Laboratory 4

CE 324P Fall 2015

Properties &

Behavior of

Engineering

Materials

Concrete

Testing

1

COMPRESSIVE, FLEXURAL, AND TENSILE STRENGTH OF CONCRETE

Concrete cylinders and/or beams are generally cast during construction from the same concrete

being used in the structure. Destructive strength tests are typically performed on these specimens.

These test specimens are stored in a temperature-controlled moist room until the specified age of

testing, which is usually 28 days. In this lab you will determine the compressive, flexural, and

tensile strengths of the concrete mixtures that you prepared during Lab 3. Strengths will be

determined at 7 and 28 days after casting.

FACTORS AFFECTING STRENGTH OF CONCRETE

The strength of concrete is affected by many factors. Key among them are:

Mixture Proportions

Age

Uniformity

Degree of Consolidation

Nature of Load

Curing Conditions

Temperature

In addition, there are many factors related to the testing conditions which affect the strength of

concrete including:

Sample Moisture Condition

Roughness of Loading Surface

Loading Rate

End Restraint

Aspect Ratio of Test Specimen

Size of Test Specimen

It should be noted that the compressive, flexural, and tensile strengths determined from destructive

tests of cylinders and beams are not necessarily the same as the strength of the concrete in the

actual structure. The cylinders and beams are cured in a temperature-controlled moist room and

are tested 28 days after the concrete is placed. The concrete in the structure, on the other hand, is

exposed to the natural environment and may have a higher or lower strength than the laboratory

specimen depending on the temperature and moisture of the natural environment. Furthermore, the

structure is expected to have a life of 50 to 100 years and the strength of the concrete at this time

will be necessarily different than at 28 days. The standard laboratory tests are, therefore, intended

to provide an assessment of the quality of the concrete during construction, not to predict the long-

term in-service properties.

2

OVERVIEW OF DESTRUCTIVE TESTS

COMPRESSIVE STRENGTH OF CYLINDRICAL CONCRETE SPECIMENS

(ASTM C39, 2015)

You will determine the compressive strength of cylinders that you cast during Lab 3 during two

lab sessions by applying an axial load to the specimen at a rate of 35 7 psi/sec until failure.

One of the most important factors affecting the results of this test is the aspect ratio

(height/diameter (H/D)) of the cylinder. The influence of the aspect ratio is shown in Fig. 1. The

shaded areas represent regions of the sample that are restrained from expanding by the test machine

platens. Therefore, the shaded area is in a state of triaxial compression, even though the load is

only applied axially. When concrete is confined triaxially, the apparent compressive strength

increases. Therefore, a cylinder with an aspect ratio of 1 will be able to resist higher loads than a

cylinder with an aspect ratio of 2 since the cylinder with an aspect ratio of 2 will have a zone of

unconfined compression. ASTM defines standard cylinders as having an aspect ratio of 2, so that

the end restraint does not influence the test results.

Figure 1: Relationship between Cylinder Aspect Ratio and End Restraint

H/D=1.0 H/D=1.5 H/D=2.0

RestrainedDepth

Diameter

Height

3

FLEXURAL STRENGTH OF CONCRETE (ASTM C78, 2015)

The most common procedure used to determine the flexural strength of concrete is described in

ASTM C78 (2015). A standard beam is placed on simple supports and is subjected to transverse

loads at the third points of the span (Fig. 2). Under this loading condition, the top of the beam is

subjected to compressive stresses and the bottom of the beam is subjected to tensile stresses.

Because the tensile strength of concrete is less than the compressive strength, a crack will form

when the stress along the bottom fiber reaches the tensile strength of the concrete.

The tensile stress along the bottom fiber may be calculated from the applied load. The tensile stress

along the bottom fiber at failure is known as the modulus of rupture (MOR), fr. In this lab manual

it is also referred to as flexural strength. ASTM procedures also exist for beams subjected to a

single load at midspan (ASTM C293, 2010). The third-point loading method (ASTM C78, 2015)

is more common because the bending moment is constant between the load points.

The standard beam specimens are required to have a square cross-section and the distance between

supports is equal to three times the depth of the cross-section. The relationship between flexural

stress, , and applied moment, M, is:

I

Mc (1)

where c is the distance from the neutral axis to the extreme fiber and I is the moment of inertia.

The maximum moment Mmax occurs between the point loads, as shown in Fig. 2:

6

maxPL

M (2)

where P is the total applied load and L is the span.

