Biography Concrete Design Book


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In the design and analysis of reinforced concrete members, you are presented The overall goal is to be able to design reinforced concrete structures that are. Reinforced concrete design was my favourite subject i ever read in my life and i have gone through several books for this one subject which. Rev. ed. of: Reinforced concrete / James G. MacGregor, James K. Wight. .. This book presents the theory of reinforced concrete design as a direct application of.

She has co-authored two books on design of masonry structures and more than papers and reports. She is an active member of several engineering societies, currently serves on the Board of Directors of the Masonry Society, and served as Vice-President of the Earthquake Engineering Research Institute.

John Pao, M. Pao received his B. Pao has more than 30 years of experience related to structural design of high-rise residential and office buildings, shopping centers, sport arenas, parking garages, and institutional buildings. Pao's design projects involve a variety of structural materials, including reinforced and post-tensioned concrete, structural steel, wood, and masonry. His creative and innovative design approaches have won accolades from clients and colleagues from Canada and the United States.

He is a licensed engineer in over twenty jurisdictions in the United States and Canada. His passions for structural design and engineering education have inspired him to give back to the profession and co-author this textbook. Pao has taught reinforced concrete design courses at various institutions since the mids. The amount of creep that takes place over a period of time depends on the grade of steel and the magnitude of the stress.

Creep of the steel is of little significance in normal reinforced concrete work, but it is an important factor in prestressed concre te where the prestressing steel is very highly stressed. This shrinkage is liable to cause cracking of the concrete, but it also has the beneficial effect of strengthening the bond between the concrete and the steel reinforcement.

Shrinkage begins to take place as soon as the concrete is mixed, and is caused initially by the absorption of the water by the concrete and the aggregate.

Further shrinkage is caused by evaporation of the water which rises to the concrete surface. During the setting process the hydration of the cement causes a great deal of heat to be generated, and as the concrete cools, further shrinkage takes place as a result of thermal contraction. Even after the concrete has hardened, shrinkage continues as drying out persists over many months, and any subsequent wetting and drying can also cause swelling and shrinkage.

Thermal shrinkage may be reduced by restricting the temperature rise during hydration, which may be achieved by the following procedures. I Use a mix design with a low cement content. A low water-cement ratio will help to reduce drying shrinkage by keeping to a minimum the volume of moisture that can be lost. If the change in volume of the concrete is allowed to take place freely without restraint, there will be no stress change within the concrete.

Restraint of the shrinkage, on the other hand, will cause tensile strains and stresses. The restraint may be caused externally by fix. For a long wall or floor slab, the restraint from adjoining concrete may be reduced by using a system of constructing successive bays instead of alternate bays. Tllis allows the free end of every bay to contract before the next bay is cast. Thermal stresses and strains may be controlled by the correct positioning of movcment or expansion joints in a structurc.

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When the tensile stresses caused by shrlnkoge or thermal movcment exceed the strength of the concrete, cracking will OCcur To cOlltrol the crack widths, steel reinforcement must be prOvided close to the cuncr! CalculatiOIl 01Strtutl l"ductd by Shrinkage a Shrinkage Restrolned by the Reinforcement The shrinkage stresses caused by reinforcement in an otherwise unrestrained mem- ber may be calculated quite simply. The member shown In ngure 1. Hence from equation 1. This feature is accompanied by localised bond breakdown, adjacent to each crack.

The equilibrium of the concrete and reinforcement is shown in figure 1. Thermal Movement: The differentiallhermal strain due to a temperature change Tmay be calcu- lated as T. The overall thermal contraction of concrete is, however, frequently effective in producing the first crack in a restrained member, since the required temperature changes could easily occur overnight in a newly cast member. EXample 1.

Ultimate tensile strain or concrete [. It is a phenomenon associated with many materials, but it is particularly evident with concrete. The precise behaviour of a particular concrete depends on the aggregates and the mix design, but the general pattern is illustrated by considering a member subjected to axial compression.

For such a member, a typical vari;jtion of defor- mation with time is shown by the curve in figure 1. Thus the compressive stresses in the steel are increased so thl' the.

II IlIrgcr proportion of Ihe load. Redistribution of stress between concrete lind sleel occurs primarily in the uncracked compressive areas and has little effeci on the tension reinforcement other than reducing shrinkage stresses in some instances.

The provision of reinforcement in the compressive zone of II flexural member, however, often helps to restrain the deflections due to creep.

The durability of the concrete is influenced by I the exposure conditions 2 the concrete quality 3 the cover to the reinforcement 4 the width of any cracks.

