Monitoring of strain and seismic vibrations in structures

ABSTRACT There are a number of approaches to the modelling of cracks in beam

structures. That fall into three main categories; local stiffness reduction, discrete

spring models, and complex models in two or three dimensions. This paper compares the different approaches monitoring of strains

and vibrations for structural health monitoring using low frequency vibration,

Simple models of crack flexibility based on beam elements are adequate. This paper also addresses the effect of the excitation for breathing cracks, where the beam stiffness is bilinear, depending on whether the crack is open or closed.

Most structural health monitoring methods assume that the structure is behaving linearly, whereas in practice the response will be nonlinear to an extent that varies with the form of the excitation. This paper will demonstrate these effects for a simple beam structure.

Materials Electrical strain gauge Piezoelectric material : Sensor and actuator application Arduino Uno R3 specimen under consideration : 2 Reinforced Concrete beams (100X100X500

mm) with M20 grade concrete and Fe 250 steel. Reinforcement provided was 2 x 6 dia at top and bottom along with stirrups

of diameter 6 dia @ 80 mm c/c. Experimental study was performed in two phases – Healthy and various

damaged conductance and susceptance signatures are taken for each specimens.

LCR meter with connecting fixture, and VEE PRO software for data acquisition.

Frequency range 100 kHz – 250 kHz

IntroductionStress

Stress is “resistive force developed per unit area" - the ratio of applied force F and cross section - defined as "force per area".

Fn = normal component force𝑆𝑡𝑟𝑒𝑠𝑠=σ=

𝐹𝑜𝑟𝑐𝑒(𝐹𝑛)𝐴𝑟𝑒𝑎 (𝐴)

Scope Of Project

To cast M25 grade concrete specimens which would include 6 cubes, 6 cylinders and 6 beams of standard size.

To calculate the deflection observed. To find the modulus of elasticity from the stress vs.. strain

curve and compare it with theoretical value.

Experimental WorkTo carry out our experiment we have casted the following specimens of M25 grade of concrete according to IS 456 :

Specimen NosBeams(500 mm x 100 mm x

100 mm)6

Cube(150 mm x 150 mm x 150 mm)

6

Cylinder(dia=150 mm , h=300 mm)

6

Mix Design Specifications

Data assumptions required : Grade of cement (fck) 25 MPa Maximum size of aggregate 10 mm Degree of Workability medium Degree of quality control Fair Type of exposure moderate Compressive strength of cement 53 N/mm2

Specific gravity of cement 3.15 Specific gravity of coarse aggregate 2.78 Specific gravity of fine aggregate 2.54 Water absorption of coarse aggregate 0.3% Water absorption of fine aggregate 0.2% Free moisture content in CA & FA NIL

Final Mix Design Ratio :

Concrete Grade

Cement W/C Coarse Aggrega

te

Fine Aggrega

teM-25 1 0.54 2.51 1.96M-25 390

kg/m3

210.6 kg/m3

978.84 kg/m3

762.61 kg/m3

Experimental Work The characteristic strength achieved

after 28 days of casting of specimens is as follows : Batch Cube no. Strength

(MPa)Average (MPa)

1 1 25.8 25.732 26.53 24.9

2 1 26.2 26.202 273 25.4

3 1 25.2 26.062 273 26

Strain Measurement

Strain Measurement There are two methods of measuring strain

1) Experimental method2) Analytical method

Analytically strain can be measured by calculating stress on the specimens and then using the following equations :

Experimentally it can be obtained : Electrically Mechanically

ELECTRICAL MEASUREMENT OF STRAIN

Electrical Measurement of StrainWheatstone Bridges for electrical strain measurement In practice, strain measurements rarely

involve quantities larger than a few Millis train (e x 10-3). Therefore, to measure the strain requires accurate measurement of very small changes in resistance.

To measure such small changes in resistance, strain gages are almost always used in a bridge configuration with a voltage excitation source.

Types of electrical strain gauges

Wire type strain gauge :It consisted of a carbon film resistance element applied directly to the surface of the strained.

