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
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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