Development of diagonal strut width formula for infill wall with reinforced opening in modeling seismic behavior of RC infilled frame structures

Development of diagonal strut width formula
for infill wall with reinforced opening in
modeling seismic behavior of RC infilled
frame structures
Cite as: AIP Conference Proceedings 1977, 020062 (2018); https://doi.org/10.1063/1.5042918
Published Online: 26 June 2018
Ida Ayu Made Budiwati, and Made Sukrawa
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AIP Conference Proceedings 1977, 020062 (2018); https://doi.org/10.1063/1.5042918
© 2018 Author(s).
1977, 020062
Development of Diagonal Strut Width Formula for Infill
Wall with Reinforced Opening in Modeling Seismic
Behavior of RC Infilled Frame Structures
Ida Ayu Made Budiwati1, a) and Made Sukrawa1
1
Department of Civil Engineering, Faculty of Engineering, University of Udayana, Kampus Bukit Jimbaran Bali,
Indonesia
a)
Corresponding author: [email protected]
Abstract. The numerical study was conducted to determine equation of diagonal strut width to model infilled reinforced
concrete (RC) frame structures with reinforced opening. The equation is necessary because, despite the opening, infill
masonry wall in RC frame is capable of strengthening existing structures. Validation models of diagonal strut (ST) and
shell elements (SH) were first made in SAP2000 to mimic the behavior of tested infilled frame RC structures with
opening reported by others. The valid models were then used to predict the equivalent width of diagonal strut for the
infill wall with opening percentage of 10, 20, 30, 40, 50 and 60%. The fitted data were then plotted and simple regression
analysis was used to obtain equation that correlate between the opening percentage (r) and the stiffness reduction
coefficient (c) associated with the wall opening. The proposed equation was then applied to model 2-6 storey infilled
frames together with the shell element models for the wall opening ratios of 10, 20, 30, 40, 50 and 60%. It was revealed
that the ST and SH models can mimic the true behavior of tested infilled RC frame with reinforced opening up to the
maximum load. The equivalent strut width formula is then proposed in the form of wds = (d/4).c and c = (1.0565r2 2.281r + 1.3764). The d is diagonal length of the strut. Interestingly enough, the model with door opening is stronger than
the model with window opening of equal opening ratio. More interestingly, the model with door opening is stronger than
the model with solid infill due to the contribution of lintels to stiffen the structure. The data obtained from these models
suggest that despite the opening, the infill wall should be considered in modeling the structure to have more accurate
response.
INTRODUCTION
Infilled frame is a structure consisting of columns and beams made of reinforced concrete or steel with an infill
wall inside of it [1]. The composite action between the brittle wall and the more ductile frames make this type of
structure very stiff and strong to resist seismic lateral load [2]. Often time, however, the existence of infill wall is not
included in modeling the frame structure. Moreover, if there are opening in the wall, then the contribution of infill
wall is thought to be trivial and therefore, can be ignored. This ignorance may negatively affect the performance of a
structure such as development of soft story caused by increased stiffness of stories where the infill walls are present.
The phenomenon has made the topic more interesting to many researchers to develop methods of modeling infilled
frame structure with wall opening [2, 3, 4, 5].
Part of this paper was published as final project report of undergraduate student at Civil Engineering Department
of Udayana University under supervision of the authors.
There are two common methods of modeling infilled frame structures, they are diagonal strut and shell element
methods. The first method is very popular and widely accepted among structural engineers as it can explain its
behavior under lateral load graphically. The second method is rarely used for modeling infilled frame structures.
However, the shell element model has many advantages over diagonal strut model. With shell element, the stress
distribution on the wall can be directly obtained. Interaction between the frame and the wall at the interface can also
be included in the shell element model. It can also model the opening in the wall easily to obtain a model as real as
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020062-1
possible. However, the response of shell element model is not always similar to that of the real structures.
Accordingly, it is necessary to compare it to the diagonal strut model that already gain its popularity as the method is
recommended by FEMA [6].
Strut width equation for wall with opening has been proposed by Asteris [3] for unreinforced opening (without
lintel around the opening). In practice, however, wall opening is often time reinforced with RC lintels to prevent
premature damage of wall due to concentrated stresses at the corners of opening [5, 7]. The equation of strut width
for wall with reinforced opening, however, is not yet clearly determined. In this study, effort has been made to
develop equation of strut width for infill wall with reinforced opening, by comparing the response of tested infilled
frame with the response of models using strut diagonal and shell element. The formula is then applied to 2-6 storey
infilled frames with varying percentage of wall opening.
