DEFORMATIONS.
Instructive lessons are to be had from a study of the various
alterations in form to which metallic bridgework is liable, which
alterations may be due simply to the development of stress of ordinary
amount, and are then generally small; or to abnormal stresses, the
result of some distortion in the bridge structure itself not originally
intended, and possibly extreme. In addition to these there may be
deformations due to settlement, to “creeping” of parts of the structure
relative to the rest, to temperature changes, to rust, and to original
bad workmanship. In any instance quoted below the methods adopted to
ascertain the amounts of such alterations were quite simple, even crude;
but as care was exercised, and no attempt made to measure any very
minute changes, the results may be accepted as practically correct.
Dismissing for the present changes of form such as are to be expected,
and touched upon in other places in this work, with respect to the
particular parts of bridge structures affected by them, a few instances
will be adduced of alterations which, though not very surprising, are
such as in the design of the work are hardly likely, in most instances,
to have been contemplated.
A case has already been referred to in which, owing to eccentric loading
of main girders, these were, as to the top flanges, flexed sideways a
considerable amount. It is proposed to supplement this by further
remarks relative to somewhat similar cases. A like effect is frequently
to be observed in trough or twin girders, in which the rails are
supported upon longitudinal timbers resting upon projecting ledges
formed by the bottom angle-bars of such troughs. In old forms of this
arrangement it is common to find the two girders forming the trough
connected only by bolts passing through the timbers, or just above them
and below the rails; or connected by narrow strips, which serve no other
purpose than to prevent the sides spreading at the bottom. The top
flanges in such cases commonly curve inwards on the passage of the
running load, accompanied of necessity by an increase of compressive
stress upon the outer edges of the flanges, and perhaps by the working
of any flange-joint which may exist. This, both as to flexing of the top
flange and the working of a joint, was noticed in the case of a bridge
twenty-three years old, very similar to that illustrated in Figs. 8 and
9, and described on pages 13 and 14. The top flange consisted, however,
of a bridge rail riveted to the top edge of the web, butting at a joint,
and covered by thick cover strips (see Fig. 48). The joint itself was
poor, and depended largely upon the character of the butt, which was not
sufficiently good to prevent the top member kinking at this point, under
the joint influence of transverse effort and compressive stress, with
possibly some help from bolts passing through timber and webs, though
these being loose, the author does not think them at all responsible.
Although not strictly relevant, it may be remarked in passing that it is
very objectionable to use bolts as was done in this instance; for as the
timber settles down on its seat, taking the bolts with it, these bear
hard in the webs, enlarging or even, as in this case, tearing the holes,
accompanied by injury to the bolts themselves. The practice is now
almost obsolete, but the example is instructive as showing the
impropriety of securing timbers by bolts passing through them at right
angles to the action of the load, unless these bolts are quite free to
move with the timber as it compresses.
If trough girders must be used, the better plan is to connect the two
sides by a continuous bottom plate, the trough thus formed being
properly drained, if the timber is not bedded in asphalt concrete; or to
introduce stiff diaphragms at intervals beneath timbers, if the depth
suffices.
In the case just quoted the curvature of the top members of the girders
was inwards, but in the instance given below, of twin girders 26 feet
effective span, with longitudinal timbers between, resting, as before,
upon the inner ledge formed by the bottom flanges, the curvature was
observed in three out of four girders to be 1/2 inch in a contrary
direction, the fourth remaining straight.
[Illustration: FIG. 48.]
[Illustration: FIG. 49.]
An inspection of the accompanying section, Fig. 49, will, perhaps,
render the reason evident when it is noticed that the top members are
very unsymmetrical in form, the effect of this being to give these
members, under stress, a strong tendency to flex outwards, apparently
more than sufficient to counteract the tendency of an eccentric
application of load on the bottom flange to bring them inwards. It is to
be observed that the eccentricity of the flange appears to be not
materially in excess, and is actually so, only because the thinness of
the web--1/4 inch--renders it incompetent to keep the bottom flange up
to its work, and so secure the full effect of the eccentric loading in
limiting the outward tendency, due to the section of the top member,
the effects of which are thus more apparent than would have been the
case with a stiffer web. Ties across from one bottom flange to the other
prevent the want of symmetry noticed in these--which, by the way, is on
the wrong side for utility--from having any particular effect.
To give one other example of the consequences of eccentric loading, a
bridge of 48 feet effective span may be quoted. This bridge carried four
lines of way supported by five main girders, trussed by kicking-struts
in such a manner as to form a bastard arch. A part section and plan are
given in Figs. 50 and 51.
[Illustration: FIG. 50.]
[Illustration: FIG. 51.]
The floor consisted of Lindsay’s troughing resting upon the lower
flanges of the main girders, the three middle girders, subject to
eccentric loading, sometimes on one side, sometimes on the other, were,
with dead load only, straight; but the two outer girders, liable to
loading only on one side, had, under repeated applications of such a
load, assumed a permanent curve towards the rails--13/16 inch in one
case and 1 inch in the other--which curvature, no doubt, increased when
a live load came upon the contiguous roads, though this was not
measured. It should be remarked in passing that, owing to settlement and
the canting of the abutments, the three middle girders were also
“down”--in one case 3/4 inch. The girders, with one near road loaded,
deflected 1/8 inch--greatly less than would have been the case had the
main girder not been trussed. The bridge, at the time these particulars
were obtained, had been in existence six years.
