The superstructure is a spatial structure formed by beams, ties, and in road bridges and, in some cases, railway bridges, also by a reinforced concrete or ribbed steel slab of the roadway.
Due to the significant complexity of taking into account the actual operating conditions of the superstructure as a spatial structure, approximate methods of accounting for the load distribution between the main beams have become widespread in design practice.
The nature of the distribution of forces between parts of the spatial structure depends on the degree of rigidity of the elements and their connections.
In the absence of intermediate cross-links or their significant compliance, which makes it possible to ignore their influence, the distribution of the temporary vertical load between the main beams is expressed by the law of the lever.
With rigid transverse bracing, the deformations of which are insignificant in comparison with the deflections of the main beams, it is possible to neglect the curvature of the cross-sections of the superstructures under a temporary vertical load, asymmetrically located across the bridge, and to assume the distribution of this load between the main beams by the method of "eccentric compression".
The eccentric compression method is widely used in the design of metal road bridges.
For bridges for a single-track railroad, e = O, i.e., the temporary vertical load is equally distributed between the main beams.
With wide spans and relatively small spans, the deflections of the main beams are commensurate with the deformations of the crosslinks, and the span in the cross section is noticeably curved. The eccentric compression method becomes roughly approximate, especially when determining the design forces in the sections of beams close to the supports.
Lever and eccentric compression methods are also of little use for the widespread structures of span structures with wide box-shaped (closed profile) beams, the horizontal slabs of which take a significant part in the work of the span structures in torsion.
It became necessary to develop new methods of spatial calculation of spans, using design schemes reflecting the actual conditions of their operation.
The theoretical foundations of such a calculation were created by a number of Soviet and foreign scientists such as S.G. Galerkin, P.F.Papkovich, V.Z. Vlasov, S.P. Timoshenko, A.A.Umansky, B.E. Ulitsky, V. G. Don-chenko, G. Gomberg, Guyon and others
The design of spans with continuous beams is further complicated by the static indeterminacy of the beams.
The calculation of continuous beams can be performed along the lines of influence, for the calculation of the ordinates of which the author has compiled tables nearby. Note that the calculation of continuous beams is possible without calculating the areas of influence lines, since to determine the most advantageous position of the live load on the beam when calculating the design force in any of its sections, it is enough to know the shape of the influence line, which can be obtained without any calculations , as a kinematic model of the line of influence, and the support moments at a given load can be calculated by a simple and convenient iterative method of balancing the support moments.