TESTING OF STRUTS. 289 



Both ends fixed, p _ A. f 



:t K 



One end fixed and one , p _ A . f 

 rounded 4 ^ 



The values of/ and C are variable to some extent for 

 a given metal, but the following values given by Rankine 

 and others may be expected to give results which are not 

 very far wrong : 



Materials. Pounds Tons 



per sq. in. per sq. in. C 



Cast iron 8,000 35-75 T ^ 



[34,000 15-00 T^^ 



Wrought iron... \ to to to 



( 38,000 17-00 ^3 



Mild steel 67,200 30-00 ^ 



150. Johnson's Parabolic Formula. On Fig. 152 

 are plotted curves representing graphically the three 

 formulas of Euler, Rankine, and Johnson when applied 

 to wrought iron pillars. Ratios of I to k are abscissae, and 

 buckling stresses in pounds per square inch are plotted as 

 ordinates. 



For Euler 's curve, the buckling stress 



A 



E being taken as 30,000,0001bs. per square inch. 

 For Rankine's curve, 



P _ f 

 A ~ 



/, the "elastic limit" stress in compression, being taken 

 as 36,0001bs. per square inch, and C as 



The third curve is that of Professor Johnson. It is 

 parabolic in form, and is tangent to Euler's curve. The 

 general form of Johnson's formula is 



P ,_ 

 A *~ 



U2 



