Density, Mass Density, Specific Weight, Specific Volume and Relative Density

1) Density (r)

The basic definition of the density of a substance is the ratio of the mass of a given amount of the substance to the volume it occupies. Thus, density of a fluid is its mass per unit volume and the SI unit is kg/m³.The density of a fluid, denoted by ‘r’ (lowercase Greek letter ‘rho’).

Fluid density is temperature dependent and to a lesser extent it is pressure dependent. For example the density of water at sea level at 4^oC is 1000 kg/m³ , whilst at 50^oC is 988 kg/m³.

2) Mass Density (r)

The mass density of a fluid is its mass per unit volume, normally stated in kilograms per cubic metre (kg/m³ ). The symbol used for mass density is `rho’ (r).

Typical mass densities are:

Material	Mass density (kg/m3)
Water	1000
Sea water	1024
Mercury	13.6 x 10^3
Oil	800 - 900
Air	1.23

Since a molecule of a substance has a certain mass regardless of its state (solid, liquid or gas), the mass density is proportional to the number of molecules in a unit volume of the fluid. As the molecular activity and spacing increase with temperature, fewer molecules exist in a given volume of fluid as temperature rises. Therefore, the mass density of a fluid decreases with increasing temperature. Further by application of pressure a large number of molecules can be forced into a given volume, it is to be expected that the mass density of a fluid will increase with increasing pressure.

3) Weight Density/Specific Weight (w or g)

The weight density (also called specific weight) of a fluid is its weight per unit volume, with unit of Newton per cubic metre (N/m³). The weight density is calculated by multiplying the mass density by 9.8, the value for the gravitational acceleration. It is denoted by a symbol ‘w’ or ‘g’ (Greek letter ‘gama’). As it represents the force exerted by gravity on a unit volume of fluid, it has units of force per unit volume.

Weight Density = Mass Density x g

The mass density ‘r’ and specific weight ‘w’ are related as indicated below.

where g is acceleration due to gravity.

The specific weight depends on the acceleration due to gravity and the mass density. Since the acceleration due to gravity varies from place to place, the specific weight will also vary. Further the mass density changes with temperature and pressure, hence the specific weight will also depend upon temperature and pressure.

4) Specific Volume (v)

Specific volume of a fluid is the volume of the fluid per unit mass. Thus it is the reciprocal of mass density. It is generally denoted by ‘v’. In SI units specific volume is expressed in cubic meter per kilogram i.e., m³/kg. The specific volume of water is 

                                                   1 /ρ=1/1000 = 0.001 m³ /kg

For liquids the mass density, the specific weight and specific volume vary only slightly with the variation of temperature and pressure. It is due to the molecular structure of the liquids in which the molecules are arranged very compactly (in contrast to that of a gas). The presence of dissolved air, salts in solution and suspended matter will slightly increase the values of the mass density and the specific weight of the liquids.

For gases the values of the above properties vary greatly with variation of either temperature, or pressure, or both. It is due to the molecular structure of the gas in which the molecular spacing (i.e., volume) changes considerably on account of pressure and temperature variations.

5) Relative Density (RD)

The relative density is the ratio of the density of a substance to some standard density. The standard density chosen for comparison with the density of a solid or a liquid is invariably that of water at 4°C. The relative density of a fluid is the mass density of the fluid compared to the mass density of water at 4°C. RD is a pure ratio. So, it has no units. It is also sometimes referred as specific gravity.

Example Question

If a 25 litre volume of oil has a mass of 20 kilograms, determine the oil’s mass density, weight density, relative density and specific volume.

     Mass density = mass/volume

                           = 20/0.025

                           = 800 kg/m³

  Weight density = mass density x g

                           = 800 x 9.8

                           = 7840 N/m

Relative density = mass density of oil/ mass density of water

                           = 800/1000

                           = 0.8

Specific volume = 1/r

                           = 1/800

                           = 1.25 x10 ^ -3 m³ /kg

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Drawing Board

Drawing board is rectangular in shape and is made of four to six strips of well-seasoned soft wood such as pine, fir, oak etc. and about 25 mm thick. The wooden strips are cleated at the back by two battens by means of screws to prevent warping. One of the edges of the board is used as the working edge, on which the T-square is made to slide. It should be perfectly straight. In some boards, this edge is grooved throughout its length and a perfectly straight ebony edge is fitted inside this groove. This provides a true and more durable guide for the T-square to slide on. 

