Nonlinear dynamic behavior of structural frames constructed with 3D ...

1 St international conference on seismic retrofitting, Tabriz-Iran, 20-22 October 2008
Nonlinear dynamic behavior of structural frames constructed with
3D wall panels with Vertical Irregular arrangement
Omid Rezaifar 1 , Majid Gholhaki 2
1,2- Assistant Professor, Faculty of Civil Engineering, Semnan University, Semnan, Iran
rezayfar@yahoo.com
mgholhaki@semnan.ac.ir
ABSTRACT
The current study investigates the hysteresis behavior for combined systems, RC frame, and pre-cast 3D wall
sandwich panels, in non-linear material properties. The seismic behavior of building constructed by 3D wall
panels is studied for absorb of energy and dissipation of it with material nonlinearities. The results are compared
regular bending RC frames to complete box type shotcrete sandwich panels system and present the differences of
hysteresis behavior for each system and any of cases with irregularity in vertical stiffness such as soft story. In
this study, material nonlinearity simulated with Drucker-Prager failure criteria. Behavior of FEM model verified
with experimental result. Seventy-three frames analyzed and result were investigated and compared. Compare of
energy dissipation for stories and influence of soft story are presented.
Keywords: panel structures, dynamic behavior, nonlinear analysis.
1. INTRODUCTION
3-D wall panels are used in construction of exterior and interior bearing and non-load bearing walls and floors of
building of all types of construction. This system consists of a welded wire space frame integrated with a
polystyrene insulation core. The wall panel is placed in position and Wythe of concrete are applied to both sides.
Wall panel receives its strength and rigidity by the diagonal cross wires welded to the welded-wire fabric on each
side. This combination produces a truss behavior, which provides rigidity and shear terms for full composite
behavior, Salmon et al [1]. Speeds in construction, weight lightening and thermal insulation are the marked
privileges for building built up with such innovative system.
Figure 1- Details of 3D panel
One of the most evident limitations of such box type system is in parking floor at lower level. Due to vehicle
maneuver, some internal walls are replaced by RC frames and the bearing walls are discontinued. Such nonuniformity
in vertical stiffness influences on structural performance under transient dynamic loads under
earthquakes.
The problem is described as to investigate the seismic behavior of up to five stories building including one parking
floor combined with box type 3D system. The study may extend to any combination of 3D bearing wall system and
RC framework.
As a background of the subject, Moehle [2, 3], studied seismic response of four stories RC building. Wood [4]
investigates dynamic performance of RC frame with variable stiffness. Lu et al [5] presented the results of the
earthquake simulation tests on two of the frames with strength and stiffness irregularities.
2. DYNAMIC ANALYSIS
Non-linear Von-Misses and Drucker-Prager criterion as two elastic-perfect plastic model with bi-linear stress-strain
curve are taken in dynamic analysis. The governing equilibrium equation of a finite element system for dynamic
response is
M U
CU
KU R
Where M, C, and K are mass, dampers and stiffness matrices and R are exerted load vectors. U
, U
and U Are
acceleration, velocity and displacement system, respectively. The quasi-static time history method is used for
1

Acc. cm/s 2
1 St international conference on seismic retrofitting, Tabriz-Iran, 20-22 October 2008
analysis. Ground acceleration record as it shown is adopted, figure 2. The duration of record is totally 21 seconds
with the maximum amplitude of 700.8 Gall. The major exerted energy is occurred at the first 10 second.
800
600
400
200
0
-200
5 10 15 20 25
-400
-600
-800
Figure 2- used ground acceleration record
Both linear and non-linear material models are considered in current study. The analysis is performed in ANSYS
environment and two non-linear elements, shell 91 and solid 65 are adopted for concrete at system and component
level, respectively. The orthogonal wire meshes are modeled by beam 23.
Material properties of shotcrete and wire meshes are tabulated in table 1. All details are those experimentally
measured, [6].
Table 1- Material properties used in analysis(stresses in kg/cm 2 )
Material Poisson
ratio
Specific
Gravity T/m 3
Young
Modulus
Yield stress Tensile
strength
Compression
strength
Steel bars 0.28 7.855 2.06e6 4700 - -
Concrete 0.2 2.4 2.4e5 - 30 300
Shotcrete 0.15 2.2 1.5e5 - 28 180
In addition, the stress-strain curves for welded wire meshes are obtained through tensile test. It was based on ASTM.
