The Anatomy of Bridgework
by William Henry Thorpe · English · Gutenberg #44371 · 324,812 chars · public domain (US)
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Title: The Anatomy of Bridgework
Author: William Henry Thorpe
Release date: December 6, 2013 [eBook #44371]
Most recently updated: October 23, 2024
Language: English
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Transcriber's Notes:
Text between underscores represents _italics_, small capitals have been
transcribed as ALL CAPITALS.
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(such as [T] and [U]) represent the shape rahter than the letter itself.
More Transcriber's Notes may be found at the end of this text.
THE
ANATOMY OF BRIDGEWORK
THE
ANATOMY OF BRIDGEWORK
BY
WILLIAM HENRY THORPE
ASSOC. M. INST. C. E.
WITH 103 ILLUSTRATIONS
[Illustration]
London
E. & F. N. SPON, LIMITED, 57 HAYMARKET
New York
SPON & CHAMBERLAIN, 123 LIBERTY STREET
1906
PREFACE
In offering this little book to the reader interested in Bridgework, the
author desires to express his acknowledgments to the proprietors of
“Engineering,” in which journal the papers first appeared, for their
courtesy in facilitating the production in book form.
It may possibly happen that the scanning of these pages will induce
others to observe and collect information extending our knowledge of
this subject--information which, while familiar to maintenance engineers
of experience, has not been so readily available as is desirable.
No theory which fails to stand the test of practical working can
maintain its claims to regard; the study of the behaviour of old work
has, therefore, a high educational value, and tends to the occasional
correction of views which might otherwise be complacently retained.
60 WINSHAM STREET,
CLAPHAM COMMON, LONDON, S.W.
_October_, 1906.
CONTENTS
CHAPTER I.
INTRODUCTION--GIRDER BEARINGS.
PAGE
Pressure distribution--Square and skew bearings--Fixed bearings--
Knuckles--Rollers--Yield of supports 1
CHAPTER II.
MAIN GIRDERS.
_Plate webs_: Improper loading of flanges--Twisting of girders--
Remedial measures--Cracks in webs--Stiffening of webs--[T]
stiffeners 9
_Open webs_: Common faults--Top booms--Buckling of bottom booms--
Counterbracing--Flat members 17
CHAPTER III.
BRIDGE FLOORS.
Liability to defects--Impact--Ends of cross and longitudinal
girders--Awkward riveting--Fixed ends to cross girders--Plated
floor--Liberal depths desirable--Type connections--Effect of “skew”
on floor--Water-tightness--Drainage--Timber floors--Jack arches--
Corrugated sheeting--Ballast--Rail joints--Effect of main girders
on floors 20
CHAPTER IV.
BRACING.
Effect of bracing on girders--Influence of skew on bracing--Flat
bars--Overhead girders--Main girders stiffened from floor--
Stiffening of light girders--Incomplete bracing--Tall piers--Sea
piers 34
CHAPTER V.
RIVETED CONNECTIONS.
Latitude in practice--Laboratory experiments--Care in considering
practical instances--Main girder web rivets--Lattice girders
investigated--Rivets in small girders--Faulty bridge floor--
Stresses in rivets--Cross girder connections--Tension in rivets--
Defective rivets--Loose rivets--Table of actual rivet stresses--
Bearing pressure--Permissible stresses--Proposed table--Immunity of
road bridges from loose rivets--Rivet spacing 45
CHAPTER VI.
HIGH STRESS.
Elastic limit--Care in calculation--Impact--Examples of high stress
--Early examples of high stress in steel girders--Tabulated
examples--General remarks 61
CHAPTER VII.
DEFORMATIONS.
Various kinds--Flexing of girder flanges--Examples--Settlement
deformations--Creeping--Temperature changes--Local distortions--
Imperfect workmanship--Deformation of cast-iron arches 73
CHAPTER VIII.
DEFLECTIONS.
Differences as between new work and old--Influence of booms and web
structure on deflection--Yield of rivets and stiffness of
connections--Working formulæ--Set--Effect of floor system--
Deflection diagrams--Loads quickly applied--“Drop” loads--Flexible
girders--Measuring deflections--New method of observing deflections
--Effect of running load 85
CHAPTER IX.
DECAY AND PAINTING.
Examples of rusting of wrought-iron girders--Girder over sea-water
--Rate of rusting--Steelwork--Precautions--Red-lead--Repainting--
Scraping--Girders built into masonry--Cast iron--Effect of sea-
water on cast iron--Examples--Tabulated observations--Percentage of
submersion--Quality of metal 96
CHAPTER X.
EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES.
Purpose--Methods of examination--Calculations--Stress in old work--
Methods of reducing stress--Repair--Loose rivets--Replacing wasted
flange plates--Adding new to old sections--Principles governing
additions--Example--Strengthening lattice girder bracings--Bracing
between girders--Strengthening floors--Distributing girders 107
CHAPTER XI.
STRENGTHENING OF RIVETED BRIDGES BY CENTRE GIRDERS.
Principal methods in use--Method of calculation--Adjustments--
Connections--Method of execution--Checks--Effect of skew on method
considered--Results of calculation for a typical case--Probable
error--Practical examples--Special case--Method of determining
flexure curves 122
CHAPTER XII.
CAST-IRON BRIDGES.
Limitations of cast iron--Stress examples--Advantages and
disadvantages--Foundry stresses--Examples--Want of ductility of
cast iron--Repairs--Restricted possibilities 141
CHAPTER XIII.
TIMBER BRIDGES.
Perishable nature--Causes of decay--Sag--Lateral bracing--Piles--
Uncertainty respecting decay--Examples--Conditions and practice
favourable to durability--Bracing--Protection--Repair--Piles--Cost 149
CHAPTER XIV.
MASONRY BRIDGES.
Definition--Cause of defects or failure--Spreading of abutments--
Closing in--Example--Stop piers--Example of failure--Strength of
rubble arch--Equilibrium of arches--Effect of vibration on masonry
--Safety centring--Methods of repair--Pointing--Rough dressed
stonework 157
CHAPTER XV.
LIFE OF BRIDGES--RELATIVE MERITS.
Previous history--Causes of limited life--Tabulated examples of
short-lived metallic bridges--Timber and masonry bridges--
Durability--Maintenance charges--First cost--Comparative merits--
Choice of material 165
CHAPTER XVI.
RECONSTRUCTION AND WIDENING OF BRIDGES.
CONCLUSION.
Measuring up--Railway under-bridges--Methods of reconstruction in
common use--Reconstruction of bridges of many openings--Timber
staging--Traffic arrangements--Sunday work--Railway over-bridges--
Widenings--Junction of new and old work--Concluding remarks--Study
of old bridgework 172
INDEX 187
THE
ANATOMY OF BRIDGEWORK.
CHAPTER I.
INTRODUCTION.
No book has, so far as the author is aware, been written upon that
aspect of bridgework to be treated in the following pages. No excuse
need, therefore, be given for adding to the already large amount of
published matter dealing with bridges. Indeed, as it too often happens
that the designing of such constructions, and their after-maintenance,
are in this country entirely separated, it cannot but be useful to give
such results of the behaviour of bridges, whether new or old, as have
come under observation.
In the early days of metallic bridges there was of necessity no
experience available to guide the engineer in his endeavour to avoid
objectionable features in design, and he was, as a result, compelled to
rely upon his own foresight and judgment in any attempt to anticipate
the effects of those influences to which his work might later be
subject. How heavily handicapped he must have been under these
conditions is evident from the mass of information since acquired by the
experimental study of the behaviour of metals under stress, and the
growth of the literature of bridgework during the last forty years. That
many mistakes were made is little occasion for surprise; rather is it a
cause for admiration that some very fine bridges, still in use, were
the product of that time. Much may be learned from the study of defects
and failures, even though they be of such a character that no
experienced designer would now furnish like examples.
Modern instances may, none the less, be found, with faults repeated,
which should long since have disappeared from all bridgework, and are
only to be accounted for by the unnatural divorce of design and
maintenance already referred to. As the reader proceeds, it may appear
that details are occasionally touched upon of a character altogether too
crude and objectionable to need comment; but the consideration of these
cases is none the less interesting, and, so far as the author’s
observation goes, not altogether unnecessary.
Most of the instances cited are of bridges, or parts of bridges, of
quite small dimensions; but it is these which most commonly give
trouble, both because the effects of impact are in such cases most
severely felt, and possibly because the smaller class of bridges is very
generally designed by men of less experience, than large and imposing
structures.
The particulars given relate in all cases to bridges of wrought iron,
unless otherwise described.
An endeavour has been made to secure some kind of order in dealing with
the subject, but it has been found difficult to avoid a somewhat
disjointed treatment, inseparable, perhaps, from the nature of the
matter. Finally, the reader may be assured that every case quoted has
come under the writer’s personal notice.
GIRDER BEARINGS.
In girder-work generally, and more particularly in plate-girders,
considerable latitude obtains in the amount of bearing allowed. Clearly,
the surface over which the pressure is distributed should be
sufficiently ample to avoid overloading and possible crushing or
fracture of bedstones where these exist; but if no knuckles are
introduced, this is an extremely difficult matter to insure. A long
bearing may deliver the load at the extreme end of the surface on which
it rests, or, more probably, near the face.
If the girder is made with truly level bearings, and the beds set level,
it will certainly, when under load, throw an extreme pressure upon that
part of the bearing surface immediately under the forward edge of the
bearing-plate. These considerations probably account for bedstones
frequently cracking, in addition to which possibility there is the
disadvantage that the designer does not know where the girder will rest,
and cannot truly define the span. The variation of flange-stress due to
this cause may, in a girder of ordinary proportions, having bearings
equal in length to the girder’s depth, be as much as 15 per cent. above
or below that intended.
If great care be taken in setting beds, in the first instance, to dip
toward the centre of the span an amount depending upon the anticipated
girder deflection, it may be possible to insure that when under full
load the girder bearing shall rest equally upon its seat; but this is
evidently a difficult condition to obtain practically, is good only for
one degree of loading, and may at any time be nullified by a disturbance
of the supports, as, for instance, the very common occurrence of a
slight leaning forward of abutment walls.
Double or treble thicknesses of hair-felt are sometimes placed beneath
girder bearings, with the object of securing a better distribution of
pressure, no doubt with advantage; but this practice, though it may be
quite satisfactory as applied to girders carrying an unchangeable load,
hardly meets the case for loads which are variable. Notwithstanding the
faulty nature of the plain bearing ordinarily used for girders of
moderate span, its extreme simplicity commends it to most engineers. It
must be admitted that no serious inconvenience need be anticipated in
the majority of cases, particularly if the bearings are limited in
length, do not approach nearer than 3 inches to the face of bedstones,
and are furnished with hair-felt or similar packing.
[Illustration: FIG. 1.]
Whether with long or short bearings, the forward edge should be at right
angles to the girder’s length. In skew bridges it is sometimes seen that
this edge follows the angle of skew. The effect on the girder is to
twist it, as will be clear from a little consideration. In evidence of
this the case may be quoted of a lattice girder of 95 feet effective
span and 7 feet deep, which, resting on a skew abutment right up to the
masonry face at a rather bad angle (about 15 degrees), was, after twenty
years, found canted over at the top to the extent of 4 inches, with the
further result of springing a joint in the top flange at about the
middle of the girder, causing some rivets to loosen. The bedstone was
also very badly broken at the face, and had to be replaced in the course
of repairs (Fig. 1). This girder had, in addition to the canting from
the upright position at its end, and the distortion of the top flange, a
curvature in the same direction, though less in amount, at the
bottom--an effect very common in the main girders of skew bridges, and
possibly accounted for in part by a tendency of the girder end to creep
along the abutment away from the point at which it bears hardest, under
frequent applications and removals of the live load, and accompanying
deflections.
This tendency to travel may be aggravated in bridges carrying a
ballasted road, in which there may be a considerable thickness of
ballast near the bearings, by the compacting and spreading of this
material taking effect upon the girder end, tending to push it outwards,
being tied only by a few light cross-girders badly placed for useful
effect. The movement may be prevented in new work for moderate angles of
skew by carrying the end cross-girders well back, and securing them in
some efficient manner; or by the introduction of a diagonal tie
following the skew face, and attached to cross and main girder flanges
(Fig. 2)--a method which may be applied to existing work also.
[Illustration: FIG. 2.]
For such a case as that cited it is imperative that ballast pressure at
the girder end should be altogether eliminated.
The fixing of girder ends by bolts--a practice at one time usual--hardly
calls for remark, as it is now seldom resorted to unless for special
reasons; but it may be well to point out the weakening effect of holes
for any purpose in bedstones. Bed-plates commonly need no fixing; the
weight carried keeps them in position, or if, in the case of very light
girders upon separate plates, it is considered well to secure these from
shifting, it may best be done by letting the plate in bodily a small
amount, or by means of a very shallow feather sunk into a chase.
[Illustration: FIG. 3.]
As an improvement upon the plain bearing usually adopted, it is an easy
matter so to design girder-ends as to deliver the load by a narrow strip
of bearing-plate carried across the bottom flange, distributing the
pressure upon the stone, if there be one, by means of a simple
rectangular plate of sufficient stoutness (Fig. 3). An imperfect knuckle
will by this means result, with freedom to slide, and the girder span be
defined within narrow limits. A true knuckle is, of course, the best
means of securing imposition of the load always in the same place; but
this by itself is not sufficient where the girder is of a length to make
temperature and stress variations important, in which case rollers, or
freedom to slide, become necessary. Bridges exist in which
roller-bearings have been adopted without the knuckle, or its
equivalent, but this is wholly indefensible, as it is obvious that the
forward roller will in all probability take the whole load, and cannot
be expected to keep its shape and roll freely under this mal-treatment.
It is sometimes asserted that rollers are never effective after some
years’ use; that they become clogged with dirt, and refuse to perform
their office.
There is no reason why rollers should not be boxed in to exclude dirt by
a casing easily removed, some attention being given to them, and any
possible accumulation of dirt removed each time the bridge is painted.
