14 



H. T. EOVEY ON THE STRENGTH OF 



Table III. 



TRANSVERSE STRENGTH OP RED PINE. 



In the preceding tables the vakies of the skin-stress (/) and the coefficient of elasticity 

 (^,) have been determined by means of the following formulae : 



(W \ 2 



E.= 



1 Ajf P_ 

 4: A-0 bcP' 



b, d, I being the breadth, depth and length between the centres of support of the beam, Wi 

 the weight of the beam, W., the load upon the beam which causes fracture, and A D the 

 increment of deflection corresponding to the increment A TV of the load. 



This last formula may be thus obtained : 



The deflection D for any load W is given by the equation, 



J>: 



P 



(gPF.+ ^F,) 



4 E bd 

 and the deflection Z) + A Z> for a load IF + A W by the equation, 



Hence 



D+ ^D = 

 A i) = 



and therefore E = 



4E bd' 



P 

 4E bd' 



1 l\W P 

 é AB bd^' 



AfV 



In order to find the direct tensile coefficient of elasticity of the timber, special specimens 

 were prepared about -75 square inch in section, and the extension observed under a direct 

 stress. 