The final diameter of wires after cold drawing manufacturing is 3.5 mm. There is one stage annealing work have to
be done to release the residual stresses.
3. VERIFYING MODELING WITH EXPERIMENT RESULT
Fem model of one panel is analyzed with drucker-prager criteria. This panel was constructed and tested versus shear
loading. Panel in various dimensions tested. Setup of panel test can be seen in figure 3.
Figure 3- setup of panel test
Result of experiment obtained. FEM model result and test result compared. It can be seen that result of FEM
modeling is compatible and verified. Accuracy of modeling in nonlinear material with drucker-prager for concrete
compared with experimental.
4. SENSITIVITY ANALYSIS
To reduce the executive time of analysis, using of panel symmetry in thickness, only one-half of the 3D panel is
modeled for shear loading. the analysis of full panel and one-half thickness have same shear and bending behavior.
In dynamic analysis, especially when material behavior is considered as non-linear, the time step sizing in the
analysis becomes important to get results that are more accurate. Therefore, it should be chosen infinitesimal. In The
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1 St international conference on seismic retrofitting, Tabriz-Iran, 20-22 October 2008
present study, t is taken as identical for all cases and equal 0.005 sec.. Table 2 shows the sensitivity analysis to
obtain minimum it for all models.
Table 2 - Sensitivity of Base absorbed shear to the time interval it
t (sec.) 0.02 0.01 0.005 0.002 0.001
Base absorbed shear (Ton) 1019 753 530 522 520
In order to evaluate dynamical characterizing e.g. periods and mode shapes of all frames, the Modal analysis is
conducted. As example for the model with four stories and three spans, that has 12 meters height. The period
obtained from linear analysis is 0.509 sec.. The theoretical period is equal to 0.451 sec from equation 1.
3
4
(1) T H
For concrete frames is equal to 0.07, that shows low percentage of error and adequate precision for modeling.
F2S1
Table 3- figure of models
F*S*001 F*S*002 F*S*003 F*S*004 F*S*005 F*S*006 F*S*007
F2S2
F5S2
F5S3
F5S4
5. NUMERICAL MODELS
To investigate the changes in building stiffness constructed in combination of 3D panels and RC frames, the
following figures are eight types of frames with different panel distribution in spans. All beams and column cross
sections are 30 by 30 cm dimensions with 2.5% reinforcement density. The frames span length is identical for all
models and plan of each floor is 400 centimeters. Figures of all models are presented in table 3.
Different stiffness in level of each system leads to different base shear for each case; furthermore, distribution of
shear is different because of mass distribution. Applying the base acceleration record to all models in both linear and
non-linear analysis, it can estimate the distribution of base shear, which could balance the dynamical equilibrium of
the structural system.
To investigate the real behavior of structure, dynamical analysis on models are performed by incorporate the
material nonlinearity for concrete by drucker-prager criteria.
6. HYSTERESIS BEHAVIOR OF FRAMES UNDER EARTHQUAKE RECORDS
Applying the NAGHAN base acceleration record to all models in both linear and non-linear analysis, one can
estimate the base shear that could balance the dynamical equilibrium of the structural system. Hysteresis of frames
investigated and compared in this section. Energy dissipation and overall behaves of models is obtained. It has only
presented three models and some results of it.
Models have some different value of frequency. Bare frame frequency is 4.0, soft storey frame 5.84, semi soft storey
30, and full panel is about 40 Hz. Some of these frequencies are presented in table 4. It shows that full panel systems
have higher frequency in compare of bare frames and soft story frames. Soft storey frames have frequency higher
than bare frame and little than full panel systems. Soft storey frequency is more similar to bare frame. It is because
of low stiffness of concrete columns in first story. The value of frequency is increased by increasing height of
system generally. F2S1001, bare frame absorbed 73.725 kN base shear. It deformed 33.51 mm at upper point of
frame. It shows that hysteresis curve of frame is fat. Energy Dissipation of frame is higher than other models, and is
same of bare frame models in theoretically. The complete list of top displacement and base shear is presented in
table 5.
