CONDITION ASSESSEMENT OF STRUCTURES USING

VIBRATION TECHNIQUE

C.K.FAIZAL (2005CES3183)

DEPARTMENT OF CIVIL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY DELHI

MAY 2007

CERIFICATE

“I do certify that this project report explains the work carried out by me in the

M.Tech project under the supervision of Dr.SURESH BHALLA and co-supervision of

Prof. ASHOK GUPTA .The contents of this report including text, figures tables

etc.have not been reproduced from other sources such as books, journals, reports,

manuals, websites etc.Wherever limited reproduction from another source had been

made the source had been duly acknowledged at that point and also listed in the

reference.”

C.K.Faizal.

(2005CES3183)

CERTIFICATE This is to certify that the M.Tech project thesis entitled “Condition

Assessment of Structures using Vibration Technique” Submitted by C.K.Faizal

(2005CES3183) to the Indian Institute of Technology, Delhi is record of original

bonafide research work carried out by him.

The contents of this report have not been submitted to any other University or

Institute for the award of any degree or diploma.

(Dr. Suresh Bhalla) (Prof. Ashok Gupta) Supervisor Co-Supervisor

Department of Civil Engineering, Department of Civil Engineering,

Indian Institute of Technology, Indian Institute of Technology,

New Delhi – 110016 New Delhi-110016

CERTIFICATE This is to certify that the M.Tech project thesis entitled “Condition

Assessment of Structures using Vibration Technique” Submitted by C.K.Faizal

(2005CES3183) to the Indian Institute of Technology, Delhi is record of original

bonafide research work carried out by him.

The contents of this report have not been submitted to any other University or

Institute for the award of any degree or diploma.

(Dr. Suresh Bhalla) (Prof. Ashok Gupta) Supervisor Co-Supervisor

Department of Civil Engineering, Department of Civil Engineering,

Indian Institute of Technology, Indian Institute of Technology,

New Delhi – 110016 New Delhi-110016

ABSTRACT

Structural Health Monitoring holds the Promise for improving the structural

performance with an excellent cost /benefit ratio. Condition assessment is a technique

used in health monitoring in the damage detection, to ensure the serviceability and the

durability of the structures.

In this report condition assessment of the structures using low frequency technique is

being done through experimental modal analysis and computational analysis software

ANSYS 9.0 over structural elements beam and steel frame.

In the Experimental Modal Analysis, investigation is carried over a 2m and 4m

Reinforced concrete beam and rectangular hollow section steel frame.

Response of the structure is obtained through accelerometer, PZT and

electric strain gauge

Aglient Multimeter is used as data analyzer for data acquisition

FFT analysis and FRF is carried out using MATLAB

In the computational Analysis using ANSYS 9.0 the Modal Analysis is done both in

the 1D and 3D modeling. Damage induced analysis is carried in the ANSYS 9.0 and

the difference in the modal frequency is noted, which was compared in the

experimental modal analysis of the damage induced analysis of the beam.

In 1D and 3D modal analysis experimentally and analytically the results were found

in close agreement with small error. Damage induced Analysis is done in 3D

modeling in computational analysis it has to be checked with the experimental modal

analysis.

Damage detection and Condition assessment of the beams were carried out with Mode

shape curvature and Flexibility method, changes in the beam element were compared

with the real time experimental specimen and damage detection was found in very

close approximation.

LIST OF TABLES Page Table 5.1 Elemental damage at various loads 26 Table 5.2 Change in flexibility of the beam elements 27 Table 5.3 Elemental damage in symmetric condition 28 Table 5.4 Elemental damage in unsymmetric condition 29 Table 5.5 Flexibility change in elements 4m beam 30 Table 6.1 1D ANSYS Output 20

Table 6.2 3D ANSYS Output 22

Table 6.3 3D ANSYS Output for Damaged Beam 25

Table 6.4 4m beam 1D analysis symmetric 39

Table 6.5 4m beam 1D analysis unsymmetric 39

Table 6.6 4m beam 3D analysis symmetric 40

Table 6.7 4m bean 3D analysis unsymetric 40

Table 7.1 Comparison of1D Analysis 42

Table 7.2 2m beam Experimental frequencies with PZT 43

Table 7.3 2m beam Experimental frequencies with Accelerometer 43

Table 7.4 2m beam Experimental frequencies with ESG 44

Table 7.5 4m beam experimental frequencies in symmetric 44

Table 7.6 4m beam experimental frequencies in unsymmetric 45

LIST OF FIGURES

Page

Fig 2.1 Function for FRF Generation 6

Fig 4.1 Bonded Metallic Strain Gauge 14

Fig 4.2 Basis Model of Accelerometer 15

Fig 4.3 Accelerometer attached to the Beam 16

Fig 4.4 Aglient Multimeter 16

Fig 4.5 Responses by PZT Patch 17

Fig 4.6 Regions Analyzed for PZT Patch 18

Fig 4.7 FFT Analysis for PZT Patch Response 18

Fig 4.8 FFT Analysis for Accelerometer Generated Response 19

Fig 4.9 FFT Analysis of Accelerometer generated response 20

Fig 4.10 Experimental mode shapes of frames 21

Fig 5.1 Experimental set up of 2m beam 31

Fig 5.2 PZT, Accelerometer and strain gauge set up 31

Fig 5.3 Crack formation at the center of 2m beam 31

Fig 5.4 Experimental set up for 4m beam 32

Fig 5.5 Crack formation at the loading point 32

Fig 6.1 1D Mode Shapes 35

Fig 6.2 Beam modeling 36

Fig 6.3 3D Mode Shapes 37

Fig 6.4 3D Mode shapes of the damaged beam 38

NOMENCLATURE [F] Flexibility Matrix

][ "iF∆ Curvature Change at Location I

I Moment of Inertia

[K] Stiffness Matrix

m Mass of single degree of Freedom

M(x) Bending moment at a section of a beam

ω Angular Frequency

jα Scalar damage index for jth member

v” Curvature of the beam

ijβ Damage location for i th mode at j th location

ν Poisson’s ratio

*iiφφ Pre-damage and Post –damage i th mode shape vector respectively

[ ]φ Mode shape Matrix

Chapter 1 INTRODUCTION 1.1 BACKGROUND

Major civil engineering structures such as bridges, containment vessels, dams,

offshore structures, buildings etc. constitute a significant portion of the national

wealth. The maintenance costs of these structures is substantially high, and even a

small percentage reduction in the maintenance cost amounts to significant saving.

One of the most cost effective maintenance methods is structural health monitoring.

Early detection of problems, such as, cracks at critical locations, delaminations,

corrosion, spalling of concrete etc., can help in prevention of catastrophic failure and

structural deterioration beyond repair.

Structural health monitoring has great potential for enhancing the

functionality, serviceability and increased life span of structures and, as a result,

could contribute significantly to the economy of the nation. The concept of long-term

monitoring of civil engineering structures is evolving as a result of the requirement of

cost-effective maintenance of complex structures and the development of new sensor

technologies

1.2 IMPORTANCE OF CONDITION ASSESSMENT

Accurate Condition Assessment of civil engineering structures has become

increasingly important. The need for quantitative global damage detection methods

that can be applied to complex structures, has led to the development of methods that

examine changes in vibration characteristics of the structure. Doebling et al (1996)

provided an extensive overview of vibration-based detection methods. Those are non

destructive methods based on the fact that structural damage usually causes a decrease

in the structural stiffness, which produces changes in the vibration characteristics of

the structure. Damage is determined through the comparison between the undamaged

and the damaged states of the structure

The most common dynamic parameters used in damage detection are the natural

frequencies and the mode shapes. But changes in natural frequencies alone cannot

provide spatial information about structural damage. Therefore mode shape

information is additionally needed to uniquely localize the damage

1.3 OBJECTIVES AND SCOPE OF STUDY

The primary objective of this study is to identify the damage induced in the

structures using low frequency techniques, to locate the damage location and

determine the severity of the damage, so that the life span of the structures can be

assessed and maintenance cost can be reduced.

