EXPERIMENTS WITH BUILT-UP COLUMNS. 637 



For several years past, and especially since the collapse of the 

 Quebec Bridge, scores of formulae for columns have been brought 

 forward, and much excellent experimental work has been done. 

 The researches of Lilley, Burr, Buchanan and of Talbot and Moore 

 on steel struts has supplemented what Hodgkinson did with cast- 

 iron and Christie with wrought iron. Lilley's work has thrown 

 much light on the subject of secondary flexure, mainly in the case 

 of hollow cylinders. Buchanan has given the results of actual 

 tests to destruction of full-sized bridge struts. Burr tested a large 

 model of the strut whose failure wrecked the Quebec Bridge. 

 Talbot's and Moore's researches are especially valuable, inasmuch 

 as they show how unexpectedly and how seriously stresses vary 

 from place to place in a column. They applied numerous extenso- 

 meters to longitudinal and lacing members of actual bridge struts 

 and deduced the corresponding stresses. A very important finding 

 of theirs was that the actual stresses were very much greater than 

 the measured deflections would account for. They ascertained 

 that, in the particular columns which they tested, the maximum 

 stresses in the lacing bars were such as would be produced by 

 transverse loads varying from 2 to 6 per cent, of the central com- 

 pressive load. 



Painstaking work has been done by Moncrieff, who analysed 

 the experiments of others in the endeavour to find what deflection 

 it would be safe to assume for the calculation of bending moments 

 and shearing forces. 



The well-known formulae of Rankine, Gordon and Euler, as 

 well as the straight-line formula, so popular in America, have been 

 examined and criticised by numerous writers to the technical press. 

 One writer points out that, if Rankine's formula be put in a certain 

 form, it will be found to be based upon a certain assumed eccen- 



tricity of loading, this eccentricity varying as ^ where 1 is the 



length of the column and h its least transverse, dimension. Again, 

 if the straight -line formula be looked at in a similar manner, it also 

 wiU be found to be based upon an assumed eccentricity, the eccen- 

 tricity in this case, however, varying as the length of the column 

 simply. 



Claxton Fidler bases his formula upon the assumption that the 

 modulus of elasticity of the material on one side of a column differs 

 from that on the other side by an amount equal to the greatest 

 known difference in the values of the said modulus ; in other words, 

 he goes back and deals with the causes of the deflections which 

 others assume. 



Keelhoff derives a formula by calculating the bending moment 

 and shear corresponding to an indefinitely small deflection. 



A number of investigators appear to apply Euler's method of 

 reasoning to determine a critical load, which corresponds to any 

 deflection, and then proceed in a way which is tantamount to 

 giving the said indefinite deflection a definite value. 