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Resul
ts
1 St international conference on seismic retrofitting, Tabriz-Iran, 20-22 October 2008
Table 4- Models frequencies
Name BARE FRAME SOFT STOREY FULL PANEL
F2S1 4.38 6.60 27.52
F2S2 3.99 5.84 39.99
F2S3 3.87 5.56 45.50
F4S4 1.97 3.82 23.00
F5S3 1.58 3.47 14.78
F5S4 1.56 3.40 17.22
Table 5- linear and nonlinear top displacement and base shear of frames
001 002 003 004 005 006
Name
Lin. NonL. Lin. NonL. Lin. NonL. Lin. NonL. Lin. NonL. Lin. NonL.
T.D. 20.41 18.88 19.41 10.37 0.34 0.30
F2S1
B.S. 82.86 45.44 212.71 44.05 52.60 43.16
T.D. 154.39 67.50 88.95 39.70 36.70 9.46 2.87 11.07 3.63
F5S2
B.S. 335.03 74.14 489.78 603.18 81.27 581.29 187.85 935.82 292.31
T.D. 157.04 72.70 99.89 53.04 23.99 10.97 1.40 5.68 1.02 6.31 2.78
F5S3
B.S. 471.99 101.95 839.32 1170.20 98.50 1430.00 216.58 961.86 244.31 1519.20 647.55
T.D.: Top Displacement in unit of mm, B.S.: Base Shear in unit of kN
Bare frame (001) of F2S2 models sustain earthquake by plastic residual deformation and have 33.51 mm
displacement for top point. Its relative base shear is 73.73 kN. It can be seen that linear analysis obtained different
value for top displacement and base shear. Linear top displacement for this model is 20.84 mm and its base shear is
130.9 kN. It has some adequate strength for sustain records but deformed non-elastic. Its top displacement for
nonlinear analysis is about 22.00 mm in 74.96 kN base shear. The linear analysis of this model lead to 14.03 mm in
241.75 kN base shear for respective point. Other models of frames with various percent of panel in its spans have
good response in analysis. Full panel system in this model has 0.23 mm top displacement in 147.16 kN of base
shear. The linear analysis obtained 0.13 mm top point displacement and 94.33 kN of base shear, that is not correct in
compare of nonlinear analysis. It shows that nonlinear analysis is necessary for this type of systems, and linear
results are not truthful.
In this model, hysteresis curve at first cycles of records is linear and lied on elastic line of frame behavior. Frames
deformed plastic at the next cycles of record with higher magnitude of acceleration. After pick of acceleration,
deformation has residual component that shake structure around another zero point in hysteresis diagram. After this
time in record structural energy loop is turn around second zero point that shows plastic residual deformation. In this
secondary loop curve slope is same with initial curve slope. Investigate of curves shows that frame have linear
behavior up to 20 kN base shear. After this point plastic deformation caused descent of base shear, absorb. It shows
that linear analysis is not useful for the frames. The hysteresis loop shape is compatible with another bare frame in
theoretically.
Base shear in soft floor model of this series, 003, is 74.964 kN by 18.92 mm deformation. Structure deformed
linearly less than 25 kN of base shear. This model has residual plastic deformation and structure has linear
delocalized hysteresis curve.
Table 6- compare of bare frame and soft floor for F2S2(units are in kN,mm)
frames Base shear Pick disp. Max. disp. Energy
F2S2001(Bare frame) 73.725 33.51 45 3400
F2S2003(Soft floor) 74.964 18.92 24 2250
003/001 (Soft/bare) 1.02 0.57 0.53 0.66
Compare of 001 and 003 shows in table 6. Base shear of soft floor frame is 2 % more than bare frame. Soft floor
drift for top point is 57 percent of bare frame. It shows that soft floor system have different dynamic property and
behaves too different. In soft floor, base shear is more than bare frame and drift is less than it is. Based on hysteresis
curve of soft floor frame, it bears seismic excite on the limit capacity of soft floor. By the other word, little change
in excited motion can destroyed frame from first story. Area of hysteresis diagram shows the capacity of earthquake
resistance of frame. Flexibility of soft frames is too less than bare frame and top drifts of structure shows that bare
frame drift is 2 times of correspondent point in soft floor. Secondary slope after plastic residual deformation in
frame is similar to initial linear loops of hysteresis curve.
