﻿Wire or Jape including the Effect of Stiffness. 103 

 i 

 and 



'ic 



1 



W 



t*a r" Z&'Sinnaa Z 2 sinh 2 a# j 

 o I dnh| " 4sinh*j| 



P 



Ix cosh a.r / sinh nx Z 2 sinh 2a# £ 2 



H ^ + 



-^ - , ^2 



[> 3/ 2 j_ Z 3 ") 

 24 ft , ,a/ + a 2 _ . , 2 aH ( 8 ) 

 oatanh^ losintr — 



The third term can be neglected in comparison with the 

 second and the fourth is quite inappreciable, so that in this 

 case the correction for stiffness is 



3w 2 / 2 Z(wU 2 /Ei 



8T 2 a " 8 



3 / T 



This is g l\/ TfTf times the correction for free ends, and in 



+ l i -j i • 3x7920x3-11 



the example considered is 5 = 9237 times as 



o 



great =0*012 inch in the 10 chains, a quantity which would 



be worth considering in base-line measurement, though it 



would not be likely of course that such a large bay as 10 



chains in sag would occur in such an operation. 



Writing x= ^ — x' in the expression for -^, it reduces to 



dy __ iv fl , I "1 

 tx~%[2~ X ~~JeT*' y 



so that when x r =0 at the support, the effect of the stiffness 



wl 

 is equal to ^- =9° 9 ; in the example. To find the bending- 



moment at the support we have 

 M=EI^ 



''ifl- "I rU-fl*) „o„rlv, 



ivl . 



= - practically, 



