under endlong compression. 197 



G that fracture occurs when the stress at the outermost layer 

 exceeds 62 tons per square inch ; both of these give a rough agree- 

 ment to the experimental results, but it is worth while noting that 

 the observed points are not far from a straight line of the type 



P + aW=0, 



where a and /3 are constants. 



This formula is very similar in appearance to 



M = Py 1 +W l l , 



where M = bending moment at the centre of the strut-beam, and 

 the other symbols are as previously stated, the two formulae may 

 be reduced to identity by assuming that collapse occurs when 

 simultaneously the bending moment exceeds a certain value, and 

 when the central deflection is greater than a certain amount, both 

 amounts being independent of P and W. This also suggests that 

 the simplest way to get an approximate relation between P and 

 W is to find W when P = and to join this point to the value of 

 P when W is zero. This method should at any rate give a better 

 idea of experimental conditions than that of assuming that the 

 strut-beam collapses when the outermost layer reaches the Break- 

 ing Stress. 



3. While upon this subject it is worth noticing that for some- 

 what similar reasons the ordinary Eulerian equation for struts is 

 only an approximation. That this ideal formula fails to represent 

 fact, is mainly due to the non-homogeneity of material, and is 

 aided by want of straightness in the strut and by eccentric loading. 

 Some experiments with struts were carried out on the same 

 apparatus as that mentioned above (a larger machine being used 

 for the higher loads) with a large number of struts of different 

 lengths and with no side load applied. 



According to Euler the relation between P and I for those 

 struts should have been 



PI" = 63,400. (Formula, 1). 



For purposes of comparison a table of experimental results is 

 given and Eulerian values are also shown tabulated. Professors 

 Ayrton and Perry 1 have considered the effects of (1) non-axial 

 loading, (2) non-homogeneity of material, and (3) want of straight- 

 ness in the strut, and have justified the use of the formula (often 

 known as the Gordon formula) 



P = — C — 



1 + bl*' 



where b and c are constants. 



1 Engineer, 1886, pp. 464 and 513. 



15—2 