Fig. 1 Bottom Surface of Drawing Board

Fig. 2 Top Surface of Drawing Board

Drawing board is made of soft wooden platens. It is used for supporting the drawing paper/tracing paper for making drawings. Almost perfect planning of the working surface of the drawing board is to be ensured. Drawing board should be softer enough to allow insertion and removal of drawing pins. Drawing board is made in various sizes. Standard drawing boards are designated as follows as per IS: 1444-1989. D2 and D3 size of drawing board is normally recommended for using in schools and colleges.

Table 1. Standard Sizes of Drawing Boards

Sl. No.	Designation	Size (mm)	To be used with sheet sizes
1	D0	1500 x 1000 x 25	A0
2	D1	1000 x 700 x 25	A1
3	D2	700 x 500 x 15	A2
4	D3	500 x 350 x 15	A3

Now-a-days the drawing boards are available with laminated surfaces. The flatness can be checked by placing a straight edge on its surface. If no light passes between them, the surface is perfectly flat. Large size boards are used in drawing offices of engineers and engineering firms. The drawing board is placed on the table in front of the student, with its working edge on his left side. It is more convenient if the table-top is sloping downwards towards the student. If such a table is not available, the necessary slope can be obtained by placing a suitable block of wood under the distant longer edge of the board.

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Coarse aggregate

When the aggregate is sieved through 4.75mm sieve, the aggregate retained is called coarse aggregate. They are obtained by natural disintegration or by artificial crushing of rocks. Gravel, cobble and boulders come under this category. The maximum size of aggregate can be 80 mm. In general, 40mm size aggregate used for plain cement concrete (PCC) and 20mm size is used for reinforced cement concrete (RCC).

The size is governed by the thickness of section, spacing of reinforcement, clear cover, mixing, handling and placing methods. For economy the maximum size should be as large as possible but not more than one-fourth of the minimum thickness of the member. For reinforced sections the maximum size should be at least 5 mm less than the clear spacing between the reinforcement and also at least 5 mm less than the clear cover. Aggregate more than 20 mm size is seldom used for reinforced cement concrete structural members. The size range of various coarse aggregates is given below.

Table 1: Size range of coarse aggregate

Coarse aggregate	Size variation (mm)
Fine gravel	4 – 8
Medium gravel	8 – 16
Coarse gravel	16 – 64
Cobbles	64 – 256
Boulders	>256

Classification of Aggregates as per Shape

The shape is one of the most effective ways of differentiating aggregates. Aggregate is derived from naturally occurring rocks by blasting or crushing etc., so, it is difficult to attain required shape of aggregate. But, the shape of aggregate will affect the workability of concrete. So, we should take care about the shape of aggregate. Aggregates are classified according to shape into the following types.

1) Rounded Aggregate

The rounded aggregates are completely shaped by attrition (the resistance of a granular material to wear) and available in the form of seashore gravel. Rounded aggregates result in the minimum percentage of voids (32 – 33%) hence gives more workability. They require a lesser amount of water-cement ratio. They are not considered for high-strength concrete because of poor interlocking behavior and weak bond strength. It is used mainly in road construction for filling voids between angular aggregates.

Example: River or seashore gravels, desert seashore and windblown sands

Fig. 1 Rounded Aggregate

2) Irregular Aggregates/ Partially Rounded Aggregates

The irregular or partly rounded aggregates are partly shaped by attrition and these are available in the form of pit sands and gravel. Irregular aggregates may result 35- 37% of voids. These will give lesser workability when compared to rounded aggregates. The bond strength is slightly higher than rounded aggregates but not as required for high strength concrete. It is used in low strength or medium-strength concrete, road construction etc.

Example: Pit sands and gravels, land or dug flints, cuboid rock

Fig. 2 Irregular Aggregate

3) Angular Aggregates

The angular aggregates consist of well defined edges formed at the intersection of roughly planar surfaces and these are obtained by crushing the rocks. Angular aggregates result maximum percentage of voids (38-45%) hence gives less workability but this problem is minimized by filling voids with rounded or smaller aggregates. They give 10-20% more compressive strength due to development of stronger aggregate-mortar bond. So, these are useful in high strength concrete manufacturing.

