CHAPTER 1. INTRODUCTON TO REINFORCED CONCRETE · CHAPTER 1. INTRODUCTON TO REINFORCED CONCRETE 1.1. INTRODUCTION Traditionally, the study of reinforced concrete design begins directly

AAiT, School of Civil and Environmental Engineering Reinforced Concrete I

Chapter 1 – Introduction to Reinforced Concrete Page 1

CHAPTER 1. INTRODUCTON TO REINFORCED CONCRETE

1.1. INTRODUCTION

Traditionally, the study of reinforced concrete design begins directly with a chapter on materials,

followed by chapters dealing with design. In this material, a departure is made from that

convention. It is desirable for the student to have first an overview of the world of reinforced

concrete structures, before plunging into the finer details of the subject. Accordingly, this section

gives a general introduction to reinforced concrete and its applications. It also explains the role

of structural design in reinforced concrete construction, and outlines the various structural

systems that are commonly adopted in buildings.

That concrete is a common structural material is, no doubt, well known. But, how common it is,

and how much a part of our daily lives it plays, is perhaps not well known — or rather, not often

realized. Structural concrete is used extensively in the construction of various kinds of buildings,

stadia, auditoria, pavements, bridges, piers, breakwaters, berthing structures, dams, waterways,

pipes, water tanks, swimming pools, cooling towers, bunkers and silos, chimneys,

communication towers, tunnels, etc. It is the most commonly used construction material,

consumed at a rate of approximately one ton for every living human being. “Man consumes no

material except water in such tremendous quantities”.

1.2. PLAIN AND REINFORCED CONCRETE

1.2.1. PLAIN CONCRETE

Concrete may be defined as any solid mass made by the use of a cementing medium; the

ingredients generally comprise sand, gravel, cement and water. That the mixing together of such

disparate and discrete materials can result in a solid mass (of any desired shape), with well-

defined properties, is a wonder in itself. Concrete has been in use as a building material for more

than a hundred and fifty years. Its success and popularity may be largely attributed to (1)

durability under hostile environments (including resistance to water), (2) ease with which it can

be cast into a variety of shapes and sizes, and (3) its relative economy and easy availability. The

main strength of concrete lies in its compression-bearing ability, which surpasses that of

traditional materials like brick and stone masonry. Advances in concrete technology, during the



past four decades in particular, have now made it possible to produce a wide range of concrete

grades, varying in mass density (1200−2500 kg/m3) and compressive strength (10 −100 MPa).

Concrete may be remarkably strong in compression, but it is equally remarkably weak in tension

[Figure 1-1(a)]. Its tensile strength is approximately one-tenth of its compressive strength.

Hence, the use of plain concrete as a structural material is limited to situations where significant

tensile stresses and strains do not develop, as in hollow (or solid) block wall construction, small

pedestals and ‘mass concrete’ applications (in dams, etc.).

1.2.2. REINFORCED CONCRETE

Concrete would not have gained its present status as a principal building material, but for the

invention of reinforced concrete, which is concrete with steel bars embedded in it. The idea of

reinforcing concrete with steel has resulted in a new composite material, having the potential of

resisting significant tensile stresses, which was hitherto impossible. Thus, the construction of

load-bearing flexural members, such as beams and slabs, became viable with this new material.

Its utility and versatility are achieved by combining the best features of concrete and steel.

Consider some of the widely differing properties of these two materials that are listed below in

Table 1-1.

Table 1-1- Complementary properties of Concrete and Steel

Concrete Steel

Strength in Tension Poor Good

Strength in Compression Good Good, but slender bars will buckle

Strength in Shear Fair Good

Durability Good Corrodes if unprotected

Fire resistance Good Poor, suffers rapid loss of strength at high temperature

It can be seen from this list that the materials are more or less compatible. The steel bars

(embedded in the tension zone of the concrete) compensate for the concrete’s incapacity for

tensile resistance, effectively taking up all the tension, without separating from the concrete

[Figure 1-1(b)]. The bond between steel and the surrounding concrete ensures strain

compatibility, i.e., the strain at any point in the steel is equal to that in the adjoining concrete.

Moreover, the reinforcing steel imparts ductility to a material that is otherwise brittle. In



practical terms, this implies that if a properly reinforced beam were to fail in tension, then such a

failure would, fortunately, be preceded by large deflections caused by the yielding of steel,

thereby giving ample warning of the impending collapse [Figure 1-1(c)].

Tensile stresses occur either directly, as in direct tension or flexural tension, or indirectly, as in

shear, which causes tension along diagonal planes (‘diagonal tension’). Temperature and

shrinkage effects may also induce tensile stresses. In all such cases, reinforcing steel is essential,

and should be appropriately located, in a direction that cuts across the principal tensile planes

(i.e., across potential tensile cracks). If insufficient steel is provided, cracks would develop and

propagate, and could possibly lead to failure.

Reinforcing steel can also supplement concrete in bearing compressive forces, as in columns

provided with longitudinal bars. These bars need to be confined by transverse steel ties [Figure

1-1(d)], in order to maintain their positions and to prevent their lateral buckling. The lateral ties

also serve to confine the concrete, thereby enhancing its compression load-bearing capacity.

The development of reliable design and construction techniques has enabled the construction of a

wide variety of reinforced concrete structures all over the world: building frames (columns and

beams), floor and roof slabs, foundations, bridge decks and piers, retaining walls, grandstands,

water tanks, pipes, bunkers and silos, folded plates and shells, etc.

(a) Plain concrete beam

cracks and fails in

flexural tension under a

small load

(b) Reinforced concrete

beam supports loads

with acceptably low

deformations



(c) Ductile mode of failure

under heavy loads

(d) Reinforced concrete

column

Figure 1-1 - Contribution of steel bars in reinforced concrete

1.3. ADVANTAGES AND DISADVANTAGES OF REINFORCED CONCRETE FOR A

STRUCTURE

The choice of whether a structure should be built of reinforced concrete, steel, masonry, or

timber depends on the availability of materials and on a number of value decisions.

