If one end of a prismatic beam AB with fixed ends is given a transverse displacement (\(\Delta\)) without rotation, then the moment induced at A or B due to the displacement is

Explanation:

This is a case of pure transverse displacement of a fixed-fixed prismatic beam with no rotation — typically referred to as "sway" in structural analysis.

• Beam AB is fixed at both ends.

• One end is displaced transversely by $\Delta$ (without rotation).

• This introduces equal and opposite end moments to maintain equilibrium.

For such a case, the induced moment at each end (A or B) is:\(6EI \Delta / L^2\)

Additional Information

• Transverse displacement refers to the movement of a structural member perpendicular to its longitudinal axis.

• For a horizontal beam, transverse displacement means vertical movement.

• For a vertical column, transverse displacement means horizontal movement (also called sway).

• A beam fixed at both ends is displaced sideways (laterally) at one end without rotation.

• This displacement is parallel to the direction of the applied shear or lateral force, not along the length of the beam.

• To maintain fixity (zero rotation), internal moments develop at both supports.