Reinforced Concrete Design - CE 217

Dr. Oussama ELALAOUI

Majmaah University 1436-1437

Chapter II

Properties of Reinforced Concrete

3

Lecture Goals

• Concrete Properties

• Steel Properties

The designer needs to be knowledgeable about the properties of concrete and reinforcing steel before he begins to design reinforced concrete structures. This chapter introduces to several of these materials properties of particular importance to the designer.

Outline

2.1. Concrete Mixing and Proportioning

2.2. compressive strength

2.3. stress-strain curves of concrete

2.4. tensile strength of concrete

2.5. Flexural Strength (Modulus of Rupture) of Concrete

2.6. Shear Strength

2.7. Poisson’s Ratio

2.8. Shear Modulus

2.9. Modular Ratio

2.10. Volume Changes of Concrete 4

Outline

2.10.1. Shrinkage

2.10.2. Expansion Due to Rise in Temperature

2.10.3. Creep

2.11. Models for Predicting Shrinkage and Creep of Concrete

2.12. Fire Resistance

2.13. High-Performance Concrete

2.14. Lightweight Concrete

2.15. Fibrous Concrete

2.16. Steel Reinforcement

5

6

2.1. Concrete Mixing and Proportioning

◊ Quality

◊ Workability

◊ Economical

In the design of concrete mixes, three principal

requirements for concrete are of importance:

7

• Quality of concrete is measured by its strength

and durability. The principal factors affecting the

strength of concrete :

1) assuming a sound aggregates (interaction and adhesion

between cement paste and aggregates, well graded)

2) W/C ratio (for complete hydration W/C =0.25 by weight)

3) quality of cement

4) adequate mixing of the concrete ingredients

Concrete Mixing and Proportioning

8

4) proper placing, finishing and compaction of the

fresh concrete (mechanical concrete mixers, time of mixing)

5) curing conditions (temperature not below 10°C while the

concrete gains strength)

6) the extent to which hydration has progressed

(affected by moisture and temperature).

Durability of concrete is the ability of the concrete

to resist disintegration due to freezing and thawing

and chemical attack.

Concrete Mixing and Proportioning

9

Concrete Mixing and Proportioning

10

• Workability of concrete may be defined as a

composite characteristic indicative of the ease

with which the mass of plastic material may

deposited in its final place without segregation

during placement, and its ability to conform to

fine forming detail.

Concrete Mixing and Proportioning

11

• Workability measured by slump test

1. Layer 1: Fill 1/3 full. 25 stokes

2. Layer 2: Fill 2/3 full. 25 stokes

3. Layer 3: Fill full. 25 stokes

4. Lift cone and measure slump (typically 2-6 in.)

1 2 3 4

12”

slump

Concrete Mixing and Proportioning

12

Concrete Mixing and Proportioning

Slump test - The measurement of the consistency of the

mix is done with the slump-cone test. The recommend

consistency for various classes of concrete structures .

13

• Economical takes into account effective use of

materials, effective operation, and ease of

handling. The cost of producing good quality

concrete is an important consideration in the

overall cost of the construction project.

Concrete Mixing and Proportioning

14

Concrete Mixing and Proportioning

• Admixtures – Applications:

• Improve workability

• Accelerate or retard setting and hardening

• Aid in curing

• Improve durability

15

Concrete Mixing and Proportioning

Admixtures

– Air-Entrainment: Add air voids with bubbles

• Help with freeze/thaw cycles, workability, etc.

• Decreases density: reduces strength, but also decreases W/C

– Superplasticizers: increase workability by chemically releasing water from fine aggregates.

16

Concrete Mixing and Proportioning

• Types of Cement

– Type I: General Purpose

– Type II: Lower heat of hydration than Type I

– Type III: High Early Strength

• Higher heat of hydration

• quicker strength (7 days vs. 28 days for Type I)

17

Concrete Mixing and Proportioning

– Type IV: Low Heat of Hydration

• Gradually heats up, less distortion (massive structures).