1. Economy.

2. Suitability of material for architectural and structural function.

3. Fire resistance.

4. Rigidity.

5. Low maintenance.

6. Availability of materials.

On the other hand, there are a number of factors that may cause one to select a material other

than reinforced concrete. These include:

1. Low tensile strength.

2. Forms and shoring.



3. Relatively low strength per unit of weight or volume.

4. Time-dependent volume changes.

1.4. THE DESIGN PROCESS

1.4.1. OBJECTIVES OF DESIGN

A structural engineer is a member of a team that works together to design a building, bridge, or

other structure. In the case of a building, an architect generally provides the overall lay-out, and

mechanical, electrical, and structural engineers design individual systems within the building.

The structure should satisfy four major criteria:

1. Appropriateness.

2. Economy.

3. Structural adequacy.

4. Maintainability

1.4.2. THE DESIGN PROCESS

The design process is a sequential and iterative decision-making process. The three major phases

are the following:

1. Definition of the client’s needs and priorities.

2. Development of project concept

3. Design of individual systems.

1.5. DESIGN CODES AND HANDBOOKS

1.5.1. PURPOSE OF CODES

National building codes have been formulated in different countries to lay down guidelines for

the design and construction of structures. The codes have evolved from the collective wisdom of

expert structural engineers, gained over the years. These codes are periodically revised to bring

them in line with current research, and often, current trends.

The codes serve at least four distinct functions:

1. They ensure adequate structural safety, by specifying certain essential minimum

requirements for design.



2. They render the task of the designer relatively simple; often, the results of sophisticated

analyses are made available in the form of a simple formula or chart.

3. The codes ensure a measure of consistency among different designers.

4. They have some legal validity, in that they protect the structural designer from any

liability due to structural failures that are caused by inadequate supervision and/or

faulty material and construction.

The codes are not meant to serve as a substitute for basic understanding and engineering

judgment. The student is, therefore, forewarned that s/he will make a poor designer if s/he

succumbs to the unfortunate (and all-too-common) habit of blindly following the codes. On the

contrary, in order to improve her/his understanding, s/he must learn to question the code

provisions — as, indeed, s/he must, nearly everything in life!

1.5.2. INTRODUCTION TO EUROCODES

The development of the Eurocodes started in 1975; since then they have evolved significantly

and are now claimed to be the most technically advanced structural codes in the world. There are

ten Eurocodes covering all the main structural materials (see Figure 1-2). The structural

Eurocodes were initiated by the European Commission but are now produced by the Comité

Européen de Normalisation (CEN) which is the European standards organization. CEN is

publishing the design standards as full European Standards EN (Euronorms):

EN 1990: Eurocode: Basis of design (EC0)

EN 1991: Eurocode 1 Actions on structures (EC1)

Part 1-1: General actions – Densities, self-weight and imposed loads

Part 1-2: General actions on structures exposed to fire

Part 1-3: General actions – Snow loads

Part 1-4: General actions – Wind loads

Part 1-5: General actions – Thermal actions

Part 1-6: Actions during execution

Part 1-7: Accidental actions from impact and explosions

Part 2: Traffic loads on bridges

Part 3: Actions induced by cranes and machinery



Part 4: Actions in silos and tanks

EN 1992: Eurocode 2: Design of concrete structures (EC2)

Part 1-1: General rules and rules for buildings (EC2 Part 1-1)

Part 1-2: General rules - Structural fire design (EC2 Part 1-2)

Part 2: Reinforced and pre-stressed concrete bridges (EC2 Part 2)

Part 3: Liquid retaining and containing structures (EC2 Part 3)

EN 1993: Eurocode 3: Design of steel structures (EC3)

EN 1994: Eurocode 4: Design of composite steel and concrete structures (EC4)

EN 1995: Eurocode 5: Design of timber structures (EC5)

EN 1996: Eurocode 6: Design of masonry structures (EC6)

EN 1997: Eurocode 7: Geotechnical design (EC7)

EN 1998: Eurocode 8: Earthquake resistant design of structures (EC8)

EN 1999: Eurocode 9: Design of aluminum alloy structures (EC9)

All Eurocodes follow a common editorial style. The codes contain ‘Principles’ and ‘Application

rules’. Principles are identified by the letter P following the paragraph number. Principles

are general statements and definitions for which there is no alternative, as well as,

requirements and analytical models for which no alternative is permitted unless specifically

stated.

Application rules are generally recognized rules which comply with the Principles and

satisfy their requirements. Alternative rules may be used provided that compliance with

the Principles can be demonstrated, however the resulting design cannot be claimed to be wholly

in accordance with the Eurocode although it will remain in accordance with Principles.

1. Eurocode: Basis of structural design

In the Eurocode system EN 1990, Eurocode: Basis of Structural Design overarches all the other

Eurocodes (EN 1991 to EN 1999). EN 1990 defines the effects of actions, including geotechnical

and seismic actions, and applies to all structures irrespective of the material of construction. The

material Eurocodes define how the effects of actions are resisted by giving rules for design and

detailing of concrete, steel, composite, timber, masonry and aluminum. (See Figure 1-2).



2. Eurocode 1: Actions on Structures

Eurocode 1 contains in ten parts all the information required by the designer to assess the

individual actions on a structure. It is generally self-explanatory.

Figure 1-2 - The Eurocode Hierarchy

3. Eurocode 2: Design of concrete structures

There are four parts to Eurocode 2;

Eurocode 2, Part 1–1: General rules and rules for buildings, is the principal part which is

referenced by the three other parts.

Eurocode 2, Part 1–2: Structural fire design, gives guidance on design for fire resistance of

concrete structures. Although much of the Eurocode is devoted to fire engineering methods, the

design for fire resistance may still be carried out by referring to tables for minimum cover and

dimensions for various elements.



Eurocode 2, Part 2: Bridges, applies the general rules given in Part 1–1 to the design of

concrete bridges. As a consequence both Part 1–1 and Part 2 will be required to carry out a

design of a reinforced concrete bridge.

