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Dec. 24, 1946.STABILIZING
2,413,019
M. R. WOLFARD
MEANS FOR TENSION ELEMENTS HANGING
WITH SAG TO SUSTAIN LOADING BETWEEN SUPPORTS
2 Sheets-Sheet 1
Filed March 2l, 1942
237
BY
'
’
~
'?
v
Y '
ATTOFINAEY`
Dec. 24, 1946.
'
»
M. R. WoLFARD
2,413,019
STABILIZING MEANS FOR TENSION ELEMENTS HANGING
WITH SAG TO SUSTAIN LOADING BETWEEN SUPPORTS
INVENTOR.
BY W
A Tram/¿Y
2,413,019
Patented Dec., 24, 1946
STATES PATENT OFFICE
UNl'i"
2,413,019
STABILIZING MEAN S FOR r.TENSION ELE
MENTS HANGING WITH SAG T0 SUSTAIN
LOADING BETWEEN SUPPORTS
Merl R. Wolfard, Cambridge, Mass.
Application March 21, 1942, Serial No. 435,686
8 Claims. (Cl. 14-19)
2
l
This invention relates to improvements in
stabilizing means for tension elements hanging
with sag to sustain loading between supports.
More particularly it relates to stabilizing
improvements,
comprising
migratory-loading
means, including dead load coacting with ten
sioned elements to stringently restrict up and
said load carried by the other member. This
migration of loading is considered to occur in a
positive sense when the loading at a particular
point is increasing, as compared with the static
loading of that point; and in a negative sense
when loading which has migrated in a positive
` sense to a particular point is moving away from
that point, baci; to the place where it was when
the structure was static. Thus migration of
carrying structure in a suspension bridge or in 10 loading increases the loading of a particular
point, beyond its, static loading; and it occurs
other long and slender spanning structures that
in that direction which impedes and restricts
hang with sag to sustain dead and live loading
undulatory upward movement of the structure at
between towers.
that particular point. That is, an increasing of
A leading ob'ect ci the present invention is
the magnitude of that migratory loading which is
to restrict swaying and vibrating movements re~
becoming carried at a particular point opposes
sulting from the intermittent incidence of live
rise of that point.
loadings, whether of winds or trañic or both,
The invention impe'des and restricts undulatory
especially to restrict the amplitude of those move
movements by causing dead loading to migrate to
ments which would be aggravated by the cumu
lative influence of either or both of these dis 20 particular control regions of the structure. Each
end-half-portion or" the structure has at least
turbing forces.
one such control region, In particular the pres
It is well known that, when a cable or other
ent invention provides a structure in which dead
tension element hangs with sag between towers,
loading will migrate` to and from such particular
and is unrestrained, the advent of downward
pressure, as of a trañ‘ìc loading, on one end~half- 25 control regions in an upper lengthwise> tension
element. Inl each end-half-portion of the span
portion ci the sagged element causes upward
the migration will be from and to another and
movement ci the other end-half-portion of that
lower lengthwise tension element in the Same
sagged element; and, conversely, the advent of
end-hali-portion of the span.
an4 upward pressure, as by the upward component
It is intended to make suitable expression in
of a gust ci’ wind, on one end-half-portion of the
the appended claims so that the patent will» cover
sagged element causes downward movement of
whatever there is~ of patentable novelty in the
the other end-halÍ-portion. of that sagged ele
structure thus disclosed for migration of dead
ment. These upward and downward` movements
loading upward and downward between regions
are initial movements of undulations in the cable.
that are in the same end-half-portion of the
The invention provides means for restricting
span.
such up and down movements at predetermined
In my co~pending application Serial No. 626,661
regions ci the length of the span, by migration
I disclose and claim a structure wherein there is
of dead loading. This migration of loading pri
migration of dead loading across the center of a
marily restricts rising and falling movements
span, from a controlfregion in one end-half
within the spanning structure. The elimination
porticn of the span to a control region in the
of such movements markedly aids in restricting
other end-half-portion.
lateral sway also.
