CHAPTER 1. INTRODUCTON TO REINFORCED CONCRETE

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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 PLAIN AND REINFORCED CONCRETE 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 welldefined 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 Chapter 1 Introduction to Reinforced Concrete Page 1

2 past four decades in particular, have now made it possible to produce a wide range of concrete grades, varying in mass density ( kg/m3) and compressive strength ( 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.) 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 Chapter 1 Introduction to Reinforced Concrete Page 2

3 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 Chapter 1 Introduction to Reinforced Concrete Page 3

4 (c) Ductile mode of failure under heavy loads (d) Reinforced concrete column Figure 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. Chapter 1 Introduction to Reinforced Concrete Page 4

5 3. Relatively low strength per unit of weight or volume. 4. Time-dependent volume changes THE DESIGN PROCESS 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 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 DESIGN CODES AND HANDBOOKS 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. Chapter 1 Introduction to Reinforced Concrete Page 5

6 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! 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 Chapter 1 Introduction to Reinforced Concrete Page 6

7 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). Chapter 1 Introduction to Reinforced Concrete Page 7

8 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 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. Chapter 1 Introduction to Reinforced Concrete Page 8

9 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 DESIGN PHILOSOPHIES 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 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 Chapter 1 Introduction to Reinforced Concrete Page 9

10 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 (now ACI ). 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 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. Chapter 1 Introduction to Reinforced Concrete Page 10

11 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 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 Chapter 1 Introduction to Reinforced Concrete Page 11

12 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 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. Chapter 1 Introduction to Reinforced Concrete Page 12

13 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. II. 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. 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: Chapter 1 Introduction to Reinforced Concrete Page 13

14 III. 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. 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 Chapter 1 Introduction to Reinforced Concrete Page 14

15 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 MATERIALS BEHAVIOR OF CONCRETE UNDER COMPRESSION 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 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. Chapter 1 Introduction to Reinforced Concrete Page 15

16 Figure 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 = Chapter 1 Introduction to Reinforced Concrete Page 16

17 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, f cr, 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, f cr satisfy this requirement can also be reduced., required to Figure 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% Factors Affecting Concrete Compressive Strength Water/cement ratio. Moisture conditions during curing. Type of cement. Temperature conditions during curing. Chapter 1 Introduction to Reinforced Concrete Page 17

18 Supplementary cementitious materials. Aggregate. Mixing water. Age of concrete Maturity of concrete Rate of loading 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 to 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 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 ( ). 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. Chapter 1 Introduction to Reinforced Concrete Page 18

19 Figure 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 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 E c 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 E c under service load conditions (static loading). Chapter 1 Introduction to Reinforced Concrete Page 19

20 Figure 6 Various descriptions of modulus of elasticity of concrete ( I T initial tangent, T tangent, S secant ) 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 Chapter 1 Introduction to Reinforced Concrete Page 20

21 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 to 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 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 f ct is obtained: 2P (1) fct dl where P is the maximum applied load, d is the diameter and L the length of the cylinder. Chapter 1 Introduction to Reinforced Concrete Page 21

22 REINFORCING STEEL Figure 7 Cylinder splitting test for tensile strength 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 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. Chapter 1 Introduction to Reinforced Concrete Page 22

23 Figure Typical stress-strain curves for reinforcing steels For all grades, there is an initial linear elastic portion with constant slope, which gives a s modulus of elasticity E that is practically the same for all grades. The Code specifies that the value of E s to be considered in design is 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) 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. Chapter 1 Introduction to Reinforced Concrete Page 23

24 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 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 Permanent actions The characteristic value of a permanent action G 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 G k,sup and a lower value G k,inf may occasionally be used 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: Chapter 1 Introduction to Reinforced Concrete Page 24 k The characteristic value Q k and combinations of the characteristic value with other variable actions, multiplied by different combination factors: The combination value 0Qk The frequent value 1Q k The quasi-permanent value 2Qk Explanations of the representative values and the design situations in which they arise are given below. The factors generally reduce the value of a variable action present in an accidental x situation compared with the characteristic value. A. Combination value of 0Qk The combination value is used for checking: 1. Ultimate limit states;

25 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 Q k because of the low probability of the most unfavourable values of several independent actions occurring simultaneously. B. Frequent value 1Q k 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 1Q k of a variable action Q is determined so that the total proportion of a chosen period of time during which Q exceeds 1Q k is less than a specified small part of the period. C. Quasi-permanent value 2Qk 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 quasipermanent value 2Qk is defined so that the total proportion of a chosen period of time during which Q exceeds 2Qk is a considerable part (more than half) of the chosen period 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. Chapter 1 Introduction to Reinforced Concrete Page 25

26 Consider the case of permanent action G and one variable action k Q only. For the ultimate limit state the characteristic values should be magnified, and the load may be represented as GGk QQk, 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 Q 1 and Q 2 simultaneously. If Q 1 and Q 2 are independent, i.e. the occurrence and magnitude of Q 1 does not depend on the occurrence and magnitude of Q 2 and vice versa, then it would be unrealistic to use Q Q as the two loads are unlikely to act at their maximum at the same time. Joint Q,1 k,1 Q,2 k,2 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: Q,1 k,1 0,2 Q,2 k,2 Q Q (2) Or Q Q (3) 0,1 Q,1 k,1 Q,2 k,2 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; Chapter 1 Introduction to Reinforced Concrete Page 26 k

27 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: G Q Q (4) G, J k, j Q,1 k,1 Q, i 0, i k, i G, j,sup Gk, j,sup is used when the permanent loads are unfavourable, and G, j,inf Gk, j,inf is used when the permanent actions are favourable. Numerically, Gj,,sup 1.1, Gj,,inf 0.9, and Q 1.5 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, Gj,,inf 1.15 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: G Q Q (5) G, j k, j Q,1 k,1 Q, i 0, i k, i Chapter 1 Introduction to Reinforced Concrete Page 27

28 G, j,sup Gk, j,sup is used when the permanent loads are unfavourable, and G, j,inf Gk, j,inf is used when the permanent actions are favourable. Numerically, Gj,,sup 1.35, Gj,,inf 1.0, and Q 1.5 when unfavourable and 0 when favourable (EN1990) G Q (6) G, j k, j Q, i 0, i k, i G Q Q (7) G, j k, j Q,1 k,1 Q, i 0, i k, i Numerically, 0.925, G, j,sup 1.35, G, j,inf 1.0 and 1.5 when unfavourable and 0 when favourable (EN 1990) The above combinations assume that a number of variable actions are present at the same time. Q is the dominant load if it is obvious, otherwise each load is in turn treated as a dominant k,1 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 G,inf and G,sup Chapter 1 Introduction to Reinforced Concrete Page 28 Q, 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 1.1 G,sup and that in the anchor span will be 0.9 G, cnf. The possible explanation for G,sup 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 where G A Q Q (8) k, j d 1, i k,1 2, i k, i A d is the design value of accidental action, k,1 the accidental action and Q ki, are other variable actions. Q is the main variable action accompanying 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