CHAPTER 5 CONCRETE CORE DRILLING STRAIN GAGE TECHNIQUE...

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CHAPTER 5

CONCRETE CORE DRILLING STRAIN GAGE TECHNIQUE

5.1 INTRODUCTION

Concrete core-drilling strain gage technique is a technique that can be

used to evaluate the in-situ stresses on concrete structural members. This

chapter describes the development of the technique for measurement of in-situ

stress on concrete structures subjected to biaxial stress condition. A special

strain gage rosette configuration consisting of six electrical resistance strain

gages aligned radial- and tangential- direction around the core is used to

evaluate the in-situ stress.

Experimental studies were carried out to evaluate the existing stress in

the laboratory specimens by core drilling strain gage technique with a known

biaxial stress field. Numerical studies were also carried out to compare the

experimental evaluation. Calibration constants were evaluated experimentally

to evaluate the stresses from the measured strain and compared with numerical

analysis using finite element method.

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5.2 THROUGH HOLE ANALYSIS FOR BIAXIAL STRESS

CONDITION

The introduction of hole in a stressed body relaxes the stresses at that

location. This occurs because every perpendicular to a free surface (the

surface of hole in this case) is necessarily a principal axis on which the shear

and normal stresses are zero. The elimination of these stresses on the surface

of the hole changes the stresses in the immediately surrounding region,

causing the local strains on the surface of the test object to change

correspondingly. This is the basis of the hole drilling strain gage technique of

existing stress measurement.

The stress release for a plate with a hole in uniaxial compressive stress

condition is presented in Chapter 3.2. The released stresses for this case are

given in Equations (3.7), (3.8) and (3.9).

In cases where the stresses are of biaxial with two nonzero principal

stresses, it can be incorporated in the analysis by employing the superposition

principle, which is applicable to linear-elastic material as shown in Figure 5.1.

Figure 5.1. Stress states in biaxial stressed body at A(r, )

Y

XX

X

r

arA

YY

Y

XX

X

r

arA

Y

Y

X

Y

r

arA

=+

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The released stresses at the point A(r, ) due to biaxial stress in the X and Y

direction can be derived as follows:

2cos4322 2

2

4

4

2

2

ra

ra

ra yxyxR

r (5.1)

2cos322 4

4

2

2

ra

ra yxyxR (5.2)

2sin232 2

2

4

4

ra

rayxR

r (5.3)

where, a= hole radius and r = arbitrary radius from hole center. The loadings

and stresses are in XY plane. Therefore zz=0 and it is a plane stress problem.

So components zx= zy=0. The strain can be calculated from stress using the

Equations (5.4) and (5.5)

C

RRr

r E(5.4)

C

Rr

R

E(5.5)

Here, EC = Modulus of elasticity and = Poissons ratio.

5.3 CONCRETE CORE-DRILLING STRAIN GAGE TECHNIQUE

Residual stress evaluation for homogenous materials like metal can be

evaluated by using blind hole drilling technique, an ASTM method(2002).

This concept was extended to evaluate the in-situ stress in concrete structural

elements using concrete core-drilling strain gage (CDSG) technique. Concrete

core-drilling strain gage (CDSG) technique was developed by suitable

placement of electrical resistance strain gages around the core for assessment

of in-situ stress. Six strain gages of 30mm gage length were used where three

strain gages placed radially and the remaining three placed tangentially to the

indented core. Each of the radial gages R1, R2 and R3 were of 30mm gage

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length with orientation along 0 , 225 and 90 respectively. Each of the

tangential gages T1, T2 and T3 were of 30mm gage length and placed

diametrically opposite to the respective radial gages as shown in Figure 5.2.

Figure 5.2. Strain gage rosette configuration

In order to increase the strain response a half bridge configuration in

the Wheatstone bridge circuit was adopted by suitably combining radial- and

tangential- gages. This will magnify the strain response. On drilling an

annular core of 50 mm diameter, the strain gage measures the change in strain

due to core drilling. A standard concrete core cutting machine, with diamond

tipped cutting tool, was used in this method. Strain gage data logger with a

resolution of 1micro-strain was used to measure the strain.

Combining the radial gage R1 and tangential gage T1 in Wheatstone

bridge circuit was denoted as gage SG1. Similarly, combination of radial gage

R2 and tangential gage T2, and radial gage R3 and tangential gage T3 are

denoted as gage SG2 and gage SG3, respectively. The total strain release from

a Radius of holeRR Radial gage circle radiusRT Tangential gage circle radius

SG1 = R1 T1SG2 = R2 T2SG3 = R3 T3

a = R1- T1

b = R2- T2

c = R3- T3

1

R32

R1

R2

T1

T3

T2

RR

RT

a

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the gages SG1, SG2 and SG3 are a, b and c, respectively. Here, a = R1- T1,

b = R2- T2 and c = R3- T3.

From the released strain response from the gages, the existing stresses

can be evaluated by employing the formula given below.

222,1 24

14 bacac

ca

BA(5.6)

ca

cba 22tan (5.7)

where, 1,2 are major and minor principal stresses; a, b, c are the released

strain from the strain gages SG1, SG2 and SG3, respectively; and is the

direction of principal stress. A and B are the calibration constants for the

chosen configuration. These calibration constants can be evaluated

experimentally.

5.4 THEORETICAL ANALYSIS FOR POSITIONING OF GAGES

Theoretical analysis using the closed form solution available for plate

with through hole was carried out to choose configuration that will give the

maximum response for an applied stress state.

Eighteen different possible configurations were considered for this

study to use it for evaluation of in-situ stress. Each configuration was

identified with the gage circle radius i.e. R50T35 denotes radial gages aligned

in the radius of 50mm and tangential gages aligned in the radius of 35mm with

respect to the centre of the hole. Figure 5.3 shows various positioning of the

eighteen strain gage configuration considered.

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R40T30 R45T30 R45T35 R45T40

R45T45 R45T50 R50T35 R50T40

R50T45 R50T50 R55T35 R55T40

R55T45 R55T50 R60T35 R60T40

R60T45 R60T60

Figure 5.3 Various gage configurations studied

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For the analysis, the existing compressive stress of x = -1 N/mm2,

y = 0 N/mm2 and x= 0 N/mm2, y = -1 N/mm2 was considered. Modulus of

elasticity (EC) of 31623 N/mm2 and Poissons ratio ( ) of 0.17 were used in

the analysis. From the closed form solution available for the through hole

analysis (Equations (5.1) (5.2) and (5.3)), the released stress experienced

along various points along the gage length were calculated. From the released

stresses, strain release along the gage orientations was calculated using

Equations (5.4) and (5.5). The released strains were calculated for different

strain gage positions. Graphs were plotted between the strain values and the

corresponding distance along their gage length. Figure 5.4 shows the released

strain distribution for radial gages R1, R2 and R3 for the applied stress cases

x = -1 N/mm2, y = 0 N/mm2 and x= 0 N/mm2, y = -1 N/mm2

respectively. The maximum strain response occurred at the edge of the hole

and decreases away from the hole.

