COLUMNS AND STRUTS 



101 



The limit for use in each case is the value of x(= - j for the point 



at which Johnson's straight line becomes tangent to Euler's curve. 

 59. Cooper's modification of Johnson's straight-line formula. In 

 his standard bridge specifications Theodore Cooper has adopted 

 Johnson's straight-line formulas, modifying them by the introduc- 

 tion of a factor of safety. Thus, for medium steel, Cooper specifies 

 that the following formulas shall be used in calculating the safe 

 load. For chords 



(133) 

 For posts 



(134) 



- = 8,000 - 30 - for live-load stresses, 

 " . 



p i 



- = 16,000 60- for dead-load stresses. 

 A t 



P I 



= 7,000 40- for live-load stresses, 



A t 



- = 14,000 - 80 - for dead-load stresses, 



-A. t 



P I 



-7 = 1 0,000 60- for wind stresses. 

 A t 



For lateral struts 

 (135) 



P I 



= 9,000 50 - for initial stresses. 



By initial stress in the last formula is meant the stress due to 

 the adjustment of the bridge members during construction. 



60. Eccentrically loaded columns. In a column that carries an 

 eccentric load (for example, a column carrying a load on a bracket 

 or the post of a crane) there is a definite amount of bending stress 

 due to the eccentricity of the load in addition to the column stress. 

 As the nature of column stress is such that it is impossible to de- 

 termine its amount, the simplest method of handling a problem of 

 this kind is to determine its relative security against failure as a 

 column and failure by bending. That is to say, first determine its 

 factor of safety against failure as a column under the given column 

 load. Then consider it as a beam and find the equivalent bending 



