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.