INFILLED FRAME WITH OPENING
Diagonal Strut Model
To model infill frame structures subjected to lateral forces, diagonal struts can be used in which the
elements can only receive the compressive force and are free to rotate. The effective width of diagonal strut is
necessary. There are some provisions to account the structural rigidity of the infill frame structure when modeled as
diagonal strut. Many equations have been proposed to calculate the width of diagonal strut for solid infill wall
structures (equation 1 – 3). Other formulae also proposed by other researchers such as Smith and Carter, Mainstone,
Liaw and Kwan and many others as reported in Asteris [3]. However, the formulae are similar and not discussed
here [8].
wds
wds
d
3
d
4
0.175 O1h col
wds
where
O1
(1)
(2)
0.4
.rinf
ª Em etinf sin 2T º
«
»
¬« 4 E fe I col hinf ¼»
(3)
1
4
For wall with opening, Asteris [3] has proposed diagonal strut width formulae that take into account
reduction of wall stiffness due to the opening. Diagonal strut width of the wall with opening without lintel can then
be calculated by reducing the strut width from that of the solid wall. The formulation of reduction factor is as
follows.
O 1 2D w 0.54 D w1.14
(4)
where O is reduction factor for diagonal strut width and Dw is the ratio of opening to wall areas.
Shell Element Model
When modeled using shell elements, the wall is divided into small area using a number of elements. The contact
area between the frame and the wall is taken into account and is modeled as gap elements. The stiffness property of
the gap element has been proposed by Dorji and Tambiratnam [9] in the following equation.
Kg
0.0378 Eit 347
(5)
where, Kg is the gap element stiffness (N/mm), Ei is the modulus of elasticity of the wall (MPa), and t is the wall
thickness (mm).
020062-2
Material Properties
The modulus of elasticity of concrete, Ec (MPa) is calculated using equation available at ACI 318M-11 [10] for
normal concrete with a density, wc of 1440 to 2560 kg/m3.
1.5
Ec
wc 0.043 f 'c
(6)
with f'c is concrete compressive strength (MPa). The formula is used for frame concrete and lintels.
The modulus of elasticity of masonry wall, Em (MPa) is determined in accordance with FEMA-356 [6].
Em
550 f 'm
(7)
with f'm is the wall compressive strength (MPa).
METHODS
Development of strut width formula is done by comparing the response of diagonal strut model (MDS) to
that of shell element models (MSE) using experimental results (by others) as reference. The models are considered
valid when the responses of the two models are similar to that of the reference. Based on the valid models more
MDS and MSE of various wall opening were made to obtain relation between opening ratio and stiffness reduction
factor using the strut width of solid wall as standard (with reduction factor of 1). The equation of strut width is then
applied to model infilled frame of 2-6 storey structures with various percentages of openings to study the range of
applicability of the models. Discussion and conclusion were made based on the result of validation model and the
applied models.
Validation Models
For the validation models, reference structures of one storey one bay RC infill frame with central opening of
various percentages, with lintel around the opening were used. The structures were tested using cyclic lateral load by
Sigmund and [5]. Among the many test specimens, 3 were used for validation. They are solid infill frame (SIF),
infill frame with door openings of 13% (IFDO), and infill with window openings of 12% (IFWO). In accordance to
the laboratory test, the model was loaded with axial load of 365 kN, applied to the columns. For the lateral load,
however, the force was applied monotonically in steps of 10 kN until maximum load of SIF, IFDO and IFWO are
277, 310 and 258, respectively.
The infilled frame and shell element models for wall with central door opening reinforced with lintels are shown
in Fig. 1. The material data used are based on research from Sigmund and Penava [5] where the characteristic
compressive strength (f’c) of the frame concrete is 58 MPa. With weight of concrete (wc) of 2500 kg/m3 then then
elastic modulus (Ec) is 41000 MPa. The characteristic compressive strength (f’t) of the lintel is 30 MPa with Elastic
modulus (Ec) of 29440 MPa. The beam and columns dimensions are 12/20 and 20/20 and the lintels are 12/12 For
the 120 mm thick masonry wall the compressive strength (f’m) is 2.7 MPa and elastic modulus (Em) of 3900 MPa.
