392 CHAIN BRIDGE, 



The first ol these modes of failure would be 

 obviated by giving sufficient weight to the pier, 

 and thus making its friction greater than the 

 horizontal tension. Suppose the weight of the 

 pier and bridge with supports resting on the 

 pier to be z, and that friction be 4- of the 

 pressure, then -|- = 332, /, z = 1 660 tons ; a 



weight which would probably be surpassed in 

 this bridge. 



The second mode of failure might be prevented 

 as below ; suppose w be the weight of the part 

 whose section is k a h n k, g its center of 

 gravity, w^ the pressure on n from the loaded 

 bridge and pillars, L and M points in perpen- 

 diculars from G and n to the horizon, and ki 

 perpendicular to ca, then make w x kl + w' 

 X KM = force in AC x ki, or ~ horizontal force 

 X distance MC. In this respect the pier seems 

 to have more than sufficient strength. 



The third mode of failure above is avoided by 

 giving sufficient weight to the wedge, whose 

 end is bah, or by fastening it well with cramps 

 to the other parts of the masonry. 



Where there are no cramps used, let ^ be the 

 weight of the wedge, and as this weight acts 

 in the direction ha perpendicular to the horizon. 



