CHAP. X.] SPECIAL CASES OF LOADING. 147 



CHAPTEE X. 



CONTINUOUS GIRDER SPECIAL CASES OF LOADING. 



98. Total uniform Load. If a span is loaded with a uni- 

 formly distributed load of p pounds per unit of length, the 

 simple moment a/rea is a pa/rdbolic segment whose vertical axis 

 passes through the centre of the span. [PI. 16, Fig. 62.] 



The ordinate D C" is ~ p P, and hence the area 



It will be advantageous here to take p X 2 as the unit of the 

 moment scale ; and therefore 



The vertical height of the cross-lines at the pole distance b 



from the middle is 2ft -. If. then, we take b = - \, we have 

 X, b 



and therefore 



OP = Q R = 3 3tt ftj* that is 



2. Moments. 



If the moments A' A" and B' B" are known, we can find 

 the end tangents of the first equilibrium polygon by drawing 

 A" B", dropping a vertical through the middle D, and laying 



off D E = 2 x \p V = \p P = \p X 2 (|y. The lines A" E 



and B" E are, then, these end tangents. "With the help of 

 these we may easily construct the parabola. 



3. Shearing force. 



If we draw in the first force polygon, lines parallel to the 



