ON STRESS DISTRIBUTION IN ENGINEERING MATERIALS. 471 



bending moment and shear at each cross-section to be calculated, and 

 hence the maximum tension and pressure in the spar. 



A paper published by Messrs. Cowley and Levy (' Critical Loading of 

 Struts and Structures,' R.S. Proc, Sec. A, vol. 94, pp. 405-422) gives an 

 extension of the method of Booth, Bolas, and Berry to the case where the 

 nodes are not all in one straight line, but makes the same assumption that 

 the nodes remain fixed in position when the load is applied. 



In the experiments described by Major Low, a model of a wing frame- 

 work was constructed to scale, with the top and bottom spars of xylonite 

 and the struts and cross-wires of steel. This model was then loaded by 

 suspending a set of equally spaced leaden weights from the spars (see 

 fig. 3, which shows the model loaded). Five amounts of total loading were 

 employed — 10, 20, 30, 35, and 40 lbs. weight. The stresses and deflections 

 were calcidated from the theory set forth above, in every case, save when 

 the load was 40 lbs. weight, for which load the length of the bay considered 

 exceeded Euler's limiting length for the ideal strut (Pl'l EI > tt^). It has, 

 however, been previously pointed out by Major Low himself ('Aeronautical 

 Journal, ' April 1914, p. 144) that the true criterion for instability in the case 

 of a continuous beam is given by the length of spar between two successive 

 points of inflexion lying in the same bay ; Cowley and Levy, in their 

 paper of 1918 (loc. cit.), merely state that the fact of Eider's length being 

 exceeded in any one bay does not necessarily involve elastic instability, 

 and this has been known for some time to other workers in this subject. 

 Major Low's attention was called recently to this point, and he had his 

 1914 criterion applied to the example in question,'- He then found that 

 elastic instability had been theoretically reached for his greatest total load 

 of 40 lbs., although the observations gave no evidence of any abrupt 

 change of type in the equilibrium configuration. It has to be remembered, 

 however, that in the experiments referred to the elastic-limit was passed 

 before this value of the load was reached. The theory was then tested 

 in two distinct ways : — (1) by measuring the actual deflections of the 

 central line, calculating from these the curvatures and obtaining from the 

 latter the bending moments and the stresses, (2) by direct observation of 

 the stress, using the optical metliod described in the B.A. Report, 1914.^ 



The results are shown in Figs. 4-8, which are taken from Major Low's 

 paper. The curves giving the calculated and observed deflections show 

 significant discrepancies, especially for the higher loads. These dis- 

 crepancies become strUcing when the deflection is measured from the line 

 joining the nodes instead of from the horizontal. If this is done, the 

 maximum deflection in the second bay is actually of opposite sign for the 

 observed and calculated cases. Major Low suggests, on p. 31 of the paper 

 referred to, that this is probably due to the fact that the inner bay of the 

 upper spar was more severely strained and stressed than any other, with 



^ The criterion then becomes identical with that for elastic instability of a single 

 strut, under uniform transverse load, whose terminal points coincide with the points 

 of inflexion. It has been shown by Professor Perry (Phil. Mag. March 1892) and by 

 Arthur Morley {PJnl. Mag. .Tune 1008) that for such a strut Euler's formula gives the 

 condition of instability. 



" ' Experimental Determination of the Distribution of Stress and Strain.' By' 

 Professors Filon and Coker, B.A. Report, 1914, pp. 201-210. 



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