experimental evaluation of strain in concrete elements

Experimental

Evaluation Of Strain

In Concrete

ElementsGuided By : Prof. Digesh Joshi

Prepared By : Ankit Ahir (11BCL003)

Rekan Gadhecha (11BCL009)

Nakul Gami (11BCL010)

Nisarg Gandhi (11BCL011)

Contents

Introduction

Objective

Scope of work

Experimental Work

Methods of strain measurement

Mechanical measurement of strain

Electrical measurement of strain

Experimental Setup

Results and Discussion

Conclusion

INTRODUCTION

Introduction

Stress

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 force

𝑆𝑡𝑟𝑒𝑠𝑠 = σ =𝐹𝑜𝑟𝑐𝑒 (𝐹𝑛)

𝐴𝑟𝑒𝑎 (𝐴)

Introduction

• Types of stress:

Tensile stress

Compressive

Shearing stress

Bending Stress

Introduction Strain

Strain is the normalized measure of

deformation representing thedisplacement between particles in the

body relative to a reference line.

It is a unit-less quantity and is denoted by

symbol ε.

Increase in length Tensile Strain

Decrease in length Compressive Strain

Introduction Types of Strain

Linear Strain

𝑆𝑡𝑟𝑎𝑖𝑛 = ε =Δ𝑙

𝑙

Lateral Strain

Strain in x-direction = εx = (𝜎𝑥 − µ𝜎𝑦)/𝐸

Strain in y-direction = εy = (σy − µσx)/E

Introduction

Volumetric Strain

𝑉𝑜𝑙. 𝑆𝑡𝑟𝑎𝑖𝑛 = 𝛥𝑉/𝑉

𝑉 = 𝛥𝑥(1 + 𝜀𝑥)𝛥𝑦(1 + 𝜀𝑦)𝛥𝑧(1 + 𝜀𝑧)

= 𝑉0(1 + 𝜀𝑥 + 𝜀𝑦 + 𝜀𝑧)

Therefore, Volumetric strain = 𝑒 =𝑉−𝑉0

𝑉0= 𝜀𝑥 + 𝜀𝑦 + 𝜀𝑧

Introduction

Shear Strain

A condition in or deformation of an elastic body caused by forcesthat tend to produce an opposite but parallel sliding motion of the body's planes.

𝑆hear displacement per

unit length = ΔL/h

= CC’/BC

= tanΦ

INTRODUCTION

Methods to find out Modulus of elasticity (E) :

Analytically it can be calculated by the equation as given in clause 6.2.3 of IS 456 : 2000

𝐸 = 5000 𝑓𝑐𝑘

here, Fck= Compressive Strength of Concrete

Experimentally two methods has been used for finding modulus of elasticity in stress vs.strain diagram :

(1) Secant method :

It is given by the slope of a line drawn from the origin to a point on the curvecorresponding to a 40% stress of the failure stress.

(2) Chord method :

If the modulus of elasticity is found out with reference to the chord drawn between twospecified point on the stress strain curve then such value of modulus of elasticity is known aschord modulus.

Objective of Project

The main objective is to

experimentally measure strain

electrically and mechanically

on PCC specimens

Scope Of Project

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

To calculate the deflection observed.

To find the modulus of elasticity from the stress vs.. strain curve andcompare it with theoretical value.

EXPERIMENTAL WORK

Experimental Work

To carry out our experiment we have casted the following specimens of M25 grade

of concrete according to IS 456 :

Specimen Nos

Beams(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

Experimental Work

Mix Design SpecificationsData 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

Experimental Work

Concrete

Grade

Cement W/C Coarse Aggregate Fine Aggregate

M-25 1 0.54 2.51 1.96

M-25 390 kg/m3 210.6 kg/m3 978.84 kg/m3 762.61 kg/m3

Final Mix Design Ratio :

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 25.73

2 26.5

3 24.9

2 1 26.2 26.20

2 27

3 25.4

3 1 25.2 26.06

2 27

3 26

Strain Measurement

Strain Measurement

There are two methods of measuring strain

1) Experimental method

2) Analytical method

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

σ

ε= 𝐸

Experimentally it can be obtained :

Electrically

Mechanically

MECHANICAL MEASUREMENT OF STRAIN

Mechanical measurement of strain

Mechanical strain gauge is used to determine strain

at critical location on the surface.