Deformations due to settlement may be very considerable. The author
recalls two instances affecting continuous girders. In the first of
these, a bridge twenty years old, of two spans of about 50 feet each,
and with girders 4 feet 6 inches deep, the centre pier had sunk 4
inches, reducing the spans, as respects the dead load, practically to
the condition of simple beams, just resting, but hardly bearing, upon
the piers when free of live load.
In the second case, also of two openings of about 55 feet each, with
girders 8 feet deep, one abutment had sunk about 3 inches, more than
doubling the stresses over the centre pier. It is manifest that
continuous girders should only be adopted where settlement of the
supporting points is not likely to occur to any material degree. If this
cannot be relied upon, the theoretical flange sections may hardly be
worked to with any prudence; it being then advisable to make a liberal
allowance for settlement stresses, in which case any economical
advantage that should exist will probably disappear. It is, however, to
be acknowledged that so long as the girders are in touch, under dead
load, with the bearings intended to support them, the stresses due to a
live load are unaltered, the principal effect in this case being that
the variation in stress due to the live load ranges between limits that
are higher or lower in the scale of stress than is the case with
bearings undisturbed; still, if it is desired that the maximum stress
shall not exceed, say, 6 tons per square inch, it can hardly be a matter
of indifference that settlement shall induce a maximum of, perhaps, 10
tons, as in that case the stress must be 4 tons nearer the limit of
statical strength.
Before leaving this matter it may be well to point out that in the case
of continuous girders of uniform section a moderate settlement of the
piers may even be advantageous by reducing the moments over the piers,
and possibly making them equal to those obtaining near the middle of the
spans, in which case there will be less inequality of stress in the
booms and a reduction of the maximum stress.
Bridges consisting of simple main girders connected by cross-girders may
be very prejudicially affected by unequal settlement; for instance, if
one girder bearing settles more than the others, a twist is put upon the
structure very trying to the floor-girder connections, and possibly to
the main girders; to the web if a plate girder, or to the verticals if
an open-webbed truss with rigid cross-girder attachments. Indeed,
settlement of this kind may be much more destructive to a metallic
bridge than to an arch of brick or masonry, the commonly accepted
opinion notwithstanding.
Instances of deformations due to the creeping of some part of the
structure away from its work, are within the author’s knowledge, rare;
except in the case of the ends of main girders in skew bridges, already
referred to.
Distortion, the result of temperature changes, is frequently to be
observed in any considerable length of girder flange or parapet where
there is not freedom of movement, unless due provision is made to check
it.
It is quite common to see parapets out of line, either because the ends
are not free, or because the light work of the parapet being more
exposed to the sun’s rays than the girder work to which the lower part
is attached, expanding to a greater degree, is subject to considerable
compressive force, and buckles under its influence. The cure for this
condition is obviously to provide such parapets with free or flexible
joints at moderate distances apart, or to make the parapet sufficiently
stiff to take the stresses developed, without crippling. A parapet may
also go out of shape if directly attached to the top flange of a girder
liable to heavy loading, particularly if the girder be shallower than
the parapet, simply by its inability to maintain truth of line under the
compressive stress, which it shares with the top flange of the girder
proper.
Rivets spaced too far apart, by allowing the plates or other parts to
spring open slightly, and permitting moisture to enter, results in the
growth of rust, which, as it swells in forming, forces the parts
asunder, and may set up considerable stress.
Flat bars riveted together by rivets spaced 12 inches apart may from
this cause be forced asunder, as much as 1/2 inch, sufficient to set up
a stress, with any practicable thickness of bar, much exceeding the
elastic limit.
Local distortions may occur as the result of imperfect workmanship or
careless erection, causing quite possibly very severe local stresses; or
girder flanges may be out of straight as a result of riveting up along
one side first, instead of advancing the riveting simultaneously along
the whole breadth of the flange. The injury done by drifting is well
known, and there is reason to think considerable damage is sometimes
done to girderwork during manufacture by rough treatment to make the
work come together; but the author has little to offer with respect to
these matters that is not common knowledge. It may, however, be pointed
out in passing that a bridge upon the design of which great care has
been expended, with the idea that theoretical propriety shall not be
violated, may be completely spoiled in this respect by careless
construction. Fortunately, both steel and wrought iron, if of good
quality, are long suffering. Incompetent erection will sometimes result
in the true girder camber not appearing, or in differences as between
girders supposed to be similar. This is not, of course, a deformation in
the sense in which the word has previously been used, but it is
desirable to bear the fact in mind as a possible cause of defective
camber in dealing with questions of deformation.
The foregoing has reference chiefly to alterations of form in bridgework
of wrought iron or steel, but a case of considerable interest is that of
a cast-iron arched structure, of which the author made a very complete
examination.
[Illustration: FIG. 52.]