Eurocode 2, Part 3: Liquid retaining and containment structures, applies the general rules given

in Part 1–1 to the liquid-retaining structures.

1.6. DESIGN PHILOSOPHIES

1.6.1. INTRODUCTION

Over the years, various design philosophies have evolved in different parts of the world, with

regard to reinforced concrete design. A ‘design philosophy’ is built up on a few fundamental

premises (assumptions), and is reflective of a way of thinking.

The earliest codified design philosophy is the working stress method of design (WSM). Close

to a hundred years old, this traditional method of design, based on linear elastic theory, is still

surviving in some countries, although it is now sidelined by the modern limit states design

philosophy.

Historically, the design procedure to follow the WSM was the ultimate load method of design

(ULM), which was developed in the 1950s. Based on the (ultimate) strength of reinforced

concrete at ultimate loads, it evolved and gradually gained acceptance. This method was

introduced as an alternative to WSM in the ACI code in 1956 and the British Code in 1957.

Probabilistic concepts of design developed over the years and received a major impetus from the

mid-1960s onwards. The philosophy was based on the theory that the various uncertainties in

design could be handled more rationally in the mathematical framework of probability theory.

The risk involved in the design was quantified in terms of a probability of failure. Such

probabilistic methods came to be known as reliability-based methods. However, there was

little acceptance for this theory in professional practice, mainly because the theory appeared to

be complicated and intractable (mathematically and numerically).

In order to gain code acceptance, the probabilistic ‘reliability-based’ approach had to be

simplified and reduced to a deterministic format involving multiple (partial) safety factors (rather

than probability of failure). The European Committee for Concrete (CEB) and the International

Federation for Pre-stressing (FIP) were among the earliest to introduce the philosophy of limit



states method (LSM) of design, which is reliability-based in concept. Based on the CEB-FIP

recommendations, LSM was introduced in the British Code CP 110 (1973). In the United States,

LSM was introduced in a slightly different format (strength design and serviceability design) in

the ACI 318−71 (now ACI 318-95).

Thus, the past several decades have witnessed an evolution in design philosophy — from the

traditional ‘working stress method’, through the ‘ultimate load method’, to the modern ‘limit

states method’ of design.

1.6.2. WORKING STRESS METHOD (WSM)

This was the traditional method of design not only for reinforced concrete, but also for structural

steel and timber design. The conceptual basis of WSM is simple. The method basically assumes

that the structural material behaves in a linear elastic manner, and that adequate safety can be

ensured by suitably restricting the stresses in the material induced by the expected ‘working

loads’ (service loads) on the structure. As the specified permissible (‘allowable’) stresses are

kept well below the material strength (i.e., in the initial phase of the stress-strain curve), the

assumption of linear elastic behavior is considered justifiable. The ratio of the strength of the

material to the permissible stress is often referred to as the factor of safety.

The stresses under the applied loads are analyzed by applying the methods of ‘strength of

materials’ such as the simple bending theory. In order to apply such methods to a composite

material like reinforced concrete, strain compatibility (due to bond) is assumed, whereby the

strain in the reinforcing steel is assumed to be equal to that in the adjoining concrete to which it

is bonded. Furthermore, as the stresses in concrete and steel are assumed to be linearly related to

their respective strains, it follows that the stress in steel is linearly related to that in the adjoining

concrete by a constant factor (called the modular ratio), defined as the ratio of the modulus of

elasticity of steel to that of concrete.

However, the main assumption of linear elastic behavior and the tacit assumption that the

stresses under working loads can be kept within the ‘permissible stresses’ are not found to be

realistic. Many factors are responsible for this — such as the long-term effects of creep and

shrinkage, the effects of stress concentrations, and other secondary effects. All such effects

result in significant local increases in and redistribution of the calculated stresses. Moreover,

WSM does not provide a realistic measure of the actual factor of safety underlying a design.



WSM also fails to discriminate between different types of loads that act simultaneously, but have

different degrees of uncertainty. This can, at times, result in very unconservative designs,

particularly when two different loads (say, dead loads and wind loads) have counteracting

effects.

Nevertheless, in defense against these and other shortcomings leveled against WSM, it may be

stated that most structures designed in accordance with WSM have been generally performing

satisfactorily for many years. The design usually results in relatively large sections of structural

members (compared to ULM and LSM), thereby resulting in better serviceability performance

(less deflections, crack-widths, etc.) under the usual working loads. The method is also notable

for its essential simplicity — in concept, as well as application.

1.6.3. ULTIMATE LOAD METHOD (ULM)

With the growing realization of the shortcomings of WSM in reinforced concrete design, and

with increased understanding of the behavior of reinforced concrete at ultimate loads, the

ultimate load method of design (ULM) evolved in the 1950s and became an alternative to WSM.

This method is sometimes also referred to as the load factor method or the ultimate strength

method.

In this method, the stress condition at the state of impending collapse of the structure is analyzed,

and the non-linear stress−strain curves of concrete and steel are made use of. The concept of

‘modular ratio’ and its associated problems are avoided entirely in this method. The safety

measure in the design is introduced by an appropriate choice of the load factor, defined as the

ratio of the ultimate load (design load) to the working load. The ultimate load method makes it

possible for different types of loads to be assigned different load factors under combined loading

conditions, thereby overcoming the related shortcoming of WSM.

This method generally results in more slender sections, and often more economical designs of

beams and columns (compared to WSM), particularly when high strength reinforcing steel and

concrete are used.

However, the satisfactory ‘strength’ performance at ultimate loads does not guarantee

satisfactory ‘serviceability’ performance at the normal service loads. The designs sometimes



result in excessive deflections and crack-widths under service loads, owing to the slender

sections resulting from the use of high strength reinforcing steel and concrete.

1.6.4. LIMIT STATES METHOD (LSM)

The philosophy of the limit states method of design (LSM) represents a definite advancement

over the traditional design philosophies. Unlike WSM, which based calculations on service load

conditions alone, and unlike ULM, which based calculations on ultimate load conditions alone,

LSM aims for a comprehensive and rational solution to the design problem, by considering

safety at ultimate loads and serviceability at working loads.