To test the behaviour of rollers under somewhat unfavourable conditions
for their proper action--that of the bearings of main roof trusses of
crescent form, 190 feet span--the author, some thirty years since, took
occasion to make the necessary observations, and found evidence of a
moderate roller movement, though there was in this case no direct
horizontal member to communicate motion. With girders resting upon
columns, particularly if of cast iron, a roller and knuckle arrangement
is most desirable for any but very small spans, as, if not adopted, the
result will be a canting of the columns from side to side--a very small
amount, it is true, but sufficient to throw the load upon the extreme
edges of the base, though the knuckle alone will relieve the top of this
danger. The author at one time took the trouble to examine, so far as it
could be done superficially and without opening out the ground to make a
complete inspection possible, a number of bridges crossing streets, in
which girders rested upon and were secured to cast-iron columns standing
in the line of kerb; and he found cracks, either at the top or bottom,
in about one of every four columns.
When girders passing over columns are not continuous, it may be
difficult to find room for a double roller and knuckle arrangement; but
this inconvenience may be overcome by carrying one girder-end wholly
across the column-top, and securing the next girder-end to it in a
manner which a little care and ingenuity will render satisfactory, one
free bearing then serving to carry the load from both girders.
Though the wisdom of using rollers is apparent in spans exceeding some
moderate length, say 80 feet--as to which engineers do not seem quite
decided--and varying with the conditions, it need not be overlooked that
in some cases masonry will be sufficiently accommodating to render them
unnecessary; piers, if sufficiently tall and slender, will yield a small
amount without injury, and though shorter, if resting upon a bottom not
absolutely rigid, will rock and give the necessary relief; but it is
obvious, if the resistance to movement is sufficiently great, and the
girder cannot slide or roll on its bearings, bedstones will probably
loosen, as, indeed, frequently happens.
CHAPTER II.
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.
CHAPTER III.
BRIDGE FLOORS.
The floors of bridges commonly give more trouble in maintenance, and
their defects are more frequently the cause which renders reconstruction
necessary, apart from reasons not concerning strength, than any other
part of such structures. When it is considered that this portion of a
bridge is first affected by impact of the load which comes upon it, and
is usually light in comparison with the main girders further removed
from the load, and to which the latter is transferred through the more
or less elastic floor, the fact will be readily appreciated by those not
already familiar with it.
The end attachments of cross and longitudinal girders are very liable to
suffer by loosening of rivets, or, more rarely, by breaking of the
angle-irons which commonly make such a connection. A not unusual defect
of old work, which may also sometimes be seen in work quite new, where
the cross-girder depth has from any cause been restricted, is the
extremely cramped position of the rivets securing the ends. There is
small chance of these ever being properly tight, if the act of riveting
is rendered difficult by bad design. This is the more objectionable if
it happens that cross-girder ends abut against opposite sides of the web
of an intermediate main girder, and are secured by the same rivets
passing through. At the best such rivets will not be well placed to
insure good workmanship, and the severe treatment to which they become
subject, as the cross-girders take their load and deflect under it,
will be very apt to loosen them. The author has seen a case of this kind
(see Figs. 11 and 12)--rather extreme, it is true--in which nearly the
whole of the cross-girder end rivets were loose, some nearly worn
through, thus allowing the cross-girders to be carried, not by their
attachments, but by resting upon the main-girder flanges, which in turn,
by repeated twisting, tore the web for a length of 4 feet; there was
also pronounced side flexure of the top booms. The movements generally
on this bridge (of 42-feet span), whether of main or cross-girders, were
very considerable and disturbing. It was removed after about
twenty-three years’ use.
[Illustration: FIG. 11.]
[Illustration: FIG. 12.]
There is no necessity, as a rule, for the ends of cross-girders attached
to the same main girder at opposite sides to be placed in line. The
author prefers to arrange them to miss, by which device each connection
is entirely separate, the riveting can be more efficiently executed,
erection is simplified, and the rivets will be more likely to keep
tight. Other special cases of cross-girder ends will be dealt with under
the head “Riveted Connections.”
It is sometimes contended that cross-girders attached at their ends by a
riveted connection should be designed as for fixed ends, in which case
they are usually made of the same flange section throughout, with a view
to satisfy the supposed requirements. But a girder to be rightly
considered as having fixed ends must be secured to something itself
unyielding. With an outer main girder of ordinary construction, and no
overhead bracing, this is so far from being the case as to leave little
occasion for taking the precaution named. As the cross-girders deflect,
the main girders will commonly yield slightly, inclining bodily towards
the cross-girders, if these are attached to the lower part of the main
girders. The force requisite to cant the main girders in this manner is
usually less than that which corresponds to fixing the cross-girder
ends, and is, generally, slight. It is, of course, necessary that this
measure of resistance at the connection should be borne in mind for the
sake of the joint itself, quite apart from any question of fixing.
Possibly, in quite exceptional cases, where very stiff main girders are
braced in such a manner as to prevent canting, it may be proper to
consider the cross-girder ends as fixed, or for those near the bearings
of heavy main girders; but the author has not met with any example where
cross-girders, apart from attachments, appear to have suffered from
neglect of this consideration.
With cross-girders placed on either side of a main girder, and in line,
it may also, for new work, be desirable to regard the ends as fixed, and
to detail them with this in view. It does not, however, appear wise to
carry this assumption to its logical issue, and reduce the flange
section to any appreciable extent on this account. The fixity of the
ends will, in any such case, be imperfect; and when one side only of an
intermediate main girder is loaded, it can have but a moderate effect in
reducing flange stress at the middle of the loaded floor beam.
[Illustration: FIG. 13. FIG. 14. FIG. 15.]
Similar reasons affect the design of longitudinal girder attachments to
cross-girders, which, if intended to support rails, cannot of necessity
be schemed to come other than in line. Where the floor is plated as one
plane surface, there will not usually be any trouble resulting if no
special precautions are used, as the plate itself will insure that the
longitudinals act, in a measure, as continuous beams, relieving the
joints of abnormal stress. If the plating is, however, designed in a
manner which does not present this advantage, or if the floor be of
timber, it is better to decide whether the connections shall be
considered as fixed, and made so; or avowedly flexible, and detailed in
such a manner as to possess a capacity for yielding slightly without
injury. Those connections are most likely to suffer which are neither of
the one character nor the other, offering resistance without the ability
to maintain it. Figs. 13, 14, and 15 give representations of three
“spring joint” methods of insuring yield in a greater or less degree.
For small longitudinals it is, perhaps, sufficient to use end angles
with very broad flanges against the cross-girder web; these to be
riveted in the manner indicated in Fig. 15.
Liberal depth to floor beams is distinctly advantageous where it can be
secured, rendering it easier to design the ends in a suitable manner, by
giving room near mid-depth of the attachment to get in the necessary
number of rivets; or where the ends are rigidly attached direct to
vertical members of an open-work truss, the greater depth is effective
in reducing the inclination of the end from the vertical, with a
correspondingly reduced cant of the main girders and flexure of the
vertical member, with smaller consequent secondary stresses. In any case
deep girders will contribute to stiffness of the floor itself,
favourable in railway bridges to the maintenance of permanent-way in
good order.
[Illustration: FIGS. 16, 17, 18.]
A point in connection with skew-bridge floors occasionally overlooked is
the combined effect of the skew, and main girder camber, in throwing the
floor structure out of truth, if no regard has been paid to this. The
result is bad cross-girder or other connections; or, in the case of
bearers running over the tops of main girders, a necessity for special
packings to bring all fair (Fig. 17). The author has in such cases,
where cross-girders are used, set the main girder beds at suitable
levels, in order that the cross-bearers may all be horizontal (see Figs.
16 and 18). This may not always be permissible; but, however the
difficulty may be met, it should be dealt with as part of the design.
For small angles of skew only may it be neglected.
Rivets attaching cross-girder angles to the web will occasionally
loosen, probably due in most cases to bad work, together with some
circumstance of aggravation, as in the case of a bridge floor consisting
of girders spaced 3 feet 6 inches apart, with short timber bearers
between, carrying rails. In many girders the top row of rivets, of
ordinary pitch and size, had loosened, allowing the web, about 1/4 inch
thick, a movement of 1/8 inch vertically. The rails being very close
down upon the cross-girder tops, though not intended to touch, had at
some time probably done so, and by “hammering” produced the result
described.
Plated floors are often found which are objectionable on account of
their inability to hold water, arising sometimes from bad work, as often
from wide spacing of rivets. With rivets arranged to be easily got at,
and pitched not more than 3 inches apart, a tight floor may be expected;
but it is still necessary to drain the floor by a sufficient number of
holes, provided with nozzles projecting below the underside of the
plate, and sufficiently long to deliver direct into gutters, where these
are necessary. Drain-holes should not be less frequent than one to every
50 square feet of floor, if flat, and may advantageously be more so.
Gutters should slope well, and care be taken to insure practicable
joints and good methods of attachment--a matter too often left to take
care of itself, with considerable after-annoyance as a result.
The use of asphalt, or asphalt concrete, to render a plated floor
water-tight is hardly to be relied upon for railway bridges, though no
doubt effective for those carrying roads. It is extremely difficult to
insure that it shall stand the jarring and disturbance to which it may
be subject, and under which it will commonly break up, and make matters
worse by holding moisture, and delaying the natural drying of the floor.
In bulk, as in troughs, it may be useful, but in thin coverings on
plates it cannot be depended upon.
Floors having plated tops are sometimes finished over abutments or piers
in a manner which is not satisfactory, either as regards the carrying of
loads or accessibility for painting. If the plates are carried on to a
dwarf wall with the intention that the free margin of the plate shall
rest upon it, there will be a difficulty in securing this in an
efficient manner. Commonly such a wall is built up after the girder work
is in place, making it difficult to insure that the wall really supports
the plate, the result being that this may have to carry itself as best
it can. In any case, severe corrosion will occur on the underside, and
the plate rust through much before the rest of the floor; the masonry
also will usually be disturbed.
It appears preferable to form the end of the floor with a vertical
skirting-plate having an angle or angles along the lower edge. This may
come down to a dwarf wall, but preferably not to touch it, the skirting
being designed to act as a carrying girder. A convenient arrangement is
shown in Fig. 19, which may be used either for a square or skew bridge.
It will be seen that the plate-girders have no end-plates, the skirting
referred to being carried continuously along the floor edge, and
attached to each girder-web, the whole of the more important parts being
open to the painter.
[Illustration: FIG. 19.]
Trough floors consisting of one or other of the forms of pressed or
rolled section present the objection that it is almost impracticable to
arrange an efficient connection at the ends, if they abut against main
girders, and but little connection is, as a rule, attempted, and
sometimes none. The result is that the load from these troughs is
delivered in an objectionable manner, and the ends being open or
imperfectly closed, water and dirt escape on to the flange, or other
ledge, which supports them. A description of pressed floor which
promises to overcome this objection, and provide a ready means of
attachment to the webs of plate-girders, or of booms having vertical
plate-webs, has within the last few years been introduced. This has the
ends shaped in such a manner as to close them and provide a flat surface
of sufficient area for connection by rivets. Each hollow is separately
drained by holes with nozzles. Whether this type of trough will develop
faults of its own, due to over-straining of the metal in the act of
pressing, remains to be seen; but as it appears possible to produce the
desired form without any material thinning or thickening of the metal,
the contention that no severe usage accompanies the process appears to
be reasonable.
That form of troughing in which the top and bottom portions are
separately formed, and connected by a horizontal seam of rivets at
mid-depth, is found in use upon railway bridges to be very liable to
loosening of those rivets near the ends; less surprising, perhaps,
because the sloping sides are usually thin.
It is a distinctly difficult matter to join two or more lengths of any
trough flooring having sloping sides, in a workmanlike manner; the fit
of covers is apt to be imperfect, and some rivets, being difficult of
access, are likely to be but indifferently tight, so that if the joint
occurs where it will be more than lightly stressed, trouble will
probably follow. A bad place for such joints is immediately over girders
supporting the troughs, as there the stress will be most severe, any
leakage come directly upon the girder, and remedial measures be more
difficult to carry out.
Timber floors of the best timber, close jointed, are more durable than
might be supposed. The disadvantage is a difficulty in ascertaining the
precise condition of the timber after many years’ use. The author has
seen timbers, 9 inches by 9 inches, forming in one length a close floor,
carried by three girders, and supporting two lines of way, which, when
taken out, could as to a considerable part be kicked to pieces with the
foot; whilst in another case, with the same arrangement of girders and
close-timbered floor, the wood, after being in place for thirty-two
years, was, when taken out, found to be perfectly sound, with the
exception of a very few bad places of no great extent. In this instance,
however, it is known that the floor--pitch-pine--was put in by a
contractor who prided himself upon the quality of the timber that he
used; the floor being also covered with tar concrete, which had in this
instance so well performed its office as to keep the timber quite dry on
the top.
Jack arches between girders make an excellent floor for road bridges,
though heavy; and for small bridges may be used to carry rails, if the
girders are designed to be stiff under load. The apprehension that
brickwork or concrete will separate from the girder-work, or become
broken up under even moderate vibration, does not seem to be well
founded, if the deflection is small and the brickwork or concrete good.
The use of corrugated sheeting as a means of rendering the underside of
a bridge drop dry cannot be too strongly deprecated. If it must be
adopted, the arrangement should be such as to permit ready removal for
inspection and painting. It is evident that by boxing up the floor
structure, rust is favoured, and serious defects may be developed, not
to be discovered till the sheeting is removed, or something happens.
[Illustration: FIG. 20.]
A case may be instanced in which it was found, on taking down sheeting
of this description, that the floor girders, previously hidden, were
badly wasted in the webs. One of these girders had cracked, as shown in
Fig. 20, and others were in a condition only less bad.
In any floor carrying ballast or macadam, if means are not adopted to
keep the road material from the structure of the floor, or from the main
girders, corrosion may be serious in its effects. Cinder ballast is,
perhaps, the worst in this respect, in its action upon steel or
ironwork, being distinctly more damaging than any other kind commonly
used.
