Art. 115. COMBINATIONS OF BUCKLING AND BENDING. 193 



Terms higher than those given are negligible in practical 

 examples. Now 



61 



_5wLV 120* 2 \ * TFLW 

 H58T7V 120 / 384 P\ 



It will be noted that the first term of tlrs expression for 

 the maximum deflection is equal to the deflection when the trans- 

 verse load only is acting, and 'the second term is the additional 

 deflection due to the addition of P. The second term is usually 

 small compared with the first, and may be neglected in order to 

 simplify the practical applications of the equation. A further 

 simplification may be made by .substituting i/gWLJ/t maxi- 

 mum moment due to transver.se load. 



(65) 



= approximately 



Substituting the value of ?/ 



(6G) 



The law of super-position of stresses holds when the last 

 term is negligible. < 



Equation (66) is best solved by trial. A numerical example 

 will illustrate the application of the above equations and the 

 effect of the approximations. 



Assume a column of 2 channels 15 in.X33 lbs.X360 in. long; 

 10=12% Ibs. per inch; 7=625; A=19.8 sq. in. #=30,000,000. 

 P=180,000 Ibs. 1F=4,500 Ibs. 



M t =y s 'WIr=% 4,500X360=202,500 in. Ibs. 



180.000 



El 30,000,000 X625 

 02^0.0000096 



1/ 2 0L=0.0031X180=0.558=32.0 

 P L 2 _ 180,000X360X360 

 EI~ 30,000,000X625 



=0.0031 



=-1.245 