Example: Crushed rocks of all types; talus; screes

Fig. 3 Angular Aggregate

4) Flaky Aggregates

When the aggregate thickness is small when compared with width and length of that aggregate it is said to be flaky aggregate, or on the other, when the least dimension of aggregate is less than the 60% of its mean dimension then it is said to be flaky aggregate or an aggregate is said to be flaky if its least dimension is less than 3/5 (0.6) of the mean dimension. The use of flaky aggregates reduces the flowing capacity of concrete. They lead to segregation in concrete and harshness of concrete. Flaky aggregates also have very low crushing strength so should not be used in high-strength concrete and road construction.

Example: Laminated rocks

Fig. 4 Flaky Aggregate

5) Elongated Aggregates

When the length of aggregate is larger than the other two dimensions then it is called elongated aggregate or the length of aggregate is greater than 180% of its mean dimension or The aggregate is said to be elongated if its greater length is greater than 9/5th of its mean dimension. Elongated aggregates also have very low crushing strength so should not be used in high-strength concrete and road construction.

Fig. 5 Elongated Aggregate

6) Flaky and Elongated Aggregates

When the aggregate length is larger than its width and width is larger than its thickness then it is said to be flaky and elongated aggregates. Flaky, elongated, flaky and elongated aggregates are not suitable for concrete mixing. These are generally obtained from the poorly crushed rocks.

Fig. 6 Flaky and Elongated Aggregate

Classification of Coarse Aggregates Based on Natural or Artificial Formation

Basically, coarse aggregates are classified as either natural or artificial.

1) Natural Aggregates

These are the aggregates that are found from natural sources. Natural aggregates are further divided into two categories as stated below.

a) Gravel

The main origin of gravel is river beds, stream deposits, etc. These aggregates are formed by weathering of bedrock and subsequent transportation and deposition by water, ice, gravity, etc.

b) Crushed Aggregates

Crushed aggregates are obtained from the quarries. They are widely available in the market. Crushed aggregates are small rock fragments that are subjected to mechanical processing such as crushing, washing and sizing.

2) Artificial Aggregates

Artificial aggregates are used because they are in case environment-friendly materials. They are manufactured from various pollutant by-products such as ash, power station solid waste, rice husk ash, furnace slag, granite powder, iron ore slag, over burnt brickbats etc. By using these industrial by-products, we can reduce environmental pollution and protect natural resources.

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Aims/Benefits of Town Planning

Town planning has gained a lot of importance today. New towns are being developed. It has become very important for the town planners to concentrate on old development as well as the new development. It is essential that old and new development are linked properly. Energy efficiency in planning should be the goal of any town planner, urban designer or an architect. The aims of town planning are as follows.

1. To correct the past errors as far as possible.
2. To provide civic aesthetics of the town.
3. To attempt an orderly appropriate and balanced arrangements of land use.
4. To develop healthy, attractive and efficient environment in the city.
5. To promote a high level of culture.
6. To create and maintain an attractive central core and make it the cultural, financial, commercial and entertainment centre.
7. To provide an interrelated balanced transportation system adequate to meet the needs of everyone in the urban community.
8. To encourage the attraction, retention and expansion of a sufficient number and variety of industries and business activities to provide jobs to the people and to get more income to municipality.
9. To create a sense of dignity, identity, pride and responsibility in the social environment.
10. To suggest the schemes which will control the future growth and development of the city.
11. To insure against the possible future errors.
12. To concentrate for development of full potentials of human resources through wide variety of programmes, facilities and other incentives.
13. To establish and maintain a consistent housing policy providing for decent housing open to all persons in the community at reasonable prices and rents.
14. To encourage vigorous programmes of inspection, maintenance of health environment in the city.
15. Suggestions will be given to provide maximum housing facilities as per the income through various concerned authorities.
16. To encourage the development of neighbourhoods as social and recreational units and promote the neighbourhood organizations and involvement in the improvement of local services, facilities, transportation and living conditions.
17. Suggestions will be made for efficient transportation facilities in the city including new roads, widening the roads repairing maintenance depending upon the localities and functional zones.
18. To develop parks and recreation facilities to optimum standards based on local needs preserving as many sites of natural and historical significance as possible.
19. To provide maximum educational and medical facilities.
20. To provide maximum utility service facilities to reach all people of the city.
21. To promote maximum co-operation between Government and public to get the benefits of development schemes of urban development.
22. To implement effective measure of slum clearance programmes in the city and controlling the further development of slum in the city.
23. Suggestions will be made to demolish old structures of public and private houses.
24. To suggest relocation, redevelopment and renewal of structure in the city.
25. To create maximum green and open spaces in the urban limit.
26. Measures will be suggested to control the pollution of air, water, noise etc.
27. Improvement and modernization of water supply, sewerage, electricity etc.
28. Improvement of site development for residential industrial, public and semi-public use.

