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

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

(c) Also, at what inclination angle is the shear stress a maximum?

cos 20 1+ = o o' = r cos? (6.4a) 2 sin 20 7' = 7 sin 0 cos 0 = o (6.4b)