the role othe role of string in hybrid string structuref string in hybrid string structure

Engineering Structures 21 (1999) 756769

The role of string in hybrid string structureMasao Saitoh *, Akira Okada

College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo 101, Japan

Abstract

In general, tension structure can be classified into two groups depending on the kinds of tension elements used: (1) membranestructures and (2) string structures. Such tension members as cable, rod and chain belong to the string. Cable especially is a mostimportant and representative member. Furthermore, the string structures are divided into two types: thoroughbred tension structuresand hybrid tension structures. A thoroughbred structure is a tension structure such as cable-net which is made of strings only. Asfor tension member, hybrid tension structures can be divided into the following two categories: (1) structures using members, suchas semi-rigid hanging members, which are made by changing the properties of tension members for the pure tension structure; (2)structures made by combining tension members with such rigid members as flat arches, beams and struts. Beam string structures(BSS) are typical of this type.

Here, hybrid string structures (HSS) are defined as having the characteristics of the latter. HSS are conceptually opposed tothoroughbred tension structures. HSS are aimed not only at the structural rationality including system, detail and construction but alsothe sophistication of structural expression. This paper reports mainly on the following items concerning string structure, especially theHSS: (1) the role of string; (2) tensile force in string; (3) stress and displacement control by prestressing in string of HSS; (4)classification of HSS by tensile force occurring in string; (5) a method for introduction of initial tensile force to string; and (6)some actual examples of HSS which the authors have designed. 1999 Elsevier Science Ltd. All rights reserved.

Keywords: String; String structure; Hybrid string structure; Tensile force of string; Structural design; Detail design

1. The role of string in hybrid string structure(HSS)

1.1. Tensile force in strings of HSS

The initial tensile force To (PS in a broad sense)which occurs in a string under dead load can be indicatedas the sum of the tensile force Te (existing tensile force)caused by the equilibrium and the tensile force Tp (PSin a narrow sense) which is introduced intentionally tocontrol the behavior.

To 5 Te 1 Tp

The value of Te changes depending on the weight ofthe dead load, structural system and degree of redun-dancy. Furthermore, Tp varies depending on the purpose

* Corresponding author. Fax: 00 81 3 3293 8253.

0141-0296/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved.PII: S0141- 02 96 (98)00 02 9- 7

for which the PS is introduced (stress control, avoidanceof the occurrence of compression in tension members).

The tensile force T1 which occurs in the string underthe additional loads can be expressed using theincremental tensile force Ta under the additional loads:

T1 5 To 1 Ta 5 Te 1 Tp 1 Ta

1.2. Classification of string structure

In string structures, the structural system, analyticalmethod, details and construction method greatly dependupon the amount of Tp for string tensile force, in parti-cular. Fig. 1 shows the classification of string structurescarried out under this concept by noting the amount ofPS applied to the string (Tp) and the role of the string.

The characteristics of each of the string structural sys-tems are explained below.

[A]: This type of structure contains the systems ofcable net, cable girder and tensegrity. The main purposeof PS in this system is to produce an initial tensile force

757M. Saitoh, A. Okada / Engineering Structures 21 (1999) 756769

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758 M. Saitoh, A. Okada / Engineering Structures 21 (1999) 756769

(To) which is larger than the anticipated incrementalcompressive force in order to prevent the tensile forcefrom being reduced to zero under an additional load.Furthermore, there is a case in which PS is set up fromthe viewpoint of securing stiffness against any eccentricdistributed load. This system is also characterized by thenecessity of an existing tensile force in order to obtaina target shape for the dead load. This structural systemcontains cable grids made by setting both sag and riseof a cable net at zero. In this case, PS is set up mainlyfor the purpose of controlling deformation.

[B]: Tensegric truss is contained in this group. [B] isgreatly different from [A] in the following ways.Although the string tensile force is established with thesame aim as that set up in group [A], the axial force ofa strut connecting each string is relatively strong and thisstrut plays an important role in the structure.

[C]: This system contains a structure made by com-bining strings with other relatively rigid members. Abeam string structure formed by combining beams orarches with strings is typical of this structural system.Introduction of PS can be actively utilized for the controlof the stress and deformation of rigid members. Theamount of PS (Tp) is determined by the purpose of con-trol or the weight of the dead load.

