RESEARCH ARTICLE

Fabrication and Construction of Cable-Supported Ribbed-BeamComposite-Slab Structure

Wentao Qiao1,2 • Qi An3 • Dong Wang4 • Mingshan Zhao5

Received: 21 June 2016 / Revised: 30 August 2016 / Accepted: 5 January 2017

� Tianjin University and Springer-Verlag GmbH Germany 2017

Abstract The cable-supported ribbed-beam composite-

slab structure (CBS) is a new prototype of the cable-

supported structure system, which has many merits, such as

long-span availability and enabling a reduction in costs

involved. Based on existing research pertaining to cable-

supported structures, this study proposes a standard con-

struction process (including assembling, casting, and

installation) using a construction method based on defor-

mation control. A theoretical analysis is conducted and a

simulation using a 1:5-scaled physical model shows that

deformation can be controlled in accordance with the

results of analysis, although experimental results indicate

that practical tension applied to the cable is larger than the

theoretical value (error of 6.8%). When construction is

completed, the distribution pattern of the practical cable

force is mostly consistent with that of the theoretical pre-

diction (average error of 7.6%), which indicates that the

analytical model matches closely with the real CBS in

terms of structural behavior.

Keywords Cable-supported ribbed-beam composite slab �Pre-stress � Cable tension � Fabrication and construction �Deformation

Introduction

The cable-supported ribbed-beam composite-slab structure

(CBS) is a new prototype of cable-supported structure

system [1]. It typically combines the merits of rigid

structures (such as shell and grid structures) and flexible

structures (such as cable network structures). Cable net-

work structures enable a self-balancing system because of

the action of pre-stressed cables and highly efficient

mechanical features; thus, they have been widely used in

the public buildings throughout the world. The beam-string

structure (BSS), cable-supported truss structure, cable-

supported barrel-vault structure, and the suspend-dome are

all types of cable-supported structure systems that are used

widely.

Zhao et al. [2] made an introduction to the structural

performance of BBS, and it is indicated that BBS can span

over longer distances and use less materials than the tra-

ditional structures (such as simple-beam, arch, or truss) due

to the action of struts and cables. The suspend-dome

structure is composed of an upper single-layer latticed-

shell, middle struts, and lower cables [3, 4]. The out-plane

stability of the single-layer latticed-shell structure is greatly

improved by appropriately adding members of vertical

struts, loops, and radial cables. The suspend-dome structure

uses rational mechanics and has an elegant configuration,

as such it is one of most popular structures used by engi-

neers and architects. Chen et al. [5–8] introduced struts and

cables to the cylindrical latticed-shell structure and then

proposed a new cable-supported structure, i.e., cable-

& Wentao Qiao

tottyer@126.com

1 School of Civil Engineering, Shi Jiazhuang Tiedao

University, Shijiazhuang 050043, China

2 Department of Architecture, MIT, Cambridge 02139, USA

3 School of Civil Engineering, Tianjin University,

Tianjin 300072, China

4 Department of Civil and Environmental Engineering, UAH,

Huntsville 35899, USA

5 School of Civil and Environmental Engineering, Nanyang

Technological University, Singapore 308232, Singapore

123

Trans. Tianjin Univ.

DOI 10.1007/s12209-017-0075-9

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supported barrel-vault structure. In this way, the horizontal

thrust at supports is reduced due to the action of struts and

strings, and the poor out-plane stability of the cylindrical

latticed-shell structure is improved. The highlight of the

cable-supported barrel-vault structure is that the horizontal

thrust of supports can be almost totally eliminated through

design optimization, which means that this kind of grid

vault can be better applied without considering giant-thrust

balancing elements.