In this study, the investigation was carried out on concrete beams of 2m and 4m

length using low frequency techniques. The response of the beam was obtained from

accelerometer, piezoelectric ceramic patch and electric strain gauge. Further, from the

frequency response function, the modal frequencies were obtained and were compared

with the finite element method analysis.

Again, inducing damage in the beam, modal frequency has to be obtained, and

from the experimental modal analysis using the change in flexibility method and the

mode shape curvature method the condition assessment and damage detection has to

be carried out.

Experimental mode shapes of the structural elements were obtained using the

dynamic technique.

1.4 ORGANISATION OF THESIS This thesis consists of total of eight chapters including this introductory chapter.

Chapter 2 presents a detailed review of the literature work done earlier in the field of

the structural health monitoring (SHM). Chapter 3 presents the various damage

detection methods in SHM and their implication. Chapter 4 presents the experimental

work carried out in this project work under various boundary conditions and the

details of the experimental mode shapes of the steel frame. Chapter 5 presents the

computational method followed in this work to determine the damage location and

severity of the structural elements. Chapter 6 presents the numerical work carried out

in the ANSYS9.0 over structural elements and various elements used and modelling

details of the beams. Chapter 7 presents the comparison of the experimental and

numerical work carried in this project and details are shown in histograms. Finally,

conclusions and recommendations are presented in Chapter 8.

Chapter 2

LITERATURE REVIEW

2.1 INTRODUCTION

The interest in the ability to monitor a structure and detect damage at the

earliest possible stage is pervasive throughout the civil, mechanical and aerospace

engineering communities.

Existence of structural damage in an engineering system leads to

modification of the vibration modes. These modifications are manifested as changes

in the modal parameters (natural frequencies, mode shapes and modal damping

values), which can be obtained from results of dynamic (vibration) testing. Changes

in the modal parameters may not be the same for each mode since the changes depend

on the nature, location and severity of the damage. This effect offers the possibility of

using data from dynamic testing to detect, locate and quantify damage.

Modal parameters can be easily obtained from measured vibration responses.

The responses are acquired by some form of transducer, which monitors the

structural response to artificially induced excitation forces or ambient forces in the

service environment. Low input energy levels are sufficient to produce measurable

responses since the input energy is dynamically amplified.

2.2 EFFECTS OF STRUCTURAL DAMAGE ON FREQUENCY

The presence of damage or deterioration in a structure causes changes in the

natural frequencies of the structure. The most useful damage location methods (based

on dynamic testing) are probably those using changes in resonant frequencies because

frequency measurements can be quickly conducted and are often reliable. Abnormal

loss of stiffness is inferred when measured natural frequencies are substantially lower

than expected

2.3 METHODS OF DAMAGE DETECTION AND LOCATION

At modal nodes (points of zero modal displacements), the stress is minimum

for the particular mode of vibration. Hence, the minimal change in a particular modal

frequency could mean that the defect may be close to the modal node. The other

modal frequency variations can still be used to determine the magnitude of damage.

2.4 FACTORS TO CONSIDER USING NATURAL FREQUENCIES FOR

DAMAGE DETECTION IN PROTOTYPES

Some factors to consider when using vibration testing for integrity assessment

and for successful utilization of vibration data in assessing structural condition,

measurements should be taken at points where represented. The simplest way of

achieving this is to conduct a theoretical vibration analysis of the structure prior to

testing. The best positions would be those points where the sum of the magnitudes of

the mode shape vectors is maximized.

2.5 LOW FRQUENCY TECHNIQUE

Low frequency techniques are based on the analysis of structural dynamic

response measurements, typically made by subjecting the structure to low frequency

vibrations. By this analysis, a suitable set of parameters is identified, and any

variation in these parameters is an indication of the changing state of the structures.

Damage in a structure alters its modal parameters, namely the stiffness matrix and the

damping matrix .In these techniques, the structure is excited by appropriate means

and the response data is processed to obtain a quantitative index or a set of indices

representative of the condition of the structure.

2.6 EXPERIMENTAL MODAL ANALYSIS

Experimental modal analysis (EMA) was used to identify the modal

parameters of the structure: the resonant frequencies, modal damping ratios (MDR)

and mode shapes.

Linearity of the structural behavior is one of the basic assumptions of the

method. EMA can be used to monitor damage. Variations of the resonant frequencies

and mode shapes are mainly due to changes of the global and local linear stiffness

properties, while the variations of the MDR's are associated with an increase of the

internal energy dissipation or attenuation. Mode shapes are obtained by analysis of

the vibration response at multiple locations. Their changes are valuable indicators for

damage monitoring, since they provide local information.

2.7 TYPES OF VIBRATION

All vibration is a combination of both forced and resonant vibration. Forced

vibration can be due to

1. Internally generated forces

2 .Unbalances.

3. External loads.

4. Ambient excitation

Resonant vibration occurs when one or more of the resonance or natural

modes of vibration of a machine or structure is excited. Resonant vibration typically

amplifies the Vibration response far beyond the level deflection, stress, and strain

caused by static loading.

2.8 MODES

Modes (or resonance) are inherent properties of a structure. Resonances are

determined by the material properties (mass, stiffness, and damping properties), and

boundary conditions of the structure. Each mode is defined by a natural (modal or

resonant) frequency, modal damping, and a mode shape. If either the material

properties or the boundary conditions of a structure change, its modes will change.

For instance, if mass is added to a vertical pump, it will vibrate differently because its

modes have changed.

At or near the natural frequency of a mode, the overall vibration shape

(operating deflection shape) of a machine or structure will tend to be dominated by

the mode shape of the resonance.

2.9 FRF MEASUREMENTS

The frequency response function (FRF) is a fundamental measurement that

isolates the inherent dynamic properties of a mechanical structure. Experimental

modal parameters (frequency, damping, and mode shape) are also obtained from a set

of FRF measurements.

The FRF describes the input-output relationship between two points on a

structure as a function of frequency. Since both force and motion are vector

quantities, they have directions associated with them. Therefore, an FRF is actually

defined between a single input degree of freedom (point & direction), and a single

output degree of freedom.

Fig: 2.1 Functions for FRF Generation

An FRF is a measure of how much displacement, velocity, or acceleration

response a structure has at an output DOF, per unit of excitation force at an input

DOF. Figure so indicates that an FRF is defined as the ratio of the Fourier transform

of an output response (X (w)) divided by the Fourier transform of the input force (F

(w)) that caused the output.

Depending on whether the response motion is measured as displacement,

velocity, or acceleration, the FRF and its inverse can have a variety of names,

· Compliance = (displacement / force)

· Mobility = (velocity / force)

· Inheritance or Receptance = (acceleration / force)

· Dynamic Stiffness = (1 / Compliance)

· Impedance = (1 / Mobility)

· Dynamic Mass = (1 / Inertance)

2.10 MODAL ANALYSIS APPLICATION

Mode shapes and resonant frequencies of a structure (its modal response) can

be predicted by using a mathematical model known as a Finite Element Model

(FEM). An FEM uses points connected by elements possessing the mathematical

properties of the structure’s materials. Boundary conditions define how the structure

is fixed to the ground and what force loads are applied. After defining the model, a

mathematical algorithm computes the mode shapes and resonant frequencies. The

practical benefit is that it is possible to predict the vibration response of a structure

before it is even built.

After building the structure, it’s good practice to verify the FEM using

experimental modal analysis. This identifies errors in the model and leads to

improvements in future designs. Professionals can also use experimental modal

analysis without FEM models. In this case, the goal is to identify the modal response

of an existing structure in order to resolve vibration problems.

One of the common vibration problems identified by modal analysis is when

a forcing function excites the resonant frequency of a structure. A forcing function is

the mechanism that forces the structure to vibrate. Real world examples include

rotating imbalance in an automobile engine, reciprocating motion in a machine, or

broadband noise from wind or road conditions in a vehicle. The frequency of the

forcing function is extracted from a frequency domain analysis of its signal. When a

resonant frequency of the structure coincides with the frequency of the forcing

function, the structure may exhibit large vibrations that lead to fatigue and failure.