[D]: This structural system enables strings to producetensile force in order to obtain a balanced target shapeof the frames. In this case, the initial tensile force is onlyan existing tensile force (Te) produced by the dead load.Moreover, for the purpose of creating a target shape inconstruction work, it is important to evaluate the deadload accurately and to set up and regulate the length ofstrings as well as to evaluate an elastic modulus. Thistype of structural system also contains a one-way sus-pended roof and a dish-shaped suspended roof to bothof which PS (Tp) is not applied as well as a hangingroof and a cable-stayed structure.

[E]: In this system, strings are usually inserted into astructure in order to maintain stability of its main frames.The amount of PS (Tp) applied to the strings is estab-lished with the aim of preserving tensile force in thesame way as seen in the system of [A]. However, it isa characteristic that the value of the existing tensile force(Te) is almost zero.

[F]: In structural system [F], strings are installed inorder to maintain the form resistance of a rigid frame.The string has such a significant effect as to exert brac-ing effects. Also it is characterized by stiffening andreducing stress against additional loads acting out-of-plane. Since only a small amount of PS (Tp) is appliedto the string, a reduction in the tensile force of the stringto some degree during additional loading is allowed for.

[G]: It is a special feature that only a small amountof PS necessary to secure the straightness of the stringand to eliminate its initial structural stretch is applied tothe string. The string functions mainly to exert in-plane

bracing effects. It is not expected that this structural sys-tem can maintain the form resistance of a main frameas seen in [F].

[H]: The structural system belonging to this categoryis formed by combining two or more of the aforemen-tioned systems from [A] to [E]. The SKELSION struc-tural system which is made by adding vertical stiffnessto a beam string structure is included in this system.

1.3. Role of string in HSS and classification of HSS

HSS is a structure which has obtained new excellentdegrees of efficiency by adding strings [1,2,5]. Theadditional areas of efficiency can be divided broadly intothe following two categories: architectural expressionsin which the clearness, lightness and logic of a structurecan be explained and the degree of freedom in theexterior design can be expanded, and development instructural efficiency. With regard to the latter, the roleor effects of strings can be arranged as follows:

[Passive effects of strings](1) Formation of a balanced system, stabilization of a

frame and elimination of reaction to external forces.(2) Bracing effects.(i) In-plane stiffening;(ii) maintenance of form resistance and increase in

global buckling load.[Active effects of strings](3) Stress control of bending or compressive members

(active stress control).(4) Control of displacement and shape of frames

(active displacement control).(5) Increase in stiffness achieved by expecting geo-

metrical stiffness.With regard to the active effects of strings, the struc-

tural efficiency of a frame can be changed by controllingthe amount of PS applied to strings. The passive effectsof strings indicates the efficiency which can be obtainedsimply by installing strings.

It is a characteristic feature that structural membersfor the HSS such as bending or compressive membersand strings are as important as each other in the struc-ture. Therefore, (2 ii), (3) and (4) are listed under thestring effects of the HSS. When viewing Fig. 1 from thispoint of view, the HSS can be divided into [B], [C], [F]and [H]. Fig. 2 indicates the analytical results obtained incases where the HSS has actually been applied in Japan.

2. Method of establishing PS

2.1. Purpose of PS

With regard to a cable structure, in general, PS isintroduced to strings with the following points as a tar-


Fig. 2. Role of string in actual building projects.

get. These purposes of PS are closely related to the roleof the strings as mentioned above.1. Additional performance in resistance for compressive

force of strings.2. Security of straightness for strings.3. Additional stiffness, especially geometrical stiffness.4. Elimination of initial stretch of strings.5. Decrease in the stress of bending members and com-

pressive members (active stress control).6. Control of deformation and the shape of frames

(active deformation control).7. Stiffening of frames (addition of bracing effects and

increase in buckling load).The stress control function in point (5) and the defor-

mation control function in (6), both of which are oftenutilized in recent cable structures, are explained brieflyas follows.

2.2. Stress control by prestressing in string

In order to explain the stress control function, a beamstring structure with trussed beams is taken as anexample (Fig. 3). The beam stress (shown with an axisof upper and lower chords) can be expressed as the sumof the following three stresses: stress under the loadingof simple beams, stress induced by the introduction ofPS into strings and stress caused by the eccentricity (thedisagreement between a strings end and a neutral axisof the beam).

