288 TESTING OF STRUTS. 



which, written otherwise, becomes 



which is Rankine's formula, / being the elastic limit 

 stress in compression for the material in question. 



Here the constant C only depends on the / and E of the 

 material. In Gordon's formula, which is similar in form, 

 the smallest diameter, d , takes the place of k, the constant 

 varying with the section as well as the material. 



It is as follows, the notation being the same as before, 

 except that d is the least diameter of the column : 



l + a(4 



Bovey* gives the values of/ in this formula as 80,000 

 for cast iron, 36,000 for wrought iron, 67,200 for mild 

 steel, and 114,0001bs. per square inch for hard steel ; and 

 the values of the constant a : 



Kind of Section. Cast Iron. W I 'Jf ht Mild Steel. ]*f 



Solid Rectangular -^ 



,, Round -ffa H^TG rrb-TT T$TJ 



Hollow Rectangular ... ^j 



Round J&Q 5^ ^^ 3-5^ 



In Gordon's and Rankine's formulas I is the length of 

 the pillar between the supports. If L is the length of a 

 pillar with rounded or free ends, and I is the length of a 

 pillar of similar material and section, but fixed at both 

 ends, then for the two buckle under the same load 



/ = 2L ; 



and for the case of a pillar fixed at one end only and 

 rounded at the other, 



1= -L 



These relations will be clear from an inspection of Figs. 

 147, 148, and 149. Rankine's formula for the three cases 

 then becoming : 



Both ends rounded, _ A. f 



* Bovey, "Strength of Materials." 



