University of New Mexico

Civil Engineering Department

Civil Engineering Materials Laboratory, CE 305L

STATIC MODULUS OF ELASTICITY AND POISSON'S RATIO OF CONCRETE in compression

ASTM C469

Scope

This ASTM test method covers the determination of the modulus of elasticity (Young's modulus) of molded concrete cylinders.

References

ASTM C469 Static Modulus of Elasticity and Poisson's Ratio of Concrete in Compression

ASTM C39 Compressive Strength of Cylindrical Concrete Specimens

ASTM C617 Capping Cylindrical Concrete Specimens

ASTM C192 Making and Curing Concrete Test Specimens in the Laboratory

Definitions

Young's Modulus of Elasticity - Young's modulus, E , is the ratio between stress and strain within the working stress range of the concrete ( E has units of stress, i.e., force per unit area, e.g., psi)

Poisson's Ratio – Poisson's ratio, ν , is the negative of the ratio between the lateral strain and the longitudinal strain within the working stress range of the concrete ( ν is an elastic parameter and is dimensionless)

Working Stress Range - 0 to 40% of the ultimate unconfined compressive strength of the concrete.

Stress - Load per unit area, P/A (units of force per length squared, e.g., psi)

Strain - Ratio of length change per an initial gage length, dL/L_o (strain has units of length per unit length, e.g., in./in.).

Apparatus

Compression Testing Machine

Compressometer - The compressometer consists of two yokes, one of which is rigidly attached to the specimen and the other attached at two diametrically opposite points. At one point on the circumference of the rotating yoke, midway between the two supporting pivot points, a pivot rod shall be used to maintain a constant distance between the two yokes. At the opposite point on the circumference of the rotating yoke, the change in distance between the yokes (i.e., the gage reading) is equal to the sum of the displacement due to specimen deformation and the displacement due to rotation of the yoke about the pivot rod.

Extensometer - The extensometer consists of a third yoke between the two compressometer yokes attached at the mid-height of the specimen at two diametrically opposite points. Midway between these two points is placed a pivot rod to maintain a constant distance between the compressometer yokes. The extensometer yoke is hinged at the pivot point to permit rotation of the two segments of the yoke in the horizontal plane. At the opposite point on the circumference, the two segments shall be connected through a dial gage. The change in distance between the two segments (i.e., the gage reading) is equal to the sum of the radial displacement due to specimen deformation and the displacement due to opening of the yoke about the pivot rod.

Materials

6” x 12” Moist-cured concrete cylinders (capped)

Procedure

Download the procedure for Modulus of Elasticity and Poissan's Ratio here

Download the Excel form for Modulus of Elasticity and Poissan's Ratio here

1) Attach the compressometer/extensometer to the test specimen.

2) Place the specimen, with attached compressometer/extensometer, on the lower platen of the test machine.

3) Carefully align the axis of the specimen with the centerline of the upper thrust block of the crosshead.

4) Lower the crosshead down until contact is almost made with the specimen.

5) Zero the dial gages.

6) Load the specimen at a rate of 35 psi per second (990 lb/s) until a load of 20% of ultimate is reached. Stop loading at this 20% value and reduce the load to zero. Note the dial gage reading on the compressometer.

7) If the dial gage readings (deformations) are not zero, repeat step 6 until the dial gages, upon unloading, are zero.

8) Perform the final loading cycle and continue the loading until 40% of ultimate load is achieved, recording without interruption, the applied load and longitudinal deformation at set intervals. (Load slowly, recording dial gage readings at 2000 lb increments; if data acquisition is used, sample deformations and load simultaneously once per second).

9) Calculate stress and longitudinal strain as follows:

Stress, σ = P/A

where P is the applied load and A is the cross-sectional area of the cylindrical specimen.

Strain, ε_x = d/L_o

where d is the longitudinal specimen deformation and L_o is the gage length.

The deformation, d is equal to

d = gI

where g is the longitudinal dial gage reading and

where e 1 is the eccentricity of the compressometer pivot rod from the axis of the specimen and e 2 is the eccentricity of the longitudinal dial gage from the axis of the specimen. If these eccentricities are equal, then I=0.5. The gage length is the distance between yokes, and is generally equal to 8 in. (for 6 in. diameter specimens).

10) Plot the stress-strain curve (stress on the ordinate and strain on the abscissa).

11) Calculate E to the nearest 50,000 psi as follows:

where σ₂ is the stress corresponding to 40% of ultimate load, σ₁ the stress corresponding to a strain of 0.00005, and ε₂ the strain at a stress of σ₂.

12) Calculate lateral (radial) strain as follows:

Strain, ε_y = d'/D

where d' is the radial specimen deformation and D is the specimen diameter.

The deformation, d' is equal to

d' = g'I'

where g' is the radial dial gage reading and

where e' 1 is the eccentricity of the extensometer pivot rod from the axis of the specimen and e' 2 is the eccentricity of the radial dial gage from the axis of the specimen. If these eccentricities are equal, then I'=0.5.

13) Plot the lateral strain versus the longitudinal strain curve (lateral strain on the ordinate and longitudinal strain on the abscissa).

14) Calculate ν to the nearest 0.01 as follows:

where ε_t2 is the lateral strain produced by stress σ₂ , and ε_t1 is the lateral strain produced by stress σ₁.

15) After loading to 40% and recording the load versus displacement data, unload the specimen.

16) Remove the compressometer (the compressometer may be left in place when appropriate to generate the entire stress vs. strain curve to failure).

17) Perform an unconfined compression test in accordance with ASTM C39. The specified loading rate is 35 psi/s.

Report

1) Report the compressive strength (nearest 10 psi) and unit weight of the concrete (0.1 pcf).

2) Plot the stress-strain diagram.

3) Report the measured value of Young's modulus (nearest 50,000 psi).

4) Report the measured value of Poisson's ratio (nearest 0.01).

Questions

1) Calculate the value of E using the A.C.I. expression:

Compressometer/Extensometer

Sample in compressometer/extensometer

Sample Data from CE 305 Fall 2003

The A.C.I expression used to calculate the modulus of elasticity is:

The unit weight of the concrete used in the test is 140.5lb/ft³

The corresponding value for the modulus of elasticity, E = 4.26(10⁶) psi.

The error between the experimental value and using the A.C.I equation is:

%Error = 100(4.26(10⁶)- 4.50(10⁶))/4.26(10⁶)

%Error = 5.6%