When introducing PS, stress reverse to that of simplebeams occurs. (In this example, tensile stress occurs inupper chords and compressive stress occurs in lowerchords.)

By using this property, the stress of beams can be

changed with the amount of PS. The optimum amountof PS is usually set up so that the stress of beams is mini-mized.

The conditions for this are as follows:1. Equalization of members: to let the positive bending

moment be the equal to that of the negative.2. Minimization of a section: to make the stress intensity

for beams the minimum.3. Minimization of weight: to make the sum of the strain

energy of beams the minimum.In cases where a rise of beams is low and a section

area is not changed depending on the stress, (1) is gener-ally adopted.

Fig. 3 shows the stress of beams when introducing theoptimum tensile force (the PS amount which is 1.02times the total load) obtained under condition (1) into thestrings. The stress of the beams in this case is reduced byabout 20% of the stress of simple beams. It is clearlyshown that the introduction of PS exerts an effect on thereduction of stress.

2.3. Displacement control by prestressing in strings

In this section, a beam string structure is alsoexplained as an example. The introduction of PS intostrings causes upward deformation in this structure.

When producing and constructing beams for ordinarystructures, coordinates made by cambering a finishedshape by deflection induced by dead load are often usedfor control values. As for beam string structures, sincedeflection can be eliminated due to the introduction ofPS into strings, it is possible to fix control values on thebasis of coordinates for a finished shape through thewhole process extending from design and production ofmembers to construction work.

In addition to that, production and construction workcan be improved by utilizing the deformation controlfunction in order to simplify supports and to eliminateconstruction errors.

3. Method for introduction of initial tensile force tostring

The most important problem in the investigation ofthe introduction of the string tensile force To under thedead load is one of deciding when the installation of thestrings, the induction and regulation of the tensile forceshould be carried out. In cases where the tensile forcewhich occurs with the installation of strings is Ts andthe incremental tensile force induced by the executionwork is DTo, To can be expressed by the following equ-ation:

To 5 Ts 1 DTo


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The value for Ts is determined according to the instal-lation time for the strings. For example, the Ts valuewhen strings are fitted before finishing work is smallerthan when they are fitted. However, after installation,relatively large deformation occurs in the strings.

A method for introducing the tensile force to the stringis decided in consideration of the length of members,the degree of error produced in the manufacture and theconstruction, construction term, workability, safety andcost as well as the amount of Ts. Standard methods forintroducing the tensile force are shown in Fig. 4.

Fig. 5 shows the effects of the combinations of twokinds of method on the introduced tensile force for theBSS, a temporary stage lowering method and a methodfor hauling-in strings.

4. Detail design

The most popular material used for strings of HSS iswire rope. Wire rope made by bundling fine high tensilestrength materials has flexibility and the strength toweight ratio is high. Also a great advantage of wire ropeis that there is no limit to the length of members froma manufacturing and a transportation viewpoint.

At the stage of planning and designing HSS, the fol-lowing points must be noted in order to exhibit thecharacteristics and advantages of cables:1. To use cables continuously with as long a length as

possible.2. To lessen the number of points for adjusting the

length of a cable.3. To introduce the prescribed amount of PS accurately

with little force at a reduced number of points.4. To reduce the number of metallic materials fitted to

Fig. 4. Method of introduction of tensile force to string.

the middle of a cable and to simplify their mechanismto follow the movement of the cable.

In the design of HSS based on these points, it is ofimport to establish a design method for clamps fitted tothe middle part of cables (hereafter referred to as middleclamp). The middle clamp is a metal fitting attached tothe middle part of a cable to join it to other members.It has the following characteristics:

I A cable can be used continuously without the necess-ity of cutting it at the clamping part.

I A cable can be bent in a shape of a polygonal linewith a system utilizing its flexibility.

I The clamps grip is caused by friction. Namely, slid-ing of clamps caused by the difference (sliding force)in the tensile force between both sides of the clampsdoes not occur as frictional force is produced throughthe exertion of a compressive force (clamping force)in a direction at right angles to the axis of the cable.The resistance against the sliding of clamps inducedby this clamping force is called grasping force.