Electrical Measurement of Strain

Electrical strain gauge transform force, pressure, strain etc. into the resistance change that can be measured.

Strain operate on the principal that the change to the foil due to strain will cause changes to the electrical resistance in a define way.

In tensile force – gauge will become longer and the resistance will increased.

In compressive force – gauge will become shorter and the resistance will decrease.

Calculation of gauge factor Calculation of gauge factor :

Gauge factor = =

Factors considered for Selection and Installation for Bonded Metallic Strain Gauges :

Grid material and configuration Backing material Bonding material and method Gage protection Associated electrical circuitry

Application of Electrical strain gauge

The strain gauges can be used in automatic signaling system in structural buildings.

In old buildings and the structures in the seismic zone, signaling is done when some parameters exceed.

For the most cases displacement (deformation), strain, force and acceleration parameters are measured. Nevertheless most of these above-mentioned parameters are converted to the strain measurements.

Experimental Setup For Beam

Results and Discussion Electrical Strain Gauge Results for

Cubes

Results and DiscussionLoad (kN) Stress (MPa) Strain

0.00 0.00 0.000002.95 0.13 0.0000010

40.55 1.80 0.0000150149.25 6.63 0.0000360234.45 10.42 -0.0000790421.80 18.75 -0.0005290572.65 25.45 -0.0021390

Results and DiscussionLoad (kN) Stress (Mpa) Strain Load (kN) Stress (Mpa) Strain0.0000 0.0000 0.0000000 81.2420 12.0356 -0.00024900.0980 0.0044 0.0000000 88.3960 12.7111 -0.00028500.0980 0.0044 0.0000000 94.6680 13.2933 -0.00032201.5680 0.0711 0.0000000 104.0760 14.2000 -0.00036003.8220 0.1733 0.0000000 112.4060 14.8622 -0.00040005.7820 0.2622 0.0000010 122.0100 15.6311 -0.00044106.2720 0.2844 0.0000010 132.0060 16.3733 -0.00048007.3500 0.3333 0.0000020 140.6300 16.8889 -0.00051908.3300 0.3778 0.0000020 149.4500 18.0578 -0.00055709.8000 0.4444 0.0000020 159.6420 18.8889 -0.0005930

11.3680 0.5156 0.0000020 171.8920 19.3511 -0.000627012.6420 0.5733 0.0000020 180.8100 20.3111 -0.000659015.2880 0.6933 0.0000020 192.5700 20.8889 -0.000699016.9540 0.7689 0.0000020 205.5060 21.4222 -0.000737019.8940 0.9022 0.0000020 217.0700 22.0044 -0.000778025.9700 1.1778 0.0000030 230.3000 22.7200 -0.000824029.6940 1.3467 0.0000040 243.0400 23.3822 -0.000882034.4960 1.5644 0.0000060 253.8200 23.6489 -0.000954037.3380 1.6933 0.0000090 265.3840 24.3467 -0.001023041.9440 1.9022 0.0000130 280.2800 24.6756 -0.001103045.3740 2.0578 0.0000140 293.1180 24.9200 -0.001190050.2740 2.2800 0.0000180 313.1100 25.7378 -0.001280056.1540 2.5467 0.0000240 327.7120 26.0489 -0.001371062.2300 2.8222 0.0000300 344.6660 26.0933 -0.001478060.6620 2.7511 0.0000360 361.0320 26.0267 -0.001599074.0880 3.3600 0.0000420 372.4000 25.9289 -0.0016000

Results and Discussion Calculation of Modulus of Elasticity for

cubes by : Secant Modulus Chord Modulus

Results and Discussion

Electrical Strain Gauge Results for Beams

Results and DiscussionLoad(kN) Deflection

(mm)0 0.0000000

0.49 0.00120000.98 0.00360001.47 0.00680001.96 0.01080002.94 0.01840003.43 0.02120003.92 0.02440004.41 0.02760004.9 0.0312000

5.39 0.03440005.88 0.03800006.37 0.04120006.86 0.04520007.35 0.0480000

Load (kN) Deflection (mm)