In this case, the mode-shape information can be used to redesign or modify

the structure to move the resonant frequencies away from the forcing function.

Structural elements can be added to increase the structure’s stiffness or simple

changes made to increase or decrease the mass. These changes will act to change the

structure’s resonance frequency values.

Chapter 3 DAMAGE IDENTIFICATION METHODS

3.1 INTRODUCTION

Based on the amount of information provided regarding the damage state,

Farrar and Jauregui (1998) defined four distinct objectives of damage detection

a) To identify the damage.

b) To determine the location of the damage.

c) To determine the severity of the damage.

d) To determine the remaining useful life of the structure.

3.2 DAMAGE INDEX METHOD

The damage index method was developed by Stubbs and Kim (1994) to locate

damage in structures given their characteristic mode shapes before and after damage

.For a structure that can be represented as a beam, a damage index, β , is developed

based on the change in strain energy stored in the structure when it deforms in its

particular mode shape. For location jth on the beam this change in the ith mode the

damage index β ij was defined as…

Where β ij = ∫∫∫ ΦΦ+Φ ∗∗L

i

L

i

b

ai dxxdxxdxx

0

2"2

0

"2" )]([))]([)]([( … (3.1)

∫∫∫ ∗ΦΦ+ΦL

i

L

i

b

ai dxxdxxdxx

0

2"2

0

"2" )]([))]([)]([(

Where )(" xiΦ and )(*" xiΦ are the second derivatives of the ith mode shape

corresponding to the undamaged and the damaged structures, respectively.

Here, ‘a’ and ‘b’ are the limits of a segment of the beam where the damage is

being evaluated. L is the length of the beam

For mode shapes obtained from ambient data, the modes are normalized such that

1}}{{}{ =nT

n M ψψ …. (3.2)

3.3 MODE SHAPE CURVATURE METHOD

Pandey, Biswas and samman (1991) assume that structural damage only

affects the structure’s stiffness matrix and its mass distribution. The pre and post-

damage mode shapes for the beam in its undamaged and damaged conditions can then

be estimated numerically from the displacement mode shapes with a central

difference approximation or other means of differentiation. Given the before and after

mode shapes, the author consider a beam cross section at location’ x ‘along the length

of the beam, v”(x) is

v”(x)=M(x)/(EI)

Where E is the modulus of elasticity and I the moment of inertia of the section.

From the equation, it is evident that the curvature is inversely proportional to the

flexural stiffness, EI. Thus, a reduction of stiffness associated with damage will, in

turn lead to an increase in curvature. Differences in the pre and post –damage

curvature mode shapes will, in theory be in the damage curvature mode shapes will in

theory be largest in the damaged region. For multiple modes the absolute values of

changes in curvature associated with each mode are summed to yield a damage

parameter for a particular location

3.4 CHANGE IN FLEXIBILTY METHOD

Pandey and Biswas (1994) show that for the undamaged and damaged

structures, the flexibility matrix, [F], can be approximated from the unit –mass-

normalized modal data as follows

[F] ∑=

ΦΦ≈n

i

Tiii

1

2 }{}{/1 ω ..…. (3.3)

and [F]* ∑=

ΦΦ≈n

i

Tiii

1

**2* }{}{/1 ω .…..(3.4)

Where ω I is the ith modal frequency, iφ ith unit –mass-normalized mode, n

the number of measured modes and the asterisks signify properties of the damaged

structure. From the pre and post –damage flexibility matrices, a measure of the

flexibility change caused by the damage can be obtained from the difference of the

respective matrices as

[ ∗−=∆ ][][] FFF …… (3.5)

Where ][ F∆ represents the change in flexibility matrix. For each column of

this matrix 11max ijj δδ = , i =1…………..n. The column of the flexibility matrix

corresponding to the largest change is indicative of the degree of freedom where the

damage is located.

3.5 CHANGE IN UNIFORM LOAD SURFACE CURVATURE

The coefficients of the ith column of the flexibility matrix represent the

deflected shape assumed by the structure with a unit load applied at the ith degree of

freedom. The sum of all columns of the flexibility matrix represents the deformed

shape assume by the structure if a unit load is applied at each degree of freedom and

this shape is to as the uniform load surface. Change in curvature of the uniform load

surface can be used to determine the location of damage. In terms of the curvature of

the uniform load surface, F”, the curvature change at location l is evaluated as

follows

=∆ "F Fi*”-F” …… (3.6)

Where ∆F” represents the absolute curvature change. The curvature of the

uniform load surface can be obtained with a central difference operator.

3.6 CHANGE IN STIFFNESS METHOD

Zimmerman and Kaouk (1994) have developed a damage detection method

based on changes in the stiffness matrix that is derived from measured modal data.

The eigenvalue problem of an undamaged, undamped structure is

( }0{}]{[][ =+ iKMi ψλ …… (3.7)

The eigenvalue problem of the damaged structure is formulated by first

replacing the pre-damaged eigenvectors and eigenvalues with a set of post-damaged

modal parameters and second, subtracting the perturbations in the mass and stiffness

matrices caused by damage from the original matrices. Letting dM∆ and dK∆

represents the perturbations to the original mass and stiffness matrices, the Eigen

value equation becomes

}0{}]]{[][[ ** =∆−+∆− iddi KKMM ψλ …… (3.8)

Two forms of a damage vector, }{ iD for the ith mode are then obtained by

separating the terms containing the original matrices from those containing the

perturbation matrices. Hence,

**** }]]{[][(}]){[][(}{ iddiiii KMKMD ψλψλ ∆+∆=+= ….. (3.9)

To simplify the investigation, damage is considered to alter only the

stiffness of the structure of the structure (i.e. ]0[=∆ dM ). Therefore, the damage

vector reduces to

*}]{[}{ idi KD ψ∆= .…. (3.10)

In a similar manner as the modal-based flexibility matrices previously

defined, the stiffness matrices, before and after damage, can be approximated from

incomplete mass-normalized modal data as

∑≈ TiiiK φφω 2][ ……. (3.11)

And ∑≈ TiiiK **2**][ φφω ……. (3.12)

Equation (6) is subtracted from equation (14) to obtain ][ dK∆ . This matrix

is multiplied by the ith damaged mode shape vector to obtain the ith damage vector as

shown in equation (4). A scaling procedure discussed by Zimmerman and kaouk was

used to avoid spurious readings at stiff locations of the measured response is lower.

Chapter 4

EXPERIMENTAL AND DATA PROCESSING TOOLS

This study has investigated the low frequency dynamic response technique

utilizing accelerometer, electrical strain gauge and piezoceramic (PZT) patches.

4.1 HARDWARE REQUIREMENTS

For practical application of the technique, the following hardware

components are used

1. Electrical strain gauge, accelerometer and piezoceramic (PZT) patches are

bonded to the structures, which acts as integrated sensors.

2. Data analyzer, for structural frequency response function acquisition. In

this study

34411A Agilent multimeter was used

3. A personal computer, for graphic control and display.

4. Electro Dynamic Shaker machine with its Function generator.

4.2 EXPERIMENTAL APPROACH

Build analytical models

- Determine theoretical sensitivity of method

- Address sensor placement

- Discuss the design of experiments

Experimental verification-

- Test simple structural level specimens with various damage, work up through

building block element

- Assess feasibility of implementing method in SHM system

System architecture

- Sensor integration

- Test samples with realistic sensors

- Test method on representative structures

4.3 STRAIN GAUGE

A strain gauge is a device used to measure deformation (strain) of an object.

The most common type of strain gauge consists of an insulating flexible backing

which supports a metallic foil pattern. The gauge is attached to the object by a suitable

adhesive. As the object is deformed, the foil is deformed, causing its electrical

resistance to change. This resistance change, usually measured using a Wheatstone

bridge, is related to the strain by the quantity known as the gauge factor.