The LSM philosophy uses a multiple safety factor format which attempts to provide adequate

safety at ultimate loads as well as adequate serviceability at service loads, by considering all

possible ‘limit states’ (defined in the next section). The selection of the various multiple safety

factors is supposed to have a sound probabilistic basis, involving the separate consideration of

different kinds of failure, types of materials and types of loads. In this sense, LSM is more than

a mere extension of WSM and ULM. It represents a new ‘paradigm’ — a modern philosophy.

1. Limit States

When a structure or structural element becomes unfit for its intended use, it is said to have

reached a limit state. The limit states for reinforced concrete structures can be divided into three

basic groups:

I. Ultimate limit states. These involve a structural collapse of part or all of the structure.

Such a limit state should have a very low probability of occurrence, because it may lead

to loss of life and major financial losses. The major ultimate limit states are as follows:

a) Loss of equilibrium of a part or all of the structure as a rigid body. Such a failure would

generally involve tipping or sliding of the entire structure and would occur if the

reactions necessary for equilibrium could not be developed.

b) Rupture of critical parts of the structure, leading to partial or complete collapse. The

majority of this document deals with this limit state. Chapters 3 consider flexural failures;

Chapter 4 shear failures; and so on.



c) Progressive collapse. In some structures, an overload on one member may cause that

member to fail. The load acting on it is transferred to adjacent members which, in turn,

may be overloaded and fail, causing them to shed their load to adjacent members, causing

them to fail one after another, until a major part of the structure has collapsed. This is

called a progressive collapse. Progressive collapse is prevented, or at least is limited, by

one or more of the following:

i. Controlling accidental events by taking measures such as protection against

vehicle collisions or explosions.

ii. Providing local resistance by designing key members to resist accidental events.

iii. Providing minimum horizontal and vertical ties to transfer forces.

iv. Providing alternative lines of support to anchor the tie forces.

v. Limiting the spread of damage by subdividing the building with planes of

weakness sometimes referred to as structural fuses.

A structure is said to have general structural integrity if it is resistant to progressive collapse. For

example, an explosion or a vehicle collision may accidentally remove a column that supports an

interior support of a two-span continuous beam. If properly detailed, the structural system may

change from two spans to one long span. This would entail large deflections and a change in the

load path from beam action to catenary or tension membrane action. Most building Codes

require continuous ties of tensile reinforcement around the perimeter of the building at each floor

to reduce the risk of progressive collapse. The ties provide reactions to anchor the catenary

forces and limit the spread of damage. Because such failures are most apt to occur during

construction, the designer should be aware of the applicable construction loads and procedures.

d) Formation of a plastic mechanism. A mechanism is formed when the reinforcement

yields to form plastic hinges at enough sections to make the structure unstable.

e) Instability due to deformations of the structure. This type of failure involves buckling

f) Fatigue. Fracture of members due to repeated stress cycles of service loads may cause

collapse.

II. Serviceability limit states. These involve disruption of the functional use of the

structure, but not collapse. Because there is less danger of loss of life, a higher

probability of occurrence can generally be tolerated than in the case of an ultimate limit

state. Design for serviceability is discussed in Chapter 4. The major serviceability limit

states include the following:



a) Excessive deflections for normal service. Excessive deflections may cause machinery

to malfunction, may be visually unacceptable, and may lead to damage to nonstructural

elements or to changes in the distribution of forces. In the case of very flexible roofs,

deflections due to the weight of water on the roof may lead to increased depth of water,

increased deflections, and so on, until the strength of the roof is exceeded. This is a

ponding failure and in essence is a collapse brought about by failure to satisfy a

serviceability limit state.

b) Excessive crack widths. Although reinforced concrete must crack before the

reinforcement can function effectively, it is possible to detail the reinforcement to

minimize the crack widths. Excessive crack widths may be unsightly and may allow

leakage through the cracks, corrosion of the reinforcement, and gradual deterioration of

the concrete.

c) Undesirable vibrations. Vertical vibrations of floors or bridges and lateral and

torsional vibrations of tall buildings may disturb the users. Vibration effects have rarely

been a problem in reinforced concrete buildings.

III. Special limit states. This class of limit states involves damage or failure due to abnormal

conditions or abnormal loadings and includes:

a) Damage or collapse in extreme earthquakes,

b) Structural effects of fire, explosions, or vehicular collisions,

c) Structural effects of corrosion or deterioration, and

d) Long-term physical or chemical instability (normally not a problem with

concrete structures).

2. Limit state design process

Limit-states design is a process that involves

1. The identification of all potential modes of failure (i.e., identification of the significant

limit states),

2. The determination of acceptable levels of safety against occurrence of each limit state,

3. Structural design for the significant limit states.

For normal structures, step 2 is carried out by the building-code authorities, who specify the load

combinations and the load factors to be used. For unusual structures, the engineer may need to



check whether the normal levels of safety are adequate. For buildings, a limit-states design starts

by selecting the concrete strength, cement content, cement type, supplementary cementitious

materials, water–cementitious materials ratio, air content, and cover to the reinforcement to

satisfy the durability requirements of Eurocode. Next, the minimum member sizes and minimum

covers are chosen to satisfy the fire-protection requirements of the local building code. Design is

then carried out, starting by proportioning for the ultimate limit states followed by a check of

whether the structure will exceed any of the serviceability limit states. This sequence is followed

because the major function of structural members in buildings is to resist loads without

endangering the occupants. For a water tank, however, the limit state of excessive crack width is

of equal importance to any of the ultimate limit states if the structure is to remain watertight. In

such a structure, the design for the limit state of crack width might be considered before the

ultimate limit states are checked. In the design of support beams for an elevated monorail, the

smoothness of the ride is extremely important, and the limit state of deflection may govern the

design.