Rail-joints upon bridge floors are to be avoided where practicable by
the use of rails as long as can be obtained; if the bridge is small
enough, crossing it in one length. At each joint there is likely to be
hammering and working extremely detrimental to floor members and
connections; indeed, it may happen that loose rivets will be found in
the neighbourhood of such joints, and nowhere else on the bridge. Where
rail-joints cannot be avoided, their position should, if there be any
choice, be judiciously selected, and the plate-layers taught to close
the joints and jam the fish-bolts.
[Illustration: FIG. 21.]
As rail-joints upon a bridge may injuriously affect the floor, so also
will a weak floor be very trying to the rails. A remarkable instance of
this has come under the writer’s notice, where a bridge (Fig. 21) of
three 33-feet spans, having outer and centre main girders, with
cross-girders spaced 3 feet apart, resting upon the girder flanges, but
not attached, and carrying two roads, had the permanent-way in a very
bad state. The rails proper, with supplementary angle-plates, rested
direct upon the cross-girders, which were decidedly light, and the whole
floor had much “life” in it, the ill-effect of which was shown in
thirteen breaks in the angle-plates, in each case near their ends,
generally at holes.
It appears probable that severe stresses may be thrown upon the parts of
a floor, whether placed at the level of the bottom booms or of the top,
by changes of length in the booms due to stress. The author has,
unfortunately, no direct evidence to offer in reference to this, tending
either for or against the contention. If an unplated floor of cross and
longitudinal girders of usual arrangement be at the bottom boom of a
large bridge, as the boom lengthens with the imposition of load upon the
bridge, all the cross-girders from the centre towards the abutments will
be curved horizontally, the middle portion being restrained by the
longitudinals from moving bodily with the ends. Each cross-girder except
that at the centre, if there be one, will thus present a figure in plan,
concave towards the abutment to which it is nearest. This will be
accompanied by stressing of the connections, and a transfer to the
longitudinals of as much of the tensile stress properly belonging to the
booms as the stiffness of the cross-girders may communicate.
This in itself will hardly be considerable, and will be the less on
account of a slight yielding which may be expected at the end
connections of each longitudinal; but the effect upon the cross-girders
by horizontal bending will be much marked. If the case be supposed of a
200-feet span in steel at ordinary loads and stresses, carrying one line
of way, with cross-girders 20 feet apart, and having no floor-plates, it
may be ascertained, neglecting for the moment any slight yielding of the
longitudinal girder connections, that upon the bridge taking its full
live load there will be the following approximate results: Movement at
each end of the end cross-girders of 3/10 inch, equivalent to a force of
7-1/2 tons, tending to bend them horizontally, and a mean stress on the
outer edges of the girders, 12 inches wide, of 8 tons per square inch
due to flexure, which, compounded with the ordinary flange stresses,
will seem to give rather alarming results. There will also be a
longitudinal stress in the rail-girders, at centre part of bridge, of
3/4 ton per square inch. Normal elongation of the longitudinal girder
bottom flanges, and compression of the top, modifies the figures
unfavourably as to the cross-girder top flange. Yielding of the
connections named before has been neglected in arriving at these
stresses. If they are sufficiently accommodating to give freely, to a
mean extent, as between the top and bottom of each joint, of 1/29 inch,
these results will disappear. It is evident, however, that we cannot
rely upon good work yielding without the existence of considerable
forces to cause it. In the issue it is justifiable to apprehend that the
flexing and stressing of the cross-girders will be considerable.
The most favourable case has been taken; if now it is assumed that the
floor has continuous plating, the results would seem to be much more
astonishing. It will appear on this supposition that the boom stresses,
instead of being taken wholly by the booms, are about equally divided
between these and the floor structure, each cross-girder connection
communicating its share of boom stress to the floor, which for the end
cross-girders will approach 40 tons at each connection--considerably
more than the vertical reaction under normal loads.
Palpably, these conclusions must be greatly modified by the yield of
longitudinal girder ends, and slip of the floor rivets in transverse
seams. If these rivets be 3-1/2 inch pitch and 3/4 inch in diameter, the
stress at each, as estimated, would be sufficient to induce shear of
about 6 tons per square inch--more than enough to cause “slip.” After
making this allowance, it is still evident there must be very serious
forces at work about the ends of cross-girders under the conditions
supposed, probably not less than one half the amounts named, as with
this reduction the floor rivets should not yield, given reasonably good
work. It is to be observed that the effect of live load only has been
introduced, on the presumption that the longitudinals and floor-plating
have not been riveted up till the main girders have been allowed to
carry the major part of the dead load; but even this cannot always be
conceded. The deduction appears to be that the floor and cross-girder
connections should be studied with special reference to these possible
effects, either with the object of rendering the communication of these
forces harmless, or making the floor so that it shall take little or no
stress from the main booms, by arranging joints across the floor
specially designed to yield, the ends of longitudinals being schemed
with the same object. Where there is no plating, the case is, perhaps,
sufficiently provided for by making the cross-girders narrow, and the
longitudinal girder connections flexible, or by putting these girders
upon the top of the cross-girders, when stretching of the bottom flanges
of the rail-bearers under load may be expected, within a little, to keep
pace with the lengthening of the main booms.
It would appear that light pressed troughs running across the
longitudinals would, by yielding in every section, also furnish relief,
as compared with the rigidity of flat plates.
By placing the floor at a level corresponding to the neutral axis of the
main girders, the communication of stress to the floor may be avoided;
but it seldom happens that there is so free a choice as to floor height
relative to the girders. This solution is, therefore, of limited
application.
It is obvious that somewhat similar effects must obtain to those
considered in detail, when the floor structure lies at the level of top
booms, but with forces of compression from the booms to deal with,
instead of tension.
CHAPTER IV.
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.
CHAPTER V.
RIVETED CONNECTIONS.
Considerable latitude is observable in the practice of engineers in the
use of rivets. Numberless experiments to determine the resistance of
riveted connections have from time to time been made, but these are not
to be considered by themselves as final, when the results of experience
in actual construction, are available for further enlightenment.
The class of workmanship so largely influences the degree in which
rivets will maintain their integrity that it is only by the observation
of a large number of cases, including all degrees of workmanship, that
any reliable conclusions may be drawn. In this respect laboratory
experiments have an apparent advantage, as the conditions may be kept
sensibly the same; but, on the other hand, no such investigation
reproduces the circumstances of actual use, which alone must in the end
determine the utility of any inquiry for practical application.
The author has studied the particulars of a number of cases to ascertain
under what conditions as to stress, having due regard to the effects of
vibration, rivets will remain tight, or become loose. Every loose rivet
that may be found cannot, of course, be taken as being due to excessive
stress; the more frequent cause is indifferent work, evidenced by the
fact that neighbouring rivets will frequently be found quite sound,
though the failure of some will cause a greater stress upon the
remainder. When rivets loosen as the direct result of over-stress, it is
usually by compression of the shank and enlargement of the hole, or by
stretching of the rivet and reduction of its diameter. Instances of
failure by partial or complete shear are extremely rare; indeed, the
author has never yet found one, though when a rivet has first worked
loose, as a result of excessive bearing pressure or bad work, it is not
uncommon to find it cut or bent as an after consequence.
In estimating stresses at which rivets have remained tight, or loosened,
as the case may be, examples have generally been chosen in which there
could be no reasonable doubt as to the amount of those stresses by the
ordinary methods of computation. This is clearly most important, as, if
any appreciable uncertainty remained as to the degree of stress, the
results deduced would be of little value. For this reason those
instances in which the loads upon girders, or parts of girders, may find
their way to the supports by more than one route, are to be regarded
with caution, as are those in which full loading possibly never obtains,
but which may, on the other hand, perhaps have been frequent. The
working diameter of the rivet as it fills the hole has been used in
making the computations; in some cases from direct measurement from
particular rivets, in others with a suitable allowance for excess
diameter of hole, according to the class of work under consideration.
Dealing first with main girders, it may be said that rivets attaching
the webs of plate girders to the flange angles rarely loosen, though
subject to considerable stress. In illustration of this may be named a
bridge for two lines of way, 85 feet effective span, having two main
girders with plate webs, and cross-girders resting on the top flanges,
previously referred to (see Fig. 26).
The girders, which were 6 feet 9 inches deep, had a bearing upon the
abutments of 4 feet; the rivets were 7/8 inch in diameter and 4 inches
pitch. There is in a case of this kind some little uncertainty as to
what is the stress on the flange angle rivets at, or very near to, the
bearings; but, taking the vertical rows of rivets at the web joints near
the ends as presenting less uncertainty, the stress per rivet works out
at 4·8 tons, being 4 tons per square inch on each shear surface, and 11
tons per square inch bearing pressure upon the shank in the web plate,
which was barely 1/2 inch thick. This bridge was frequently loaded upon
both roads, but with one road only carrying live load, the stresses in
the more heavily loaded girder would be fully 90 per cent. of those
obtaining as a maximum. There was on this bridge, which had been in use
31 years, considerable movement and vibration.
It is by no means uncommon to find cases of rivets in main girders
taking 11 tons per square inch bearing pressure--occasionally more--and
remaining tight. As furnishing an instructive, though slightly
ambiguous, instance of rivets in single shear, may be cited a bridge not
greatly less than that just referred to, of about 65 feet span, carrying
two lines of way, there being two outer and one centre main girder of
multiple lattice type, with cross-girders in one length 4 feet apart,
riveted to the bottom booms of the main girders; these rivets, by the
way, were in tension. The floor was plated, the road consisting of stout
timber longitudinals, chairs, and rails (Fig. 29).
[Illustration: FIG. 29.]
It should be noted that there is in this case some difficulty in
ascertaining the precise behaviour of the cross-girders, affecting the
proportion of load carried by the outer and the inner main girders.
Strict continuity of all the cross-girders could only obtain if the
deflection of the main girders were such as to keep the three points of
suspension of each cross-girder in the same straight line. A close
inquiry showed that this was very far from being the case, and that
while each cross-girder at the centre of the bridge would, under load,
by relative depression of the middle point of support, be reduced to
the condition of two simple beams, those at the extreme ends of the span
would behave as continuous girders.
With both roads carrying engine loads equal to those coming upon the
bridge, the author estimates that for the centre main girder the shear
on the rivets of the end diagonals, secured by one rivet only, was 14·9
tons per square inch, and the bearing pressure 16·3 tons; the flange
stress being 7·1 tons per square inch net. The outer main girders are
most heavily stressed when but one road, next to the outer girder
considered, carries live load. For this condition the stresses work out
at 9 tons per square inch shear on the rivets of the end diagonals, and
9 tons bearing pressure, the flange stress being 5·7 tons per square
inch on the net section.
Without intending to throw any doubt upon the substantial truth of these
results, it must be admitted that instances of greater simplicity of
stress determination are much to be preferred. For purposes of
comparison, but not as having any other value, the results have also
been worked out on the supposition of all cross-girders acting each as
two simple beams, and also for strict continuity, and are here
tabulated, together with the conclusions given above.
The cross-girders were moderately stressed, and the tension on the
rivets attaching them to the main girders probably did not exceed 3 tons
per square inch.
It should be pointed out that the traffic over the bridge was small. The
centre main girder but seldom bore its full load, though at all times
liable to receive it. Much importance cannot, therefore, be attached to
the results for this girder, other than as showing how a structure may
stand for many years, though liable at any time to the development of
stresses which would commonly be regarded as destructive, or nearly so.
EXAMPLES OF RIVET STRESSES, ETC., IN LATTICE GIRDERS.
---------------------------------+-----------+------------+---------
| Cross- | Cross- |
| Girders | Girders as | Correct
| as Simple | Continuous | Results.
-- | Beams. | Beams. |
+-----------+------------+---------
| Stress in Tons per Square Inch.
---------------------------------+-----------+------------+---------
Centre girder, 63 ft. span (both | | |
roads loaded): | | |
Rivets in diagonals--Shear | 13·7 | 17·2 | 14·9
Do. Bearing | | |
pressure | 15·0 | 18·8 | 16·3
Flange | | |
stress | 6·8 | 8·5 | 7·1
| | |
Outer girder, 66 ft. span (near | | |
road loaded): | | |
Rivets in diagonals--Shear | 9·6 | 8·2 | 9·0
Do. Bearing | | |
pressure | 9·6 | 8·2 | 9·0
Flange | | |
stress | 5·9 | 5·1 | 5·7
---------------------------------+-----------+------------+---------
The material and workmanship of the bridge were good. The rivets of the
centre girder end diagonals, 1 inch in diameter, were originally 7/8
inch, but on becoming loose were cut out, the holes reamered, and
replaced by the larger size, which remained tight, and to which the
stress figures apply. The rivets in the diagonals near the centre, 7/8
inch in diameter, which were subject to reversal of stress, occasionally
worked loose, and were more than once replaced. The riveting in the
outer girder diagonals, subject to smaller stresses, much more
frequently developed, also gave trouble, particularly those liable to
counter stresses.
Apart from looseness of rivets, the general appearance and behaviour of
the bridge, which had been in existence about twenty years, was not
suggestive of any weakness.
Of smaller girders, an example showing the necessity for care in
discriminating, if it be possible, between looseness of rivets resulting
from over-stress and that due to other influences may first be quoted.
Two trough girders, of 11 feet effective span, each of the section shown
in Fig. 30, 11-1/2 inches deep at the ends, 14 inches at the middle,
with 1/4-inch webs, and rivets 3/4 inch in diameter, of 4-1/2-inch
pitch, showed certain defects, of which one, it may be incidentally
mentioned, was a cracked web (Fig. 31). From the nature of the
arrangement the lower web rivets, which were loose, would receive the
first shock of the load coming upon the span, but there were evidences
indicative of original bad work. The angle bars gaped, suggesting that
these had first been riveted to the bottom plate, and left sufficiently
wide to allow the web to be afterwards inserted, the rivets failing to
pull the work close, and then readily working loose. Here there is
considerable uncertainty as to how much of the loosening is to be
attributed to bad work, and how much to stress. It may, however, be
remarked that whatever bearing stress was the ultimate result of the
load hammering on the lower angle flanges, loosening rivets never
perhaps really tight, the stress of 7 tons per square inch bearing
pressure on the upper rivets, though aggravated by considerable
impactive force, was not sufficient to loosen these. The girders were
taken out after being in place sixteen years.
