As shown in the last term of equation 3.7, thermal strain is the product of the coefficient of thermal expansion and temperature change, which is usually within the range of -22 to 65 C. Since cement paste and aggregate have dissimilar thermal coefficients, the coefficient for concrete depends upon its composition and also the moisture condition at the time of temperature change. The role of aggregate is similar to that in shrinkage and creep, namely, the aggregate restrains the thermal movement of the cement paste since the latter has a higher thermal coefficient. The coefficient of thermal expansion for concrete is related to thermal coefficients of cement paste and aggregate as follows (Hobbs, 1971):
Creep is defined as the gradual increase in strain with time for a constant applied stress after accounting for other time-dependent deformations not associated with stress, namely, shrinkage or swelling and thermal strain. Hence, creep is reckoned from the elastic strain at loading, which depends upon the rate of application of stress (see Section 3.2) so that the time taken to apply the load should be quoted. Also, since the secant modulus of elasticity increases with time, the elastic strain decreases so that creep should be taken as the strain in excess of the elastic strain at the time in question. However, the change in elastic strain is usually small and creep is reckoned from the elastic strain on first application of load. Like other engineering materials, concrete can suffer a time-dependent failure, which is known as creep rupture or static fatigue. Figure 3.7 represents the general strain-time history of such a material. Initially, there is a high rate of primary creep and then a steady rate of secondary creep before failure occurs after the tertiary creep stage, as characterised by the rapid development of strain. In the case of concrete, the stress needs to exceed approximately 0.6 to 0.8 of the short-term strength for creep rupture to occur in either compression or tension. Concrete is often described as a brittle material since it readily cracks under small strains, but in the case of creep rupture it can develop large strains prior to failure, providing an advantage of early warning in the case of sudden and catastrophic failure. Figure 3.8 illustrates the pattern of stress and strain for varying rate of loading and level of sustained stress leading to creep rupture; actual experimental results for compression were obtained by Rusch (1960) and for tension by Domone (1974). Very high rate of loading produces a near linear stress-strain curve with a higher strength than in the usual standard test (Fig. 3.8(a)), but decreasing the rate of loading or increasing the test duration produces non-linear curves due to creep and microcracking with a lower strength (creep rupture). The creep rupture envelope tends to a constant limit of between 0.6 and 0.8 of the usual short-term strength, depending on the type of concrete and mode of loading. With sustained stresses below approximately 0.6 of short-term strength, creep rupture is avoided and time-dependent strain due to primary and some secondary creep takes place for several years. Depending on the type of mix and other factors, creep of dry-stored concrete can be between two and nine times the elastic strain at loading, with around 70% occurring after one year under load (Brooks, 2005).
As stated earlier, the definition of creep is the increase in strain for a constant sustained stress and is determined from concrete specimens after deducting any drying shrinkage (measured on a separate specimen) and the initial elastic strain. Figure 3.9(a) shows the components of strain involved. In the case of sealed concrete, which represents mass or large-volume concrete where little or no moisture is lost, only basic creep occurs, but when the concrete is allowed to dry additional drying creep occurs even though drying shrinkage has been deducted from the measured strain; the sum of basic and drying creep is sometimes called total creep. Creep is a partly reversible phenomenon. When the load is removed, there is an immediate, almost full, elastic recovery of the initial elastic strain, followed by a gradual decrease of strain called the creep recovery (Fig. 3.9(b)). The recovery quickly reaches a maximum and is only small, e.g. 1±25% of the 30-year creep (Brooks, 2005). Consequently, creep is mostly irreversible in nature.
