Manchester Memoirs, Vol. lix. (191 5), No. %. 15 



the effect of an arbitrary movement of each support can 

 therefore be quickly investigated. 



Moments due to the endlong loadings acting through 



distances equal to the deflections of the spar from 



its initial position. 



These moments usually become of importance if 



the wires be badly adjusted or injured in such a way as 



to cause the points of attachment to lie other than in one 



straight line. An extreme case is of course presented if 



one of the inner wires happens to break during the flight 



of the machine. They may be estimated by drawing the 



deflection curve for the spar under its uniform and 



bracing wire moments, this deflection curve being the 



funicular polygon of the bending moment curve. The 



horizontal components of the pulls in the wires, viz., 



ILPd cos Q, when multiplied by the deflections as given by 



the curve will give a reasonable approximation to the 



additional bending moments, which may be added to 



those already found. 



For a full development of this method the reader is 



referred to a paper on Struts and Ties under lateral and 



non-axial loads. 2 



Conclusion. 



It will be seen that in many cases the exact determi- 

 nation of the stresses in a spar is exceedingly complex. 

 The most serious point likely to be overlooked in practice 

 is the moment due to the points of attachment not lying 

 on the neutral axis. The spar is rendered stronger and 

 the calculations simplified by arranging for the wires to 

 be connected in the correct position, but where this 

 cannot be done the graphical method given above renders 

 the determination of the additional stresses easily and 

 quickly determinable. 



- "Struts and Ties under lateral and non-axial loads." C. II. Lander, 

 / } h il. Mag . , J a n . , 1 9 1 4 . 