[Illustration: FIG. 32.]
[Illustration: FIG. 30.]
[Illustration: FIG. 31.]
An instance of undoubted excessive bearing pressure was found in the
cross-girders of a bridge, mentioned on p. 15, of which so many web
plates were cracked. This bridge, carrying two lines of way, had outer
main girders, and long cross-girders with 1/4-inch webs and 3/4-inch
rivets, 4 inches pitch. The rivet stresses work out at 4·3 tons per
square inch on each shear surface, and 24 tons per square inch bearing
pressure. For one road only being loaded, the latter figure falls to
18·5 tons. The traffic over this bridge, twenty years old, was
considerable, rapid, and heavy. It is hardly necessary to add that a
large number of the rivets were loose, one of which is shown in Fig. 32.
[Illustration: FIG. 33.]
To take another case relating to a floor system of extremely bad design
(Fig. 33). The main girders were 11 feet apart, 35 feet span, the floor
having two cross-girders only, spaced at 11 feet 3 inches, and 9 inches
deep, supporting hog-backed trough longitudinals. The cross-girders were
at their ends but 6-3/4 inches deep, the distance from the bearing of
cross-girders to centre of longitudinals carrying a rail being 2 feet 10
inches, in which length were eight rivets in the web and angles at the
top, and six at the bottom, all 3/4 inch in diameter.
The shear stress on the upper rivets works out at 7·3 tons per square
inch on each shear surface, the bearing pressure 20·6 tons per square
inch. On the lower rivets the shear stress becomes 9·7 tons, and the
bearing pressure 27·4 tons, per square inch. Care was exercised in
computing these stresses, that part of the bending moment carried by the
web being allowed for, but it must be admitted that the result is,
probably, approximate only. The sketch here given shows the cross-girder
end and section. The rivets, though in double shear, were, as might be
expected, loose, notwithstanding that the traffic over the bridge was
moderate, and quite slow. The floor system was remodelled after twelve
years’ use.
In illustration of the behaviour of rivets in the ends of long
cross-girders, both shallow and weak, and many years in use under heavy
traffic, may be cited connections having end angle bars to the
cross-girders, with six rivets through the web of main girders. The
bearing pressure worked out at 7·8 tons per square inch. Many rivets
were loose, but it should be remarked that the workmanship was not of
the best class, and the cross girders flexible: a characteristic very
trying to end rivets, and inducing a stretch in some, already referred
to as a possible cause of loosening. This will be apparent if the
probable end slope of weak girders be considered. The author concludes
that this inclination should not, for ordinary cases, exceed 1 in 250;
but the ratio must largely depend upon the degree of rigidity of the
part to which the connection is made. It is commonly regarded as bad
practice to submit rivets to tension, yet this is frequently, though
unintentionally, permitted in end attachments, without any attempt to
limit the amount of tension. With suitable restrictions, there appears
no serious objection to rivet tension for many situations.
Another instance of cross-girder end connections of a different type is
illustrated in Fig. 34.
The main girders of the bridge were 12 feet apart, each cross-girder end
carrying its share of the half of one road. The mean bearing pressure
upon the rivet shanks works out at 5·8 tons per square inch for the six
rivets of the original joint, but in the particular joint shown some of
the rivets had loosened, making the bearing pressure upon the remainder
about 8·7 tons per square inch. It is apparent there must have been
considerable stress on the top and bottom rivets which loosened. These
two rivets would also, because of difficult access, be in all likelihood
insufficiently hammered up. The joints worked rather badly; the loose
rivets had “cut” to a considerable extent, a process materially assisted
by the gritty nature of the ballast (limestone), particles of which,
getting into the joint, contributed to the sawing action; this had
clearly been taking effect for some considerable time. (See Fig. 35.)
[Illustration: FIG. 34.]
[Illustration: FIG. 35.]
The two cases of cross-girder ends given are both rather exceptional in
character, and in each case the defects appear to be due to general bad
design and workmanship rather than to any serious excess of bearing
pressure. This may be illustrated by taking the common case of
cross-girders, 2 feet deep, carrying two roads, and having end angle
irons riveted to the web and stiffeners of the main girders by ten
rivets in single shear at each end. In this example, which is, for old
work, simply typical, and does not relate to any specific instance, the
bearing pressure on the rivets will work out at from 6 to 8 tons per
square inch, and will seldom be accompanied by looseness of rivets, and
then only as a result of faulty work.
Some sketches of rivets taken from old bridges have already been given
in connection with the cases to which they belong; a few others are here
shown (Figs. 36 to 40) to further illustrate what may be the actual
condition of rivets after some years’ use, and how different from the
ideal rivet upon which calculations are based. These are, however, bad
instances.
[Illustration: FIG. 36.]
[Illustration: FIG. 37.]
[Illustration: FIG. 38.]
[Illustration: FIG. 39.]
[Illustration: FIG. 40.]
It should be noticed that rivets may, if in double shear, be loose in
the middle thickness, due to enlargement of the hole in the central part
and compression of the rivet, and yet show no sign of this by testing
with the hammer. There is, however, generally marked evidence of another
kind in the “working” of the inner part, as, for instance, the web of a
plate girder, in which case a discoloration due to rust is to be found
along the edges of the angle bars, or a movement may be detected on the
passage of live load. Red rust is, in fact, frequently an indication of
something wrong, when no other evidence is apparent. In plate girders
having [T] or [L] bars brought down and cranked on to the top of shallow
cross-girders, it is not uncommon to find the rivets attaching these
bars to the cross-girder tops loose, due to causes already dealt with.
The riveted connection should, as to strength, bear some relation to the
strength and stiffness of the parts secured, if the rivets are to remain
sound.
It may be well to give here a summarised statement of the results
already named, for purposes of ready reference. These by themselves are
not sufficient to enable working stresses to be deduced, though they are
instructive. The author has found many instances of shear and bearing
stresses in excess of those usually sanctioned, under which the rivets
behaved well, but is not now able to give precise particulars of these.
EXAMPLES OF RIVET STRESSES.
---------+-----+---------+------+------+--------+-----------------
-- |Span | Where |Shear |Single|Bearing | Tight or Loose.
| in | Found. |Stress| or |Pressure|
|Feet.| | in |Double|in Tons |
| | | Tons |Shear.| per |
| | | per | | Square |
| | |Square| | Inch. |
| | |Inch. | | |
---------+-----+---------+------+------+--------+-----------------
Main {| 85 | Web | 4·0 | D | 11·0 | Tight.
girders {| 66 |Diagonals| 9·0 | S | 9·0 | Many loose.
{| 63 | „ | 14·9 | S | 16·3 | Tight generally.
| | | | | |
{| 11 | Web | 1·4 | D | 7·0 | Tight.
Small {| 26 | „ | 4·3 | D | 24·0 | Many loose.
girders {| 11 | „ | 7·3 | D | 20·6 | Loose.
{| 11 | „ | 9·7 | D | 27·4 | Loose.
| | | | | |
End {| 27 | Ends | 5·4 | S | 7·8 | Loose.
connec- {| 12 | „ | 1·8 | D | {5·8 |}Many loose.
tions {| | | | | {8·7 |}
| | | | | |
(Type | | | | | |
case) | 26 | „ | 4·8 | S | 7·0 | Tight.
---------+-----+---------+------+------+--------+-----------------
It is probable that the fact of a rivet being in single or in double
shear largely affects its ability to resist the effects of bearing
pressure, as commonly estimated. In the first case, the rivet-shank must
bear heavily on the half-thickness of the plates or bars through which
it passes, rather than on the whole thickness; and it is to be supposed
that under this condition it will work loose at a lower average stress
than if it were in double shear, and the pressure better distributed.
[Illustration: FIG. 41.]
[Illustration: FIG. 42.]
The author has no very definite information in support of this
contention, but suggests that for double shear the permissible bearing
pressure may probably be as much as 50 per cent. greater than for rivets
in single shear; the difference being made rather in the direction of
increasing the allowable load on double-shear rivets, than in reducing
that upon rivets in single shear. The propriety of this is evident when
it is considered that the practice has commonly been to make no
distinction, so that whatever bearing pressures are found to be
sufficient for both cases may be increased for those capable of taking
the greater amount. Figs. 41 and 42, here given, illustrate the
behaviour of rivets under the two conditions.
With reference to the amounts of the stresses to which rivets may be
subject, the author concludes, as a result of his experience, coupled
with a consideration of known laboratory tests, that for all dead load
these may be quite prudently higher than is frequently taken. For iron
the shear stress to be 10 per cent. less than the stress of parts
joined; and the bearing pressure--for single-shear rivets, 20 per cent.;
and for double-shear rivets, 80 per cent. greater. For ordinary mild
steel the shear stress to be 20 per cent. less than the stress in parts
connected, and the bearing pressure equal to it for single-shear rivets;
and 50 per cent. more for rivets in double shear, though the two latter
values may probably approach those for wrought iron in steel of the
higher grades sometimes used in bridge-work. For live load, or part live
and part dead load, the same rules may apply, the reduction of the
nominal working stress, arrived at by any one of the methods in use
which may be adopted, affecting both the parts connected, and the rivets
connecting them. For reverse stresses it is advisable to keep the shear
stress in any rivet so low, say 3 tons per square inch, that the
frictional resistance of the parts gripped by the rivets shall be
sufficient to prevent any tendency to slip under the influence of the
smaller of the two forces to which the part is liable, to insure that,
if brought to a bearing in one direction by the greater force, it shall
not go back with reversal of stress. This requirement may be open to
some question with respect to good machine-riveted work, but for
hand-riveted connections it may certainly be adopted with wisdom.
The following table will show at a glance how the stresses proposed vary
with the unit stresses governing the main sections.
PROPOSED TABLE OF RIVET STRESSES.
-----------+-------------+----------------+----------------
Unit Stress| |Bearing Pressure|Bearing Pressure
in |Shear Stress.|for Single-Shear|for Double-Shear
Member. | | Rivets. | Rivets.
-----------+-------------+----------------+----------------
_Wrought Iron.--Tons per Square Inch._
3·0 | 2·7 | 3·6 | 5·4
4·0 | 3·6 | 4·8 | 7·2
5·0 | 4·5 | 6·0 | 9·0
6·0 | 5·4 | 7·2 | 10·8
7·0 | 6·3 | 8·4 | 12·6
_Steel.--Tons per Square Inch._
4·0 | 3·2 | 4·0 | 6·0
5·0 | 4·0 | 5·0 | 7·5
6·0 | 4·8 | 6·0 | 9·0
7·0 | 5·6 | 7·0 | 10·5
8·0 | 6·4 | 8·0 | 12·0
9·0 | 7·2 | 9·0 | 13·5
-----------+-------------+----------------+----------------
NOTE.--Tension on rivets to be limited to one-half the permissible
shear stress, the holes being slightly countersunk under snap-head.
It may be objected that the shear stresses in the proposed table are
somewhat high for wrought iron and steel. This feature is intentional,
and is supported by the consideration that whereas there may be loss of
strength in the members of a structure by waste, there is no such loss
in rivets, if the work is so designed that there shall be no loosening.
Any allowance that may be desirable for loose or defective field rivets
is left to be dealt with as may be considered advisable for each
particular case, the table as it stands being applicable only to
riveting not below the standard of first-rate hand work.
Cases of loose rivets in main girders over 50 feet span, due to any
cause but bad work, are extremely rare, unless resulting from the action
of some other part of the structure. It may be stated broadly that for
railway bridges of less than perfect design, the nearer the rail, the
more loose rivets, generally at connections. This is, no doubt, largely
due to the severe impact of the load, the effects of which are greater
near the rail, both because of the small proportion of dead load, and
because this effect has been but little modified by the elasticity of
any considerable length of intervening girder-work. In addition to this,
it is quite usual to find the rivets more heavily stressed, even though
the load be considered as “static,” in the floor system than in the
main-girders, though the reverse should be the case. It is unfortunate
that those parts which require the best riveting--viz., the
connections--are commonly dealt with by hand; and for this reason it is
the more necessary to design these with the greatest care.
Any arrangement which favours the gradual acceptance of stress by one
part from another will contribute to the integrity of riveted
connections, and lessen the liability of the material to develop faults.
In other branches of design this is well recognised, but appears in much
old bridge work to have been entirely overlooked.
Bridges carrying public roads very seldom furnish examples of loose
rivets; the conditions are generally much more favourable, impact being
practically absent, full loading infrequent, and the proportion of dead
load to live, high.
It is, perhaps, hardly necessary to insist upon rivets being, apart from
mere considerations of strength, sufficiently near together to insure
close work and exclude moisture. Outside edge seams should never be more
widely spaced than 16 times the thickness of the plates; 12 thicknesses
apart is better. In the case of angle, tee, and channel sections, the
greater stiffness of the section makes wider spacing allowable up to,
say, 20 times the thickness; but this must be governed largely by the
amount of riveting required to pull the parts close together. Where more
than four thicknesses are to be gripped by the rivets, 3/4 inch in
diameter is hardly sufficient to insure tight work, and quite unsuitable
if the plates exceed 5/8 inch thick.
CHAPTER VI.
HIGH STRESS.