My experiments indicate that, when migratory
The term “migration ci loading” signifies the
down swaying and vibrating movements through
out all large portions of the lengthwise load
shifting of loading, which is being sustained by
a structure, to and from a particular point of
that structure, when intermittent live loadings
of the structure tend to move that point upward
and downward. The term “migration of load
ing.” is only applied to a shitting of load from
loading is applied at only two regions and all
effects are considered,_ the optimum is to locate
these two regions approximately equi-distant
from theV center of the span, at about three
tenths to four-tenths of the length of the span
apart from each other. However, beneñcial prac
one member to another which occurs when both 50 tical results are attained by locating these two
regions anywhere within the range of one
members support a load in common and are so
quarter to one-half of the length of the span
related to one another that a decrease or increase
in the amount ci said load“ carried by one mem
apart.
The herein disclosed method of restricting un
crease or decrease respectively of the amount of 55 dulations of' a structure by migration of loading
ber must be accompanied by a proportionate in
2,413,019
3
4
permits a reduction in the number and weight
of the restraining elements required, as com
pared with the usual method of approach where
the attempt is made to tie or hold panel points
of a truss in a ñxed position.
above the element 236, which extend from the
vicinity of one tower 228 to the vicinity of the
other tower 223. The upper of these tension ele
ments, 232, is shown as being a series of two rods,
one of which is in each end-half-portion of the
span, with their ends passing through holes in
coupling plates 231 and the T-bars 236, at the
The migratory-loading feature of the inven»
tion is characterized by providing a rapid in
crease in magnitude of the restraining load,
towers and also at the middle of the span.
upon the occurrence of 'only a very slight move
lower of these tension elements 234 is shown as
ment of the restrained region.
The
consisting of a series of four separate rods each
rangement of migratory loading is very eiîective
extending between two adjacent couplings 231.
in restricting up and down sway within any long
and slender structure that hangs with sag be
tween supports, whether the tendency to cause
such movements is traffic loading, or wind pres
The element 234 hangs with greater sag in each
end-half-portion of the span than does the co
extensive portion of the tension element 232 which
is above it.
In each end-half-portion of the span there is
a region 230 of the upper tension element 232
from which a tie 233 extends downward and
makes junction with the lower tension element
234. From these tie junctions, sections of the
load-carrying element 236 depend, and extend
lengthwise of the span, each with sag below the
coextensive portion of the element 234 which is
above it. In each end-half-portion of the span,
sure at any one of said regions; or whetherit is
merely the crescendo of an undulating wave
within the structure, irrespective of the place or
cause of the initiation of that wave.
Another departure from previous practice, in -,
point of attack, is that, to restrain vibrating
movements within the main load carrying length
wise members of a suspension bridge, the pre
ferred embodiment of the present invention em«
ploys forces which are predominantly vertical,
in contra-distinction to forces having large hori
zontal and lengthwise components. This per
mits enormous reduction in the massiveness oi
one such section of element 236 extends from a
junction 23! to the vicinity of the top of the
nearer tower and another extends to the mid
portion of the span, where the coupling 231 joins
it to the upper and lower tension elements 232,
Other features and advantages of the inven 30 234. Each of these sections of the element 236
tion, and details of construction will appear from
functions as a load-carrying element by support
the drawings herewith, and from the description
ing its coextensive portion of the bridge platform
which follows, showing embodiments. It is to be
E29 by hangers at intervals. Thus dead load im
understood however, that the invention is not
posed by hangers on the element 236 is sustained
limited t0 the specil'ic constructions here shown
in part by the element 234 in each end-half-por
for illustrating its principles.
tion of the span at a tie-junction 23|.
In the accompanying drawings, Figures 1-4 are
For embodying the migratory loading feature
diagrammatic showings of side elevations of four
of the invention, the stress in each tie 233 may
different suspension bridges, each of which em
be such that it supports only about half or less
bodies the invention.
