228 Mechanics of Materials 2 $8.5 In the case of a normal stress the relationship between the direction cosines is simply l=l,m=mo and n=n中 since the stress and the normal to the plane are in the same direction.Egn.(8.29)then reduces to that found previously,viz.eqn.(8.18). 8.5.Principal stresses and strains in three dimensions-Mohr's circle representation The procedure used for constructing Mohr's circle representation for a three-dimensional principal stress system has previously been introduced in $13.77.For convenience of refer- ence the resulting diagram is repeated here as Fig.8.8.A similar representation for a three-dimensional principal strain system is shown in Fig.8.9. T Principal circle 2 Fig.8.8.Mohr circle representation of three-dimensional stress state showing the principal circle,the radius of which is equal to the greatest shear stress present in the system. Principal arcle Fig.8.9.Mohr representation for a three-dimensional principal strain system. EJ.Heam.Mechanics of Materials 1.Butterworth-Heinemann.1977.228 Mechanics of Materials 2 $8.5 In the case of a normal stress the relationship between the direction cosines is simply 1 = 14, m = m# and n = n6 since the stress and the normal to the plane are in the same direction. Eqn. (8.29) then reduces to that found previously, viz. eqn. (8.18). 8.5. Principal stresses and strains in three dimensions - Mohr’s circle representation The procedure used for constructing Mohr’s circle representation for a three-dimensional principal stress system has previously been introduced in Q 13.7? For convenience of refer￾ence the resulting diagram is repeated here as Fig. 8.8. A similar representation for a three-dimensional principal strain system is shown in Fig. 8.9. t Fig. 8.8. Mohr circle representation of three-dimensional stress state showing the principal circle, the radius of which is equal to the greatest shear stress present in the system. Fig. 8.9. Mohr representation for a three-dimensional principal strain system. J. ’ E.J. Hearn. Mechanics of Materids I, Butterworth-Heinemann, 1977