﻿Wire or Tape including the Effect of Stiffness. 123 



(Fig. 4.) Let I be the whole length of the tapes in sag, 

 the chord being supposed horizontal, iv be the weight per unit 

 of length of the lighter tape, w' the excess weight per unit of 

 length of the heavier over the lighter, rl the fraction of 



(l-n)l 



FIG. 4. 



the whole length covered by the heavier, and nl, (1 — r)l 

 the distances from either end to the middle of the heavier 

 tape, Ri and R 2 the vertical reactions, and T the horizontal 

 component of the tension. 



Taking moments about the R 2 support, we have 



id 2 . , 7 ,. „ w -^ wl 



R 1 Z= — +ic'rl(l-r)h or R 1 = ~ +w'r(l -r)l. 



We also have the following moment equations for the 

 several sections: — 



icr 



T 0< y = R v v 5- , from x = to x — nl — \rl\ 



T y=U x x— -j-— ^(x — nl + ^rl) 2 , from x=nl — \rl to ,v = nl + \rl\ 



T a y = Ri^' ly w f rl(x~nl), from x = nl4-\rl to x = l. 



Therefore 



T ^ =B«-wx, from x = to x = (n-Ml; 

 ax 



T d f- =R 1 - wx - id' {x -nl + \r I) , from x = (n-\ r)l to x = {n + | r) 1 : 

 ax 



T ^ =R l -icx-iv'rU from x={n + \r)l to x=l. 



Therefore m. ) (' / /M 2 ; O mo .- 



T 2 1 ( -f- ) a^ = 2I -xsag correction = 



Jo \ddnJ 

 j- (R 1 -wx) 2 dx-2w' (Ri-wxXx-nl + lrridx + w'A {x-nl + .\/'/)V.i 



f 1 f' 



(»+*»■)* 