See in Fig. 1.
020062-3
(b)
(a)
FIGURE 1. Modeling of infill wall structures with doors opening (a) Diagonal strut model, (b) Shell element model
To consider the nonlinear behavior of structure, the stiffness of structure was reduced by modifying the concrete
modulus, Ec to become secant modulus and the section modulus, Ix and Iy using the cracked cross section. The
details of the factored numbers are shown in Table 1.
Load
(%)
0
20
40
70
95
100
TABLE 1. Modification Factor (MF) of E and I
Lateral Load (kN)
MF I
MF
E
MS
MDO
MWO
Beam
Col.
0
0
0
1
1
1
55.40
62.00
51.60
1
1
1
110.80 124.00 103.20
1
1
1
193.90 217.00 180.60
1
1
1
263.15 294.50 254.10
0.6
0.6
0.8
277.00 310.00 258.00
0.5
0.4
0.7
The width of diagonal struts used in the model was determined by trial and error, so that the forces versus
displacements curves were in line with the curves of shell element models and experimental results. Once the
models responses similar to that of the experimental, then the process is continued by creating diagonal strut and
shell element models for simple one storey one bay infilled frame structures with openings ratios of 10 %, 20 %, 30
%, 40 %, 50 %, and 60 %. Once the two models showed the same responses, a formula considering relation
between wall stiffness and opening ratio was then used to propose equation of strut width of infill wall with
reinforced opening.
Results from these studies are presented as curves of lateral loads versus lateral displacements plotted
together with the experimental results. For the validation model, the strut width of solid wall (MS) was determined
according to eq. 2, while for walls with opening (MDOst and MWOst) the widths were determined by trial and
error. Table 2 shows the diagonal strut width for the whole validation models.
The load displacements curves of the validation models are given in Fig. 2. It can be seen that the behavior
of the structures modeled as strut or shell element are similar to those of the experimental results for solid model
and models with opening. It can be concluded that the shell element model is valid to be used to develop diagonal
strut model for infilled frame with reinforced opening.
TABLE 2. Width of diagonal strut for validation models
Model
Name
MS
MDOst
MWOst
Width
of
Opening
350
500
Height
of
Opening
900
600
Width
of
Strut
642
710
720
H
(mm)
L
(mm)
D
(mm)
1613
2000
2569
H and L are height and width of the column; d is diagonal length of the infill
020062-4
(b)
(a)
(c)
FIGURE 2. Load-displacement curves (a) Solid wall, (b) Wall with door opening, (c) Wall with window opening
Analysis of Diagonal strut Width on the Infilled Frame Model
Based on the results of validation model, it is shown that the shell element and diagonal strut models can
simulate the experimental results well. The model was used for reference on modeling one-storey one-bay infilled
frame structure to formulate the relation between the wall stiffness and the opening ratio.
Infilled frame structure with various opening ration was modeled with shell elements and diagonal strut and
their behavior were compared. The comparison was conducted base on the load-displacement curves resulted from
each model. To have the curves similar between shells and struts models, diagonal strut widths were adjusted by
trial and error and the final width of struts are shown in Table 3.
TABLE 3. Diagonal strut width for varying wall opening
Opening
0% 10% 20% 30% 40% 50% 60%
Percentage
Diagonal
Strut Width
642
750
620
475
430
330
240
Displacement results of the infilled frame structures with various opening were used to obtain the wall stiffness.
The relation between the wall stiffness coefficient, c, and the wall opening ratio, r, is plotted in a graph shown in
Fig. 3. It can be seen from the figure that the wall stiffness coefficients reduce as the opening percentage increase. A
simple regression analysis between the percentage of opening r and wall stiffness coefficient c was used. The
020062-5
proposed diagonal strut width is given in eq. (8) and (9), where wds is the width of the diagonal strut, d is the
diagonal length of the infill (center to center), c is the wall stiffness coefficient determined from Figure-3.
d
c
4
wds
(8)
c = 1.0565r2 - 2.281r + 1.3764
(9)
Application of Strut Equation on the Infill Frame Model
6000
6000
6000
(a)
3500
3500
3500
3500
3500
3500
3500
3500
3500
To study the applicability of the proposed equation obtained from the validation model, the formula is applied to
create ST model of 2-6 storey as shown in Figure 4. The dimensions of columns are as shown in the Table 4. All
beams have dimensions of 250x400 mm. The 150 mm thick infill wall was placed in the center bay with opening of
10 %, 20 %, 30 %, 40 %, 50 %, and 60 % as shown in deail in Fig. 5 with lintels of 150 by 150 mm. The structures
were subjected to earthquake load according to
SNI 17 [11] and gravity load. Load displacement curves were determined from the analysis.