– Type V: Sulfate Resisting

• For footings, basements, sewers, etc. exposed to soils with sulfates.

18

Concrete Mixing and Proportioning

Pri

nci

pal

pro

pe

rtie

s o

f go

od

co

ncr

ete

19

Uniaxial Stress versus Strain Behavior in Compression

Ec

o u

0.45f’c

fc

f’c 12”

6”

2.2. compressive strength

–Maximum useable strain, u

•ACI Code: u = 0.003

•Used for flexural and axial compression

–Compressive Strength, f’c

• Normally use 28-day strength for design strength

20

Stress–strain curve and modulus of elasticity of concrete. Lines a–d represent (a) initial tangent modulus, (b) tangent modulus at a stress, fc, (c) secant modulus at a stress, fc, and (d) secant modulus at a stress f c/2.

2.2. compressive strength

21

– Modulus of Elasticity, Ec

• Corresponds to secant modulus at 0.45 f’c

• ACI 318-02 (Sec. 8.5.1):

where w = unit weight (pcf)

90 pcf < wc <155 pcf

For normal weight concrete

(wc 145 pcf)

2.2. compressive strength

22

Compute Ec for f’c = 4500 psi for normal weight (145 pcf) concrete using both ACI equations:

)('33)( 5.1 psifwpsiE cc

)(',)( psif00057psiE cc

2.2. compressive strength

Test on a standard concrete cylinder to determine the modulus of elasticity of concrete.

where w = unit weight (pcf) 90 pcf < wc <155 pcf

For normal weight concrete (wc 145 pcf)

23

The standard strength test generally uses a cylindrical sample. It is tested after 28 days to test for strength, fc. The concrete will continue to harden with time and for a normal Portland cement will increase with time as follows:

2.2. compressive strength

24

Types of compression failure

There are three modes of failure.

[a] Under axial compression concrete fails in shear.

[b] the separation of the specimen into columnar pieces by what is known as splitting or columnar fracture.

[c] Combination of shear and splitting failure.

2.2. compressive strength

25

2.3. stress-strain curves of concrete

Typical stress–strain curves of concrete.

Standard capped cylinders ready for testing.

26

2.4 Tensile Strength

Cylinder splitting test [6]: (a) configuration of test, (b) distribution of horizontal stress, and (c) cylinder after testing.

Concrete cylinder splitting test.

2.4 Tensile Strength

27

)(')( psif7to5f

ld

P2f

cct

ct

(Not given in ACI Code)

2.4 Tensile Strength

Considering an element on the vertical diameter and at a distance y from the top fibers, the element is subjected to a compressive stress:

and a tensile stress:

P

Concrete Cylinder

Poisson’s

Effect

28

– Tensile strength ~ 8% to 15% of f’c

– Modulus of Rupture, fr

• For deflection calculations, use:

– Test:

2

6

bh

M

I

Mcf r

ACI Eq. 9-10

2.5 Flexural strength (modulus of rupture) of concrete

)('5.7 psiff cr

P

fr

Mmax = P/2*a

unreinforced

concrete beam

29

• Pure shear is seldom encountered in reinforced concrete members because it is usually accompanied by the action of normal forces. An element subjected to pure shear breaks transversely into two parts.

• Shear strength may be considered as 20 to 30% greater than

the tensile strength of concrete, or about 12% of its

compressive strength.

2.6 Shear strength

30

• Poisson’s ratio μ is the ratio of the transverse to the

longitudinal strains under axial stress

• within the elastic range. This ratio varies between 0.15 and

0.20 for both normal and lightweight concrete.

• Poisson’s ratio is used in structural analysis of flat slabs,

tunnels, tanks, arch dams, and other statically indeterminate

structures.

• For isotropic elastic materials, Poisson’s ratio is equal to 0.25.

An average value of 0.18 can be used for concrete.

