SEISMIC ANALYSIS OF RC FRAMED STRUCTURES
RETROFITTED WITH STEEL BRACES
Ciro FAELLA
Full Professor
University of Salerno
Via Ponte don Melillo, 84084 Fisciano (SA), Italy
[email protected]
Carmine LIMA
Research Assistant
University of Salerno
Via Ponte don Melillo, 84084 Fisciano (SA), Italy
[email protected]
Enzo MARTINELLI
Assistant Professor
University of Salerno
Via Ponte don Melillo, 84084 Fisciano (SA), Italy
[email protected]
Roberto REALFONZO
Associate Professor
University of Salerno
Via Ponte don Melillo, 84084 Fisciano (SA), Italy
[email protected]*
Abstract
Existing Reinforced Concrete (RC) structures designed for gravitational loads only are
generally vulnerable to seismic events. They do not generally comply with the more advanced
seismic safety standards and are often in need for retrofitting. The introduction of diagonal
steel bracings is among the most common technical solution for improving seismic
performance of existing RC structures. Nevertheless, several issues dealing with both analysis
and design of RC frames strengthened by steel bracings under seismic action are still open.
This paper presents the numerical simulation of existing RC frames retrofitted by using steel
bracing with different arrangement and distribution throughout the structure. The nonlinear
analyses performed in OpenSEES by using the model generated by CDSwin focuses on RC
structures retrofitted with concentric X-braces which are often employed for seismic
strengthening of existing structures. After a short overview of the most recent contributions
on the above mentioned aspect, the paper outlines the numerical models employed for
simulating the behaviour of both RC frames and steel bracings. Then, the results of seismic
nonlinear analyses are carried out for demonstrating the facility and effectiveness of the two
software in modelling and simulating nonlinear behaviour of diagonal steel braces. Moreover,
the effect of bracing patterns is investigated and the most effective one in the case of a
relevant case-study is pointed out.
Keywords: Existing RC frames, steel bracings, earthquake, retrofitting, structural scheme
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1. Introduction
Existing Reinforced Concrete (RC) structures built during the last decades in seismic regions
(such as a wide part of Italy and the Mediterranean area) do not generally comply with the
more advanced seismic codes currently adopted in the same regions [1][2] and are often in
need for retrofitting. Several seismic retrofitting techniques are currently available and
employed in practical applications, even though issues are still open (or not completely solved
by the same codes) about the rational design of these retrofitting interventions. A thorough
State-of-the-Art Report collecting the most well-established techniques for seismic retrofitting
of RC structure is available in [3]. In particular, several “member-level techniques” (basically
aimed at enhancing the capacity in terms of strength and/or ductility of single elements of the
existing structures) are described and functionally distinguished by the so-called “structurelevel techniques”. The latter ones mainly aim at reducing the demand on the existing structure
by introducing further elements (i.e., RC shear walls) or substructures (e.g., steel bracings)
able to resist the seismic excitation. A rational strategy for a possible synergic application of
both techniques has been also conceived and presented in the scientific literature [4]. Bracing
systems are widely utilised in steel buildings and several models are currently available for
describing their response under the cyclic actions induced by seismic excitation [5].
Moreover, using steel bracing systems in seismic retrofitting of existing RC structures is
actually an attractive technique, as it is characterized by high architectural and functional
compatibility with respect to the original purposes of the existing structure. This is the key
motivation for a series of recent studies aimed at investigating the possible strengthening of
RC frames by means of dissipative steel bracings [6][7]. As a matter of principle, the design
of steel bracing in RC frames can be approached according to the well-established “capacity
design” philosophy. Moreover, the key aspect of connection overstrength needs to be
completely revisited in the case of steel braces connected to RC joints [8]. Another issue of
concern deals with the distribution of steel braces throughout the existing RC frame and the
definition of rational structural schemes for bracing systems to be employed in seismic
retrofitting. Few recent studies actually addressed this topic by either proposing experimental
and numerical results on steel frame with different braces configurations [9], or examining
different bracing patterns for a given RC structures considered as a case-study [10], or
approaching the problem of defining an optimal bracing configuration [11].