Like shrinkage, creep can be expressed in units of microstrain (10ÿ6), but because of the dependency on stress, specific creep (Cs) is often used with units of 10ÿ6 per MPa. Other terms are creep coefficient (@) . The creep coefficient is defined as the ratio of creep to the elastic strain on loading and for a unit stress:
The effects of creep can be realised from another viewpoint. When a concrete specimen is loaded and then prevented from deforming, then creep will manifest itself as a gradual decrease or relaxation of stress with time, as illustrated in Fig. 3.10. Relaxation is of interest in connection with loss of prestress in prestressed and post-tensioned concrete and cracking processes (see Section 3.3). Apparatus for the determination of creep of any type of concrete is recommended in ASTM C512 (1987) and for prefabricated aerated or lightweight concrete by BS EN 1355 (1997). Alternative methods are described in Neville et al. (1983) and Newman and Choo (2003). There have been many theories proposed to explain the creep of hardened cement paste and concrete, which are too numerous to include within the scope of this chapter. Most agree that creep at normal stresses is caused by the internal movement of water adsorbed or held within the C-S-H, since concrete from which all the evaporable water has been removed exhibits little or no creep unless high temperatures are involved. Movement of water to the outside environment is required for drying creep to occur. Although basic creep is associated with sealed or mass concrete, it is thought that internal movement of water occurs because all the pores do not remain full of water. The dependency of basic creep on strength is indirect evidence that empty or part-empty pores are a main factor. Creep also occurs at high temperatures when non-evaporable water is removed and this is thought to be due to movement of interlayer or zeolitic water, viscous flow or sliding between gel particles (Illston et al., 1979; Mindess and Young, 1981; Neville et al., 1983; Bazant, 1988; Brooks, 2001). The source of creep of concrete is the hydrated cement paste and not normal weight aggregate of good quality. Some light aggregates may exhibit creep. However, like shrinkage, the role of aggregate is an important factor in creep due to the restraining influence on the cement paste through its stiffness or modulus of elasticity and volume concentration. The relationship between modulus of elasticity of aggregate and relative creep of concrete is shown in Fig. 3.11. For a constant water/cement ratio, the volume of cement paste or total aggregate in concrete has a significant effect on creep (Neville and Brooks, 2002). However, in practice, concretes with similar workability normally have similar cement paste contents and so the differences in creep are not large.
For example, in normal weight concretes having aggregate/cement ratios of 9, 6 and 4.5, and corresponding water/cement ratios of 0.75, 0.55 and 0.40, the cement paste contents are 24, 27 and 29%, respectively. On the other hand, when the cement paste content is constant, an increase in water/cement ratio increases creep as shown in Fig. 3.12.
Since creep is related to the water/cement ratio it can be expected to be related to strength. Indeed, it has been found that over a wide range of mixes made with similar materials, creep is approximately inversely proportional to the strength of the concrete at the age of application of load. Moreover, for stresses less than approximately 0.6 of the short-term strength, creep is proportional to the applied stress, so that combining the dual influences leads to the stress/ strength ratio rule, namely, that creep is approximately proportional to the stress/ strength ratio (Neville et al., 1983). Consequently, since the strength increases with age, creep can be expected to decrease as the age at loading increases (Fig. 3.13).
Experimental work on saturated concrete specimens exposed to the atmosphere at different relative humidities shows that the drier the atmosphere the higher the creep. Figure 3.14 demonstrates that trend, the 100% curve approximating to that of basic creep so that the additional creep for 75 and 50%relative humidities is drying creep. If the concrete is allowed to dry out prior to application of load then creep is much less. However, it is ill-advised to allow concrete to dry out prematurely in order to reduce creep because of the risk of inadequate curing and cracking due to restrained or differential drying shrinkage (see Section 3.3.6). Creep of concrete is affected by size of member in a similar manner to drying shrinkage (see Fig. 3.6). Expressing size as the volume/exposed surface area ratio (V/S) or effective thickness ( 2V=S), which represents the average drying path length, total creep decreases as the volume/surface ratio or size increases (Fig. 3.15). Of course, it is the drying creep component that is influenced since basic creep is unaffected by size. This can be seen when the size of the member is large (mass concrete) when no moisture transfer to the environment takes place and basic creep occurs. It is also apparent from Fig. 3.15 that the influence of shape of concrete member is a secondary factor in creep and can be neglected. The influence of temperature on creep is complex and not fully understood, as it depends upon the time when the temperature of the concrete rises relative to the time of application of load (Neville et al., 1983). Figure 3.16 demonstrates different experimental results for concrete stored at elevated temperature in water (basic creep). Compared with normal-temperature creep, heating just prior to loading accelerates creep, and heating just after loading produces an additional component termed transitional thermal creep. In the case of drying concrete (total creep), elevated temperature causes increases in creep in a similar manner, but when the evaporable water has been removed (between approximately 80 and 120 ëC) there is a decrease in creep before increasing again (Neville et al., 1983). At very high temperatures, such as in fire, very high creep occurs, termed transient