54 Mr. J. H. C. Searle on the Effect of 



Similarly, 



~* Jo V" d? h d? J ?+ J, I ' fq W J /p W ) f 

 where f = — . 



"* 2 l/'df J« rffj„- 



At a clamped or pivoted end ail terms except integrals 



vanish by (10) and (11). At a free end — ,' fc f = —f^f = 0, 

 and by (12) d * "? 



P d% n df» U * 



.'. at a free end all terms except the integrals vanish. 

 Hence, 



j>* + f tt^=°- • • • (47 > 



Consider the Dotential energy of bending. 

 It is 



C l d 2 v 2 



IT? A 2 T^ 1 ' ^ d 3 ^ . r^ 4y J V 



* EA ^L^rf7,-^ v+ J^ W ' l 'J - 



But by (5), 



«^ + 



d 2 l> Q d*v 



rn -?-=■ = ?»/c 



dx* ' ^ 9 flfoW 