2.7 Poisson’s ratio

31

• The modulus of elasticity of concrete in shear ranges from about

0.4 to 0.6 of the corresponding modulus in compression.

• From the theory of elasticity, the shear modulus is taken as

follows:

2.8 Shear modulus

)(

12

EcG

C

where μ = Poisson’s ratio of concrete. If μ is taken equal to 0.16 , then. '

CCCf 24,500 0.43E G

32

2.9 Modular ratio

• The modular ratio n is the ratio of the modulus of elasticity

of steel to the modulus of elasticity of concrete: n = Es/Ec.

• Because the modulus of elasticity of steel is considered

constant and is equal to 29×106 psi and

2

c

c

c

c

mmNinff

42psiinf

f

500n /'

''

'

For normal-weight concrete

c

51

c fw33E '.

33

2.10 Volume changes of concrete

• Concrete undergoes volume changes during hardening. If it

loses moisture by evaporation, it shrinks, but if the concrete

hardens in water, it expands.

• The causes of the volume changes in concrete can be

attributed to changes in moisture content, chemical reaction

of the cement with water, variation in temperature, and

applied loads.

34

–Shrinkage: Due to water loss to atmosphere (volume loss).

• Plastic shrinkage occurs while concrete is still “wet” (hot day,

flat work, etc.)

• Drying shrinkage occurs after concrete has set

• Most shrinkage occurs in first few months (~80% within one

year).

• Cycles of shrinking and swelling may occur as environment

changes.

• Reinforcement restrains the development of shrinkage.

2.10.1 Shrinkage

35

Many factors influence the shrinkage of concrete caused by the

variations in moisture conditions :

1.Cement and Water Content.

2.Composition and Fineness of Cement.

3.Type, Amount, and Gradation of Aggregate.

4.Ambient Conditions, Moisture, and Temperature.

5.Admixtures.

6.Size and Shape of Specimen.

2.10.1 Shrinkage

36

Shrinkage of an Unloaded Specimen

* 80% of shrinkage occurs in first year

MacGregor (1997)

2.10.1 Shrinkage

• Concrete shrinks at a high rate during the initial period of hardening, but at later stages the rate diminishes gradually.

• It can be said that 15 to 30% of the shrinkage value occurs in 2 weeks, 40 to 80% occurs in 1 month, and 70 to 85% occurs in 1 year.

37

2.10.2 Expansion Due to Rise in Temperature

• Concrete expands with increasing temperature and

contracts with decreasing temperature.

• The coefficient of thermal expansion of concrete varies

between 4 and 7×10−6 per degree Fahrenheit (An average

value of 5.5×10−6 /°F (12×10−6 /°C) can be used for ordinary

concrete).

• In long reinforced concrete structures, expansion joints

must be provided at lengths of 100 to 200 ft (30 to 60 m).

• The width of the expansion joint is about 1 in. (25 mm).

38

Deformation in a loaded concrete cylinder: (a) specimen unloaded, (b) elastic deformation, (c) elastic plus creep deformation, and (d) permanent deformation after release of load.

2.10.3 Creep

• In a loaded concrete, plastic strains ε2 (due to creep effect) develop in addition to elastic ones ε1 .

• Under sustained load, plastic deformation (strains) continues to develop

over a period that may last for years.

• This slow plastic deformation under constant stress is called creep.

39 39

•Like shrinkage, creep is not completely reversible.

•If load is then released, the elastic strain, ε1, will be recovered, in

addition to some creep strain. The final permanent plastic strain, ε3 =

(1 − α)ε2, will be left. The ratio α ranges between 0.1 and 0.2.

P

P

L

dL, elastic

dL, creep

=dL/L

2.10.3 Creep

40

• Creep takes place in the hardened cement matrix around the

strong aggregate.

• The different factors that affect the creep of concrete :

1.Level of Stress.

2.Duration of Loading (18 to 35% occurred in 2 weeks, 30 to 70%

occurred in 3 months, and 64 to 83% occurred in 1 year).

