The centre girder of fixed depth being then required to carry a definite load at a definite flange stress, will deflect a definite amount at this stress. If this deflection equalled the extreme depression m of the old girder work, no adjustment would be necessary, the centre girder then carrying no initial dead load, as by the first method; but for centre girders designed for economical flange stress the deflection will in ordinary cases greatly exceed this, the depth generally being small, and in order to ensure that the new girder shall do its full work, some dead load must be put upon it. In the act of adjustment the cross-girders must be lifted and the centre girder depressed, till the joint movement equals the excess s of the centre girder deflection over m, when the new girder will carry the proper amount of initial load, and upon further deflection under live load give the full measure of relief. The amount of “lift” or upward flexure of the old girder work, and the depression or “drop” of the new girder, during adjustment, will depend upon relative stiffness, and may be ascertained as follows:—
For unit reactions at the centre of the cross-girders the upward flexure of these may be ascertained, as also the upward flexure of the two outer girders when subject to forces of the same total amount (one-half to each) applied at the cross-girder ends. The sum of these movements will give the total lift of the centre cross-girders, when all are subject to unit lifting forces; similarly, the depression of the centre girder for unit loads applied at the cross-girders may be determined. There will then be known the movements upwards and downwards of the old and new work when being drawn together by unit forces applied as stated.
If
| l | = | lift due to unit loads, |
| lt | = | total lift due to adjustment, |
| d | = | drop due to unit loads, |
| dt | = | total drop due to adjustment, |
| s | = | deflection excess = gross adjustment, |
there will then be
d l + d × s = dt,
total drop of centre girder under adjustment,
l l + d × s = lt,
total lift of centre cross girders under adjustment,
dtd × unit load =