RELATION BETWEEN THE STATIC AND DYNAMIC … dynamic modulus of elasticity, experimentally measured...

RELATION BETWEEN THE STATIC AND

DYNAMIC MODULUS OF ELASTICITY,

EXPERIMENTALLY MEASURED

CRISTÓBAL LARAFRANCISCO DE LA MORAGIOVANNI CASCANTEMAHESH PANDEY

OUTLINE

2

• INTRODUCTION

• BACKGROUND

• METHODOLOGY

• RESULTS

• CONCLUSION

NDT in Canada 2017 Conference (June 6-8, 2017)

INTRODUCTION

3NDT in Canada 2017 Conference (June 6-8, 2017)

BACKGROUND METHODOLOGY RESULTS CONCLUSION

ELASTIC MODULUS or YOUNG’S MODULUS

• CONSTANT STRESS/STRAIN

𝜎𝑛𝑥 = 𝐸 ∗ 𝜀𝑥

𝐸 =𝜎𝑛𝑥𝜀𝑥

• 𝜎𝑛𝑥 = Stress direction strain(x)

• 𝜀𝑥 = Strain

INTRODUCTION



STATIC MODULUS (ES)

• Strain range: 10-4 to 10-3

• 5 - 50 [Gpa]

DYNAMIC MODULUS (ED)

• Strain levelsless than:~10-7

• ED > ES

0

5

10

15

0 0.001 0.002 0.003

Str

ess [

GPa]

StrainDynamic Range

Static Range

INTRODUCTION



STRUCTURAL RELEVANCE

• Static modulus

• Compute Deformations

• Building Codes [GPa]:

o 80 𝑓′𝑐

o 150 𝑓′𝑐

• On site quality check

o Cost

o Time Consuming

Δx

INTRODUCTION



ACI 318S-14

RC-DF (Limestone)

RC-DF (Class 2)RC-GDL

RC-DF (Basaltic)

-

10

20

30

40

5 15 25 35 45 55

Sta

tic M

odulu

s o

f Ela

sticity [

GPa]

f'c [MPa]

Samples

INTRODUCTION



OBJECTIVE

• Function Relationship Es(Ed)

• Cost effective method to evaluate Es

SCOPE

• 34 concrete cylinders

• Randomly Selected

INTRODUCTION



STATIC MEASURE

ASTM C 469-14

• 𝐸 =𝑆2−𝑆1

𝜖2 − 50∗10−6

S2= Stress 40% f’c

S1= Stress at ε1 (50 ∗ 10−6)

ε2 = Strain at “S2”

40% f’c

f’c

0

5

10

15

0 0.001 0.002 0.003

Str

ess [

GPa]

Strain

INTRODUCTION



DYNAMIC MEASURE

ASTM C 215-14

• Force Resonance Method

• Impact Resonance Method

INTRODUCTION



DYNAMIC MEASURE

ASTM C 215-97

Transverse Mode Longitudinal Mode

INTRODUCTION



WAVE PROPAGATION

P-waves

• 𝑣𝑝 =𝑀

𝜌=

𝐸𝐷∗(1−𝑣)

𝜌∗(1+𝑣)∗(1−2𝑣)

• Phase Velocity 𝜐𝑝 = 𝑓 𝜆

𝜐𝑝 = 𝑓𝑛 ∗ (2 𝐿)

(Richart, Hall, & Woods, 1970).

INTRODUCTION



PREVIOUS RELATIONS

• 𝐸𝑆 = 0.83 𝐸𝐷 Lydon & Balendran (1986)

• 𝐸𝑆 = 0.23 ൗ𝐸𝐷1.4

𝜌 Popovics (1975)

INTRODUCTION



Dynamic Testing Static Testing Analysis

• 34 cylinder

• Dimensions

• D ≈ 15 cm

• h ≈ 30 cm

INTRODUCTION




• Equipment

• Hammer

• Hydrophone

• 3 dynamic measures

INTRODUCTION




• Equipment

• Hydraulic Press

• Strain Gauge

f’c

0

5

10

15

0 0.001 0.002 0.003

Str

ess [

GPa]

Strain

INTRODUCTION




• Dynamic Analysis

• Range Sweep:

2 kHz – 10kHz

• Find peaks ratio:

𝑓𝑡 = 0.6125 𝑓𝑙

𝐶 𝑀 𝑓𝑡2 = 𝐷 𝑀 𝑓𝑙

2

𝑓𝑡 = 1.78041𝑑

𝐿 𝑇𝑓𝑙

INTRODUCTION



0.00 0.03 0.05 0.08 0.10

Vib

rational

Am

plitu

de

Time [S]

n=2.60kHz

n'= 4.29kHz

2 3 4 5 6

SPECTRAL

AM

PLIT

UD

Frequency (kHz) Thousands

Fundamental Frequencies:

• Longitudinal ≈ 4.29 kHz

• Transversal ≈ 2.60 kHz

2.60

4.29= 0.606 ≈ 0.6125

INTRODUCTION



-

10

20

30

40

50

10 15 20 25 30 35

Sta

tic

Modlu

sof

Ela

sticity

(GPa)

Dynamic Modulus of Elasticity (GPa)

Samples

Trendline (-10%)

Trendline (+10%)

Poly. (Samples)

𝐸𝑠 = 0.0326 𝐸𝐷2 − 0.3639 𝐸𝐷 + 8.8158

INTRODUCTION



-

10

20

30

40

10 15 20 25 30 35

Sta

tic M

odlu

s o

f Ela

sticity (

GPa)


Samples

Lydon and Balendran (1986)

-10%

10%

INTRODUCTION



-

10

20

30

40

10 15 20 25 30 35

Sta

tic

Modlu

sof

Ela

sticity

(GPa)


Samples

Popovics 1975

-10%

+10%

INTRODUCTION



• New correlation ES(ED) proposed

• Further study

• New methodology – More cost effective

• No transducers

• Using transverse/longitudinal ratio

22

THANK YOU!

Questions?

NDT in Canada 2017 Conference (June 6-8, 2017)


REFERENCES

ACI. (2011). Building code requirements for structural concrete (ACI 318S-11). ACI 318.

ASTM International. (1997). C 215 Standard Test Metod for Fundamental Transverse, Longitudinal and Torsional Resonant Frequencies of Concrete Specimens. Annual Book of ASTM Standards. American Society for Testing and Materials.

ASTM International. (2002). C 469 Standard Test Method for Static Modulus of Elasticity and Poisson's Ratio of Concrete in Compression. American Society for Testing and Materials.

Gobierno del Distrito Federal. (October 6th, 2004). Gaceta Oficial del Distrito Federal. Normás Técnicas Complementarias para diseño y construcción de Estructuras de Concreto, págs. 88-194.

Neville, A. (1996). Properties of Concrete (4th ed.). New York: John Wiley & Sons, Inc.

Richart, J. F., Hall, J. J., & Woods, R. D. (1970). Vibrations of Soils. Englewood Cliffs, New Jersey: Prentice Hall.

RELATION BETWEEN THE STATIC AND DYNAMIC … dynamic modulus of elasticity, experimentally measured...

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