The present paper is also intended at investigating the effect of different bracing
configurations on the seismic response of retrofitted RC frames. In particular, the study
focuses on concentric X-braces which are often employed for seismic strengthening of RC
existing structures. Thus, Section 2 presents an existing RC frame which is considered as a
case-study. Moreover, the same section reports the key steps in the design procedure of steel
braces intended for retrofitting and the various possible bracing configurations considered in
this study. Finally, Section 3 outlines the key aspects of numerical models employed for
simulating the behaviour of both RC frames and steel bracings and summarizes the results of
the seismic analyses carried out on those retrofitted structures pointing out the influence of the
bracing configuration on the seismic demand of the existing concrete members. Moreover,
insights about the action values at the foundation level are also considered and the main
favourable and unfavourable aspects of the various possible configurations are pointed out.
2. Presentation of the case-study
This paper addresses a critical issue in designing steel bracings for seismic retrofitting of
existing buildings: it investigates the influence of brace distribution throughout the existing
frame. A 4-storey school building lying in the neighbourhood of L’Aquila is examined as a
case-study (Figure 1 shows its floor plan and the 3D model developed in CDSwin [1]).
150
x
350
350
35x50
35x50
350
350
35x50
35x50
350
350
35x50
35x50
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350
35x50
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45x24
35x50
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45x24
35x50
45x24
35x50
45x24
35x50
35x50
350
350
35x50
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35x50
35x50
45x24
35x50
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35x50
35x50
35x50
35x50
35x50
y
35x50
35x50
35x50
35x50
345
1035
345
345
35x50
35x50
3500
Figure 1. Typical floor plan with braced frames
A nominal life of 50 years and functional type III (Cu = 1.5) have been assumed according to
NTC 2008 [13]. Moreover a site class C and the topographic category T1 have been also
considered for defining the design spectra for the four relevant Limit States (Table 1).
Table 1: Parameters of the seismic design spectra
Spectral dates
PVr
TR [years]
ag [m/s2]
ag/g
F0
TC* [s]
CC
SS
S
TB [s]
TC [s]
TD [s]
2.1
Limit States of Service
SLO
SLD
81%
63%
45
75
0.908
1.155
0.093
0.118
2.347
2.317
0.277
0.291
1.60
1.58
1.50
1.50
1.50
1.50
0.148
0.153
0.444
0.459
1.970
2.071
Ultimate Limit States
SLV
SLC
10%
5%
712
1462
2.792
3.574
0.285
0.364
2.385
2.419
0.351
0.365
1.48
1.46
1.29
1.17
1.29
1.17
0.174
0.178
0.521
0.534
2.739
3.058
Design of a steel bracing sub-structure
The steel bracings have been designed for retrofitting the structure under consideration by
performing a static linear analysis [13]. Table 2 reports the values of masses and horizontal
static forces used in designing steel bracings according to NTC 2008 [13] and using a force
reduction factor q=4.
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Table 2: Masses and forces used in design steel bracings
Floor
4
3
2
1
Masses [ton]
239.40
388.43
385.84
371.74
1385.41
h [m]
3.80
3.80
3.30
3.00
H [m]
13.90
10.10
6.30
3.00
Forces [kN]
936.60
1104.21
684.17
313.89
T = 0.36 s
Sd (T) = 2.15 m/s2
Fh = 3038.88 kN
Table 3 summarises relevant data about steel diagonals in the bracing substructure.
Table 3: Relevant data about the steel bracings
Floor
4
3
2
1
2.2
Forces [kN]
304.40
358.87
222.36
102.01
Bracings in tension [kN]
409.55
934.85
1160.06
1293.17
Section
HEA100
HEB140
HEB160
HEB180
Overstrength
1.36
1.20
1.22
1.32
Alternative distributions of the steel braces within the existing RC frame
Three alternative patterns have been considered even though the number of diagonals placed
on each level has been kept constant. The sections designed and reported in table 3 have been
introduced in the models developed by using CDSwin [1] at each floor by considering the
distributions reported in Figure 2.
Façade X
Façade Y
Bracing distribution
Pattern 1
Pattern 2
Pattern 3
Figure 2: Distributions of steel bracings on the two facades
The following analyses are intended at investigating the seismic response of the structures
retrofitted by means of the bracings distributed according three different patterns depicted in
Fig 1. Particularly, their influence on relevant response parameters, such as displacement
demand, foundation actions and the internal forces distribution, is particularly addressed.