3.Strength and Age of Concrete.

4.Ambient Conditions.

5.Rate of Loading.

2.10.3 Creep

41

2.10.3 Creep

6. Percentage and Distribution of Steel Reinforcement in Reinforced

Concrete Member.

7. Size of Concrete Mass.

8. Type, Fineness, and Content of Cement (cement creeps about 15

times as much as concrete).

9. Water–Cement Ratio.

10.Type and Grading of Aggregate.

11.Type of Curing (High-temperature steam curing of concrete,

proper use of a plasticizer → reduce the amount of creep.

42

• Creep develops not only in compression but also in

tension, bending, and torsion.

• For normal concrete loaded after 28 days, Cr = 0.13 𝑡3

,

where Cr = creep strain per unit stress per unit length.

• Repeated loading and unloading cycles in compression

lead to a gradual accumulation of plastic deformations.

2.10.3 Creep

43 43

2.11 Models for predicting shrinkage and creep of concrete

2.11.1 Shrinkage calculation according to ACI 209R-92 Model

Six models can be used to predict shrinkage and creep of concrete:

ACI 209R-92, B3, GL-2000, CEB 90, CEB MC 90–99, and AASHTO.

The shrinkage strain is defined as

(2.10)

where t = age of concrete after casting (days) tc = age of the concrete drying commenced, usually taken as the age at the end of moist curing (days) f = constant in determining shrinkage strain, depends on curing method shape and size factors according to Table 2.4 Kss = shape and size correction factor for shrinkage according to Eq. 2.11 Ksh = relative humidity correction factor for shrinkage according to Eq. 2.12 εshu = ultimate shrinkage strain 780×10−6 in/in or (mm/mm).

44

2.11.1 Shrinkage calculation according to ACI 209R-92 Model

45

2.11.1 Shrinkage calculation according to ACI 209R-92 Model

46

2.11.2 Creep calculation according to ACI 209R-92 Model

The total load-dependent strain at time t , εic(t, t0) of a concrete

member uniaxially loaded at time t0 with a constant stress σ may

be calculated as follows:

47

Usually, the total load-dependent strain is presented with compliance

function, also called creep function, J(t, t0), which represent the total

load-dependent strain at time t produced by a unit constant stress that

has been acting since time t0.

2.11.2 Creep calculation according to ACI 209R-92 Model

48

2.11.2 Creep calculation according to ACI 209R-92 Model

49

2.11.2 Creep calculation according to ACI 209R-92 Model

50

2.11.2 Creep calculation according to ACI 209R-92 Model

51

Shrinkage and Creep calculation example (ACI 209R-92 Model)

Calculate shrinkage strain and creep compliance and coefficient for the concrete specimen given below. Use the ACI 209R-92 model. Given factors:

52

Shrinkage and Creep calculation example (ACI 209R-92 Model)

Shrinkage and Creep calculation example (ACI 209R-92 Model)

53

2.5) a b

54

2.12. Fire Resistance

• Fire resistance of a material is its ability to resist fire for a

certain time without serious loss of strength, distortion, or

collapse.

• In the case of concrete, fire resistance depends on the

thickness, type of construction, type and size of aggregates,

and cement content.

• It is important to consider the effect of fire on tall buildings

more than on low or single-story buildings because occupants

need more time to escape.

55

2.12. Fire Resistance

• Reinforced concrete is a much better fire-resistant material than

steel. Steelwork heats rapidly, and its strength drops appreciably

in a short time. Concrete itself has low thermal conductivity.

• The effect of temperatures below 250◦C is small on concrete,

but definite loss is expected at higher temperatures.

56

2.13. High-Performance Concrete

• Concrete with strengths exeeding 6000 psi are refered to as high-

strength concretes.

• Another name sometimes given to them is high-performance

concretes because they have excellent charcteristics besides just

high strengths ( toughness, energy absorption, durability, stiffness,

and a relatively higher ductility than normal concrete.

