\fdO'^ - Old Forge Coal Mines

RAILROAD CONSTRUCTION. 287
120 = 12,231 pounds. Multiplying this weight by -/ / =
8.56 feet, we have 12,221 X 8.50= 104,612 pounds, which,
divided by o d, 16 feet, = 6,538 pounds = the pressure of
the backing. This pressure to a scale of 4,000 pounds to
the inch equals 1.63 inches. P, the center of pressure,
is at ^ of the height of b d measured from d. At P erect a
perpendicular to the back of the wall. Lay off on this perpendicular
the distance /*//= 1.63 in. Draw /*/, making
the angle ;//*/= 33° 41' = the angle of wall friction. At //
draw a perpendicular to P n^ intersecting the line P t \n h.
Draw h k, completing the parallelogram ;/ h k P\ h n, or its
equal k J\ will represent the friction of the backing against
the wall and the diagonal h P, which, to the same scale, =
7,857 pounds, will be the resultant of the pressure of the
backing and the friction. Produce P // to 5. The section
a b d c oi the wall is a trapezoid. Its area is 84 square feet,
which, multiplied by 154 pounds, the weight of rubble per
cubic foot, gives 12,936 pounds, as the weight of the wall,
which, to a scale of 4,000 pounds to the inch, = 3.23 inches.
Find the center of gravity g of the section a b d c, diS explained
in Art. 1488. Through g draw the vertical line
g ty intersecting the prolongation of P h in /. Lay off from
/, on g i, the distance / z\ 3.23 inches = weight of the wall,
and on Is, the distance I in = 1.96 inches, the length of the
resultant P h\ complete the parallelogram I in u v. The diagonal
/ u is the resultant of the weight of the wall and the
pressure. The distance c r from the toe c to the point where
the resultant / u cuts this base is 3.6 feet, or nearly \ of the
base c d. This guarantees abundant stability to the retaining
wall.
The distance o f\s obtained as follows : c d=S feet ; bat-
ter of c a = 1 inch for each foot of length of ^ ^= 16 inches;
hence, a o = S feet — 16 inches = 6 feet 8 inches; a b =
2. 5 feet; therefore, ^/= 12.73 — (6 feet 8 inches — 2. 5 feet) =
8 56 feet.
(862)
See Art. 1491.
(863) See Art. 1491 and Figs. 409, 410, and 411