Fig: 4.1-Bonded Metallic Strain Gauge

In this project two 5mm strain gauge with a gauge factor of 2.09 are attached

on the 4m steel beam. Both the gauges are attached at the centre parallel to the central

axis of the steel beam as shown in the pictures below:

In this study, a reinforced concrete beam of 4m lengths, 0.15m widths, 0.2m

heights were instrumented with electric strain gauge, peizoceramic patches and

accelerometers. Fig shows the measurement set up, consisting of the test structure,

digital multimeter, a personal computer and shaker machine. The structure was

excited by the shaker machine and the vibration responses were measured using the

Agilent 34411A digital multimeter. The multimeter records measurements from all

the sensors one by one.

In the case of ESG, the multimeter measures the resistance with time and was

used to convert it into strain. In the case of Accelerometer and PZT patch, the

instantaneous voltage across the terminals was measured in time domain.

In all the measurement, a sampling interval of 1 millisecond was set in the

multimeter. After each measurement, the data recorded in the multimeter was

transferred to the PC via the USB interface. Now, the transferred data was

transformed from time domain to frequency response functions (FRF) was obtained.

4.4 ACCLEROMETER

An accelerometer is a linear seismic transducer, which produces an electric

charge proportional to the applied acceleration. A simple model of an accelerometer is

shown in Figure. A mass is supported on a piece of piezoelectric ceramic crystal,

which is fastened to the frame of the transducer body. Piezoelectric materials have the

property that if they are compressed or sheared, they produce an electric potential

between their extremities, and this electric potential is proportional to the amount of

compression or shear. As the frame experiences an upward acceleration it also

experiences a displacement. Because the mass is attached to the frame through the

spring-like piezoelectric element, the resulting displacement it experiences is of

different phase and amplitude than the displacement of the frame. This relative

displacement between the frame and mass causes the piezoelectric crystal to be

compressed, giving off a voltage proportional to the acceleration of the frame.

Fig: 4.2 Basis model of Accelerometer

Fig: 4.3 Accelerometer attached to the beam

From the frequency response function, the first 3 modal frequencies were

obtained from the Accelerometer, PZT and ESG

The equipment used in the data acquisition was AGILENT MULTIMETER,

data was collected at an interval of 1millisecond and the duration of the data

acquisition was kept to 20sec. Fig: 4.4 show the front and the rear views of the

multimeter.

Fig: 4.4 Aglient Multimeters 4.5 EXPERIMENTAL ANALYSIS By conducting random vibration analysis on the Beam with the help of

impact hammer resistance is measured through electronic strain gauge and voltage

through accelerometer and peizoceramic patches. The data obtained is transformed

into frequency response function. From the plot modal frequencies of the first 3

modes is noted.

The smart piezo transducers were attached to the surface using CNX

adhesive and were soldered through wires to the multimeter. Multimeter was

appropriately calibrated to get the readings for time duration of 20 seconds with small

time interval of 1 milliseconds in order to capture the first few nodal frequencies Two

strikes were given by the hammer in order to generate sufficient response for time

duration of 20 seconds. These two strikes can be seen in the form of two peaks in the

fig:4.5. The response generated by the PZT patch and the region analyzed from the

response patch was shown in the fig: 4.6.The response of the PZT from time domain

to frequency domain through fast fourier transform and first three fundamental

frequency is considered for the analysis was shown in the fig:4.7.

4.5.1 Experiment on 2m concrete Beam

Experiment on 2m RC beam was carried out on a symmetric support condition

for the condition assessment as shown below

Simply supported overhanging 20cm on both sides.

RESPONSE FROM PZT(1)

-0.7-0.6-0.5-0.4-0.3-0.2-0.1

00.10.20.3

0 5 10 15 20 25

Time(Sec)

Volta

ge(V

)

Area Analyzed

Fig: 4.5 Responses by PZT Patch

Due to some uncontrolled noise, the damping nature is shown in the Response

of the PZT, in analysis it is eliminated by Filtering technique and the Frequency

Response

The following region was analyzed for frequency response to obtain the experimental

values of modal frequencies for the 4-meter concrete beam

Hammer 1

Hammer 2

Responses by PZT patch

Analyzed Response from PZT

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0 500 1000 1500 2000 2500 3000

Time (sec)

Volta

ge (V

)

Fig: 4.6 Regions Analyzed for PZT Patch

0

2 5

5 0

0 5 0 1 0 0 1 5 0 2 0 0

F r e q u e n c y ( H z )

Resp

onse

Fig: 4.7 FFT analyses for PZT patches

4.5.2 Experiment on 4m concrete beam

On 4m RC beam experiment was carried out in 2 support conditions as shown

below.Fig:4.8 shows the FFT analysis for the PZT patch response and the first 3

fundamental frequencies under the symmetric support condition. Fig 4.9 shows the

FFT analysis of the accelerometer generated response and first four fundamental

frequencies under the unsymmetric condition.

Similarly the experiment is repeated after inducing the damage in the RC

beam under the same support conditions. The fundamental frequencies of the

damaged RC beam were noted and condition assessments of the structures were

carried out.

1st mode at 41.16Hz

2nd mode at 60.78Hz

3rd mode at 98.566Hz

Supported condition1: Overhanging of 50cm on either side. (Symmetric)

Supported condition 2: Over hanging 50cm and 100cm on either side. (Unsymmetric)

- 5

0

5

1 0

1 5

2 0

2 5

0 2 5 5 0 7 5 1 0 0 1 2 5 1 5 0 1 7 5 2 0 0 2 2 5 2 5 0 2 7 5 3 0 0

F r e q u e n c y ( H z )

Res

pons

e(v)

1 s t m o d e a t 2 2 H z 2 n d m o d e a t 6 8 H z 3 r d m o d e a t 1 4 2 H z

Fig: 4.8 FFT Analyses for PZT Patch Response

(Support condition 1)

The first three distinct peaks in the FRF are seen at 14.53 Hz, 31Hz and

63.99Hz indicating them to be the first three modes of vibration for the 4-meter

concrete beam.

1st mode at 14.53Hz 2nd mode at 31Hz 3rd mode at 63.99Hz

0

10

20

0 50 100 150 200 250

Frequency (Hz)

Res

pons

e(v)

1st peak at 24.9 Hz 2nd peak

70.04 Hz 3rd peak at 130.03 Hz

4th peak at 195.4 Hz

Fig: 4.9 FFT Analyses for Accelerometer generated response

(Supported condition 2)

The peaks obtained using the PZT are at 24.90 Hz, 70.04 Hz, 130.03 Hz

and 195.40 Hz.

4.5.3 Experimental mode shapes on Steel frame

A hollow rectangular steel frame of sectional cross section .05m× .025m was

tested for experimental mode shapes using ICAT software. During experiment the

steel frame were held in free-free support conditions and the excitation was given a

plane at different equivalent point with the help of hammer which was connected to

the digital multimeter .The response were read at a point through out the experiment

with accelerometer and the response were directly read into FRF plot by multimeter .

The frame was modelled in the ICAT software with the same number of nodes

as the excitation points in the experiment and the FRF were assigned in the model at

their respective nodal point and analyzed.

The frame was analyzed in the ANSYS and frequencies were found, Table 4.1

shows the experimental and numerical frequencies of the frame.

Fig:4.11 shows the mode shapes obtained from the ICAT software .In the ansys as

the boundary condition were not simulated as in experimental conditions the result

were prone to erroneous .