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Concrete can be exposed to a wide range of conditions such as the soil, sea water, stored chemicals or the atmosphere. The severity of the exposure governs the type of concrete mix required and the minimum cover to the reinforcing steel. A dense. Adequate cover is essential to prevent corrosive agents reaching the reinforce- ment through cracks and pervious concrete. The thickness of cover required depends on the severity of the exposure and the quality of the concrete as shown in table 6.

The cover is also necessary to protect the reinforcement against a f'dpid rise in temperature and subsequent loss of strength during a fire. Information concern- ing this is given in Part 2 of BS 81 10, while durability requirements with related design calculations to check and control crack widths and depths are described in chapter 6.

For example. The concrete strength is assessed by measuring thc crushlngltrength of cubes or cylinders of concrete made from the mix. Exposure conditions and durability can also affec t the choice of the mix design and the grade of concrete.

A structure subject to corrosive conditions in a chemical plant, for example. Although Ordinary Portland cement would be used in most structures, other cement types can also be used to advantage.

Blast-furnace or sulphate. The concrete mix may either be classified as 'designed' or 'prescribed'. A 'designed mix' is one where the contractor is responsible for selecting the mix proportions to achieve the required strength and workability, whereas for a 'prescribed mix' the engineer specifies the mix proportions, and the contractor is responsible only for providing a properly mixed concrete containing the correct constituents in the prescribed proportions. The nominal size of a bar Is the diameter of an equivalent circular urea.

Mild-steel bars can readily be bent, so they are often used where small radius bends are necessary. High-yield bars are manufactured either with a ribbed surface or in the form of a twisted square.

Ribbed bars are usually described by the British Standards as type 2 bars provided specified requirements are satisfied, and these are the bars most commonly used. Square twisted bars have inferior bond characteristics and are usually classified as type 1 bars, although these are more or less obsolete.

All deformed bars have an additional mechanical bond with the concrete so that higher ultimate bond stresses may be specified as described in section 5. The bending of high-yield bars through a small radius is liable to cause tension cracking of the steel, and to avoid this the radius of the bend should not be less than three times the nominal bar size see figure 5.

High-yield steel bars are only slightly more expensive than mild-steel bars. Therefore, because of their Significant stress advantage, high-yield bars are the more economical. Floor slabs, walls, shells and roads may be reinforced with a welded fabric of reinforcement, supplied in rolls and having a square or rectangular mesh. This can give large economies in the detailing of the reinforcement and also in site labour costs of handling and fixing.

The cross-sectional areas and perimeters of various sized bars, and the cross- sectional area per unit width of slabs are listed in the appendix. Reinforcing bars in a member should either be straight or bent to standard shapes. These shapes must be fully dimensioned and listed in a schedule of the reinforcement which is used on site for the bending and fixing of the bars. Standard bar shapes and a method of scheduling are specified in BS R for mild steel; Y for high yield deformed steel, type I ; T for high yield deformed steel, type 2; this notation is generally used throughout this book.

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Despite the difficulty in assessing the precise loading and variations in the strength of the concrete and steel, these requirements have to be met.

The permissible stress method has proved to be a simple and useful method but it does have some serious inconsistencies.

Because it is based on an elastic stress distribution, it is not really applicable to a semi-plastic material such as concrete, nor is it suitable when the deformations are not proportional to the load, as in slender columns. It has also been found to be unsafe when dealing with the stability of structures subject to overturning forces see example 2.

In the load factor me thod the ultimate strength of the materials should be used in the calculations.

As this method does not apply factors of safety to the material stresses, it cannot directly take accou nt of the variability of the materials, and also it cannot be used to calculate the deflections or cracking at working loads.

The limit state method of design overcomes many of the disadvantages of the previous two methods. This is done by applying partial factors of safety, both to the loads and to the material strengths, and the magnitude of the factors may be varied so that they may be used either with the plastic conditions in the ultimate state or with the more elastic stress range at working loads.

This flexibility is particularly important If rull benent. Thus, any way in which a structure may cease to be fit for use will constitute a limit state and the design aim is to avoid any such condition being reached during the expected life of the structure.

The two principal types of limit state are the ultimate limit state and the serviceability limit state. The possibility of buckling or overturning must also be taken into account, as must the possibility of accidental damage as caused, for example, by an internal explosion. Other limit states that may be reached include 4 Excessive vibration - which may cause discomfort or alarm as well as damage. The relative importance of each limit state will vary according to the nature of the structure.

The usual procedure is to decide which is the crucial limit state for a particular structure and base the design on this. Checks must also be made to ensure that all other relevant limit states are satisfied by the results produced. Except in special cases, such as water- retaining structures, the ultimate limit slate is generally critical for reinforced concrete although subsequen t serviceability checks may affect some of the details of the design. Prestressed concrete design, however, is generally based on service- ability conditions with checks on the ultimate limit state.

