Hinged End Support ( 2D & 3D) Reactions in Structural Analysis

 

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A hinged support is a support provided to the structural element that facilitate rotational movement of the structure at that point but do no allow translational movement. A hinge support is represented as shown in fig-2 ,while drawing free-body diagram of a structure.

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Fig.1. Hinged Support at End A

Hinge Support Reactions 2D

Consider a beam whose end 'A' is supported using a hinge. Let the beam be subjected to an inclined load of P at a particular angle.

Even under the action of load, the end A is restrained from translational movement along x and y-direction. This means Δx = 0; Δy=0; This would result in corresponding support reaction along x and y direction as Rx and Ry as shown in fig.2.

Fig.2. Hinged End Support ( 2D ) Reactions

But as shown in fig.2, the bending of the beam under the action of load P creates a rotation at A i.e. θA which is not equal to zero. This is because, a hinge support do not restrain rotational movement. Hence, there is no moment created at a hinge support. Hence,

Support reactions at a hinge support in 2D Structure are [Rx, Ry] = 2 nos

Hinge Support Reactions 3D

In 3D, there is no much confusions to arise, as there is no rotational moment neither in 2D nor in 3D. The only difference is the consideration of reaction along the third axis, i.e. the Z-axis. Hence,

Support reactions at a Hinge Support in 3D Structure are [ Rx, Ry, Rz] = 3 nos

Also Read: 

Fixed End Support Reactions in 2D & 3D 

Roller Support Reactions in Structural Analysis