ADDIS ABABA UNIVERSITY ADDIS ABABA INSTITUTE · PDF file1.5.2. INTRODUCTION TO EUROCODES BS EN...

ADDIS ABABA UNIVERSITY ADDIS ABABA INSTITUTE OF TECHNOLOGY SCHOOL OF CIVIL AND ENVIRONEMNTAL

ENGINEERING

Reinforced Concrete I Chapter one: Introduction to Reinforced Concrete

1.1. INTRODUCTION C

oncr

ete

Con

cret

e

• 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. Stadium, auditorium

• 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 NOT CLEAR

Generally….

Extensively used in….

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.

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.

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

• 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.).

• The main strength of concrete lies in its compression-bearing ability, which surpasses that of traditional materials like brick and stone masonry.

What is concrete?

Why is it popular?

What are it’s advantages and disadvantages?

It’s advantages… It’s disadvantages

combining the best features of concrete and steel. combining the best features of concrete and steel.

1.2. PLAIN AND REINFORCED CONCRETE 1.2.2. REINFORCED CONCRETE

concrete with steel bars embedded in it

combining the best features of concrete and steel.

What is Reinforced concrete?

Why is it versatile?

What are the advantages of the steel bar embedded in it?

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

• compensate for the concrete’s incapacity for tensile resistance, effectively taking up all the tension, without separating from the concrete

• 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.

• the reinforcing steel imparts ductility to a material that is otherwise brittle.

How do tensile stresses occur?

Directly

Indirectly

direct tension or flexural tension

Shear, Temperature and shrinkage effects

1.3. ADVANTAGES AND DISADVANTAGES OF CONCRETE

Advantages Disadvantages

1. Economy. 2. Suitability of material for

architectural and structural function.

3. Fire resistance. 4. Rigidity. 5. Low maintenance. 6. Availability of materials.

1. Low tensile strength. 2. Forms and shoring. 3. Relatively low strength per unit of

weight or volume. 4. Time-dependent volume changes.

Advantages Disadvantages

1.4. THE DESIGN PROCESS

Objectives of Design

The design process

The structure should satisfy four major criteria: 1. Appropriateness. 2. Economy. 3. Structural adequacy. 4. Maintainability

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.

What do we mean by structural engineer?

1.5. DESIGN CODES AND HANDBOOKS 1.5.1. PURPOSE OF CODES

Purpose of codes

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!

The codes serve at least four distinct functions: ensure adequate structural safety, by specifying certain essential minimum requirements for design. 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. ensure a measure of consistency among different designers. 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.

1.5.2. INTRODUCTION TO EUROCODES BS EN 1990: Eurocode: Basis of design (EC0)

BS 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

BS 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)

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

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

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

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

BS EN 1997: Eurocode 7: Geotechnical design (EC7)

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

BS 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.

1.5.2. INTRODUCTION TO EUROCODES

1.5.2. INTRODUCTION TO EUROCODES

Eurocode: Basis of structural design

• overarches all the other Eurocodes (EN 1991 to EN 1999). • 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.

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.

There are four parts to Eurocode 2; Eurocode 2, Part 1–1: General rules and rules for buildings • Eurocode 2, Part 1–2: Structural fire design • Eurocode 2, Part 2: Bridges • Eurocode 2, Part 3: Liquid retaining and containment

Eurocode 2: Design of concrete structures

1.6. DESIGN PHILOSOPHIES 1.6.1. INTRODUCTION

Working stress method of

design (WSM)

Ultimate load method

Reliability-based methods

Limit states method (LSM)

• The earliest codified design philosophy • based on linear elastic theory, • it is now sidelined by the modern limit states design philosophy.

• developed in the 1950s. • Based on the (ultimate) strength of reinforced concrete at ultimate loads. • was introduced as an alternative to WSM in the ACI code in 1956 and the

British Code in 1957.

• developed over the years and received a major impetus from the mid-1960s onwards.

• was based on the theory that the various uncertainties in design could be handled more rationally in the mathematical framework of probability theory.

• there was little acceptance for this theory in professional practice, mainly because the theory appeared to be complicated and intractable (mathematically and numerically).

• is reliability-based in concept. • 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).

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 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 method

Advantages

Disadvantages

• 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.

• does not provide a realistic measure of the actual factor of safety underlying a design. • fails to discriminate between different types of loads that act simultaneously, but have different degrees of uncertainty.

• 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.

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

1.6.3. ULTIMATE LOAD METHOD (ULM)

• 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 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.

• 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.

The method

Advantages

Disadvantages • 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.

• 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.

1.6.4. LIMIT STATES METHOD (LSM)

• 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’.

• 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.

