(a) Equations 6.4a and 6.4b are expressions for normal (σ’) and shear (τ) stresses, respec...

(a) Equations 6.4a and 6.4b are expressions for normal (σ’) and shear (τ) stresses, respectively, as a function of the applied tensile stress (σ) and the inclination angle of the plane on which these stresses are taken (θ of Figure 6.4). Make a plot showing the orientation parameters of these expressions (i.e., cos2 θ and sin θ cos θ) versus θ.

(b) From this plot, at what angle of inclination is the normal stress a maximum?

(c) At what inclination angle is the shear stress a maximum?

Figure 6.4 Schematic representation showing normal (σ’) and shear (τ’) stresses that act on a plane oriented at an angle u relative to the plane taken perpendicular to the direction along which a pure tensile stress (σ) is applied.

 (6.4a)

 (6.4b)