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Type of Loads on Structures

The objective of a structural engineer is to design a structure that will be able to withstand all the loads to which it is subjected while serving its intended purpose throughout its intended life span. In designing a structure, an engineer must consider all the loads that can realistically be expected to act on the structure during its planned life span. The loads that act on civil engineering structures can be grouped according to their nature and source into three classes: (1) dead loads due to the weight of the structural system itself and any other material permanently attached to it; (2) live loads, which are movable or moving loads due to the use of the structure; and (3) environmental loads, which are caused by environmental effects, such as wind, snow, and earthquakes.

In addition to estimating the magnitudes of the design loads, an engineer must also consider the possibility that some of these loads might act simultaneously on the structure. The structure is finally designed so that it will be able to withstand the most unfavorable combination of loads that is likely to occur in its lifetime.

1) Dead Loads

Dead loads are gravity loads of constant magnitudes and fixed positions that act permanently on the structure. Such loads consist of the weights of the structural system itself and of all other material and equipment permanently attached to the structural system. For example, the dead loads for a building structure include the weights of frames, framing and bracing systems, floors, roofs, ceilings, walls, stairways, heating and air conditioning systems, plumbing, electrical systems etc. The calculation of dead loads of each structure are calculated by the volume of each section and multiplied with the unit weight.

The weight of the structure is not known in advance of design and is usually assumed based on past experience. After the structure has been analyzed and the member sizes determined, the actual weight is computed by using the member sizes and the unit weights of materials. The actual weight is then compared to the assumed weight and the design is revised if necessary. The unit weights of some common construction materials are given in Table 1. The weights of permanent service equipment, such as heating and air-conditioning systems, are usually obtained from the manufacturer.

Table 1: Unit Weights of Construction Materials

Sl. No.	Material	Unit Weight (kN/m^3)
1	Aluminum	25.9
2	Brick	18.8
3	Plain Cement Concrete	24
4	Reinforced Cement Concrete	25
5	Structural Steel	77.0
6	Wood	6.3

2) Live Loads/ Imposed loads 

Live loads are loads of varying magnitudes and positions caused by the use of the structure. Live loads are either movable or moving loads without any acceleration or impact. These loads are assumed to be produced by the intended use or occupancy of the building including weights of movable partitions or furniture etc. Live loads keep on changing from time to time. Sometimes, the term live loads are used to refer to all loads on the structure that are not dead loads, including environmental loads, such as snow loads or wind loads. However, since the probabilities of occurrence for environmental loads are different from those due to the use of structures, the current codes use the term live loads to refer only to those variable loads caused by the use of the structure. 

The magnitudes of design live loads are usually specified in building codes. In India, the minimum values of live loads to be assumed are given in IS 875 (part 2)–1987. It depends upon the intended use of the building. The position of a live load may change, so each member of the structure must be designed for the position of the load that causes the maximum stress in that member. Different members of a structure may reach their maximum stress levels at different positions of the given load. For example, as a truck moves across a truss bridge, the stresses in the truss members vary as the position of the truck changes.

Table 2: Minimum Floor Live Loads for Buildings

Sl. No.	Occupancy or Use	Live Load (kPa)
1	Hospital patient rooms, residential dwellings, apartments, hotel guest rooms, school classrooms	1.92
2	Library reading rooms, hospital operating roomsand laboratories	2.87
3	Dance halls and ballrooms, restaurants, gymnasiums	4.79
4	Light manufacturing, light storage warehouses,wholesale stores	6.00
5	Heavy manufacturing, heavy storage warehouses	11.97

Buildings Subjected to Environmental Loads

Because of the inherent uncertainty involved in predicting environmental loads that may act on a structure during its lifetime, the consequences of the failure of the structure are usually considered in estimating design environmental loads, such as due to wind, snow and earthquakes. In general, the more serious the potential consequences of the structural failure, the larger the magnitude of the load for which the structure should be designed.