The method

1.6.4. LIMIT STATES METHOD (LSM)

Limit states

• 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.

a) Loss of equilibrium b) Rupture c) Progressive collapse d) Formation of a plastic

mechanism e) Instability f) Fatigue

• 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.

a) Excessive deflections b) Excessive crack widths c) Undesirable vibrations

a) Damage or collapse in extreme earthquakes

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

c) Structural effect of corrosion or deterioration

d) Long – term physical or chemical instability

• involves damage or failure due to abnormal conditions or abnormal loadings and includes:

Incl

udes

….

Def

initi

on…

.

Ultimate limit states Serviceability limit states Special limit states

1.7. MATERIALS 1.7.1. BEHAVIOR OF CONCRETE UNDER COMPRESSION

Compressive strength of concrete

Factors Affecting Concrete Compressive strength

• 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.

• Water/Cement ratio • Type of cement • Supplementary cementitious materials • Aggregate • Mixing water • Moisture conditions during curing. • Temperature conditions during curing • Age of concrete • Maturity of concrete • Rate of loading

1.7.1. BEHAVIOR OF CONCRETE UNDER COMPRESSION

• 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. I • n addition, discrepancies in the tests will lead to apparent differences in strength.

Statistical variations in concrete strength


• 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.

Stress-Strain Curves


• 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 ; 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 (IT) , tangent modulus (T)( (at a specified stress level), secant modulus (S) (at a specified stress level), etc.

• 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).

Modulus of Elasticity

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.

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. BEHAVIOR OF CONCRETE UNDER TENSION

• 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 • In an elastic homogeneous cylinder, this loading produces a nearly uniform tensile stress across the loaded plane • From theory of elasticity concepts, the following formula for the evaluation of the splitting tensile strength fct is obtained:

Splitting tensile strength

2ct

PfdL

1.7.4. REINFORCING STEEL

• 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 the figure below.

• For all grades, there is an initial linear elastic portion with constant slope, which gives a modulus of elasticity that is practically the same for all grades.

• The Code specifies that the value of to be considered in design is 2 ×105 MPa N/mm2. • 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).

Stress-Strain Curve

1.8. EUROCODE’S RECOMMENDATIONS FOR LIMIT STATES DESIGN 1.8.1. ACTIONS

• The term action is used in the Eurocodes in order to group together generally 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.

Introduction

• The main actions to be used in load cases used for design are: a. Permanent actions G: e.g. self‐weight of structures and fixed equipment; b. Variable actions Q: e.g. imposed loads on building floors and beams; snow loads on roofs; wind loading on walls and roofs c. Accidental actions A: e.g. fire, explosions and impact.

Representative values of actions

• The characteristic value of a permanent action 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 and a lower value may occasionally be used.

Permanent actions

1.8. EUROCODE’S RECOMMENDATIONS FOR LIMIT STATES DESIGN

1.8.1. 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:

a. The characteristic value and combinations of the characteristic value with other variable actions, multiplied by different combination factors:

b. The combination value c. The frequent value d. The quasi‐permanent value

• The ‘ ’ factors generally reduce the value of a variable action present in an accidental situation compared with the characteristic value.

Variable actions

a. Combination value of 0 kQ

b. Frequent value of 1 kQ

c. Quasi‐permanent value of 2 kQ

• Ultimate limit states; • Irreversible serviceability limit states (e.g. deflections which fracture

brittle fittings or finishes).

• Ultimate limit states involving accidental actions; • Reversible serviceability limit states, primarily associated with frequent

combinations.

• Ultimate limit states involving accidental actions; • Reversible serviceability limit states (


1.8.1. ACTIONS 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 2. The limit state being considered 3. The number of variable loads acting simultaneously

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.


1.8.1. ACTIONS I. Ultimate limit state

1. Persistent and transient situations – fundamental combinations.

Equilibrium

, ,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.

Strength

, ,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


1.8.1. ACTIONS I. Ultimate limit state

2. Accidental design situation

3. Seismic design situation


1.8.1. ACTIONS II. Serviceability limit state

1. Characteristic combination

2. Frequent combination

3. Quasi‐permanent combination

• 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.

• This represents a combination that is likely to occur relatively frequently in service conditions, and is used for checking cracking.

• This will provide an estimate of sustained loads on the structure, and will be appropriate for the verification of creep, settlement, etc.


1.8.2. MATERIAL Partial factors for materials

Partial factors for materials for ultimate limit states

Partial factors for materials for serviceability 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. MATERIAL Concrete

Design compressive strengths

Stress‐Strain relations for the design of cross‐sections

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

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.




1. Parabolic‐ Rectangular




2. Bi – Linear stress‐strain relation




3. Rectangular stress‐strain relation


1.8.2. MATERIAL Reinforcing steel


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