40 than half of the aggregate of loading which is
In Figure 1 a load-carrying element 236 ex
existing at the junction 23| when the structure
tends the full length of the span between towers
is static. Preferably the tension in each such
228, 228, and extends to beyond those towers to
tie 233 will be made to be such that the upper
usual or suitable anchorages (not shown). Be
tension element at a particular region 230 sup
tween the towers this element 236 consists of a -` ports less than one-quarter of the aggregate of
succession of sections which depend with sag from
dead loading which ris at the junction 23l below
a lengthwise tension element 234 and are joined
that region when the structure is static. Each
together endwise by coupling plates 231. The
of the several sections of the element 236 which
plates which belong in the right hand portion of
depend from a junction 23| has greater curvature
the figure are omitted in order to show the sepa~
at its lowest sagged portion than elsewhere along
rateness of the sections. The sections of the ele
its length. For graphic illustration the major
the required restraining elements.
ment 236 are preferably bars having a shape and
cross sectional area that is distributed with depth
adapted to resist downward bending, and with its
tension-carrying lower area more than twice its
compression carrying upper area. This element
is represented as being composed of T-bars with
the stem of the T upward; and the height of the
stem of the T is greatly exaggerated in the draw
ings in order to give opportunity for indicating
sundry connections clearly. The middle two sec
tions are shown shorter than the two end sec
tions, thus indicating that commercial lengths of
bars may be used for these diiîerent sections, for
example, 60 foot length for the middle and 90
foot length for the end sections.
The end sec
tions ma'y advantageously be longer than those
in the mid-portion of the span because the sag
in the end sections is greater than is the sag in
the sections at the middle portion of the span.
-This relation of section lengths locates the below
described junctions 23| at positions which are
optimum for stabilization of the structure as a
Whole.
There are two tension elements, 232 and 234,
part of each end-half part of each such sec
tion is represented as being straight; but for op
timum utility, and particularly for attaining sta
bility in a relatively light structure, these end
half parts should be slightly sagged.
Preferably there is a tie 235 extending from
the lowest sagged portion of each said section of
the element 236 upward to the tension element
234 above it. The stress in these ties 235 should
be such as will support only a small part of the
total of dead load which is at its lower end when
the structure is static, in order that the loading
imposed at each junction 231 shall be large.
With this structure, the loading imposed on
the tension element 234 at the junction 23| in
each end-half-portion of the span exceeds that
which is imposed on the same element 234 at
any other point in the same end-half-portion of
the span when the structure is static. In the
structure of Figure 1, as shown and described,
it is much greater. Therefore a magnitude of
dead loading is available, at each tie junction
23|, to migrate to a particular region 230 of the
upper tension element 232 above it, when inter
aaia'oie
6
the towers 238. The junctions 24| are located a
little outside of the lengthwise range which is
mittent live loadings tend to move that particu
lar region upward. This may occur, for exam
ple, when a trafñc load, by entering upon the
left hand end portion of the bridge, tends to
straighten the upper tension element 232 in the
right hand half of Figure l; or when an Vupward
component of wind pressure tends directly to lift
optimum for stabilization of the structure as a
whole, but the locations are nevertheless within
the range f or good practical results.
Figure 3 isl similar to Figure 2, with correspond
ing reference numerals of the 25o-251 series, but
with yet another load-carrying element 258 hav
or move a region 230 upward.
ing a series of sections depending below the ele
I believe this control acts instantly, by the up=
per element 232 picking up countervailing load, 10 ment 255, which corresponds to the element 245
in Figure 2. VIn this Figure 3 the platform is
and is eifective to match and to balance the tend
supported at l5 points, in which the points H, I,
ency of either of the regions 23e, 230 to move
J, K, L, M, N and O are added to those desig
upward, until that tendency to move upward eX
nated in Figure 2.
