of the Thin-plate Beam, 353 



Again, referring to the portion cd : — 



Q 



dy _ M a (a — x) Q{a — x) 2 

 dx E.I + 2E.I * 



Now when a?=a, y=0. 



p _ M^_ a 2 _ _Q_ a 3 

 1 ~ E . I * 2 2E . I ' 3 ' 



. M?(a-s) 2 _ Q(a-^) 3 



* ,2/ 2E.I 6E.I 



_ Q(a — a) 8 f a 2 -c 2 a-x \ 

 " 2E.I 1 2a 3 J 



and deflexion at c = y Q = Q^-Q 3 fa + 3c) 

 ^ 12aE . I 



Also referring to the portion oc : — 



<fy_ M?-Q(a-c) 



^ " E.I X > 



Q 

 M a —Q(a — c) x 2 n 

 • -y= ^71 .y+^ii. 



Now when x = c, 



q Ma-Q(a-c) c 2 , n Q(a-c) 3 (a + 3c) 

 ye=y - = ETI '2 + ° 11= l2aE7I * 



_ Q(a-c) 2 (a + 2c) _ Q(a-c) 2 9 

 " y ~ 12E.I 4aE.I ' X ' 



j , „ . q Q(a — c) 2 (a + 2c) 



and deflexion at o = y n = — — - 7™ T ■ 



,yo i2E.I 



Now, in the general case fig. 2, c is level with d. 

 Therefore, putting y e = ?/ c we get : — 



/ in. a . —m.a\ / m.c . —m.c\ 



Q(a-c) 3 (a + 3c) = -io.a f (* + e )-( g + * ) I w(a 2 -c 2 ) ~ 



12a m 3 [ m.a_ -m.a j + 2 ??l 2 . 1 / 



*■ ^ J ° 



an equation from which Q may be obtained when m is 

 known. 



Phil. Map. S. 6. Vol. 31. No. 184. April 1916, 2 B 