thermal strain (Khoury et al., 1985). The type of cement will affect creep if the strength changes at the time of application of load. When the stress/strength ratio at the age of loading is the same, most Portland cements lead to approximately the same creep, but the strength development under load is a factor, e.g. creep will be lower for a greater strength development (Neville and Brooks, 2002). The latter influence is apparent when certain mineral admixtures, such as fly ash and ground granulated blast-furnace slag, are used as partial replacements for Portland cement. The resulting slower pozzolanic reaction often leads to a later strength development than in the case of Portland cement. Figure 3.17 shows the general trends for fly ash, blast-furnace slag, silica fume and meta- kaolin, which are mainly based on the analysis of results of previously published data (Brooks, 2000). That analysis accounted for any changes in aggregate content and water/cementitious materials ratio on creep by considering the relative stress/strength ratio so that the effect of just the mineral admixture could be assessed. Although there is a large variation, it can be seen that fly ash and slag can lead to significant reductions in creep. In the case of the finer mineral admixtures: silica fume and metakaolin, there are larger reductions in creep for replacement levels of up to 15%, but then for silica fume creep increases as the replacement level increases. Generally, the addition of chemical admixtures, plasticisers and super- plasticisers, to make flowing concrete causes a 20% reduction in creep at a constant stress/strength ratio, although the effects do vary widely (Brooks, 2000). When the same admixtures are used as workability aids or water reducers, creep will be less due to the lower water content. As well as reducing shrinkage (see Section 3.3), the use of a shrinkage-reducing admixture appears to reduce drying creep, although experimental verification is limited. For design purposes, estimation of elastic deformation, creep and drying shrinkage are considered together in Codes of Practice. From only a knowledge of strength, mix composition and physical conditions, BS 8110: Part 2 (1985) gives creep and shrinkage after 6 months and 30 years, depending upon the relative humidity and size of member. ACI 209 (1992) and CEB-FIP (1999) methods express creep and shrinkage as functions of time and allow for all the main influencing factors that have been discussed earlier. Alternative models are available by Bazant and Baweja (1995) and Gardner and Lockman (2001). Creep and drying shrinkage estimates by all methods are not particularly accurate (+- (30% at best) mainly because they fail to account for the type of aggregate (Brooks, 2005). For more accurate estimates and for high performance concretes containing several admixtures, short-term tests are recommended. The test duration should be of at least 28 days using small laboratory specimens made from the actual concrete mix and then measured creep and shrinkage-time data extrapolated to obtain long-term values, which are then adjusted according to the required member size and the average relative humidity of the storage conditions (Brooks and Al-Quarra, 1999). All methods of prediction give an estimate of the creep function (equation 3.6) and drying shrinkage, the total strain, t; to, at age t when determined from age to being given by:
The importance of creep in structural concrete lies mainly in the fact that, in the long term, it can be several times the elastic deformation when first loaded.
Consequently, the designer has to assess creep in order to comply with the serviceability requirement of deflection in particular. There are other effects of creep, most of which are detrimental, such as loss of prestress in prestressed concrete and differential movements in tall buildings, but creep can be beneficial when relieving stress induced by restraint of deformations.
Shrinkage of concrete is caused by loss of water by evaporation or by hydration of cement, and also by carbonation. The resulting reduction in volume as a fraction of the original volume, i.e. volumetric strain, is equal to three times the linear strain, so in practice shrinkage is simply measured as a linear strain. The units are mm per mm, usually expressed as microstrain (10ÿ6). When freshly laid and before setting, concrete can undergo plastic shrinkage due to the loss of water from the surface or by suction by dry concrete below, a situation that can lead to plastic cracking (see Section 3.3.2). Plastic shrinkage is greater the larger the cement content of the mix and it can be minimised by complete prevention of evaporation immediately after casting. Even when no moisture movement to or from the set concrete is possible autogenous shrinkage occurs, which is caused by loss of water used by the hydrating cement. Except in large volume pours (mass concrete), autogenous shrinkage is not distinguished from shrinkage of hardened concrete due to loss of water to a dry surrounding environment. In normal strength concrete, auto- genous shrinkage is small (50 to 100 10^-6),but can be large in high performance concrete, i.e. high durability and high strength concrete. Such concrete usually contains a high cementitious materials content consisting of cement and a mineral admixture, such as silica fume or fly ash. In addition, the mix has a low water/cementitious materials ratio so that a superplasticising chemical admixture is required to make the mix workable. Such composition yields a finer pore structure than normal strength concrete, which causes high early autogenous shrinkage when measured from initial set but, when measured from the age of 28 days, it is small. If concrete is stored continuously in water during hydration, the concrete expands due to absorption of water by the cement paste, a process known as
swelling. In concrete made with normal weight aggregate, swelling is 5±10% of shrinkage of hardened concrete. On the other hand, swelling of lightweight aggregate concrete can be much greater, viz. 25±80% of shrinkage after 30 years (Brooks, 2005).
