US2413019A

US2413019A - Stabilizing means for tension elements hanging with sag to sustain loading between supports

Info

Publication number: US2413019A
Application number: US435686A
Authority: US
Inventors: Merl R Wolfard
Original assignee: Individual
Current assignee: Individual
Priority date: 1942-03-21
Filing date: 1942-03-21
Publication date: 1946-12-24
Anticipated expiration: 1963-12-24

Description

Dec. 24, 1946.

STABILIZING MEANS FOR TENSION ELEMENTS HANGING WITH SAG TO SUSTAIN LOADING BETWEEN SUPPORTS M. R. WOLFARD Filed March 2l, 1942 2 Sheets-Sheet 1 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 Patented Dec., 24, 1946 UNl'i" STATES PATENT OFFICE STABILIZING MEAN S FOR r.TENSION ELE- MENTS HANGING WITH SAG T SUSTAIN LOADING BETWEEN SUPPORTS 8 Claims.

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 tensioned elements to stringently restrict up and down swaying and vibrating movements throughout all large portions of the lengthwise loadcarrying structure in a suspension bridge or in other long and slender spanning structures that hang with sag to sustain dead and live loading between towers.

A leading ob'ect ci the present invention is to restrict swaying and vibrating movements resulting from the intermittent incidence of live loadings, whether of winds or traic or both, especially to restrict the amplitude of those movements which would be aggravated by the cumulative influence of either or both of these disturbing forces.

It is well known that, when a cable or other tension element hangs with sag between towers, and is unrestrained, the advent of downward pressure, as of a trac loading, on one end-half portion ci the sagged element causes upward movement ci the other end-half-portion of that sagged element; and, conversely, the advent of an4 upward pressure, as by the upward component of a gust ci wind, on one end-half-portion of the sagged element causes downward movement of the other end-hal-portion. of that sagged element. These upward and downward` movements are initial movements of undulations in the cable.

The invention provides means for restricting such up and down movements at predetermined regions ci the length of the span, by migration of dead loading. This migration of loading primarily restricts rising and falling movements within the spanning structure. The elimination of such movements markedly aids in restricting lateral sway also.

The term migration ci loading signifies the 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 loading. is only applied to a shitting of load from one member to another which occurs when both members support a load in common and are so related to one another that a decrease or increase in the amount ci said load carried by one member must be accompanied by a proportionate increase or decrease respectively of the amount of 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 loading increases the loading of a particular point, beyond its, static loading; and it occurs in that direction which impedes and restricts undulatory upward movement of the structure at that particular point. That is, an increasing of the magnitude of that migratory loading which is becoming carried at a particular point opposes rise of that point.

The invention impe'des and restricts undulatory movements by causing dead loading to migrate to particular control regions of the structure. Each end-half-portion or" the structure has at least one such control region, In particular the present invention provides a structure in which dead loading will migrate` to and from such particular control regions in an upper lengthwise tension element. Inl each end-half-portion of the span the migration will be from and to another and lower lengthwise tension element in the Same end-hali-portion of the span.

It is intended to make suitable expression in the appended claims so that the patent will cover whatever there isof patentable novelty in the structure thus disclosed for migration of dead loading upward and downward between regions that are in the same end-half-portion of the span.

In my co-pending application Serial No. 626,661 I disclose and claim a structure wherein there is migration of dead loading across the center of a span, from a controlfregion in one end-halfporticn of the span to a control region in the other end-half-portion.

My experiments indicate that, when migratory 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 threetenths to four-tenths of the length of the span apart from each other. However, benecial practical results are attained by locating these two regions anywhere within the range of onequarter to one-half of the length of the span apart.

The herein disclosed method of restricting undulations of' a structure by migration of loading 3 permits a reduction in the number and weight of the restraining elements required, as compared with the usual method of approach where the attempt is made to tie or hold panel points of a truss in a xed position.

The migratory-loading feature of the inven tion is characterized by providing a rapid increase in magnitude of the restraining load, upon the occurrence of 'only a very slight movement of the restrained region. rangement of migratory loading is very eiective in restricting up and down sway within any long and slender structure that hangs with sag between supports, whether the tendency to cause such movements is traffic loading, or wind pressure 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 lengthwise members of a suspension bridge, the preferred embodiment of the present invention em ploys forces which are predominantly vertical, in contra-distinction to forces having large horizontal and lengthwise components. This permits enormous reduction in the massiveness oi the required restraining elements.

Other features and advantages of the invention, and details of construction will appear from the drawings herewith, and from the description which follows, showing embodiments. It is to be understood however, that the invention is not limited t0 the specil'ic constructions here shown for illustrating its principles.

In the accompanying drawings, Figures 1-4 are diagrammatic showings of side elevations of four different suspension bridges, each of which embodies the invention.

