Chapter 5
EXPERIMENTAL V ALIDATION OF FINITE ELEMENT M ODELS
5.1 INTRODUCTION
Shake table is a basic testing facility for development of earthquake resistant
techniques. This is a platform excited with hydraulic actuators to simulate different types
of periodic and random motions, such as artificial earthquakes and other dynamic testing.
This is the only experimental technique available for direct simulation of inertia forces,
which can be used to simulate different types of motion such as recorded earthquake
ground motions, sine sweeps, etc. Shake table tests results enhance further the
understanding of the behaviour of structures and calibration of various numerical tools
used for analysis. This facility can be utilized for verification of earthquake resistant
design of buildings, other structures, mechanical components, devices, etc. The shake
table facility at Earthquake Engineering and Vibration Research Centre (EVRC) at
Central Power Research Institute (CPRI), Bangalore is used to carryout the sine sweep
tests on 2D RC frame with and without masonry infill. Analysing the results of sine
sweep test, the natural frequencies and damping of the RC frames are obtained. The tests
are conducted for all configurations of masonry infill in 2D RC frames of one bay three
storeyed models using sine sweep method to find the natural frequencies and damping in
the in plane direction.
5.2 TEST M ETHODS
Presently the test methods belong to three major categories. They are proof
testing, generic testing and fragility testing. Proof testing is used to qualify the structure /
equipment for a particular requirement. The structure / equipment must be subjected to
the particular response spectrum, time history, or other parameters defined for the
mounting location. Generic testing may be considered as special case of proof testing.
The objective is to show the qualification for a wide variety of application during one
test. Fragility testing is used to determine the ultimate capability of the
structure/equipment. Such information may be used to prove adequacy for a given
requirement or application. The types of motion available to simulate the seismic
environment are of two types; single frequency and multiple frequencies. The method
chosen will depend on the nature of the expected vibration environment and also on the
nature of the structure
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5.2.1 SINGLE FREQUENCY AND MULTIPLE FREQUENCY TESTS
When the seismic ground motion has been filtered due to predominant structural
mode, the resulting floor motion may consist of one predominant frequency. In this case,
a short duration steady state vibration can be a conservative input excitation to the
structures, Further; single frequency testing may be used to determine the natural
frequencies and damping of the structures. If it can be shown that the structure has no
resonances, or only one resonance or resonance are widely spaced and do not interact, or
if otherwise justified, single frequency test may be used to fully test the structure.
Multiple frequency testing is intended to provide a broad band test motion that is
particularly appropriate for producing a simultaneous response from all modes of a multi
degree of freedom system. This testing provides a closer simulation of a typical motion
without introducing a higher degree of conservation. Consideration must also be given to
the choice of single axis or multiple axis testing. Seismic ground motion occurs
simultaneously in all directions in a random fashion. However, for test purposes, single
axis, biaxial and tri-axial tests are allowed. If single axis or biaxial tests are used to
determine the three dimensional environment, they should be applied in a conservative
manner to account for the absence of input motion in other orthogonal directions.
5.2.2 SINGLE AXIS, BIAXIAL AND T RI-AXIAL TESTS
Single axis test should be conducted when the input motion can be shown to be
essentially unidirectional, or when the equipment / structure tested can be shown to
respond independently in each of the three orthogonal axes. Biaxial tests should be
performed with simultaneous inputs in a horizontal and vertical axis. The selection of the
horizontal axis may include the principal axes or some other direction selected to expose
potential failure mode. Tri-axial tests are performed with a simulator capable of
independent motions in all three orthogonal directions. Among all the above methods, triaxial test is most suitable since earthquake produces random motions simultaneously in
all three directions.
5.3 SHAKE TABLE TESTS ON 2D RC FRAMES
RC frame structures are constructed outside the laboratory and suitable
arrangements were made to move the frame structures to the shake table. Precautions
were taken such that no structural damage occurs during transportation and placing of the
structure on the shake table. 5T forklift is employed to carry the frames into the
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laboratory and then 15T overhead crane was used to place the specimen on the shake
table (Refer fig.5.1 to 5.8).