Fig: 4.10 Steel frame

4.6 EXPERIMENTAL AND ANSYS MODAL FREQUECIES ON STEEL

FRAME

E X P E R I M E N T A L A N D A N S Y S M O D A L F R E Q U E N C Y

0

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

M O D E S

FREQ

UEN

CY(

Hz)

E X P E R I M E N T A L A N S Y S

E X P E R I M E N T A L 2 1 . 7 2 9 4 6 8 . 2 9 3 6 2 0 0 . 8 6 5 2 7 1 . 8 7 6 4 5 8 . 7 6 5 6 9 5 . 7 0 8 7 0 7 . 8 6 2 8 2 5 . 7 7 8 5 2 . 5 6 2

A N S Y S 2 1 . 1 4 9 7 3 . 9 8 4 2 1 5 . 2 2 2 8 4 . 1 2 4 7 3 . 5 2 4 7 1 9 . 6 1 3 7 3 2 . 8 5 1 8 5 5 . 2 2 3 8 7 5 . 2 5

1 2 3 4 5 6 7 8 9

Table 4.1: EXPERIMENTAL AND ANSYS FREQUENCIES OF STEEL FRAME

4.7 EXPERIMENTAL MODE SHAPES OF STEEL FRAME

MODE 1 MODE 2

MODE 3 MODE 4

Fig4.11: EXPERIMENTAL MODE SHAPES OF FRAME

MODE 5 MODE 6

MODE 7 MODE 8

4.8 CONCLUDING REMARKS

In this chapter the sensors used, the data acquisition, support conditions of the

beams with which the experiments were done and the steel frame on which the

experimental mode shapes was carried were described.

In the experimental mode shape on the steel frame the boundary condition

were just supported on the floor and in the ANSYS it was in free-free end condition

by which the ansys comparison was in erroneous.

Chapter 5 CONDITTON ASSESSMENT OF CONCRETE BEAMS

5.1 INTRODUCTION

In this chapter the condition assessment of the concrete beams was carried out

using Change in Flexibility Method and the Mode shape curvature method .The

experimental mode shapes was tried over a hollow rectangular cross-section steel

frame using the frequency response function in ICAT modeling software .

5.2 DAMAGE LOCATION AND IDENTIFICATION METHOD 2m BEAM

This method requires only the information of the natural frequency changes of

the damaged structure and the mode shapes of the undamaged structure. The basic

framework of this work has been presented in Naidu et al., 2002.

The governing equation of motion for dynamic system is

[M]{..x } +[C] {

.x } + [K] {x} = {F (t)} …. (5.1)

Where

[M]=Mass matrix; [C] =Damping matrix; [K] =stiffness matrix.

The eigen frequencies and mode shape vectors of the dynamic system is given by

{ω}= {ω1, ω2, ω3, ω4......} …. (5.2)

{Ф}= {Ф1, Ф2, Ф3, Ф4 ……} …. (5.3)

The angular frequency can be replaced by cyclic frequency, f, and as such set of

natural frequencies in Hertz is given by

{f}= {f1, f2, f3, f4 …} …. (5.4)

After the structure is damaged, the shift in frequency is given by,

{∆f}m= { ∆f1, ∆ f2, ∆f3, ∆f4, ……} …. (5.5)

Sorting the shift frequencies in the descending order we have

{∆f}m= { ∆f1, ∆ f2

, ∆f3, ∆f4

, ……} …. (5.6)

The Damage indicator or Damage metric, DI for each element is given by

DIx=∑

∑

=

=

∆

∆∆

m

i

i

m

i

iipx

f

fIEI

1

1 ; DIy=∑

∑

=

=

∆

∆∆

m

i

i

m

i

iipy

f

fIEI

1

1 ; DIz= ∑

∑

=

=

∆

∆∆

m

i

i

m

i

iipz

f

fIEI

1

1

Where m=number modes chosen

P=number elements in the structure

i=number chosen mode shapes

f∆ =shift frequency

E∆ =element deformation parameter.

ipxE∆ = longitudinal displacement of node i+ 1

ipyE∆ = ½*{curvature value of node i+1 + curvature value of node i)

ipzE∆ =rotation of node i+1 – rotation i)

The damage metric index computed for the damaged beam elements of the 2m

and 4m beam were shown below. Fig: 5.1 shows the elemental damage at various

loads over the 2m beam in the symmetric condition .In the figures a threshold damage

metric index of 70% were taken. The beam was divided in 50 elements so that each

element was of 4cm in length.

During experiment the loads were applied at the center and it is found that the

bending cracks were found at the center and the shear cracks the support conditions as

shown in the Fig:5.7 and Fig:5.9..From the figures shown below it was evident that

the elemental damage propagation were taking place at the center and support

condition.

In the 2m beam numerical analysis only the modal displacement were used

,hence the damage location were found to be in close approximation with the

experiment but the severity of the damage location were not in much correlation.

5 0 K N

7 0

7 5

8 0

1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8 3 1 3 4 3 7 4 0 4 3 4 6 4 9

E L E M E N T S N O

DAM

AGE

MET

RIC

7 0 K N

7 0

7 5

8 0

1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8 3 1 3 4 3 7 4 0 4 3 4 6 4 9

E L E M E N T S N O

DAM

AGE

M

ETR

IC

8 0 K N

7 0

7 5

8 0

1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8 3 1 3 4 3 7 4 0 4 3 4 6 4 9

E L E M E N T S N O

DAM

AG

E

MET

RIC

8 3 K N

7 0

7 5

8 0

1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8 3 1 3 4 3 7 4 0 4 3 4 6 4 9

E L E M E N T S N O

DAM

AGE

M

ETRI

C

Fig 5.1: ELEMENTAL DAMAGE AT VARIOUS LOADS

5.3 CHANGE IN FLEXIBILITY 2m BEAM

In this method the change in flexibility of the beam was calculated using the

pandey and biswas and the change in elemental flexibility was plotted.

Fig:5.2 shows the change in elemental flexibility of the 2m beam .From the

figures it is clear that the bending and the shear crack development at the center and

support was in correlation with the high flexibility change in the plots at the center

and support elements as shown below .

5 0 K N

0

0 . 0 0 0 0 0 0 0 0 2

0 . 0 0 0 0 0 0 0 0 4

0 . 0 0 0 0 0 0 0 0 6

0 1 0 2 0 3 0 4 0 5 0 6 0

E L E M E N T N O

FLE

XIB

ILIT

Y

7 0 K N

0

0 . 0 0 0 0 0 0 0 2

0 . 0 0 0 0 0 0 0 4

0 . 0 0 0 0 0 0 0 6

0 . 0 0 0 0 0 0 0 8

0 1 0 2 0 3 0 4 0 5 0 6 0

E L E M E N T N O

FLEX

IBIL

ITY

8 0 K N

0

0 . 0 0 0 0 0 0 0 4

0 . 0 0 0 0 0 0 0 8

0 . 0 0 0 0 0 0 1 2

0 . 0 0 0 0 0 0 1 6

0 1 0 2 0 3 0 4 0 5 0 6 0

E L E M E N T N O

FLEX

IBIL

ITY

8 3 K N F A I L U R E L O A D

0

0 . 0 0 0 0 0 0 0 6

0 . 0 0 0 0 0 0 1 2

0 . 0 0 0 0 0 0 1 8

0 . 0 0 0 0 0 0 2 4

0 . 0 0 0 0 0 0 3

0 1 0 2 0 3 0 4 0 5 0 6 0E L E M E N T N O

FLEX

IBIL

ITY

Fig: 5.2: CHANGE IN FLEXIBILITY OF THE BEAM ELEMENT

5.4 DAMAGE LOCATION AND IDENTIFICATION 4m BEAM

Damage metric index were computed on the 4m beam under the symmetric

and unsymmetric conditions .In the symmetric condition only the final damage

inspection was done, whereas in the unsymmetric condition damage assessment at

various load levels were carried out.

In the unsymmetric condition the bending cracks at the center and shear cracks

at the unsupported condition found in experimental as shown in Fig:5.8 and Fig:5.9

was in correlation with the elemental damage at the corresponding element numbers.

