is best to keep these tension stresses low or even to make them non-existent; but in high trestles it becomes necessary to permit and provide for them.

It is when trestles are on sharp curves that great batters must be used, in order to provide against the overturning tendency of the combined centrifugal force and wind load. In such cases as these with high trestles it becomes necessary to divide up the transverse bracing of the lower portion of the tower by placing short vertical columns in the middle of the bents, and bracing longitudinally between the vertical columns of alternate adjacent bents.

In very high trestles, especially when located on sharp curves, the combinations of column stresses for live load, dead load, traction load, centrifugal load, and wind load run extremely high, and demand great column sections; consequently in such cases it becomes necessary for the designer to use considerable good judgment so as to reduce the total stress to reasonable limits. For instance, the traction stresses can be cut down to less than one half by riveting the longitudinal girders of an intermediate span to the towers at both ends. This reduces the thrust of train owing to the increased length of structure used for determining the equivalent uniform load, and fixes the tops of the towers so as to make a point of contraflexure at mid-height, thus reducing the lever-arm and therefore the bending moment to one half.

Again, unless the grade be heavy, it is often legitimate to assume that the velocity of train is materially lessened by the sharp curve by the time that the train reaches the high portion of the trestle; and, as the centrifugal load varies as the square of the velocity, the stresses from this load will be greatly reduced by the assumption.

Again, the prevailing high winds and the centrifugal loads may act against each other instead of together, and the combination may be lowered in amount by recognizing this fact.

In short, the designer in such a case can use his judgment to great advantage, and thus save considerable metal that is not really needed, although it might be required if a strict adherence to the specifications were enforced.