BRACING.
Bracing, whether to strengthen a structure against wind, to insure the
relative positions of its parts, or for any other purpose, cannot be
arranged with too great care and regard to its possible effects. Forces
may be induced which the connections will not stand, with loose rivets
as a consequence, and inefficiency of the bracing itself; or, the
connections holding good, stresses in the main structure may, perhaps,
be injuriously altered.
To take a not uncommon case, let us suppose a bridge consisting of four
main girders placed immediately under rails of ordinary gauge, and
braced in vertical planes only, right across from one outer girder to
the other. If the roads were loaded always at the same time, nothing
objectionable would result; but, as a fact, this will be the exception.
When one pair of girders only takes live load, and deflects, the bracing
under the six-foot will endeavour to communicate some part of this load
to the other pair of girders. If the bracing is so designed that some
correctly calculated portion of the load can be transferred in this
manner, without over-stressing the bars and riveted connections, there
will be no harmful consequences; but if not, the bracings will most
probably work at the ends; this, indeed, is what frequently happens.
There is one other effect which will ensue, if the bracing is wholly
efficient; a certain twisting movement of the bridge will occur, which
increases the live load upon the outer girder on the loaded side of the
bridge to the extent of 10 per cent., with a corresponding lifting force
at the outer girder on the unloaded side. These amounts are not serious,
but wholly dispose of any advantage it is conceived will be gained by
causing the otherwise idle girders to act through the medium of the
bracing. In road bridges of similar arrangement, over which heavy loads
may pass on any part of the surface, it is clear that the use of bracing
between girders should not be taken as justifying the assumption that
the load is distributed over many girders, and correspondingly light
sections adopted, unless the effect of twisting on the whole bridge is
also considered, and justifies this view; for, as already stated in the
case of the railway bridge, the net result may be to increase the girder
stresses instead of reducing them. Generally, it may be deduced that the
better plan for railway bridges is to brace the girders in pairs,
leaving, in the case supposed, no bracing between the two middle
girders, though there will be no objection to connecting these by simple
transverse members of no great stiffness, to assist in checking lateral
vibration. For road bridges of more than five longitudinal girders,
equally spaced, it may be advantageous to brace right across, the
twisting effect with this, or a greater, number of girders not, as a
rule, leading to any increase of load on any girder. Figs. 22 to 25 give
the distribution of live load, placed as shown, for 3, 4, 5, and 6
girders.
It is to be observed that these statements do not apply to cases where
there may be also a complete system of horizontal bracing, the effect of
which, in conjunction with cross diagonals, may be greatly different,
with considerable forces set up in the bracing, and a modification of
girder stresses.
These effects may be so considerable as to call for special attention in
design where such an arrangement is adopted.
[Illustration: FIG. 22.]
[Illustration: FIG. 24.]
[Illustration: FIG. 23.]
[Illustration: FIG. 25.]
Somewhat similar straining to that first indicated may occur in bracings
placed between the girders of a bridge much on the skew. If this is, on
plan, at right angles to the girders, as is commonly and properly the
case, the ends will evidently be attached to the girders at points on
their length at different distances from the bearings, which points,
even with both girders loaded, deflect dissimilar amounts, and the
bracing will, if at one end attached near a rigid bearing, transfer some
part of the load from one girder to the other, notwithstanding that
both girders may be of the same span and equal extraneous loading. It
would not be difficult to ascertain the amount of load so transferred
from a consideration of the relative movements if free, and the loads on
the two girders necessary to render these movements equal, if the
deflections were simply vertical; but as there will be some twisting and
yielding of the girders on their seats, the calculation becomes
involved. If the bracing is placed at about the middle of the girders,
the effects noted will be greatly reduced; first, because the difference
of movements near the centre will be less; second, any given difference
will correspond to a smaller transference of load; and, third, because
each girder will there be more free to twist than at the ends. It
therefore appears that bracings between the girders of a skew bridge
should not be placed near the bearings, though they may be put, with
much less risk of injury, near the middle.
Cross-girders on a skew bridge are subject to forces somewhat similar to
those which may affect bracing, rendering it desirable to design their
attachments in a manner which shall not aggravate the matter, but rather
reduce the effects of unequal vertical displacement of their ends where
secured to the main girders.