6000
6000
6000
6000
(b)
6000
6000
(c)
FIGURE 3. Relationship between the wall stiffness coefficient (c), percentages of opening (r) and correlation coefficient (R)
(a)
(b)
FIGURE 4. Infill frame structures of 2-6 storey. (a) 2 storey (b) 6 storey
020062-6
TABLE 4. Dimension of the frame elements
Level
1
2
3
4
5
6
2
Storey
300x300
250x250
3
Storey
300x300
300x300
250x250
Column (mm)
4
5
Storey
Storey
350x350 450x450
300x300 400x400
300x300 350x350
250x250 300x300
250x250
6
Storey
500x500
450x450
400x400
350x350
300x300
250x250
FIGURE 5. Geometry of the opening in the infill wall
Modeling of diagonal strut width on 2-6 story RC structure was obtained from strut width equation (8) and (9).
The resulting strut width for each percentage of opening is given in Table 5.
TABLE 5. Diagonal strut width of 2-6 storey RC frame structure
% of opening
10
20
30
40
50
60
c
Strut width (mm)
1.16
2012
0.96
1671
0.79
1367
0.63
1099
0.50
868
0.39
674
The analyses of infilled frames structures of 2, 3, 4, 5 and 6 storey were carried out using strut model (ST) and
shell element model (SH). The number following the ST and SH correspond to the number of storey and percentage
of opening in the infill wall. The load displacement curves from the analyses are plotted in Fig 6.
(a)
(b)
020062-7
(c)
6
5
5
4
Storey
Storey
4
3
2
SH510
ST510
SH520
ST520
3
2
SH530
1
ST530
SH540
ST540
SH550
ST550
SH560
ST560
1
SH610
ST610
SH620
ST620
SH630
ST630
SH640
ST640
SH650
ST650
SH660
0
0
0
5
10
15
20
25
ST660
0
5
10
15
20
25
30
35
40
45
Displacement (mm)
30
Displacement (mm)
(d)
(e)
FIGURE 6. Displacements of 2-6 storey models. (a) 2 storey, (b) 3 storey, (c) 4 storey, (d) 5 storey, (e) 6 storey
From the graphs, it is obvious that the load-displacement curves of strut and shell element models are of similar
characteristics. The increasing ratio of wall opening give increasing displacements in the models. In lower floor
level, the ST and SH models show closer value of displacement. As the levels increase the discrepancy is revealed.
The different of top level displacements between shell and strut models with opening of 50-60% were only 4-10%.
DISCUSSION
From the validation models it was found that the behavior of infilled RC frame with reinforced opening can be
modelled using shell element or diagonal strut using equation proposed in equation 8 and 9. Both models mimic the
true behavior of the tested structures well. Adjustment of E and I due to non-linearity of materials and cracks
development as the load increases is necessary to have good results, especially at higher load levels. Interestingly
enough, the model with door opening is stronger than the model with window opening of equal opening ratio. More
interestingly, the model with door opening is stronger than the model with solid infill. This is possible with the
contribution of lintels to stiffen the structure. The data obtained from these models suggest that despite the opening,
the infill wall should be considered in modeling the structure to have more accurate response.
Conformance between sheel element model and the diagonal strut models was also observed from the 2-6 storey
models. Variation of responses are observed. For models with opening ratios of 50% and 60% showed that the
displacements on the top floor for strut models were 4%-10% more rigid than those of the shell element models. For
the purpose of structural design, however, the accuracy of models is adequate. Accordingly, the proposed equation
of diagonal strut width for the analysis of infilled RC frame with reinforced opening can be used.
CONCLUSIONS
Based on results from numerical analyses the following formula for the equivalent width of diagonal strut of
infilled frame with reinforced opening is proposed in equation 8 and 9. The application of the formula on infilled RC
frame structures of 2-6 storey showed that the behavior of strut models correspond to that of the shell element
model.
ACKNOWLEDGMENT
This research is partially supported by research project of Hibah Unggulan Program Studi Fakultas Teknik 2016
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