The loss of water from hardened concrete stored in dry air causes drying shrinkage. To some extent the process is reversible, i.e. re-absorption of water will cause expansion of the concrete, but not back to its original volume (see Fig. 3.3(a)). In normal concretes, reversible shrinkage is between 40 and 70% of the drying shrinkage depending upon the age of the concrete when first drying occurs. If the concrete is cured so that it is fully hydrated at the time of exposure, more of the drying shrinkage is reversible but, if drying is accompanied by hydration and carbonation, the porosity of the cement paste will decrease, thus preventing some ingress of water (Neville and Brooks, 2002).
Another type of shrinkage that occurs in concrete is carbonation shrinkage, which normally accompanies drying shrinkage, although it is different in nature. Carbonation, which is known to be a potential cause of corrosion of steel in reinforced concrete, describes the reaction of calcium hydroxide with the carbon dioxide of the atmosphere in the presence of moisture. The carbon dioxide first dissolves in moisture and then reacts with calcium hydroxide to form calcium carbonate, the process resulting in a volume contraction known as carbonation shrinkage. The rate of carbonation depends upon the permeability of the concrete, the moisture content and the relative humidity of the environment, the severest conditions for high carbonation shrinkage being 55% relative humidity and high water/cement ratio (Neville, 1995). The effect of carbonation shrinkage in concrete is normally small as it is restricted to the outer layers, but can cause warping of thin panels. A practical benefit is in the manufacture of porous concrete blocks where curing in an atmosphere of carbon dioxide results in the calcium carbonate products being deposited in the pores. This restricts moisture movement (reversible shrinkage) and enhances strength. The pattern of concrete subjected to cycles of drying and wetting, simulating daily weather changes in practice, is illustrated in Fig. 3.3(b). The magnitude of the cyclic change depends upon the duration of periods, the ambient humidity and the composition of the concrete, but it is important to note that drying is slower than wetting. Consequently, shrinkage resulting from a prolonged dry weather can be reversed by a short period of rain. Generally, shrinkage of lightweight aggregate concrete is more reversible than that of normal weight concrete. Three mechanisms are thought to be responsible for reversible drying shrink- age: capillary tension, disjoining pressure and changes in surface energy (Mindess and Young, 1981). Removal of water from larger capillaries of the cement paste to the drier outside air causes little shrinkage, but this disturbs the internal equilibrium so that water is transferred from smaller capillaries to larger ones. When capillaries empty, a meniscus forms and a surface tension is developed. This induces a balancing compressive stress in the calcium silicate hydrate (C-S-H) and results in a volume contraction or shrinkage. Stresses are higher in smaller capillaries and when the humidity is low due to the increasing curvature of menisci, but at very low humidity capillary stresses do not exist because the menisci are no longer stable. With the disjoining pressure theory, the adsorption of water on the C-S-H particles affects the Van der Waals surface forces of attraction between adjacent particles in areas of hindered adsorption. The adsorbed water creates a disjoining pressure, which increases with the thickness of the adsorbed water. When the disjoining pressure exceeds the Van der Waals forces the particles are forced apart and swelling occurs. Conversely, as the pressure decreases due to a reduction in relative humidity, the particles are drawn together and drying shrinkage occurs. The change in surface energy is thought to be responsible for drying shrinkage occurring at very low humidity (below 40%) when capillary stress and disjoining pressure are no longer present. Solid particles are subjected to a pressure due to surface energy and the pressure is decreased by water adsorbed on the surface. Loss of water will allow the surface energy pressure to increase, resulting in further shrinkage. A significant part of the initial drying shrinkage is irreversible and this is explained by the changes that take place in the C-S-H. When adsorbed water is removed on first drying, additional physical and chemical bonds are formed as the particles become more closely packed. Moreover, additional bonds can occur due to hydration and carbonation (see later). Consequently, the porosity and connectivity of the pore system of the C-S-H change with drying, which reduces ingress of water on re-wetting. Drying shrinkage of concrete is affected by several factors, the main ones as recognised by Codes of Practice being: water/cement ratio, aggregate, relative humidity, size of member and time. Figure 3.4 demonstrates that, for a constant volume of aggregate, drying shrinkage increases as the water/cement ratio increases and, for a constant water/cement ratio, drying shrinkage increases as the volume of the aggregate decreases. The influence of