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Chapter 5

EXPERIMENTAL VALIDATION OF FINITE ELEMENT MODELS

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 METHODS

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 TRI-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, tri-

axial 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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Fig. 5.3: Infill with accelerometer fixed Fig. 5.4: Stilt model mounted on shake table

with accelerometers fixed

Fig.5.1: Infill model mounted on Shake table Fig. 5.2: Infill model mounted on Shake Table

laboratory and then 15T overhead crane was used to place the specimen on the shake

table (Refer fig.5.1 to 5.8).

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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

Fig.5.7: Models on the Shake table Fig.5.8: Stilt frame models on shake table

Fig.5.6: Model being shifted to shake table Fig.5.5: Model being shifted using fork lift

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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).

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.

Fig.5.8 (a): Shake Table Facility at EVRC, CPRI, Bangalore

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5.3.1 ACTUATORS

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 3mx3m

Exciting direction X,Y,Z (Simultaneous, Individual)

Degrees of freedom Six, 3 translational, 3 rotational

Maximum height of specimen 10m

Displacement /Maximum stroke – X& Y

Z-direction

150mm

100mm

Velocity 1000mm/s (X,Y& Z)

Acceleration 1.0g

Frequency range 0.1 to 50Hz

Yawing moment 100kN-m

Overturning moment 400kN-m

Actuators:

Vertical

Horizontal

4nos of 180kN

4nos. of 150kN

Control system 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

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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 ANALYSIS 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) = =−

1002

12x

ω

ωω

75.52

644.5862.5

x

− x 100 = 5.8692%

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: 516-

1959 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 456-

2000 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.

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

Fig. 5.10: Infilled RC frame Model on Shake Table

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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.

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).

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

Fig.5.10 (a): Solid 65 Element Fig.5.10 (b): Solid 45 Element

Fig. 5.10(c): Link Element (Spar 8)

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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.

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.

Fig.5.10 (d): FE Model Fig. 5.10(e): Containment pattern

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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 ANALYSIS 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

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• 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 Material

Young's

Modulus, E

( N/mm2 ) Poisson's Ratio, µ

Density, ρ

(Kg/m3 )

1 Concrete (M25) 25000 0.17 2500

2 Steel(HYSD Bars) 200000 0.30 7850

3 Brick Masonry 1500 0.15 2000

The above values have been adopted from the literature and from IS codes IS-

456-2000 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

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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

Shake Table FE Model Natural frequency

(Hz)

Damping

(%)

1. 1B3S1 8.0910 6.0387 29.5 5.93

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

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Table 5.7: Top storey acceleration for in-plane excitation

Sl.

No.

Model

Designation

Top storey Acceleration response

Zone-IV Zone-V Kobe

Shake

table

FE

analysis

Shake

table

FE

analysis

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.

Lateral defection (Ux) Vertical deflection (Uy)

a) Bare frame b) Fully infilled frame c) Infilled model with stilt floor

Fig. 5.12: Strut models

Fig.5.13: Typical deflected shape and stress contour pattern in bare RC frames(load case 1 only shown)

Normal stress (Sx) Deflection (Uz)

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Fig.5.14: Typical deflected shape and stress contour pattern in plain masonry

infilled RC frames(Results for load case 1 only shown )

Lateral defection (Ux) Vertical deflection (Uy)

Deflection (Uz) Normal stress (Sx)

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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)

Deflection (Uz) Normal stress (Sx)

Lateral defection (Ux) Vertical deflection (Uy)

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Normal stress(Sx) Deflection (Uz)

Vertical deflection (Uy) Lateral defection (Ux)

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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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)

Lateral deflection (Ux) Vertical deflection (Uy)

Deflection (Uz) Normal stress (Sx)