Based on result of analyzing using of wall panels in half spans of first floor (F2S2004) is changed base shear up to
86.5 kN and decrease roof displacement to 2 mm. This structure almost behaves linearly. Shear deformation that
caused the linear deformation make hysteresis curves linear with no energy dissipation. It shows that in more than
80 kN loading structure initials to deformed non-linearly. Linear hysteresis curve shows that most of input energy
must be supported by structural element.
4

FORCE (kN)
FORCE (kN)
FORCE (kN)
FORCE (kN)
1 St international conference on seismic retrofitting, Tabriz-Iran, 20-22 October 2008
F2S2001
F2S2003
100
80
60
40
100
80
60
40
20
20
0
-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02
-20
-40
0
-0.025 -0.02 -0.015 -0.01 -0.005 0 0.005
-20
-40
-60
-80
-60
ROOF DISP. (m)
ROOF DISP. (m)
Figure 4- hysteresis loops of force-displacement of F2S2001 and F2S2003
-100
F2S2004
100
15
F2S2005
80
60
10
40
20
5
0
-0.00025 -0.0002 -0.00015 -0.0001 -0.00005 0 0.00005 0.0001 0.00015 0.0002 0.00025
-20
-40
0
-0.0003 -0.0002 -0.0001 0 0.0001 0.0002 0.0003
-5
-60
-80
-10
-100
-15
ROOF DISP. (m)
ROOF DISP. (m)
Figure 5- hysteresis loops of force-displacement of F2S2004 and F2S2005
Full panel structure, “005” model, absorbed base shear is increased to 147 kN and roof displacement is 2.5 mm.
Energy curve in this model is fatter than 004 models, but it has little energy dissipation in compare with full frame.
Structural responses for F5S4 shows higher capacity for energy loss in compare with 2 and three spans models.
It can be seen, the hysteresis center changes because plastic deformation of structure. The record is caused the bare
frame structure reach to yield point at 25 mm. Failure mechanism is taken place at 75 mm. as shows in roof
displacement history the frame material lead to plastic form at 1.6 time of record. Secondary horizontal axis shows
the plastic deformation.
Soft story frame, 003, has same base shear like bare frame, but soft story frame cannot sustain the record. Failure
mechanism occurred at 1.4 sec. of record by 25 mm deformation in roof level.
Soft story frame more stiffened than bare frame. This fact can be seen in the hysteresis loops by first slope of curves.
“004” model, that has some walls in first story absorbed more base shear than bare and soft story frame.
Deformation response of frame is almost linear and has little damping by narrow hysteresis loops. Maximum roof
displacement is 1 mm for this frame. Mechanism of failure is taken place at 1.6 time of record.
“005” and “006” models responses are similar to “004”. In these models, deformation and damping increased by
added panel in compare to “004”. Full panel frame, “007” has complete response with record. No failure occurred in
full panel model. The energy dissipation is more than soft storey frames such as 004 and 005 and 006, but is less
than bare frame.
Structures response after 450 kN base shear indicated non-linear behavior.
Damping of full panel system is only 7% of bare frame. Soft story frame in this case has 10% damping of full panel
system. Table 4 shows the maximum base shear and top displacement in hysteresis curves of systems.
Some of these frequencies are presented in table 4. Frequency contents of these models are same as mentioned
before.
This model behaves like as three spans with five stories buildings. It sustained earthquake up to 1 mm could be
shown the influence of panel in soft floor. Full frame in this series deformed 7.7 cm at roof when the record reach to
1.5 second and followed by plastic stable deformation and caused change the zero point of building shakes.
Top displacement Time history of F5S4 models is presented in figure 6 and 7. Plastic deformation in 001 model
shows the nonlinear behavior of columns. In 003 model with soft storey after 25 mm deformation structure failed.
