Stress Transformation

The state of plane stress shown in Fig2.3 may be described in a rotated coordinate system:

Fig. 2.3

is now replace by

and

is now

. These new quantities do not represent a new state of stress but rather an equivalent representation of the original one. The values of stress components in the new coordinate system can be obtained by considering the FBD as follows:

Fig. 2.4

Solving equation (1) and (2) with trigonometric identities,

With equation (A) & (B) the desired complete state of stress in the new coordinate system can be found. Note that

is +ve in the CCW direction.

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