ceeds whatever magnitude of dead loading is
In Figure 4 there is an upper tension element
available to migrate to that particular region
35?. and a lower tension element 354 which at
233. No matter how often the tendency to move
upward is repeated, no matter what thefre
each tower are held together and against length
wise slip relative to each other. The 'saer in the
lower element Se@ is much greater than the sag
quency of that tendency is, and irrespective of
what the source of that tendency is, the migra
tion oi loading impedes and restricts that upward 20 in the upper element 352; and there is an inter
mediate tension element 359, held against length»
movement. The opposition to rise is so imme
wise slip at the mid-portion of the upper ele
diate and can be made so effective that succes
ment 352, Iwhich on each side of the lengthwise
sive dynamic impulses cannot build up undula
center of the span connects that upper element
tions of substantial consequence. Thus the
to the lower element 3M at a junction point 35i.
structure provides a magnitude of dead loading
Each junction 36! is preferably located at more
which, in operation, migrates to a particular con
than one=eighth of the span length from the
trol region 23e, and there impedes and restricts
center oi the span, being shown in Figure e at
undulatory movements.
At a particular control region no more than in
cipient rise can occur until the initiating irn
pul‘se exceeds the magnitude of dead loading
which is available t-o migrate to that Particular
control region.
Therefore, for a suspension
,bridge which is exposed to winds, the invention
provides positive control against the amplifying
of undulations. This results because, Iwith the
30
about one-sixth of the span length, which place-s
the junctions 35i, 36! in that lengthwise range
which is optimum for over-all stabilization. Each
junction point 38! is also below a straight in
dex line (not shown) which might be project
ed, from the point of support of the element 352
El at the top of the more distant tower,l through
the location where that element is held with the
element 359 at the mid-portion of the span, said
line being extended over the junction 361. In
this type of structure the intermediate tension
element 355, which connects the midportion of
the upper element 352 with the lower element
354 at the junctions 33t, together with that ex
tent of the lower tension element 35d which is
between those junctions, form a diamond shaped
structure of the invention, it is not diflicult to
provide a magnitude of dea-d loading, available
to migrate, which exceeds the initiating impulse
of each Isingle gust of wind. A substantial rise
of a control region, caused by heavy traino load
ing may occur without detrimental effect. The
repetitive sequence or" such loadings is too in
frequent to cause successive amplifying of un
- loop. This diamond loop affords a substantial
dulations in a suspension bridge.
degree of stability without there being a strut
In Figure 2 the tension elements 25,2 and 2te
across its mideportion; but preferably there is
extend the full length of the span between the
such a strut 352, as illustrated, which i's held fast'towers 233. These elements lshould be held, by
between the lower element 352 and the midpor
any convenient means (not shown), against
tions of the elements 359, 352 where these two
50
lengthwise slip relative to each other at their
elements are held together. This strut acts pri
mid-portions 2d? and also at the towers. Be
marily as a spreader to hold those elements in
tween these held locations each half portion of
a fixed relationship to each other at the center
the lower tensio-n element 25.4 hangs with greater
of the span. The height of this strut should
sag than the coeXtensive portion of the tension 4 preferably be between one-third and two-thirds
element 252 which is above it. In each end-half
of the sag of the lower element 354 in its span
portion of the 'span there is a particular region
between the towers.
24e of the element Zei! from which a tie 263 eX
Each portion of the element 35e, extending
tends downward to a junction with the element
from its held middle to a junction 3e l, combines
244 below that region. Also a load-carrying ele
with that portion ‘of the element 354 which ex
(Si)
ment 2de, corresponding to 236 in Figure l, de
tends thence to a tower to constitute a lower
pends in four sections from five l-ocations 238,
element in an end-'half-p-,ortion of the span hav
2M, Zell, 2M, 238 in the element 24d. Each of
ing greater sag than the coextensive portion of
these four sections has greater sag than the co
the element S52 above it, between `the said held
extensive lengthwise portion of the element Zilli
locations at the center of the span and at the
which is above it. Preferably also there are ties
tower. In each end-half-portion of the span
255 extending upward from the lowest sagged
there is a migratory loading tie 353 extending
portions of these depending sections, to the ele
upward from the junction 361 to a particular
ment 24e above. The stress in these ties should
äoiâtrol region 35d' of the upper tension element
be made to be small, when the structure is static,
s .
