478 PRACTICAL MATHEMATICS 



XIX (pages 315, 316, 317, 318) 



(1) 84-67 ft. tons, 112-4 ft. tons, 60-17 ft. tons 



(2) 50 ft. tons, 50 ft. tons, 37-5 ft. tons 



(3) M = 12-3 x - 0-750 2 , M = 12-30 - 12(0 - 4) - 0-375(0 - 8) 2 , 



M = 50-46 ft. tons when x = 8-4' 



(4) For AC, M . : for CB, M . - 



ft. tons when x = 19-43' 



(5) For BC, M = 11-70 - |^ ; for CA, M = 11-70 - 13-5(0 - 12) 



- (0 - 18) 2 ; M max = 130-74 ft. tons when = 16-76' 



W //0 2 3 \ w ( IW la? 4 



-- + ' at the end 



wl* 

 ~3EI 



M M W / N W l 2 2X % W 



(7) M = -(a- 0)+-( 2 -0 2 ), J = 



s 

 at the centre 8 = _ + 



Wa wa 2 W/a \ w fa? A 



(8) Fixing couple = + , M = (- - x) + - (- - tf), 



W fax 2 \ w /a 2 3 \ Wa 3 wa 4 



/\ TIT /i \i 



(9) M- (/ - ^) 3 , = 



_ __ 



" " " ~ ' 



_ _ 



6/EIl 2 2 " " T ~ 20/' vax 30E 



,,,_. ,, wa . . w , 2wa 4 



(10) M= _. (a -*)- - (a - 0) 3 , yn 



3a 2 2 4 \ 



_L /I'll" 



<*0~2EIV"~ 27 6aET V" 2 f) 



. _. . 5wa 2 ,_ wa . . zo , 



(11) Fixing couple = -^7-, M = (a 0) (a 0) 3 - 



/ 2 \ w f 



{ ax ) -- =r=- { a?x 

 \ 2/ 6aEI \ 



, 



dy _ ze?a / 2 \ w ( $ 3a 2 2 _ 4 \ 5wa 2 x 



' ~2~ ~W 24~ 



240EI 



