﻿10 Prof. L. N. G. Filon : Investigation of Stresses 



remained stationary, but, as the inclination of the nicols to 

 the horizontal diminished down to 15° and less, the breadth 

 of this band increased until finally, when the axes of the 

 nicols were horizontal and vertical, the whole field was 

 uniformly dark. This proved that the axes of stress in the 

 bar were everywhere horizontal and vertical, and consequently 

 that the shear was zero everywhere. 



These results were to be expected, since for this type of 

 strain the equations of elasticity can be solved exactly ; but 

 it nevertheless appeared that an experimental verification was 

 not without value, particularly as previous observers have 

 generally used, in order to produce bending stresses in glnss, a 

 straining- frame equivalent to doubly supporting and centrally 

 loading. 



§ 6. Bands under a Point of Concentrated Load. Theory. 



Coming now to the second part of the experiments, these 

 were intended to verify certain approximate formulae for the 

 stresses in a bar in the immediate neighbourhood of a point 

 of concentrated load. 



In a paper " On an approximate solution for the bending 

 of a beam of rectangular cross-section under any system of 

 load," Phil. Trans. A. vol. cci. pp. 63-155, the author has 

 shown (see pp. 92-94, formulae (77)-(80)) that immediately 

 below such a point, where a load W per unit breadth of the 

 bar is applied, the stresses are given by 



P=- — r cos£' + ^|'cos2<f>' 

 _4W g ,Sy cos2^_4W f ( _ ir /A>cos^' 



U= rcos 6 % cos 2d> 



irr T irr z 



+ 



-> v=o\b J 2 v +\ (2v+l)! irb 2 „ =0 V J \b J v+1 



irb 



o W . . ,, 



S= — jt sm 26' 



4- — 



irb 





where x is measured horizontally from the point of concentrated 