-10

0

10

20

30

40

25 35 45 55 65 75

Distance from centre of hole in mm

R1R2R3

-10

0

10

20

30

40

25 35 45 55 65 75


R1R2R3

( x=-1 N/mm2, y=0 N/mm2) ( x=0 N/mm2, y=-1 N/mm2)

Figure 5.4 Released strain variations along the radial gages

Figures 5.5 and 5.6 show the released strain distribution for 30 mm

gage length, tangential gages at various positions of their gage circle radius for

the applied stress conditions x = -1 N/mm2, y = 0 N/mm2 and x= 0 N/mm2,

y = -1 N/mm2. Comparatively a higher strain response is noticed at a gage

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circle radius of 30mm. The magnitude of released strain is lesser for areas

away from the core. The strain variation is almost negligible for gage circle

radius beyond 50mm.

-40

-30

-20

-10

0

10

-30 -20 -10 0 10 20 30Distance from centre of hole in mm

T1T2T3

-40

-30

-20

-10

0

10


T1T2T3

Gage circle radius =30mm Gage circle radius =35 mm

-40

-30

-20

-10

0

10

-30 -20 -10 0 10 20 30


T1T2T3

-40

-30

-20

-10

0

10

-30 -20 -10 0 10 20 30


T1T2T3

Gage circle radius =40 mm Gage circle radius =45 mm

-40

-30

-20

-10

0

10

-30 -20 -10 0 10 20 30


T1T2T3

-40

-30

-20

-10

0

10

-30 -20 -10 0 10 20 30


T1T2T3


Figure 5.5 Released strain variations along tangential gages - ( x=-1.0 N/mm2, y=0.0 N/mm2)

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-40

-30

-20

-10

0

10


T1T2T3

-40

-30

-20

-10

0

10


T1T2T3


-40

-30

-20

-10

0

10

-30 -20 -10 0 10 20 30


T1T2T3

-40

-30

-20

-10

0

10

-30 -20 -10 0 10 20 30


T1T2T3


-40

-30

-20

-10

0

10

-30 -20 -10 0 10 20 30


T1T2T3

-40

-30

-20

-10

0

10

-30 -20 -10 0 10 20 30


T1T2T3


Figure 5.6 Released strain variations along tangential gages - ( x=0.0 N/mm2, y=-1.0 N/mm2)

From the released strains, strain for the 30mm length gage was

obtained by integrating and taking average of the strain variation for 30mm.

The strain responses for various gages at different positions are given in

Tables 5.1 to 5.2.

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Table 5.1 Radial gages response for applied stress

R1 R2 R3 R1 R2 R3Gage circleradius in

mm Micro-strain Micro-strain

60 -6.21 1.7 13.07 13.07 1.73 -6.2155 -6.93 2.04 15.19 15.19 2.09 -6.9350 -7.55 2.52 17.72 17.72 2.57 -7.7545 -7.73 3.18 20.58 20.58 3.24 -7.7340 -6.36 4.18 23.18 23.18 4.24 -6.36

Appliedstress x= -1 N/mm

2, y=0 N/mm2 x=0 N/mm2, y= -1 N/mm2

Table 5.2 Tangential gages response for applied stress

T1 T2 T3 T1 T2 T3Gage circleradius in

mm Micro-strain Micro-strain60 -3.34 -2.88 -2.7 -2.7 -2.89 -3.3450 -5.78 -3.89 -2.71 -2.71 -3.99 -5.7745 -7.92 -4.81 -2.36 -2.36 -4.68 -7.9240 -11.22 -5.88 -1.45 -1.45 -5.81 -11.2235 -16.46 -8 0.52 0.52 -8.11 -16.4730 -25.08 -9.15 4.54 4.53 -8.62 -25.09

Appliedstress x= -1 N/mm

2, y=0 N/mm2 x=0 N/mm2, y= -1 N/mm2

Using radial and tangential gages, various possible strain gage

configurations were worked out. Their combined response when connected in

half bridge circuit was calculated. Based on the experimental feasibility and

comparatively good strain response, the suitability of the gage position and

configuration was finalized.

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For radial and tangential gages, the combined response when

connected in half bridge circuit was calculated for SG1, SG2, and SG3 and

given in Table 5.3.

Table 5.3 Strain response for different configurations

SG1 SG2 SG3 SG1 SG2 SG3Configuration Micro-strain Configuration Micro-strainR40T30 37 26 37 R45T50 21 14 21R45T30 33 24 33 R55T40 20 15 20R45T35 28 22 28 R50T45 20 14 20R50T35 26 21 26 R60T40 19 15 19R45T40 25 18 25 R50T50 18 12 18R55T35 24 20 24 R55T45 18 13 18R50T40 22 16 22 R60T45 17 13 17R60T35 22 19 22 R55T50 16 11 16R45T45 23 16 23 R60T60 12 9 12

Applied Stress of x= -1 N/mm2 and y= -1 N/mm2

Based on the experimental feasibility and comparatively good strain

response, the suitability of the gage position and configuration was selected.

For the given applied stress, the half bridge circuit is expected to give higher

strain response for radial gages placed at a gage circle radius of 40mm and

tangential gage circle radius of 30mm. However, considering experimental

feasibility, this positioning may cause damage to the gages during the drilling

operation as the portion of the gages falls on the core radius of 25mm.

Therefore the corresponding strain gage configuration R40T30 was avoided in

practice. The similar condition applies for R45T30, R45T35, R45T40,

R45T45 and R45T50 hence not suitable. The response of other strain gage

configurations like R60T40, R50T50, R55T45, R60T45, R55T50 and R60T60

are comparatively small. Hence these configurations were also not chosen.

Remaining configurations R50T35, R55T35, R50T40, R60T35, R55T40 and

R50T45 were all giving good responses. Based on the experimental feasibility

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and comparatively higher strain response, the suitability of the gage position

and configuration was selected. Out of eighteen, the strain gage configuration

R50T35 which provides a comparatively high and consistent strain response in

all gages was selected to evaluate the in-situ stress.