3. Numerical analysis
Nonlinear Time History (NLTH) analyses have been carried out on the 3D structural model
by using the “OpenSees” computer program [14]. Indeed, a tcl input file has been generated
by CDSwin [1] and then it has been processed in OpenSEES [14]. Non-linear behaviour of
RC beams and columns has been simulated through a lumped plasticity model by introducing
plastic hinges at both ends of each element (in particular the beamWithHinges element has
been adopted by using the OpenSEES default library introducing Concrete01 and Steel01
materials for concrete and steel, respectively [14]). Moreover, the buckling effect has been
considered in modelling steel bracings [15]: in particular, the non-linear behaviour has been
implemented through truss elements by using the Uniaxial Hysteretic Material currently
available in OpenSees [14]; a threshold for the axial action, both in tension and compression,
has been evaluated according to NTC 2008 provisions [13]. Pinching factors equal 0.8 and 0.2
have been used for simulating the reduction in terms of deformation and force capacity,
respectively.
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1.00
1 400
0.80
1 200
0.60
1 000
0.40
800
Axial Force [kN]
stress / force
Figure 3 shows on the left the general behaviour of the elements employed in OpenSees [14]
for simulating the cyclic response of dissipative elements taking into account the pinching
effect. This general relationship has been specialized for the steel braces under consideration
and their cyclic response is represented by the graph on the right of Figure 3. A clearly
unsymmetrical behaviour can be observed therein as a result of the reduced strength in
compression.
0.20
0.00
-0.20
-0.40
600
400
200
-0.60
0
-0.80
-200
-1.00
-0.010
-0.005
0.000
0.005
0.010
-400
-0.40%
-0.20%
0.00%
0.20%
0.40%
0.60%
0.80%
Drift
strain / displacement
Figure 3: Hysteretic behaviour of steel bracings:
OpenSees hysteretic model (on the left), bracing response (on the right).
Nonlinear Time History analyses have been performed for the four Limit States (SLO, SLD,
SLV and SLC) defined by NTC 2008 [13]. Consequently, four sets of 7 accelerograms
matching with the design spectra defined in table 1 have been selected by using Rexel
v.3.2beta [16] for each Limit State and for the two main directions in plan. Thus, a total
number of 56 accelerograms has been used for performing 14 analyses for each Limit States:
7 of those in X-direction with a 30% of the action in Y-direction and 7 analyses in Y-direction
with a 30% of the seismic action in the X-direction. According to NTC 2008 [13] the demand
in terms of forces and/or displacements for each limit state and direction has been evaluated
as mean of the response evaluated through the 7 dynamic nonlinear analyses.
3.1
Results in terms of displacement demand on the retrofitted structures
Figure 4 outlines the displacement demand evaluated on the existing structure and the
structures retrofitted with the three analysed patterns. It shows that the displacement demand
on the existing members is evaluated for the retrofitted structures (regardless the particular
pattern adopted for the bracing system) is much lower than the corresponding values obtained
of the existing one.
Existing
Pattern 1
Pattern 2
Pattern 3
0.20
0.18
0.16
top [m]
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
SLO
SLD
SLV
SLC
Direction X
SLO
SLD
SLV
Direction Y
Figure 4: Displacement demand.
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SLC
Moreover, among the various retrofitted structures, the one adopting bracing pattern n.3
(Figure 2) results in the lower values of displacement demand. The better performance of the
same structure is also confirmed by the analysis in terms of the interstorey drifts (Figure 5)
Pattern 2
Pattern 1
Existing
Pattern 3
4
3
3
Floor
Floor
Pattern 3
4
2
1
Pattern 2
Pattern 1
Existing
2
1
SLC
SLV
SLD
SLO
0
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
0
0.00%
1.40%
0.50%
Interstory drift - Direction X
Pattern 2
Pattern 1
Existing
Pattern 3
4
4
3
3
Floor
Floor
Pattern 3
1.00%
1.50%
2.00%
Interstory drift - Direction X
2
1
Pattern 2
Pattern 1
Existing
2
1
SLD
SLO
0
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
SLC
SLV
0
0.00%
1.40%
0.50%
Interstory drift - Direction Y
1.00%
1.50%
2.00%
Interstory drift - Direction Y
Figure 5: Interstorey drifts.
3.2
Actions at the foundation level due to the various bracings patterns
Figure 6 shows the value of the axial forces in the columns at the first floor of the building.
