370 Mechanics of Materials §14.10 and from egn.(14.12), 1E v=26K Therefore,equating, E 1 E 20-1=26 E+113 2G+6永2 6K+2G13 E 12KG 9KG i.e. E= (3K+G) (14.13) 14.10.Strains on an oblique plane (a)Linear strain Consider a rectangular block of material OLMN as shown in the xy plane(Fig.14.8).The strains along Ox and Oy are &x and y,and ysy is the shearing strain. Xyasing acos 8e.Ty a sin 8 e,acos e+y a sin 8 2L a sndey M 8才M a sin e、 a51r8 0 to OM M Movement of parallel N -acos 8 acos 8Ex Fig.14.8.Strains on an inclined plane. Let the diagonal OM be of length a;then ON a cos 0 and OL a sin 0,and the increases in length of these sides under strain are ea cos 6 and e,a sin 6(i.e.strain x original length). If M moves to M',the movement of M parallel to the x axis is Exacos0+Ysasine and the movement parallel to the y axis is Eya sin370 and from eqn. (14.12), Mechanics of Materials Therefore, equating, .. i.e. 9KG (3K + G) E= 414.10 (14.13) 14.10. Strains on an oblique plane (a) Linear strain Consider a rectangular block of material OLMN as shown in the xy plane (Fig. 14.8). The strains along Ox and Oy are E, and cy, and yxy is the shearing strain. C, a cos 8+ xv a sin 8 / Q +.-acosR-+ + a cos 8 E, Fig. 14.8. Strains on an inclined plane. Let the diagonal OM be of length a; then ON = a cos 8 and OL = a sin 8, and the increases in length of these sides under strain are &,a cos 8 and E~U sin 8 (i.e. strain x original length). If M moves to M', the movement of M parallel to the x axis is &,a cos 8 + ?,,a sin 8 Eya sin 8 and the movement parallel to the y axis is