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Loads for Masonry Arches 157

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LOADS FOR MASONRY ARCHES 157. Live Loads for Highway Bridges.—For the floors of open spandrel arch bridges, live loads should be considered in the same manner as for slab bridges (see Art. In investigations of arch rings, live loads ore usually taken as uniformly distributed. The loading which should be used in any design depends upon the location of the bridge, the character of traffic, and the length of span.

A heavy (20-t•on) motor truck may bring a load of about 140 pounds per square foot upon a bridge of short span (about 40 feet). Bridges 60 to 100 feet span subjected to traffic of motor trucks and heavily loaded wagons may be considered to carry about 100 pounds per square foot. For longer bridges this load may be lessened, bridges over 200 feet being designed for about 75 per square foot.

For bridges less than 100 feet in length carrying street railways, a load of 1S00 funds per foot of length for each track may be taken. For spans of 200 feet or more, this may be reduced to 1200 pounds per foot of track. These loads are considered as distributed over a width of about. 9 feet, giving loads of 200 and 1:13 pounds per square foot respectively. For spans between 100 and 200 feet, the loads may vary according to the length of span.

For light traffic lines on country roads, a load of 1200 pounds per foot of track may be used for arches less than 100 feet in length and 1000 pounds per foot for those 200 feet or more in length. Fre quently bridges must be built for special service, or where the traffic conditions are unusual and should be designed for any loads that may reasonably be expected to come upon them. Traffic conditions are constantly undergoing important changes, and in determining the loading to be used in any particular instance, it is desirable to con sider the possible effect upon future traffic of the rapid increase in the use of heavy auto-trucks and traction engines. As masonry 'arches are structures of permanent character, the probable future development of traffic should be considered and liberal loadings used in design.

158. Live Loads for Railway Arches.—Standard locomotive load ings are used in the design of floor systems for open spandrel arches, as in beam bridges, and are also sometimes employed in investiga tions of arch rings. Equivalent uniform loadings may, however, commonly be used in arch-ring design.

Loadings should correspond with the heaviest locomotive and train loads to be expected. For spans less than about GO feet, a load of S000 pounds per foot of track, or 1000 pounds per square foot of road surface is frequently used. When the span is SO feet or more a load of 5600 pounds per foot of track, or about 700 pounds per square foot, is used, which are approximately the same as Cooper's E 40 loading. Impact is not taken into account in the arch-ring investigation.

A concentrated load upon a fill may be considered as distributed downward through the fill at an angle of 45° with the vertical, the top of the distributing slope being taken from the ends of the ties.

Wheel loads are taken as distributed over three tics and then trans mitted to the filling.

159. Dead Loads.—In arch bridges, the dead weights of the arch ring and of the filling or structure above constitute the principal loads upon the arch rings. The live loads are much less in amount, and are important mainly as producing unsymmetrical loading when the load does not extend over the whole arch. In computing the dead load upon an arch ring, the actual weights of the materials to be used should be taken when they are accurately known. It is common to assume the weight of earth filling as 100 pounds per cubic foot, and that of concrete of other masonry as 150 pounds per cubic foot.

In open-spandrel arches the dead weights act vertically through the columns or walls supporting the floor of the roadway, and may be readily computed. When the spandrels are filled with earth, each section of the arch ring is assumed to carry the weight of the filling and roadway vertically above it.

The earth pressures upon the inclined back of the arch ring are not actually vertical, but may have certain horizontal com ponents. For arches of small rise, these horizontal pressures are small and may be neglected, but when the rise of the arch is large, the horizontal earth thrusts may be considerable, and should be taken into account, although their omission is usually an error on the safe side. While the amount of horizontal earth pressure cannot be exactly determined, it is usual to use Rankine's minimum value for unit horizontal earth pressure in terms of the unit vertical pressure, which is in which H is the horizontal and V the vertical unit pressure, and 4 the angle of friction for the earth. For ordinary earth filling, this would make the unit horizontal pressure at any point approximately one-fourth of the unit vertical pressure at the same point, the prob ability being that a horizontal pressure of at least this amount may always be developed.

The methods used for determining pressures upon retaining walls evidently are not applicable to this case. The actual horizontal earth pressure may vary within rather wide limits, and cannot be accurately determined. In retaining-wall design, the maximum earth thrust which may come against the wall is computed, while for the arch we need to know the minimum horizontal pressure which may be relied upon to help sustain the arch. That the actual pres sure may sometimes be considerably more than the computed mini mum is quite probable.

When an arch carries a continuous masonry wall, as in an opening through the wall of a building, or the spandrel wall at the end of an arch bridge, the wall itself would arch over the opening and be cap able of self-support if the arch were removed. The load upon the arch would therefore he only that due to a triangular piece of Nvall immediately above t he arch as in the case of a stone lintel. (See Section 53.)