THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



DECEMBER 1891 



LX. The Influence of Surface- Loading on the Flexure of 

 Beams. By Prof. C. A. Carus Wilson*. 



[Plate n.] 



rpHE practical treatment of the problem of beam-flexure at 

 J- the present time is based on the hypothesis enunciated 

 by Bernoulli and Eulerf, that the bending-moment is pro- 

 portional to the curvature. 



This assumes that the cross sections remain plane after 

 flexure and neglects the surface-loading effect. 



Saint- Venant has shown % that the first assumption is 

 untenable ; but that, neglecting the surface-loading, Ber- 

 noulli s results are strictly true for one particular case of 

 loading, that, namely, of a beam doubly supported and carry- 

 ing a single isolated load, where, although the cross sections 

 are distorted, the central displacement is zero. 



I propose in this paper to describe some experiments made 

 with a view to determining the actual state of strain in a 

 beam doubly supported and centrally loaded, the surface- 

 loading effect being taken into account. 



The method of investigation adopted is based upon the 

 following assumptions : — 



x. Q* T j h ? trUG State ° f Strain at the centre of the beam ma Y 

 be found by superposing on the state of strain due to bending 



only, that due to surface-loading without bending. 



* Communicated by the Physical Society : read June 26, 1891. 

 T lodhunter and Pearson's < History of Elasticity,' vol. i. 

 X Pearson s 'Elastical Researches of Saint- Venant ' 

 Phil. Mag. S. 5. Vol. 32. No. 199. Dec. 1891. 2 K 



