MAIN GIRDERS; PLATE-WEBS.
It is seldom that girders of this description--or, indeed, of any
other--show signs of failure from mere defect of strength in the
principal parts, even though somewhat highly stressed; and instances
tending to support this statement will be given in a later chapter. For
the present, it is proposed to indicate peculiarities of behaviour only,
generally, but not always, harmless.
Though now less often done, it was at one time common practice to load
plate-girders on the bottom flange by simply resting floor timbers,
rails, troughs, or cross-girders upon them. In outside girders one
result of this is to cause the top flange to take a curve in plan,
convex towards the road, every time the live load comes upon the floor
of the bridge, upon the passing of which the flange resumes its figure,
though still affected by that part of the load which is constant.
A bridge of 47 feet span, carrying two lines of way, having one centre
and two outside girders, with a floor consisting of old Barlow rails,
resting upon the bottom flanges, showed the peculiarity named in a
marked degree.
The outside girders, under dead load only, were, as to the top flanges
(see Figs. 4 and 5), 1-1/4 inch and 1-1/16 inch respectively out of
straight in their length, but upon the passing of a goods engine and
train curved an additional 1-1/8 inch, or 2-3/8 inches in all, for one
outside girder, and 2-3/16 inches for the other.
The centre girder, having a broader and heavier top flange, curved 5/8
inch towards whichever road might be loaded. The effect of such
horizontal flexure is clearly to induce stresses of tension and
compression in the flanges, which, being (for the top flange) compounded
with the normal compressive stress due to load carried, results in a
considerable want of uniformity across the section.
[Illustration: FIG. 4.]
In the case under notice, the writer estimates the stresses for an outer
girder top flange at 4·5 tons per square inch compression for simple
loading, and 5·5 tons per square inch of tension and compression, on the
inner and outer edges, due to flexure, resulting when compounded in a
stress of 1 ton per square inch tension on the inside, and 10 tons per
square inch compression on the outside edge. In this rather extreme case
the stress on the inner edge, or that nearest the load, is reversed in
character.
The effect described appears to be not wholly due to the twisting
moment. It is apparent that whatever curvature may be induced by
twisting alone must be aggravated in the compression flange by its being
put out of line.
The writer does not attempt here to apportion the two effects in any
other way than to say that the greater part of the flexure appears to be
due to the secondary cause. Consistent with this view of the matter is
the fact that the inclination of the girder towards the rails greatly
exceeded the calculated slope of the Barlow rail-ends when under load,
being about five times as great. The inference is that the floor rails
bore hard at their extreme ends, at which point of bearing the
calculated twisting moment accounts for less than one-half of the
flexure observed in the flanges.
[Illustration: FIG. 5.]
The girders upon removal in the course of reconstruction again took the
straight form, showing that the very frequent development of the
stresses named had not sensibly injured the metal, though the bridge
carried as many as three hundred trains daily in each direction, and had
done so for very many years.
The deformation of the top flange only has been noticed, yet the same
tendency exists in the bottom, though the actual amount is much less,
both because the lower flanges are in tension, and are also in great
degree confined by the frictional contact of the cross bearers, even
where no proper ties are used. In the case dealt with the bottom flanges
of the outer girders curved 1/8 inch outwards only.
With the broad flanges commonly adopted in English practice, twisting of
the girders, under conditions similar to the above, will not generally
be a serious matter; but with narrow flanges possessing little lateral
stiffness it might be a source of danger.
[Illustration: FIG. 6. FIG. 7.]
The twisting may be limited in amount by introducing a cross-frame
between the girders, from which they are stiffened; by strutting the
girders immediately from the floor itself, in which case they cannot
cant to a greater extent than that which corresponds to the floor
deflection; or by designing the top flange to be unsymmetrical with
reference to the web, as in Figs. 6 and 7, with the object of insuring
that under the joint effect of vertical loading and twisting, the stress
in the flange shall at maximum loads be uniform across the section, and
allow it to remain straight. This may be secured by making the
eccentricity of the flange section equal to that of the loading. For
instance, if the load be applied 3 inches away from the web centre, the
flange should have its centre of gravity 3 inches on the other side of
the centre line. It can be shown that this is true throughout the length
of the girder, and irrespective of the depth. An instance in which
flange eccentricity being in excess, curvature outwards resulted, will
be found in a later chapter on deformations, etc. It will not generally
be necessary to make the bottom flange eccentric, as it is commonly tied
in some way; but if done, the eccentricity should be on the same side as
for the top. The flanges remaining straight under these conditions are
not subject to the complications of stress referred to in the case first
quoted. The author has adopted both the last named details in bridges
where he has been obliged to accept unfair loading of the kind
discussed.