5.5 NUMERICAL ANALYSIS

Numerical analysis was carried out to study the influence of released

strain around the hole and to get the calibration constants for the chosen

configuration. A plate with a central hole under compressive stress was

analyzed. The calibration constants evaluated numerically was validated on a

model having dimension of 500x500x100mm with a known stress

combination of x = -2N/mm2 and y = -3N/mm2.

5.5.1 Numerical Calibration

Numerical analysis was carried out to evaluate the calibration constants

by using finite element analysis. Finite element model of dimensions

500x500x100mm with core diameter of 50mm was created using ANSYS

since the core was drilled with 50mm diameter. During experiments, a

maximum depth of 50mm was cut with the incremental of 10mm. Hence five

models with depth of 10mm, 20mm, 30mm, 40mm and 50mm were used for

the study. Apart from this, a model of dimension 500500100mm without

core also was created.

SOLID95 element was used in modeling the geometry. The element is

defined by 20 nodes having three degrees of freedom per node: translations in

the nodal x, y, and z directions. A coarser mesh was adopted for portion away

for hole and finer mesh near the hole, where the strain gages were installed

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over the plate. Uniform stress of, x = -1N/mm2 was considered for the

analysis. The stress was applied as pressure load on the elements lying on the

surface as shown in Figure 5.5. Translations along the loading direction not

allowed at the other end of the model were given as the boundary conditions.

A typical model with loading and boundary condition used for the study is

shown in Figure 5.7.

Modulus of elasticity (EC) of 31623 N/mm2 and Poissons ratio ( ) of

0.17 were used in the analysis. Loading and boundary conditions were

applied on six models and analysed using ANSYS. For the evaluation of in-

situ stresses, it was assumed that the gages SG1, SG3 and SG2 were aligned

along y axis, x axis and 45 to the x axis respectively as shown in Figure 5.7.

Figure 5.7 Typical model showing loading and boundary condition

From the analysis strain distribution on the surface of the model was

obtained. Figures 5.8 to 5.12 show the contours of strain for different core

depths of 10mm, 20mm, 30mm, 40mm and 50mm.

R1

R3T2

T1

T3

R2

113

x y

Figure 5.8 Contours of strain for core depth of 10mm

x y


x y


114

x y


x y


From the analysis, the released strains along the gage orientations were

calculated by deducting the strain from the model with core and without core.

The released strain variation along R1, R3, T1 and T3 gage were calculated

and shown in Figures 5.13 to 5.16.

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0

10

20

30

40

0 50 100 150 200 250Distance in mm

10mm20mm30mm40mm50mm

Figure 5.13 Released strain distribution along gage R1

-20

-10

0

10

20

0 50 100 150 200 250Distance in mm


Figure 5.14 Released strain distribution along gage R3

116

-10

0

10

-40 -20 0 20 40Distance in mm


Figure 5.15 Released strain distribution along gage T1

-20

-10

0



Figure 5.16 Released strain distribution along gage T3

From these plots, it is observed that the released strain is less for

smaller depth of cut and as the drilling depth increases the magnitude of

released strain also increases. Further, as expected the strain release is higher

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near the vicinity of the core and beyond 150mm away from the core the

released strain is negligible.

From the released strain distribution, the strain response for each of the

radial- and tangential- gages of 30mm gage length was obtained by integration

and averaging the strain variation over the gage length. By using this method

strain response was calculated for various core depths of 10mm, 20mm,

30mm, 40mm and 50mm and are given in Table 5.4. From the released strain

values of radial- and tangential- gages the total response of gage SG1, and

SG3 were calculated by adding the strain response of each radial and

tangential gages. The calibration constants were calculated by using Equations

(5.11) and (5.12). The strain response for radial and tangential gages and

calibration constants are given in Table 5.4. Figure 5.17 shows the calibration

constants evaluated numerically for various core depths. These constants are

used to evaluate the existing stresses from the released strains.

Table 5.4 Calibration constants evaluated numerically

Strain response ConstantR1 R3 T1 T3 aC cC A B

Depthmm

Micro-strain 10-6 10-6

10 10.2 -2.0 -2.4 -4.9 12.57 2.83 7.7 4.8720 16.2 -4.6 -4.7 -8.2 20.86 3.58 12.22 8.6430 18.3 -6.3 -4.8 -10.6 23.12 4.33 13.725 9.39540 18.8 -7.2 -4.7 -12.3 23.47 5.06 14.265 9.20550 18.7 -7.8 -4.3 -14.2 23.03 6.41 14.72 8.31

Applied stress C = -1.0 N/mm2

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0

10

20

30

40

50

0 4 8 12 16Calibration constant

AB

Figure 5.17 Calibration constant for different core depths

5.5.2 Validation

In order to validate the calibration constants evaluated numerically for

the chosen configuration, finite element analysis was carried out with a known

stress state of x = -2 N/mm2 and y = -3 N/mm2. The same model of

dimensions 500 500 100mm with central hole of 50mm diameter with

varying depths 10mm, 20mm, 30mm, 40mm and 50mm used for evaluating

the calibration constant was used here. A model with out hole of dimension

500 500 100 mm was also used for analysis.

The biaxial stress was applied as pressure load on the two adjacent side

of the model on the elements lying on the surface. It may be noted that this

stress state was assumed to be uniform over the thickness. Translations along

the loading direction were not allowed at the end of the model as the boundary

conditions. Uniform stress of, x= -2 N/mm2 and y = -3 N/mm2 was

considered for the analysis.

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Modulus of elasticity (EC) of 31623 N/mm2 and Poissons ratio ( ) of

0.17 were used in the analysis. Loading and boundary conditions were

applied to the model and analysis was carried out on six models using

ANSYS. Typical model showing the loading and boundary conditions for

validation is shown in Figure 5.18. For the evaluation of in-situ stresses, it is

assumed that the gages SG1, SG3 and SG2 were aligned along y axis, x axis

and 45 to the x axis respectively. From the analysis strain distribution on the

surface of the model was obtained. Figures 5.19 to 5.23 show the strain

contours for different core depths of 10mm, 20mm, 30mm, 40mm and 50mm

respectively

Figure 5.18 Typical model used for numerical validation

x y

Figure 5.19 Contours of released strain for 10mm depth - validation

120

x y


x y


x y


121

x y


From the analysis, the released strains were obtained for the three gages

SG1, SG2 and SG3. Released strain variations along the radial gages R1, R2

and R3 and tangential gages T1, T2 and T3 for different core depth of are

given in Figures 5.24 and 5.29.