I A representative example of a middle clamp is shownin Fig. 6. The middle clamp is composed of two plateswhich contain both sides of a cable and bolts for con-necting and tightening these two plates.

The middle clamps are designed usually in the orderof stages mentioned below:

1. To set up grasping force and clamping force, both ofwhich are necessary to resist the assumed slidingforce.

2. To compute the number of bolts and their diameternecessary to produce clamping force.

3. To compute the length of the plates on the basis ofthe allowable surface pressure of the cables.

4. To compute the thickness of the plates in regard totheir bending strength.

Grasping force and clamping force established in(1) are the foundation for the computations in (2)(4)and the factors which are greatly concerned with theirdesign and cost in the stage of determining the size ofclamps. However, under the present conditions, designdata necessary for the establishment of the clampingforce of cables has yet to be prepared.

In order to obtain basic data regarding the clampingforce which is necessary for HSS, experiments were car-ried out using a model shown in Fig. 7.

The experimental model was made for a fitting partfor a strut of HSS and a cable. In the experiments, slidingforce was produced by introducing tensile force into oneend (T1) of the cable after the cable was clamped witha plate installed at the lower part of the strut. This wasdone under the condition that the initial tensile force wasproduced in the cable. The bending angle of the cableand its clamping force were adopted as main experi-


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Fig. 6. A representative example of a middle clamp.

mental parameters. During the experiments, a steel rodwas fitted to the end of the strut to protect it from hori-zontal deformation. Figs. 8 and 9 show examples of theexperimental results. The ordinate in the figure indicatesa value obtained by non-dimensioning sliding force, thedifference in the tensile force of the cable between bothsides of the clamp with its clamping force. The abscissashows the sliding amount of the cable at the locationwhere the clamp is installed.

Fig. 8 shows the results obtained in the case of thebending angle being 0 with the clamping force of thecable (target value: 216 tf) as a parameter. The non-dimensional sliding force when the cable begins to slideshows fixed values almost at the range of 0.30.4. As aresult, the linear relationship between the clamping forceand the grasping force for the clamp was confirmed.

Furthermore, after the cable begins sliding, the grasp-ing force tends to increase. It is thought that this iscaused by wedging effects due to the difference betweenthe diameter of the clamping part of the cable and thatof the non-clamping part. This tendency is marked byan increase in the clamping force.

Fig. 9 shows the experimental results when the clamp-ing force of the cable is constant (target value: 8 tf) withthe bending angle of the cable as a parameter. It is seenthat the wider the bending angle of the cable, the greaterthe sliding force when the cable begins to slide. It canbe evaluated that this is caused by the effects of existing

Fig. 7. Experimental apparatus for obtaining grasping force of middle clamp.

friction resulting from the compressive force of the strutunder the initial conditions.

As mentioned above, the basic characteristics of thegrasping force and the clamping force of cables wereexplained based on the experimental results. It isexpected that middle clamps will be smaller and simpli-fied in the future.

5. The role of strings in actual hybrid stringstructures

HSSs which were designed by the authors and con-structed in Japan are presented in view of [a] image andtechnology ([b] structural system, [c] method for intro-duction of tensile force and [d] construction)[3].

5.1. Project 1: Green Dome Maebashi (1990)168 m3 122 m

[a]: Since the construction site is located in a favoredplace which is contiguous to a river with an abundanceof flowing water and surrounded by grand mountains,the buildings first requirement was for harmony withnature. The exterior view is one of both sharpness andlight.

[b]: In order to actualize a flat dome covering an ovalplan, the BSS was employed. Since the horizontal thrustof the BSS is small and a large opening can be installedat the eaves, the exterior view has one of both sharpnessand lightness.

[c] and [d]: The tensile force of the strings was estab-lished with the aim of minimizing and equalizing thebending moment in bending members. On a centralstage, after the BSS was erected, the tensile force wasintroduced to the strings using jacks installed at the endsof the 68 strings (Figs. 10 and 11).


Fig. 8. Relationship between sliding force and sliding amount obtained from experiment (u 5 0 ).

Fig. 9. Relationship between sliding force and sliding amount obtained from experiment (target value of clamping force: Nt 5 8 tf).