It should be remarked that by the two first methods, if the stiffening
frames are wide apart and attached direct to the web, there is a
liability for this to tear, under distress, rather than keep the girder
in line.
There is one other possible consequence of throwing load upon the
flanges of a girder of a much more alarming nature. In girders not very
well stiffened, it may happen that the frequent application of load in
this manner finally so injures the web-plate, just above the top edge of
the bottom angle-bars, as to cause it to rip in a horizontal direction.
More likely is this to happen with a centre girder taking load first on
one side, then on the other, and again on both together. Cases may be
cited in which cracks right through the webs 3 feet or more in length
have resulted from this cause. It is very probable, however, that in
some of these cases the matter was aggravated by the use of a poor iron
in the webs, as at one time engineers, from mistaken notions of the
extreme tenuity permissible in webs near the centre of a girder, would,
if they could not be made thin enough, even encourage the use of an
indifferent metal as being quite good enough for that part of the work.
An instance of web-fracture from somewhat similar causes may be here
given.
In a bridge of 31 feet 6 inches effective span, and consisting of twin
girders carrying rails between, as shown in Figs. 8 and 9, the load
resting upon the inner ledges, formed by the bottom flange, induced
such a bending and tearing action along the web just above the
angle-bars, as to cause a rip in one of the girders, well open for some
distance, and which could be traced for 14 feet as a continuous crack.
[Illustration: FIG. 8.]
[Illustration: FIG. 9.]
It will be noticed in the figure that the [T] stiffeners occur only at
the outer face of the web, and that the inner vertical strips stop short
at the top edge of the angles, the result being that under load the
flange would tend to twist around some point, say A, at each stiffener,
inducing a serious stress in the thin web at that place, while away from
these stiffeners the web would be more free to yield without tearing.
The fact that at a number of the stiffeners incipient cracks were
observed, some only a few inches long, suggests this view of the matter.
A case of web-failure from other influences coming under notice showed
breaks at the upper part of the web extending downwards.
In this bridge, of 32 feet span, which had been in existence thirty-two
years, the webs--originally 1/4 inch thick--were, largely because of
cinder ballast in contact with them, so badly wasted as to be generally
little thicker than a crown-piece, and in places were eaten through; in
addition to which, the road being on a sharp curve, the rail-balks had
been strutted from the webs to keep them in position, the effect of
which would be to exert a hammering thrust upon the face of the web at
the abutting ends, and assist in starting cracks in webs already much
corroded. A feature of this case, tending to show that the breaks
resulted as the joint effect of waste and ill-usage by the strut
members, rather than by excessive stress in the web as reduced, is to be
found in the fact that the girders when removed were observed to be in
remarkably good shape--i.e. the camber, marked on the original drawings
to be 1-1/2 inch, still showed as a perfectly even curve of that rise,
which would hardly have been the case if the lower flange had been let
down by web-rupture, the result of excessive web-stresses.
Occasionally webs will crack through the solid unwasted plate, in a line
nearly vertical; not where shear stress is greatest, but generally at
some other place, and from no apparent cause, either of stress or
ill-usage. The writer has observed this only in the case of small
girders not exceeding 2 feet in depth; and, for want of any better
reason, attributes these cracks to poor material, coupled with some
latent defect. In a bridge having some thirty cross-girders, each 26
feet long, about every other one had a web cracked in this manner after
many years’ use.
Web-cracks of the kind first indicated, are perhaps, the most probable
source of danger in plate-girders, of any which are likely to occur. The
fault is insidious, difficult to detect when first developed, and
perhaps not seen at all till the bridge, condemned for some other
reason, has the girders freely exposed and brought into broad light. The
manner in which old girders are sometimes partly concealed by
timberwork, or covered by ballast, makes the detection of these defects
an uncertain matter, unless sufficient trouble is occasionally taken to
render inspection complete.