57

2.13. High-Performance Concrete

• This improvement in concrete quality may be achieved by:

Using a new generation of additives and superplasticizers, which

improves the workability of concrete and, consequently, its

strength.

the use of active microfillers such as silica fume, fly ash, and

polymer improves the strength, porosity, and durability of concrete

the addition of different types of fiber to the concrete mix

enhances many of its properties, including ductility, strength, and

toughness.

Consolidation (excess water and air sqeezed out → optimum air

content)

58

2.14. Lightweight Concrete

• Lightweight concrete has been made lighter (90 to 115 lb/ft3) than

conventional normal-weight concrete (145 lb/ft3) and, consequently,

it has a relatively lower density. It can be produced with a

compressive strength of 2500 to 5000 psi for practical applications.

• Basically, reducing the density requires the inclusion of air in the

concrete composition. This, can be achieved in 4 distinct ways:

1. By omitting the finer sizes from the aggregate grading, thereby

creating what is called no-fines concrete. It is a mixture of

cement, water, and coarse aggregate only ( 3

4 −

3

8) mixed to

produce concrete with many uniformly distributed voids.

59

2.14. Lightweight Concrete

2. By replacing the gravel or crushed rock aggregate with a hollow

cellular or porous aggregate (lightweight aggregate ). Lightweight

aggregate may be natural, such as pumice, pozzolans, and volcanic

slags; artificial (from industrial by-products), such as furnace clinker

and foamed slag; or industrially produced, such as perlite,

vermiculite, expanded clay, shale, and slate.

3. By creating gas bubbles in a cement slurry, which, when it sets,

leaves a spongelike structure. This type is called aerated concrete.

4. By forming air cells in the slurry by chemical reaction or by vigorous

mixing of the slurry with a preformed stable foam (This type is

called cellular concrete).

60

2.15. Fibrous Concrete

• Fibrous concrete is made primarily of concrete constituents and

discrete reinforcing fibers.

• The brittle nature of concrete and its low flexural tensile strength

are major reasons for the growing interest in the performance of

fibers in concrete technology.

• Various types of fibers—mainly steel, glass, and organic polymers—

have been used in fibrous concrete.

61

• Generally, the length and diameter of the fibers do not exceed 3

in. (75 mm) and 0.04 in. (1 mm), respectively.

• The addition of fibers to concrete improves its mechanical

properties, such as ductility, toughness, shear, flexural strength,

impact resistance, and crack control.

2.15. Fibrous Concrete

62

2.16. Steel Reinforcement

Stan

dar

d R

ein

forc

ing

Bar

Mar

kin

gs

63 63

• Most common types for non-prestressed members:

hot-rolled deformed bars

welded wire fabric

2.16. Steel Reinforcement

64

Areas, Weights, Dimensions

2.16. Steel Reinforcement

65

2.16. Steel Reinforcement

66

• ASTM A615 - Standard Specification for Deformed and Plain-Billet Steel Bars

Grade 60: fy = 60 ksi, #3 to #18

– most common in buildings and bridges

Grade 40: fy = 40 ksi, #3 to #6

– most ductile

Grade 75: fy = 75 ksi, #6 to #18

• ASTM A616 - Rail-Steel Bars

• ASTM A617 - Axle-Steel Bars

• ASTM A706 - Low-Alloy-Steel Bars

more ductile GR60 steel

min. length of yield plateau = 5

2.16. Steel Reinforcement (Types)

67

2.16. Steel Reinforcement (Stress-strain curves)

68

Es = Initial tangent modulus = 29,000 ksi (all grades)

Note: GR40 has a longer yield plateau

Stress

Strain

0.20

GR 40

GR 60 (less ductile)

Es

1

2.16. Steel Reinforcement

69

1. Structural concrete : Theory and design, M.Nadim Hassoun,

Akthem Al-Manaseer, 5 th edition.

References