5.2. Project 2: Urayasu Municipal Sports Center(1995)108 m 3 52 m

[a]: The image was one of waves lapping the beach.A curved large roof covers two arenas, large and small.

[b]: Seven duplex type BSS units with Vierendeeltrussed beams composed of H-shaped cross-section steelare installed in the longitudinal direction of the building.The roof surface, which is supported by six cylindricalcolumns at the periphery and is raised about 5 m by V-shaped supports on the columns, appears to be floating.

[c] and [d]: After structural steel work was carried outon stages, the tensile force was introduced using a jack

for a couple of BSS and two ties connecting columns(Figs. 12 and 13).

5.3. Project 3: Amagi Dome (1991)diameter 43 m

[a]: The concept for the shape of a membrane roofplaced on massive folded plate walls was created fromthe image of a bird folding its wings or a cloud float-ing above a green forest.

[b]: This structure originates in the double-layer BSSsystem. The roof is a cable structure which is called atension strut dome. Its basic formation is one in which


Fig. 10. Exterior view, Project 1.

Fig. 11. Interior view, Project 1.


wheel type cable girders are supported by tension trussat the periphery.

[c]: This system has the property of introducing axialforce to all members by hauling in the ends of the upperchord cables of the roof. The tensile force of strings was

Fig. 13. Structural model, Project 2.

introduced with jacks utilizing this property after thelengths of all the strings (made of cables and rods) con-stituting the roof were regulated.

[d]: A method was employed in which the entire roofis raised up by using temporary compression ringsinstalled at the periphery after the roof was erected atthe level of the arena. After raising up the roof, finalintroduction of the tensile force to the strings was carriedout (Figs. 14 and 15).

5.4. Project 4: Izumo Dome (1992)diameter 140 m,rise 49 m

[a]: The design expresses the elaborate fineness foundon traditional Japanese umbrellas and, by using large-section glulam, skeleton with shadows. The exteriorview looks like an uneven lighting hood made of foldedpapers designed by Le Crint.

[b]: The three-dimensional tension string dome struc-ture with a relatively high rise is designed to increaseboth strength and stiffness by combining radiallyarranged wooden arches with strings. Hoop cables workeffectively against symmetrical loads, and braces made




of rods are effective against additional loads, especiallyasymmetrical loads such as those of snow and wind.

[c]: For hoops to which a large amount of tensile forceis introduced, the method of installation after hauling-in was used. In this method, hoops are fitted to fixedlocations while being extended outward by jacks.

[d]: The push-up method, in which after the archesare formed on the ground, the central stage is pushed upaccompanied by moving of periphery supports, was used(Figs. 16 and 17).

5.5. Project 5: Sakata Municipal Gymnasium (1991)53 m 3 68 m, 41 m 3 31 m

[a] To construct as flat and light a gymnasium aspossible was the theme established in first considerationof harmony with the adjacent art museum. The twoarenas are figures that appear as though two white swansare about to rise from a paddy field and into the airabove.

[b]: This building has a distinctive characteristic inthat the canti-truss (CT) at both sides support the BSS.Backstays are installed at the outsides of the CTs. A



large amount of tensile force occurs in the backstaysunder the self-load, but when it snows an arch mech-anism is formed, and the tensile force in the backstaysis reduced.

[c]: After the lengths of strings were regulated, thetensile force was introduced to the strings by pullingdown the middle parts of the cables and fitting them tostruts. This was done by human power under both theskeleton and finished loads.

[d]: After the BSS units were assembled on theground, they were raised by the lift-up method, in whichthree BSS units were lifted as a set pair using ropeswhich were hung from the CTs (Figs. 18 and 19).

5.6. Project 6: Kita-Kyushu Anoh Dome (1994)61.8 m 3 108 m

[a]: This building is near Mount Sarakura, where theparaglider originated in Japan. The image of a parag-lider which landed in a green forest resulted in the basicconcept for this dome. The interior view is suggestiveof trees in a forest because of the soft sunlight which




pours through the membrane and onto the wooden archesand supports.

[b]: The system is the same as that of Project 5 inwhich the BSS was combined with the CT. The con-struction site is well known for its typhoons so it wasimportant to plan a wind-resistant building. The systemis designed so that a tension arch, which is formed withvalley cables and backstays, can resist blow-up windsof typhoon.

