18 Sir G. Greenhill on 





Here a=b = q, 





1 d 2 Vl 1 d 2 V2 1 d 2 Vs 1 d^ 

 <f dx~ 2 " ~^ 2 ' 9? 25" ~ ^' ? 35*" " ~^ 4 ' ? d^ 



= 2%, (3) 



1 /72 



~ 2 73 = 2 %tB 8 (- 277 4 — 2773) = 0, when x = Z, . . 



• • (4) 



B 2 ch jZcos 5/— B 3 (shg/cos^+ch j^sin jZ) = 0, ") 



B f * 



g? = th ql + tan jZ. J 



'. . (5) 



At ^=0, and measuring 77 downward, 



= bending moment at = ~Pl—pb \ xndx, . (6) 



* 

 and integrating by parts, 



^ xrjdx = x§r}dx—§§ydx, .... (7) 

 in which 



§q Vl dx = 4(773 + 774), JjVjhAK = i»7 2 , ... (8) 



J ^ 2 ^ ^ l(-7 ?3 + r 74 ), $q 2 V*dx = -J>?i, • ■ (9) 



jg^cfo? = i(77 1 H-77 2 ), §§q 2 Vsdw = iv±, •'• - < 10) 



J^ 4 ^ = J( — 771 + 772), §§q 2 r)idx =~iVs, • -t 11 ) 



§q{v3-v±)dx=yi, ^fivz-vi) = Kis+v*)* • ( 12 ) 



§2q 2 X V dx = B 2 ^(-77 3 + ^) + B 2 (r7 1 -l) + 2B3^r7 1 -B 3 (77, + 77 4 ), (13) 

 77 X = ch gZ cos #7, ?7 2 = sh ^Zsin g'/, 77 3 = sh ^Z cos gZ, 77 4 = ch<^sin ^, (14) 



=^- I ^»7<i^ = ( — Iq sh ql cos ql + Iq ch ql sin ql + ch ql cos ql— T)(thql + tsinql) 

 -03 Jo 



+ 2lq ch ^Z cos <?Z — sh ^/ cos ql — chql sin ^/ 



= ^^fi + ^SfJ- a, » / - tan ^ • •••••• (15) 



2Pfg» _ 2g» f 1 B 2 _ / chgl 00s gh l^..! ri6> 



P 6B 3 _ B 3 JT" to T3 *' ? B 3 ~ <? \cos ql + chqt )' 3 fe ? ~ 1; {lb) 



