"LE PONT VIERENDEEL." XLIIL 



It should be observed that no hypothesis is made as to the 

 invariability or articulation of the corners of the panel, which is 

 taken as constructed, continuous at the angles. 



The axis of the vertical B F, before deformation, is taken as 

 a reference line (during the following investigation, where 

 co-ordinate axes are required, the vertical axes cf the verticals are 

 taken as the axis of x, and the horizontal lines through the centre 

 of gravity of the flanges as the axis of Y. 



The lower flange is inclined to the horizontal at B by an 

 angle a lf due to the deformation of the longitudinal under the 

 influence of loading between the right-hand support and the 

 vertical B F. As the flanges are supposed to be identical, the 

 upper flange is also inclined at angle a : . Further, the point B, 

 that is, the intersection of the axis of B F with the axis of the 

 lower flange, advances through a distance a', to the left due to- 

 the lengthening of the lower flange, and the corresponding F 

 recedes to the right by a similar amount, due to the compression 

 of the upper flange. Now, suppose the end vertical A K cut 

 horizontally at its middle point and the two semi-panels slightly 

 separated, as shown at G, Fig. 3. 



The interior forces at the section G are q vertical, P horizontal 

 and a moment m. Now refer the panel to co-ordinate axes and 

 let AXj, Ay x be the linear displacements of the centre of gravity 

 of G, and a 2 its angular variation as belonging to the lower semi- 

 panel. Ax}, Ay}, a,\ are the corresponding quantities for the upper 

 semi-panel. 



These six quantities give three equations, thus : — 



(4) A X] = - A x } 



(5) a 2 = - a.\ 



(6) Ay 1= Ay| 



With the aid of these equations the values of P q and m can 

 be found, thus : — 



aiD+ X^ x+ X (D 



: ) ^j 



