# Modulus of Elasticity and Poisson Ratio of concrete

## Modulus of Elasticity and Poisson Ratio of Concrete (with example)

Outline

• Find the modulus of Elasticity of concrete
• Find Poisson’s Ratio of Concrete

Introduction

–        Standardardized test of concrete

•  American Society for Testing and Materials (ASTM)

–        Specifications include

•  Correct mix
•  Properly affixing strain gauges
• Properly capping the cylinder with sulfur

Procedure

•  Select (5) 4in diameter by 12in length concrete with 28-day age with 4 ksi design strength.
• Cap all the bearing surfaces with sulfur to make the end flat.
• Mark area where strain gauges will be attached.
•  Clean area with chemical cleaners and sand paper.
•  Affix strain gauges on their designated area, one vertical and one horizontal, using glue.
• Attach wire to strain gauges by soldering.
• Test voltage of the strain gauges.
•  Place and center samples on the Satec Universal Testing Machine.
•  Connect the wires to the P3500 strain indicator, which in turn is connected to a computer for recording.
• Set gauge factor to 2.055 +/- .5% and zero the strain readings.
•  Continue testing until failure of the specimen.

Organizing the data

• Compute the stress by dividing the load by the cross-sectional area.
• Graph the strength against the vertical and horizontal strains of each specimen.
• Find values for the Young’s Modulus and Poisson’s ratio from the data.
• Calculate the theoretical values the Young’s Modulus and Poisson’s ratio.

Calculation Procedures

•    Young’s Modulus

–        E=(s1-s2)/(e2-.000005)

•   s1=the stress corresponding to the longitudinal strain of 50 micro strain.
•   s2=the stress corresponding to .4f ‘c.
•   E2=the longitudinal strain corresponding to s2.
•  Based on ASTM C 469
•  Poisson’s Ratio

–        n=(Lateral Strain)/(Longitudinal Strain)

Conclusion

•  All specimens performed under the theoretical values of E.

–        Average E= 2.60E6 psi

•   Average Poisson Ratio= .119691

Power Point Presentation with an example has been embedded below for better understanding.