MECHANICAL PRINCIPLES. 10$ 



and are so generally accurate that it is seldom necessary to cal- 

 culate these values from formulae. 



For the determination of the ultimate load of columns 

 numerous formulae have been developed, predicated upon, or 

 modifications of, two original and well-known formulae, those 

 of Rankine and of Gordon. The following is 



RANKINE'S FORMULA FOR COLUMNS. 



P S 



7 = 72J where 



A= section area; 



P=load on vertical column; 



S *= maximum unit stress; 

 r = radius of gyration; 

 / = length of column; 



q = coefficient, depending upon kind of material and the 

 arrangement of the ends. (Note. Where steel is used, and both 

 ends fixed, q = l -1-25,000.) 



The Gordon Formula for Strength of Columns. Notwith- 

 standing steel made into columns has shown a working value 

 of 20% in excess of iron up to lengths of 90 radii of gyration, 

 it is only recently that this allowance was made, some mills still 

 retaining without modification the formula invented by Lewis 

 Gordon in 1840, after tests made before the British Board of 

 Trade, and which is as follows. 



ULTIMATE STRENGTH OF COLUMNS. 

 40,000 



Square bearing = - 



i + 



36,000^ 



For safe resistance : quiescent loads, as for a building, divide by 4. 

 For safe resistance: moving loads, as in bridges, divide by 5. 