1.7. MATERIALS

1.7.1. BEHAVIOR OF CONCRETE UNDER COMPRESSION

1.7.1.1. Compressive strength of concrete

Generally, the term concrete strength is taken to refer to the uniaxial compressive strength as

measured by a compression test of a standard test cylinder, because this test is used to monitor

the concrete strength for quality control or acceptance purposes. For convenience, other strength

parameters, such as tensile or bond strength, are expressed relative to the compressive strength.

1.7.1.2. Statistical Variations in Concrete Strength

Concrete is a mixture of water, cement, aggregate, and air. Variations in the properties or

proportions of these constituents, as well as variations in the transporting, placing, and

compaction of the concrete, lead to variations in the strength of the finished concrete. In addition,

discrepancies in the tests will lead to apparent differences in strength. The shaded area in Figure

1-3 shows the distribution of the strengths in a sample of 176 concrete-strength tests.



Figure 1-3 - Distribution of concrete strengths.

The mean or average strength is 3940 psi, but one test has strength as low as 2020 psi and one is

as high as 6090 psi.

If more than about 30 tests are available, the strengths will generally approximate a normal

distribution. The normal distribution curve, shown by the curved line in Figure 1-3, is

symmetrical about the mean value, x of the data. The dispersion of the data can be measured by

the sample standard deviation, S , which is the root-mean-square deviation of the strengths from

their mean value:

( 1-1)

The standard deviation divided by the mean value is called the coefficient of variation, V:

( 1-2)

This makes it possible to express the degree of dispersion on a fractional or percentage basis

rather than an absolute basis. The concrete test data in Figure 1-3 have a standard deviation of

615 psi and a coefficient of variation of or 15.6 percent. 615/3940 = 0.156.



If the data correspond to a normal distribution, their distribution can be predicted from the

properties of such a curve. Thus, 68.3 percent of the data will lie within 1 standard deviation

above or below the mean. Alternatively, 15.6 percent of the data will have values less than

x s Similarly, for a normal distribution, 10 percent of the data, or 1 test in10, will have

values less than ̅(1-aV), where a=1.282, Values of a corresponding to other probabilities can

be found in statistics texts.

Figure 1-4 shows the mean concrete strength, crf , required for various values of the coefficient

of variation if no more than 1 test in 10 is to have strength less than 3000 psi. As shown in this

figure, as the coefficient of variation is reduced, the value of the mean strength, crf , required to

satisfy this requirement can also be reduced.

Figure 1-4 - Normal frequency curves for coefficients of variation of10, 15, and 20 percent.

NB: Poor control…………….…..V > 14%

Average control…………….V = 10.5%

Excellent control……………V < 7%

1.7.1.3. Factors Affecting Concrete Compressive Strength Water/cement ratio. Moisture conditions during curing.

Type of cement. Temperature conditions during curing.



Supplementary cementitious materials. Age of concrete

Aggregate. Maturity of concrete

Mixing water. Rate of loading.

1.7.1.4. Stress-Strain Curves

Typical stress-strain curves of concrete (of various grades), obtained from standard uniaxial

compression tests, are shown in Figure 1-5. The curves are somewhat linear in the very initial

phase of loading; the non-linearity begins to gain significance when the stress level exceeds

about one-third to one-half of the maximum. The maximum stress is reached at a strain

approximately equal to 0.002; beyond this point, an increase in strain is accompanied by a

decrease in stress. For the usual range of concrete strengths, the strain at failure is in the range of

0.003 to 0.005.

The higher the concrete grade, the steeper is the initial portion of the stress-strain curve, the

sharper the peak of the curve, and the less the failure strain. For low-strength concrete, the

curve has a relatively flat top, and a high failure strain.

When the stress level reaches 70–90 percent of the maximum, internal cracks are initiated in the

mortar throughout the concrete mass, roughly parallel to the direction of the applied loading.

The concrete tends to expand laterally, and longitudinal cracks become visible when the lateral

strain (due to the Poisson effect) exceeds the limiting tensile strain of concrete (0.0001—0.0002).

The cracks generally occur at the aggregate-mortar interface. As a result of the associated larger

lateral extensions, the apparent Poisson’s ratio increases sharply.



Figure 1-5 - Typical stress-strain curves of concrete in compression

The descending branch of the stress-strain curve can be fully traced only if the strain-controlled

application of the load is properly achieved. For this, the testing machine must be sufficiently

rigid (i.e., it must have a very high value of load per unit deformation); otherwise, the concrete is

likely to fail abruptly (sometimes, explosively) almost immediately after the maximum stress is

reached. The fall in stress with increasing strain is a phenomenon which is not clearly

understood; it is associated with extensive micro-cracking in the mortar, and is sometimes called

softening of concrete.

1.7.1.5. Modulus of Elasticity

The Young’s modulus of elasticity is a constant, defined as the ratio, within the linear elastic

range, of axial stress to axial strain, under uniaxial loading. In the case of concrete under

uniaxial compression, it has some validity in the very initial portion of the stress-strain curve,

which is practically linear [Figure 6]; that is, when the loading is of low intensity, and of very

short duration.

Various descriptions of Ec are possible, such as initial tangent modulus, tangent modulus (at a

specified stress level), secant modulus (at a specified stress level), etc. — as shown in Figure 6.

Among these, the secant modulus at a stress of about one-third the cube strength of concrete is

generally found acceptable in representing an average value of Ec under service load conditions

(static loading).



Figure 6 – Various descriptions of modulus of elasticity of concrete

( I T≡ initial tangent, T ≡ tangent, S ≡ secant )

1.7.2. BEHAVIOR OF CONCRETE UNDER TENSION

Concrete is not normally designed to resist direct tension. However, tensile stresses do develop

in concrete members as a result of flexure, shrinkage and temperature changes. Principal

tensile stresses may also result from multi-axial states of stress. Often cracking in concrete is a

result of the tensile strength (or limiting tensile strain) being exceeded. As pure shear causes

tension on diagonal planes, knowledge of the direct tensile strength of concrete is useful for

estimating the shear strength of beams with unreinforced webs, etc. Also, knowledge of the

flexural tensile strength of concrete is necessary for estimation of the ‘moment at first crack’,

required for the computation of deflections and crack widths in flexural members.