Principle:

When the test component is trained the knife edge

undergoes a small relative displacement.

This displacement is amplified through a mechanical(or sometimes optical) linkage and magnified

displacement or strain is displayed on calibrated

scale.

Mechanical measurement of strain

It has mainly 4 parts :

1. It has SS bar on which gauge is placed.

2. Reference bar : Reference bar has two reference

points which are fixed at 10 cm shown in a fig.

Mechanical measurement of strain

3. Reference pins or stud shown in fig

which has same dimension as that

hole on reference bar.

4. A SS bar has two conical point fixed at

distance of 10 cm shown in fig .

Mechanical measurement of strain

Procedure for measuring mechanical strain

Fixed two reference pins to the surface on test specimen.

Reference pins can be fixed with any strong adhesive.

Reference pins should be fixed at a center distance of

10cm. This distance is checked with the standard bar.

Take the initial reading of the dial gauge on the referencebar.

Mechanical measurement of strain

Check the center distance of the reference pins fixed on the surface

The difference in reading indicate the variation of the reference pins from the standard

gauge length of 10 cm

ELECTRICAL MEASUREMENT OF STRAIN

Electrical Measurement of Strain

Wheatstone Bridges for electrical strain measurement

In practice, strain measurements rarely involvequantities larger than a few millistrain (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

Foil-type strain gauges :

The common form consists of a metal

foil element on a thin epoxy support

manufactured using printed-circuit

techniques.

Major advantage – almost unlimited

pane configurations are possible.

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.

Electrical Measurement of Strain

Calculation of gauge factor :

𝑅 =𝜌𝑙

𝐴

Gauge factor = 𝐹 =𝑑𝑅

𝑅

𝑑𝐿/𝑙=

𝑑𝑅

𝑅

𝜀

Factors considered for Selection and Installation for BondedMetallic Strain Gauges :

Grid material and configuration

Backing material

Bonding material and method

Gage protection

Associated electrical circuitry

Electrical Measurement of Strain

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.

Electrical Measurement of Strain

Multi-Channel Monitoring System

It is possible to construct monitoring system

gradually by adding additional measurementunits upon necessity.

The central server and workplace of tracking

and management in this case can be placed

at any location that is the same or different

from the building monitored.

Electrical Measurement of Strain

Installation of electrical strain gauge on concrete surface:

step 1 : step 2 :

Smoothening of surface polishing of surface by AREDLITE

by glass paper

Electrical Measurement of Strain

Step 3: Marking the position of the strain gauge on surface

Step 4: Step 5:

Attaching the strain shouldering with lead wire

gauge

Electrical Measurement of Strain

Step 6: Step 7:

Connection with P3 Recording the reading

strain indicator

Electrical Measurement of Strain

EXPERIMENTAL SETUP

Experimental Setup For Beam

Setup for Electrical Strain measurement in beams

Experimental Setup

Experimental Setup

Connection with P3 Settings in P3 software

RESULTS AND DISCUSSION

Results and Discussion

Out of the 18 specimens casted testing was done as follows:

Mechanical

Strain Gauge

Electrical Strain

Gauge

Cubes 4 2

Cylinders 6 0

Beams 0 6

Results and Discussion

Mechanical Strain Gauge Results for cubes

Results and Discussion

Load (kN) Stress (Mpa)

