6 LANDER, Stresses in the Main Spars of Monoplanes. 



for all the wires is approximately equal to the total load 

 on the spar but the exact magnitude of which is influenced 

 by the shape and area of the diagram of bending moments, 

 the other along a line joining the point of attachment 

 to the point where the neutral axis of the spar cuts the 

 fuselage of the machine. These second components 

 produce bending moments which vary uniformly in mag- 

 nitude from Pd cos 6 at the point of attachment to zero 

 at the fuselage. The diagram of bending moment caused 

 thereby on any span is thus of trapezium or triangular 

 form. 



Let Fig. $a represent a spar of this type and let 

 P 1 P a P s represent the forces induced in the wires attached 

 to the spar at points FGH respectively. These points 

 lying at a distance d below the neutral axis. If P 1 be 

 resolved along a line perpendicular to BE and along a 

 line FE, then the perpendicular component of P k will 

 represent the vertical reaction at the point B. The force 

 along FE will induce moments in the spar which will vary 

 in magnitude uniformly from B to E being zero at this 

 latter point. Similarly P 2 and P s will produce vertical 

 reactions at C and D respectively and induce moments 

 which vary uniformly from C to E and from D to E 

 respectively, being zero at this latter point. 



The bending moment diagram caused by these 

 approximately horizontal components will be as shown in 

 Fig. 4, but this diagram cannot y et be accurately drawn, 

 since PJPJ*^ are still unknown. 



In order to find the magnitudes of P P 9 P t and so 

 enable the bending moment diagram for the approxi- 

 mately horizontal components to be drawn, it is necessary 

 to make certain approximations, which are, however, 

 usually so close to the truth as to render them well 

 within the limit of error allowable on work of this des- 



