

Manchester Memoirs, Vol. lix. (191 5), No. 2. 13 



By inspection of the complete diagram the justifi- 

 cation of our statement that by producing the supporting 

 wires to cut the neutral axis, and considering this as 

 equivalent to the original system so far as reactions were 

 concerned, it is more apparent. Although the neglected 

 moments are large in magnitude, they only extend over 

 very short lengths of the beam, and so their effect on the 

 reactions, which is due to the moments of area of their 

 diagrams, is small, thus the portion neglected at C is 

 shown approximately by the triangular diagram nmx 

 {Fig. 6) and in comparison with the area of the diagram 

 caused by the approximately horizontal components of 

 the force in the wire is of small account when finding 

 reactions. The excess moments involved at the supports 

 are of course extremely important in themselves, since 

 they increase and decrease rapidly. From the diagram 

 it is also apparent how by attaching the wires even a 

 short distance below the neutral axis, large bending 

 moments are set up. In the case outlined above, which 

 is representative of ordinary practice, the moment at C is 

 increased from 55 ft. lbs. when the wires are attached 

 centrally {Figs. 1 and 2) to 99 ft. lbs. when the eccentricity 

 amounts only to 2 ins., or in other words the moment at 

 C is increased by 80 per cent. 



In a number of monoplanes the maximum bending 

 moment occurs at B owing to the length of the cantilever 

 portion. It does not follow, however, that the maximum 

 stress will occur at this point since the greatest direct 

 compressive force in the spar is that induced in the 

 inward spar, and the total stress is that due to the com- 

 bined action of the bending moment and the direct 

 compression. In the design of a spar, however, it is 

 advisable to bear in mind that a large overhang at the 

 outer end will usually increase the maximum bending 