Fig.5.1: Infill model mounted on Shake table
Fig. 5.2: Infill model mounted on Shake Table
Fig. 5.4: Stilt model mounted on shake table
with accelerometers fixed
Fig. 5.3: Infill with accelerometer fixed
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Fig.5.6: Model being shifted to shake table
Fig.5.5: Model being shifted using fork lift
Fig.5.8: Stilt frame models on shake table
Fig.5.7: Models on the Shake table
EVRC, housing the tri-axial shake table with six degrees of freedom, capable of
performing a diverse range of seismic qualification test requirements on structures,
equipments, sub structures and components as per national & international standards has
been established at CPRI, Bangalore in the year 2003. The tri-axial shake can strictly
simulate the earthquake ground motion without any distortion. The shake table can
vibrate in three axes with six degrees of freedom with a 10T pay load capacity of all
welded steel construction. The advanced control system allows the reproduction of
earthquake ground motions with high precision and little distortion. The RC frames are
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mounted on the shake table as shown in fig. 5.1 to 5.8. The shake table at EVRC, CPRI in
Bangalore is shown in fi.5.8 (a).
Fig.5.8 (a): Shake Table Facility at EVRC, CPRI, Bangalore
During pre-testing, the frame structure is thoroughly checked for any cracks or
damage after placing it on the shake table. At specified locations on the frames,
accelerometers were mounted and the accelerometers were connected to the data
acquisition system.
Sine sweep tests are conducted along the in-plane direction as exploratory tests to
determine the natural frequencies and damping at very low acceleration level so that the
masonry infill and RC frames are not damaged. After each tests the frames are
thoroughly checked for any damage or cracks in the masonry infill and RC frames. The
frames are then removed from the shake table, taken outside the laboratory and the
masonry infill is removed at ground floor level using mechanical cutting machine without
damaging the RC frame. The specimen is again placed on the shake table and testing
continued.
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5.3.1 A CTUATORS
The tri-axial shake table consists of eight servo hydraulic actuators (4 vertical and 4
horizontal) to provide the motion inputs. Actuators change their alignment as tests are
run, with self aligning bearing assemblies. Each of the actuators has two hydraulic
bearing assemblies, one at each end of the cylinder. Actuators are fitted with three –stage
servo valve. The shake table is mounted on a concrete base of dimensions 15mx15mx5m
weighing 2500T. Table 5.1 & 5.1(a) give the details of shake table & details of actuators.
Table 5.1 Salient features of Shake table facilities of CPRI, Bangalore
Description
Specification
Maximum pay load
100 kN
Table dimension
Exciting direction
Degrees of freedom
Maximum height of specimen
3mx3m
X,Y,Z (Simultaneous, Individual)
Six, 3 translational, 3 rotational
10m
Displacement /Maximum stroke – X& Y
Z-direction
150mm
100mm
Velocity
Acceleration
Frequency range
Yawing moment
Overturning moment
Actuators:
Vertical
Horizontal
Control system
1000mm/s (X,Y& Z)
1.0g
0.1 to 50Hz
100kN-m
400kN-m
4nos of 180kN
4nos. of 150kN
DCS2000 (Digital Control System)
Table 5.1(a): Details of actuators
Vertical Actuators
Horizontal Actuators
Quantity, Nos
4
Quantity, Nos
4
Dynamic Thrust
170 kN
Dynamic Thrust
120 kN
Static Thrust
± 211 kN
Static Thrust
± 154 kN
Supply Pressure
280 Bar
Supply Pressure
280 Bar
Maximum Velocity
1.0 m/sec
Maximum Velocity
1.0 m/sec
Working Stroke
± 100 mm
Working Stroke
± 150 mm
Total Stroke
± 119 mm
Total Stroke
± 169 mm
Bearings
Hydrostatic
Bearings
Hydrostatic
5.3.2 CONTROL SYSTEM
Digital Control system of tri-axial shaker system has hardware and software. The
hardware is a digital Signal Processing (DSP) card, which is floating point digital signal
processor providing real time processing. The DSP card controls the servo hydraulic
46
system through the use of transducers and servo valves which, being analogue, are
interfaced to it through a number of conditioning cards. Multiple safety limits can be set
on any signal with the limit acting among indicate, trip or shut.
5.4 RESONANCE SEARCH TEST
In this test, a sinusoidal input with continuously varying frequency at 1 octave
/min is applied to the structure in the in-plane direction. The frequency is varied from 0 to
50 Hz. The percentage of steady state resonance response obtained depends on the sweep
rate and the damping of the structure. Maximum response is obtained separately at every
frequency in the test range. Consequently, this test produces the most thorough search for
all resonant frequencies and it is customarily used for this purpose as an exploratory test,
with a low input level. At resonance frequency the transfer function (TF) of response to
input motion generally exceeds 2, there is a phase shift between input and response
motion and also there is sudden dip in the coherence at the point. Table 5.2 gives
Resonance test parameters. The transfer functions of response to input motion at natural
frequency in the analysis is presented in fig. 5.11(a) & 5.11(b). The experimental results
are tabulated in table 5.3, 5.4 & 5.5.
