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.