Based on the concept of cable-supported structure sys-

tem [1], Chen and Qiao [9] proposed the CBS prototype,

which consisted of an upper reinforced concrete (RC) slab,

middle struts, and lower cables. The forces of cables act on

the slabs through struts, and the struts act as flexible sup-

ports for the slabs. When used as a floor or roof, CBS can

span long-distances due to this configuration, and the uti-

lization efficiency of the indoor space is improved. Qiao

and Chen [10] theoretically analyzed the static features of

the CBS, proposed a design method, and investigated

certain factors affecting the associated mechanical prop-

erties. The construction or shaping of cable-supported

structures is more complex than that of the traditional

structures because of the flexible elements involved. Nie

and Li [11] analyzed the static features of the one-way BSS

with the co-working of the supporting structure, and

simultaneously studied the influence of certain factors on

mechanical characteristics, including grouting, support

form, and corrosion. This research provided a valuable

reference for the construction of beam-string and similar

structures. With the mid-span vertical displacement as the

main control target for pre-stress stretching, the stretching

once in tension bed method was proposed for the lower

cable of the truss string structure, as it is an effective

construction method for truss and BSSs [12]. Wang et al.

[13] proposed the use of a temporary supporting frame,

segment lifting, and a method of high-altitude splicing

construction to construct the suspend-dome structure of

Chiping Gymnasium. In addition, Wang et al. [14] used a

series of internal force measures for the struts, cables, and

other key elements during the construction of a suspend-

dome structure, and the measured results were then used to

control the construction to make sure that the suspend-

dome was constructed as what was designed originally.

Guo et al. [15] introduced a detailed lifting installation of

the upper grid shell and installation and tensioning of the

lower pre-stressed cables, thereby inventing the strut-ad-

justment method and implementing it in the construction of

a long-span suspend-dome structure for the first time.

This study analyzes the construction of CBS to provide

more information about this process, so that it can be

practically applied to buildings in the future. In addition,

the existing construction methods for cable-supported

structures are analyzed and combined to determine a

feasible construction method for CBS based on deforma-

tion control, which also shows the mechanical features of

elements at each construction stage.

This study also uses a numerical simulation and exper-

imental work to study the basic fabrication and construc-

tion method for CBS based on deformation control. Results

show that the proposed construction method is feasible and

reasonable for CBS, which can provide both a theoretical

and practical foundation for applying the cable-supported

ribbed-beam composite-slab structure.

Fabrication and Construction Process

Figure 1 shows the basic method used to fabricate a stan-

dard CBS unit, which includes a upper RC slab, a ribbed

beam, steel struts, and lower cables. All elements are

prefabricated and assembled together on site. The con-

nection between the strut and beam includes two rotation

axes in different directions, and efficiently transmits the

cable force (shown in Fig. 2). Each of the cable’s ends is

fixed to the beam bottom, and Fig. 3 shows anchorage of

the cable end.

Three main CBS construction phases are identified as

follows. First, all key elements are prefabricated and then

assembled together on site; second, the concrete is cast

Fig. 1 Fabrication of unit

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among slabs and ribbed beams, which provides a firm

connection between the prefabricated elements; and finally,

the sliding support is set at one end of CBS, so that it can

slide in the direction of the horizontal span. For the sliding

bearing at the end of CBS, slotted bolt holes connected

with bolts are set in the girder; the CBS sliding end is thus

restrained in a vertical direction, but is free to move in a

horizontal direction. This configuration enables the cable

force to act efficiently on the slabs, and enables the release

of horizontal force. As shown in Fig. 1, an integrated

structure is formed when the prefabricated elements are

assembled together, i.e., one standard CBS unit. The slab is

connected with the ribbed beam via four angle steel ele-

ments, which efficiently deals with the shear forces existing

between the slabs and ribbed beams.

The key steps of CBS construction are as follows.

Step 1. Standard span construction of CBS. Supported by

a temporary scaffold, the prefabricated ribbed-

beam elements are assembled. When one span of

CBS has been constructed, the scaffold is then

moved to the next span. As indicated by the red

circles in Fig. 4, steel-bar cages are constructed

among the prefabricated ribbed-beam elements.

Step 2. The concrete is cast into the steel-bar cages, and

the prefabricated ribbed beams are connected

firmly together. The struts and cables under upper

beams are constructed, the cables are pre-

stressed, and finally, a complete self-balancing

structure system is formed. Steps 1 and 2 are

shown in Fig. 4.

