CHAPTER IX. 

 THE TESTING OF STRUTS OR PILLARS 



149- The testing of short cylindrical specimens in 

 compression has already been described in detail. In the 



case of these, the ratio of -p '~jr. is purposely made small, 



usually not exceeding 3 : 1, or, better still, 2:1, in order 

 that failure may take place by crushing alone. Here the 

 relation between the load and the stress developed in the 

 material is a simple one : 



where / c is the compressive stress per unit area, P the 

 total load, and A the area of the cross-section. The 

 most important point to be determined from such a test 

 is the value of / c , corresponding to the elastic limit in 

 compression. 



When the length of the specimen is increased much 

 beyond the above limits, the relation between load and 

 stress becomes less simple. Imagine a compression speci- 

 men in which the length is very great relatively to the 

 diameter, say 200 to 1. If this is placed between the 

 compression plates of a testing machine, and a load 

 applied directly along its axis, common experience will 

 indicate that, when the load has reached a certain value, 

 the bar will begin to bend, and the deflection will 

 continue to increase until the extreme fibres have passed 

 their elastic limit, when collapse will rapidly ensue. 

 These cases form the two extreme limits which are found 

 to exist for compressive loading, that is, when the pillar 

 is relatively short, failure takes place by crushing alone, 

 the stresses due to bending being inappreciable ; while, in 

 the second case, where the length is very great in propor- 

 tion to the diameter, failure is due to the bending action, 

 the stress caused by the crushing being negligible. 



The actual conditions in what may be called pillars, 

 or columns, or struts, in practice, such as the struts in 

 framed structures, connecting rods, and pillars in build- 

 ings, lie between the two limits which have been indica- 

 ted. Various formulas have been devised to meet the case. 



For short pillars, the formula is 