The moment of inertia for a rectangular cross section, I, is:

12

3bhI (3)

where b is the width of the cross section and h is the overall depth. Substituting Eq. 2 and Eq. 3

into Eq. 1 and taking c equal to h/2 gives the relationship for the modulus of rupture, fr:

2

rPL

fbh

(4)

4

Figure 2: Setup for Flexure Test and Assumed Distribution of Stress

Load should be applied to the beam at a constant rate such that the extreme fiber stress increases

at a rate between 125 and 175 psi/min (2-3psi/sec).

ACI 318 defines the relationship between the modulus of rupture (fr) and the specified compressive

strength (f'c) as:

crc fff 127 (5)

L/3 L/3 L/3

h = L/3

Moment Diagram

LongitudinalStress

compressive

tensile

P/2 P/2

5

SPLIT TENSILE STRENGTH OF CONCRETE SPECIMENS (ASTM C496, 2011)

Another means of assessing the tensile strength of concrete is the split-cylinder test, also known

as the Brazilian test. In this test, a uniform line load is applied along the length of a cylindrical

specimen creating the stresses as shown in Fig. 3. The load at which the specimen splits apart is

then used to estimate the tensile strength, fsp:

DL

Pf sp

2 (6)

where P is the applied load, D is the diameter of the cylinder, and L is the length of the cylinder.

Figure 3: Setup for Split-Cylinder Test and Assumed Distribution of Stress

Load should be applied at a constant rate such that the tensile stress increases at a rate between

100 and 200 psi/min (10-20lbs/sec) (1.67-3.33psi/sec).

The tensile strength determined from the split-cylinder test is typically within the following range:

cspc fff 84 (7)

where the tensile and specified compressive strengths are given in units of psi.

Load

Wood

Wood

Steel Bar

Plane of Tensile Failure

CompressionTension

Variation of Horizontal

Stress across Plane of

Tensile Failure

6

COMPRESSIVE STRESS-STRAIN CURVES

Concrete is composed of aggregate and hardened cement paste. Although the compressive stress-

strain curve for aggregate is nearly linear, the stress-strain curve for concrete is linear only for low

stress levels. Figure 4 shows the stress-strain relationships for three cylinders that were cast from

the same batch of concrete. The slope of the curve reduces dramatically for stresses larger than

one-half the compressive strength.

Figure 4: Measured Compressive Stress-Strain Relationship

MODULUS OF ELASTICITY OF CONCRETE (ASTM C469, 2014)

Because the compressive stress-strain relationship for concrete is nonlinear, ASTM C469 (2014)

defines the chord modulus of elasticity using two specific data points (Fig. 5):

)(

)(

12

12

cc

cc ffE

(8)

where E is the chord modulus of elasticity; fc2 is the stress corresponding to 40% of the compressive

strength of the concrete; fc1 is the stress corresponding to longitudinal strain c1; c2 is the

longitudinal strain corresponding to stress fc2; and c1 is 0.000050 in./in. The chord modulus and

compressive stress are expressed in psi in Eq. 8. The chord modulus of elasticity should be

reported to the nearest 50,000 psi (50 ksi).

0

1,000

2,000

3,000

4,000

5,000

6,000

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

Strain

Str

es

s (

ps

i)

7

Figure 5: Points Used to Define the Chord Modulus of Elasticity

The ACI Building Code (ACI 318, 2005) provides an equation to estimate the modulus of elasticity

of concrete Ec given the specified compressive strength cf :

cc fwE 5.133 (9)

where w is the unit weight of concrete in pcf and Ec and cf are in psi.

SHAPE OF STRESS-STRAIN CURVE

The shape of the stress-strain curve is a result of the nature of the failure mechanisms within

concrete. Because concrete is a brittle material, failure is a result of cracking. This cracking results

because concrete is a heterogeneous material. Cracks begin to form at a stress level of about 1/3

cf . The first cracks formed are called bond cracks and occur at the interface between the paste

and the coarse aggregate. With increasing stress, more bond cracks develop. At stress levels of

about 3/4 cf cracks begin to extend into the paste. The extent of paste cracking increases with

increasing stress until large continuous cracks develop and the concrete reaches its capacity in

compression.

This process of progressive cracking, also known as micro-cracking, is reflected in the shape of

the stress-strain curve.

8

REFERENCES

American Concrete Institute. (2008). Guide for Modeling and Calculating Shrinkage and Creep

in Hardened Concrete. (ACI 209.2R-08). Farmington Hills, MI.

