Geometry of Deformation  
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Diagram shows a shaft A B with an aluminum segment on the outside and a brass shaft in the inside. Both the shafts are centered on the central axis x. A torque T is applied at B. The radial and longitudinal lines are shown on the shaft. The deformation of the shaft is shown with a counterclockwise segment of angle phi subscript B, angle of twist.

Since aluminum shaft (1) and bronze shaft (2) are bonded together, shaft (2) twists through the same angle as shaft (1):

ϕ1=ϕBϕ2=ϕB

Combine these two equations to obtain the geometry of deformation equation:

ϕ1=ϕ2

This equation expresses the relationship between the angles of twist in the two shafts for the given support conditions.