Van Nostrand's eclectic engineering magazine . a constant. Let Px = c* (a constant). Then P»=cwyo and c /Px Vi From the discussion of Case Y. we seethat n must be the ratio of the axes of theellipse to which the pressures are respec-tively parallel. Hence if the arch be asemi-ellipse and 0 B bo given, we have OBOA 0A = OR From these data draw the curve of thesoffit. The thrust along the soffit at A = ,pQ. At 0 or B it is T =px9i. At other points it may be gotten from eq.(27) Caife Y. We can determine the curve of pressuresby a method similar to that used in the lastcase. Here, howev
Van Nostrand's eclectic engineering magazine . a constant. Let Px = c* (a constant). Then P»=cwyo and c /Px Vi From the discussion of Case Y. we seethat n must be the ratio of the axes of theellipse to which the pressures are respec-tively parallel. Hence if the arch be asemi-ellipse and 0 B bo given, we have OBOA 0A = OR From these data draw the curve of thesoffit. The thrust along the soffit at A = ,pQ. At 0 or B it is T =px9i. At other points it may be gotten from eq.(27) Caife Y. We can determine the curve of pressuresby a method similar to that used in the lastcase. Here, however, the curve K K willnot be parallel to C A, since the thrustsalong C A are not constant, but increasefrom A to 0. Assume A K (Fig. 44)= I A L, then the arch must be so propor-tioned that K K shall fall within the mid-dle third. If the arch C A B is not to be a semi-ellipse (as above assumed) but only a seg-ment of one, a few trials will enable us toget the ellipse from the data alreadygiven. The strictly true curve of equilibrium Fig. required by earth pressure is the Geostaticarch. 6. An arch built with the curve discussedin Case VI., is known as the Hydrostaticarch, from the fact that the loadmg theredescribed is similar to the pressure of waterupon a vertical arch. For if MY (Fig. 45) be the surface ofthe water, then its pressure on C A B isnormal and proportioned at each point tothe depth below MY. This pressure, as has been shown, may be resolved into avertical and horizontal pressure at eachpoint, this vertical and horizontal pressurebeing equal in intensity 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
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