Reinforced Thin-plate Beam. 285 



When = 0, = 0, or Ai + B^O. 



„ a = n, = <£, or Aj . e + Bi.£ = m sE.i +*' 



I/id _u A\vn^ hi I . 



z#/i 4- $m 2 E . Ii 



m?i — mn. 



m'-Hj.Wo — <? c 



a _ (c w^^+^ e . ii) - _ w 



m[e —e Q ) 



and E . J-! . , 2 — _ 2 , 



ail ttii p . — p„ \ ni 



an expression for the bending moment at any point 

 between o and c. 



Whe„, = „, k. = &r + -b-)(«- + #-.'H.'w._- 



*=0, M 



2 (w . n + (fr m 2 E.Ii) iv 

 m(e -e Q ) ™ 



and 2F T _ io(<r — .?; 2 ) (am + cfrw E Ii)(g + <? ) 



m & • -Li y — 9 + — 7"^ ^T" 



- >»Vo -e ) 



_1 f W q (^ (a ~ ?l) + g - m(g - '°) - 2(t ai + m 2 E . Ift) j . 



m 1 m(a-n) e -m(a— n) j ' 



an expression giving the deflexion at any point between o 

 and c, and from which the maximum deflexion is obtained 

 by putting x — 0. 



Equating the above expressions for M ft we have : 



</>»i 2 E 



f t / »»» i —mn\ -i / m(a - n) , —m(a—ri)\ \ 



f Iifa -+^0 ) . 1(V + £ Q | 



| ?2i?i —nut ' m{a—n) —m(a—n) j 



o J / v»w —mn\ / ma —ma\ ) 



^ Zw\a(e —e )-n (e — e )\ 



/ mn —mn\ / m(a—n) -m(a-n)\ ' 



(«o — «o )(«o '« ) 



w 



from which to obtain the slope ^ of the beam at c. 



At this position the .'dope of the unstiffened plate would 

 be given by 



/ mn —mii\ 

 ma — ma 



The form assumed by the free portion cd of the plate 



m 2 E .I<k 



''o 



