HYDRATION OF CEMENT

On adding water to cement, the silicates and aluminates present in the cement start a chemical reaction and form a spongy gel. The chemical reaction that takes place between cement and water is referred to as hydration of cement. During this process, a large quantity of heat is evolved. The quantity of heat in calories, liberated on complete hydration of cement is called heat of hydration. The different cement compounds hydrate at different rates and liberate different quantities of heat. The quantity of heat liberated depends upon the amount of different constituents in the cement. There are two ways in which the compounds present in the cement may react with water. In the first case, on addition of water, cement compounds dissolve to produce a super saturated solution from which different hydrated products are precipitated. In the second type of reaction the water is hydrolyzed i.e. the water attracts the cement compounds in the solid state converting the compounds into hydrated products.

HYDRATION PRODUCTS

The following are the important products of hydration of cement:

1. Calcium Silicate Hydrate (C-S-H)
2. Calcium Aluminate Hydrates
3. Calcium Hydroxide [Ca(OH)₂]

Calcium Silicate Hydrate (C-S-H): The main products of hydration of C₃S and C₂S with water are calcium silicate hydrate (C-S-H) gel and calcium hydroxide, Ca(OH)₂. Calcium silicate hydrates are the most important products of hydration of cement. It makes up 50 to 60 % of the volume of solids in a completely hydrated cement paste.

C₃S gives a faster rate of reaction accompanied by greater heat evolution which contributes to the early strength of cement. A cement having higher quantity of C₃S content is better for cold weather concreting. Making the approximate assumption that both C₃S and C₂S produce C₃S₂H₃ as the final product of hydration, their equations of hydration can be written as follows:

(i)         For C₃S

2C₃S             +             6H                                 C₃S₂H₃              +                3Ca(OH)₂

(100)                            (24)                                   (75)                                         (49)

(ii)        For C₂S

2C₂S             +             4H                                 C₃S₂H₃              +                3Ca(OH)₂

(100)                            (21)                                   (99)                                         (22)

Figure 1. Development of strength of pure compounds

It can be seen that C₃S produces comparatively lesser quantity of calcium silicate hydrate and more quantity of Ca(OH)₂, than that formed in the hydration of C₂S. Ca(OH)₂ is not a desirable product in the concrete mass, as it is soluble in water and gets leached out making the concrete porous, particularly in hydraulic structures. Under such conditions it is desirable to use cement with higher percentage of C₂S content. C₂S rather hydrates and hardens slowly. It is responsible for the later strength of concrete. It provides less heat of hydration and greater resistance to chemical attack. Figure 1 shows the development of strength of pure compounds. It is found that the ultimate strength for both C₃S and C₂S are nearly the same. Thus, a higher percentage of C₃S results in rapid hardening, higher heat of hydration and an early gain in strength. On the other hand, a higher percentage of C₂S results in slow hardening, less heat of hydration and greater resistance to chemical attack.

Calcium Aluminate Hydrate: The hydration of C₃A leads to the formation of a calcium aluminate system CaO-Al₂O₃-H₂O_. The amount of C₃A in most cement is comparatively small, but its behaviour is very important. The reaction of C₃A with water is very violent and leads to immediate stiffening of paste. The immediate stiffening of paste is called flash-set. To prevent flash-set, 2 to 3% of gypsum is added at the time of clinker grinding. The hydrated C₃A do not contribute to the strength of concrete. As it hydrates very fast, it may contribute a little to the early strength of concrete. On the other hand, their presence is harmful to the durability of concrete particularly where the concrete is likely to be attacked by sulphates. On hydration, C₄AF is believed to form a system of the form CaO-Fe₂O₃-H₂O. This hydrated product also does not contribute anything to the strength. It acts as a flux and accelerates the rate of reaction in the kiln. The hydrates of C₄AF show a comparatively higher resistance to the attack of sulphates than the hydrates of C₃A as shown in figure 2.

Figure 2. Rate of hydration of pure compounds

Calcium Hydroxide: Calcium hydroxide, Ca(OH)₂ is produced during the hydration of C₃S and C₂S. It constitutes about 20 to 25% of the volume of solids in the hydrated phase. The presence of Ca(OH)₂ makes the concrete porous, weak and undurable. Ca(OH)₂ also reacts with sulphates present in water or soil to form calcium sulphate which further reacts with C₃A and causes deterioration of concrete. This is known as sulphate attack.

The effect of Ca(OH)₂ can be reduced by converting it into cementitious product by the use of bending materials like fly ash, silica fume and other such pozzolanic materials.

