COMPRESSION AND CROSS BENDING 145 



and reducing, the stress due to cross bending is 



M v y^ 



A = -- Pl*~ (73) 



'7*- 



where the minus sign is to be used when P is compression and the plus 

 sign is to be used when P is tension. 



The factor c may be taken equal to 10 for columns, beams and bars 

 with hinged ends as in Fig. 77; equal to 24 where one end is hinged 

 and the other end is fixed ; and equal to 32 where both ends are fixed. 



The total stress in the member due to direct stress and cross bend- 

 ing will therefore be for columns with hinged ends 



*~A (74) 



Formula (74) is general, and applies to all forms of sections and 

 all forms of loading. The second term in the denominator is minus 

 when P is compression, and plus when P is tension. 



In finding the stress due to weight of member and direct loading, 

 the value for /^ given by formula (73) must be multiplied by the sine 

 of the angle that the member makes with a vertical line. 



Combined Compression and Cross Bending. The method of 

 calculating direct and cross bending stresses will be illustrated by cal- 

 culating the stresses in the end post of a bridge due to direct compres- 

 sion, weight, eccentricity of loading, and wind moment. 



The end post is composed of two io-inch channels weighing 15 

 Ibs. per foot with a 14" x J^" plate riveted on the upper side and laced 

 on the lower side with single lacing. The pins are placed 

 in the center of the channels giving an eccentricity of e = 1.44 inches. 

 The compressive stress P produces a uniform compression on all fibres 

 of the section ;weight of the member causes tension on the lower and com- 

 pression on the upper fibres ; eccentricity of the load P causes compres- 

 sion on lower and tension on upper fibres ; and wind moment causes com- 