In assessing a particular limit state for a structure It Is necessary to consider aU the possible variable parnmeteu such as the load. These are called 'characteristic' strengths.

This is given by fk '" fm -. The relationship between characteristic and mean values accounts for variations in results of test specimens and will, therefore, reflect the method and control of manufacture, quality of constituents. NumbQr 0 1 tQst!.

It is to be expected that not more than 5 per cent of cases will exceed the upper limit and not more than 5 per cent will fall below the lower limit. They are design values which take into account the accuracy with which the loads can be predicted. Usually, however, there is insufficient statistical da ta to allow loading to be treated in this way, and in this case the sti ndard loadings, given in BS Design Loads for Buildings, Pari I: Code of PractiCe for dead lind Imposed loads, should be used as representing characterlsllc vlllue.

It should theoretically be possible to derive values for these from a mathe- matical assessment of the probability of reaching each limit state. Lack of adequate data, however, makes this unrealistic and in practice the values adopted are based on experience and simplified calculations.

This strength will differ from that measured in a carefully prepared test specimen and it is particularly true for concrete where placing, compaction and curing are so important to the strength. Steei, on the other hand, is a relatively consistent material requiring a small partial factor of safety.

Thus, higher values are taken for the ultimate limit state than for the serviceability limit state. Recommended values for 'Ym are given in table 2. Table 2. I design assum ptions and inaccuracy of calculation 2 possIble unusual load increases 3 unforeseen stress redistributions 4 constructional lnaccurllcles. Steel 1.

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Recommended values are given in table 2. It should be noted that design errors and constructional inaccuracies have similar effects and are thus sensibly grouped together. These factors will account adequately for normal conditions although gross errors in design or construction obviously can- not be catered for. Thus the basic values of partial factors chosen afe such that under normal circumstances the global factor of safety is similar to that used in earlier design methods.

Example 2. Carry out the calculations using 1 The load factor method with a load factor "" 1. Fewer calculations are required for the permissible stress and the load factor methods, so rcducing the chances of an arithmetical error. The limit state method provides much better control over the factors of safety, which are applied to each of U1C variables.

For convenience, the partial factors of safety in the example are the sume as those recommended in BS 8 Probably, in a practical design, higher rlCIOTSof safety would be preferred for a single supporting cable, in view of the consequences of a failure. The loads sup- 1' Determine the weight of founda- tion required at A in order to resist uplift I by applying a factor of safety of 2.

Investigate lIle effect on these designs of a 7 per cent increase in the live load. Iva load bQ: A 7 per cent increase in the live load will not endanger the structure, since the actual uplift will only be 7. In fact in this case it would require an increase of 65 per cent in the live load before the uplift would exceed the weight of a 40 leN foundation.

Each individual member must be capable of resisting the forces acting on it, so that the determina- tion of these forces is an esSential part of the design process.

The full analysis of a rigid concrete frame is rarely simple; hut simplified calculations of adequate precision caD often be made if the basic action of the structure is understood.

The analysis must begin with an evaluation of all the loads carried by the structure, incJudlng its own weight. Many of the loads are variable in magnitude and position, and all possible critical arrangements of loads must be considered. Fint the structure itself is rationalised into simplified forms that represent the load. The forces in each member can then be de termined by one of the following methods. Tabulated coefficients are suitable for use only with simple.

Manual calculations are possible for the vast majority of structures, but may be tedious for large or complicated ones. The computer can be an invaluable help in the analysis of even quite small frames. Since the design of a reinforced concrete member is generally based on the ultimate limit state, the analysis is usually performed for loadings corresponding to tha t state. Prestressed concrete members. Live loads.

Recommendations for the loadings on buildings are given in the British Standards, numbers BS Part 1. Design loads for Buildings, and CP3: Chapter V: Part 2.

Wind loads. Bridge loadings are specified in BS Part 2, Specification for Loads. A table of values for some useful dead loads and imposed loads is given in the appendix. Equipment and static machinery, when permanent flxtures. A minimum partition imposed loading of 1.

Dead loads are generally calculated on a slightly conservative basis, so that a member will not need redesigning because of a small change in its dimensions. For many of them, it is only possible to make conservative estimates based on standard codes of practice or past experience.

Examples of imposed loads on buildings are: A large building is unlikely to be carrying its full imposed load simultaneously on lis floors. For this reason the British Standard Code of Practice allows a reduction In the total imposed floor loads when the columns, walls or foundations. IC desIgned.