American Concrete Institute. (2014). Building Code Requirements for Structural Concrete. (ACI

318-14). Farmington Hills, MI.

ASTM International. (2015). Standard Test Method for Compressive Strength of Cylindrical

Concrete Specimens (ASTM C39 15a). West Conshohocken, PA.

ASTM International. (2015). Standard Test Method for Flexural Strength of Concrete (Using

Simple Beam with Third-Point Loading) (ASTM C78 15a). West Conshohocken, PA.

ASTM International. (2010). Standard Test Method for Flexural Strength of Concrete (Using

Simple Beam With Center-Point Loading) (ASTM C293 - 10). West Conshohocken, PA.

ASTM International. (2014). Standard Test Method for Static Modulus of Elasticity and

Poisson's Ratio of Concrete in Compression (ASTM C469-14). West Conshohocken, PA.

ASTM International. (2011). Standard Test Method for Splitting Tensile Strength of Cylindrical

Concrete Specimens (ASTM C496 - 11). West Conshohocken, PA.

ASTM International. (2014). Standard Practice for Use of Unbonded Caps in Determination of

Compressive Strength of Hardened Concrete Cylinders (ASTM C1231 14). West Conshohocken, PA.

Cover Image: http://expeditionworkshed.org/workshed/compression-failure-high-strength-

concrete-cylinder/

9

NOTATIONS

b width of beam, in

c distance from neutral axis to extreme fiber, in

D diameter of cylinder, in

E chord modulus of elasticity, psi

Ec estimated modulus of elasticity, psi

fc specified compressive strength at 28 days (design strength), psi

fc1 stress corresponding to c2, a strain of 0.00005 in/in, psi

fc2 stress corresponding to 40% of compressive strength, psi

fcm7 measured average compressive strength at 7 days, psi

fcm28 measured average compressive strength at 28 days, psi

fcmt average compressive strength at t days, psi

fcr required average compressive strength at 28 days, psi

fr average modulus of rupture or flexural strength, psi

fsp average splitting tensile strength, psi

h height of beam, in

I moment of inertia, in4

L length of cylinder, in

M moment, lb-in

P applied load, lb

t age, days

w unit weight of concrete, pcf

c2 strain produced by stress fc2

stress, psi

10

OVERVIEW OF LABORATORY ACTIVITIES

We will devote two weeks to testing of concrete specimens. A brief overview of the activities is

listed below:

Week 1 (7 days after casting specimens)

Measure stress-strain curve for one cylinder (in compression)

Compressive tests of two cylinders

Flexure tests of two beams

Split-cylinder tests of two cylinders

Week 2 (28 days after casting specimens)

Measure stress-strain curve for one cylinder (in compression)

Compressive tests of three cylinders

Split-cylinder tests of two cylinders

Keep track of all the data from your group. You will share this data with the other groups in your

lab section.

LABORATORY PROCEDURES

A. Compressive Strength Tests (ASTM C1231, 2014)

1. Remove three cylinders from the moisture room and test as quickly as possible. 2. Wipe the ends of the cylinder. Dust the neoprene pads in the loading caps lightly with

baby powder. Place one cap on each end of the cylinder.

3. Position the cylinder in the testing machine in the orientation that it was cast. Center the specimen relative to the loading head.

4. Load each specimen at a rate of 440 lb/sec. (35 psi/sec for Humboldt machine) 5. Record the failure load for each cylinder.

B. Flexural Strength Tests (ASTM C78, 2015)

1. Remove the beams from the moisture room and test as quickly as possible. 2. Measure the distance between supports and the distance between loading points. 3. Turn the specimen on its side with respect to its molded position and center it on the support

blocks.

6. Load each specimen at a rate of 12 lb/sec. 4. Record the failure load for each beam. 5. Sketch the typical mode of failure.

11

C. Split Cylinder Tests (ASTM C496, 2011)

1. Remove the beams from the moisture room and test as quickly as possible.

2. Place the cylinder in the loading apparatus on its side between two thin wood strips.

3. Position the loading apparatus in the testing machine and center with respect to the loading

head.

4. Bring specimen into contact with loading head, making sure that the load will be applied

along diametrically opposite lines.

5. Load each specimen at rate of 25 lb/sec. (2-3 psi/sec for Humboldt machine)

6. Sketch the typical mode of failure. Estimate the percent aggregate that fractured along the

failure plane.

D. Elastic Modulus (ASTM C469, 2014)

1. Test three cylinders in compression to determine the average compressive strength at 28 days (note, would have been done during part A of this lab).

