experimental evaluation of strain in concrete elements
TRANSCRIPT
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.