The only advantage is that Ca(OH)₂ being alkaline in nature maintain pH value around 13 in concrete which resists the corrosion of reinforcements.

BUILDING BYE-LAWS

Minimum provisions designed from National Building Code (published in 1970, revised in 2005) by Town Planning Authorities, Urban Development Authorities and Municipalities, to protect the inmates living in the house, neighbours and public passing by the side of the building against structural failures, fire accidents and insanitary conditions are called BUILDING BYE-LAWS.

PURPOSE OF BUILDING BYE-LAWS

Modes of construction varies from region to region depending upon motive of owners, availability of materials, labour, construction and weather conditions. If certain rules and regulations are not made, house owner may construct residential building as per his whims and fancies. Hence, it is essential to maintain and implement the bye-laws to provide proper ventilation, privacy, security and safety between the neighbours.

OBJECTIVES OF BUILDING BYE-LAWS

•      Allows disciplined and systematic growth of buildings and towns and prevent haphazard development.

•      Protect safety of public against fire, noise, health hazards and structural failures.

•      Provide proper utilization of space. Hence, maximum efficiency in planning can be derived from these bye laws.

•      They give guidelines to the architect or an engineer in effective planning and useful in preplanning the building activates.

•      They provide health, safety and comfort to the people who live in buildings.

•      Due to these bye-laws, each building will have proper approaches, light, air and ventilation which are essential for health, safety and comfort.

MINIMUM PLOT SIZES AND BUILDING FRONTAGE

• Building frontage is the margin to be left beyond the extreme edge of the road (right of way) to the front of the building line (including excavations for foundations and projections of sunshades or balcony of superstructure).

• That is, it is the width of clearance of land to be left (before a road) within the private plot to facilitate

             • Widening of roads in future,

             • More sight distance at junctions avoiding blind corners,

             • Minimizing sound pollution for inmates of the house, and

             • To create a buffer space between public (i.e. roads) and private (plot) properties.

• Residential buildings require minimum clearance. Public buildings require more clearance. Commercial buildings as cinema halls which release a lot of rush at a time need still more clearance.

• Set back line or Front building line is the line (inside the plot) upto which we can extend our construction.

• Each plot shall have a minimum size of frontage corresponding to the type of development as given in table.

Type of residential building	Plot size (sq. m)	Frontage (m)
Detached building	Above 250	Above 12
Semi-detached building	125-250	8 to 12
Row type building	50-125	4.5 to 8

Figure 1. Building Set-back

OPEN SPACES

FRONT OPEN SPACE

Width of Street abutting the plot (m)	Front open space minimum (m)
Upto 7.5	1.5
7.5 to 18	3.0
18 to 30	4.5
Above 30	6.0

SIDE AND REAR OPEN SPACE

Height of building (m)	Side and rear open spaces (m)
10	3
15	5
18	6
21	7
24	8
27	9
30	10
40	12
45	13
50	14
55 and above	16

INTERIOR SPACE REQUIREMENT

MINIMUM SIZE OF DIFFERENT ROOMS

NO.	NAME OF ROOM	MINIMUM SIZE
1	Habitable room a)      Bed room b)      Living room c)      Drawing room d)     Dining room e)      Study room	9.5 sq. m
2	Kitchen	5 sq. m
3	a)      Bath room b)      Water closets	1.8 sq. m 1.1 sq. m
4	Store room	3 sq. m
5	Garage	12.5 sq. m
6	Staircase	15 sq. m

CREEP IN CONCRETE

Concrete creep is defined as the deformation of concrete structure under sustained load. Basically, long term pressure on stress on concrete can make it change shape. This deformation usually occurs in the direction the force is being applied. When the continuous load is removed, the strain is decreased immediately. The amount of the decreased strain is equal to the elastic strain at the given age. This quick recovery is then followed by a continuous decrease in strain, known as creep recovery that is a part of total creep strain suffered by the concrete.

Creep Coefficient:

The ratio of the ultimate creep strain to the elastic strain at the age of loading is termed as creep coefficient. The assumed data of creep coefficient are given below:

Age of Loading	Creep Coefficient
7 days	2.2
28 days	1.6
1 year	1.1

Figure 1. Creep Deflection in Bridges

FACTORS AFFECTING CREEP

1. Aggregate: The creep in aggregate is very less. It is the paste which is responsible for the creep. However, the aggregate influences the creep of concrete through a restraining effect on the magnitude of creep. The paste which is creeping under load is restrained by aggregate which do not creep. The stronger the aggregate, the more is the restraining effect and hence the less is the magnitude of creep.