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5.5 ANALYSIS USING DATA A NALYSIS PACKAGE (DAP)
Tri-axial shake table is excited as per the test parameters. The responses of the
accelerometers are recorded during testing. In order to evaluate the damping values and
identify the natural frequencies, the accelerometer responses are analyzed using, Data
Analysis Package (DAP) software. Using the transfer functions, the natural frequencies
are identified and the corresponding damping values are calculated using Half-Power
Band width method. A typical calculation to find damping is shown in fig. 5.9
Fig.5.9: Natural Frequency from transfer function
From the transfer function the natural frequency (ω) of 5.75 Hz is identified and
the magnification of 7.8481 m/s2 at this frequency is recorded. The frequency values ω1
and ω2 are obtained by multiplying the magnification value by 0.707 as shown in 5.9.
(ω) = 5.75Hz, ω1 = 5.644 & ω2 = 5.8692 Hz
Damping (ω) =
ω2 − ω1
5.862 − 5.644
x100 =
x 100 = 5.8692%
2ω
2 x5.75
5.6 CONSTRUCTION OF 2D RC FRAMES
Four 2-D frames 1 bay 3 storey frames were cast and the models consist of beams
and columns of cross section 100mmx75mm. The concrete mix is prepared using
ordinary Portland cement, fine sand and crushed gravel (<10mm) having a ratio as per
mix design for M25 concrete from IS: 10262-1982. Cement, sand and stone aggregates
are measured individually using weighing balance and machine mixed. As per IS: 5161959 edition 1.2, representative samples of 100x100x100 mm size cubes were cast at
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each stage and tested for evaluation of compressive strength. The reinforcement in beams
consist 2 nos. of 6 mm dia. MS bars throughout the member length. At the beam column
junction, both the top and bottom bars of the beam are provided with adequate
development length (development length + 10 times diameter of the bar as per IS 4562000 and SP-34. Shear reinforcement consists of 3mm MS bars having spacing of 75mm
c/c. Hoops are also provided at beam-column junctions. Column reinforcement consists
of bars are 4 nos. of 8mm dia. bars. The lateral ties consist of 3 mm diameter MS bars
placed at 75mm c/c. commercially available bricks are used for infill panels as shown in
the fig.5.10. The 4 mm diameter wires are wound at 200mm spacing in vertical and
horizontal directions on both faces of brick masonry and also wires on both faces were
stitched by 4mm wire in the transverse direction to achieve contained masonry.
Properties of different materials used in the experimental program as well as in the FE
analysis are presented in table 5.2.
Fig. 5.10: Infilled RC frame Model on Shake Table
5.7.1 FINITE ELEMENT FORMULATION
SOLID65 is used for the 3-D modeling of solids with or without reinforcing bars
(rebar). The solid 65 is capable of cracking in tension and crushing in compression. In
concrete applications, for example, the solid capability of the element may be used to
model the concrete while the rebar capability is available for modeling reinforcement
behavior. Other cases for which the element is also applicable would be reinforced
composites, and geological materials. The element is defined by eight nodes having three
49
degrees of freedom at each node: translations in the nodal x, y, and z directions. Up to
three different rebar specifications may be defined. The concrete element is similar to the
SOLID45 (3-D Structural Solid) element with the addition of special cracking and
crushing capabilities. The most important aspect of this element is the treatment of
nonlinear material properties. The concrete is capable of cracking (in three orthogonal
directions), crushing, plastic deformation, and creep. The rebar are capable of tension and
compression, but not shear. They are also capable of plastic deformation and creep. The
element solid 65 and solid 45 are shown in fig.5.10 (a) and fig.5.10 (b) respectively.
Fig.5.10 (b): Solid 45 Element
Fig.5.10 (a): Solid 65 Element
The one-dimensional creep and plasticity behavior for SOLID65 reinforcement is
modeled using LINK8 Element. The 3-D spar element is a uni-axial tension-compression
element with three degrees of freedom at each node: translations in the nodal x, y, and z
directions. As in a pin-jointed structure, no bending of the element is considered. The link
8 element is shown in fig. 5.10(c).