Soft story frame is shaking as one degree of freedom structures in this series. Deformation of roof for soft story type
was about 2.6 cm in first level, at 1.4 th second of record. After this time, structure collapsed and destroyed. In
compare of soft story first level deformation by full frame, it should be notice that first floor deformation in full
frame is about 3.2 cm. By adding 30% panel in soft story, it can be seen that structural behavior is not compatible
by one degree of freedom, and deformation of floors is uniformly. F5S4006 model with three filled spans of four
spans (75 % of spans filled with panel) in first floor, deformed compatible with records. Its drift in roof level is 0.95
mm at time of 1.5 sec. of record.
5

DISPLACEMENT (mm)
DISPLACEMENT (mm)
DISPLACMENT (mm)
DISPLACEMENT (mm)
1 St international conference on seismic retrofitting, Tabriz-Iran, 20-22 October 2008
F5S4001
F5S4003
100
30
FIRST STORY
80
60
FIRST STORY
SECOND STORY
THIRD STORY
FOURTH STORY
FIVTH STORY
25
20
SECOND STORY
THIRD STORY
FOURTH STORY
FIVTH STORY
40
15
20
10
0
-20
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
5
0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
-40
-5
TIME (sec.)
TIME (sec)
Figure 6- time history of displacement for F5S4001 and F5S4003 storey
F5S4006
F5S4007
0.80
0.60
0.40
1.50
1.00
FIRST STORY
SECOND STORY
THIRD STORY
FOURTH STORY
FIVTH STORY
0.20
0.50
0.00
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
-0.20
-0.40
0.00
0.0 0.5 1.0 1.5 2.0 2.5 3.0
-0.60
-0.80
-1.00
FIRST STORY
SECOND STORY
THIRD STORY
FOURTH STORY
FIVTH STORY
-0.50
-1.00
-1.20
-1.50
TIME (sec.)
TIME (sec.)
Figure 7- time history of displacement for F5S4006 and F5S4007 storey
Storey drifts in this model are equal in height of frame. F5S4007 sustained record fully without any failure
mechanism. Its deformation in roof level is 1.2 mm. in this model first storey drift is less than upper stories, by 25 %
decrease in lateral deformation. It behaves in first mode and deforms 12 mm at time of 2.2 of record. It shows the
enough capacity of frame in earthquake record.
7. STRESS VARIATION IN MODELS DURING RECORD
In this section, for some selected frames with different type stress treatment and strain is investigated. The critical
point of structure related to stress would be described. Failure mechanism in material is occurred in this critical
point.
It can be seen that maximum lateral displacement is 24 mm at 1.393 time of record. Because of relatively rigidity in
second and higher levels, almost all of displacement is occurred in first level. First story deformed because of
reinforced concrete columns that allowed story to have more drifts in compare of upper rigid levels. Upper levels
have no drifts related to first story level. The structure treats such as one-degree-of-freedom system.
in this frame(F5S4) conjunction of, beams and columns have maximum of stress. In-plane compressive stress in
bottom of second floor walls is maximum and its value reach to 54.4 kg/cm 2 . Maximum tensile stress restricted to
28.8 kg/cm 2 because of crack is occurred.
Models
F5S4003
F5S4004
F5S4005
Type
of
analysis
Table 7- stress variation in models
Stress (kg/cm2)
Top drift
Principal Sxy
(mm)
Vonmisses
Comp. Tens. Pos. Neg.
non-linear 24 54.40 28.8 21.60 22.8 96.80
linear 22.6 84.90 28.8 47.41 35.7 54.70
non-linear 1.16 54.00 28.8 41.00 24.8 86.60
linear 1.11 186.80 28.8 43.90 26.3 99.41
non-linear 1.00 54.00 28.8 46.70 28.8 100.00
linear 0.69 54.00 28.8 47.00 28.8 56.60
Maximum value of stress in F5S4003 is 84.9 kg/cm 2 takes place in first conjunction of first story beams and
columns. No point of frame reach to yield or crack stresses, but the level of stress in linear analysis is 37 percents
more than nonlinear analysis result. It shows that linear analysis is not commercial. It has no accurate related to
nonlinear analysis.