0

20

40

60

80

100

0 50 100 150 200 250Distance in mm


Figure 5.24 Released strain variation along the gage R1 - validation

122

0

20

40

60

80

100

120

0 50 100 150 200 250Distance in mm



0

20

40

60

80

100

120

0 50 100 150 200 250Distance in mm



123

-80

-60

-40

-20

0

20



Figure 5.27 Released strain variation along the gage T1 - validation

-60

-40

-20

0

20




124

-60

-40

-20

0

20




From the released strain variations, strain response for the gages SG1,

SG2 and SG3 (ie. a, b and c) were obtained by averaging the strain

variation of radial and tangential for the gage length of 30mm. From the

released strain, the principal stresses and direction of principal stress were

calculated using Equations (5.6) and (5.7) and are given in Table 5.5. Von-

mises stress ( Von) was calculated from the Equation (5.8).

212

22

1Von (5.8)

It is seen that the released strain for 10mm depth of cut is less. The

strain release increases with the increase in depth of cut. But after 30mm

depth, the change in strain release is less as the strain release stabilises. The

Von-mises stress for the applied stress is 2.65. The evaluated Von-mises

stress for different depths varies between 2.58 and 2.61 with an average of

2.602. The percentage error between the applied and evaluated Von-mises

stress is less than 2%.

125

Table 5.5 Evaluated released strain and Principal strain / stresses

Depth of cutQuantity 10mm 20mm 30mm 40mm 50mma(micro-strain) 33.3 51.4 58.7 61.6 64.8b(micro-strain) 38.6 61.6 69.8 72.3 72.8c(micro-strain) 42.8 67.8 76.7 79.0 80.8

1(N/mm2) -1.98 -1.95 -1.98 -1.98 -1.992(N/mm2) -2.96 -2.93 -2.96 -2.95 -2.95 (degrees) -3.05 -6.93 -6.60 -6.63 -0.19

Von-mises stressVon (N/mm2)

2.61 2.58 2.61 2.60 2.61

Ratio of Von-misesstress* 0.99 0.97 0.99 0.98 0.98

(* - applied Von-mises stress = 2.65 N/mm2)

Note :

1. Positive value of strain / stress indicates tension2. Positive sign of indicates the direction of maximum principal stress

with respect to gage SG1 is anticlockwise

5.6 EXPERIMENTAL STUDIES

The reliability of this technique for in-situ stress evaluation under

biaxial stress state was established in the laboratory, by conducting

experimental investigations on concrete specimens by applying known

stress/strain. Experimental studies on in-situ stress evaluation under biaxial

stress field using core drilling strain gage technique were carried out on ten

specimens of dimension of 500500100mm. The details of the studies are

given below.

5.6.1 Instrumentation and Testing

Experiments were carried out on 500500100mm size concrete

specimens. Ten specimens were studied for this purpose. Both trepanning

126

technique and core drilling strain gage technique were evaluated in the same

specimens by instrumenting and testing with known load / stress. The

specimens were instrumented with special rosette configuration consists of six

number of electrical resistance strain gage of 30mm length, 120 ohm

resistance pre-attached lead wire (as shown in Figure 5.2) around the intended

core. Further a three element stacked rectangular rosette was also bonded

inside the intended core to measure applied strain/stress (also used for

concrete core trepanning technique). Special protective coating was applied on

the gages since water was used as coolant during core drilling. Figure 5.30

shows the specimen instrumented with strain gages. Standard procedures

were followed for bonding the strain gages. Before bonding the strain gages

the surface of the specimen was cleaned with emery sheets. A pre coat of two

component epoxy was applied on the surface as moisture protection. All the

gages were bonded to the specimen using cynoacyralic based quick setting

cement. After bonding, the gages were protected with a layer of M-coat and

wax protection.

Figure 5.30 Instrumentation details on the specimen

A special test set-up was designed and fabricated to apply axial

compression to the specimen, by means of pedestals. The test setup is shown

R1

R3

R2

T2

T3

T1

127

in Figure 4.14. During testing, all the strain gages were connected to a data

logger and initialized before loading. Loads were applied in both directions by

means of two 300kN capacity hydraulic jacks. Applied load was monitored

by two 300kN capacity load cells. These load cells were specially designed

and fabricated for this purpose. A strain gage data logger was used to measure

the strain response. All the strain gages were connected to the strain gage data

logger. During loading, the load and strain responses were monitored in order

to know the applied strain to the specimens. After loading, strain response was

recorded from the strain gages. From the measured strain, the applied stress,

principal stresses and directions of principal stress were computed.

Core drilling strain gage technique was carried out by drilling the

stressed specimen using diamond tip drilling equipment. Before drilling all

the gage circuits were initialized. Incremental drilling was carried out in steps

of 10mm up to 50mm. At each increment, the released strain was measured

from the strain gages.

5.6.2 Calibration Constant

The calibration constants for chosen rosette configuration for core

drilling strain gage technique can always be determined by experimental

calibration. This procedure is particularly attractive since it automatically

accounts for the mechanical properties of the test material, strain gage rosette

geometry, core depth and diameter, and the strain averaging effect of the strain

gage grid. It is to be noted here that the calibration must be repeated each time

a different set of geometric parameters is involved.

Calibration constants A and B were determined experimentally by

installing the strain gage rosette on a uniaxially stressed specimen made from

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the same material as the test specimen. Three specimens were used to evaluate

the calibration constants. Strain gages were bonded on to the surface of the

specimen at centre in rosette configuration. The instrumented specimen was

loaded under uniaxial compression in a specially erected loading setup. The

specimen was placed such that the radial gage R1 of SG1 was aligned along

the loading direction and the radial gage R3 of SG3 was aligned in

perpendicular to the loading direction. Gages SG1 and SG3 were connected

to the strain gage data logger. Zero balancing of the strain gage circuits was

done before the application on load. A known load (P) was applied to the

specimen to develop calibration stress, C. Measurement of strain from gages

SG1 and SG3 ( a and c) was carried out. After unloading, the specimen was

core drilled for 10mm depth using standard core drilling equipment with

50mm diameter diamond tip drill bit. All the strain gage circuits initialized

again and the specimen loaded to the same applied load (P). Measurement of

strains a and c was carried out (after drilling). The calibration strains aC

and cC corresponding to the load, P, and the applied stress, C, are then:

aC = a a (5.9)

cC = c c (5.10)

The constants A and B (calibration constants for the gage configuration and

material) were determined from the released strains using Equations (5.11)

and (5.12).