Step 3. As shown in Fig. 5, the slabs are paved on the top

of beams, and the angle steel elements are

inserted into the holes in the slabs. After casting

concrete into the holes and belts among the slabs,

one complete span of CBS is constructed; this

process is then repeated for all subsequent spans.

Step 4. After the construction is completed, the tempo-

rary scaffold is moved and the floor becomes anFig. 2 Strut junction

Fig. 3 Anchorage of cable end Fig. 4 Steps 1 and 2 of the CBS construction

Fabrication and Construction of Cable-Supported Ribbed-Beam Composite-Slab Structure

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integrated and stable structural system. Figure 6

shows the final rendering of CBS, which has a

large interior space and highly efficient mechan-

ical properties.

Theoretical Analysis

The construction process introduced above is then stimu-

lated using the FEM software. The displacements of key

positions and cable forces are determined for each step and

these data are then used to guide and control the actual

construction of a CBS. In this paper, the gymnasium of

Hebei Normal University is taken as a prototype. The

second floor of this new gymnasium is a BSS, which is

similar to CBS as they share mechanics features and adopt

a similar construction process.

Model Parameters

To re-design the building, CBS was applied here instead of

a BSS. Each span had a length of 42.25 m, and the re-

designed gym included 13 standard spans. For the conve-

nience of manufacturing, transportation, and assembling,

4 9 4 m standard elements were designed and manufac-

tured in a factory. For a better integration, parts of the

connecting beam (shown in Fig. 7 by the dashed-line) were

cast on site so that the best structural integration can be

achieved when the prefabricated elements were connected.

A standard span was composed of ten standard units, as

shown in Fig. 1. Figure 7 shows the key dimensions of the

model. A V-type strut with a circular steel tube section

measuring 159 9 10 mm (external diameter 9 thickness)

was adopted, as shown in the cross section 2-2. A steel

strand with a diameter of 80 mm was used for the cable.

FEM Model

The FEM model is created using the FEM software (Midas/

Gen), which provides a rich library of elements. A plate

element is used to simulate the RC slab, and the ribbed

beam and strut are simulated by beam elements, but the in-

plane rotation constraint of the beam element is released

when analyzing the strut. A tension-only cable element is

adopted to stimulate the lower cables of CBS. Note that

rigid coupling is employed between the slab and ribbed

beam to enable consistent co-working and deformation.

Furthermore, the boundary condition of the FEM model is

set strictly according to the physical situation; therefore, all

degrees of freedom are fixed at one end and only vertical

degrees of freedom are fixed at the other end. Figure 8

shows the FEM model in Midas/Gen.

Cable Tension

Rational pre-stress implemented in the cables is the most

important factor guaranteeing the adequate load-bearing

capacity of CBS, and can be rationally determined using

the static equilibrium algorithm. In Step 2 of construction,

cable pre-stress is implemented after all ribbed beams have

been constructed and connected. Considering the charac-

teristics of the cable tension joint shown in Fig. 3, a

specific apparatus (based on hydraulic jacks and the prin-

ciple of action and reaction force) is designed and used for

tightening the pre-stressed cable. As shown in Fig. 9, the

jacks lift the reaction force apparatus and the force acts on

the hot-casting socket as a reaction to the force apparatus.

The screw can then be easily tightened by workers, and the

cable is thus tensioned to the designed force step by step.

The CBS deforms upwards, while pre-stress is applied;

usually, the maximum upward deformation of CBS is

Fig. 5 Step 3 of CBS construction

Fig. 6 Step 4 of CBS construction. a Exterior view. b Interior view

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limited to less than 1/600 of the span [1, 9], and in this

study, a value of approximately 70 mm is chosen as the

control goal to calculate the cable pre-stress by the static

equilibrium algorithm [9]. As each span is constructed

individually, one standard span is chosen as the calculation

model. To ensure that forces are transmitted and distributed

as evenly as possible, cable pre-stress is divided into four

grades for practical applications. The final tension control

values of the cable are listed in Table 1.

Deformation

Analysis of Step 2

The mechanical features of CBS are analyzed using the

FEM software (Midas/Gen). In Step 2, the rib beams are

assembled and connected, and pre-stress is then applied.

