1835.] 



and Drop -bars of Suspension Bridges. 



■22o 



bars, or the spaces which each link of the chain occupies in the span 

 of the bridge. If therefore the sum of these cosines, multiplied by the 

 radius b, be deducted from the span of the bridge, the difference will 

 be the length of the horizontal space occupied by the two upper links; 

 and half of this space, multiplied by the secant of a, will be the length 

 of one of those links. The sum of all the links will be the length of 

 the chain. The sum of the differences of the drop-bars, added to the 

 deflection of the upper link, will be the total deflection of the chain. The 

 roadway may be made to rise with a fair curve, by making the rise 

 bear a certain proportion to the fall or deflexion of the chain. 



The sum of the deflexion of the chain, the length of the centre drop- 

 bar, and the rise of the road, will be the height of the point of suspen- 

 sion at the standard. 



Example. 



a = 15° === angle of suspension. 



b 3= 5 feet = length of each link. 



d = 17 = number of drop-bars. 



98.625 = distance between the points of suspension. 



3.5 feet = length of centre drop-bars. 



The rise of the road = T the deflection of the chain. 



Tan. a =.2679492 



2 Tan, a 

 d 



.535898 

 17 



■-=.0315234. 



Upper 1st link, 

 1st drop-bar, ..... 



2nd 



2nd, 



3rd, 



3rd, 



4th, 



4th, 



5th 



5th 



6th 



6th, 



7th, 



7th, 



8th, , 



8th, , 



9th , 



Centre drop-bar, , , 



2 



Tang, of 

 deflection 



3 



Cosines 

 of deflec- 

 tion. 



4 



Sines 

 of de- 

 flection 



5 



Differ, 

 of drop- 

 bars in ft. 



6 



Rise of 



Roadway. 



.2679492 





.2588 



2-5418 



.5083 



.2364258 



.9731 



.2301 



1-1505 



.2301 



.2049024 



.9796 



.2007 



1-0035 



.2007 



.1733790 



.9853 



.1708 



.8540 



.1708 



.1418555 



.9901 



.1404 



.7020 



.1404 



.1103321 



.9939 



.1096 



.5480 



.1096 



.0788087 



.9969 



.0785 



.3925 



.0785 



.0472853 



.9988 



.0472 



.2360 



.0472 



.0157618 



.9998 



.0157 



.0785 



.0157 



Length of 

 drop- 

 bars. 



9.4580 

 8.0774 

 6.8732 

 5.8484 

 5.0060 

 4.3484 

 3.8774 

 3.5942 

 3.5000 



7.9175 =: sum of the cosines multiplied by 



39.5875 = horizl. dist. between drop.bars. 

 49.3125 sd i span. 



9.5250 ZZ difference. 