Similarly, the imposed loud mlly be reduced when designing 1I beam span which supports a floor area ,Ie'lter than 40 square metres. The partial factors of safety specified by BS are discussed in chapter 2, and for the ultimate limit state the loading combinations to be considered are as follows. Load combination 1 should also be associated with a minimum design dead load of 1. For load combination 1, a three-span continuous beam would have the loading arrangement shown in figure 3.

A study of the deflected shape of the beam would confirm this to be the case. Figure 3. An example of this is illustrated in figure 3. Qblllry Limit State 27 A pinl.

The deflections calculated from the load combinations arc the immediate denections of a structure. Deflection increases due to the creep of the concrete should be based only on the dead load plus any part of the imposed load which is permanently on the structure, this being considered fully in chapter 6, which deals with serviceability requirements.

To design a structure it is necessary to know the bending moments, torsional moments, shearing forces and axial forces in each member. An elastic analysis is generally used to determine the distribution of these forces within the structure ; but because - to some extent - reinforced concrete is a plastic material, a limited redistribution of the elastic moments is sometimes allowed. A plastic yield-line theory may be used to calculate the moments in concrete slabs.

The properties of the materials, such as Young's modulus, which are used in the structural analysis should be those associated with their characteristic strengths. The stiffnesses of the members can be calculated on the basis of anyone of the follOwing. The concrete cross-section described in I is the simpler to calculate and would normally be chosen. A structure should be analysed for each of the critical loading conditions which produce the maximum stresses at any particular section.

This procedure will be illustrated in the examples for a continuous beam and a building frame.

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For these structures it is conventional to draw the bending-moment diagram on the tension side of the members. Sign Conventions I For the moment-distribution analyses anti-clockwise support moments are positive as. For the ultimate limit state we need only consider the mlxlmum load of I. A continuous beam is considered to have no fix. Thls assumption is not ' Inctly true for beams framing into columns and for that type of continuous beam Ills more accurate to analyse them as part of a frame, as described in section 3.

A simplified method of analysis that can be applied to slabs is described in chapter 8. A continuous beam should be analysed for Ihe loading IIrrangements which give lhe maximum stresses at each secllon, II desotlbcd In.

The analysis to calculate the bending moments can be carried out manually by moment distribution or equivalent methods, but tabulated shear and moment cocfncients may be adequate for continuous beams having approximately equal spans and uniformly distributed loads.

Continuous Beams - The General Case Having determined the moments at the supports by, say, moment distribution, it is necessary to calculate the moments in the spans and also the shear forces on the beam.

Using the sign convention of figure 3. In manual calculations It Is usually not considered necessary to calculate the distances at ,Q, and Qa which locate the points of contraflexure and maximum moment - a sketch of the bending moment is often adequate - but if a computer is perfonning the calculations these distances may as well be determined also.

A L ood. M Figure 3. The critical Joading arrangements for the ultimate limit state are shown in figure 3. Table 3. The shearing forces, the maximum span bending moments, and their positions along the beam, can be calculated using the formulae previously derived. Thus for the first loading arrangement and span AD, using the sign convention of figure 3. Therefore VAB '" The individual bending-moment diagrams are combined in figure 3.

Similarly, figuxe 3. Such envelope diagrams are used in the detailed design of the beams, as described in chapter 7. The values from BS are mown in diagrammatic form in figure 3. The possibility of hogging moments in any of the spans should not be ignored, even ir it is not indicated by these coefficients.

Totol ultim ata load on span. J Structural Frames In situ reinforced concrete structures behave 3S rigid fmmes. They can be analysed as a complete space frame or be divided into a series or plane rrames. Bridge-deck iypes or structures can be analysed as an equivalent grillage. All these methods lend themselves to solution by the computer. The general procedure for a building rrame is to analyse the slabs as continuous members supported by the beams or structural walls.

The slabs can be either one- way spanning or two-way spanning.For load combination 1, a three-span continuous beam would have the loading arrangement shown in figure 3.

You Save: The book tries to distinguish between what belongs to the structural design philosophy of such structural elements related to strength of materials arguments and what belongs to the design rule aspects associated with specific characteristic data for the material or loading parameters.

Mcol from table 3.

See our Privacy Policy and User Agreement for details. But things turn out to be terrific! Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required. The concrete mix may either be classified as 'designed' or 'prescribed'. The overall thermal contraction of concrete is, however, frequently effective in producing the first crack in a restrained member, since the required temperature changes could easily occur overnight in a newly cast member.

An elastic analysis is generally used to determine the distribution of these forces within the structure ; but because - to some extent - reinforced concrete is a plastic material, a limited redistribution of the elastic moments is sometimes allowed.

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