The vertical deformations at the position of 1/4 span and

mid-span are collected under the action of each grade

tension, as shown in Fig. 10.

Unit(mm)

bila

tera

l sym

met

ry

cable

strut

Floor plan

Cross section 2-2

Cross section 1-1

Fig. 7 Drawing of model’s key size

Fig. 8 FEM model of CBS

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Pre-stress is applied to the cable from its two ends and

the forces are transferred from the ends to the middle;

however, because of the sag of the cable, the force is

reduced when arriving in the middle, particularly under

low-level pre-stress. As a consequence, it is clear from

Fig. 10 that the vertical displacement of 1/4 span is sig-

nificantly larger than that of mid-span under Grade 1 ten-

sion, but they become the same as the tension augments.

Under the action of the first three grades of tension, the

vertical displacement of 1/4 span alters in an even linear

proportion, but increases from Grade 3 to 4; this is because

CBS is a long-span structure with low rigidity, and it

behaves nonlinearly to a certain extent. This nonlinear

characteristic is also observed in the relationship between

tension grade and the vertical displacement of the mid-

span. The final vertical displacements of 1/4 span and mid-

span are 67.6 and 63.8 mm, respectively, both of which are

close to the control goal of 70 mm.

Figure 11 shows the horizontal displacement of the

support at the end of CBS. The tension alters evenly as it

augments, but the maximum value is only 7.6 mm. For the

boundary condition of CBS, the sliding bearing and fixed

support are adopted, respectively, at the two ends. Hori-

zontal displacement appears at the sliding bearing, which

causes the CBS to become a self-balancing pre-stressed

structure without thrust occurring at the supports. The final

deformation of CBS occurs after Step 2 of the construction

has been completed, as shown in Fig. 12, where the dashed

line represents the CBS in a horizontal zero state. All

deformation discussed in this paper occurs with respect to

this zero state. When the CBS deforms up to this zero state,

it is marked as positive; contrarily, it is marked as negative.

Analysis of Step 3

In Step 3, the prefab concrete slabs are paved on the top of

ribbed beams and the post-poured belts and holes are cast

on site; the construction phase is thus completed. Similar to

Step 2, vertical displacement is recorded at the positions of

1/4 span and mid-span, and the horizontal displacement of

the sliding support is also recorded. Under the dead load of

the slabs, the CBS in a Step 3 equilibrium state deforms

downwards. The final deformation of CBS is shown in

Fig. 13; the vertical displacements of 1/4 span and mid-

Cable

Hydraulic jack

Hot-casting socket

Reaction force apparatus

Screw

Fig. 9 Cable-tensioning joint

and apparatus

Table 1 Tension for each grade

Grade Ratio (%) Tension (kN)

1 65 1200

2 80 1500

3 90 1700

4 100 1900

Fig. 10 Maximum vertical displacement at each tension grade

Fig. 11 Horizontal displacement at each tension grade

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span are 21.2 and 15.4 mm, respectively, and the hori-

zontal displacement of the sliding support is 4.1 mm. In

addition, the internal force of the cable increases due to the

action of the dead load of concrete slabs; the calculated

value is 2533 kN, which is 633 kN larger than the tension

of 1900 kN recorded in Step 2.

Cracks

The RC rib beams deform upwards with the tensioning of

pre-stressed cable (maximum vertical deformation of

67.6 mm) and cracks appear on the top of RC rib beams.

The structure deforms downwards when paving the prefab

RC slabs on the top of RC rib beams, and as a result, the

vertical deformation decreases; when paving is finished,

the maximum deformation is reduced to 21.2 mm, as

shown in Figs. 12 and 13. In comparison with the size of a

40-m span, a deformation of 21.2 mm is small; most cracks

will close and only a few tiny cracks will ultimately

remain. Furthermore, the structure will be operational for a

long-time with small amounts of downward deformation

under the action of normal service loads (based on the zero

state, i.e., dashed lines shown in Figs. 12 and 13, and only

a few tiny cracks will appear on the bottom of RC rib

beams.

