Measurement of Workability - Slump Test

A concrete is said to be workable if it can be easily mixed, placed, compacted and finished. A workable concrete should not show any segregation or bleeding. Segregation is said to occur when coarse aggregate tries to separate out from the finer material and a concentration of coarse aggregate at one place occurs. This results in large voids, less durability and strength. Bleeding of concrete is said to occur when excess water comes up at the surface of concrete. This causes small pores through the mass of concrete and is undesirable.

There is no universally accepted test method that can directly measure the workability of concrete. The difficulty in measuring the mechanical work defined in terms of workability, the composite nature of the fresh concrete and the dependence of the workability on the type and method of construction makes it impossible to develop a well-accepted test method to measure workability. The most widely used test, which mainly measures the consistency of concrete, is called the slump test. For the same purpose, the second test in order of importance is the Vebe test, which is more meaningful for mixtures with low consistency. The third test is the compacting factor test, which attempts to evaluate the compactability characteristic of a concrete mixture. The fourth test method is the ball penetration test that is related to the mechanical work.

Slump Test

Unsupported fresh concrete flows to the sides and a sinking in height takes place. This vertical settlement is known as slump. The slump is a measure indicating the consistency or workability of cement concrete. It gives an idea of water content needed for concrete to be used for different works. To measure the slump value, the fresh concrete is filled into a mould of specified shape and dimensions and the settlement or slump is measured when supporting mould is removed. The slump increases as water content is increased. For different works different slump values have been recommended.

Slump test is the most commonly used method of measuring consistency of concrete which can be employed either in laboratory or at site of work where nominal maximum size of aggregates does not exceed 40 mm. It is not a suitable method for very wet or very dry concrete. It does not measure all factors contributing to workability and it always representative of the placability of the concrete. It is conveniently used as a control test and gives an indication of the uniformity of concrete from batch to batch. Repeated batches of the same mix, brought to the same slump, will have the same water content and water cement ratio, provided the weights of aggregate, cement and admixtures are uniform and aggregate grading is within acceptable limits. Additional information on workability and quality of concrete can be obtained by observing the manner in which concrete slumps. Quality of concrete can also be further assessed by giving a few tappings or blows by tamping rod to the base plate. The deformation shows the characteristics of concrete with respect to tendency for segregation.

Tools and Apparatus Used for Slump Test (Equipments)

• Standard slump cone (100 mm top diameter x 200 mm bottom diameter x 300 mm high)
• Small scoop
• Bullet-nosed rod (600 mm long x 16 mm diameter)
• Rule
• Slump plate (500 mm x 500 mm)

(The thickness of the metallic sheet for the mould should not be thinner than 1.6 mm.)

Fig. 1 Slump Testing Equipment

Fig. 2 Slump Cone

Procedure

• Clean the internal surface of the mould thoroughly and place it on a smooth horizontal, rigid and non-absorbent surface, such as of a metal plate.
• Consider a W-C ratio of 0.5 to 0.6 and design mix of proportion about 1:2:4 (It is presumed that a mix is designed already for the test). Weigh the quantity of cement, sand, aggregate and water correctly. Mix thoroughly. Use this freshly prepared concrete for the test.
• Fill the mould to about one fourth of its height with concrete. While filling, hold the mould firmly in position
• Tamp the layer with the round end of the tamping rod with 25 strokes disturbing the strokes uniformly over the cross section.
• Fill the mould further in 3 layers each time by 1/4^th height and tamping evenly each layer as above. After completion of rodding of the topmost layer strike of the concrete with a trowel or tamping bar, level with the top of mould.
• Lift the mould vertically slowly and remove it.
• The concrete will subside. Measure the height of the specimen of concrete after subsidence.
• The slump of concrete is the subsidence, i.e. difference in original height and height up to the topmost point of the subsided concrete in millimeters.

Fig. 3 Slump Test

The pattern of slump indicates the characteristics of concrete in addition to the slump value. If the concrete slumps evenly it is called true slump. If one half of the cone slides down, it is called shear slump. In case of a shear slump, the slump value is measured as the difference in height between the height of the mould and the average value of the subsidence. Shear slump also indicates that the concrete is non-cohesive and shows the characteristic of segregation. It is seen that the slump test gives fairly good consistent results for a plastic mix. This test is not sensitive for a stiff mix. In case of dry mix, no variation can be detected between mixes of different workability. In the case of rich mixes, the value is often satisfactory, their slump being sensitive to variations in workability. IS 456 - 2000 suggests that in the “very low” category of workability where strict control is necessary, for example, Pavement Quality Concrete (PQC) measurement of workability by determination of compacting factor will be more appropriate than slump and a value of 0.75 to 0.80 compacting factor is suggested.