High stress, provided it be well below that at which immediate injury
results, or possible failure, is not uniformly objectionable. It may be
first considered relative to the absolute and elastic limits of
strength, next with respect to the range of stress, and, finally, with
regard to the frequency of application. For practical purposes--that is,
for the continued efficiency of a structure--the limit of elasticity
must be considered to be the limit of strength, or, more strictly, the
limit for all those parts of the structure which must, so long as it
lasts, be liable to the original measure of stress. There may be places
in a bridge, however, over-stressed only in the earlier period of its
existence, which, by being over-stressed and suffering deformation,
permit the origin of this distortion to be harmlessly met in some other
way. In such a case the injury done to that part does not, of necessity,
lead to any culminating disaster; indeed, were it not for this
plasticity it is probable a large number of bridges would fail after
being in use but a short time. As for riveting, so in dealing with the
amount of stress to which a member is supposed to be liable, it should
be clearly understood by what method this has been arrived at, whether
the value assigned is the actual measure of the stress, or simply the
conventional amount arrived at in the conventional way; perhaps
neglecting web section in plate girders, or without regard to the
various influences which may reduce or increase the nominal amount of
stress, or including only a partial recognition of those influences. In
any case quoted the stress named is that at which the author arrives by
the ordinary methods of computation carefully applied, where these
appear to be sufficiently precise, unless any qualifying remark be
added. Extreme flange stress is in special cases computed, first on the
gross section by estimating the moment of inertia on that basis, and
deducing the stress at the holes from the ratio of net to gross section
at the extreme fibres; a method more correct than by reference to the
moment of inertia of the net section. Any exhaustive refinement in the
study of stresses is not attempted, both because it is beyond the
author’s powers of analysis, and for the reason that such results are
not comparable with the results of ordinary methods of calculation in
practice. Effective spans are taken at moderate values, and all
exaggeration is avoided.
The effects of impact in any part vary so much with nearness to, or
remoteness from, the living load, and the frequency of development of
the maximum stress from all causes acting together is so much affected
by the same consideration, that it is apparent a nominal stress which
may be harmless in one part of a bridge may be destructive in some
other, a statement borne out by observation. Stress, as ordinarily
stated--i.e., at so much per square inch, uniform across a section--is
seldom a cause of trouble. In nearly all cases of failure there is an
accompanying localised destructive stress, either in rivets or
elsewhere, with crippling or deformation of some essential part. In the
tension flanges of main girders with uncomplicated stress, this may run
up to an amount very considerably beyond the ordinary limits without
producing signs of distress. The same remark applies to the compression
flanges, if these be in themselves sufficiently stiff, or properly
restrained from side flexure. In support of the above statement may be
quoted the following instances relating to wrought-iron structures:--
A bridge of 60 feet effective span, having girders immediately under the
rails, had a flange stress of 6·3 tons per square inch. Another of 64
feet span, carrying two lines of way, with outside main girders and
cross-girders, had the flanges of the former stressed to 6·8 tons per
square inch. A third, of 76 feet span, of similar construction to the
last, was stressed in the main girder flanges to 7·5 tons per square
inch. The webs were not included in the computation; the figures,
therefore, compare with ordinary practice. In these three cases the main
girders showed no signs of distress, referable to the results stated,
though the top flanges in the last case were curved inwards. The effect
of this flexing of the flange would be, of course, to increase the
amount of compressive stress along one edge, though to what degree
cannot now be stated.
[Illustration: FIG. 43.]
[Illustration: FIG. 45.]
[Illustration: FIG. 44.]
A further instance of considerable flange stress occurred in a bridge of
seven nearly equal continuous spans, 25 feet generally, the end and
greatest span being 29 feet 6 inches, centre to centre of bearings. Some
details of the bridge are given in Figs. 43 to 45. The four inner main
girders under rails were 2 feet deep, with webs 1/2 inch thick over
piers, and 3/8 inch at abutments, having flanges of two [L] bars, 3
inches by 3 inches by 5/8 inch. There were also two outer girders of the
same depth, with single [L] bars. Plate diaphragms of full girder depth
and particularly stiff were carried right across the bridge at the
centre of the spans, and over the piers. The girders, though evidently
designed to be continuous, had very poor flange joints at each bearing,
of little more than one half the flange strength (see Fig. 45). It is
doubtful if the girders acted with strict continuity for long after
erection, as the excessive stress in the rivets of the flange joint
would, for that condition, have been nearly sufficient to shear them. It
is probable that this being so, the joints first yielded, relieving the
bending moment over the piers, and increasing it near mid-span. Whether
the end spans be considered as strictly continuous with the rest, or as
simple beams, the maximum bending moments would not greatly differ,
though occurring for continuity over the pier, for free beams at the
centre. There is, however, an intermediate condition which makes the
moments at these two places less than either maximum, but equal to each
other; a condition of semi-continuity agreeable to a partial efficiency
of the joints referred to. It is this state which has been calculated,
giving the minimum stress value that can be accepted. The diaphragm has
been assumed to transfer to the outer girders a due proportion of the
load. With this explanation it may now be stated that, under engine
loads corresponding to those running, the flange stress worked out at
7·4 tons per square inch tension, web included, or 9·7 tons per square
inch without considering the web; which stresses, it is more than
probable, may have been greater. The figures include the consideration
of anything which may contribute to lowering the stress, and are hardly
to be compared with those worked to in ordinary design of new work, in
which it would be quite usual to neglect the assistance of the outer
girders and the webs, to work to heaviest engine-loads, and possibly
include an allowance for the effects of settlement. Dealt with in this
way the girders would seem to be of about one-fourth the strength that
would be required in the design of a new bridge, in which certain
elements of strength would be deliberately ignored.
The ironwork was in good condition, there was no ordinary evidence of
weakness apart from the calculated results, the vibration was distinctly
moderate, and the deflection, though not recorded, was certainly small.
The bridge did, indeed, seem somewhat inert under load, and favours a
suspicion, the author entertains, that old girderwork long overstressed
may have a sensibly higher modulus of elasticity than newer work at more
moderate stresses. The traffic was not very considerable, and both
roads, of the same spans, but seldom loaded at the same time; though
with this construction of bridge there would in either case be very
little difference. The author recalls no reason for supposing that the
piers had yielded in any sensible degree. The bridge was rebuilt after
some thirty-six years’ use.
Stress of considerable amount in the flanges of a latticed main girder
of 63 feet span has already been noticed in the chapter on “Riveted
Connections,” which for the tension boom worked out to 7·1 tons per
square inch, the flanges in this case showing no signs of weakness. An
instance has also been given in dealing with a case of side flexure in
which the extreme fibre stress was calculated to be 10 tons per square
inch, the girder recovering its form when relieved of load.
As to stress in cross-girder flanges, an example may be quoted of a
bridge of 109 feet span, carrying two roads, having outside main
girders, with cross-girders between; these latter were stressed in the
flanges to 6·7 tons per square inch (webs not included), if the partial
distribution among the girders (which were spaced 6 feet apart) by the
rails and longitudinal timbers be neglected. There is some reason to
think in this instance that distribution had the effect of reducing the
stress quoted, as the observed deflection of the cross-girders was
materially less than that calculated for girders acting independently of
each other, though this may be in part due to a cause already hinted at.
Rigidity of the cross-girder ends, where attached to the heavy main
girders, would also tend to moderate the stress. No very definite
conclusion can therefore be deduced from this instance.
To take another case of less uncertainty, the bridge of 35 feet span
(see Fig. 33), referred to in “Riveted Connections,” may again be cited.
The extreme fibre stress in the cross-girder flanges worked out at 6·3
tons per square inch, web included, or 6·5 tons, exclusive of the web.
It cannot be said in this example that the girders showed no signs of
weakness, as the deflection under live load was 1/2 inch on the span of
11 feet, in addition to a permanent set of 3/4 inch, largely due,
however, to “working” rivets.
A better and altogether conclusive case of the way in which
cross-girders may occasionally suffer considerable stress, and show no
sign, is furnished by two cross-girders, of which some particulars are
here given. These girders occurred in the floor of a very acute angled
skew bridge, riveted at one end to the main girders in a manner which
was very far from fixing the ends, resting at the other end on a masonry
abutment. The first girder was about 19 feet effective span, 12 inches
deep in the web, with angle bar and plate flanges. The girders were
spaced 6 feet apart, and were connected under the rails by [T]-bars,
cranked down to face the webs, and riveted through. Though these [T]’s
had little stiffness, yet the frequent vertical movements of the girders
relative to each other, under passing loads, had broken the majority of
the [T]-bars at the bends, so that no notice need be taken of these as
transferring load from any one cross-girder to its neighbour. The floor
covering consisted of timbers about 4 inches thick, also incompetent to
transfer any sensible proportion of the load on a girder to others 6
feet distant. Upon the floor was cinder ballast, with sleepers, chairs,
and ordinary bull-headed rails. The stress to which the girder was
liable works out at 8·4 tons per square inch, on the extreme fibres of
the net section, web included; or 9·1 tons, neglecting the web, under
engine-loads of a common amount. The other girder had an effective span
of about 22 feet, as before 12 inches deep in the web, with angle bar
and plate flanges. The stress per square inch was 10·5 tons, web
included, or 11·1 tons per square inch, neglecting the web. This girder
carried three rails, one of which was near to the abutment bearing, so
that there was no great difference in the stress induced whether all
three rails were loaded or the pair only. The traffic over the bridge
was very great, but of moderate speed. It must have been a common
occurrence for the girders to take the full loads. The heavier engines
passed scores of times in a day--lighter engines probably one hundred
times. The bridge was about twenty years old, yet these cross-girders,
when removed, showed no other sign of age and wear than that due to
rust.
[Illustration: FIG. 46.]
All the foregoing instances relate to wrought-iron bridges. Two cases of
steel construction are here added, the first of these furnishing an
example of high girder stress somewhat remarkable. This was found in a
trough girder of a strange pattern, of which a section is here given
(Fig. 46). The bridge to which it belonged carried a siding, over which
engines of less than the heaviest class sometimes passed at a crawling
pace. The larger of the two girders carrying the rails was 15 feet 8
inches effective span. The sides of the trough consisted each of two
vertical plates, originally 1/2 inch thick, but wasted to an aggregate
thickness of 5/8 inch. These plates 6 inches deep, were connected at
their lower edges to angle bars, 3 inches by 3 inches by 1/2 inch, which
again were riveted to a bottom plate 16 inches wide, originally 1/2 inch
thick, wasted to 3/8 inch. Lying in the bottom of the trough, and
riveted through the inner angle flanges, was a bridge-rail. Assuming
that the metal retained its elastic properties from top to bottom of the
section, at whatever stress, this works out at 32 tons per square inch
at the extreme top fibre, and 15 tons at the bottom, on the net section.
As puddled steel, of which the girders were made, may have a tenacity of
45 to 55 tons per square inch, the assumption is probably correct. The
author has no record of the deflection, but it may be remarked it was
such that to stand under the girder, with a tank engine passing over,
required some determination.
A point of additional interest in this little bridge is that, though
made of steel, it dates as far back as 1861, having been in use
thirty-two years when removed. The particular variety of steel used was
known as Firth’s puddled. The evidence of this consists in
correspondence showing that permission had been asked of the controlling
authority, by the only users of the siding, to apply this material, with
no evidence of any refusal. At about the same time this steel was also
used upon the railway concerned in the top flanges of some girders of
considerable span. The appearance of the trough girders to which the
foregoing particulars apply was distinctly different to that which might
be expected in ordinary wrought iron. The top edges of the vertical
plates were wasted away, smooth, and rounded in a manner strongly
suggestive of a steely character. Finally, the way in which the girders
held up to their work for so long is, by itself, conclusive on the
point. The bridge-rail appeared to be of wrought iron, the different
modulus of elasticity of which has been included in the calculation upon
which the preceding results are based. That these girders stood so well
is, perhaps, largely due to the fact that the load carried by them was,
though varying within wide limits, practically free from impact, which,
had the load passed over quickly, would, with girders so small, shallow
and flexible, have been very sensible.
The second instance of steel construction in which somewhat high stress
is manifest is that of some steel troughing of the Lindsay pattern, used
in a bridge built in 1885. The troughs ran parallel to the rails, having
an effective span of 18 feet 8 inches. The depth of the section (which
is shown in Fig. 47), was 8-1/2 inches, making a ratio of depth to span
of 1/28. The road was of ballast, sleepers, chairs, and 85-lb. rails.
[Illustration: FIG. 47.]
Assuming this to be carried on six troughs, which corresponds to 11 feet
3 inches of width, the extreme fibre stress works out at 7·5 tons per
square inch, under usual engine-loads. The bridge when examined after
fourteen years’ use was in good condition, and at that time but little
rusted; but the end seam rivets were, as is not uncommon with such
troughing, loose. The traffic over the bridge was considerable, but not
at great speed.
On the opposite page are set out the results which have been given, in
tabulated form, as was done for rivet stresses, to enable ready
comparison to be made.
EXAMPLES OF HIGH STRESS.
--------------+-----+---------+---------------+--------+-----------
|Span | Part | Stress per |Tension |Condition.
| in |Stressed.| Square Inch. | or |
|Feet.| +-------+-------+Compres-|
-- | | | Webs | Webs | sion. |
| | | In- | not | |
| | |cluded.| In- | |
| | | |cluded.| |
--------------+-----+---------+-------+-------+--------+-----------
Wrought-iron | | | | | |
main girders, |60·0 |Flange | .. | 6·3 |Tension | Good.
plate | | | | | |
| | | | | |
Wrought-iron | | | | | |
main girders, |64·0 | „ | .. | 6·8 | „ | Good.
plate | | | | | |
| | | | | |
Wrought-iron | | | | | |
main girders, |76·0 | „ | .. | 7·5 | „ | Fair.
plate | | | | | |
| | | | | |
Wrought-iron | {| „ | 7·4 | 9·7 | „ |}
main girders, |29·5{| „ | 6·3 | 8·3} |Compres-|}Good.
plate | {| | | } |sion |}
| | | | | |
Wrought-iron | | | | | |
main girders, |63·0 | „ | 7·1 |Tension | Fair.
lattice | | | | | |
| | | | | |
Wrought-iron | | | | | |
main girders, |47·0 |Flange | 10·0 | .. |Compres-| Fair.
plate | |edge | | |sion |
| | | | | |
Wrought-iron | | | | | |
cross-girders,|26·0 |Flange | .. | 6·7 |Tension | Fair.
plate | | | | | |
| | | | | |
Wrought-iron | | | | | |
cross-girders,|11.0 | „ | 6·3 | 6·5 | „ | Bad; loose
plate | | | | | | rivets.
| | | | | |
Wrought-iron | | | | | |
cross-girders,|19·0 | „ | 8·4 | 9·1 | „ | Good, but
plate | | | | | | rusted.
| | | | | |
Wrought-iron | | | | | |
cross-girders,|22·0 | „ | 10·5 | 11·1 | „ | Good, but
plate | | | | | | rusted.
| | | | | |
Steel trough | {| „ | 15·0 | „ |}Fair,
girder |15.7{|Top edge | 32·0 |Compres-|}but
| {| | | |sion |}rusted.
| | | | | |
Steel |18·7 |Flanges | 7·5 | .. |Tension | Fair,
troughing | | | | |and Com-| but
| | | | |pression| rusted.
