ON STRESS DISTRIBUTION IN ENGINEERING MATERIALS. 



473 



the result that the discrepancies in this bay were of the same order as 

 the total deflection in the second bay, and it was therefore not surprising 

 that the serious percentage difference between observed and calculated 

 results in the first bay should be transmitted to the second bay in the form 

 of discrepancies of the same order as the total deflection in the latter bay. 

 fie, therefore, limits his detailed comparisons to the first bay alone, and 

 the curves of figs. 6, 7, and 8 refer exclusively to the stresses in this bay. 



STRESS IN BAY "A" DUE TO BENDING 

 MOMENT ONLY, 35 LBS LOAD 



15709. E) 



OptLccd-Values 



CaicuicLtedVabies 



'abtjes fromCurvatim 



CX'2-72 is the Point at which 



^ when, there hs iwUnswii 



or Compress Lort in the Spar. 



Fig. 8. 



Even over this restricted range, the stresses determined by the three 

 methods disagree among themselves to a considerable extent. It is not 

 easy to see why there should be this disagreement between the values given 

 by the optical method and those given by the curvatures. The obvious 

 explanation, that the discrepancy is due to the spars having been over- 

 strained (and that this undoubtedly occurred was shown by the ' creeping ' 

 or increase of both deflection and stress with time, without the load being 

 increased, which was shown in both curvature and optical observations) 

 is, unfortunately, disposed of by the following considerations : — 



If we consider a rectangular strip under pure flexure of curvature 



Bottom 

 of Spar 



Fig. 9 (A), 



Fig. 9(B). 



1/R, the stretch at distance z from the neutral axis is z/R. Hence, the 

 stress, calculated from the curvature is Ez/R. 



Let AOB (Figs. 9 (A), 9 (B)) represent the trace of the cross-section 

 of the spar on the central vertical plane of the beam. 