A= ( aC+ cC)/ (2 C) (5.11)

B= ( aC- cC)/ (2 C) (5.12)

This procedure was repeated for other depth of cut 20mm, 30mm, 40mm

and 50mm. Calibration constant evaluated for different depths using three

specimens is given in Table 5.6.

129

Table 5.6 Calibration constant evaluated experimentally

Specimen 1aC cC A BDepth in

mm Micro-strain 10-6

10 32 6 6.07 4.15220 64 8 11.5 8.94430 79 8 13.9 11.3440 86 6 14.7 12.7850 79 3 13.1 12.14

C = -3.131 N/mm2



10 53 7 6.325 4.84920 100 10 11.595 9.48730 120 12 13.914 11.38440 127 11 14.546 12.22750 122 7 13.598 12.122

C = -4.743 N/mm2



10 54 5 5.904 4.90320 104 8 11.208 9.60730 122 10 13.209 11.20840 128 13 14.11 11.50850 124 13 13.71 11.108

C = -4.996 N/mm2

Average constant was calculated from the calibration constants

evaluated from the three specimens. Experimentally evaluated constants were

compared with the numerically evaluated and given in Table 5.7. The

comparison of constants evaluated experimentally and numerically is shown

in Figure 5.31. It is seen that there is variation between experimentally and

numerically evaluated constants. This may be due to the strain averaging

effect between numerical and experimental evaluated constants. Also for the

130

numerical analysis the material properties assumed was homogenous. Also in

the analysis the stress distribution across the depth is uniform but in

experiments the stress distribution across the depth may not be uniform. All

these factors may contribute to the difference between the experimental and

numerical values. The experimentally evaluated constants were used to

calculate the stresses from the released strain.

Table 5.7 Comparison of calibration constants

Experimental (Average) NumericalA B A BDepth ofcut mm 10-6 10-6 10-6 10-6

10 6.099 4.635 7.7 4.8720 11.434 9.346 12.22 8.6430 13.673 11.31 13.725 9.39540 14.45 12.171 14.265 9.20550 13.468 11.789 14.72 8.31

0

10

20

30

40

50

0 4 8 12 16Calibration constant

A (EXP)B (EXP)A (NUM)B (NUM)

Figure 5.31 Comparison of Calibration Constants for the Core Depths

5.6.3 Experimental Evaluation

Experimental studies for assessment of stresses under biaxial stress

condition were carried out. Ten specimens were tested with different

131

combination of loads / stresses. The test specimens were identified as SP1,

SP2, SP3, SP4, SP5, SP6, SP7, SP8, SP9 and SP10. The results of each

specimen are given below:

5.6.3.1 Test results of Specimen SP1

The Specimen SP1 was biaxially stressed by loading 156kN and 105kN

in two orthogonal directions. The strain developed and the calculated

principal strain / stress and Von-mises stresses based on the measured strain in

the Specimen SP1 are given in Table 5.8.

Table 5.8 Applied strain and stress for Specimen SP1

Applied strain Principal strain Principal stressa = -33micro-strainb = -14micro-strainc = -3micro-strain

1 = - 2.5micro-strain2 = - 33.5micro-strain

= 82.53

1 = -0.27N/mm2

2 = -1.11 N/mm2

Von = 1.00 N/mm2

Note :



Core drilling was carried out on the stressed Specimen and during

drilling released strain was measured from the gages SG1, SG2 and SG3.

From the measurement of released strain the principal stresses and direction of

principal stress were evaluated from the Equations (5.6) and (5.7). Each depth

of cut, corresponding calibration constants (A, B) were used. Von-mises stress

( Von) was calculated from the principal stresses. Table 5.9 gives the released

strain and the evaluated principal stresses for Specimen SP1. Released strain

vs. depth of cut for a Specimen SP1is given in Figure 5.32.

132

Table 5.9 Released strain and evaluated stress for Specimen SP1

Depth of cutQuantity 10mm 20mm 30mm 40mm 50mm Average

a(micro-strain) 5 8 10 10 9b(micro-strain) 7 14 16 17 16c(micro-strain) 12 23 27 30 27

1(N/mm2) -0.29 -0.27 -0.28 -0.26 -0.28 -0.282(N/mm2) -1.11 -1.09 -1.07 -1.12 -1.06 -1.09(degrees) 78.40 84.35 81.81 81.65 83.74 81.99


1.00 0.98 0.96 1.02 0.95 0.98

Von-mises stressratio 1.00 0.98 0.96 1.02 0.95 0.98

% error in Von-mises stress ratio -0.21 -1.60 -3.82 1.61 -4.79 -1.77

Note :



0

10

20

30

40

50

0 20 40 60 80 100Micro-strain

SG1SG2SG3

Figure 5.32 Released strain vs. depth of cut for Specimen SP1

133

From the principal stress evaluated for different depths, average

stresses were calculated. The evaluated average principal stresses, direction of

principal stress and Von-mises stress are 1= -0.28 N/mm2, 2= -1.09 N/mm2,

= 81.99 and Von=0.98 N/mm2. The percentage error in the applied and

evaluated Von-mises stress is -1.77%. The applied and evaluated principal

stresses, direction of principal stress and Von-mises stress are given in

Figure 5.33.

Figure 5.33 Applied and evaluated stress for Specimen SP1


Biaxial stress was applied to the Specimen SP2 with the load of 221kN

and 109kN in two orthogonal directions. The strain developed and the

corresponding principal strain / stress and Von-mises stresses calculated are

given in Table 5.10.

