354 Mr. B. C. Laws on the Strength 



The resultant bending-raoments at o, c, and d, are : — 

 a, t»t w tiQ w f 2a. m ., 1 Q(a — c) 2 







.« J. a ■«(<■•+ «;~) . i Q(a- C ) 2 



Wl' 2 I e m - a __ e -m-« "J 2a 







/ to. a , —m.ci\ ^ , 



S a ' m (% +%__) -\ 1 Q(a 2 -o 2 ) 



At c : M - IVT 



c c 



Aid: m:-m?=-^ 



e — e 

 o o 



2a 



It will be found that the resultant bending-moment at c is 

 the greatest, and must be used for calculating the stress 

 in the material of the plate due to bending. 



Fig. 5. 



Now consider the diagram fig. 5, we have :- 



m 2 t 2 

 Stress due to P = -y^- . E, 



9j9 9 »*> 



and elongation of the plate (beam) = 2a x ^- = ,, . 



Length of the curve ccj = S = 2c + 



4D 5 

 3c 



„ „ dc or o 7 ^! — 5 = (a— c) + 7 



Therefore elongation of the beam = S -*- 2s - 2a, 



8d" 



3(a — c) 



4D 2 16^ 2 _ m 2 t 2 a 



3c 3 (a — c) ~ 6 



or 



D 2 + — . M 2 = mH2a ' G 



a — c 



8 



an equation from which to determine t when D and a 7 are 

 known. 



Now 



m.a —m.a 



.«_ 1 S 





^0 



E.ll 



a( e o + e o ~^ \ 



3 \ m.a —m.a I 



\ e. —e. J 



e — e 

 o o 



iv.a 2 _ Q{a-c) 2 (a + 2c) 

 2m 9 12 



}■ 