so that the dead loading atv the junction 2M,
In each end portion of the span a tension ele
available to migrate, shall be large as explained
ment 35S depends from the junction 3e! and
with reference to Figure 1.
from the nearer tower, and hangs Iwith sag b'e
lin this structure the platform 23e is supported
"low the coveXtensive portion of the element 354
at the seven points, A, B, C, D, E, F and G, thus
providing eight panels of equal length between 75 above it. 'Fromithe lowest sagge'd ’portion of this
2,413,919
7
8
element 356 a tie 355 extends upward to the
element 354 above it.
span having greater sag in that end-half-portlon
between said held places than the co-extensive
portion of that other of these elements which is
above it; the combination in which in each end
half-portion of the span there is a tie extending
‘
Preferably also there are intermediate ties 355
which extend upward from the bridge platform,
each being connected to each of the three ten
sion elements which are above its respective point
of attachment to the platform. These interme
downward from a control region of the said upper
element, these particular control regions being
diate ties should be tensioned so as to apply a
slight loading to each of these three elements, to
provide a slight sag in each.
spaced apart from each other at a distance which
is in the> range of one-quarter to one-half of the
These sags are lO length of the span, each said tie being connected
less than the curvatures of these elements at
to the lower said element and making therewith
a junction for imposing on said tie a part of
»the aggregate of dead loading which is at that
junction when the structure is static; and in each
the regions of the ties 353-and are too small to
be realistically indicated in the drawings. The
intermediate ties 355 stabilize those three ele
ments to which they are attached, and also con
tribute appreciably to the upholding of the plat
form where they respectively are attached.
end-half-portion of the span there is at least one
depending load-carrying element connected to
the said lower sagged element at the said junction
and extending thence lengthwise of the span;
some of said dead load being imposed on this de
In Figure 4 the platform is supported primarily
at ñve panel points of the span, with only sup
plementary support at the intermediate ties 355. 20 pending element, thus being sustained at the said
When it is desirable to support the platform at
junction when the structure is static, the load
more points than are indicated in Figure 4 the
ing so sustained being sufficient to make the ag
successive sections of tension elements which are
gregate magnitude of dead loading which is im
lowest in the combination of tension elements
posed on said lower sagged element at that junc
shown should preferably each have a cross-sec 25 tion when the structure is static exceed the mag
tional area which is distributed vertically to re
nitude of dead loading which is imposed at any
sist downward bending and is distributed hori
other location of equal extent in said lower sagged
zontally to provide in its lower part a tension
element in the same end-half-portion of the
carrying area of more than twice that area of its
upper part which carries compression. That is, -
the depending element 356 at each end portion
of the span, and that section of the element 354
which depends from and between the junctions
35| may have a T cross section with the stem
of the T upward, and be arranged to have all
of the essential characteristics which are set
span; and the stress in the tie when the struc
ture is static being of a magnitude less than half
of the aggregate magnitude of dead loading which
is at the said junction of that tie with the lower
sagged element; thereby leaving at each said
junction a magnitude of dead loading which is
available to migrate from the lower sagged ele
ment to a said region of the upper element when
that region tends to move upward.
2. A structure as in claim l, in which the stress
in each tie which extends downward at a said
40 particular control region of the upper tension
forth in the description of the element 236 of
Figure 1.
By the general arrangement in Figure 4 a
bridge can be built with relatively few parts, with
light weight, and with a stability which is ex
element is, when said structure is static, such
ceptional for the small amount of material used.
that the dead loading which the tie imposes on
This is particularly true in spans of moderate
its respective said region of the upper tension
length where a suspension bridge of usual type
element is less than one-fourth of the said aggre
would be so unstable that hitherto the idea of 4: gate magnitude of dead loading which is at the
building such would be rejected in favor of a
junction of that tie with the lower tension ele
heavier and more massive truss. In this field the
ment.
stabilized suspension bridge herein disclosed is
3. A structure as in claim 1, further charac
capable of effecting an enormous saving of weight
terized in that, in each end-half-portion of the
and cost.
