When arches are used to strengthen bridge trusses, such as the lattice and other forms on the American principle, the pressure on the arch and size of the timber can be calculated in the same manner as curved ribs (Art. 359). Mr. Haupt remarks with reference to the introduction of arched ribs for the purpose of strengthening trusses, that our calculations must be based to some extent upon uncertain data, for when two systems are combined, we cannot be certain that each sustains an equal portion of the weight; but, on the other hand, we are sure that the assertion sometimes made, that either one or the other necessarily sustains the whole load, is erroneous. Much depends upon the manner of making the connection. If an ordinary truss be constructed, and arches added after it has settled to a considerable extent by the application of heavy weights, it is very clear that the arch will bear but a small proportion of the load; but if the arch is introduced previous to the removal of the false works, and both systems be allowed to settle together, it is fair to suppose that the strain upon each will be in proportion to the respective powers of resistance.

The usual method of constructing bridges is to make the truss of such strength as is supposed to be sufficient to support the weight, and to add the arch as additional security.

Mr. Haupt is of opinion that it is decidedly preferable to reverse this arrangement, making the arch the main dependence, and using a light truss in combination with it, merely to prevent change of figure in the arch and to give the proper elevation or inclination to the roadway.

It is very evident that an arch can be made to sustain the whole of the weight; for if a truss has settled, it may be raised to any extent, by the addition of arches and suspension rods. In this case, the rule for proportioning the braces, so as to increase in arithmetical progression from the middle to the end, is no longer applicable: there is no more strain at the ends than in the centre, and but little at any point, and in this case the truss is of no other use than to stiffen the arch and carry the roadway.*