P.1.5. A shear stress ty acts in a two-dimensional field in which the maximum allowable shear stress is denoted by Tmax and the major principal stress by o1. Derive, using

the geometry of Mohr's circle of stress, expressions for the maximum values of direct stress which may be applied to the x and y planes in terms of these three parameters. \text { Answer: } \quad \sigma_{x}=\sigma_{I}-\tau_{\max }+\sqrt{\tau_{\max }^{2}-\tau_{x y}^{2}} \sigma_{y}=\sigma_{I}-\tau_{\max }-\sqrt{\tau_{\max }^{2}-\tau_{x y}^{2}}

Fig: 1

Fig: 2

Fig: 3