Fig. 5.10(c): Link Element (Spar 8)
The geometry of 2D models is developed as per the dimensions and properties for
different materials such as concrete; steel and masonry are assigned as per table 5.2. The
RC frame members are modeled by using 8 noded solid 65 elements, the masonry
elements are modeled by using 8 noded solid 45 elements and the reinforcement is
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modeled by using Link 8 spar elements. The element aspect ratio has been maintained at
1.0. Fig.5.10 (d) shows one bay three storey 2D RC frame with contained masonry panels
meshed using link8 elements representing reinforcement in vertical and horizontal
directions and the fig.5.10 (e) shows the reinforcement elements. Modal analysis is
carried out and fundamental natural frequencies for all load cases are tabulated in table
5.4, 5.5and 5.6. The spectral analysis is carried out on the models for three spectral data
namely IS: 1893 Zone IV response spectrum IS: 1893 Zone V response spectrum and
Kobe earthquake spectrum. The response in terms of acceleration is observed in all the
models and the values are tabulated as shown in 5.6 & 5.7.
Fig.5.10 (d): FE Model
Fig. 5.10(e): Containment pattern
5.7.2 FINITE ELEMENT ANALYSIS
Two types of analysis are performed to study the behaviour of 2D-infilled RC frames
with plain and contained masonry, namely
•
Modal analysis
•
Response spectrum analysis
Modal Analysis: Modal analysis is the study of natural dynamic characteristics of
structures.
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This analysis characterizes the dynamic properties of an elastic structure by
identifying its mode of vibration. The response of the structure is different at each of the
different natural frequencies. These deformation patterns are called mode shapes. Both
natural frequency and mode shape are used to help the design of structural system mainly
for dynamic applications.
Response spectrum analysis: The spectrum is a graph of spectral value versus frequency
that captures the intensity and frequency content of time-history loads. A response
spectrum represents the response of single-DOF systems to a time-history loading
function. It is a graph of response versus frequency, where the response might be
displacement, velocity, acceleration, or force. It reflects the frequency content, amplitude
of ground motion and effect of subsequent filtering by the structure. Acceleration
spectrum is a plot of natural period of vibration of single degree of (SDOF) oscillator
with specific value of damping versus peak absolute acceleration of oscillator mass when
subjected to a base acceleration equal to the earthquake accelerogram (i.e., ground
acceleration). The design response spectrum is a smooth response spectrum specifying
level of seismic resistance required for the design.
The response history analysis (RHA) procedure provides structural response as a
function of time, but structural design is usually based on the peak values of forces and
deformations over the duration of the earthquake-induced response. The peak value of the
nth mode contribution to response can be obtained from the earthquake response spectrum
or design spectrum.
5.8 DIAGONAL STRUT MODEL A NALYSIS OF FRAMES
The various frames were also analyzed by incorporating diagonal struts to replace
the infill masonry in the RC frames as proposed by Stafford Smith using STAAD Pro
software for the purpose of comparing the results. The various models are shown
fig.5.12. The results obtained on these models are tabulated in tables 5.4 & 5.5.
5.9 MODEL DETAILS
Designation of various models used in the experimental program is as given below.
•
1B3S1-one bay three storey bare frame
•
1B3S2-one bay three storey frame with plain masonry infill
52
•
1B3S3-one bay three store frame with contained masonry infill
•
1B3S4-one bay three storey frame with plain masonry infill with stilt
•
1B3S5-one bay three storey frame with contained masonry infill with stilt
Table 5.2: Material Properties
Sl.No
1
2
3
Material
Concrete (M25)
Steel(HYSD Bars)
Brick Masonry
Young's
Modulus, E
( N/mm2 )
25000
200000
1500
Poisson's Ratio, µ
0.17
0.30
0.15
Density, ρ
(Kg/m3 )
2500
7850
2000
The above values have been adopted from the literature and from IS codes IS456-2000 and IS-1786 -1979.
Table 5.3: Resonance search test parameters
Sl. No
Description
Remarks
1
Type of vibration
Sinusoidal sweep
2
Axis of vibration
In-plane direction
3
Frequency(Range)
0 to 50 Hz
5
Acceleration (Peak)
0.1g
6
No. of sweeps
One up sweep per axis
Frequency range of operation for shake table test is only from 0-50 Hz. Natural
frequency up to 50 Hz only could be identified.
5.10
DISCUSSION OF RESULTS
Finite Element analysis is carried out on 2D RC frames using classical FE
software ANSYS ver.11. The results of the numerical analysis are listed in table 5.4 to
5.7. Shake table tests were carried out along the In-plane direction on bare frame and
different combinations of RC frames with contained masonry infill panels and frames
with plain masonry infill panels. The responses of the structures were recorded and the
resonant frequencies were obtained. The resonant frequencies obtained from the
experiments are presented in table 5.4, 5.5 & 5.6 and the top storey acceleration
responses are presented in Table 5.6 & 5.7. The typical deflection diagrams and stress
contour patterns for bare frames, plain masonry and contained masonry infill frames are
53
shown in fig. 5.13, 5.14 & 5.15 respectively and for plain masonry & contained masonry
infilled frame with stilt floor are shown in fig.5.16 & 5.17. Very encouraging results were
observed and numerical results obtained on FE models were found to be in good
agreement with experimental results.