the aggregate is to restrain the shrinkage of the cement paste. Aggregates of low stiffness (low modulus of elasticity) provide less restraint and result in more drying shrinkage than non- shrinking good quality aggregates. Thus, lightweight aggregate concrete has a higher drying shrinkage than normal weight aggregate concrete as shown in Fig. 3.5. The size of aggregate hardly affects shrinkage but, at a constant water/ cement ratio, larger aggregate allows the use of a leaner mix (more aggregate by volume) to achieve the same workability, which results in less shrinkage. Most aggregates are dimensionally stable; however, there are exceptions and the use of aggregates having high drying shrinkage should be avoided. As already mentioned, the relative humidity of the air surrounding the concrete is a main factor and the lower the humidity the greater the loss of water and drying shrinkage. Similarly, an important factor is the size of member. Drying shrinkage of a large member is less than that of a small member because it is more difficult for water to escape from the former, which has a longer drying path The effect of size is expressed as the volume/surface area ratio (V=S) or effective thickness ( 2V=S), the surface area being that exposed to drying (see Fig. 3.6). There is a secondary influence of shape of member on drying shrinkage that is normally neglected. Drying shrinkage occurs over a long period of time with a high initial rate after exposure to drying, which then gradually decreases to a very low rate after several years. It is believed that shrinkage does not have an ultimate value, although for design purposes, a final value after a time of 50 years is often assumed. Typically, a shrinkage-time characteristic would be 20% of 20-year shrinkage occurring in two weeks, 60% occurring in three months and 75% occurring in one year (Neville and Brooks, 2002).
Accelerators, retarders and other chemical admixtures that affect the rate of strength development of concrete will also affect the rate of drying shrinkage; however, the long-term shrinkage is not affected to a great extent. With water- reducing admixtures (plasticisers and superplasticisers) there is a general increase in drying shrinkage of 20% due to the presence of the admixture itself, e.g. as in the case of flowing concrete (Brooks, 1999) but, when used as a water reducer, shrinkage is affected by the change in mix proportions as well as the admixture. Nowadays, shrinkage-reducing chemical admixtures are available, which appear to reduce shrinkage by suppressing hydration of cement. Any reduction in strength can be offset by decreasing the water/cement ratio, thus reducing shrinkage even more. When the mix proportions are unchanged, the use of certain mineral admix- tures (fly ash, blast-furnace slag) as partial replacement of cement do not affect long-term drying shrinkage appreciably (Brooks, 1999). On the other hand, for a constant water/cementitious materials ratio, increasing the level of cement replacement by silica fume and metakaolin reduces both autogenous and drying shrinkage of high performance concrete. For example, drying shrinkage is reduced by approximately 25% for a 10% replacement of cement (Brooks and Megat Johari, 2001). Drying shrinkage causes loss of prestress in prestressed concrete, increases deflections of asymmetrically reinforced concrete and, together with differential temperature, contributes to the warping of thin slabs. As discussed in Section 3.3.6, restraint of shrinkage often leads to cracking. Several methods are available for estimating drying shrinkage and swelling for design purposes and these are considered together with creep in Section 3.2.4.
The design and analysis of some types of structure require the knowledge of volume changes in concrete members subjected to external load. In this case, Poisson’s ratio is required, viz. the ratio of lateral strain to the axial strain resulting from an axial load. Figure 3.2 shows the trends of lateral, axial and volumetric strains as the level of stress is increased up to failure. At low levels of stress, there is a lateral extension and an axial contraction so that Poisson’s ratio is approximately constant and negative, but this sign is ignored in concrete technology. As the stress approaches failure, the Poisson’s ratio increases rapidly due to vertical cracking and the volumetric strain changes from a contraction to an extension. In general, for practical levels of stress, Poisson’s ratio lies in the range of 0.15 to 0.20 when determined from strain measurements in a static modulus of elasticity test. An alternative method is to determine Poisson’s ratio by dynamic means using ultrasonic and resonant frequency tests (Neville, 1995; Neville and Brooks, 2002). In the latter case, the dynamic Poisson’s ratio is greater than that from a static test, typically ranging from 0.2 to 0.24. With both the static and dynamic methods, the measured Poisson’s ratios are elastic values. Under a sustained load, the term creep Poisson’s ratio strictly applies, but for stresses less than approximately 0.5 of the short-term strength, creep Poisson’s ratio can be assumed to be similar to the elastic value (Neville, 1995).