[c]: The introduction of the tensile force to the stringswas conducted by pulling down the strings and insertingthem into the lower end of the struts under the weightof the beams.

[d]: A pair of two BSS units equipped with temporarybraces was elevated using a crane and welded to the CTswhich have been exactly set by the pre-loading system(Figs. 20 and 21).

5.7. Project 7: Subway station for Nihon University(1996)20 m 3 40 m

[a]: A futuristic subway station suffused with brightlight was proposed. The design was done with the aim



of constructing a new system which embraces people inan atmosphere of lightness and transparency radiatingfrom an atrium space.

[b]: The structural system SKELSION [4] was used,which can resist horizontal loads by adding bracingstrings (BS) to the BSS. The SKELSION was createdwith the concept of uniting columns and beams, both ofwhich are arbitrarily arranged, in a body with stringsarranged in a woven pattern. There is a high degree offreedom for space planning.

[c]: The tensile force of the SS was introduced bypulling both ends of the string using a jack. As for theBS, by shortening the distance between two plates at thepoint where the six BSs are connected, the tensile forcewas introduced to these BSs simultaneously by using ajack.

[d]: The tensile force to the SS and BS was introducedin stages. Although a sliding method using the self-bal-ancing system of SKELSION was possible, it was notemployed for this building (Figs. 2224).




Fig. 24. Face joint for six bracing strings, Project 7.

5.8. Project 8: Horinouchi Town Gymnasium (1996)span 38 m, spacing 3 m

[a]: This project was designed in order to actualize asnow-resistant wooden vault which can be constructedat low cost in heavy snowfall districts (snow load1050 kg/m2, snowfall depth 3.5 m). The design wasmade with the aim of expressing local color and fresh-ness.

[b]: Under the self-load, the self-balancing mechanismof the BSS is formed and the structural rationality isrealized. Furthermore, when it snows, a trussed mech-anism is formed with inclined posts and strings. Thisresults in a string truss structure (STS) with reducedstress and additional stiffness.

[c]: When the BSS units were assembled on theground, the lengths of the rods for the lower chords wereregulated and then the tensile force was introduced bythe self-load. After the BSS units were assembled, a turnbuckle was used to tension the diagonal strings to thedegree necessary to secure their straightness.

[d]: Each BSS unit fabricated on the ground was liftedby a crane for installation at a fixed location. When the


work was completed, compressive force which occurredduring the finishing work was released by looseningscrews at the lower parts of the posts (Figs. 25 and 26).

5.9. Project 9: Iwadeyama School Gymnasium(1996)span 36 m, spacing 3.5 m

[a]: Under the basic concept of the creation of abright futuristic space for children in snowy districts, atransparent building with a light and sharp appearancewas planned for the building.

[b]: In order to make the roof as thin and flat as poss-ible, a structural system combining the string truss struc-ture (STS: see Project 8) with the SKELSION wasdesigned.

[c]: The introduction of tensile force to the strings forthe lower chords of the STS was carried out by insertingstruts after regulating the lengths of the strings. A smallamount of tensile force was introduced to the diagonalstrings with rods using a turn buckle. The bracing stringsof the SKELSION were tensioned by a jack pullingdown all the lower joint connections simultaneously.

[d]: After the completion of the STS for the entire




roof, the roof was raised to the fixed height by ropeshanging from the tops of the peripheral columns. Theintroduction of tensile force to the bracing strings wascarried out after the roof was lifted (Fig. 27).

References

[1] Saitoh M. Recent development to hybrid tension structures. In:Proceedings of IASS, Copenhagen, 1991:17786.

[2] Saitoh M, Okada A, Endoh S. Structural design and constructionof the tension lattice dome. In: Proceedings of IASS, Toronto,1992:53041.

[3] Saitoh M, Okada A. Conceptual design of tension structures. In:Proceedings of SEIKEN-IASS, Tokyo, 1993:46572.

[4] Saitoh M, Okada A. Development and application of SKEL-SION. In: Proceedings of IASS, Milan, 1995:88996.

[5] Saitoh M, Okada A. From image to technology: the role of stringin hybrid string structures. In: Proceedings of IASS, Stuttgart,1996:66370.

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