The Strength of Columns. 15 



any lateral bending. These are technically termed " short 

 columns," as this kind of fracture usually occurs when the 

 ratio of the length to the least transverse dimension is not 

 particularly large. The " carrying strength" of a short 

 column — that is to say, the greatest load it will bear with- 

 out fracture — will, provided the centre of stress of each 

 cross section coincide with its centre of gravity, be found 

 by multiplying the area of the least cross section in square 

 inches by the compressive resistance of the material in 

 pounds to the square inch. If, however, the column be 

 loaded with a weight less in any given ratio than its carry- 

 ing strength, then the stress in every part of the column 

 will he diminished in the same ratio. The carrpng 

 strength of a short column and the compressive stress 

 upon any part of it under a load less in any given proportion 

 than the carrying strength, can therefore be determined with 

 ease and precision. With regard to such columns I have at 

 present nothing further to say. 



The second class includes those columns in which a lateral 

 bending precedes fracture, and of which the fracture is a 

 complex phenomenon, intermediate in its character between 

 that of beams and that of short columns. To these the 

 appellation of '' long columns" is given by writers upon the 

 subject, fracture of this kind occurring usually when the 

 ratio of length to least transverse dimension is comparatively 

 large. It will at once be evident that the question of the 

 breaking and safe working load of a long column is one of 

 comparative intricacy. 



The question of the breaking load of a long column was 

 first investigated by Euler, whose paper on the subject is to 

 be found in the Berlin Memoirs for 1747, and a resume oi 

 whose ' conclusions is given in Unwin's Machine Design, p. 

 48, &c. Unwin states that " Euler 's rules assume the elas- 

 ticity of the bar to be unimpaired. In that case no increase 

 of the load would directly cause bending, but a point is 

 reached at which the equilibrium of the bar becomes 

 unstable. With less loads, the bar, if bent, will restore 

 itself to straightness by its elastic resistance to bending ; 

 with greater loads it is unable to do so, and if any flexure 

 is produced, however slight, that flexure will be increased 

 by the action of the load until the bar breaks." 



According to this view the strength of a long column of 

 square or circular section is proved to vary directly as the 

 fourth power of its diameter, directly as the modulus of 