To calculate the long-term deformation and deflection of structural concrete members for their design life, the relations between stress, strain, time and temperature are required. In common with other engineering materials, concrete deforms almost elastically when a load is first applied, but under sustained load, the deformation increases with time at a gradually reducing rate under normal environmental conditions. Timber behaves in a similar manner, whereas steel only creeps under very high stress at normal temperature or under low stress at very high temperature. With all engineering materials, dimensional instability can occur at high loads in the form of a time-dependent failure or creep rupture, but this can be avoided with concrete if stresses are kept below approximately 60% of the short-term strength. Elasticity and creep are considered in Sections 3.2.1 and 3.2.4, respectively. In addition to deformation caused by the applied stress, time-dependent volume changes due to shrinkage (or swelling) and temperature variation of concrete are of considerable importance because they can contribute signifi- cantly to elasticity and creep of concrete members in assessing the total time- dependent deformation. There are different types of shrinkage, the most com- mon being drying shrinkage, the rate of which gradually reduces with time. Like creep, drying shrinkage is associated with the movement of gel water within and from the hardened cement paste. Shrinkage and temperature movement are discussed in Sections 3.2.3 and 3.2.5, respectively. In other practical cases, movements are often partly or wholly restrained thereby inducing tensile stress, the level of which needs to be minimised to avoid cracking. Concrete is of course very weak in tension so that cracks must be avoided or controlled as they can impair durability as well as structural integrity, besides being aesthetically undesirable. The subject of non-structural or intrinsic cracking processes, as opposed to structural cracking associated with external loading, is dealt with in Section 3.3. First, the different types of cracks are described (3.3.1) then plastic shrinkage cracking (3.3.2), followed by early-age thermal cracking (3.3.3), types of restraint (3.3.4 and 3.3.5) and drying shrinkage cracking (3.3.6). Theoretical aspects of cracking are summarised under fracture mechanics in Section 3.3.7, which precedes Future trends and suggested further information (3.4), and finally References (3.5).
The planning and construction of a building should be aimed at fulfilling the following requirements:
1. Strength and stability
2. Dimensional stability
3. Resistance to dampness
4. Resistance to fire
5. Heat insulation
6. Sound insulation
7. Protection against termite attack
9. Security against burglary
10. Lighting and ventilation
11. Comforts and convenience
1. Strength and Stability: Building should be capable of transferring the expected loads in its life period safely to the ground. Design of various structural components like slabs, beams, walls, columns and footing should ensure safety. None of the structural components should buckle, overturn and collapse.
2. Dimensional Stability: Excessive deformation of structural components give a sense of instability and result into crack in walls, flooring etc. All structural components, should be so designed that deflections do not exceed the permissible values specified in the codes.
3. Resistance to Dampness: Dampness in a building is a great nuisance and it may reduce the life of the building. Great care should be taken in planning and in the construction of the building to avoid dampness.
4. Resistance to Fire: Regarding achieving resistance to fire, the basic requirements laid down in the codes are:
(a) the structure should not ignite easily.
(b) building orientation should be such that spread of fire is slow.
(c) In case of fire, there should be means of easy access to vacate building quickly.
5. Heat Insulation: A building should be so oriented and designed that it insulates interior from heat.
6. Sound Insulation: Buildings should be planned against outdoor and indoor noises.
7. Protection from Termite: Buildings should be protected from termites.
8. Durability: Each and every component of the building should be durable.
9. Security against Burglary: This is the basic need the owner of the building expects.
10. Lighting and Ventilation: For healthy and happy living natural light and ventilations are required. Diffused light and good cross ventilation should be available inside the building.
11. Comforts and Conveniences: Various units in the building should be properly grouped and integrated keeping in mind the comfort and convenience of the user.
12. Economy: Economy without sacrificing comfort, convenience and durability is another basic requirement of the building.