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Table 5.4: Natural frequencies for in-plane shaking
SL. No
MODEL
Shake Table
Frequency (Hz)
FE Model
Frequency (Hz)
Strut Model
Frequency (Hz)
1.
1B3S1
14
15.572
30.54
2.
1B3S2
29.50
33.258
34.42
3.
1B3S3
35.5
37.552
-
4.
1B3S4
15.50
16.74
14.095
5.
1B3S5
15.80
16.897
-
Table 5.5: Natural frequencies for out of plane shaking
SL. No
MODEL
Shake Table
Frequency (Hz)
FE Model
Frequency (Hz)
Strut Model
Frequency (Hz)
1.
1B3S1
20.500
22.309
19.140
2.
1B3S2
11.000
14.779
13.266
3.
1B3S3
8.500
14.837
-
4.
1B3S4
12.200
15.296
14.00
5.
1B3S5
12.500
16.897
-
Table 5.6: Acceleration and damping for in-plane excitation
SL.
No
MODEL
Designation
Maximum acceleration
(m/s^2)
Frequency & Damping
Shake table
1.
1B3S1
8.0910
6.0387
Natural frequency
(Hz)
29.5
2.
1B3S2
5.3110
4.5900
35.5
4.47
3.
1B3S3
5.4400
4.5950
30.5
6.47
4.
1B3S4
5.5820
4.8100
15.5
5.67
5.
1B3S5
8.2230
7.2680
15.0
5.67
Shake Table
FE Model
55
Damping
(%)
5.93
Table 5.7: Top storey acceleration for in-plane excitation
Top storey Acceleration response
Sl.
No.
Model
Designation
Zone-IV
Shake
FE
table
analysis
Zone-V
Shake
FE
table
analysis
Kobe
Shake
table
FE
analysis
1.
1B3S1
8.0910
6.0387
9.842
9.2020
30.9990
28.4580
2.
1B3S2
5.3110
4.5900
9.367
6.9618
11.8590
12.6200
3.
1B3S3
5.4400
4.5950
8.223
6.9620
9.0890
12.3900
4.
1B3S4
5.5820
4.8100
9.432
7.2879
14.2230
13.0190
5.
1B3S5
8.2230
8.2230
9.019
7.2676
12.1190
9.2857
Fig. 5.11(a): Transfer function with a natural frequency of 31Hz
Fig. 5.11(b): Transfer function with a natural frequency of 15Hz
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5.11 CONCLUSION
The results of the experimental tests compared with the results obtained from FE
model analysis clearly bring out the influence of masonry infill and contained masonry
infill on fundamental natural frequency and other dynamic characteristics of 2D RC
frames. Each test gives an insight on the influence of both the mass and stiffness
characteristics of the infill panel on RC frames. The effect on resonant frequency is
considerable due to change in position of infill in the RC frames. The experimental
results are in good agreement with the results obtained on FE models.
a) Bare frame
b) Fully infilled frame
c) Infilled model with stilt floor
Fig. 5.12: Strut models
Vertical deflection (Uy)
Lateral defection (Ux)
Deflection (Uz)
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Normal stress (Sx)
Fig.5.13: Typical deflected shape and stress contour pattern in bare RC frames(load case 1 only shown)
Lateral defection (Ux)
Vertical deflection (Uy)
Deflection (Uz)
Normal stress (Sx)
Fig.5.14: Typical deflected shape and stress contour pattern in plain masonry
infilled RC frames(Results for load case 1 only shown )
58
Deflection (Uz)
Normal stress (Sx)
Lateral defection (Ux)
Vertical deflection (Uy)
Fig.5.15: Typical deflected shape and stress contour pattern in contained masonry
infilled RC frames (Results for load case 1 only shown in the contours)
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Lateral defection (Ux)
Vertical deflection (Uy)
Deflection (Uz)
Normal stress(Sx)
Fig.5.16: Typical deflected shape and stress contour pattern in plain masonry infilled
RC frame with stilt floor(Results for load case 1 only shown)
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Lateral deflection (Ux)
Vertical deflection (Uy)
Normal stress (Sx)
Deflection (Uz)
Fig.5.17: Typical deflected shape and stress contour pattern in contained masonry infilled
RC frame with stilt floor (Results for load case 1 only shown)
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