272 Prof. J. Perry on Struts and 



The curvature being always small is + -A, and we take the 



+ or — sign according to the sign given to bending-moment, 

 and hence we have generally for struts 



or 



and for tie-rods we have merely to write — F x instead of F. 



I shall assume for the present that EI is constant every- 

 where. 



Now <f>{x) can always be developed in a Fourier's series. 

 But it will sometimes be found convenient to express it in the 

 form 



<p [x) = a + rx + tx 2 + % cos sx + bi sin sx + 



a 2 cos 2sx + b 2 sin 2s# + &c. + a,- cos is# + h sin 2s# + &c, 

 where s = ^. 



Terms in «# 3 , ^ 4 , &c, may easily be taken also. 

 We may put this symbolically as 



$ i x ) = a o + TX + tx 2 + (a { , b { , is) . ... (6) 



Whatever ^ may be, we may express it symbolically as 



y f = a +(a i ,pi,is) (7) 



Hence (5) may be written : — 

 For struts : 



<te»- EI* - EI + 2EI EIV 2Z / 



-M^-^+M'^'^+El' ") ; • • (8) 



and for tie-rods we have the same equation, if — Fi be sub- 

 stituted for F. 



TT 

 Now if n 2 be written instead of ^^ i n the case of a strut, 



F x . JL1 



and instead of ^ in the case of a tie-rod, we have the fol- 

 lowing solutions. 



