Where there is no natural rock to build the masonry into or against, enough artificial stone must be put down to balance the bridge and load.
The entire weight of the bridge and load being 4,500,000 lbs. and the whole tension, as above found, 6,642,500 lbs., or upon each tower 3,321,250 lbs.; this is the tension tending to draw the masonry out of each shaft. This tension must be reduced on account of the inclination of the pulling force. The tower is one hundred feet high. The distance on the line of tension from the top of the tower to the anchoring, as already found, is 295.2 feet; whence the actual effort to move the anchor masonry, is thus,
295.2 to 100 as 1,660,625 to the effort or 562,542 lbs. If rock weighs 160 lbs. per cubic foot, which is resisted by a column of masonry of 3,321,250/160 = 20,758 cubic feet, or 20 × 20 × 52 feet, or by a mass 15 × 15 × 91 feet.
The height of towers being one hundred feet, and the mean thickness being one fifth of the height, we have mean section 20 × 20; or top 12 × 12, and base 28 × 28.
Assuming the horizontal distances between the centres of the vertical suspenders as five feet, their lengths, then, will be found by formula
and placing for _Y^2_ the distances 5, 10, 15, 20, etc., we have, commencing at the centre,
┌───────┬──────────────┬───────────────┬───────────────┐ │Centre.│ 5 │ 10 │ 15 │ ├───────┼──────────────┼───────────────┼───────────────┤ │ 0 │5^2/500^2 × 90│10^2/500^2 × 90│15^2/500^2 × 90│ │ 0 │ .009 │ .036 │ .081 │ └───────┴──────────────┴───────────────┴───────────────┘
┌───────┬───────────────┬───────────────┬───────────────┐ │Centre.│ 20 │ 25 │ 30 │ ├───────┼───────────────┼───────────────┼───────────────┤ │ 0 │20^2/500^2 × 90│25^2/500^2 × 90│30^2/500^2 × 90│ │ 0 │ .144 │ .225 │ .360 │ └───────┴───────────────┴───────────────┴───────────────┘
┌───────┬───────────────┬───────────────┬───────────────┐ │Centre.│ 35 │ 40 │ 45 │ ├───────┼───────────────┼───────────────┼───────────────┤ │ 0 │35^2/500^2 × 90│40^2/500^2 × 90│45^2/500^2 × 90│ │ 0 │ .490 │ .576 │ .729 │ └───────┴───────────────┴───────────────┴───────────────┘
┌───────┬───────────────┬─────────────────────┐ │Centre.│ 50 │ _d_ │ ├───────┼───────────────┼─────────────────────┤ │ 0 │50^2/500^2 × 90│(_d_^2)/(_b_^2) × _a_│ │ 0 │ .900 │ _h_ │ └───────┴───────────────┴─────────────────────┘