Strength of the Thin- plate Bea\ 



34i> 



&c. — existent at the ends of the beam. It may, however, 

 be determined indirectly in a fairly simple manner by the 

 aid of nothing more than the differential equation of the 

 second order, and the object of this thesis is to indicate 

 the method of attack. 



Consider a strip of plate, of unit width and thickness t? 

 constituting a beam of length rt\ = 2a, and subject to a 

 uniformly distributed load w per unit length due to a head 

 of water h. 



Take the axis of X at the mid-surface of the plate, i. e., in 

 a plane distant t/2 from the supporting surfaces, o — the 

 centre of the unsupported span — as origin, and the axis- 

 of Y downwards. 



Tiie appearance of the beam is shown diagrammatical! j 

 in fig. 2. 



Fij?. 2. 



DzaxfrcLTTL - sJieuz-Cn-j Disjaos-ziton of Fortes _ 

 ^ \ actinjj an iea.7n. JtUyeot- to vjUformly discnbtrfiaci 



The solution is obtained by dividing the problem into two 

 parts, viz. : — 



First. Assume the beam, under the action of a uniformly 

 distributed load w per unit length (Q being removed), subject 

 to a horizontal pull P and retaining its horizon tality at the 

 ends d and d 1 (fig. 3). 



Fis. 3. 



Load ZP only 

 ( Q rc77Wi'ed,) 



Second. Take the beam under the action of a concentrated 