As pointed out earlier, concrete is very weak in tension, the direct tensile strength being only

about 7 to 15 percent of the compressive strength. It is difficult to perform a direct tension test

on a concrete specimen, as it requires a purely axial tensile force to be applied, free of any



misalignment and secondary stress in the specimen at the grips of the testing machine. Hence,

indirect tension tests are resorted to, usually the flexure test or the cylinder splitting test.

1.7.2.1. Stress-Strain Curve of Concrete in Tension

Concrete has a low failure strain in uniaxial tension. It is found to be in the range of 0.0001 to

0.0002. The stress-strain curve in tension is generally approximated as a straight line from the

origin to the failure point. The modulus of elasticity in tension is taken to be the same as that in

compression. As the tensile strength of concrete is very low, and often ignored in design, the

tensile stress-strain relation is of little practical value.

1.7.2.2. Splitting Tensile Strength

The cylinder splitting test is the easiest to perform and gives more uniform results compared to

other tension tests. In this test, a ‘standard’ plain concrete cylinder (of the same type as used for

the compression test) is loaded in compression on its side along a diametric plane. Failure

occurs by the splitting of the cylinder along the loaded plane [Figure 7]. In an elastic

homogeneous cylinder, this loading produces a nearly uniform tensile stress across the loaded

plane as shown in Figure 7.

From theory of elasticity concepts, the following formula for the evaluation of the splitting

tensile strength fct is obtained:

2ct

Pf

dL

(1)

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



Figure 7 – Cylinder splitting test for tensile strength

1.7.3. REINFORCING STEEL

As explained earlier, concrete is reinforced with steel primarily to make up for concrete’s

incapacity for tensile resistance. Steel embedded in concrete, called reinforcing steel, can

effectively take up the tension that is induced due to flexural tension, direct tension, ‘diagonal

tension’ or environmental effects. Reinforcing steel also imparts ductility to a material that is

otherwise brittle. Furthermore, steel is stronger than concrete in compression also; hence,

concrete can be advantageously reinforced with steel for bearing compressive stresses as well, as

is commonly done in columns.

1.7.3.1. Stress-Strain Curves

The stress-strain curve of reinforcing steel is obtained by performing a standard tension test.

Typical stress-strain curves for the three grades of steel are depicted in Figure 1-8.



Figure 1-8 - Typical stress-strain curves for reinforcing steels

For all grades, there is an initial linear elastic portion with constant slope, which gives a

modulus of elasticity sE that is practically the same for all grades. The Code specifies that the

value of sE to be considered in design is 2 ×105 MPa N/mm

2. The stress-strain curve of mild

steel (hot rolled) is characterized by an initial nearly elastic part that is followed by an yield

plateau (where the strain increases at almost constant stress), followed in turn by a strain

hardening range in which the stress once again increases with increasing strain (although at a

decreasing rate) until the peak stress (tensile strength) is reached. Finally, there is a descending

branch wherein the nominal stress (load divided by original area) decreases until fracture occurs.

(The actual stress, in terms of load divided by the current reduced area, will, however, show an

increasing trend).

1.8. EUROCODE’S RECOMMENDATIONS FOR LIMIT STATES DESIGN

The salient features of LSM, as prescribed by the Code, are covered here. Details of the design

procedure for various limit states of collapse and serviceability are covered in subsequent

sections.



1.8.1. ACTIONS

The term action is used in the Eurocodes in order to group together generically all external

influences on a structure’s performance. It encompasses loading by gravity and wind, but

includes also vibration, thermal effects, fire and seismic loading.

Separate combinations of actions are used to check the structure for the design situation being

considered. For each of the particular design situations an appropriate representative value for

each action is used.

1.8.1.1. Representative values of actions

The main actions to be used in load cases used for design are:

Permanent actions G: e.g. self-weight of structures and fixed equipment;

Variable actions Q: e.g. imposed loads on building floors and beams; snow loads on

roofs; wind loading on walls and roofs

Accidental actions A: e.g. fire, explosions and impact.

1.8.1.2. Permanent actions

The characteristic value of a permanent action kG may be a single value if variability is known

to be low (e.g. the self-weight of quality-controlled factory-produced members). If the variability

of G cannot be considered as small, and its magnitude may vary from place to place in the

structure, then an upper value ,supkG and a lower value

,infkG may occasionally be used.

1.8.1.3. Variable actions

Up to four types of representative value may be needed for the variable and accidental actions.

The types most commonly used for variable actions are:

The characteristic value kQ

and combinations of the characteristic value with other variable actions, multiplied by

different combination factors:

The combination value 0 kQ

The frequent value 1 kQ

The quasi-permanent value 2 kQ

Explanations of the representative values and the design situations in which they arise are given

below. The ‘ x ’ factors generally reduce the value of a variable action present in an accidental

situation compared with the characteristic value.

A. Combination value of 0 kQ

The combination value is used for checking:

1. Ultimate limit states;



2. Irreversible serviceability limit states (e.g. deflections which fracture brittle fittings or

finishes).

It is associated with combinations of actions. The combination factor 0 reduces

kQ because of

the low probability of the most unfavourable values of several independent actions occurring

simultaneously.

B. Frequent value 1 kQ

The frequent value is used for checking:

1. Ultimate limit states involving accidental actions;

2. Reversible serviceability limit states, primarily associated with frequent combinations.

In both cases the reduction factor 1 multiplies the leading variable action. The frequent value

1 kQ of a variable action Q is determined so that the total proportion of a chosen period of time

during which Q exceeds 1 kQ is less than a specified small part of the period.

C. Quasi-permanent value 2 kQ

The quasi-permanent value is used for checking:

1. Ultimate limit states involving accidental actions;

2. Reversible serviceability limit states.

Quasi-permanent values are also used for the calculation of long-term effects (e.g. cosmetic

cracking of a slab) and to represent combinations of variable seismic actions. The quasi-

permanent value 2 kQ is defined so that the total proportion of a chosen period of time during

which Q exceeds 2 kQ is a considerable part (more than half) of the chosen period.