1 = -0.27 N/mm2

2 = -1.11 N/mm2

= 82.53Von = 1.00 N/mm2

Applied

1 = -0.28 N/mm2

2 = -1.09 N/mm2

= 81.99Von = 0.98 N/mm2

Evaluated

a

2

b

c 1

134


Applied strain Principal strain Principal stressa = -86micro-strainb = 15micro-strainc = 26micro-strain

1 = 41.8micro-strain2 = -101.8micro-strain

= 70.61

1 = 0.80 N/mm2

2 = -3.08 N/mm2

Von = 3.55 N/mm2

Note :



From the measurement of released strain the principal stresses,

direction of principal stress and Von-mises stress were evaluated and given in

Table 5.11. Released strain vs. depth of cut for Specimen SP2 is given in

Figure 5.34.



a(micro-strain) -1 -2 -3 -4 -6b(micro-strain) 2 3 4 4 2c(micro-strain) 29 55 68 70 68

1(N/mm2) 0.92 0.82 0.82 0.79 0.84 0.842(N/mm2) -3.22 -3.14 -3.20 -3.07 -3.14 -3.15(degrees) 70.67 70.25 70.62 70.96 70.96 70.69


3.77 3.62 3.68 3.53 3.63 3.65


% error in Von-mises stress ratio 6.00 1.92 3.58 -0.57 2.29 2.64

Note :



135

0

10

20

30

40

50

-20 0 20 40 60 80 100Micro-strain

SG1SG2SG3




principal stress and Von-mises stress are 1= 0.84 N/mm2, 2= -3.15 N/mm2,

= 70.69 and Von= 3.69N/mm2. The average percentage error in the

applied and evaluated Von-mises stress is 2.64%. The applied and evaluated

principal stresses, direction of principal stress and Von-mises stress are given

in Figure 5.35.

Figure 5.35 Applied and evaluated stresses for Specimen SP2

1 = 0.84 N/mm2

2 = -3.15 N/mm2

= 70.69Von = 3.65 N/mm2

Evaluated

1 = 0.80 N/mm2

2 = -3.08 N/mm2

= 70.61Von = 3.55 N/mm2

Applied

a

2

b

c 1

136


Specimen SP3 was loaded with 202kN and 83kN in two directions to

create biaxial stress. The strain developed and the corresponding principal

strain / stress and Von-mises stresses calculated are given in Table 5.12.


Applied strain Principal strain Principal stressa = -117micro-strainb = -26micro-strainc = 39micro-strain


= -4.73

1 = 0.65 N/mm2

2 = -3.62 N/mm2

Von = 3.99 N/mm2

Note :






Figure 5.36.

0

10

20

30

40

50

-20 0 20 40 60 80 100Micro-strain

SG1SG2SG3


137




1(N/mm2) 0.81 0.73 0.67 0.58 0.54 0.672(N/mm2) -3.76 -3.66 -3.53 -3.45 -3.54 -3.59(degrees) 85.93 85.44 85.76 85.60 85.51 85.65


4.22 4.07 3.91 3.77 3.84 3.96


% error in Von-mises stress ratio 5.88 2.14 -2.02 -5.40 -3.77 -0.65

Note :





principal stress and Von-mises stress are 1= 0.67N/mm2, 2= -3.59N/mm2,


applied and evaluated Von-mises stress is -0.65%. The applied and evaluated


in Figure 5.37.

138



Specimen SP4 was loaded with 231kN and 102kN in two directions.

The strain developed and the corresponding principal strain / stress and Von-

mises stresses calculated are given in Table 5.14.




= -72.60

1 = 1.75 N/mm2

2 = -4.07 N/mm2

Von = 5.18 N/mm2

Note :






Figure 5.38.

1 = 0.65 N/mm2

2 = -3.62 N/mm2

= 85.27Von = 3.99 N/mm2

Applied

a

2

b

c1

1 = 0.67 N/mm2

2 = -3.59 N/mm2

= 85.65Von = 3.96 N/mm2

Evaluated

139




1(N/mm2) 1.76 1.77 1.71 1.80 1.80 1.772(N/mm2) -4.14 -4.13 -4.16 -4.12 -4.18 -4.15(degrees) -72.72 -72.29 -73.33 -72.88 -72.70 -72.79


5.25 5.24 5.23 5.26 5.31 5.26


% error in Von-mises stress ratio 1.33 1.29 1.00 1.53 2.64 1.56

Note :



0

10

20

30

40

50

-40 -20 0 20 40 60 80 100Micro-strain

SG1SG2SG3


140




=-72.79 and Von= 5.26N/mm2. The percentage error in the applied and

evaluated Von-mises stress is 2.64%. The applied and evaluated principal


Figure 5.39.



The Specimen SP5 was stressed biaxially by loading 342kN and 94kN

in two directions. The strain developed and the corresponding principal

strains / stresses and Von-mises stresses calculated are given in

Table 5.16.

1 = 1.75 N/mm2

2 =-4.07 N/mm2

= -72.60Von = 5.18 N/mm2

Applied

a

2

b

c1

1 = 1.77 N/mm2

2 =-4.15 N/mm2

= -72.79Von = 5.26 N/mm2

Evaluated

141




= 82.20

1 = 0.13 N/mm2

2 = -2.99 N/mm2

Von = 3.05 N/mm2

Note :






Figure 5.40.




1(N/mm2) 0.23 0.14 0.17 0.14 0.12 0.162(N/mm2) -3.18 -2.94 -3.02 -3.08 -3.02 -3.05(degrees) 80.78 82.98 82.79 81.48 80.54 81.71


3.30 3.01 3.11 3.15 3.08 3.13


% error in Von-mises stress ratio 8.14 -1.32 1.83 3.27 0.95 2.57

Note :



142



principal stress and Von-mises stress are 1= 0.16 N/mm2, 2= -3.05 N/mm2,

= 81.71 and Von= 3.13N/mm2. The percentage error in the applied and

evaluated Von-mises stress is 2.57%. The applied and evaluated principal


Figure 5.41.

0

10

20

30

40

50

0 20 40 60 80 100Micro-strain

SG1SG2SG3



a

2

b

c1

1 = 0.13 N/mm2

2 = -2.99 N/mm2

= 82.20Von = 3.05 N/mm2

Applied

1 = 0.16 N/mm2

2 = -3.05 N/mm2

= 81.71Von = 3.13 N/mm2

Evaluated

143


Biaxial load was applied to the Specimen SP6 by loading of 178kN and

130kN in two orthogonal directions. The strain developed and the

corresponding principal strain / stress and Von-mises stresses were calculated

and are given in Table 5.18.


Applied strain Principal strain Principal stressa = -77micro-strainb = -77micro-strainc = -49micro-strain

1 = -43.2micro-strain2 = -82.8micro-strain

= -67.50

1 = -1.87 N/mm2

2 = -2.94 N/mm2

Von = 2.57 N/mm2

Note :






Figure 5.42.

