3.1 Explicit application of the theory of the ellipse of elasticity to the analysis of the arch of the bridge
Going to the explicit definition of the distribution of elastic weights made by the SNOS (1989), all the calculations reported there were developed considering an arch which is the projection on their mean inclined plane of one of the two couples of inclined parabolic arches that are placed symmetrically to the vertical longitudinal median plane of the bridge. Such arch is placed on a plane inclined of about a = 8.63° to the vertical (such that sin a = 0.15) and consists of a truss beam with parabolic axis of 150 m of span and 37.5 m of rise in such plane, having extrados and intrados lines both described by parabolic functions so as to determine a cross-high of the arch of 4 m at the keystone and of 8 m at the abutment. On the basis of this model, the elastic weights of the structure have been calculated according to a symmetric structural discretisation with 28 elements of different As extensions as reported in Fig. 7.
In the Report, the procedure adopted to calculate the elastic weights AG = As/EJ is not really apparent. An attempt of careful analysis is provided in Ferrari (2006). Also, the elastic weights are actually
The constant C in Eq. (9) is also evaluated in 555390001 • m2.
Anyway, tables are presented in which the left reaction and the deflections of the arch are determined for a unitary load located at the various elastic elements. In practice, these influence coefficients, which are later used for the design of the truss members, are determined by a true application of the theory of the ellipse of elasticity as applied to the arch.
3.2 Evaluation of the loads
The SNOS Report analyses independently, one by one, the various loadings on the arch, for subsequent superposition of effects:
- permanent weight of the arch;
- permanent weight of the upper girder beam, of the bridge piers and vertical actions induced by the wind acting on the girder beam;
- accidental vertical load on the upper girder beam;
- temperature effects and compression on the arch due to the horizontal thrust H;
- direct horizontal wind action on the arch.
For each listed item, the SNOS reports the calculation of the stresses in the various arch's elements, as well as the final value that arises by the superposition of effects.
The Report by the SNOS provides the calculation of the stresses in the various bar elements of the arch and at the stone abutments as compared to the target admissible values that are summarised below. This is done for the final geometries of the structural members. On the other end, the Report does not provide specific information about the design procedure that has lead, through pre-dimensioning, to such final structural dimensions. As the overall architectural and structural conception of the entire viaduct, these phases seem to be linked to the engineering practice and experience of the designer with the standards of metallic carpentry in use at the time.
The material employed in the structural members of the bridge is a wrought iron, with very low carbon percentage of about 0.01% (Nasce et al. 1984). The admissible stresses are taken differently for each structural component ofthe bridge: for the main upper and lower arch's ribs 6.0 kg/mm2; for the vertical and
Figure 8. Scheme with four test loading configurations, with indication of the four piers resting symmetrically on the arch (view from down-stream; Paderno left side, Calusco right side). Pier III is at half length of the upper continuous beam.
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