XLII. J. I. HAYCROFT. 



Let any panel be cut by a vertical section S at a distance x 

 from the nearest left-hand vertical ; the external forces applied 

 at this section can then be represented by their resultant R, and 

 their moment Mx ; the internal forces in each flange can be 

 represented by their horizontal and vertical components applied 

 at the centre of gravity of each flange, and their moment in 

 reference to the same point. Thus, in the upper flange there is 

 a horizontal force N', a vertical force T', and a moment m'. 

 Similar quantities referred to the lower flange are respectively 

 N", T", m". 



The several forces at this section being in equilibrium, the 

 following relations exist : — 



(1) N' + N" = 0. 



(2) R + T' + T" = 0. 



(3) Mx + N" H + m' + m" = 0. 



Equation (1) shows that the horizontal components are 

 equal, but of opposite signs ; either of them may be designated N. 



Equation (1) is also true when the section S is not vertical, 

 so long as its trace does not intersect the axis of a vertical 

 within the boundary lines of the girder ; thus N is constant 

 throughout the length of either flange included between the axes 

 of any two adjoining verticals. 



The above equations can be replaced by the following : — 



(2) R + T' + T" = O 



(3) Mx + N H + m' + m" = 0. 



There are here two equations and five unknowns ; the three 

 equations wanted are furnished from the conditions of deforma- 

 tion. 



Take the first panel, A K F B, Fig. 2, and consider the 

 loading on the lower flange, i.e., the cross girders are fixed to the 

 lower end of the verticals ; the reaction of the support is taken 

 as R. 



Let I t S! be respectively the moment of Inertia and area of 

 cross section of the flanges, and I 2 S 2 corresponding quantities for 

 the verticals. 