1.8.1.4. Load combinations for design

The values of actions to be used in design are governed by a number of factors. These include:

1. The nature of the load. Whether the action is permanent, variable or accidental, as the

confidence in the description of each will vary.

2. The limit state being considered. Clearly, the value of an action governing design must be

higher for the ultimate limit state than for serviceability for persistent and transient design

situations. Further, under serviceability conditions, loads vary with time, and the design

load to be considered could vary substantially. Realistic serviceability loads should be

modeled appropriate to the aspect of the behavior being checked (e.g. deflection, cracking

or settlement). For example, creep and settlement are functions of permanent loads only.

3. The number of variable loads acting simultaneously. Statistically, it is improbable that all

loads will act at their full characteristic value at the same time. To allow for this, the

characteristic values of actions will need modification.



Consider the case of permanent action kG and one variable action kQ only. For the ultimate

limit state the characteristic values should be magnified, and the load may be represented as

G k Q kG Q , where the factors are the partial safety factors. The values of G and Q will be

different, and will be a reflection of the variabilities of the two loads being different. The gamma

factors account for:

1) The possibility of unfavourable deviation of the loads from the characteristic values

2) Inaccuracies in the analyses

3) Unforeseen redistribution of stress

4) Variations in the geometry of the structure and its elements, as this affects the

determination of the action effects.

Now consider the case of a structure subject to variable actions 1Q and 2Q simultaneously. If 1Q

and 2Q are independent, i.e. the occurrence and magnitude of 1Q does not depend on the

occurrence and magnitude of 2Q and vice versa, then it would be unrealistic to use

,1 ,1 ,2 ,2Q k Q kQ Q as the two loads are unlikely to act at their maximum at the same time. Joint

probabilities will need to be considered to ensure that the probability of occurrence of the two

loads is the same as that of a single load. It will be more reasonable to consider one load at its

maximum in conjunction with a reduced value for the other load. Thus, we have two

possibilities:

,1 ,1 0,2 ,2 ,2Q k Q kQ Q (2)

Or

0,1 ,1 ,1 ,2 ,2Q k Q kQ Q (3)

Multiplication by 0 is said to produce a combination value of the load. It should be noted that

the values of and 0 vary with each load.

The above discussion illustrates the thinking behind the method of combining loads for an

ultimate limit state check. Similar logic is applied to the estimation of loads for the different

serviceability checks.

I. Ultimate limit state

The following ultimate limit states shall be verified as relevant:

a) EQU: Loss of static equilibrium of the structure or any part of it considered as a rigid

body, where:

Minor variations in the value or the spatial distribution of actions from a single

source are significant, and

The strengths of construction materials or ground are generally not governing;



b) STR: Internal failure or excessive deformation of the structure or structural members,

including footings, piles, basement walls, etc., where the strength of construction

materials of the structure governs;

c) GEO: Failure or excessive deformation of the ground where the strengths of soil or rock

are significant in providing resistance;

d) FAT: Fatigue failure of the structure or structural members.

Combinations of actions

1) Persistent and transient situations – fundamental combinations.

In the following paragraphs, various generalized combinations of loads are expressed

symbolically. It should be noted that the ‘+’ symbol in the expressions does not have the normal

mathematical meaning, as the directions of loads could be different. It is best to read it as

meaning ‘combined with’.

EN 1990 gives three separate sets of load combinations, namely EQU (to check against loss of

equilibrium), STR (internal failure of the structure governed by the strength of the construction

materials) and GEO (failure of the ground, where the strength of soil provides the significant

resistance).

Equilibrium: Equilibrium is verified using the load combination Set A in the code, which is as

follows:

, , ,1 ,1 , 0, ,G J k j Q k Q i i k iG Q Q (4)

, ,sup , ,supG j k jG is used when the permanent loads are unfavourable, and , ,inf , ,infG j k jG is used when

the permanent actions are favourable. Numerically, , ,sup 1.1G j ,

, ,inf 0.9G j , and 1.5Q

when unfavourable and 0 when favourable.

The above format applies to the verification of the structure as a rigid body (e.g. overturning of

retaining walls). A separate verification of the limit state of rupture of structural elements should

normally be undertaken using the format given below for strength. In cases where the

verification of equilibrium also involves the resistance of the structural member (e.g.

overhanging cantilevers), the strength verification given below without the above equilibrium

check may be adopted. In such verifications, , ,inf 1.15G j should be used.

Strength: when a design does not involve geotechnical actions, the strength of elements should

be verified using load combination Set B. two options are given. Either combination (6.10) from

EN 1990 or the less favourable of equations (6.10a) and (6.10b) may be used:

, , ,1 ,1 , 0, ,G j k j Q k Q i i k iG Q Q (5)



, ,sup , ,supG j k jG is used when the permanent loads are unfavourable , and , ,inf , ,infG j k jG is used when

the permanent actions are favourable. Numerically, , ,sup 1.35G j ,

, ,inf 1.0G j , and 1.5Q

when unfavourable and 0 when favourable (EN1990)

, , , 0, ,G j k j Q i i k iG Q (6)

, , ,1 ,1 , 0, ,G j k j Q k Q i i k iG Q Q (7)

Numerically, , ,sup , ,inf0.925, 1.35, 1.0G j G j and 1.5Q when unfavourable and 0 when

favourable (EN 1990)

The above combinations assume that a number of variable actions are present at the same time.

,1kQ is the dominant load if it is obvious, otherwise each load is in turn treated as a dominant

load and the other as secondary. The dominant load is then combined with the combination value

of the secondary loads. Both are multiplied by their respective values.

The magnitude of the load resulting from equations (6.10a) and (6.10b) will always be less than

that from equation (6.10).