Fig: 5.3: ELEMENTAL DAMAGE IN SYMMETRIC CONDITION

3 0 K N U S Y M M E T R I C

0 . 4

0 . 5

0 . 6

0 . 7

0 . 8

0 . 9

1

1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9 3 1 3 3 3 5 3 7 3 9 4 1E L E M E N T S

DA

MA

GE

MET

RIC

4m SYMMETRIC

40

60

80

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41

ELEMENTS

4 1 K N U N S Y M M E T R I C

0 . 4

0 . 5

0 . 6

0 . 7

0 . 8

0 . 9

1

1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8 3 1 3 4 3 7 4 0E L E M E N T S

DA

MA

GE

MET

RI

C

6 0 K N U N S Y M M E T R I C

0 . 4

0 . 5

0 . 6

0 . 7

0 . 8

0 . 9

1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9 3 1 3 3 3 5 3 7 3 9 4 1E L E M E N T S

DA

MA

GE

MET

RIC

6 8 K N U N S Y M M E T R I C

0 . 4

0 . 5

0 . 6

0 . 7

0 . 8

0 . 9

1

1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9 3 1 3 3 3 5 3 7 3 9 4 1E L E M E N T S

DA

MA

GE

MET

RIC

Fig: 5.4: ELEMENTAL DAMAGE IN UNSYMMETRIC CONDITION

5.5 CHANGE IN FLEXIBILITY METHOD ON 4m BEAM

Change in flexibility of the 4m beam was computed accordingly. The beam

was divided into 40 elements hence the overhanging of the beam was up to 10th

element and from the 35th element at the other end.

A T 3 0 K N

0 . 0 0 E + 0 0

4 . 0 0 E - 2 4

8 . 0 0 E - 2 4

1 . 2 0 E - 2 3

0 1 0 2 0 3 0 4 0 5 0E L E M E N T S

FLEX

IBIL

ITY

A T 4 1 K N

0

4 E - 1 0

8 E - 1 0

1 . 2 E - 0 9

0 1 0 2 0 3 0 4 0 5 0E L E M E N T S

FLE

XIBI

LITY

A T 6 0 K N

0

6 E - 1 0

1 . 2 E - 0 9

1 . 8 E - 0 9

2 . 4 E - 0 9

0 . 0 0 0 0 0 0 0 0 3

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5

E L E M E N T S

FLEX

IBIL

ITY

A T 6 8 K N

0

0 . 0 0 0 0 0 0 0 0 2

0 . 0 0 0 0 0 0 0 0 4

0 . 0 0 0 0 0 0 0 0 6

0 . 0 0 0 0 0 0 0 0 8

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5E L E M E N T S

FLEX

IBIL

ITY

Fig: 5.5: FLEXIBILITY CHANGE IN ELEMENTS OF 4m BEAM UNSYMMETRIC CONDITION

Fig 5.6: EXPERIMENTAL SET UP OF 2m BEAM

Fig5.7: PZT, ELECTRIC STRAIN GAUGE AND ACCELEROMETER SETUP

Fig 5.8: CRACK FORMATION AT THE CENTER OF 2m BEAM

Fig 5.9: EXPERIMENTAL SETUP FOR 4m BEAM

Fig 5.10: CRACK FORMATION AT LOADING POINT

5.6 CONCLUDING REMARKS

In this chapter it is shown that the Condition Assessment done with flexibility

and mode shape curvature is plotted in histogram and the experimental pictures

shown concludes that damage detection and the condition assessment is in very close

approximation.

The change in the flexibility of the elements beyond the overhanging was very

high as the curvature method is applicable within the support condition only, beyond

the overhanging it is more flexible.

Chapter 6

FINITE ELEMENT ANALYSIS 6.1 INTRODUCTION

In this chapter analytical detail of the experiments was described through the

modelling software ANSYS 9.0. Elements used in analysis for 1D and 3D,

computational results of the analysis and the mode shapes were given.

By using the modelling software ANSYS 9.0, the beam is modeled with

different beam elements in 1D and 3D modelling.

6.2 SPECIFICATIONS OF ELEMENTS

In 1D analysis the beam is modeled using BEAM4 element (i.e. 3D Elastic 4)

Specification of BEAM4:

Nodes

I, J, K (K orientation node is optional)

Degrees of Freedom

UX, UY, UZ, ROTX, ROTY, ROTZ

In 3D analysis the beam is modeled using SOLID45 element (i.e. Brick 8 node45)

Specification of SOLID45:

Nodes

I, J, K, L, M, N, O, P

Degrees of Freedom

UX, UY, UZ

6.3 COMPUTATIONAL RESULTS

By using ANSYS 9.0 analysis software, computational analysis is carried

over a 4m span beam both in 1D and 3D modeling. In 1D analysis the ANSYS output

is compared with the analytical value.

Table 6.1 shows the ansys 1D frequencies of the 2m beam, Fig: 6.1 shows

the mode shapes of the 1D analysis and element modelling .

6.3.1 1D ANALYSIS (2m Concrete Beam)

1 D M O D E

0

5 0 0

1 0 0 0

1 5 0 0

2 0 0 0

1 D M O D E

1 D M O D E 1 6 . 9 3 6 7 . 5 3 1 5 1 . 2 2 6 6 . 9 4 1 3 . 3 5 8 8 . 9 7 9 1 . 7 1 0 2 0 1 2 7 1 1 5 4 4

1 2 3 4 5 6 7 8 9 1 0

Table: 6.1 1D ANSYS Output

1D ANALYSIS MODESHAPES IN ANSYS

Fig: 6.1 1D Mode Shapes

6.3.2 3D ANALYSIS

Table 6.2 and Fig 6.2 shows the ansys output of the 3D analysis and the

element modelling of the 2m beam at the various load level.

3D ANALYSIS: ANSYS OUTPUT (2m Concrete Beam)

A N S Y S D A T A

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

M O D E S

CH

AN

GE

IN H

z(%

)

B E F O R E D A M A G E A T 5 O K N A T 7 0 K N A T 8 0 K N A T 8 3 K N ( F A I L U R E L O A D )

B E F O R E D A M A G E 4 1 . 0 6 5 8 . 3 3 1 0 2 . 7 1 2 2 . 6 1 3 5 . 5 1 5 5 . 3 1 6 6 . 2 2 0 3 . 3 2 1 6 . 1 2 2 7 . 2

A T 5 O K N 4 1 5 8 . 2 2 1 0 2 1 2 2 1 3 5 1 5 4 . 9 1 6 5 . 2 2 0 2 . 1 2 1 5 . 2 2 2 6 . 2

A T 7 0 K N 3 6 . 0 9 5 3 . 6 9 6 . 6 3 1 1 7 . 5 1 3 3 . 3 1 5 1 . 4 1 6 3 . 2 2 0 0 . 3 2 1 2 . 8 2 2 3 . 4

A T 8 0 K N 2 9 . 8 2 5 2 . 2 4 9 3 . 2 7 1 1 2 . 6 1 3 0 . 2 1 4 9 . 2 1 6 0 . 4 1 9 8 . 2 2 1 0 . 9 2 2 1

A T 8 3 K N ( F A I L U R E L O A D ) 2 3 . 3 6 5 0 . 2 6 9 2 . 4 7 1 0 5 . 6 1 2 9 . 6 1 4 8 . 3 1 6 0 . 2 1 9 8 2 0 9 . 7 2 2 0

1 2 3 4 5 6 7 8 9 1 0

Table: 6.2 3D ANSYS Output

Fig: 6.2 showing the Beam Modeling and Nodal Points.

3D ANALYSIS MODE SHAPES IN ANSYS 9.0 (2m Concrete Beam)

Fig: 6.3 3D Mode Shapes

In 3D analysis, the beam is modeled into block volume, Using solid45, and brick

element. The block is meshed into hexagonally of dimensions (0.1× .05× .05) m3. In order to

eliminate the longitudinal mode shapes the beam is supported as pinned-pinned conditionAs

in experimental setup the beam is over hanged by 0.2m at both the ends.

The torsional effect can be seen in the 3D analysis, which can be compared with

the experimental data.

6.4 DAMAGE INDUCED ANALYSIS IN CONCRETE BEAM

To stimulate the damage condition (Crack) in the Beam, the Beam is modeled

in three sub beams in which the propagation of the crack is varied by varying the width and

the height of the crack between the sub beams. The beams are glued in the ANSYS so that it

behaves as a monolithic beam with the crack propagation.