Linear stress Shear stress Sxy, in F5S4003 is 47.41 kg/cm 2 in positive and 35.7 kg/cm2 in negative. Nonlinear
positive stress is 21.6 kg/cm2 and 22.8 kg/cm2 in negative. It shows 54 % decrease for positive stress. Nonlinear
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1 St international conference on seismic retrofitting, Tabriz-Iran, 20-22 October 2008
maximum negative stress restricted to crack stress and this fact is not seen in linear analysis. As it shows, stress
distribution is changed in nonlinear analysis because of crack effect.
Any stress figure shows the critical corner at first story level in frame with soft story. Conjunction in corner of first
story level reaches to crack stress during record. In linear analysis stress, variation is symmetric and has similar
tensile and compressive maximum stress. Tensile stress cannot be got more value than crack limit, and it shows the
non-realistic result of linear analysis in compare to nonlinear analysis.
Figure 8- F5S4003 von-misses nonlinear stress variation
Von-misses stress in linear analysis is 57.4 kg/cm2 and 96.8 kg/cm2 in nonlinear analysis. This value first occurs in
first corner and then developed to another first story conjunction. Higher value of stresses in nonlinear analysis
shows the realistic treat in nonlinear analysis and danger of linear analysis because of non-realistic response that is
shown of frame. This fact is because of crack control and increase of non-symmetric stresses in tensile and
compressive.
F5S4004 models have 25% wall surface in first floor. Drift rate of this model shows the more homogeneous than
soft story frame. In fact, base shear in semi-soft story frame distributed in height of frame. Opposite of soft story
frame types drift is not occurs in first floor. The form of columns deformations shows the different behavior of them
respected to its location. Corner columns treated in flexural deformation but middle columns have shear behavior.
Maximum drift in nonlinear analysis is 1.16 mm. in linear analysis this values decreased to 1.11 mm. maximum
principal stress value in this structure is 54 kg/cm2 in nonlinear analysis. Linear analysis shows 246% increase in
principal stress value. Maximum stresses for this model and F5S4003 models are same and equal to 54 kg/cm2.
Distribution of tensile stresses shows that occurred cracks are first started from corner of first story level in beams
conjunction. Secondary point of failure is in walls in first floor. In fact, critical point is wall panels in first story after
conjunction of first story corners.
Distribution of nonlinear shear stress in walls shows the maximum negative stress equal to 24.8 kg/cm2 and positive
stresses as 41 kg/cm2. These stresses in linear analysis manner are 26.3 kg/cm2 and 43.9 kg/cm2, respectively.
A von-misses stress in this structure shows that nonlinear analysis return 86.6 kg/cm2 value for it. Linear analysis
von-misses stresses are equal to 99.41 kg/cm2 at maximum point.
In fact, adding walls in first floor makes nonlinear result near to linear, but those have shown some difference
between them yet. Von-misses stresses in linear analysis are 12.8% more than nonlinear stresses.
Figure 9- F5S4005 Non-linear von-misses stresses. (Linear, Non-linear)
F5S4005 frame Lateral top deformation is 1.0 mm. Deformation of columns shows fewer shears than 003 and 004
columns. Linear analysis shows 0.69 mm for lateral deformation and is different with nonlinear deformation.
Greater lateral deformation in nonlinear analysis shows the energy loss in structure because of material nonlinearity.
The maximum of principal stress in nonlinear and linear analysis is almost same and equal to 54 kg/cm2. in fact, this
observation shows that adding panel in first floor leads frames to be treated as linear and don’t have nonlinear
behavior. However, maximum stress is equal in linear and nonlinear analysis, but distribution of them is not same
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1 St international conference on seismic retrofitting, Tabriz-Iran, 20-22 October 2008
and nonlinear analysis cause the extended stress in wall surface because of limited tensile stress. In both analyses,
linear and nonlinear, critical point is first corner of first story.
Maximum shear stress in nonlinear analysis is 46.7 kg/cm2 in positive. Important observation is difference of
distribution between linear and nonlinear analysis.
Von-misses stress value for nonlinear analysis is 100 kg/cm2 and linear analysis von-misses stress value is 56.6
kg/cm2. Distributing of stress in both linear and nonlinear are shows that frame bear loads with arch act and conduct
it to basic corners.
In fact, all of models such as F5S4005 show the critical point in the first corner of soft floor.
Comparing of stress and strains in F5S4004 model shows that cracks are taken place in 45-degree direction related
to frame axis.