--------------+-----+---------+-------+-------+--------+-----------
It would be unwise to infer from the instances which have been quoted
that high stress may be regarded with complaisance. In the most
conscientious engineering work there should still be a liberal margin
for material possibly defective, or even bad, for waste and
deterioration, and for the aggregate effect of minor errors in design,
any one of which considerations, except the first, by itself might not
be of great importance. The conclusion which may, however, be derived
from this and the previous chapters is, that bridge failures are less
likely to occur from high stress of a kind readily calculated than from
failure in detail, obscure and little suspected, the reason for which is
not perhaps apparent, till the attention is forcibly directed to it by
the refusal of the structure to sustain the forces to which it may be
liable.
CHAPTER VII.
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.
CHAPTER VIII.
DEFLECTIONS.
Deflection, considered only as a fraction of the span, and without
regard to other conditions affecting it, is of very little use as an
indication of a girder’s fitness for its work; but when taken with
reference to the depth of the girder, the nature and amount of the load
producing flexure, and, further, with regard to the quality of the
workmanship and normal properties of the material of which the beam is
constructed, it may be of some little service in helping to form a
reliable opinion. This consideration applies with less force, perhaps,
to new work than to old, in which there may be unknown influences at
work, or unknown defects which by excessive deflection may be betrayed.
Though too much importance should not be attached to results of
deflection tests in any one instance, yet the practice of observing such
movements, and considering them with reference to each case, gives a
good general idea of what may be expected in a fresh instance, any
material departure from which should be a reason for specific inquiry as
to the cause. A further reason with new work is found in the evidence it
affords as to whether the loads carried travel to the supports really as
intended, or by some route not contemplated; or, in the case of floor
beams, in what way the load is distributed amongst them, if, indeed,
there be any such distribution.
The author has commonly found that new work gives greater deflections
than old--i.e., while calculation gives the same result for each, it
does not apply equally well to both. The differences may be accidental,
but are probably due to other causes, perhaps to the fact that new work
has not by repeated applications of load lost the resilience of parts
liable to considerable local stress, such as is very liable to occur at
connections, so that the deflection is, whilst new, greater than after
many years’ use, by which time such parts may develop a definite “set,”
and contribute in a less degree, or not at all, to the total elastic
deformation.
It is also possible, as already suggested, that repeated high stress may
reduce the ratio of strain to stress, the material gradually becoming
more rigid, the modulus of elasticity being, in fact, increased.
In girders of ordinary construction, the major part of the deflection is
due to the booms, the remainder to the web; the latter is for plate
girders a small amount only, and is commonly neglected, but for open web
constructions it may be quite appreciable. For any given type of web
arrangement the deflection due to the web will, for all depths, remain a
constant quantity for the same span and unit stress; and though a
moderate fraction of the whole deflection for a shallow girder, it may
be a very considerable part for a girder of great depth, in which that
part due to the booms is, of course, smaller, since the deflection due
to these varies inversely as the girders’ depths.
Deflection, being dependent upon the elasticity of the material, is of
necessity very largely influenced by the value of its modulus E, itself
liable to considerable variation, and is increased in a small degree by
the yield of joints and rivets, which effect, apart from the initial
“set” of the girders, appears to be negligible. The stiffness of members
in resisting angular distortion at connections must also, for open-web
riveted structures, affect the result, making it somewhat less, and,
finally, section excess at joints and gusset attachments has an
influence in modifying deflection as compared with that due to the
normal gross sections simply.
From these considerations it is apparent that any simple deflection
formula must be largely empiric in its nature. For plate girders of
uniform depth and flange stress, the writer has found the following to
give good results:--
S^2
----- × _f_ = deflection in inches.
D × C
The span S and depth D are, as a matter of convenience, taken in feet;
the constant C is for wrought iron 3500, and for mild steel 4000; _f_ is
the mean of the extreme tensile and compressive stresses of the booms,
in tons per square inch, estimated upon the gross sections.
This, though satisfactory for plate girders, is not so suited to girders
having open webs, in which the deflection will more nearly be
(3S S^2 )
(-- + -----) × _f_,
(C D × C)
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.
The influence of the girder’s inertia in modifying drop-load effects
will also be less marked in deep--i.e., light--girders than in girders
shallow and heavy.
It is, notwithstanding all this, desirable that the depth of main
girders should be liberal for economy’s sake, and also that of floor
beams, for reasons already dealt with; the probability of the drop load
is somewhat remote, and, though possible, would simply induce, if it
occurred, an increment of stress rather more important in deep girders,
making it specially desirable in these to give particular attention to
the detailing of any connections liable to suffer from impact effects.
It should be remarked that for short and very flexible beams, generally
outside the limits of practice, there may also be, under quickly moving
loads, a material increase of stress due to the centrifugal effort of
the load on running round the deflection curve, and in rising upon the
steep part of the curve beyond the girder’s centre. Where advisable,
these effects may be modified by cambering the rail.
For pin bridges in which there may be spring in the pins, excess stress
in some eye-bars due to inequalities of length, and a want of that
rigidity peculiar to riveted structures, the deflection will be greater
than above indicated for girders of the ordinary English type.
The method in common use for measuring the deflections of girders but a
moderate distance above the ground by means of sliding-rods, though
crude, gives, with care, results sufficiently accurate for most
practical purposes; but some points necessary to remember may be
mentioned with propriety. The lower rod should rest firmly upon
something solid, say a stone, well bedded and free from any tendency to
rock; the upper end should bear against some part of the girder above,
presenting a hard surface, free from dirt or scale, and as the running
load approaches the bridge it should be ascertained that there is no
slack, that the rods bear hard at the top and bottom. The upper end
having been depressed, care is to be exercised to make sure of the
reading before the rods alter their relation to each other. These
precautions are so self-evident that an apology is almost necessary for
mentioning them.
To ascertain deflections with a single pair of rods is only allowable
when the girders rest firmly on their bearings; if felt has been placed
under the girder ends, or if the bedstones are insecure or rocking, it
is necessary to use three pairs of rods, one pair at the middle and a
pair at each end, in which case the mean of the two end readings must be
deducted from the reading of that at the centre to get the desired
result.
In the case of a number of spans in series, each resting upon sill
girders common to two sets of bearings, this method also gives results
of indifferent reliability, as the depression of each end may be greater
as the travelling load comes upon and leaves the span than when it is
precisely over the middle, and it is in general out of the question to
secure by this mode simultaneous readings for a particular position of
the running load, which are what is required.
The author suggests, as a means of ascertaining deflections free from
these objections, that it should be done by first measuring the slope at
one end, and from this deducing the deflection at the centre.
This is to be accomplished by means of a little instrument, consisting
of a telescope with cross-hair sights, and fitted with a reflecting
prism at the eye-piece capable of being turned round, so that the
observer has a wide choice as to the position he assumes with reference
to the instrument, and may look either directly through it, or at right
angles to the axis of the telescope. This is clamped at one end of the
girder over the bearing, at the other end a scale is secured, to which
the telescope is directed, the cross hair being made to sight on the
zero of the scale, or the reading noted. For a girder supposed to
deflect to uniform curvature (say, with uniform depth and uniform
stress, the ordinary case) the reading observed will be four times the
deflection; every 1/10 inch actual reading on the scale will correspond
to 1/40 inch of girder deflection.
Apart from the deflection, this method gives a ready means of observing
the end slope, a quantity of equal value for purposes of comparison. As
with girders of similar proportions, and similarly stressed, the
deflection will at all spans be the same fraction of the span; so should
the end slope be a constant quantity under similar conditions, the
diagram, Fig. 54, will make the principle quite clear.
[Illustration: 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 section 0·27 1·00
Hog-backed girders, ends half of centre depth, varying
flange section 0·24 1·08
_Varying Stress_:
[1]Girders of uniform depth and flange section 0·32 0·87
[1]Hog-backed girders (as above), but uniform flange
section 0·29 0·97
[1]Bow-string girders of uniform flange section 0·16 1·30
[Footnote 1: For uniform loading.]
It is apparent that, if preferred, the scale, instead of being in
inches, divided suitably, may, for each type of girder, be amplified to
the proper degree, so that the amount of the deflection may be read off
at once.
This method of dealing with deflections is quite independent of the
character of the bearings, and is applicable to girders at any height
above ground or over water; but its use would hardly be practicable for
very small beams, or those in an awkward position, or near which it
would be impossible to remain with a running load upon the bridge.
There is a possible source of error in the use of the instrument, most
likely to occur with triangulated girders, with which, if the instrument
is placed at the top of an end post, the reading observed may be the
joint effect of deflection and of local flexure of the members meeting
near the telescope. This may be tested, and, if necessary, allowed for,
by first sighting upon a scale at the next apex, and observing the
effect of the moving load. Again, as girders sometimes cant towards the
running load, if the instrument is placed on one edge of a girder, and
the cantings of the two ends are dissimilar, a false reading will
result, which may be amended by ascertaining the amount of cant at each
end, and correcting for the effect of the difference between the cants
upon the observation. Only in exceptional cases is it likely that either
of these considerations would need attention.
The author has secured with this instrument very promising results,
notwithstanding that under a running load there is a slight haziness of
the scale as seen through the telescope, due to “dither,” largely the
result of imperfections which may be remedied.
Deflections may sometimes be conveniently taken, by a quick-eyed
observer, with a good surveyor’s level and a specially-divided staff
held at the centre of the girder. The divisions preferred by the author
for this purpose are 1/10 inch, plainly marked, which may be seen at 50
feet distance with sufficient clearness to make possible readings by
estimation between the divisions to, say, 1/50 inch. But it is clearly
desirable not to rely upon a single observation only, where all the
evidence is gone so soon as the sight has been taken.
In rail-bearers, or other short girders, it may not be practicable to
adopt such methods, either on account of an inability to find a suitable
place for the instrument, or to read with any telescope with sufficient
promptitude as the load passes rapidly over. The use of rods may also be
out of the question, as the errors attending their manipulation may be
serious where but a small movement has to be noted, this being
complicated in some instances by the bearings being insecure, and
working to an extent which obscures the measurement sought. In such
cases it is preferable to use a stiff slat lying along the girder, which
bears, through short blocks over the girder bearings, upon the flanges;
the deflection is then read by direct measurement of the girder’s
depression at the centre, relative to the slat.
The author is, unfortunately, not able to give any precise information
on the effect of running-load as against a load that is stationary in
connection with girder deflections. It is by no means easy in ordinary
work upon a railway to secure facilities for making such comparative
tests. It may, however, be confidently stated, as a result of such
observations as he has made, that the deflection due to a load coming
rapidly upon a bridge is, as to the main girders of, say, a 50 feet
span, but little greater than that due to the same load stationary; it
may be, perhaps, 5 to 10 per cent. more.
It is evident that to determine the precise difference where the
quantity to be measured is so small needs apparatus of a more delicate
character than that in common use, and the control of an engine, or
engines, for the purpose of making the special tests, conditions which
on a busy line can only be secured by special arrangements previously
made.
CHAPTER IX.
DECAY AND PAINTING.
The author has collected particulars as to the amount and rate of
rusting in metallic structures which are of some interest. In all such
instances it is very necessary to note the conditions which have
obtained during the process of wasting, as without this, misleading
conclusions may be drawn. The information given relates in all cases to
wrought iron, unless otherwise stated.
A plate-girder bridge, having girders under rails, was found to be badly
rusted. The atmospheric conditions were unusually trying, the air being
damp and impregnated with acid fumes from adjacent steel works. That the
wasting was largely due to this latter cause was indicated by the fact
that the girders nearest to the steel works suffered more than those
farther removed and partly sheltered from the corrosive influence.
The webs were in places eaten right through, having lost a mean amount
of about 1/8 inch full on each surface in twenty-eight years. Painting
had not been well attended to.
In a similar bridge, not a great distance from this, but sufficiently
far away to modify the conditions for the better, considerable wasting
was also observed, but more particularly where the girders had been
built into masonry, which, loosening with the constant movement of the
girder-ends, had allowed moisture to collect, and rust to develop,
without the chance of repainting these surfaces. The amount of waste at
the places indicated was, as in the last case, about 1/8 inch on each
face, and in the same time, other parts of the girders having suffered
less.
[Illustration: FIG. 58.]
A third plate-girder bridge, with outer main girders, cross-girders, and
plated floor, carrying a road over a railway and sidings, and which was
known to have been neglected in the matter of painting, was very badly
rusted, both as to the cross-girders and floor-plates. The atmosphere
was somewhat damp; the chief cause of deterioration was, however, the
smoke and steam from locomotives, which frequently stood for some time,
during shunting operations, directly under the bridge. The webs of the
cross-girders, which were originally 1/4 inch thick, had rusted into
occasional holes during fourteen years--i.e. 1/8 inch from each surface
in that time. When removed a little later the wasting was so complete
that it was possible to knock out with a light hammer the remains of the
web between flanges and stiffeners, so as to leave an open frame only.
One of the cross-girders was so treated by the men engaged upon the
work, when it presented the appearance shown in Fig. 58.
In another case--that of a bridge with lattice girders under rails--the
ends were built into masonry, which had, of course, loosened, with the
usual result. The air of the locality was certainly pure, but somewhat
damp. The general condition of the ironwork was good, but end-bars of
the diagonal bracing, where they had been closed in, had lost 1/8 inch
on each surface in thirty-three years. The top flanges immediately under
the timber floor were in a very fair state, which is of some interest
when it is considered that these were made of steel of the same kind as
that already noticed as being used in the construction of small girders
(see Fig. 46, _ante_), described in the chapter upon “High Stress,” both
cases dating from the year 1861. The painting upon the lattice-girder
bridge had been pretty well attended to; but in the case of the small
steel girders it had been greatly--perhaps altogether--neglected; this,
coupled with adverse atmospheric conditions, had produced the result
that the rate of rusting had for the small girders been much greater
than that of the steel top flange referred to, being fully 1/8 inch on
each surface, as against a negligible amount under the more favourable
circumstances.