DAMAGED INDUCED 3D ANALYSIS: ANSYS OUTPUT (2m Concrete Beam)

A N S Y S D A M A G E I N D U C E D B E A M

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

M O D E

FREQ

UEN

CY(

Hz

)

5 0 K N 7 0 K N 8 0 K N 8 3 K N

5 0 K N 4 1 5 8 . 2 1 0 2 1 2 2 1 3 5 1 5 5 1 6 5 2 0 2 2 1 5 2 2 6

7 0 K N 3 6 . 1 5 3 . 6 9 6 . 6 1 1 8 1 3 3 1 5 1 1 6 3 2 0 0 2 1 3 2 2 3

8 0 K N 2 9 . 8 5 2 . 2 9 3 . 3 1 1 3 1 3 0 1 4 9 1 6 0 1 9 8 2 1 1 2 2 1

8 3 K N 2 3 . 4 5 0 . 3 9 2 . 5 1 0 6 1 3 0 1 4 8 1 6 0 1 9 8 2 1 0 2 2 0

1 2 3 4 5 6 7 8 9 1 0

Table 6.3: 3D ANSYS Out put of Damaged Beam

MODE SHAPES OF 2m CONCRETE BEAM AFTER DAMAGE INDUCED

Fig: 6.4 3D Mode shapes of the Damaged Beam

6.5 ANSYS ANALYSIS OF 4m CONCRETE BEAM

1D ANSYS ANALYSIS (4m SYMMETRIC)

4 m 1 D A n a l y s i s S Y M M E T R I C

01 02 03 04 05 06 07 0

M O D E S

FRE

QUE

NC

Y(H

z)

1 D M O D E S

1 D M O D E S 9 . 0 2 1 9 . 1 6 4 6 0 . 3 7 1

1 2 3

Table 6.4: 4mBeam 1D Analysis symmetric

1D ANSYS ANALYSIS (4m UNSYMMETRIC)

4 m 1 D A n a l y s i s U N S Y M M E T R I C

0

2 0

4 0

6 0

8 0

1 0 0

M O D E S

FREQ

UEN

CY(

H z)1 D M O D E S

1 D M O D E S 1 2 . 1 3 6 3 7 . 0 8 5 9 0 . 7 9

1 2 3

Table 6.5: 4mBeam 1D Analysis Unsymmetric

3D ANSYS ANALYSIS (4m SYMMETRIC)

3 D S Y M M E T R I C

0

2 0

4 0

6 0

8 0

M O D E S

FREQ

UEN

CY(

Hz

)

B E F O R E D A M A G E A F T E R D A M A G E

B E F O R E D A M A G E 1 4 . 5 2 9 3 1 6 3 . 9 8 9

A F T E R D A M A G E 6 . 6 4 2 1 4 . 4 5 1 4 1 . 1 5 4

1 2 3

Table 6.6: 4mBeam 3D Analysis symmetric

3D ANSYS ANALYSIS (4m UNSYMMETRIC)

3 D A N S Y S U N S Y M M E T R I C

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0

1 4 0

M O D E S

FREQ

UEN

CY(

Hz)

B E F O R E D A M A G E A T 3 0 K N A T 4 1 K N A T 6 0 K N A T 6 8 K N

B E F O R E D A M A G E 2 5 . 4 5 7 8 7 . 8 7 4 1 2 3 . 2 4 8A T 3 0 K N 2 5 . 1 5 2 8 7 . 2 7 3 1 2 2 . 8 5 4A T 4 1 K N 2 1 . 5 4 3 8 0 . 1 0 1 1 1 5 . 3 9 1A T 6 0 K N 1 6 . 4 4 1 7 1 . 9 3 6 1 0 2 . 7 5 8A T 6 8 K N 9 . 6 3 8 6 0 . 6 4 2 8 6 . 3 2 1

1 2 3

Table 6.7: 4m Beam 3D Analysis Unsymmetric

6.6 CONCLUDING REMARKS

In this chapter the beam element used in the ANSYS9.0, modeling, meshing

done in the beam is described .The analytical computation done in the software and

the results were shown in the histogram. The change in the frequencies at the various

load levels was shown.

Chapter 7

COMPARISION OF RESULTS 7.1 INTRODUCTION

In this chapter the experimental and analytical results were compared and in the

experiment the three sensors Electric Strain Gauge, PZT and Accelerometer performance was

also interpreted

7.2 1D ANALYSIS

In 1D analysis, analytically modal frequency of the simply supported beam can be obtained by

MEI

Lnfn 2

2

2π

= …. (7.1)

Where

L=length of the beam

E=Youngs modulus of concrete (i.e. ckf5000 )

I=Moment of inertia

M=mass of the concrete block

N=mode number

For the beam under consideration, the numerical values are

L=4m, 2/20 mmNfck = , E=2.236E10 N/mm 2 , I=10-4mm4, M=75kg/m2

The Modal Frequency that is obtained by ANSYS and Analytical are

compared and the Percentage of error is given below.

Table 7.1: Comparison of 1D Analysis

MODES ANALITICAL (Hz)

ANSYS (Hz) PERCENTAGE ERROR

1 16.95 16.934 0.09 2 67.80 67.528 0.40 3 152.55 151.17 0.90 4 271.20 266.87 1.60 5 423.75 413.30 2.47 6 610.20 588.85 3.50 7 830.55 791.69 4.68 8 1084.80 1019.90 5.98 9 1372.95 1271.30 7.40 10 1695.00 1543.80 8.92

7.3 EXPERIMENTAL DATA

In 3D analysis, the ANSYS modal frequency obtained was compared with the

first 3 modal frequency obtained from the accelerometer, PZT and ESG was

compared below it is found that the accelerometer and PZT were giving close value.

Table 7.2, Table 7.3, Table 7.4 gives the experimental values obtained by the

sensors at various damaged location.

7.3.1 DAMAGED INDUCED 2mCONCRETE BEAM

P Z T D A T A

0

5

1 0

1 5

2 0

M O D E S

CH

AN

GE

IN H

z(%

)

B E F O R E D A M A G E A T 5 0 K N A T 7 0 K N A T 8 0 K N A T 8 3 K N

B E F O R E D A M A G E 0 . 2 3 6 2 4 . 2 1 2 6 4 . 0 1 0 5 2 . 0 7 5 4 8 . 8 9 0 9 9 . 6 6 5 7 1 7 . 7 5 7 8 . 8 6 5 2 1 3 . 1 5 1 1 7 . 6 5 3

A T 5 0 K N 0 . 1 2 9 1 1 . 9 0 8 8 4 . 0 9 9 9 2 . 3 1 3 1 8 . 2 8 8 . 4 9 7 6 1 5 . 3 2 3 8 . 2 1 8 1 1 . 4 7 1 1 4 . 9 5 7

A T 7 0 K N 2 . 4 5 8 6 4 . 7 6 5 5 3 . 5 7 1 4 2 . 8 1 9 8 6 . 3 1 8 2 6 . 1 4 0 5 1 3 . 2 8 3 4 . 7 4 3 4 8 . 7 8 9 9 1 2 . 8 5 9

A T 8 0 K N 5 . 4 9 5 1 . 8 2 8 5 7 . 2 5 9 1 3 . 6 0 3 8 4 . 6 1 2 7 4 . 9 1 0 1 1 1 . 6 9 7 1 . 5 3 9 7 6 . 2 5 0 9 5 . 9 6 7 2

A T 8 3 K N 1 2 . 0 0 4 2 . 0 5 0 8 1 4 . 3 4 . 0 3 2 7 1 . 8 5 7 4 1 . 6 6 2 3 9 . 0 3 9 6 1 . 6 5 6 7 3 . 6 1 3 6 3 . 4 5 4 9

1 2 3 4 5 6 7 8 9 1 0

Table 7.2:2m Beam Experimental frequencies with PZT

A C C D A T A

0

5

1 0

1 5

2 0

2 5

M O D E S

CH

AN

GE

IN H

z(%

)

B E F O R E D A M A G E A T 5 0 K N A T 7 0 K N A T 8 0 K N A T 8 3 K N

B E F O R E D A M A G E 1 . 4 4 6 7 3 . 3 1 0 8 4 . 3 2 9 1 . 3 2 5 7 9 . 3 8 2 4 9 . 4 1 3 8 1 7 . 5 5 7 8 . 3 9 4 1 3 . 1 1 6 1 9 . 3 6 1