8. DISCUSSION
Compare of models under nonlinear analysis shows it have different behavior related to usage percent of walls.
Bare frames reach to plastic point in columns during record. Different behavior of frames cause of lateral
displacement shows that homogenous stiffness in height of frames, first mode of deformation is governed. For soft
story high frames because of height of frames, second mode in lateral deformation is participated. By adding panel,
first mode would be the governed mode in frame.
Specific characteristics of frames lead to different behavior and it would cause to resonant, if characteristics of
record were compatible with frame characteristics.
Soft story frames have failure mechanism in first floor columns. However, maximum response time for all models
are not same, but in this record most of frames has maximum response at 2 second of record length. Percent of total
drift in soft story frame is occurred in first floor and upper levels deformed almost same.
Based on this study maximum relation of length to height of frames are better to be 1.25. Frame height more than
1.25 times of length of frame because of more absorbed base shear in compare of bearing walls in first floor lead to
mechanism for it. The ratio of H/L and relative base shear is presented in table 8.
Models because of different stiffness have various bas shear. As it mentioned, those have not been same in absorbed
base shear. In addition, nonlinear analysis leads to more accurate results than linear analysis. This panels because of
its special internal elements dont usually use in construction, has special behavior. Model, that has some walls in
first story absorbed base shear more than bare and soft story frame. Deformation response of frame is almost linear
and has little damping by narrow hysteresis loops.
Table 8- ratio of base shear to frame weight
Name W
(kN)
H/L
ratio
FULL
Frame
SOFT
Storey
25%
PSS
33%
PSS
50%
PSS
66%
PSS
75%
PSS
FULL
Panel
F2S1 64 1.50 0.71 0.69 0.67
F2S2 128 0.75 0.58 0.59 0.68 1.15
F2S3 192 0.50 0.49 0.44 0.76 0.82 0.96
F5S2 320 1.88 0.23 0.25 0.59 0.91
F5S3 480 1.25 0.21 0.21 0.45 0.51 1.35
F5S4 640 0.94 0.21 0.15 0.49 0.50 0.65 0.89
Hysteresis curve for base shear indicated versus top lateral deformation. It was considered to determine the nonviscous
damping and energy loss of frames. Based on the hysteresis curves bare frames has most energy loss in
compare of another frame. Soft story frames has energy dissipation more than full panel system and less than bare
frames. Hysteresis curves of frames shows the level of material stress and capacity of systems, soft frames with
some spans filled with panels has linear responses and has less energy loss. Full panel system response based on
hysteresis curve is linear and has little damping.
Hysteresis curves shows that energy loss of homogenous systems are more than another frame.
Critical point of frames for soft story systems are in corners of first level at conjunction of beams and columns.
Maximum stresses in beams and walls are occurred between first corner and L/4 of spans. These points are cracked
first during record and should be considered accurate.
In this models linear analysis lead to non-realistic behavior of system and has different distribution of stresses and
crack in compare with nonlinear analysis. This incorrect stresses leads to non-realistic absorbed base shear and so
incorrect shear distribution in height.
9. CONCLUSIONS
Hysteresis of frames investigated and compared in this section. Energy dissipation and overall behaves of models is
obtained.
By adding 30% panel in soft story, it can be seen that structural behavior is not compatible by one degree
of freedom, and deformation of floors is uniformly. Hysteresis of frames investigated and compared in this
section. Energy dissipation and overall behaves of models are obtained.
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1 St international conference on seismic retrofitting, Tabriz-Iran, 20-22 October 2008
In F2s2003, soft storey model, Structure deformed linearly less than 25 kN of base shear. This model has
residual plastic deformation and structure has linear delocalized hysteresis curve.
Base shear of soft floor frame is 2 % more than bare frame. In soft floor, base shear is more than bare frame
and drift is less than it is.
Flexibility of soft frames are too less than bare frame and top drifts of structure shows that bare frame drift
is 2 times of correspondent point in soft floor.
In half-span wall in first floor, Shear deformation that caused the linear deformation makes hysteresis
curves linear with no energy dissipation.
Full panel structure, “F2S2005” model, absorbed base shears are increased. Energy curve in this model is
fatter than 004 models, but it has little energy dissipation in compare with full frame.
