Reactions are forces that are created in the supports of a structure, when these supports restrain the displacement at that point. If the support do not restrain the movement at that point, there are no reactions. Based on this, there are several types of supports provided to the structure.
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Fixed End Support ( 2D & 3D) Reactions in Structural Analysis |
All the components of a structure are connected and linked using supports and connections as shown in fig.1 below. In the figure, you can see a beam supported using two columns at the ends of the beam.
Fig.1. Supports in a Framed Building Structure Image Credits: ASCE Library |
Fixed End Support Reactions in 2D
- Under the action of load ‘P’,
the end A remains as such but the end B deflects.
- Deflection at point B results
in a displacement of Δy a non-zero value and corresponding Θb ( slope at B).
- There are no reactions at B, as
the end is not restrained. The end is free to move.
Support
Reactions @ B = re =0;
Reactions At End A
- The fixed end ‘A’restricts the movement of end BEAM along x direction, as a result of which displacement along x-axis is zero. Hence, Change in distanceΔx = 0;
- Similarly, The end ‘A’restricts the displacement along y-axis, hence Δy = 0;
- Unlike, end B, the end A do not allow any deflection i.e (Δy = 0), and hence the slope at A is θA = 0;
Hence at End A, (Fixed End) the Horizontal, vertical and rotational movement is restrained; Δx= 0; Δy = 0; θA = 0 that leads to reactions Rx, Ry and M. Where Rx is the reaction caused along x-direction, Ry is the reaction along Y-direction and the rotation resisted creates reaction in the form of moment M.
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