2. Mix Proportions: The amount of paste content and its quality is one of the most important factors influencing creep. A paste structure which is poorer undergoes higher creep. Therefore, it can be said that creep increases with increase in water/cement ratio. In other words, it can also be said that creep is inversely proportional to the strength of concrete.

3. Age: It has been observed that for a given type of concrete, the creep decreases as the age at the time of application of load increases as the strength increases with age.

Figure 2. Variation of creep with age

4. Fineness of cement: Fineness of cement affects the strength development at the early ages and thus influences the creep. In the early ages the strength development is very less in finest cement hence the creep of concrete is the greatest, but after 1000 days it became least due to the high gain of strength. 

5. Degree of Hydration: The greater the degree of hydration of the cement at the time of load application, the greater will be the development of strength and as creep varies inversely with strength so lower will be the rate and total amount of creep.

BOUSSINESQ’S SOLUTION OF VERTICAL STRESSES DUE TO A CONCENTRATED LOAD

In 1885, Boussinesq published equations to determine the state of stress in a subgrade material. He investigated the stresses in a semi-infinite, elastic, isotropic and homogenous solid medium, loaded manually on its upper plane surface by a concentrated point load. The material is also considered weightless and unstressed.

Figure 1. Stresses due to a concentrated load

Figure 1 shows a horizontal surface of the elastic continuum subjected to a point load Q at point O. the origin of the coordinates is taken at O. Using logarithmic stress function for the solution of elasticity problem, Boussinesq proved that the polar stress σ_R at point P(x,y,z) is given by-

Where,

R = polar distance between the origin O and point P.

β = angle which the line OP makes with the vertical.

Obviously,

Or,

 Where,

 And,

 And,

 The vertical stress at a point P is given by-

 Where,

The coefficient I_B is known as the Boussinesq influence coefficient for the vertical stress. The values of I_B can be determined for the given value of r/z from the above equation. The computed values are tabulated as shown in the table below.

Table 1. Values of Boussinesq's Coefficient (I_B)

The following points are worth noting when using the above equation:

1. The vertical stress does not depend upon the modulus of elasticity (E) and the Poisson’s ratio (ν). But the solution has been derived assuming that the soil is linearly elastic. The stress distribution will be the same in all linearly elastic materials.

2. The intensity of vertical stress just below the load point is given by-

3. At the surface (z = 0), the vertical stress just below the load is theoretically infinite. However, in an actual case, the soil under the load yields due to a very high stresses. The load point spreads over a small but finite area, and therefore, only finite stresses develop.

4. The vertical stress (σ_z) decreases rapidly with an increase in r/z ratio. Theoretically, the vertical stress would be zero only at an infinite distance from the load point.

5. Boussinesq solution can even be used for negative (upward) loads. For example, if the vertical stress decreases due to an excavation is required, the negative load is equal to the weight of the soil removed. However, as the soil is not fully elastic, the stresses determined are necessarily approximate.

6. The field measurements indicate that the actual stresses are generally smaller than the theoretical values given by Boussinesq’s solution at shallow depths. Thus, the Boussinesq solution gives conservative values and is commonly used in soil engineering problems.

Limitations of Boussinesq’s Solution:

1. The solution was initially obtained for determination of stresses in elastic solids. Its application to solids may be questioned, as the solids are far from purely elastic solids.

2. The application of Boussinesq’s solution can be justified when the stresses changes are such that only a stress increase occurs in the soil. The real requirement for use of the solution is not that the soil be elastic (i.e. fully recoverable), but it should have a constant ratio between stress and strain. When the stress decrease occurs, the relation between stress and strain is not linear and, therefore, the solution is not strictly applicable. If the stresses included in the soil are small in comparison with the shear strength of the soil, the soil behaves somewhat elastically and the Boussinesq solution can be used.

3. For practical cases, the Boussinesq solution can be safely used for homogenous deposits of clay, man-made fills and for limited thickness of uniform sand deposits. In deep sand deposits, the modulus of elasticity increases with an increase in depth and, therefore, the Boussinesq solution will not give satisfactory results. In this case, the assumption of proportionality between stress and strain cannot be justified. For such a case, non-linear elastic solutions or elastic-plastic solutions are required.

4. The point load applied below ground surface cause somewhat smaller stresses than are caused by surface loads, and therefore, the Boussinesq solution is not strictly applicable. However, the solution is frequently used for shallow footings, in which z is measured below the base of the footing.