The Anatomy of Bridgework

by William Henry Thorpe

(3SC + S²D × C) × f,

the constant C being 3900 and 4450 for iron and steel respectively. The latter values of C correspond to normal values of the modulus of elasticity of 11,700 and 13,350 tons for iron and for steel, it being assumed that any slight rivet yield is off-set by any small section excess—say, 5 per cent.; it may, however, happen that section excess is greater than assumed, in which case some allowance may properly be made for this by increasing C.

To adapt the formulæ to girders other than those having parallel booms and uniform stress, the results, as deduced above, may be multiplied by constants given in column B of the Table given on [page 93].

The practice of adopting for E in deflection formulæ a quantity much smaller than its nominal amount, with the object of allowing in riveted girder work for the yield of rivets and of joints, can hardly now be defended, whatever may have been a case at a time when workmanship was much inferior, when there was no machine riveting, and joints were, owing to the small weight of plates and bars, three times as numerous.

The initial “set” of a girder consequent upon first loading is a quantity quite distinct from deflection proper, and may be so small as to be negligible, or read 10 per cent. of the true deflection, varying with design and workmanship.

No estimate of girder deflection can be even approximately true if there is, at the level of the top or bottom flanges, a plated or otherwise rigid floor system which is not taken into account, as this will have the effect of very materially reducing the boom stress. To neglect this influence, where it exists, must necessarily lead to disappointing results, and it is quite practicable in many instances to include it in the calculation.

The influence of angular distortion between the various members has been neglected. It may be pointed out, however, that the resistance accompanying these movements in girders having riveted connections, though unimportant as affecting deflection, is worth some consideration in regard to secondary stress. For girders of similar type and unit stress these angular variations will be the same in amount for any span, but will generally be of less importance in large girders than in small, because in large girders the ratio of the breadth of members to their length is commonly less.

When determining the probable deflection of any girder of exceptional figure, it will be found convenient to make a strain diagram—an old device, in which the actual alterations of length being ascertained for all members, the girder is carefully set out to a suitable scale, with the lengths of members increased or reduced by the actual estimated amounts. The distorted figure resulting will then give the probable deflection. The value of E for this purpose should never be taken at less than the normal amount, and may for a considerable excess of metal in joints and gussets be made as much as 10 per cent. greater, this being a convenient means of making the necessary correction.

The effect of loads quickly applied may here be considered in connection with elastic deformations of girders of the same span, but different depths. If these be designed for similar loads and unit stresses, the deflections due to webs and booms of the girders compared will bear the same relation, each to each, as do the weights, whether in both cases the loads be inert or quickly applied, from which it follows that the mechanical “work” done by the loads in falling through the deflection heights is, neglecting inertia, always in proportion to the girderwork weights, and is a similar amount per ton, which as the total length of members remains substantially unaltered, corresponds to a similar amount of work per unit of section, or similar stress, irrespective of the depth of the girders.

But for a “drop” load, as when there is some obstruction upon a railway bridge, there will be in addition a further amount of work to be absorbed, which is to be considered the same whatever the girder’s depth, and will for deep girders be a larger amount per ton of girderwork than in those that are shallow; this, taking effect on members of the same aggregate length, but lighter, will develop a higher stress than in girders of lesser depth, more particularly in the booms.