71. Ties and Guard-Rails. The length of ties for single-track bridges is10feet.
For double-track bridges the length is in most cases the same. In some double track bridges, however, either each tie or every third tie extends entirely across the bridge. In other cases every third tie on one track extends to the opposite track, thus act ing as a support for the foot-walk which is laid upon them. It is the best prac tice to limit the length of the ties on double-track bridges to 10 feet, since, if they extend into the opposite track in any way whatsoever, unnecessary expense is incurred whenever repairs or renewals are made, because both tracks must necessarily be disturbed to some extent.
The size of the ties varies with the weight of the engines and the spacing of the stringers or girders on which they rest. They are usually sawed to size instead of hewn, and the following sizes may be purchased on the open market—namely, 6 by 8, 7 by 9, 8 by 9, 9 by 10, and 10 by 12 inches. Larger sizes may be obtained on special order.
The elevation blocks (see Fig. 127) should be of length to suit the width of the cover-plates and the spacing of the supports. They are usually made of the best quality of white oak, since the cost of renewal is great enough to demand that they be made of material as permanent as possible.
The guard-rails should be placed in accordance with the specifica tions (see Articles 13 and 14). Some railroads specify that the guard rails shall be in 24-foot lengths unless the bridge is shorter than 24 feet, in which case one length of timber should be used. For method of connection and other details, consult Figs. 121 to 127. The guard-rails and the ties are usually made of Georgia long-leaf yellow pine, prime inspection. Other wood, such as chestnut, cedar, and oak, may be used.
In addition to the wooden guard-rail, a steel guard-rail usually consisting of railroad rails is placed within about 8 inches of the track rail.
In designing ties, the problem is that of a simple beam symmet rically loaded with two equal concentrated loads, the weight of the rail and tie itself usually being neglected. For the case in hand,
which is that of a deck plate girder, loading E 40, the con centrated load for which the tie must be designed is, according to Specifications (Article 23, 3d part), 8 333 pounds. According to Article 23, 100 000 pounds is on four wheels. This gives 25 000 pounds on one wheel, and ac cording to Article 15, one-third of this, or 8 333 pounds, will come on one tie. Fig. 135 shows the condition of the loading, the space center to center of rail being taken as 4 feet 10 inches. Some designers take this distance as 5 feet; but as the standard rail head is about 2 inches, and the standard gauge 4 feet 8i inches, the distance here taken seems to be the more logical one.
The formula to he used in the design of this beam is that given in "Strength of Materials," and is M In this case M=10 X 8 333 = 83 330 pound-inches. In the above formula, I = bd' ± 12, and c = d _ 2, and therefore e = • Substituting the value • of the moment in the above formula, and solving for S, there results 4 499 980 bd' For a 6 by 8-inch tie, the unit-stress would then be : S6 X 8' 9801 310 pounds.
6 If a 7 by 9-inch tie is used, the unit-stress is found to be 880 pounds.
Since according to Article 15 of the Specifications, the unit-stress cannot be greater than 1 000 per square inch, it is necessary to use a 7 by 9-inch tie. If the engine loading had been E 50, the mo ment would have been 100 000 pound-inches, and then the stress in a 7 by 9-inch tie would be 1 060 pounds per square inch, and the stress in an 8 by 9-inch tie would be 930 pounds,which would neces sitate the use of the latter.
The guard-rails on this bridge will be placed according to the Lehigh Valley standard, and hence their inner face will be 4 feet 11 inches from the center of the track.
Elevation blocks will not be required, as the bridge is on a tangent.