinge is located at a point of high shear or moment, it can reduce the overall strength and stability of the beam. Therefore, it is important to carefully consider the placement of the hinge in a beam design.

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