0

10

20

30

40

50

0 20 40 60 80 100Micro-strain

SG1SG2SG3


144




1(N/mm2) -1.87 -1.84 -1.79 -1.86 -1.87 -1.852(N/mm2) -2.80 -2.84 -2.85 -2.85 -2.89 -2.85(degrees) -72.23 -71.87 -67.50 -69.18 -65.82 -69.32


2.47 2.50 2.50 2.51 2.54 2.50


% error in Von-mises stress ratio -4.00 -3.03 -3.03 -2.60 -1.34 -2.81

Note :





principal stress and Von-mises stress are 1= -1.85N/mm2, 2= -2.85N/mm2,

=-69.32 and Von= 3.2.50N/mm2. The average percentage error in the



in Figure 5.43.

145



Specimen SP7 was loaded with 164kN and 104kN in two orthogonal

directions. The strain developed and the corresponding principal strain / stress

and Von-mises stresses calculated are given in Table 5.20.




= 88.82

1 = 0.55 N/mm2

2 = -2.72 N/mm2

Von = 3.04 N/mm2

Note :






Figure 5.44.

a

2

b

c1

1 = -1.87 N/mm2

2 = -2.94 N/mm2

= -67.50Von = 2.57 N/mm2

Applied

1 = -1.85 N/mm2

2 = -2.85 N/mm2

= -69.32Von = 2.50 N/mm2

Evaluated

146




1(N/mm2) 0.66 0.57 0.55 0.54 0.58 0.582(N/mm2) -2.8 -2.75 -2.81 -2.75 -2.81 -2.78(degrees) 88.21 89.08 90.00 89.28 89.28 89.17


3.18 3.07 3.12 3.06 3.14 3.11



Note :1. Positive value of strain / stress indicates tension2. Positive sign of indicates the direction of maximum principal stress


0

10

20

30

40

50

-20 0 20 40 60 80 100Micro-strain

SG1SG2SG3


147







in Figure 5.45.



Specimen SP8 was stressed in both direction by applying load of 89kN

and 193kN in two directions. The strain developed and the corresponding

principal strain / stress and Von-mises stresses calculated are given in

Table 5.22.

1 = 0.58 N/mm2

2 = -2.78 N/mm2

= 89.17Von = 3.11 N/mm2

Evaluated

a

b

c 1

2

1 = 0.55 N/mm2

2 = -2.72 N/mm2

= 88.72Von = 3.04 N/mm2

Applied

148


Applied strain Principal strain Principal stressa = 58micro-strainb = -11micro-strainc = -71micro-strain


= -2.0

1 = 1.50 N/mm2

2 = -2.00 N/mm2

Von = 3.04 N/mm2

Note :






Figure 5.46.




1(N/mm2) 1.59 1.51 1.52 1.50 1.56 1.542(N/mm2) -2.08 -2.04 -2.03 -2.05 -2.05 -2.05(degrees) -1.68 -2.60 -2.14 -2.66 -1.68 -2.15


3.19 3.09 3.08 3.09 3.14 3.12



Note :



149

0

10

20

30

40

50

-60 -40 -20 0 20 40 60 80 100Micro-strain

SG1SG2SG3





=-2.15 and Von= 3.12N/mm2. The average percentage error in the applied

and evaluated Von-mises stress is 2.61%. The applied and evaluated principal


Figure 5.47.


1 = 1.54 N/mm2

2 = -2.05 N/mm2

= -2.15Von = 3.12 N/mm2

Evaluated

a

b

c 2

1

1 = 1.50 N/mm2

2 = -2.00 N/mm2

= -2.0Von = 3.04 N/mm2

Applied

150


Specimen SP9 was loaded with 101kN and 237kN in two directions.

The strain developed and the corresponding principal strain / stress and Von-

mises stresses calculated are given in Table 5.24.




= -0.847

1 = 1.16 N/mm2

2 = -3.41 N/mm2

Von = 4.11 N/mm2

Note :






Figure 5.48.

0

10

20

30

40

50

-40 -20 0 20 40 60 80 100Micro-strain

SG1SG2SG3


151




1(N/mm2) 1.30 1.13 1.17 1.24 1.26 1.222(N/mm2) -3.35 -3.53 -3.43 -3.53 -3.45 -3.46(degrees) -2.00 -1.64 -1.10 -0.99 -1.29 -1.40


4.16 4.21 4.14 4.29 4.22 4.20



Note :






=-1.40 and Von= 4.20N/mm2. The average percentage error in the applied

and evaluated Von-mises stress is 2.16%. The applied and evaluated principal


Figure 5.49.

152



The Specimen SP10 was stressed to the load of 78kN and 200kN in

two directions. The strain developed and the corresponding principal strain /

stress and Von-mises stresses calculated are given in Table 5.26.

Table 5.26 Applied strain and stresses for Specimen SP10



= 12.12

1 = 1.18 N/mm2

2 = -6.59 N/mm2

Von = 7.25 N/mm2

Note :






Figure 5.50.

1 = 1.22 N/mm2

2 = -3.46 N/mm2

= -1.40Von = 4.20 N/mm2

Evaluated

1 = 1.16 N/mm2

2 = -3.41 N/mm2

= -0.85Von = 4.11 N/mm2

Applied

a

b

c 2

1

153




1(N/mm2) 1.49 1.22 1.19 1.13 1.09 1.222(N/mm2) -6.24 -6.51 -6.50 -6.42 -6.55 -6.44(degrees) 15.07 12.48 12.77 12.38 12.64 13.07


7.10 7.20 7.17 7.05 7.16 7.14



Note :



0

10

20

30

40

50

-50 0 50 100 150 200Micro-strain

SG1SG2SG3


154







in Figure 5.51.


5.7 DISCUSSIONS

Theoretical analysis using the closed form solution available for plate

with through hole was carried out to choose configuration that will give the

maximum response for a applied stress state. Based on the experimental

feasibility and comparatively good strain response, the suitability of the gage

position and configuration was selected. The strain gage configuration

R50T35 which provides a comparatively high and consistent strain response in

all gages was selected to evaluate the in-situ stress. The calibration constants

for the chosen configuration were evaluated by using finite element method to

calculate the in-situ stress from the measured strain. From the numerical

analysis it is observed that the released strain is less for smaller depth of cut

1 = 1.22 N/mm2

2 = -6.44 N/mm2

= 13.07Von = 7.14 N/mm2

Evaluated

1 = 1.18 N/mm2

2 = -6.59 N/mm2

= 12.12Von = 7.25 N/mm2

Applied

a

1

b

c2

155

and the drilling depth increases the magnitude of released strain also increases.