Girder-work over sea-water, as in piers, seems to rust at a sensibly
greater rate than inland work under average conditions; but it is hardly
practicable to make any strict comparison, as in either case the rate of
oxidation is so much affected--even controlled--by the care bestowed
upon the structures. This general conclusion is based upon the results
of examination of wrought-iron girder-work over sea-water of ages
varying from fourteen to forty-four years. It should be remarked,
however, that in one case steel girders but five years old, and which
were frequently wetted with sea-spray, were found to be wasting rather
badly--the paint refusing to keep upon the surface.
It may be concluded from the above instances, and from others which have
come under notice, that wrought-iron work, if not properly cared for in
respect to painting, or under conditions otherwise bad, may be expected
to rust at a rate which corresponds to the loss of 1/8 inch on each
surface in from fifteen to thirty years; but with proper care as to
painting, and exclusive of exceptionally bad conditions, it does not
appear to waste at any measurable rate. In some instances, upon scraping
the paint from girders which had been in use for thirty years, the
author has found, beneath the original red lead, the metallic surface
bright and clean, showing no trace of rust.
Of ordinary steelwork the same cannot be said, the common experience
being that mild steel is very liable to be attacked by rust. With
passable care in the bridge-yard during manufacture, such that with
wrought iron no after-trouble would be noticeable, steel is very liable
to show, within a year of being built up, numerous little blisters on
the painted surface; any one of these being broken away discloses a
small rust-pit. This is more often seen on the flange surfaces
(horizontal) than on web surfaces (vertical), but it is probable the
position has little to do with the matter, and that it is rather due to
the fact that rust has been earlier started on the flange-plates, upon
being put through the drilling-machines and inundated with slurry, which
occurs only to a more limited extent with webs having fewer holes. The
heads of steel rivets do not show this tendency to “pit,” or to early
development of rust. The riveting is about the last operation in making
a girder, each rivet being freed of all rust by heating, and quickly
coming under the protection of oil or paint. It may happen in this way
that the heads of rivets on a girder may be exposed without protection
for as many hours only as the rest of the work for weeks, which fully
accounts for the difference in behaviour.
The essential point to be observed in all steelwork is to prevent, if
possible, the first development of rust, for once begun it is much more
difficult to arrest than in iron; for this reason, oiling of all
material for a steel bridge, at a very early stage of its existence,
cannot be too strongly insisted upon. This practice, however, makes the
work so objectionable, and even dangerous when being lifted--because of
the liability to slip--to the men engaged upon it, that it is commonly
very difficult to ensure it being done sufficiently soon to satisfy a
careful inspector. If the work is carried out under cover, the
requirement is less urgent. Strictly, all material should be oiled so
soon as rolled, but the author does not remember to have seen this done
at any of the mills he has visited, though it is common enough to find
it specified.
Ironwork does not need the extreme care which should be bestowed upon
steelwork, but it is desirable that it should be painted as soon as
possible, the surfaces being first thoroughly cleaned.
There is, probably, for painting girder work nothing to beat good red
lead as a protective coating; but there is considerable difficulty in
getting it reasonably pure, without which quality its utility will be
greatly reduced. The question of purity will, however, be found to be
largely a question of price. It may be stated broadly that, whether for
steel or for iron, the first protective covering is, perhaps, the most
important of any it will ever receive.
In repainting old work, care should be taken to remove all traces of
rust previous to laying on the new coat. It is not an altogether
uncommon practice to repaint old structures by dealing only with the
parts readily accessible, which, being less liable to rust, probably but
little need it; leaving those parts which are difficult of access, and
where rust is developing, untouched; treating the whole business as a
matter of appearance simply. This, it need hardly be said, is
indefensible. It is better rather to neglect the surfaces freely exposed
and ventilated, and devote the whole care upon those other parts,
confined and difficult to get at; taking the trouble necessary to remove
ballast, timber, or whatever may obstruct the operation, in order that
the bad places may be thoroughly scraped, and then painted. Those parts
which most need attention may cost, perhaps, to reach--and deal with
when exposed--ten times as much per yard of surface as the rest of the
superfices, which needs little, and is always accessible; but the cost
should not deter the proper carrying out of the work, as it will prove
the very worst sort of economy to deal with painting in a perfunctory
manner.
It should be noted that girder work, whether of wrought or cast iron,
when embedded in lime or cement concrete, or mortar, generally proves to
be very well preserved, provided that close contact has obtained.
Cast-iron girders, when carrying jack arches resting upon the bottom
flanges, are found after long use to be in remarkably good order, when
finally taken out, having, indeed, the surface appearance of new
girders. Much the same remarks apply to girders of wrought iron carrying
jack arches, where protected by the brickwork; provided that the girders
are sufficiently stiff to minimise deflection, and allow the masonry or
brickwork to adhere to the surfaces.
Such girders are in a very different condition to those previously
referred to, in which the ends of the girders, carrying a light floor
structure, are built into masonry where the deflection slope is
greatest; though, apart from the few cases where adherence can be relied
upon, building-in is an undesirable practice, and has the disadvantage
that after-examination is only possible by removing portions of the
masonry, which it is evident would very seldom be resorted to.
Cast iron has ordinarily--unlike wrought iron or steel--great capacity
for resisting rust, and will, after many years of absolute neglect,
appear but little the worse; an advantage which is the more pronounced
when considered relatively to the greater thickness of the thinnest
parts in cast-iron girders, the percentage of waste being
proportionately lessened.
Cast iron does, however, behave somewhat badly in sea-water, the metal
sometimes losing its original character, and becoming in time quite
soft; though, if not worn away, as by the attrition of shingle,
maintaining its original bulk.
Of some forty-five cast-iron piles belonging to various structures,
examined whilst engaged upon sea-pier work for Mr. St. George-Moore,
though the author found somewhat diverse results, in no case did there
appear to be any general softening of the whole thickness, but a
distinct change for some definite distance inwards, generally to be
decided without difficulty, beyond which the metal appeared to retain
its original character. In all cases any material depth of softening was
found close to the ground, this depth rapidly decreasing higher up,
till, at a height of 5 feet, but little if any softening could be
detected. At 2 feet above ground the softening was frequently but
one-quarter of that at ground level. There was, too, often a
considerable difference in the behaviour of different piles in the same
structure under similar conditions; one pile being found to have only
one-fourth part of the softening noticed in others, or possibly none at
all. For six different structures the amount of softening near ground
level, of about twenty-five piles examined, was as given in the table on
the next page.
The greatest depth of softening found (see No. 2) was 9/16 inch, 1 foot
above ground, in a pile thirty-six years old. The decayed material when
removed was of a soft, greasy consistency, perfectly black, which a few
hours later was found to have changed to a dry yellow powder, by the
rapid absorption, it may be supposed, of atmospheric oxygen. It is
apparent, therefore, from this example that deterioration may proceed to
a considerable depth; but it should be observed that other piles of the
set showed softening at ground level of 1/8 inch only.
SOFTENING OF CAST-IRON PILES IN SEA-WATER.
---+--------+----------+-----------+----------+---------+---------
No.| Age. | Maximum | Maximum |Mean Rate | Quality |Materials
| |Softening.| Rate of | of |of Metal.|Entered
| | |Softening. |Softening.| |by Piles.
---+--------+----------+-----------+----------+---------+---------
1 |17 years|5/16 in. |1/8 in. in |1/8 in. in|Soft |Extremely
| | |7 years |15 years | |soft
| | | | | |sandstone.
2 |36 years|9/16 „ |1/8 in. in |No result | „ |Rubble
| | |8-1/2 years| | |mound.
3 |32 years|3/8 „ |1/8 in. in |1/8 in. in|Moderate-|Fine
| | |11 years |15 years |ly hard |sand.
4 |38 years|1/10 „ |1/8 in. in |1/8 in. in|Hard |Extremely
| | |47 years |140 years | |hard rock.
5 |17 years|Small |Negligible | |(?) |Sand and
| | | | | |Shingle.
6 |14 years|Negligible|Ditto | |(?) |Sand.
---+--------+----------+-----------+----------+---------+----------
The least rate of softening noticed, apart from those structures of a
more recent date, in two of which it was very slight, occurred in a
pier thirty-eight years old (No. 4), where, of three piles tested, two
were quite hard, and the third softened 1/10 inch only.
Whatever may be the precise cause of the change, it does not appear to
be affected by the period or percentage of immersion during the rise and
fall of tides.
[Illustration: FIG. 59.]
This will be clear from the diagram, Fig. 59, which refers to four piles
(No. 3 of table), all of the same age, in the same structure. On each
pile the depth of softening is given at points in strict relation to
each other, and to the tidal range. The percentages of immersion for the
various heights are also given, from a study of which it will be
apparent that these have no relation to the amount of softening; this,
indeed, is always greatest near the ground, at whatever actual height it
may be. For instance, pile A was at ground-level softened 1/4 inch,
that point being 60 per cent. of its life under water; but on pile B, at
a point 74 per cent. of the time submerged, and 4 feet above a lower
ground-level, no softening was apparent; further, at ground-level of
this pile, the percentage being there 87, the softening was no greater
than at ground-level at pile A.
It is probable that while the percentage of submersion in moving water
hardly appears to affect the result, yet prolonged contact with wet
sand, sea-weed, or clinging shell-fish may do so. This seems to suggest
that the process of change, as between the sea-water and the iron, is
slow, and to be effective must be continuous; so that it is only found
to any considerable extent where the water in contact with the surface
is still. In the two worst cases, Nos. 1 and 2 of the table, at points 1
foot and 6 inches above ground-level, the surface was in one pile
shrouded in a thick mantle of heavy sea-weed, and in the other covered
by molluscs; in both instances the surfaces being thus kept moist and
undisturbed. The piles of the fourth case were in hard rock, were clean,
and, where accessible, always either in moving water or quite dry.
However this may be, the power to resist softening certainly appears to
vary largely with the quality of the iron. The piles, referred to above,
in which deterioration proceeded at the most rapid rate were certainly
of a soft metal, the first being markedly so. On the other hand, certain
piles (No. 4) of hard, close-grained iron suffered very little.
It may be mentioned with respect to the last named, as a matter of
interest, that the caps of the lower lengths (just above ground-level)
had been cast with short pieces of wrought iron projecting--possibly for
lifting purposes--which during thirty-eight years had altered in
character to something very like softened cast iron, but laminated, and
harder. Of about 1-1/4 inch original thickness, only 3/16 inch remained
having the semblance of wrought iron. The percentage of submersion was
about 60.
A number of piles, not included in the table, varying from fifteen to
forty-four years old, and of the same structure to which set No. 2
belonged, were all found to be hard, with the exception of one showing
3/16 inch of softening. These are omitted, because the mud surrounding
them was at the time of examination unusually high, so that the more
normal ground-level could not be reached, at which points testing might
have disclosed different results. It is probable that for any piles
standing in soft material examination below the surface would reveal
more pronounced softening than where occasionally exposed.
To meet the effects of sea-water on cast-iron piles, and for other
reasons, it is a common and good practice to make the lower lengths of
greater thickness--say, 3/8 inch more--than that sufficient for the
upper. Occasionally, also, the bottom lengths are filled with concrete,
which no doubt adds to the length of time during which they may be
relied upon.
CHAPTER X.
EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES.
In the preceding chapters defects of various kinds to which riveted
bridgework is liable have been more particularly dealt with; it is now
proposed to consider the examination of such structures, following this
by a reference to methods of repair and strengthening, leaving the
treatment of other classes of bridgework to be developed under their
proper headings, though some of the remarks immediately following will
apply to all.
The exhaustive survey of a bridge is only to be made after considerable
experience in the work, but it may be stated that in looking for defects
it is well to seek where they are least expected, till, with practice,
one knows better where to direct attention. When examining with a view
to pronouncing an opinion upon the fitness of the structure to remain in
place, if in any real doubt, it is wise to give a casting vote against
it; and finally it may be said that upon taking down a bridge condemned
for any one or more defects, it should be examined for worse. This may
seem to be somewhat pessimistic, but is based upon the teachings of
experience.
Preliminary examination of a bridge may reveal such faults or weaknesses
as at once to ensure its condemnation; but if this is not the case, and
there is a reasonable probability that the structure may be given a
fresh lease of life, it will, for the purpose of estimating the
strength, or for possible repairs, commonly be desirable to secure
precise particulars of the existing structure independently of any
drawings that may be in existence, and which will very probably be
incorrect, the finished work, if old, seldom agreeing with the contract
drawings. A final decision may in this case be deferred till after the
measuring up has been completed, the condition of the structure becoming
more familiar in the process.
It is desirable first to ascertain whether the bridge remains in good
form, whether the camber of girders appears to be what might be
expected, or agreeable with existing records, though much reliance must
not be placed upon figured cambers, it being quite common for girders to
leave the bridge yards with the camber something other than that
intended. The deflections under live load will also be observed, and
compared with the calculated result, or checked by judgment. The
calculations upon which strength and deflections are based will, of
course, refer to the actual sections, which are sometimes a little
difficult to ascertain if there has been irregular rusting. In
continuous girders also, levels having been taken, allowance should be
made for effects of settlement, if any; and with arches evidence of
movement of the piers or abutments sought for, with the like object. It
is seldom that the main flanges of girders show signs of weakness,
unless from flexure in the case of long and narrow top members,
insufficiently stiffened; but there may be want of truth from other
causes already dealt with. In plate girders the webs should be most
carefully scanned for possible cracks, particularly where cross-girders
are connected, and along the upper edges of bottom flange angles, if the
floor rest upon the flange. All riveted connections, of course, need
close attention, both for straining effects, where there is a liability
to wracking, and to detect loose rivets. Loose rivets and want of
tightness in other parts of the work may frequently be detected at
sight by a reddish bloom which appears on the neighbouring surfaces,
caused by rust working out and spreading under the effects of weather;
it may be seen round rivet-heads or along the edges of angle-bars, or
other parts where there is movement. Loose rivets, though generally to
be detected also by the hammer, may perhaps in the case of thin-webbed
cross-girders be working in the web-thickness only, possibly to a
considerable extent. This, if not otherwise evident, may sometimes be
detected by simultaneous deflection tests--with rods--at the top and
bottom flanges of a girder, at the same distance from the bearings. Any
difference in the readings may indicate loose web-rivets, or possibly a
tear in the web running parallel to the flange angles.