50 span, a said load-carrying element which de
In each of the four figures of the drawings, the
pends from the said junction therein extends to
structure provides a large dead loading at the
and is held depending also from the vicinity of
respective junctions, 23|, 24|, 25| and 36|, which
the top of the nearer said tower.
is available to migrate to the respective regions
4. A structure as in claim l, further charac
233, 240, 250, 350 of the respective upper tension
terized in that, in each end-half-portion of the
element 232, 242, 252 and 352, when intermittent
span, a said load-carrying element which depends
live loadings tend to move a said control region
from the said junction therein extends to and
upward. I believe the magnitude of the dead
is held depending also from the vicinity of the
loading thus provided for migration is adequate
top of the nearer said tower; and also a said
to impede and restrict rise at each said control
load-carrying element which depends from that
region, and thus to stabilize the bridge. This
said junction extends to and is held at and de
migration of loading is especially effective for
pends from the upper and the lower sagged ele
stabilizing suspension bridges against the impact
ments at the mid-portion of the span where they
of winds, because it inhibits the lengthwise travel
are held against lengthwise slip.
of undulations of the structure along that struc
5. A structure as in claim 1, further charac
ture.
terized in that, in each end-half-portion of the
I claim:
span, a said load-carrying element which depends
1. In a bridging structure, having two tension
fromY the said junction therein extends to and
elements, each hanging with sag between towers
is held depending also from the vicinity of the
to sustain dead and live loadings, these elements
top of the nearer said tower; and also a said load
being one below the other and being held against
carrying element which depends from that said
lengthwise slip relative to each other at the mid
junction extends across the center of the span
portion of the span, and also at the vicinities of
and is held at and depends from the said junction
said towers; that one of these elements which is
which is in the other end-half-portion of the
the lower of them in an end-half-portion of the 75 span.
2,413,0"19
6. A structure as in claim l, further charac
terized in that, in each end-half-portion of the
span, a said load-carrying element which depends
from the said junction therein extends to and
is held depending also from the vicinity of the
top of the nearer said tower; further character
ized in that each said load-carrying element
which depends from a said junction and extends
toward a tower has greater curvature at a mid
portion of its length than elsewhere along that
length.
’7. In a bridging structure, having two tension
elements, each hanging with sag between towers
to sustain dead and live loadings, these elements
being one below the other and being held against
lengthwise slip relative to each other at the mid
portion of the span, and also at the vicinities of
said towers; that one of these elements which
making therewith a junction for imposing on said
tie a part of the aggregate of dead loading which
is at that junction when the structure is static;
and, in each end-half-portion of the span, there
is means imposing at the said tie junction an
aggregate magnitude ofv dead loading which ex
oeeds the magnitude of the dead loading that is
imposed on any other location of equal extent
in said lower sagged element in the same endn
half-portion of the span; the stress in the tie
when the structure is static being of a magnitude
less than half of the aggregate magnitude of
dead loading which is at the said junction of that
tie with the lower sagged element; thereby leav
ing at each said junction a magnitude of dead
loading which is available to migrate from the
lower sagged element to a said region of the upper
element when that region tends to move upward.
8. A structure as in claim '7, in which the stress
is the lower of them in an endehalf-portion of
the span having greater sag in that end-half 20 in each tie which extends downward at a said
particular control region of the upper tension
portion between said held places than the co
element is, when said structure is static, such
extensive portion of that other of these elements
that the dead loading which the tie imposes on
which is above it; the combination in which in
its respective said region of the upper tension
each end-half-portion of the span there is a tie
element is less than one-fourth of the said aggre
extending downward from a control region of the
gate magnitude of dead loading which is at the
said upper element, these particular control
junction of that tie with the lower tension ele
regions being spaced apart from each other at a
ment.
,
distance which is in the range of one-quarter to
MERL R. WOLFARD.
one-half of the length of the span, each said tie
being connected to the lower said element and 30
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