Mr. Seaward on Suspension Chain Bridges. 429 



And the quantity of metal in the chains, &c., "J Tons. 

 16 X 404-816 feet X If in. round, = 186950 cubic V 22-525 



inches J 



Add one-third extra for the joints 7-508 



Add for the suspending or vertical rods .... 9-500 



Total 39^ 

 Making in the whole 39^ tons of chains and rods to support 

 the roadway, and allowing a strain of 15 tons on every square 

 inch of sectional area of the chains. 



We will now suppose another bridge to be built of pre- 

 cisely the same dimensions as the one already described ; but 

 instead of employing the catenary curve, the roadway in this 

 case to be supported by means of 20 straight diagonal rods as 

 shown in fig. 11, and let the weight of the roadway, chains, 

 adventitious load, &c., be still equal to 300 tons. Now if the 

 platform from E to F be divided into 21 equal parts, as ab, be, 

 cd, &c., and the rods cB, 6B, cB, &c., attached to the points 

 a, b, c, &c., then will each rod bear a twentieth part of the 

 300 tons, or 15 tons pressing perpendicularly. 



But the strain upon every one of the diagonal rods aB, SB, 

 &c., compared with the absolute weight ( 1 5 tons) pressing per- 

 pendicularly, will be as the co-secant of the angle aBH, 6BH, 

 &c., to radius : but the co-secant of the angle cBH is as the hy- 

 pothenuse <zB of the right-angled triangle a?«B : therefore it is 

 plain that the stress upon each of the diagonal rods will be 

 dii'eclly as the length of the rod itself, radius being equal to 

 B« = 33 feet. And as the equal parts ab, be, &c., are equal 

 each to 1 8 feet 8 inches, and Yn is equal to 4 feet ; the length 

 of the rods aB, 6B, &c., is easily found, and consequently the 

 strain also. Thus the length of «B is equal to 193-46 feet. 

 And as rad. (33 feet) : 15 tons : : co-sec. ^aBH (193-46 feet) : 

 87-93 tons, equal the strain on that rod. Now if we allow 

 7 tons only of strain upon every square inch of sectional area 

 of the diagonal rods, we shall thereby obtain the requisite di- 

 mensions for the rod, which for aB will be found equal to 

 12-56 square inches of sectional area. And if the length of 

 the rod be multiplied by the sectional area thus found, it will 

 give the quantity of metal in the rod, which in aB is equal 

 29-158 cubic inclies. 



In the same way the length, sectional area, and quantity of 

 metal in each of the other rods 6B, cB, ^/B, &c., may be ascer- 

 tained, as in the following table : 



Table 