[Illustration: FIG. 53.]
This bridge, built in 1839, and carrying two lines of railway, consisted
of three spans, 100 feet each, of 10 feet rise, made up of four inner
and two outer ribs, each rib being in three nearly equal parts; the
floor was of timber, the abutments and piers of masonry. As originally
constructed there was no bracing between the ribs other than the frames
indicated on the plan here given (Fig. 52), stretching from outer rib
to outer rib in the neighbourhood of the rib joints, which were simple
butts without bolts or any equivalent means of connection. The floor
was, however, braced in the horizontal plane, and the structure was also
braced over the masonry piers. After forty-two years’ use supplementary
distance-pieces were introduced between the ribs, but still no bracing
between them, or any efficient means of checking lateral movement. A
crack developing in one of the outer ribs at the crown, led to an
investigation to trace the cause, the bridge then being fifty-four years
old. Careful plumbing of the abutments revealed the fact that three out
of four abutment pilasters were out of the vertical, as shown in Figs.
52 and 53, the greatest amount being 5/8 inch in 6 feet--at that corner
from which the cracked rib had its springing; there was also other
evidence of settlement in an old crack extending from the top of the
abutment to the ground level, although this movement was very old,
certainly as to the greater part. The ribs of this span were also out of
plumb, that which was cracked being 2-1/2 inches out at the centre. The
joints of the ribs, which, as already stated, were simple butts, in some
cases opened and shut, as the load passed over, in such a way as to
suggest that the ribs were acting, in a manner, as four-hinged arches,
of which two hinges were at the springing, and the other two at the
joints, one of which would for most positions of the load be out of use,
reducing the rib to the three-hinged condition; in other words, as the
rolling load passed over the span, one or other of the two joints of a
rib would “gape” an appreciable amount at the bottom or at the top.
Observations were taken by means of a theodolite placed below, either
upon the bank or upon the tops of the masonry piers, sighting upon
suitable scales attached to the ribs to ascertain the amounts of
vertical and horizontal movement during the passage of trains over the
bridge. The principal results are set forth in the following table:--
MOVEMENTS OF CAST-IRON RIBS UNDER LIVE LOAD IN A BRIDGE OF THREE 100-FT.
SPANS.
----------------------+-------+----------+-----------
|Fall in| Rise in | Lateral
-- |Inches.| Inches. | Movement
| | |in Inches.
----------------------+-------+----------+-----------
_Span No. 1._
At A. Up road loaded | ·20 | ·08 | ·04
„ A. Down road loaded| ·08 | ·03 | ·04
„ B. Down road loaded| ·14 |No record.| ·02
_Span No. 2._
At C. Up road loaded | ·40 | ·13 | Slight.
„ C. Down road loaded| ·10 | ·05 | „
_Span No. 3._
At D. Up road loaded | ·22 |No record.| No record.
„ D. Down road loaded| ·15 | Slight. | Slight.
----------------------+-------+----------+-----------
NOTE.--The lateral movements are to either side of the mean position.
The particulars for spans 2 and 3 were obtained with the instrument set
up on the pier between these spans. The tremor of this pier was such
that no useful readings for lateral movement could be obtained. Further,
as the rolling load came upon these spans, the effect was to rock the
pier to an extent vitiating the readings for vertical displacement; but
by sighting upon the fixed abutment, and observing the amount of this
rocking, suitable corrections were made in the apparent rib movements.
The figures given in the table are thus corrected. The pier rocking was
equivalent, as an extreme, to an inclination from the vertical of 1 in
3200. An attempt to measure the horizontal movement of the pier-top was
unsuccessful, owing to the impracticability of setting up the instrument
in a suitable position, sufficiently near to the pier to enable readings
to be satisfactorily taken. This horizontal displacement probably
amounted to about 1/16 inch either way. The rise and fall of the arches,
and rocking either way of the piers, varied, as might be expected, in
accordance with the position of the running load with respect to the
spans. Summarising the results, the greatest vertical movements
downwards were 0·20 inch, 0·40 inch, and 0·22 inch for spans Nos. 1, 2,
and 3, the upward movements being 0·08 inch and 0·13 inch for the first
and second spans, there being no recorded result of this kind for the
third span. With adjacent ribs loaded, the movement of the ribs unloaded
was one from one-third to one-half of the full amounts. It is to be
noted that the lateral displacement in no case exceeded 0·04 inch either
way, nor were the vertical movements exceptional; yet, as a matter of
sensation, when seated upon the ironwork, it was a little difficult to
believe them really so moderate. Observations were also made to
ascertain the rise of the arches from winter to summer temperatures,
with the result that this was found to be 0·45 inch, 0·45 inch, and 0·55
inch for the spans in order, the extreme temperatures being fairly
representative of the English winter and summer. The structure was, as a
consequence of the examination, efficiently braced by diaphragms between
the ribs, and diagonals following the arch ribs round from springing to
springing, with satisfactory results. The crack already referred to, and
its probable causes, will be dealt with under “Cast-Iron Bridges.”
Eventually this bridge was reconstructed to meet the requirements of
growing engine-loads.