Now turning to the factors ,infG and

,supG , it will be noted that the numerical values are

different in the verification of equilibrium and that of strength. For instance, in an overhanging

cantilever beam, the multiplier for self-weight in the cantilever section will be ,sup1.1 G and

that in the anchor span will be ,0.9 G cnf . The possible explanation for ,supG being 1.1 and not

1.35 as in the strength check is that

a) The variability in self-weight of the element is unlikely to be large

b) The factor 1.35 has built into it an allowance for structural performance (which is

necessary only for strength checks)

c) The loading in the cantilever will also generally include variable actions, partial safety

factors for which will ensure a reasonable overall safety factor.

When a design involves geotechnical action, a number of approaches are given in EN 1990, and

the choice of the method is a Nationally Determined Parameter.

2) Accidental design situation

The load combination recommended is

, 1, ,1 2, ,k j d i k i k iG A Q Q (8)

where dA is the design value of accidental action, ,1kQ is the main variable action accompanying

the accidental action and ,k iQ are other variable actions.

Accidents are unintended events such as explosions, fire or vehicular impact, which are of short

duration and which have a low probability of occurrence. Also, a degree of damage is generally



acceptable in the event of an accident. The loading model should attempt to describe the

magnitude of other variable loads which are likely to occur in conjunction with the accidental

load. Accidents generally occur in structures in use. Therefore, the values of variable actions will

be less than those used for the fundamental combination of loads in (1) above. To provide a

realistic variable load combining with the accidental load, the variable actions are multiplied by

different (and generally lower) factors. Multiplier 1 is applied to the dominant action, and

2 to the others. Where the dominant action is not obvious, each variable action present is in

turn treated as dominant. Q for accidental situations is unity.

Multiplication by 1 is said to produce a frequent value of the load, and multiplication by 2 the

quasi-permanent value. Numerical values for 1 and 2 are given in EN 1990.

3) Seismic design situations

, 2, ,1 1

k j Ed i k ij i

G A Q

(9)

II. Serviceability limit state

Combination of actions

1) Characteristic combination.

, ,1 0, ,1

k j k i k ii

G Q Q

(10)

This represents a combination of service loads, which can be considered rather infrequent. It

might be appropriate for checking sates such as micro cracking or possible local non-catastrophic

failure of reinforcement leading to large cracks in sections.

2) Frequent combination

, 1,1 ,1 2, , 1k j k i k iG Q Q i (11)

This represents a combination that is likely to occur relatively frequently in service conditions,

and is used for checking cracking.

3) Quasi-permanent combination

, 2, , 1k j i k iG Q i (12)

This will provide an estimate of sustained loads on the structure, and will be appropriate for the

verification of creep, settlement, etc.

It should be realized that the above combinations describe the magnitude of loads which are

likely to be present simultaneously. The actual arrangement of loads in position and direction

within the structure to create the most critical effect is a matter of structural analysis (e.g. loading

alternate or adjacent spans in continuous beams).

Values of factors



Table 2 – Recommended values of factors for buildings

1.8.2. MATERIAL

1.8.2.1. Partial factors for materials

Table 3 – Partial factors for materials for ultimate limit states

The value for partial factors for materials for serviceability limit state verification should be taken as

those given in the particular clauses of this Eurocode. The recommended value is 1.0.

1.8.2.2. Concrete

The compressive strength of concrete is denoted by concrete strength classes which relate to the

characteristic (5%) cylinder strength ckf , or the cube strength,ck cubef .



The characteristic strength for ckf and the corresponding mechanical characteristics necessary design

are given in the following.

Poisson’s ratio may be taken equal to 0.2 for uncracked concrete and 0 for cracked concrete.

Design compressive strengths



The value of the design compressive strength is defined as

cd cc ck cf f (13)

Where:

c is the partial safety factor for concrete

cc is the coefficient taking account of long term effects on the compressive strength and of

unfavourable effects resulting from the way the load is applied.

The value of cc for use in a Country should lie between 0.8 and 1.0 and may be found in its National

Annex. The recommended value is 1.

Stress-strain relations for the design of cross-sections

For the design of cross-sections, the following stress-strain relationship may be used.

2

2

1 1 0

n

cc cd c c

c

f for

(14)

2 2c cd c c cuf for (15)

Where:

n is the exponent according to Table 3.1 of Eurocode

2c is the strain at reaching the maximum strength according to Table 3.1 of Eurocode

cu is the ultimate strain according to Table 3.1 of Eurocode

Figure 9 – Parabola-rectangle diagram for concrete under compression



Other simplified stress-strain relationships may be used if equivalent to or more conservative than the

one defined above, for instance bi-linear according to the following figure (compressive stress and

shortening strain shown as absolute values) with values of 3c and 3cu .

Figure 10 – Bi-Linear stress-strain relation

A rectangular stress distribution as given in the figure below may be assumed. The factor , defining

the effective height of the compression zone and the factor , defining the effective strength, follow

from:

0.8 50ckfor f MPa (16)

0.8 50 400 50 90ck ckf for f MPa (17)

and

1.0 50ckfor f MPa (18)

1.0 50 200 50 90ck ckf for f MPa (19)



Figure 11 – Rectangular stress distribution

1.8.2.3. Reinforcing steel

The application rules for design and detailing in this Eurocode are valid up for specified yield strength,

400 600ykf MPa.

For normal design, either of the following assumptions may be made

a. an inclined top branch with a strain limit of ud and a maximum stress of yk skf at uk ,

where t y kk f f

b. A horizontal top branch without the need to check the strain limit.

The recommended value of ud is 0.9 uk and the value of t y kf f is given in Annex C of Eurocode 2.

Figure 12 – Idealized and design stress-strain diagrams for reinforcing steel (for tension and compression)



The mean value of density may be assumed to be 7850 kg/m3.The design value of the modulus of

elasticity sE may be assumed to be 200 GPa.

Documents

CHAPTER 1. INTRODUCTON TO REINFORCED CONCRETE · CHAPTER 1. INTRODUCTON TO REINFORCED CONCRETE 1.1. INTRODUCTION Traditionally, the study of reinforced concrete design begins directly