(53) 



COLUMNS AND STRUTS 

 P I 



109 



or, iii the notation of the preceding article, 



== v - 



in which v and a- are empirical constants, this being the equation of 

 a straight line tangent to Euler's curve. This formula has the merit 

 of great simplicity, the only objection to it being that for short 

 columns it gives a value of P in excess of the actual breaking load. 

 The relation of this formula to those which precede is shown in 

 Fig. 82. 



The constants v and a- in formula (53) are connected by the relation 



where for fixed ends n = 1, for free ends n 4, and for one end fixed 

 and the other free n = 1.78. 



The table on page 110 gives the special forms assumed by John- 

 son's straight-line formula for various materials and methods of end 

 support.* 



The limit for use in this case is the value of x I = - ) for the point 

 at which Johnson's straight line becomes 

 tangent t Killer's cu r 1 "" 



Problem 107. Compute the ultimate strength of 



the column in Problem 104 by Hankine's and John- 



raiu'ht-line formulas, and compare the results. 



Problem 108. A column IK ft. long is formed by 

 joining the legs of two Carnegie steel channels, No.C8, 

 weighing 801b./ft., by two plates -a<-h 1<> in. wide 

 and | in. thick, as shown in Fig. H:5. Find the safe 

 load for this column by Johnson's straight-line for- 

 mula, usinu r a factor of safety of 4. 



Problem 109. A wrought-iron pipe 10 ft. long, 

 and of internal and external diameter 3 in. and 

 4 in. respectively, bears a load of 7 tons. What is the factor of safety? 



FIG. 83 



Trans. Amer. Soc. Civ. Eng., 1886, p. 530. 



