Figs. 54 to 57.

Strictly the character of the deflection curve is slightly modified by that part of the deflection due to the web; so that the depression at the centre would, in the case assumed above, be somewhat more than one-fourth part of the end reading, and generally will be a larger fraction of the reading than that deduced from a consideration of flange stress simply. In [Figs. 55 to 57], which are intended to explain this, it will be noticed that deflection due to the web is shown straight-lined from the bearings to the centre of the girder; this is strictly true only for a girder correctly designed for an immovable distributed load; but as there should be for girders intended for a travelling load, some excess in web members near the centre under the condition of uniform loading, the point of the figure should be rounded off to be in agreement with this case, though it is left as shown in the diagram for the sake of simplicity.

Suitable constants, including the corrections necessary, are given in column A of the table annexed for a few typical cases, and by these constants the actual readings should be multiplied to find the deflection. The constants have been worked out for depths of one-tenth the span; for greater depths they should be slightly more, and for smaller depths somewhat less, but they may be used between the limits of one-sixth and one-fourteenth, with a maximum error hardly exceeding 5 per cent., and generally much less.

The figures in column B relate to the formulæ previously stated, and apply equally well to all depths.

Tables of Multipliers for Deflection.

Uniform Stress:A.B.
Girders of uniform depth, varying flange section0·271·00
Hog-backed girders, ends half of centre depth, varying flange section0·241·08
Varying Stress:
[A]Girders of uniform depth and flange section0·320·87
[A]Hog-backed girders (as above), but uniform flange section0·290·97
[A]Bow-string girders of uniform flange section0·161·30

[A] For uniform loading.