Crossed flat bars as bracing members are objectionable on account of
their tendency to rattle, after working loose; but as this effect only
ensues in bracing which has first become loose (it being assumed that
the bars in any case are connected where they cross), this objection is
not itself vital, though greater rigidity is easily obtained by making
all such members of a stiff section.
Defective bracing between girders, from neglect of the very considerable
forces it may be called upon to communicate, is very common; the writer
has seen many such cases, of which one is here illustrated in Fig. 26.
[Illustration: FIG. 26.]
This bridge, of the section shown, and 85 feet span, had very light web
structure. The bracings, of which there were two sets, were wholly
inefficient, the end rivets being loose in enlarged holes. Upon the
passage of a train there was a positive lurching of the girder tops from
side to side. The integrity of the bridge was really dependent upon
such stiffness as there was in the girders, and unplated floor.
A common but indifferent method of keeping the top members of main
girders in line is by the use of overhead girders alone, frequently
curved to give the requisite clearance over the road. This cannot be
considered as wholly inefficient, as sometimes maintained, since it is
evident that the closed frame formed by the floor beams, the web members
of the main girders, and the overhead girder itself, must take a greater
force to distort it than would be necessary to cause deformation of a
corresponding degree, in an open frame formed by the omission of the
overhead girder; but it is not a method to be recommended, its precise
utility is difficult to estimate, and, if the cross-girder attachments
are of a rigid character, tends to increase the stresses induced at
those connections. The latter consideration is, however, not applicable
to this arrangement alone. All overhead bracing favours this by
restraining the tendency of the top booms to cant inwards when the floor
beams are loaded; and though this restraint may be quite harmless, it is
desirable that close attention be given to these effects in designing
bridges which make a complete frame more or less rigid in its character.
“Sway” bracing, sometimes introduced at right angles to the bridge
between opposite verticals, tends to emphasise these effects by
rendering the cross-section of the bridge still stiffer, besides making
it a matter of difficulty to ascertain how much of the wind forces on
the top boom is carried to the abutment by the top system of bracing,
and how much by the floor. The author does not, however, mean to suggest
that it cannot be used with propriety, but rather that extreme care is
desirable in considering its ultimate effect on the rest of the
structure.
For girders of moderate depth there may be on these grounds a distinct
advantage in abandoning overhead bracing, and securing rigidity of the
top boom, and adequate resistance to wind forces, by making the
connection between the cross-girders and the web members sufficiently
good to insure, as a whole, a stiff [U]-shaped frame; but this, with the
ordinary type of rocker arrangement under the main girder bearings, will
not be entirely free from objection, as canting of the girders due to
floor loading will throw extreme pressure on the inner end of each
rocker. There appears to be no reason why the cylindrical knuckle should
not in this case be supplanted by a cup hinge, allowing angular movement
of the girder bearing in any plane.
[Illustration: FIG. 27.]
The efficient stiffening of light girders, as in the case of
foot-bridges, from the floor, where this is at the bottom flanges,
renders very narrow top booms permissible. This is a decided advantage
where lightness of appearance is aimed at; but it is not unusual to see
an attempt made in this direction by introducing gusset plates of very
ample proportions between vertical members of the girders, and the
projecting ends of flimsy transoms, carried beyond the width of the
bridge proper, these being of a section wholly out of proportion to the
brackets they are supposed to secure. Whatever may be the amount of
strength necessary at the point A, in Fig. 27, there should not be less
throughout the transom from one girder to the other. The degree of
strength and stiffness required in this member, and in the vertical
stiffeners is not, as a rule, great. Information to enable this question
to be dealt with as a matter of calculation is somewhat scanty; but it
would appear to be sufficient to insure safety that, for an assumed
small amount of curvature in the compression member, the forces outwards
corresponding to this curvature, due to thrust, should be resisted by
verticals and transoms of strength and stiffness sufficient to restrain
it from any further flexure. It will, of course, be necessary also to
take care that the compression member is good as a strut between the
points of restraint. A simple and sufficiently precise method of dealing
with this question is much needed. In cases where the floor weight rests
on the flange projection, it is also necessary to give the transom
additional strength to an extent enabling it to resist the twisting
effort between any two of these transverse members; further, resistance
to wind on the girder has to be provided in both transoms and verticals.
