1903.] Stress and Strain in the Cross-section of a Beam. 13 



" On the Distribution of Stress and Strain in the Cross-section of 

 a Beam." By John Morrow, M.Sc. (Vict.), Lecturer in 

 Engineering, University College, Bristol. Communicated by 

 Professor Hele-Shaw, F.RS. Eeceived October 27, — Eead 

 November 26, 1903. 



Introduction. 



Our knowledge of the strains produced in materials by different 

 kinds and combinations of stress rests mainly on theoretical con- 

 siderations. Much accurate experimental work has been done in the 

 observation of direct tensile strains, but little attention has been 

 given to the lateral strain accompanying a simple tensile or com- 

 pressive strain, or to the lateral strain occurring in a bar under 

 bending forces. The latter, indeed, has, perhaps, never before been 

 measured in metal specimens. 



For some time past the writer has been making experiments with 

 the object of showing that instruments can be constructed capable of 

 measuring these lateral strains with considerable accuracy. The 

 subject is of great interest to the elastician, as it not only provides 

 a method of determining elastic coefficients, but shows the degree of 

 applicability of mathematical results ; and, further, in view of the 

 well-known discrepancies which exist between experiment and theory, 

 the subject is also of no small practical importance. 



The work here described is confined mainly to experiments on iron 

 beams, and has had for its objects the following : — 



1. The design of a comparatively simple instrument which can be 

 used for the accurate measurement of the lateral displacements in the 

 section of a beam ; 



2. The determination of the amount and distribution of this strain 

 in iron beams ; and 



3. The determination of Poisson's ratio from the observed lateral 

 displacements. 



Description of the Apparatus. 



Whilst making some experiments on the lateral constraction of tie- 

 bars,* it occurred to the author that, with a modified form of the 

 apparatus then used, measurements of the deformation of the section 

 of a beam might be made. 



After trials of several different forms of instrument, and various 

 ways of applying the load, it was decided that a long bar should be 

 placed in the testing machine, and the readings taken with the 

 mirror apparatus shown in fig. 1. The specimen S is in section 



* ' Phil. Mag.,' Sixth Series, vol. 6, No. 34, p. 417. 