In Figure 1 a load-carrying element 236 extends the full length of the span between

towers

228, 228, and extends to beyond those towers to usual or suitable anchorages (not shown). Between the towers this element 236 consists of a succession of sections which depend with sag from a lengthwise tension element 234 and are joined together endwise by coupling plates 231. The plates which belong in the right hand portion of the figure are omitted in order to show the separateness of the sections. The sections of the element 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 drawings in order to give opportunity for indicating sundry connections clearly. The middle two sections are shown shorter than the two end sections, thus indicating that commercial lengths of bars may be used for these diierent sections, for example, 60 foot length for the middle and 90 foot length for the end sections. The end sections 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,

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 elements, 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 towers and also at the middle of the span. The lower of these tension elements 234 is shown as consisting of a series of four separate rods each extending between two adjacent couplings 231. The element 234 hangs with greater sag in each end-half-portion of the span than does the coextensive 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, 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 midportion of the span, where the coupling 231 joins it to the upper and

lower tension elements

232, 234. Each of these sections of the element 236 functions as a load-carrying element by supporting its coextensive portion of the bridge platform E29 by hangers at intervals. Thus dead load imposed by hangers on the element 236 is sustained in part by the element 234 in each end-half-portion of the span at a tie-junction 23|.

For embodying the migratory loading feature of the invention, the stress in each tie 233 may be such that it supports only about half or less than half of the aggregate of loading which is existing at the junction 23| when the structure is static. Preferably the tension in each such tie 233 will be made to be such that the upper tension element at a particular region 230 supports less than one-quarter of the aggregate of dead loading which ris at the junction 23l below that region when the structure is static. Each of the several sections of the element 236 which depend from a junction 23| has greater curvature at its lowest sagged portion than elsewhere along its length. For graphic illustration the major part of each end-half part of each such section is represented as being straight; but for optimum utility, and particularly for attaining stability 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 interaaia'oie mittent live loadings tend to move that particular region upward. This may occur, for example, when a trafc 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 or move a region 230 upward.

I believe this control acts instantly, by the up= per element 232 picking up countervailing load, and is eifective to match and to balance the tendency of either of the regions 23e, 230 to move upward, until that tendency to move upward eX- ceeds whatever magnitude of dead loading is available to migrate to that particular region 233. No matter how often the tendency to move upward is repeated, no matter what thefrequency of that tendency is, and irrespective of what the source of that tendency is, the migration oi loading impedes and restricts that upward movement. The opposition to rise is so immediate and can be made so effective that successive dynamic impulses cannot build up undulations of substantial consequence. Thus the structure provides a magnitude of dead loading which, in operation, migrates to a particular control region 23e, and there impedes and restricts undulatory movements.

At a particular control region no more than incipient rise can occur until the initiating irnpulse 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 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 loading may occur without detrimental effect. The repetitive sequence or" such loadings is too infrequent to cause successive amplifying of undulations in a suspension bridge.

In Figure 2 the tension elements 25,2 and 2te extend the full length of the span between the towers 233. These elements lshould be held, by any convenient means (not shown), against lengthwise slip relative to each other at their mid-portions 2d? and also at the towers. Between these held locations each half portion of the lower tensio-n element 25.4 hangs with greater sag than the coeXtensive portion of the tension element 252 which is above it. In each end-halfportion of the 'span there is a particular region 24e of the element Zei! from which a tie 263 eX- tends downward to a junction with the element 244 below that region. Also a load-carrying element 2de, corresponding to 236 in Figure l, depends in four sections from five l-ocations 238, 2M, Zell, 2M, 238 in the element 24d. Each of these four sections has greater sag than the coextensive lengthwise portion of the element Zilli which is above it. Preferably also there are ties 255 extending upward from the lowest sagged portions of these depending sections, to the element 24e above. The stress in these ties should be made to be small, when the structure is static, so that the dead loading atv the junction 2M, available to migrate, shall be large as explained with reference to Figure 1.

lin this structure the platform 23e is supported at the seven points, A, B, C, D, E, F and G, thus providing eight panels of equal length between 6 the towers 238. The junctions 24| are located a little outside of the lengthwise range which is 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 corresponding reference numerals of the 25o-251 series, but with yet another load-carrying element 258 having a series of sections depending below the element 255, which corresponds to the element 245 in Figure 2. VIn this Figure 3 the platform is supported at l5 points, in which the points H, I, J, K, L, M, N and O are added to those designated in Figure 2.

In Figure 4 there is an upper tension element 35?. and a lower tension element 354 which ateach tower are held together and against lengthwise slip relative to each other. The 'saer in the lower element Se@ is much greater than the sag in the upper element 352; and there is an intermediate tension element 359, held against length wise slip at the mid-portion of the upper element 352, Iwhich on each side of the lengthwise center of the span connects that upper element to the lower element 3M at a junction point 35i. Each junction 36! is preferably located at more than one=eighth of the span length from the center oi the span, being shown in Figure e at 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 index line (not shown) which might be projected, from the point of support of the element 352 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 extent of the lower tension element 35d which is between those junctions, form a diamond shaped loop. This diamond loop affords a substantial degree of stability without there being a strut across its mideportion; but preferably there is such a strut 352, as illustrated, which i's held fast' between the lower element 352 and the midportions of the

elements

359, 352 where these twoelements are held together. This strut acts primarily as a spreader to hold those elements in a fixed relationship to each other at the center of the span. The height of this strut should 4 preferably be between one-third and two-thirds of the sag of the lower element 354 in its span between the towers.

