The Anatomy of Bridgework

by William Henry Thorpe

D × C × m S² = f, unit stress on gross section (3)

D and S being, as before (see “[Deflections]”), the depth and span respectively in feet, C a constant, m the deflection in inches, and f the stress per square inch on the gross section of flange.

The gross area A, of the flange, is given by

S × c × L_t 8 × D × f = gross area of flange(4)

c × L_t, being, as in [(2)], the load transferred to and carried by the centre girder.

The actual stress in the flanges will, of course, be greater by an amount due to the girder’s own weight; but this does not affect the question of relief. For any ordinary case the stress per square inch will be low; but it will manifestly be useless to assume a greater stress with a view to economy, as the effect of reducing the section will simply be to make the girder too flexible, thus causing it to be less effective than primarily intended. If, as is seldom the case, there is freedom as to the depth of girder permissible, it is evident the unit stress may be made a condition, and the depth deduced by a suitable modification of formula [(3)]; the relief desired being in this way equally well assured. Indeed, in the rare instances in which any depth may be adopted, this method is—contrary to the general rule—distinctly economical, particularly if the girder may be placed below the cross-girders, which simply rest upon it, without elaborate attachments.

Fig. 71.

Considering now the second method of applying centre girders by which the new girder is made initially to carry part of the dead load, by adjustment, it will at once be recognised as a more complex matter. The measure of relief by which the old girderwork shall benefit need not be affected by the method of applying the centre girder, and may be decided on the principles already considered. The outer girders carrying a reduced load, when the bridge is fully loaded, and the cross-girders being in part supported at their centres in the manner already described, will give a resulting depression m (see [Fig. 71]) of the centre cross-girders, below the original dead-load position, of a similar amount determined in the same way. This extreme depression determines also the lowest position of the new centre girder, which may be designed to carry the required percentage of the total bridge loads with the maximum stress and depth, as conditions, leaving the initial dead load and necessary adjustments to be ascertained. This is the common case and will be here dealt with, it being assumed to avoid ambiguity in description that the new girder lies above the cross-girders.