XLVIII. J. I. HAYCROFT. 



the support added to the weight, due to the cross girder attached 

 on top, whilst the stress in the intermediate verticals will in this 

 case be compressive, but of same value as when the load is on the 

 lower flange. 



These results show that the verticals are not affected by the 

 vertical shearing stresses, properly so called. 



It now remains to find the several values of P applied at the 

 centre of each vertical in a horizontal direction : Let Fig. 7 

 represent the semi-longitudinal with its centre at the section o o : 

 divide the longitudinal by a horizontal plane through the centre 

 lines of the verticals and separate the two portions as shown : 

 the condition of stress as far as has been investigated is shown 

 on the figure : all is symmetrical with regard to the centre 

 section o o : that section has experienced neither linear or 

 angular displacement : it is taken as the line of reference, and 

 the half of the longitudinal to the left is referred to the 

 rectangular axis o x and o y as shown. Note : The value 

 of Ayj of the section at A, considered as belonging to the lower 

 portion of the longitudinal, is equal and of the same sign as Ay', 

 of the same section considered as belonging to the upper portion 

 of the longitudinal, a similar equality exists in the sections of the 

 other verticals. 



W 

 Let W\ = ~ and let P = P x + P 2 + P 3 + P 4 + P 5 



9 



A yi 



// H \ Mds 



(T - x ) E7 



E4 ^l / Qd ^ + 4 / (?- x ) 



Mds 



The section at F considered as belonging to lower half section 

 is displaced an amount = E d, due to the deformation of the 

 lower flange proceeding from the origin O towards the vertical at 



„ xl _ „, PD ' w HD 2 , -dH 2 D 



F,thusEd= _ - 10W,- + P_ 