Deflection (mm) Strain

cube 1 cube 2 cube 3 cube 1 cube 2 cube 3

0 0.000 0.000 0 0 0.000000 0 0

50 2.222 0.002 0.012 0.008 -0.000013 -0.00008 -5.3E-05

100 4.444 0.016 0.03 0.02 -0.000107 -0.0002 -0.00013

150 6.667 0.014 0.036 0.036 -0.000093 -0.00024 -0.00024

200 8.889 0.048 0.044 0.05 -0.000320 -0.00029 -0.00033

250 11.111 0.062 0.056 0.07 -0.000413 -0.00037 -0.00047

300 13.333 0.076 0.12 0.074 -0.000507 -0.0008 -0.00049

350 15.556 0.088 0.136 0.12 -0.000587 -0.00091 -0.0008

400 17.778 0.098 0.148 0.124 -0.000653 -0.00099 -0.00083

450 20.000 0.118 0.172 0.128 -0.000787 -0.00115 -0.00085

500 22.222 0.126 0.216 0.13 -0.000840 -0.00144 -0.00087

550 24.444 0.132 0.264 0.138 -0.000880 -0.00176 -0.00092

600 26.667 0.140 - 0.18 -0.000933 - -0.0012

650 28.889 0.152 - - -0.001013 - -

700 31.111 0.152 - - -0.001013 - -

750 33.333 0.184 - - -0.001227 - -

Results and Discussion

0.000

5.000

10.000

15.000

20.000

25.000

30.000

35.000

-0.002000 -0.001800 -0.001600 -0.001400 -0.001200 -0.001000 -0.000800 -0.000600 -0.000400 -0.000200 0.000000

Str

ess

(M

Pa

)

Strain

Stress vs. Strain

Cubes

Cube 1 Cube 2 Cube 3

Results and Discussion

Electrical Strain Gauge Results for Cubes

Results and DiscussionCUBE 4

Load (kN) Stress (MPa) Strain

0.00 0.00 0.00000

2.95 0.13 0.0000010

40.55 1.80 0.0000150

149.25 6.63 0.0000360

234.45 10.42 -0.0000790

421.80 18.75 -0.0005290

572.65 25.45 -0.0021390

Results and DiscussionCUBE 5

Load (kN) Stress (Mpa) Strain Load (kN) Stress (Mpa) Strain

0.0000 0.0000 0.0000000 81.2420 12.0356 -0.0002490

0.0980 0.0044 0.0000000 88.3960 12.7111 -0.0002850

0.0980 0.0044 0.0000000 94.6680 13.2933 -0.0003220

1.5680 0.0711 0.0000000 104.0760 14.2000 -0.0003600

3.8220 0.1733 0.0000000 112.4060 14.8622 -0.0004000

5.7820 0.2622 0.0000010 122.0100 15.6311 -0.0004410

6.2720 0.2844 0.0000010 132.0060 16.3733 -0.0004800

7.3500 0.3333 0.0000020 140.6300 16.8889 -0.0005190

8.3300 0.3778 0.0000020 149.4500 18.0578 -0.0005570

9.8000 0.4444 0.0000020 159.6420 18.8889 -0.0005930

11.3680 0.5156 0.0000020 171.8920 19.3511 -0.0006270

12.6420 0.5733 0.0000020 180.8100 20.3111 -0.0006590

15.2880 0.6933 0.0000020 192.5700 20.8889 -0.0006990

16.9540 0.7689 0.0000020 205.5060 21.4222 -0.0007370

19.8940 0.9022 0.0000020 217.0700 22.0044 -0.0007780

25.9700 1.1778 0.0000030 230.3000 22.7200 -0.0008240

29.6940 1.3467 0.0000040 243.0400 23.3822 -0.0008820

34.4960 1.5644 0.0000060 253.8200 23.6489 -0.0009540

37.3380 1.6933 0.0000090 265.3840 24.3467 -0.0010230

41.9440 1.9022 0.0000130 280.2800 24.6756 -0.0011030

45.3740 2.0578 0.0000140 293.1180 24.9200 -0.0011900

50.2740 2.2800 0.0000180 313.1100 25.7378 -0.0012800

56.1540 2.5467 0.0000240 327.7120 26.0489 -0.0013710

62.2300 2.8222 0.0000300 344.6660 26.0933 -0.0014780

60.6620 2.7511 0.0000360 361.0320 26.0267 -0.0015990

74.0880 3.3600 0.0000420 372.4000 25.9289 -0.0016000

Results and Discussion

-5

0

5

10

15

20

25

30

-0.0025 -0.002 -0.0015 -0.001 -0.0005 0 0.0005

Str

ess

(M

Pa

)

Strain

Stress vs. Strain

Cubes

CUBE 4 Cube 5

Results and Discussion

Comparison between Electrical and

Mechanical Strain Gauge Readings

Results and Discussion

-5.000

0.000

5.000

10.000

15.000

20.000

25.000

30.000

35.000

40.000

-0.002500 -0.002000 -0.001500 -0.001000 -0.000500 0.000000 0.000500

Str

ess

(M

Pa

)

Strain

Stress vs. Strain

Cubes

Cube 1 Cube 2 Cube 3 Cube 4 Cube 5

Results and Discussion

Calculation of Modulus of Elasticity for cubes by :