Experimental Study

Scaled Physical Model

A 1:5 scaled model was designed and fabricated to verify

the results of the theoretical analysis model reported in the

last section. The scale factors were calculated according to

the similarity constant and similarity ratio relationship

[16]. The physical model and its construction processes are

shown in Fig. 14.

Tension and Displacement

For cable tension, the ratio of the scaled model to the full-

scale model was 1:25, and it was 1:5 for structural

Sliding hinge support

Fixed support

Prestressimplementation

Prestressimplementation

1/4 spanMid-span

1/4 spa n Rib beam

Fig. 12 Final deformation occurring in Step 2

Sliding hinge support

Fixed support1/4 spanMid-span1/4 span Concrete slab

Fig. 13 Final deformation in Step 3

Fig. 14 Scaled physical model

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displacement. The cable tension and corresponding dis-

placement of key positions in each tension grade in Steps 2

and 3 can be calculated, as listed in Table 2. In the test,

tension in Table 2 was applied to the cable grade-by-grade,

and displacements were recorded after each grade tension

had been reached. Values were then compared with the

corresponding theoretical predictions in Table 2. It is of

note that construction errors, external environment inter-

ference, and other small errors existed in the experimental

data due to friction. However, it is necessary to point out

that the key objective of constructing CBS is to control

deformation, in terms of the displacement at certain posi-

tions. As a consequence, the displacement at each grade

was closely monitored with respect to the values in Table 2

as far as possible. If the practical tension applied to the

cable deviated considerably from the corresponding tensile

force control value in Table 2, and the displacements

recorded were still not close to the control values in

Table 2, it is evident that an error had occurred in the

construction process and tensioning was thus stopped for

troubleshooting.

Data Measurement

Cable forces in the experiment were measured using an

INV3080B-BCF cable force tester, as shown in the bottom-

right photo of Fig. 15. Structural displacement was mea-

sured by a dial indicator on each standard span of the CBS;

four indicators were, respectively, mounted at two 1/4 span

points, one mid-span point, and at the sliding hinge sup-

port, as shown on the left and in the top-right photo of

Fig. 15, respectively.

Analysis of Experimental Results

The physical model test was conducted according to the

test scheme presented above and data were surveyed and

recorded. After a comparison with theoretical data, results

are listed in Tables 3, 4, 5, and 6. Note that

error = (practical value - theoretical value)/theoretical

value.

As mentioned above, structural deformation needs to be

controlled. so that it is as close to the theoretical value as

possible during cable tensioning. In the experiment, the

most ideal structural deformation obtained is shown in

Tables 4, 5, and 6. Theoretical and practical values are

close in each grade, particularly in the final grade, and all

errors are less than 4.0%. The theoretical value is imple-

mented on the cable in each grade during tensioning and

displacements; during this process, the cable force is finely

adjusted, so that the practical deformation can be con-

trolled to be as close to the theoretical value as possible.

However, it is evident from Table 3 that the practical

tensile force applied is larger than the theoretical value

when practical deformation is controlled in an ideal state;

the error in some grades is 19.6%, but this decreases to

Table 2 Control data in experiment

Grade Ratio (%) Tension (kN) Vertical displacement Horizontal displacement (mm)

1/4 span (mm) Mid-span (mm)

1 65 48 1.96 0.84 0.56

2 80 60 3.3 1.1 0.78

3 90 68 5.08 3.96 1.04

Step 2 4 100 76 13.52 12.76 1.52

Step 3 – – 101.32 4.24 3.08 0.82

Fig. 15 Distribution of dial indicators and cable force testing

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6.8% in the final grade. In Step 3, when the prefabricated

concrete slabs are paved and construction is completed, the

practical internal force of the cable is 111.05 kN, which is

larger than the theoretical value (error of 9.6%). The

practical vertical displacements on the left 1/4 span, right

1/4 span, and mid-span are 3.9, 3.81, and 2.68 mm,

respectively, which are all smaller than the theoretical

values and with errors of 8, 10.2, and 13.1%, respectively.