Fig. 4 Types of Slump 

The above IS also suggests that in the “very high” category of workability, measurement of workability by determination of “flow” by flow test will be more appropriate. However, in a lean mix with a tendency of harshness a true slump can easily change to shear slump. In such case, the tests should be repeated. Despite many limitations, the slump test is very useful on site to check day-to-day or hour to- hour variation in the quality of mix. An increase in slump, may mean for instance that the moisture content of the aggregate has suddenly increased or there has been sudden change in the grading of aggregate. The slump test gives warning to correct the causes for change of slump value. Table 1 shows the nominal slump value for different degrees of workability.

Table 1 Nominal Slump Value for Different Degrees of Workability

Sl.No.	Slump Value (in mm)	Degree of Workability
1	0 – 25	Very Low
2	25 - 50	Low
3	50 – 100	Medium
4	100 - 175	High

The Bureau of Indian standards, in the past, generally adopted compacting factor test values for denoting workability. Even in the IS:10262 of 1982 dealing with recommended guide line for Concrete Mix Design, adopted compacting factor for denoting workability. But now in the revision of IS:456 – 2000, the code has reverted back to slump value to denote the workability rather than compacting factor. It shows that slump test has more practical utility than the other tests for workability.

Although, slump test is popular due to the simplicity of apparatus used and simple procedure, the simplicity is also often allowing a wide variability and many time it could not provide true guide to workability. For example, a harsh mix cannot be said to have same workability as one with a large proportion of sand even though they may have the same slump.

Factors Affecting Slump Test

• Material properties like chemical composition, fineness, particle size distribution, moisture content and temperature of cementitious materials
• Size, texture, combined grading, cleanliness and moisture content of the aggregates
• Chemical admixtures dosage, type, combination, interaction, sequence of addition and its effectiveness,
• Air content of concrete
• Concrete batching, mixing and transporting methods and equipment
• Temperature of the concrete
• Sampling of concrete, slump testing technique and the condition of test equipment
• The amount of free water in the concrete
• Time since mixing of concrete at the time of testing

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Surface Tension

Surface tension is a force per unit length (or surface energy per unit area) acting in the plane of the interface between the plane of the liquid and any other substance. It is also an extra energy that the molecules at the interface have as compared to molecules in the interior. Due to molecular attraction, liquids possess certain properties such as cohesion and adhesion. Cohesion means inter molecular attraction between molecules of the same liquid. That means it is a tendency of the liquid to remain as one assemblage of particles. Adhesion means attraction between the molecules of a liquid and the molecules of a solid boundary surface in contact with the liquid. The property of cohesion enables a liquid to resist tensile stress, while adhesion enables it to stick to another body. Surface tension is due to cohesion between liquid particles at the surface, whereas capillarity is due to both cohesion and adhesion.

A liquid molecule on the interior of the liquid body has other molecules on all sides of it, so that the forces of attraction are in equilibrium and the molecule is equally attracted on all the sides, as a molecule at point A shown in Fig.1. On the other hand, a liquid molecule at the surface of the liquid, (i.e., at the interface between a liquid and a gas) as at point B, does not have any liquid molecule above it, and consequently there is a net downward force on the molecule due to the attraction of the molecules below it. This force on the molecules at the liquid surface, is normal to the liquid surface. Apparently owing to the attraction of liquid molecules below the surface, a film or a special layer seems to form on the liquid at the surface, which is in tension and small loads can be supported over it. For example, a small needle placed gently upon the water surface will not sink but will be supported by the tension at the water surface.

Fig. 1 Inter molecular forces near a liquid surface

The property of the liquid surface film to exert a tension is called the surface tension. It is denoted by ‘σ’ (Greek ‘sigma’) and it is the force required to maintain unit length of the film in equilibrium. In SI units, surface tension is expressed in N/m. In the metric gravitational system of units, it is expressed in kg(f)/cm or kg(f)/m. As surface tension is directly dependent upon inter molecular cohesive forces, its magnitude for all liquids decreases as the temperature rises. It is also dependent on the fluid in contact with the liquid surface; thus surface tensions are usually quoted in contact with air. The surface tension of water in contact with air varies from 0.0736 N/m [or 0.0075 kg (f)/m] at 19°C to 0.0589 N/m [or 0.006 kg (f)/m] at 100°C.