Secant Modulus

Chord Modulus

Results and Discussion

Results and Discussion

Results and Discussion

Results and Discussion

Mechanical Strain Gauge Results for Cylinders

Results and Discussion

Load (kN) Stress (Mpa)Deflection (mm) Strain

CY1 CY2 CY3 CY4 CY1 CY2 CY3 CY4

0 0 0 0 0 0 0 0 0 0

50 2.830856334 0.01 0.01 0.01 0.01 0.000667 0.000667 0.000667 0.000666667

100 5.661712668 0.02 0.02 0.015 0.02 0.001333 0.001333 0.001 0.001333333

150 8.492569002 0.02 0.02 0.02 0.02 0.001333 0.001333 0.001333 0.001333333

200 11.32342534 0.023 0.023 0.02 0.025 0.001533 0.001533 0.001333 0.001666667

250 14.15428167 0.024 0.024 0.025 0.025 0.0016 0.0016 0.001667 0.001666667

300 16.985138 0.025 0.025 0.03 0.03 0.001667 0.001667 0.002 0.002

350 19.81599434 0.03 0.03 0.035 0.03 0.002 0.002 0.002333 0.002

400 22.64685067 0.05 0.05 0.04 0.05 0.003333 0.003333 0.002667 0.003333333

450 25.47770701 0.07 0.07 0.05 0.07 0.004667 0.004667 0.003333 0.004666667

500 28.30856334 0.09 0.09 0.055 0.09 0.006 0.006 0.003667 0.006

550 31.13941967 0.1 0.1 0.07 0.1 0.006667 0.006667 0.004667 0.006666667

600 33.97027601 0.11 0.11 - 0.16 0.007333 0.007333 - 0.010666667

650 36.80113234 0.115 0.115 - 0.185 0.007667 0.007667 - 0.012333333

670 37.93347488 - - - 0.2 - - - 0.013333333

Results and Discussion

0

5

10

15

20

25

30

35

40

-0.014 -0.012 -0.01 -0.008 -0.006 -0.004 -0.002 0

Str

ess

(M

Pa

)

Strain

Stress vs. Strain

Cylinders

CY1 CY2 CY3 CY4

Results and Discussion

Calculation of Modulus of Elasticity for Cylinders by :

Secant Modulus

Chord Modulus

Results and Discussion

Results and Discussion

Results and Discussion

Results and Discussion

Electrical Strain Gauge Results for Beams

Results and Discussion

For testing specimens B1 and B2 the

strain gauges are placed in the bottom

face.

Results and Discussion

Load(kN) Deflection (mm)

0 0.0000000

0.49 0.0012000

0.98 0.0036000

1.47 0.0068000

1.96 0.0108000

2.94 0.0184000

3.43 0.0212000

3.92 0.0244000

4.41 0.0276000

4.9 0.0312000

5.39 0.0344000

5.88 0.0380000

6.37 0.0412000

6.86 0.0452000

7.35 0.0480000

Specimen B1

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 B2

Results and Discussion

0

1

2

3

4

5

6

7

8

0.0000000 0.0100000 0.0200000 0.0300000 0.0400000 0.0500000 0.0600000 0.0700000 0.0800000

Loa

d (

kN

)

Deflection (mm)

Load vs Deflection

Beams

B1 B2

Results and Discussion

For testing specimens B3, B4 and B5 the strain gauges are placed as

follows:

Strain Gauge no. Location

1 Above Neutral Axis (Compression Zone)

2 Below Neutral Axis (Tension Zone)

Results and Discussion

Load (kN)Deflection

Strain Gauge 1 Strain Gauge 2

0 0 0

0 -0.0004 0.0004

0 -0.0072 0.006

0 -0.0072 0.006

0.098 -0.0076 0.006

0.196 -0.008 0.006

0.196 -0.0084 0.0068

0.294 -0.0092 0.0072

0.294 -0.0092 0.0072

0.294 -0.0092 0.0072

0.294 -0.0092 0.0072

0.294 -0.0096 0.0072

0.294 -0.0096 0.0072

0.294 -0.0096 0.0076

0.294 -0.0096 0.0076

0.294 -0.01 0.0076

0.294 -0.01 0.0076

0.294 -0.01 0.0076

0.392 -0.01 0.0076

0.392 -0.0104 0.0076

0.392 -0.0104 0.008

0.392 -0.0108 0.008

0.49 -0.0108 0.008

0.588 -0.0108 0.008

0.686 -0.0112 0.008

0.882 -0.0116 0.0084

1.078 -0.014 0.0108

1.47 -0.0172 0.014

1.666 -0.0216 0.0176

2.156 -0.0268 0.0228

2.646 -0.0332 0.0292

3.332 -0.0396 0.0364

4.312 -0.0468 0.0444

5.194 -0.0532 0.0524

5.978 -0.0636 0.0692

Load (kN)Deflection(mm)

