286 Strength of Reinforced Thin-plate Beam. 



may be taken as approximating to that of a " sine " curve 

 in which 



m{a~n)t . 2 t? t m 2 Et 4 (a — n) ,,. 



^ = ^6158 and mE - I -y"= 31-3896 • W 



The maximum stress in the plate may be determined 

 for any assumed value of n by finding the value of <j> lrom 

 equation (c) ; thence, by determining the value of 



M« from equation (a) 



and t from equations (b) and (<J), 



the stress value due to bending may be derived from those 

 of M„ and t, and that due to stretching from the relation 



P =m 2 .E.L 



For example take the case previously cited, in which 

 a =11 in., iv = '007 ton per square inch, E = 13500, and 

 m = -10. 



If ?i = S'S in. and I 1 = 60I, we have : — 



From (c) . . . . <£ = -001461 = 15 min. 2 sec, 

 „ (a). . . . M«= -091021, 



„ (ft) and (d) . t = '176 inch. 



Q , , , , ■ ,. -091021x6 17 , Q , 

 stress due to bending = = l/'oo tons per 



square inch^ 



, , , . -01 x 13500 x-176 2 Q . n . 

 „ „ stretching = — = -d49 ton 



and P er S 1- ! "-' 



Maximum tensile stress = 17*929 tons per square inch. 



By varying m and the relation between I t and I, other 

 values of t, and of stress, may be determined, and the inter- 

 relation between " stress," " plate thickness/' and the 

 " ratio of I x to I " shown graphically. 



The graphs shown in fig. 3 indicate the relation between 

 " stress " and the " ratio of I x and I " for the condition of 

 loading etc., cited above, in a plate of thickness '176 inch, 

 where curve " a " gives the maximum stress in the plate 

 due to bending, and curve " b " the maximum stress in the 

 plate due to bending and stretching combined. 