2. Measure the longitudinal gage length of the compressometer. 3. Position the compressometer around a new cylinder and support the cylinder on on wooden

blocks. Tighten the screws of the compressometer into the concrete. Remove the

temporary supports.

4. The loading increment for your test will be the average maximum load resisted by the three cylinders tested in step 1 divided by 20. Round the loading increment to the nearest 500

lb.

5. Important Do not load the cylinder beyond 50% of the average maximum load while the compressometer is attached to the specimen.

6. Position the cylinder and compressometer on the lower platen of the testing machine. Center the cylinder.

7. Load the cylinder to approximately 50% of the average maximum load and unload without collecting data. (Press the Pause key when the applied load reaches approximately one-

half the expected failure load to stop the loading process. Press the Stop key to unload the

specimen.)

8. Change the loading rate to approximately one-quarter the rate you used for the previous tests, 110 lb/sec.

9. Zero the dial gage attached to the compressometer. 10. Begin loading the cylinder. One person is responsible for reading the load indicator on the

testing machine, and calling out each time that the load reaches a specified load level. The

other members of the group are responsible for reading the displacement indicator.

11. Press the Pause key when the applied load is equal to approximately 50% of the average maximum load. Press the Stop key to unload the specimen.

12. Remove the specimen from the test machine. Attach the temporary supports to the compressometer. Loosen the screws and remover the compressometer.

13. Change the loading rate back to the original value (440 lb/sec or 35 psi/sec for Humboldt). Place the specimen in the test machine and test to failure.

12

DATA SHEETS LAB 4 CONCRETE TESTING

COMPRESSIVE STRENGTH OF CYLINDERS

(4 x 8 cylinders)

Cylinder

ID

Age

(days)

Applied Load (lb)

Mix 1: 3,000 psi at 3 slump

Mix 2: 6,000 psi. at

3 slump Mix 3: 6,000 psi at 5

slump

1

7

2

3

4

28

5

6

SPLIT CYLINDER TESTS

(4 x 8 cylinders)

Cylinder

ID

Age

(days)

Mix 1: 3,000 psi at 3 slump

Mix 2: 6,000 psi. at 3 slump

Mix 3: 6,000 psi at 5 slump

Load (lb) % Fracture Load (lb) % Fracture Load (lb) % Fracture

1 7

2

3 28

4

FLEXURAL TESTS

(12 x 4 x 4 Beams)

Beam ID Age

(days)

Applied Load (kN)1

Mix 1: 3,000 psi at

3 slump Mix 2: 6,000 psi. at 3

slump

Mix 3: 6,000 psi at 5 slump

1 7

2

1 Convert the load to lb before calculating fr.

13

ELASTIC MODULUS

(Stress-Strain Data)

Age of Cylinder: 7 days

Gage Length: in.

Loading

Increment

Mix 1: 3,000 psi at 3 slump

Mix 3: 6,000 psi at 3 slump

Mix 3: 6,000 psi at 5 slump

Load (lb) Displacement

(in) Load (lb)

Displacement

(in) Load (lb)

Displacement

(in)

1

2

3

4

5

6

7

8

9

10

Note: The displacement measured by the compressometer is two times the average

displacement experienced by the cylinder. Therefore,

longitudinal strain = measured displacement / (gage length * 2).

14

ELASTIC MODULUS

(Stress-Strain Data)

Age of Cylinder: 28 days

Gage Length: in.

Loading

Increment

Mix 1: 3,000 psi at 3 slump

Mix 3: 6,000 psi at 3 slump

Mix 3: 6,000 psi at 5 slump

Load (lb) Displacement

(in) Load (lb)

Displacement

(in) Load (lb)

Displacement

(in)

1

2

3

4

5

6

7

8

9

10

Note: The displacement measured by the compressometer is two times the average

displacement experienced by the cylinder. Therefore,

longitudinal strain = measured displacement / (gage length * 2).

15

LAB 4 COMPRESSIVE, FLEXURAL AND TENSILE STRENGTH OF CONCRETE

Laboratory Assignment

For the laboratory assignment, you must provide the requested data and answer all questions. Follow the

guidelines for preparing laboratory assignments in the CE 324P Technical Writing Guide. A sample

assignment is included on Canvas to provide an example of the format and style. This assignment will be

graded by your laboratory TA only.

Submit a hard copy of the following to your laboratory TA in lab:

Cover sheet

Solutions to the Questions posed on the next page.