Soft story frame, F5S4003, has same base shear like bare frame, but soft story frame cannot sustain the
record.
Model, that has some walls in first story absorbed base shear more than bare and soft story frame.
Deformation response of frame is almost linear and has little damping by narrow hysteresis loops.
Deformation and damping increased by added panel. No failure occurred in full panel model. The energy
dissipation is more than soft storey frames, but less than bare frame.
Damping of full panel system is only 7% of bare frame. Soft story frame in this case has 10% damping of
full panel system.
Linear analysis is not commercial. It has no accurate related to nonlinear analysis for these models. As it
shows, stress distribution is changed in nonlinear analysis because of crack effect. Linear analysis does not
have correct response for base shear. In full frame structure maximum base shear in nonlinear is equal to
0.55 of linear analysis with same deformation value. In nonlinear cases with soft story, base shear is
reduced in compare of linear analysis, 2 to 3 times.
Any stress figure shows the critical corner at first story level in frame with soft story. Conjunction in corner
of first story level reaches to crack stress during record. In linear analysis stress, variation is symmetric and
has similar tensile and compressive maximum stress. Tensile stress cannot be got more value than crack
limit, and it shows the non-realistic result of linear analysis in compare to nonlinear analysis.
Models that have 25% wall surface in first floor. Drift rate of this model shows the more homogeneous
drifts than soft story frame. Opposite of soft story frame most of drifts is not occurs in first floor. Corner
columns treated in flexural deformation but middle columns have shear behavior.
Bare frames reach to plastic point in columns during record. Different behavior of frames cause of lateral
displacement shows that homogenous stiffness in height of frames, first mode of deformation is governed.
For soft story high frames because of height of frames, second mode in lateral deformation is participated.
By adding panel, first mode would be the governed mode in frame.
Based on this study maximum relation of length to height of frames are better to be 1.25.
Based on the hysteresis curves bare frames has most energy loss in compare of another frame. Soft story
frames has energy dissipation more than full panel system and less than bare frames. Full panel system
response based on hysteresis curve is linear and has little damping.
Maximum stresses in beams and walls are occurred between first corner and L/4 of spans.
For soft story frame, the value of base shear in nonlinear analysis is 0.21 of linear analysis, and this value is
0.85 for full panels. It shows that full panel structures have a linear behavior in compare of soft story and
frame structures.
10. REFERENCES
1. Salmon, D. C., And Einea A. ” Partially Composite Sandwich Panel Deflections”, ASCE, Journal Of
Structural Engineering, Vol. 121, No. 4, 1995;778-783
2. Moehle, J.P.,” Seismic Analysis of R/C Frame-Wall Structures”, ASCE, Journal of Structural Engineering,
Vol. 110, No. 11, 1984; 2619-2634
3. Moehle, J.P. “Seismic Response of Vertically Irregular Structures”, ASCE Journal of Structural Engineering,
Vol. 110, No. 9, 1984; 2002-2014
4. Lu, Yong,” Comparative Study of Seismic Behavior of Multistory Reinforced Concrete Framed Structures”,
ASCE, Vol. 128, No. 2 2002; 169-178
5. Wood Sharon L, "Seismic Response Of RC Frames With Irregular Profiles”, Journal Of Structural
Engineering. Vol.118, No. 2, 1992, PP 545-566
6. Jahanpoor, A.R.," An Estimate Of Ductility Behavior Of 3D Wall Panels Subjected To Cyclic Shear Loads" ,
M.Sc. Dissertation , Amirkabir University Of Technology ,March 2003
7. Rezaifar, Omid, "Nonlinear Dynamic Behavior of Combined System (3Dwall Panel +Frame) Under Cyclic
Loading", M.Sc. Thesis, Amirkabir University Of Technology, September 2003.
8.M. Z. Kabir, Omid RezaiFar And M. R. Rahbar, " Non-Linear Dynamic Behavior Of Combined System On
RC Frame Pre-cast 3d Wall Panels With Irregularities In Vertical Stiffness",13th World Conference On
Earthquake Engineering, Vancouver, B.C., Canada, August 1-6, 2004,Paper No. 3134
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