Further, the strain release is higher near the vicinity of the core and beyond

150mm away from the core the released strain is negligible. Validation of the

calibration constants was carried out with a known stress state of

x = -2 N/mm2 and y =-3 N/mm2 by finite element analysis. The applied

stresses and existing stresses obtained from the rosette equation using the

calibration constants for the hole drilling strain gage technique are matching

closely with more than 97% with respect to Von-mises stress. The calibration

constants for chosen rosette configuration were evaluated experimentally.

Calibration constants were evaluated experimentally and compared with

numerical analysis. The behavior of strain release is identical in both

experimental and numerical analysis.

Totally ten specimens were tested with different combinations of

applied stress. By using core drilling strain gage technique the existing stress

were experimentally evaluated. Table 5.28 gives the applied principal

strain/stress and Von-mises stresses based on the measured strain for all the

tested specimens. Core drilling was carried out on the stressed specimen and

during drilling released strain was measured from the gages SG1, SG2 and

SG3. It is observed from the plots of released strain vs. depth of cut, that the

strain release is at 10mm depth of cut, strain release is less. When the depth of

cut increases, the strain release also increases. When the depth of cut reaches

30mm the strain release stabilizes. Maximum strain release occurred mostly at

40mm depth. Beyond that, the strain release is less though the reduction is

small. From the measurement of released strain the principal stresses and

direction of principal stress were calculated. The experimentally evaluated

constants were used to calculate the stresses from the released strain. The

evaluated principal stresses and direction of principal stress, and Von-mises

stress for ten specimens are given in Table 5.29.

156

Table 5.28 Applied principal strain / stresses for tested specimens

1 2 1 2 VonSP Id. Micro-strain degrees N/mm2

SP1 -2.48 -33.52 82.53 -0.27 -1.11 1SP2 41.84 -101.84 70.61 0.8 -3.08 3.55SP3 40.08 -118.08 85.27 0.65 -3.62 3.99SP4 77.27 -138.27 -72.60 1.75 -4.07 5.18SP5 20.12 -95.12 82.20 0.13 -2.99 3.05SP6 -43.20 -82.80 -67.50 -1.87 -2.94 2.57SP7 32.05 -89.05 88.82 0.55 -2.72 3.04SP8 58.16 -71.16 -2.00 1.5 -2 3.04SP9 55.04 -114.04 -0.85 1.16 -3.41 4.11SP10 72.67 -214.67 12.12 1.18 -6.59 7.25

Note :



Table 5.29 Evaluated principal stresses for tested specimens

1 2 VonSPId. N/mm2 degrees

Von-misesstress ratio

% error inVon-mises

stressSP1 -0.28 -1.09 0.98 81.99 0.98 1.85SP2 0.84 -3.15 3.65 70.69 1.03 2.64SP3 0.67 -3.59 3.98 85.65 1.00 -0.65SP4 1.77 -4.15 5.26 -72.79 1.02 1.56SP5 0.16 -3.05 3.13 81.71 1.03 2.57SP6 -1.85 -2.85 2.50 -69.32 0.97 -2.81SP7 0.58 -2.78 3.11 89.17 1.02 -2.61SP8 1.54 -2.05 3.12 -2.15 1.03 2.61SP9 1.22 -3.46 4.20 -1.4 1.02 2.16

SP10 1.22 -6.44 7.14 13.07 0.98 -1.58Note :

1. Positive value of stress indicates tension2. Positive sign of indicates the direction of maximum principal stress


157

Both applied stress and stress evaluated from core drilling strain gage

technique are matching closely. The percentage error of Von-mises stress is

less than 3%. Thus the reliability of the method is established in this method.

Comparison was also made between the stress evaluated from trepanning

technique and core drilling strain gage techniques. Table 5.30 gives the

comparison of evaluated principal stress between both the techniques. Good

comparison is seen between both the techniques. The percentage of variation

of Von-mises stresses varies between 2.2% to 12.3% with the average being

around 5.1%.

Table 5.30 Comparison of evaluated stresses between core drilling strain gage technique and trepanning technique

Core drilling straingage technique Trepanning technique

1 2 Von 1 2 Von

SPId

N/mm2 N/mm2% of Vonvariation

SP1 -0.28 -1.09 0.98 -0.15 -1.11 1.04 -6.1SP2 0.84 -3.15 3.65 0.91 -2.93 3.48 4.7SP3 0.67 -3.59 3.98 0.70 -3.29 3.69 7.3SP4 1.77 -4.15 5.26 1.91 -3.74 4.97 5.5SP5 0.16 -3.05 3.13 0.38 -2.81 3.02 3.5SP6 -1.85 -2.85 2.50 -1.45 -2.70 2.34 6.4SP7 0.58 -2.78 3.11 0.67 -2.46 2.86 8.0SP8 1.54 -2.05 3.12 1.51 -2.00 3.05 2.2SP9 1.22 -3.46 4.20 1.20 -3.18 3.92 6.7

SP10 1.22 -6.44 7.14 1.26 -5.53 6.26 12.3Note :

1. Positive value of stress indicates tension2. Positive sign of indicates the direction of maximum principal stress


158

5.8 SUMMARY

Concrete core-drilling strain gage (CDSG) technique was developed by

suitable placement of electrical resistance strain gages around the core for

assessment of in-situ stress. Six strain gages of 30mm gage length were used

where three strain gages were placed radially and the remaining three placed

tangentially to the indented core. Combining the radial and tangential gages

in a half bridge whetstone bridge circuit used to improve the stress

measurement accuracy when using the core drilling method.

The suitability of the gage position and configuration has been worked

out by using closed form solution of through hole analysis. Using the closed

form solution of through hole analysis, strain gage configuration R50T35 was

selected for evaluation of the existing stresses in the biaxial stress field.

Finite element analysis was carried out for various core depths ranging

from 10mm to 50mm in an increment of 10mm. The calibration constants

were calculated for R50T30 with different core depths 10mm, 20mm, 30mm,

40mm and 50mm. Evaluation of stresses with a known stress field using the

evaluated constants was done to validate the calibration constants arrived from

the numerical study. The applied stresses and existing stresses obtained from

the study using the calibration constants for the hole drilling method are

matching closely. Experimental studies were carried out to assess the existing

stresses with a known stress field using the core drilling strain gage technique.

Calibration constants were evaluated experimentally and compared with

numerical analysis using Finite element method. The applied stresses and

existing stresses obtained from core drilling strain gage technique using the

calibration constants are matching closely. Thus the reliability of the

technique was established from the studies.

CHAPTER 5 CONCRETE CORE DRILLING STRAIN GAGE TECHNIQUE...

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