A T 5 0 K N 0 . 5 7 2 3 3 . 1 4 2 5 4 . 1 0 7 4 1 . 6 5 3 2 8 . 6 7 0 8 8 . 6 0 6 2 1 4 . 9 4 1 8 . 1 9 1 4 1 1 . 5 1 9 1 5 . 9 6 8

A T 7 0 K N 0 . 5 7 5 8 6 . 8 2 3 4 1 . 7 2 0 1 2 . 1 7 1 7 7 . 1 7 4 9 7 . 1 3 5 1 2 . 9 5 7 9 . 0 3 9 4 9 . 4 5 1 4 1 3 . 1 6 6

A T 8 0 K N 8 . 3 0 4 9 1 . 9 3 1 9 6 . 9 2 7 1 2 . 7 5 9 3 3 . 6 8 7 2 5 . 7 2 4 6 1 2 . 4 9 3 2 . 4 5 2 5 6 . 7 9 9 6 6 . 5 0 5 1

A T 8 3 K N 1 4 . 8 9 0 . 1 5 3 1 1 . 5 4 2 . 8 9 3 8 3 . 3 0 6 2 2 . 4 3 6 3 9 . 5 8 5 7 1 . 0 7 3 3 5 . 8 4 5 4 . 1 0 4 9

1 2 3 4 5 6 7 8 9 1 0

Table 7.3:2m Beam Experimental frequencies with Accelerometer

E S G D A T A

0

5

1 0

1 5

2 0

2 5

M O D E S

CH

AN

GE

INH

z(%

)

B E F O R E D A M A G E A T 5 0 K N A T 7 0 K N A T 8 0 K N A T 8 3 K N

B E F O R E D A M A G E 2 . 1 9 9 3 4 . 3 3 2 6 4 . 3 0 8 5 0 . 0 1 4 7 8 . 6 3 4 9 1 2 . 0 9 2 1 8 . 1 7 3 1 2 . 8 9 4 1 3 . 6 3 2 4 . 2 1

A T 5 0 K N 2 . 3 5 6 5 3 . 2 0 0 4 4 . 2 4 1 4 0 . 0 9 5 7 . 9 9 1 0 . 9 3 8 1 5 . 9 3 5 1 1 . 6 0 4 1 1 . 9 9 2 1 9 . 7 4 2

A T 7 0 K N 7 . 3 5 9 6 6 . 8 3 7 9 0 . 3 1 6 6 0 . 6 5 3 5 7 . 5 1 5 7 8 . 0 1 9 3 1 3 . 7 3 8 1 0 . 0 3 4 1 0 . 2 2 5 1 8 . 3 1 8

A T 8 0 K N 1 1 . 1 3 3 6 . 6 9 9 8 3 . 6 8 3 1 0 . 2 7 5 2 5 . 3 2 1 4 6 . 2 7 2 3 1 3 . 4 9 2 3 . 3 9 8 5 7 . 7 7 6 7 6 . 8 9 4 7

A T 8 3 K N 2 0 . 9 9 3 3 . 7 8 6 7 1 2 . 4 4 6 2 . 3 0 4 9 3 . 4 9 6 3 2 . 6 1 8 3 1 0 . 1 5 0 . 8 8 2 2 7 . 0 5 0 1 4 . 4 2 5 7

1 2 3 4 5 6 7 8 9 1 0

Table 7.4:2m Beam Experimental frequencies with ESG

7.3.2 DAMAGED INDUCED 4m CONCRETE BEAM

E X P E R I M E N T A L S Y M M E T R I C

0

2 0

4 0

6 0

8 0

M O D E S

FREQ

UEN

CY(

H z)

B E F O R E D A M A G E A F T E R D A M A G E

B E F O R E D A M A G E 1 4 . 6 6 3 3 2 . 5 9 8 6 5 . 9 8 7

A F T E R D A M A G E 6 . 8 5 6 1 5 . 6 5 4 4 2 . 5 5 6

1 2 3

Table 7.5: 4m Beam Experimental frequencies in symmetric condition

E X P E R I M E N T A L U N S Y M M E T R I C

0

5 0

1 0 0

1 5 0

M O D E S

FREQ

UEN

CY(

Hz)

B E F O R E D A M A G E A T 3 0 K N A T 4 1 K N A T 6 0 K N A T 6 8 K N

B E F O R E D A M A G E 2 5 . 6 2 2 8 8 . 9 9 5 1 2 5 . 8 8 6A T 3 0 K N 2 6 . 5 4 8 8 8 . 7 7 3 1 2 5 . 3 6 9A T 4 1 K N 2 2 . 6 6 5 8 3 . 5 6 4 1 2 0 . 2 6A T 6 0 K N 1 8 . 6 6 5 7 4 . 2 2 5 1 0 5 . 9 9 8A T 6 8 K N 1 1 . 1 5 4 6 3 . 8 7 1 8 9 . 2 5 6

1 2 3

Table 7.6: 4m Beam Experimental frequencies in unsymmetric condition There is considerable change in frequency, due to the damage induced in

the structure, this experimental change in frequency and modal displacement is used

in the condition assessment of the structure.

7.4 CONCLUDING REMARKS

In this chapter analytical computation and the experimental results of the

beams both in the 1D and 3D were compared and shown in the histogram .The

analytical results have been updated considering the first modes of the experimental

value. The change in experimental frequencies and numerical frequencies were shown

in histograms.

Chapter 8 CONCLUSIONS AND RECOMMENDATIONS

In this project experimental and computational modal analysis is carried over a

2m and 4m RC beams and experimental mode shapes have obtained for a rectangular

hollow cross section steel frame. The modal frequencies were calculated both

experimentally using MATLAB by Frequency Response Function and in ANSYS 1D

and 3D modelling

In 1D modelling using beam elements the modal frequencies obtained in

ANSYS and analytically computed are in close approximation.

In 3D modelling using solid elements the modal frequencies obtained in

ANSYS and experimentally obtained through accelerometer, the PZT patch,

the ESG are varying by a small margin. This may be due the isotropic

consideration in the ANSYS and variability and deviation in elastic properties

in the real structure.

The modal frequencies obtained in1D and 3D differs considerably, this is due

to torsion effect consideration in 3D Modal analysis, whereas in1D analysis it

is not considered.

In the data acquisition process it is found that PZT yields good results in

comparison to that accelerometer and electric strain gauge.

ON 2m REINFORCED CONCRETE BEAM

Damage detection and condition assessment carried over the 2m beam using

only modal displacements instead of curvature and it has been found that the

damage location can be detected conveniently but the severity of the damage

is not properly quantified.

Change in flexibility of the beam element has been found to be in close

approximation to locate the damage and the intensity of the flexibility gives

the severity of the damage occurred.

ON 4m REINFORCED CONCRETE BEAM

In the 4m beam, the curvature of the nodes of the beam elements was used and

the damage location and the severity of the damage in the beam were found to

be well correlated with actual observation.

Change in flexibility of the beam element under different support condition

was found according to damage location which is checked through

experimental pictures available.

ON STEEL FRAME

The experimental mode shape found through the frequency response function

and by using the ICAT modeling software under free suspended condition

were not in close approximation with those of computational mode shapes

obtained using ANSYS 9.0. This may due to the approximation boundary

condition adopted in computational method.

RECOMMENDATIONS

Further work can carry out in structural elements by considering various

boundary conditions and structured frames with will stimulate real time

analysis.

Assessment of different structures taking time history analysis real time data

of any earthquake can be done which will stimulate the actual scenario.

Wireless network for data acquisition for the experiments and monitoring the

structures can be done, so as to make it more feasible to the structural health

monitoring.

The condition assessment work can be carried out to plates, steel frames,

composites fibers etc.

Monitoring of the structures with the embedded sensors, data acquisition has

to be done over the structural elements which is more useful in the wireless net

work system and a compatibility study can be done over the structural health

monitoring.

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