CONTINUOUS GIRDER. [CHAP. EC 



the moments M' M" for the loaded span are always posi- 

 tive.* If we draw the lines M N and U V cutting the middle 



vertical inP and Q, then, for I = -I, P O= 1 (M' -(- M") and 



3 2 



PQ = 2 (3K' + 2H"). (SeeArts.89,90.) Since now the points 



U and V must lie under A B, 



P O < P Q' or M' + M" < Wl'+ 2fl". 



If the supports are not upon a level, it follows from this Art. 

 and Art. 92, that the intersections of S U and S V prolonged, 

 with the prolongations of the lines A A' B B', joining the sup- 

 ports of two adjacent spans, lie in the VERTICALS THROUGH THE 

 FIXED POINTS. 



96. Two successive Loaded Spans. PL 15, Fig. 59. 



1. Here also, as in Art. 92, we can prove that the prolonga- 

 tions ofSV and S x U^ intersect in the limited third vertical. 



2. Draw through B a line which -intersects S V and S x U^ in 

 T and I\, and the verticals through V, W and U t in V , W 

 and U . 



Then 



U U t : V V : : U B : V B : ; 1 : ^ 



v v : w w ; : r v : r w . 



Hence by composition 



U Ux : W W : I' V x 1 : I' W x IL ; 

 or since U 1^ : W W : U I\ : W 1\ 



U 1\ : W,,!/ : r V x 1 : T W x ^ 



If, then, the point I' moves in a vertical, the ratio I' V to 

 I' W does not change, therefore the ratio of U 1/ to W 1/ also 

 remains unchanged, and accordingly I\ must also move in a 

 vertical. If I' coincides with I, it follows from the construction 

 of Art. 93 that the point I\ becomes the fixed point I t . Hence, 

 the intersections T and I\ of verticals through the fixed points 

 I and I t with the sides S V and St U t , or with the middle 

 sides of the two polygons adjacent to the support, lie always 

 in a straight line through that support, for any heights of 

 supports. 



* A positive moment always indicates compression in lower flange. 