a) Wind Loads 

Wind loads are produced by the flow of wind around the structure. Wind load is primarily horizontal load caused by the movement of air relative to earth. The magnitudes of wind loads that may act on a structure depend on the geographical location of the structure, obstructions in its surrounding terrain, such as nearby buildings, and the geometry and the vibration characteristics of the structure itself. Although the procedures described in the various codes for the estimation of wind loads usually vary in detail, most of them are based on the same basic relationship between the wind speed ‘V’ and the dynamic pressure ‘q’ induced on a flat surface normal to the wind flow, which can be obtained by applying Bernoulli’s principle and is expressed as

q = 1/ 2 rV^2

where ‘r’ is the mass density of the air 

Wind load is required to be considered in structural design especially when the height of the building exceeds two times the dimensions transverse to the exposed wind surface. For low rise building up to four to five stories, the wind load is not critical because the moment of resistance provided by the continuity of floor system to column connection and walls provided between columns are sufficient to accommodate the effect of these forces. The horizontal forces exerted by the components of winds are to be kept in mind while designing the building. The calculation of wind loads depends on the two factors, namely velocity of wind and size of the building. In India, calculation of wind load on structures is given below by the IS-875 (Part 3) -1987. Using colour code, basic wind pressure ‘Vb’ is shown in a map of India. Designer can pick up the value of Vb depending upon the locality of the building. To get the design wind velocity Vz the following expression shall be used: 

Vz = k1.k2.k3.Vb 

Where 

k1 = Risk coefficient 

k2 = Coefficient based on terrain, height and structure size

k3 = Topography factor 

The design wind pressure is given by

pz = 0.6 V^2 * z 

where pz is in N/m^2 at height Z and Vz is in m/sec. 

Up to a height of 30 m, the wind pressure is considered to act uniformly. Above 30 m height, the wind pressure increases.

Table 3: Risk Categories of Buildings for Environmental Loads

Risk category	Occupancy or Use	Importance Factor
		Snow Loads (Is)	Earthquake Loads (Ie)
I	Buildings representing low risk to human life in the case of failure, such as agricultural and minor storage facilities.	0.8	1.0
II	All buildings other than those listed in Risk Categories I, III, and IV. This risk category applies to most of the residential, commercial and industrial buildings (except those which have been specifically assigned to another category).	1.0	1.0
III	Buildings whose failure would pose a substantial risk to human life, and/or could cause a substantial economic impact or mass disruption of everyday public life. This category contains buildings such as: theaters, lecture and assembly halls where a large number of people congregate in one area; elementary schools; small hospitals; prisons; power generating stations; water and sewage treatment plants; telecommunication centers; and buildings containing hazardous and explosive materials.	1.1	1.25
IV	Essential facilities, including hospitals, fire and police stations, national defense facilities and emergency shelters, communication centers, power stations and utilities required in an emergency, and buildings containing extremely hazardous materials.	1.2	1.5

b) Snow Loads

In many parts of the world, snow loads must be considered in designing structures. The design snow load for a structure is based on the ground snow load for its geographical location, which can be obtained from building codes or meteorological data for that region. Once the ground snow load has been established, the design snow load for the roof of the structure is determined by considering such factors as the structure’s exposure to wind and its thermal, geometric, and functional characteristics. In most cases, there is less snow on roofs than on the ground. In India, the code IS 875 (Part-4):1987 deals with snow loads on roofs of the building. 

c) Earthquake Loads

An earthquake is a sudden undulation of a portion of the earth’s surface. Although the ground surface moves in both horizontal and vertical directions during an earthquake, the magnitude of the vertical component of ground motion is usually small and does not have a significant effect on most structures. It is the horizontal component of ground motion that causes structural damage and that must be considered in designs of structures located in earthquake-prone areas. 

Fig.1 Deformation during an earthquake

During an earthquake, as the foundation of the structure moves with the ground, the above-ground portion of the structure, because of the inertia of its mass, resists the motion, thereby causing the structure to vibrate in the horizontal direction. These vibrations produce horizontal shear forces in the structure. For an accurate prediction of the stresses that may develop in a structure, in the case of an earthquake, a dynamic analysis, considering the mass and stiffness characteristics of the structure, must be performed. The response of the structure to the ground vibration is a function of the nature of foundation soil, size and mode of construction and the duration and intensity of ground motion. In India, IS 1893– 2014 gives the details of calculations for structures standing on soils which will not considerably settle or slide appreciably due to earthquake.

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