References

Appendices (include at least the following appendices)2 o Measured Data (a neat copy of the data sheet is adequate) o Notations (define all notations used in the calculations) o Engineering calculations

o Include at least example calculations for each step for which a sample calculation was not included in the solutions section

o Hand calculations and sketches should be done in pencil, not ink o Always show the formula before inserting numerical values and reference the

source of the equation used (if it is an equation you derived, present the derivation in an additional appendix)

o Keep track of significant figures o State any assumptions o Make note of any errors in testing

2 Please make sure that you mention each appendix in the solutions section of the laboratory assignment. The appendices must be discussed in order. Therefore, if you need to mention notations before measured data, you may change the order of the appendices from that suggested here.

16

Questions

Use the data measured in the laboratory to address the following:

1. In one table, summarize the average compressive, tensile, and flexural strengths for all the concrete mixtures tested in your laboratory section. Include all available measured strengths (7 and 28 days).

2. Calculate '/ cr ff and '/ csp ff (here,

'

cf is the 28 day specified compressive strength). Discuss if

the values are within the expected ranges given in Eq. 5 and 7, respectively. ACI recommends using

the equations with'

cf , but for sake of comparison, also calculate the ratios with fcmt (defined in Question

8): cmtr ff / and cmtsp ff / . A total of 6 values shall be calculated,

'/ cr ff and cmtr ff / for 7

day beam breaks, '/ csp ff and cmtsp ff / for 7 day split tensile breaks, and '/ csp ff and

cmtsp ff / for 28 day split tensile breaks. Are these values within the expected ranges? If any of the

six calculated values are out of the expected range, suggest why that might be. Discuss any differences

between rf and spf .

3. The ACI Building Code (318, 2014) relates the required average compressive strength, '

crf to the

specified compressive strength, cf as follows:

If 3000 cf psi, 1000'' ccr ff .

If 3000 5000cf psi, 1200'' ccr ff .

If 5000cf psi, 7001.1'' ccr ff .

Using the data from the three mixtures tested in your laboratory, calculate '

crf .

4. Explain how you plan to change the mixture designs in the future, if required. If the average measured

strength is less than'

crf , you must redesign the mixture to increase the compressive strength. If the

average measured strength exceeds '

crf , you may decide to redesign the mixture to reduce the

compressive strength, which will also reduce the cost of the mixture. Show a full mix redesign for one

mix, if necessary. For the redesigned mix use the costs from Lab 3 to recalculate the cost of 1yd3 of

concrete using the new proportions.

5. For this question do the following:

a. Plot the measured 7-day and 28-day compressive strengths versus the actual w/c for Mix 1 and Mix 3in your laboratory section. Discuss the effects of w/c and age on strength.

b. Using a column chart, plot the measured 7-day and 28-day compressive strengths versus age (7 and 28 days) for all 3 mixes. Discuss the effects of w/c ratio, age, and slump.

17

6. Plot the measured slump versus w/c ratio for all three mixtures.

Discuss the effects of slump on w/c. Discuss if any trends or conclusions on w/c ratio can be made from knowing the slump.

7. Compare the percentage of coarse aggregates that fractured in the split cylinder tests for the three different concrete mixtures (for both 7 and 28 days). Discuss any observed trends in the percentage of

fractured aggregates for the different concrete mixtures and different ages.

8. ACI Committee 209 (2008) developed the following relationship to describe the variation of concrete compressive strength with time:

t

tff cmcmt

85.0428 (10)

where fcmt is the estimated compressive strength of the concrete at time t, t is the age of the concrete in days, and fcm28 is the average measured concrete compressive strength at 28 days. Compare the

measured 7-day strength to the 7-day predicted strength from Eq. 10 for all three mixtures in your

laboratory section. Discuss your results.

9. Make two plots, one for 7 and another for 28 day breaks, of the relationship between longitudinal stress and strain for each mixture (i.e., your plot should have 3 lines, one for each mixture). Determine the

modulus of elasticity E for each mix at 7 and 28 days by creating a linear trend line. Estimate the

modulus of elasticity Ec of the concrete using Eq. 9 at 7 and 28 days. Compare the two values from the

slope of trend lines and Eq. 9. Note that Eq. 9 utilizes '

cf as defined as 28 day compressive strength.

For the 7 day estimate of Ec using Eq. 9 use the average 7 day compression strength as your '

cf value

and discuss if the Eq. 9 holds for this case. Plot modulus of elasticity, E, at 28 days, as a function of

w/c ratio and discuss any correlations.