Van Nostrand's eclectic engineering magazine . ntensity to each other atevery point, and also to the normal pressureof which they are the components. The above form of arch may be appliedin two cases. (1) To bear the pressure of water or otherliquid. Thus in the case of a river tunnel(such as those at Chicago) where the top of THEORY OF ARCHES. 387 the tunnel is practically on a level with thebottom of the river, we might use the hy-drostatic arch. The equation of the curve is The vertical load on the half-arch A B~J ^i ^^^ — ^=^^^iPi= thrust along arch at horizontal pressure against A B
Van Nostrand's eclectic engineering magazine . ntensity to each other atevery point, and also to the normal pressureof which they are the components. The above form of arch may be appliedin two cases. (1) To bear the pressure of water or otherliquid. Thus in the case of a river tunnel(such as those at Chicago) where the top of THEORY OF ARCHES. 387 the tunnel is practically on a level with thebottom of the river, we might use the hy-drostatic arch. The equation of the curve is The vertical load on the half-arch A B~J ^i ^^^ — ^=^^^iPi= thrust along arch at horizontal pressure against A B y in • :^-Vo^ =/llp^y = ^ ^ =R = wyoPo. (51)The thrust along the arch is constant, orT = H = V. The rise AO (= a), the depth AY(=yu), and the radii at A and B (po and p )are connected by the following approximateequations. The co-ordinates of B being x^and yi, let b = Xi-i- 30 a Then Vo PO = ^- t _ 2/n* 2yo = a + (52)(53) Pi The line of pressures in a hydrostatic arch,since T is constant, is parallel to tlte soffit,as in circular I^ximple.—Suppose the span to be 50 ft. soffit—the radius at any other point besides (Fig. 46) and the depth A Y = 16 ft. Fmd first the rise A 0. In Eq. (52)x^ = 25 yo = 16, and a few trials showthat a — rise = 20 about. Hence Po = 32| ft. and p, = these data describe the curve of the A and B being given by the equation VoPo The thrust at A = H = wy^ = lbs. •. H = 32448 lbs. Here
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