The manner in which girders with wasted and fractured webs will still
hang together under heavy loading seems to warrant the deduction that,
in designing new work, it can hardly be necessary to provide such a
considerable amount of web-stiffening as is sometimes seen; experience
showing that defects of the web-structure do not commonly occur in the
stiffening so frequently as in the plate, and then in the form of
cracks.
A case of web-buckling lies, so far, without the author’s experience.
There is no need to introduce, for web-stresses alone, more stiffening
than that which corresponds to making the stiffeners do duty as vertical
struts in an openwork girder; in which case it is sufficient to insure
that the stiffeners occurring in a length equal to the girder’s depth
shall, as struts, be strong enough in the aggregate to take the whole
shear force at the section considered, in no case exceeding this amount
on one stiffener. For thin webs in which the free breadth is greater
than one hundred and twenty times the thickness, the diagonal
compressive stress may be completely ignored, and the thickness
determined with reference to the diagonal tension stress only.
There is one fault which frequently shows itself in stiffeners though
not the result of web-stresses, and when performing an additional
function--viz., the breaking of [T] stiffener knees at the weld, where
brought down on to the tops of cross-girders, due to the deflection of
the floor, as shown in Fig. 10. When such knees are used, the angle may
properly be filled in with a gusset-plate to relieve the weld of strain
and prevent fracture.
[Illustration: FIG. 10.]
There is some little temptation in practice to make use of the solid web
as a convenient stop for ballast, or road material. Special means,
perhaps at the cost of some little trouble, should be adopted, where
necessary, to avoid this.
MAIN GIRDERS; OPEN WEBS.
With these, as with plate-girders, deficiency of strength--i.e. of
section strength--is seldom so marked as to be a reasonable cause of
anxiety. In particular instances faults in design may result in stresses
of an abnormal amount, though rarely to an extent occasioning any ill
effects. The practice of loading the bottom flanges at a distance from
the centre, the bad effects of which have already been dealt with as
applied to plate-girders, is not commonly resorted to in girders having
open webs, nor are these so liable to be heaped with ballast in
immediate proximity to essential members of the structure.
Some defects are, however, occasionally seen which may be remarked. Top
booms of an inverted [U] section are sometimes made with side webs too
thin, and having the lower edges stiffened insufficiently, or not at
all. Where this is the case, the plates may be seen to have buckled out
of truth, showing that they are unable, as thin plates, to sustain the
compressive stress to which the rest of the boom is liable. The practice
of putting the greater part of the boom section in an outer flange,
characteristic of this defect, has the further disadvantage of throwing
the centre of gravity of the section so near its outer edge as to make
impracticable the best arrangement of rivets for connection of the web
members. Further, since all the variation in boom section is thrown into
the flange-plates, the centre of gravity of the section has no constant
position along the boom--an additional inconvenience where correct
design is aimed at.
These considerations indicate the propriety of arranging the bulk, or
all, of the section at the sides, thus reducing or getting rid of the
objections named.
Where the bottom boom consists of side plates, only one point demands
attention. It is found that, though nominally in tension, the end bays
are liable occasionally to buckle, as though under compressive stress,
and need stiffening, not excepting girders which at one end are mounted
on rollers. This might seem to indicate that the rollers are of no use;
but it is conceivable the resistance arises from other causes, such as
wind forces, or as in the case of a bridge carrying a railway, in which
the rigidity of the permanent-way may be such that the bridge-structure,
in extending towards the roller end, cannot move it sufficiently,
causing a reversal of stress on the lighter portions of the bottom boom
at the knuckle end; or by the exposed girder booms becoming very
sensibly hotter than the bridge floor, and by expanding at a greater
rate, cause this effect, from which rollers cannot protect them.
In counterbracing consisting of flat bars it is desirable either to
secure these where they cross other members, or stiffen them in some
manner to avoid the disagreeable chattering which will otherwise
commonly be found to occur on the passage of the live load.
Occasionally diagonal ties are made up of two flat bars placed face to
face, to escape the use of one very thick member. Where this is done,
the two thicknesses, if not riveted together along the edges, will be
liable to open, as the result of rusting between the bars in contact,
when the evil will be aggravated by the greater freedom with which
moisture will enter the space.
Other matters relating to open-web girders will be more conveniently
dealt with under their separate headings, particularly a further
consideration of the relationship subsisting between the booms and floor
structure.