They have been evaluated at the Limit State of Life Safety for each of the three different
patterns in Figure 2. The results are reported in terms of ratio between the axial force NSd in
the braced structures and the corresponding values NSd,existing evaluated for the unstrengthened
existing one. Those data are of interest for investigating the different demand induced by the
seismic action on the foundation. Thus, the best behaviour observed in case of “pattern 3” is
confirmed by the values of the ratios NSd/NSd,existing which are lower than the ones evaluated
for the first and the second bracing patterns. Obviously, the axial forces determined for the
braced structures are greater than the ones evaluated for the existing structure (and the ratio
on the y-axes of Figure 6 are often greater than the unit) because retrofitting leads to a
significantly higher lateral strength of the structure. Further results in terms of actions at the
foundation level for other Limit States and in direction Y are omitted for sake of brevity.
Pattern 1
Pattern 2
Pattern 1
Pattern 3
Pattern 3
Direction Y - SLV
Direction X - SLV
3.00
NSd / NSd,existing
NSd / NSd,existing
Pattern 2
4.00
4.00
2.00
3.00
2.00
1.00
1.00
0.00
0.00
0
5
10
15
20
25
0
30
5
10
15
20
25
30
Base Joints
Base Joints
Figure 6: Axial actions at the foundation level: X-direction (on the left) and Y-direction (on the right).
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3.3
Results in terms of actions of the RC frames and steel bracings
The four diagrams reported in Figure 7 show the actions (NSd, VSd, Mx,Sd, My,Sd) in beams and
columns for the retrofitted structures adopting the three distributions of bracing. In particular,
the retrofitted-to-existing ratio in terms of actions on the various members is reported on the
y-axis. Since the curve which refers to the retrofitted solution adopting pattern 3 for the
bracing distribution is always below of the other two curves, this diagrams demonstrate once
again (and under another standpoint) the superior performance of pattern 3 solution with
respect to the other considered ones.
Pattern 1
Pattern 2
Pattern 3
Pattern 1
4.00
Pattern 3
Direction X - SLV
3.00
VySd / VySd,existing
NSd / NSd,existing
Direction X - SLV
2.00
1.00
3.00
2.00
1.00
0.00
0.00
0
50
100
Pattern 1
150
Frame
200
250
Pattern 2
300
0
50
100
Pattern 1
Pattern 3
150
Frame
200
250
Pattern 2
300
Pattern 3
4.00
4.00
Direction X - SLV
Direction X - SLV
3.00
MySd / MySd,existing
MxSd / MxSd,existing
Pattern 2
4.00
2.00
3.00
2.00
1.00
1.00
0.00
0.00
0
50
100
150
Frame
200
250
0
300
50
100
150
Frame
200
250
300
Figure 7: Actions in frames: axial force (on the top-left), shear (on the top-right), bending-x moment (on
the bottom-left) and bending-y moment (on the bottom-right).
4. Conclusions
In this paper the effects of alternative bracing configurations on the seismic response of
retrofitted RC frames have been investigated. As a result the distribution of steel bracings in
RC frames significantly affects the results in terms of optimizations of actions in RC frames
and at the foundation level. In particular from a general point of view the three analysed
patterns are characterized by increasing levels of distribution of steel bracing on RC frames.
The third configuration generally leads to a superior performance under the various
standpoints emphasized in section 3. In particular, the following aspects can be pointed out:
- the lateral stiffness of the structure retrofitted by adopting the above mentioned pattern
3 is significantly higher than those obtained in the other cases: this effects is of key
importance especially for the Limit State of SLO and SLD;
- the axial stresses in beam-columns determined on pattern 3 retrofitted frame are
generally lower than those induced on the same elements in the other retrofitted
solution; this effect is also beneficial for foundation elements;
- as a general trend, patterns 3 leads to the lowest values of stresses (in terms of axial,
shear and bending stresses) in RC structures.
As a concluding remark, the influence of the bracing configuration on the response of
retrofitted RC frames is not negligible, as it controls the actual lateral stiffness of the
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retrofitted structure. Although formulating general rules for a rational design of those steel
bracings is not an easy task, the implications in terms of flexural and shear stiffening induced
by the alternative configurations of braces should be carefully considered.
5. Acknowledgements
The Authors gratefully acknowledge “S.T.S. Software Tecnico Scientifico s.r.l.” for
providing CDSwin computer software.
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