It may be hardly necessary to insist that bracing intended to stiffen a
structure against wind, local crippling, or vibration, should be made
complete, not stopping short at some point, because it cannot
conveniently be carried further, as is sometimes done, unless the
strength of those parts of the structure through which the forces from
the bracing must be communicated to the abutments is sufficiently great,
considered with reference to other stresses in those parts which have
also to be endured.
Bracing stopped short in this way, making only the central part of a
bridge rigid, may have the effect of increasing the forces to which the
unstiffened end members would otherwise be liable. Such a structure
would evidently be much stiffer against wind-gusts than if no bracing
existed--the resistance to a blow would be increased; but the power to
maintain that greater resistance being confined to the intermediate
bays, the unbraced ends would be subject to greater maximum forces than
if bracing were wholly omitted. The net effect may still be better than
with no bracing, the point raised being simply that of an increase of
stress in particular end members.
In the bracing of tall piers, the rising members of which will be
subject to any considerable stress, if the diagonal members are not
finally secured when the piers are under their full load, or an initial
stress of proper amount induced in those members, the effect of loading
will be to render them slack; so that an appreciable amount of movement
at the top may occur before it can be limited by the efficient action of
the bracings. This effect under blasts of wind or continual passage of
trains may, indeed, be dangerous. Similar considerations apply to the
top wind bracing of deep girder bridges, influencing also the bottom
bracing in a contrary manner, which calls for attention in fixing the
unit stresses for such members.
The bracing of sea-piers is very liable to slacken if made with
pin-and-eye ends, as is often done for round rods. The detail presents
advantages in erection, but is not altogether satisfactory in practice.
Such connections are continually working. In the finest weather, with
the sea quite smooth but for an almost imperceptible wave movement, the
lower parts of such structures will be found, as a rule, to have some
slight motion. This is very trying to bracing; nor is there room for
surprise when it is considered that these oscillations, occurring at
about ten to each minute, never wholly cease, and amount in the course
of one year to over five million in number.
Bracing attached in such a manner that there can be no initial slack, or
slack due to wear under endless repetitions of small amounts of stress,
will have a much better chance to keep tight. The advantage presented
by round rods in offering little surface to the water, is more than
negatived by inefficiency of the usual attachments for such rods.
The author has observed that bracing of members possessing some
stiffness, and with good end attachments to ample surfaces, appears to
stand best in ordinary sea-pier work. For such structures the bracing
should consist of a few good members, with a solid form of attachment,
rather than of a multiplicity of lighter adjustable members, which will
commonly give great trouble in maintenance; being very possibly also, in
the case of sea-pier work, in unskilled hands. If round rods must be
used, they will stand much better if made of large diameter.
Before leaving the subject of bracing, it may not be out of place to
refer to wind pressure, as this may so much affect the proportioning of
the members.
Some years since the author had occasion to examine a number of
structures with respect to their stability. Of foot-bridges from 60 feet
to 120 feet long, three or four, when calculated on the basis
recommended by the Board of Trade as to pressures upon open-work
structures, worked out at an overturning pressure of from 18 lb. to 22
lb. per square foot. These bridges had been many years in existence; it
is, therefore, fair to assume that no such wind in the direction
required for overturning had expended its force upon them as to the
whole surface.
[Illustration: FIG. 28.]
Particulars were taken in 1895 of a notice-board, presenting about 12
square feet of surface, which was blown down in the great storm of March
24 of that year, at Bilston, in Staffordshire. It was situated at the
foot of a slight slope, over which the wind came, striking the
obstruction at right angles. The board was mounted on two oak posts of
fair quality and condition, which broke near the ground at bolt holes
(see Fig. 28). The force required to do this, at 9000 lb. modulus of
rupture--a moderate value--corresponds to 50 lb. per square foot on the
surface exposed above the break.
In the same neighbourhood, at the same time, considerable damage was
wrought in overturning chimney stacks, to buildings and roofs; the
general impression in the locality being that the storm was of
exceptional, even unprecedented, violence. Bilston, it should be noted,
lies high.
At Bidston Hill, near Birkenhead, on the same occasion, a pressure of 27
lb. was registered. In another part of the country it is said to have
been 37 lb. Wind is so capricious in its effects over small areas as to
render it probable that the maximum pressures have never been recorded;
but this is a matter of little importance where general stability and
strength only are concerned. The instances cited, though by themselves
insufficient to throw much light on the question, may be of use in
connection with other known examples.