Handbook of Railroad Construction; For the use of American engineers. / Containing the necessary rules, tables, and formulæ for the location, construction, equipment, and management of railroads, as built in the United States.

by George L. Vose

Let A B 6 F, represent the thickness of the wall. Its centre of gravity is at O, and is horizontally projected at m. The centre of gravity of the thrusting triangle of earth, B 4 6, is C, (found by the cutting of lines joining any two angles to the centre of the opposite sides,) is horizontally projected at C^a, and the horizontal component of the thrust is exerted at 2, tending to overthrow the wall with a leverage, 6 2.

Fig. 133.

The overthrowing power is, then, the area of the triangle B46 × the weight of the unit of area × the leverage 6 2. And the resisting power, the area AB × B6 × the weight of a unit of area by one half breadth, or m 6; or, calling w the weight of the wall, and w′ that of the triangle, B 4 6, and L and L′ the leverage respectively of the wall to resist and of the earth to overthrow; we must have at least

wL = w′L′,

and to insure stability,

wL > w′L′

or,

L = w′L′
w,

and as L = half base finally, the thickness, or