0 0

0.49 0.0088

0.98 0.0108

1.47 0.0164

1.96 0.0248

2.45 0.0348

2.94 0.0484

3.43 0.0708

Specimen B2Specimen B1

Results and DiscussionLoad (KN) Load (KN)

0 00.784 0.7840.784 0.7840.882 0.8821.078 1.0781.274 1.2741.372 1.3721.372 1.3721.568 1.5681.568 1.5681.568 1.5681.666 1.6661.666 1.6661.764 1.7641.764 1.7641.764 1.7641.862 1.8622.156 2.1562.646 2.6463.136 3.1363.822 3.8224.606 4.6065.488 5.4886.468 6.4687.154 7.1547.938 7.938

Results and Discussion Analytically checking the results

Load = 0.588 kN Deflection = 0.008 mmHence from Bending theory,

Where, f = Stress intensity in the fibery = Distance of fiber from neutral axisM = Max. Bending MomentI = Moment of inertia of section

Results and Discussion Now,

Strain = 2 x 10-5

So stress can be calculated by

Here, E= 25000 MPa Therefore theoretical value of Stress = 0.5 MPa

Now, experimentally observed stress can be calculated by bending theorySo, M = 0.0782 kNmAnd therefore, f = 0.46 MPaThus the practical and analytical values being very close, the readings are accurate.

Basics of EMI technique

Fig. : Modeling PZT-structure interaction

(a) A PZT patch bonded to structure under electric excitation(b) Interaction model of PZT patch and host structure

Piezo patch PZT patch is surface bonded or embedded inside the structures. When an alternating electric field is applied to the patch, it expands and

contracts dynamically in direction ‘1’. Hence, two end points of the patch can be assumed to encounter equal impedance Z from the host structure.

The patch (length 2l, width w and thickness h) behaves as thin bar undergoing axial vibration. The complex electro-mechanical admittance Y of the coupled system is derived as

Where, d31 is the piezoelectric strain coefficient of the PZT material, ȲE is the complex Young’s modules under constant electric field, (εɛ33)T is the complex electric permittivity at constant stress, Za is mechanical impedance of the PZT patch, ω is angular frequency and kl is the wave number.

Experimental set-up

Firstly, the PZT patch was soldered out through two electrodes present on the patch, then this patch was bonded on to the surface of specimen using a well-tested epoxy adhesive.

In this case Araldite adhesive has been used as the sensible frequency range of the PZT patch is high and the PZT patch had dual roles i.e. sensor and actuator functions.

Then, the soldered PZT patch was wired to Impedance Analyzer through Connecting Fixture of LCR meter. Then the frequency was swept through 100 kHz to 250 kHz i.e. the PZT patch transfers this vibrations to the structure through adhesive bond layer.

These vibrations are transferred to structures and reflected back from the same PZT patch through waves, which will indicate the health of the structure. The required parameters i.e. Conductance (G) and Susceptance (B) are directly measured through LCR meter for all the values of frequency.

Results for Beam 1The PZT patch was subjected to frequency range of 100-250 kHz. For this beam, the two PZT patches were employed and the responses were recorded for all the stages by impedance analyzer for both the PZT’s. PZT patch 1 peaks are more prominent and also change in signature with changes in damage level are categorically visible when compared to PZT patch 2.

Positioning StudyBEAM: The PZT is sensible for all the damages

while, PZT2 being less sensible.

Conclusion Thus we concluded that on applying compressive load on cubes and

cylinders there is reduction in its length and hence there is compressive strain developed in them.

The modulus of elasticity calculated from the results is near to the theoretical value proving the results to be accurate.

On application of flexural load on the beam and measuring strain in it, it is observed that there is tension developed below the neutral axis and compression is developed above neutral axis. Thus proving the bending theory of beam

Piezoelectric material (PZT 5H grade) being smart material is sensible at high frequencies to damages occurring in the structures. Hence EMI technique can be extensively accepted for structural health monitoring systems in the form of sensor and actuator.

It can be concluded that, PZT patch is location sensitive as it shows higher damage sensitivity when positioned near the damage zone.