Bracings between girders are very apt to display a rich harvest of
working rivets. Cross-girders and longitudinals also may have loose
rivets at their connections, and be very badly wasted, with quite
possibly cracks in the webs, or other defects already enlarged upon.
The condition of the road upon the bridge will frequently be an
indication of the state of the floor which carries it; or the existence
of rail-joints which are working badly may very properly lead to a
critical examination of the girder-work immediately below, as this is a
fruitful source of damage in light constructions. Floor-plates, where
these exist, should be scanned for leakages, drainage nozzles, and
guttering, to see that they are free, the attachments of the latter
being often loose and unsatisfactory.
Trough floors may be expected to show loose rivets near the ends, with a
probability of excessive leakage where they abut against the webs of
supporting girders.
Floor plates resting upon abutments or piers, being very liable to
serious decay, require attention, and girder-work entering masonry
should receive close scrutiny, any obstruction to a sufficient
examination being removed so far as is judged sufficient for the
purpose. The structure should, of course, be closely watched during the
passage of live load for any signs of abnormal movement, excessive
vibration, or lurching.
In addition to seeking for these various defects, or others which have
been referred to in these pages at length, it will be well always to be
alive to the possibility of faults to be seen for the first time, or of
which the author has furnished no instance.
Having formed a reliable opinion as to the state of the bridge, this, if
satisfactory, may leave to be determined only the question of strength
relative to the loads carried. It is apparent that stress limits
suitable for a new structure, which has all its life before it, of
purpose moderate to cover possible deteriorations, the growth of loads,
and other adverse influences, may to avoid immediate reconstruction,
reasonably be permitted of a higher value for a further term of years in
the case of a structure which it is known has for a considerable period
behaved well, and remains in good condition. What this higher value may
be will be greatly influenced by the circumstances of each case, and,
being largely a matter of judgment, may be expected to vary with
different engineers. Experience shows, however, that the nominal unit
stress in an old bridge may be a very considerable amount in excess of
that allowed for new work, without, of necessity, showing any ill
effects; and the author is of opinion that for old bridges in good
condition it is quite prudent to allow an excess of 33 per cent. beyond
that permissible for a new design. If the structure is too weak to
satisfy this modified condition, it may be possible to bring it within
the stress limit by a reduction of ballast or other removable dead
weight. If this expedient does not promise to be satisfactory, or the
bridge shows actual signs of weakness, or palpable defects, it will be
necessary to deal with the question of repair, strengthening, or
reconstruction.
The repair of built up bridgework resolves itself largely into a matter
of replacing loose rivets by cutting these out, rhymering the holes, if
desirable, and again riveting. It will often be sufficient to do this
with no particular precautions as to bolting up temporarily; the rivets
having been loose, may very well be spared for a time. In re-riveting
cross-girder connections it may, however, be imperative to remove all
the rivets, bolting up securely as this is done, in order to make a
tight job, taking out each bolt in turn as required, and again filling
the holes; or it may be well in a bad case first to remove all loose
rivets, substituting good bolts, in order that work which has gone out
of shape owing to defective rivets may first be brought true.
Cross-girder webs, cracked vertically or nearly so, are commonly
repaired with splice-plates on either side; but in doing this it is
undesirable to add plates of excessive thickness relative to the
web--probably poor--as by an abrupt change of web section it appears not
unlikely a fresh break may be favoured.
[Illustration: FIG. 60.]
[Illustration: FIG. 61.]
[Illustration: FIG. 62.]
[Illustration: FIG. 63.]
Replacing wasted flange-plates, or adding new plates to those which
exist, is occasionally resorted to in the case of main girders, the
flanges of which are sufficiently accessible, but the operation is
difficult, takes some little time, and should only be attempted under
the constant supervision of a thoroughly capable man. When done, if the
girder has not been relieved of load by staging, the stress under full
load will be unequally distributed between the old and the new section,
the old always taking more by the amount of the dead-load stress
previously carried. The method which the author has seen applied to
lattice girders of about 80 feet span, having good angle-bars in the
flanges, with a shallow vertical web for attachment of diagonals,
consisted in first cutting out the old flange rivets, and substituting
bolts well screwed up, till all the rivets necessary had been removed.
The new plate length having been prepared, was, on a Sunday, during a
few hours’ cessation of traffic, marked off, the temporary bolts being
removed for the purpose, and then replaced. After the plate had been
drilled, on a later Sunday, it was finally put into position, bolted up,
and riveted at leisure; cover-plates make additional trouble, but are
dealt with on the same principle. The method as shown in Fig. 60 is,
however, barely practicable for so many plates. It is preferable, if it
is proposed to add section, to do this with as little interference as
possible with existing rivets of importance. This may be accomplished,
if the existing plates are not too wasted at their edges, by riveting on
new strips or angle-bars (see Figs. 61 to 63). Occasionally the strength
of a girder is increased by the addition to the top or bottom boom of
material in such a form as sensibly to increase the depth, and thus,
while adding increased section to one boom, to reduce the stress in
each, though to dissimilar amounts. By this device also the relief is
effective only as regards the live-load stress; under dead load only the
new material does no work, provided, of course, that no relief staging
was used during the alterations. For girders carrying any considerable
proportion of dead load the method is very inefficient, though for
others, in which the live load is relatively large, the result should be
more satisfactory.
As this question of adding new section to old is of much importance in
dealing with repairs and strengthening operations, a few general remarks
upon the subject will be pertinent. The difficulty in such work commonly
is to cause the new to render any considerable assistance to the old in
those cases which occur in practice. If a bar be imagined under
longitudinal stress varying between 0 and a maximum, then, if the area
of the piece be increased at the time when it takes no stress, its
capacity for resisting the maximum amount will be increased, and for
added material of similar elasticity the unit stress proportionately
reduced. If, however, the load on the bar does not vary, the mere
addition of metal will not relieve the original section in any degree.
To take a third case, of the maximum being twice the minimum load, it
will be necessary, in order to lower the maximum unit stress by 25 per
cent., to double the original section of the bar if, as supposed, the
extra metal has been added to the piece when under the smaller load, so
that the new section is only effective in assisting to carry the
remainder of the load at such times as it may be imposed. The
relationship stands thus:--
Live load New area
---------------- × -------------- = relief.
Live + dead load New + old area
These statements will be true under the conditions named, within the
elastic limit of the material; but some advantage would be derived in
the second case, and a more marked benefit in the third, if the load
assumed to be a maximum were exceeded, or if the composite bar were
tested to destruction; as, however, these effects would be outside the
limiting conditions imposed, it must be a matter of judgment as to how
far this reserve of strength may be considered of value.
If, instead of simply adding section to the bar, some part of the
constant load is put upon the new section by the manner of attachment,
the combination will, of course, be more effective.
To apply these considerations and illustrate the way in which the two
methods of adding flange section work out when reduced to figures, the
case will be supposed of a girder 6 feet deep, carrying a load of which
one-third is dead and two-thirds live. To the flanges of this girder are
added plates equal to 50 per cent. of the original areas, in order to
reduce the stress of 7 tons per square inch to which the girder before
strengthening is liable, the depth remaining substantially unaltered.
With dead load only the original section would be stressed to 2·3 tons
per square inch, the new section being then unstressed. Under full load
the new and old material take 3·1 tons per square inch additional,
making the modified stress on the original section 5·4 tons per square
inch, as against 7 tons; or a reduction of 22 per cent. This compares
with 33 per cent., the relief due to 50 per cent. increase of flange
area under ordinary conditions of stress distribution.
Let the second method of strengthening the girder now be considered,
using, for purposes of comparison, the same total amount of new material
to increase the girder depth by an addition to the top flange. This
section will be equal to the area of one flange, which, though it may
be applied in many different ways, giving a greater or a less increase
to the depth, would probably be used in some such manner as that shown
in Fig. 64, increasing the effective depth for live-load stress by
nearly 10 inches.
[Illustration: FIG. 64.]
The added material will, as in the previous case, leave the dead-load
stress unaltered, or 2·3 tons per square inch. The stress in the bottom
flange due to live load will, however, now be 4·1 tons per square inch,
making a total stress of 6·4 tons per square inch, against 7 tons--the
original stress. The reduction here is 8 per cent. only, as compared
with 12 per cent., the relief due, under ordinary conditions, to an
increase of effective depth from 6 feet to 6 feet 10 inches, and by the
use of additional material, equal, as before, to one-half of the total
flange areas before the alteration.
The effect on the top flange need not be here gone into in detail, but
it may be said that, owing to the increase of gross section and of
depth, the ultimate stresses of both the new and old material are
greatly less than as given for the bottom flange.
Girders strengthened by the first of these two methods would, it is
probable, if tested to destruction, give results more nearly in accord
with the actual percentage increase of flange section, plastic
deformation of the metal, before failure, tending to reduce the
differences of stress on the new and old material of the sections.
[Illustration: FIGS. 65 and 66.]
Web members of lattice girders may, if weak, sometimes be dealt with by
the introduction of supplementary bars, parallel to and between the old
members, or by the addition of strips or angles to the existing
diagonals. The treatment will be largely influenced by the nature of the
old detail, which may lend itself to some one arrangement much better
than to any other.
End riveting of web members may, if it has become loose, be dealt with
by simply rhymering the holes a size larger, and re-riveting in the best
manner, if the stresses are not excessive; or it may be necessary to
devise some additional attachments by which new rivets are brought into
use (see Figs. 65 and 66). The effective relief due to supplementary
rivets will be influenced by similar considerations to those governing
increase of section.
[Illustration: FIG. 67.]
[Illustration: FIG. 68.]
Old structures are very frequently deficient in bracing, which may, in
such cases, be advantageously introduced; or girders individually weak
may be rendered collectively efficient by suitable bracing. In
considering the advisability of this, however, the case should be viewed
with regard to the possible effects of such members, as already dealt
with in the chapter relating to these questions. There it has been
pointed out that bracing between a system of parallel girders may have
the effect, under live load, of increasing the stress on the outer
girders due to twisting of the structure as a whole, though the inner
girders will, except for full loading of the whole bridge, be advantaged
as to stress values, and in any event bettered by being held up to their
work. The effect upon the outer girders may be met by increasing their
strength, if this appears to be necessary. In all such alterations the
detail should be schemed with special care to ensure simplicity in
execution, smith’s work being rigorously avoided. A good arrangement for
supplementary bracing between plate-girders, which gives little trouble
in carrying out, is shown in Fig. 67; or where the stiffeners of such
girders are in line across the bridge, the detail given in Fig. 68 may
involve less expenditure. Difficulties may be experienced in riveting,
unless great care is taken in the positioning of rivets. Fitting-bolts
are only to be relied upon as such, if they really justify the name;
they are, though easy to specify, by no means easy to secure under the
conditions of practical work. Weak cross-girders may make
alterations--in some cases considerable--necessary, to rectify the
defect of strength. The removal of old girders to make room for new is
seldom resorted to, unless the existing detail renders this a simple
operation; but it is not unusual to introduce new girders between the
old in cases where there is no plated floor to make the work difficult.
By this method there is, of course, an increase of appreciable amount in
the dead load carried by the main girders, which would in many instances
be objectionable. With deep and heavy main girders, having plate webs,
cross-girders may be strengthened by improving the end connections by
suitable gussets, and attachment to good vertical stiffeners, the fixity
of the ends thus aimed at being assured by overhead struts or girders,
from one main girder to its fellow, at intervals apart well considered
with reference to the horizontal strength of the top flanges, the whole
thus making a closed frame, as shown in Fig. 69. The method appears
feasible, but it should be stated that the author has not known it to be
applied in its entirety as a means of strengthening an old floor.
[Illustration: FIG. 69.]
A simple and very common device consists in substituting for the
ordinary cross-sleeper road, where this exists, stout timber
longitudinals under the rails, which have, where the cross-girders do
not exceed 5 feet centres, a marked distributive effect, tending to
reduce the maximum load upon any individual girder. With a similar
object, trough girders containing longitudinal timbers are sometimes
adopted where the depth available is not enough to enable sufficiently
stiff timbers to be used alone. In either case the object sought is the
same--to modify the effect of the heavier wheel loads upon isolated
cross-girders. When the spacing is so close as 4 feet, the beneficial
result of this treatment is considerable, but at 8 feet centres it can
have but a moderate effect where timbers alone are used.
Occasionally, for long cross-girders, a distributing girder is placed,
with the same intent, in the 6 feet way, its function being limited to
this use only if the depth and strength are sufficiently small to serve
this object alone, as distinct from the case in which it becomes a
carrying girder transferring load to the abutments. As a distributor
simply, the girder has to equalise the bending moments amongst the
cross-girders, to effect which it will be evident that these moments
having been ascertained for the several cross-girders previous to
alteration, for a position of the wheel loads such that the heaviest
comes upon a centre cross-girder, the mean of these moments will, when
compared with that for each girder, show the difference to be induced as
a result of introducing the distributor. These differences of moment
render necessary at the centre of the cross-girders reactions upwards or
downwards, as the case may be, of amounts competent to induce moments
below the inner rails equal to these differences.
It is these reactions which must be provided by the distributing girder
at a moderate stress, and without flexure of such an amount as sensibly
to modify the reactions. The greatest section necessary at any one point
may then be adopted for the girder throughout. The result will commonly
work out to a moderate section, but there will be no harm in a little
excess in a case
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