The practical horizontal displacement is 0.77 mm, which is

also smaller than the theoretical value (error of 6.1%).

Internal Cable Force

In each standard span of the CBS, one cable was divided

into several parts by struts; the internal forces in these parts

are not completely equal because of cable sag and the

different angles between cables and struts. The cable is

tensioned by applying pre-stress to the two end-parts of the

cable (Fig. 16 shows numbering of each part of the cable).

The internal cable force of each part of the constructed

CBS is surveyed and compared with the corresponding

theoretical values. The results in the last section indicate

that the practical construction conducted here is normal and

consistent with theoretical analysis.

In this section, we only discuss cable forces for the final

construction occurring in Step 3; comparison data are

shown in Fig. 17.

It can be seen from Fig. 17 that the in relation to the

symmetry of the structure, internal forces are basically

distributed symmetrically. The distribution pattern of the

Table 3 Differences in tension

between theoretical and

experimental values

Grade Ratio (%) Theoretical tension (kN) Practical tension (kN) Error (%)

1 65 48 57.41 19.6

2 80 60 67.08 11.8

3 90 68 74.46 9.5

Step 2 4 100 76 81.17 6.8

Step 3 – – 101.32 111.05 9.6

Table 4 Differences in 1/4 span vertical displacement between theoretical and experimental values

Grade Theoretical displacement (mm) Left 1/4 span Right 1/4 span

Practical displacement (mm) Error (%) Practical displacement (mm) Error (%)

1 1.96 2.00 2.0 2.03 3.6

2 3.30 3.11 -6.1 2.98 -9.6

3 5.08 5.21 2.4 5.24 3.1

Step 2 4 13.52 13.80 2.1 13.97 3.3

Step 3 – 4.24 3.90 -8.00 3.81 -10.2

Table 5 Differences in mid-

span vertical displacement

between theoretical and

experimental values

Grade Theoretical displacement (mm) Practical displacement (mm) Error (%)

1 0.84 0.80 -4.8

2 1.1 1.0 -9.1

3 3.96 4.06 2.5

Step 2 4 12.76 13.26 3.9

Step 3 – 3.08 2.68 -13.1

Table 6 Differences in

horizontal displacement

between theoretical and

experimental values

Grade Theoretical displacement (mm) Practical displacement (mm) Error (%)

1 0.56 0.59 5.4

2 0.78 0.75 -3.8

3 1.04 1.1 5.8

Step 2 4 1.52 1.58 3.9

Step 3 – 0.82 0.77 -6.1

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actual cable force of each part is mostly consistent with the

theoretical value; the force decreases from the two ends to

the middle.

However, friction, construction errors, data measure-

ment errors, and other external environment interferences

all cause errors between theoretical and practical values.

For example, the friction in the physical model mainly

appears at the cable-strut joints, which causes uneven

transmission of the cable force, whereas in the FEM model,

the joints are smooth and there is no friction. In addition,

the imperfections in the physical model due to construction

errors cause additional moment, which does not exist in the

FEM model. Furthermore, the effect of temperature is not

considered in the computational simulation, and although

the action of environmental temperature is small, it exists

during the physical model test. In this experiment, the

average error was about 7.6%. The maximum error

occurred at the end part of the cable; the practical value

was 111.05 kN, which was 9.37 kN larger than the theo-

retical value (error of 9.6%).

Conclusions

Based on existing research on cable-supported structures,

this study proposes a standard fabrication and construction

process for CBS using a construction method based on

deformation control. The rationality and feasibility of this

method are verified by a theoretical analysis and a test

study with a scaled physical model.

Acknowledgements Supported by the National Natural Science

Foundation of China (No. 51208317), Natural Science Foundation of

Hebei Province (No. E2016210052) and funded by Large Infras-

tructure Disaster Prevention and Mitigation Collaborative Innovation

Center of Hebei Province, China.

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1Left end part Right end part2 3 4

1'2'3'4'Middle part

Strut

Rib beam

Cable

Fig. 16 Numbering of cable parts

Fig. 17 Differences in cable force within each part between theoret-

ical and practical values

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