Each portion of the element 35e, extending from its held middle to a junction 3e l, combines with that portion of the element 354 which extends thence to a tower to constitute a lower element in an end-'half-p-,ortion of the span having greater sag than the coextensive portion of the element S52 above it, between `the said held locations at the center of the span and at the tower. In each end-half-portion of the span there is a migratory loading tie 353 extending upward from the junction 361 to a particular oitrol region 35d' of the upper tension element In each end portion of the span a tension element 35S depends from the junction 3e! and from the nearer tower, and hangs Iwith sag b'e- "low the coveXtensive portion of the element 354 above it. 'Fromithe lowest sagge'd portion of this 7 element 356 a tie 355 extends upward to the element 354 above it.

Preferably also there are intermediate ties 355 which extend upward from the bridge platform, each being connected to each of the three tension elements which are above its respective point of attachment to the platform. These intermediate ties should be tensioned so as to apply a slight loading to each of these three elements, to provide a slight sag in each. These sags are less than the curvatures of these elements at the regions of the ties 353-and are too small to be realistically indicated in the drawings. The intermediate ties 355 stabilize those three elements to which they are attached, and also contribute appreciably to the upholding of the platform where they respectively are attached.

In Figure 4 the platform is supported primarily at ve panel points of the span, with only supplementary support at the intermediate ties 355. When it is desirable to support the platform at more points than are indicated in Figure 4 the successive sections of tension elements which are lowest in the combination of tension elements shown should preferably each have a cross-sectional area which is distributed vertically to resist downward bending and is distributed horizontally to provide in its lower part a tension 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 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 exceptional for the small amount of material used. This is particularly true in spans of moderate length where a suspension bridge of usual type would be so unstable that hitherto the idea of building such would be rejected in favor of a heavier and more massive truss. In this field the stabilized suspension bridge herein disclosed is capable of effecting an enormous saving of weight and cost.

In each of the four figures of the drawings, the structure provides a large dead loading at the respective junctions, 23|, 24|, 25| and 36|, which is available to migrate to the

respective regions

233, 240, 250, 350 of the respective

upper tension element

232, 242, 252 and 352, when intermittent live loadings tend to move a said control region upward. I believe the magnitude of the dead loading thus provided for migration is adequate to impede and restrict rise at each said control region, and thus to stabilize the bridge. This migration of loading is especially effective for stabilizing suspension bridges against the impact of winds, because it inhibits the lengthwise travel of undulations of the structure along that structure.

I claim:

1. 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 midportion of the span, and also at the vicinities of said towers; that one of these elements which is the lower of them in an end-half-portion of the 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 endhalf-portion of the span there is a tie extending downward from a control region of the said upper element, these particular control regions being spaced apart from each other at a distance which is in the range of one-quarter to one-half of the length of the span, each said tie being connected 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 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 depending element, thus being sustained at the said junction when the structure is static, the loading so sustained being sufficient to make the aggregate magnitude of dead loading which is imposed on said lower sagged element at that junction when the structure is static exceed the magnitude of dead loading which is imposed at any other location of equal extent in said lower sagged element in the same end-half-portion of the span; and 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 leaving 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.

2. A structure as in claim l, in which the stress in each tie which extends downward at a said particular control region of the upper tension element is, when said structure is static, such that the dead loading which the tie imposes on its respective said region of the upper tension element is less than one-fourth of the said aggregate magnitude of dead loading which is at the junction of that tie with the lower tension element.

3. A structure as in claim 1, further characterized 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.

4. A structure as in claim l, further characterized 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; and also a said load-carrying element which depends from that said junction extends to and is held at and depends from the upper and the lower sagged elements at the mid-portion of the span where they are held against lengthwise slip.

5. A structure as in claim 1, further characterized in that, in each end-half-portion of the span, a said load-carrying element which depends fromY the said junction therein extends to and is held depending also from the vicinity of the top of the nearer said tower; and also a said loadcarrying element which depends from that said junction extends across the center of the span and is held at and depends from the said junction which is in the other end-half-portion of the span.

6. A structure as in claim l, further characterized 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 characterized in that each said load-carrying element which depends from a said junction and extends toward a tower has greater curvature at a midportion 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 midportion of the span, and also at the vicinities of said towers; that one of these elements which is the lower of them in an endehalf-portion of the span having greater sag in that end-halfportion between said held places than the coextensive 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 downward from a control region of the said upper element, these particular control regions being spaced apart from each other at a distance which is in the range of one-quarter to one-half of the length of the span, each said tie being connected 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 end-half-portion of the span, there is means imposing at the said tie junction an aggregate magnitude ofv dead loading which exoeeds 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 leaving 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 in each tie which extends downward at a said particular control region of the upper tension element is, when said structure is static, such that the dead loading which the tie imposes on its respective said region of the upper tension element is less than one-fourth of the said aggregate magnitude of dead loading which is at the junction of that tie with the lower tension element.

MERL R. WOLFARD.