Strain Gauge 1 Strain Gauge 2

0 0 0

0.098 -0.0004 0

1.47 -0.0024 0.002

1.764 -0.0072 0.0056

2.058 -0.0088 0.0064

3.332 -0.0128 0.0104

4.998 -0.0188 0.0164

5.684 -0.0232 0.0212

6.076 -0.0248 0.0232

6.468 -0.0272 0.0256

6.958 -0.0292 0.028

7.35 -0.032 0.0304

7.84 -0.0344 0.0328

8.232 -0.0368 0.0352

8.526 -0.0384 0.0372

8.82 -0.0408 0.0396

9.212 -0.0436 0.0428

9.604 -0.0464 0.0528

9.898 -0.056 0.1032

Load (kN)Deflection(mm)

Strain Gauge 1

Strain Gauge 2

0 0 0

0.882 -0.002 0.0012

1.96 -0.0084 0.0068

3.528 -0.0172 0.0136

5.782 -0.0248 0.0248

8.722 -0.0496 0.0456

Specimen B4 Specimen B5

Specimen B3

Results and Discussion

-2

0

2

4

6

8

10

12

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

Loa

d (

kN

)

Deflection (mm)

Load vs Deflection

Strain Gauge 1 (B3) Strain Gauge 2 (B3) Strain Gauge 1 (B4) Strain Gauge 2 (B4) Strain Gauge 1 (B5) Strain Gauge 2 (B5)

Results and Discussion

For testing specimens B6 the strain gauges are placed as follows:

Strain Gauge no. Location

1 Below Neutral Axis (Tension Zone)

2 Bottom Face (Tension Zone)

Results and DiscussionLoad (KN)

Deflection (mm)

Strain Gauge 1 Strain Gauge 2

0 0 0

0.784 0.0028 0.0048

0.784 0.0028 0.0052

0.882 0.0032 0.006

1.078 0.004 0.0068

1.274 0.0048 0.0076

1.372 0.0052 0.0084

1.372 0.0056 0.0088

1.568 0.0064 0.0096

1.568 0.0068 0.0104

1.568 0.0068 0.0104

1.666 0.0072 0.0104

1.666 0.0072 0.0108

1.764 0.0076 0.0112

1.764 0.0076 0.0112

1.764 0.0076 0.0112

1.862 0.0084 0.0116

2.156 0.0096 0.0136

2.646 0.012 0.0164

3.136 0.0144 0.0196

3.822 0.0176 0.0236

4.606 0.022 0.0292

5.488 0.0268 0.0348

6.468 0.0312 0.0404

7.154 0.0364 0.0448

7.938 0.0384 0.0468

Results and Discussion

0

1

2

3

4

5

6

7

8

9

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

LOA

D (

KN

)

DEFLECTION (MM)

Load vs Deflection

Front Face Bottom Face

Results and Discussion

Analytically checking the results

Load = 0.588 kN

Deflection = 0.008 mm

Hence from Bending theory,𝑓

𝑦=𝑀

𝐼

Where,

f = Stress intensity in the fiber

y = Distance of fiber from neutral axis

M = Max. Bending Moment

I = Moment of inertia of section

Results and Discussion

Now,

Strain = 2 x 10-5

So stress can be calculated by𝑆𝑡𝑟𝑒𝑠𝑠

𝑆𝑡𝑟𝑎𝑖𝑛= 𝑀𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦

Here, E= 25000 MPa

Therefore theoretical value of Stress = 0.5 MPa

Now, experimentally observed stress can be calculated by bending theory

So, M = 0.0782 kNm

And therefore, f = 0.46 MPa

Thus the practical and analytical values being very close, the readings are accurate.

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.