Fixed Support in a Plane Structure

A fixed support, also known as a built-in or immovable support, is a type of support used in structural engineering. It prevents both translation and rotation of the structure at the support location. When analyzing a structure with a fixed support, it is important to determine the number of reactions that occur at the support.

Number of Reactions

The number of reactions at a fixed support depends on the degree of freedom of the structure. In a plane structure, there are three degrees of freedom:

1. Translation in the x-direction
2. Translation in the y-direction
3. Rotation about the z-axis

Since a fixed support prevents both translation and rotation, there are three reactions that occur at the support:

1. Vertical reaction force (Fy)
This is the force exerted in the y-direction to prevent vertical translation of the structure. It acts perpendicular to the plane of the structure.

2. Horizontal reaction force (Fx)
This is the force exerted in the x-direction to prevent horizontal translation of the structure. It acts parallel to the plane of the structure.

3. Moment reaction (Mz)
This is the moment exerted about the z-axis to prevent rotation of the structure. It acts perpendicular to the plane of the structure.

Therefore, the total number of reactions at a fixed support in a plane structure is three (Fy, Fx, Mz).

Conclusion

In summary, a fixed support in a plane structure generates three reactions: a vertical reaction force, a horizontal reaction force, and a moment reaction. These reactions are necessary to prevent translation and rotation of the structure at the support location.