Surface tension has a role in capillary action, or capillarity, in which liquids climb up narrow tubes or narrow gaps between surfaces. Capillarity, which is important in the flow of water through soils as well as in flows in the human body, is the result of free surface forces and fluid-solid attractive forces. In space travel, where the pull of gravity is small, capillarity causes liquids to crawl out of open containers. Therefore, space travelers must drink with special straws that clamp shut when not in use to prevent snacks from climbing up the straw and floating freely throughout the cabin.

Surface forces are important in a wide variety of technical applications, including the breakup of jets, processes involving thin films and foams. Wicking, the drawing of fluid up into a fabric or wick as in a candle or away from the body as in the design of exercise clothing, is another process that works by capillary action. The opposite effect, waterproofing, is a manipulation of surface forces to prevent wicking. Surface tension causes striking effects that are exploited to make engaging fountain displays. In soap and water solutions, for example, variation of the concentration of the solute can cause the surface tension to vary, which in turn causes flow.

Flow driven by surface tension gradients called the Marangoni effect which stabilizes soap bubbles, among other effects. The emerging field of micromechanics creates machinery that works on nearly molecular size scales. The properties of any liquids involved in micro machines are dominated by interfacial forces. Interfacial forces are not always important, however, even when a large amount of free surface is present. In an ocean, wave motion depends on viscous forces and gravity forces, but the contribution of surface tension forces to the momentum balance in oceanic flows is negligible.

Fig. 2 Surface forces cause the curvature of interfaces in small tubes, which is called the meniscus effect

Fig. 3 Unbalanced forces at the free surface of a fluid must be accounted for by including the surface tension in fluid models. The surface tension is the tension per unit length present in an imaginary stretched film coincident with the free surface

Fig. 4 The legs of the water strider make impressions on the water surface as it walks across the free surface. The free surface acts like a membrane under tension that supports the insect

Fig. 5 Soap bubbles are composed of thin fluid layers sandwiched between two free surfaces. Surfactant molecules occupy the free surfaces and reduce the surface tension of the bubble surface compared to the surface tension of pure water. If an external force deforms or inflates the bubble, more surface is generated, reducing the concentration of surfactant molecules at the bubble surfaces. Lower surfactant concentration implies higher surface tension, however, and this locally higher surface tension pulls fluid into the thinning layer, stabilizing the film and preventing bubble rupture

Whenever a liquid is in contact with other liquids or gases, or in this case a gas/solid surface, an interface develops that acts like a stretched elastic membrane, creating surface tension. There are two features to this membrane: the contact angle ′θ′, and the magnitude of the surface tension, ′σ′ (N/m or lbf/ft). Both of these depend on the type of liquid and the type of solid surface (or other liquid or gas) with which it shares an interface. The examples of surface tension effects arise when you are able to place a needle on a water surface and, similarly, when small water insects are able to walk on the surface of the water.

For a soap bubble in air, surface tension acts on both inside and outside interfaces between the soap film and air along the curved bubble surface. Surface tension also leads to the phenomena of capillary. In engineering, probably the most important effect of surface tension is the creation of a curved meniscus that appears in manometers or barometers, leading to a (usually unwanted) capillary rise (or depression).

                                  (a) A wetted surface                                           (b) A non-wetted surface

Fig. 6 Surface tension effects on water droplets

The effect of surface tension is illustrated in the case of a droplet as well as a liquid jet. When a droplet is separated initially from the surface of the main body of liquid, then due to surface tension there is a net inward force exerted over the entire surface of the droplet which causes the surface of the droplet to contract from all the sides and results in increasing the internal pressure within the droplet. The contraction of the droplet continues till the inward force due to surface tension is in balance with the internal pressure and the droplet forms into sphere which is the shape for minimum surface area. The internal pressure within a jet of liquid is also increased due to surface tension. The internal pressure intensity within a droplet and a jet of liquid in excess of the outside pressure intensity may be determined by the expressions derived below.

i) Pressure Intensity Inside a Droplet

Consider a spherical droplet of radius ‘r’ having internal pressure intensity ‘p’ in excess of the outside pressure intensity. If the droplet is cut into two halves, then the forces acting on one half will be those due to pressure intensity p on the projected area (πr²) and the tensile force due to surface tension ‘σ’ acting around the circumference (2πr). These two forces will be equal and opposite for equilibrium and hence we have

This equation indicates that the internal pressure intensity increases with the decrease in the size of droplet.

ii) Pressure Intensity Inside a Soap Bubble

A spherical soap bubble has two surfaces in contact with air, one inside and the other outside, each one of which contributes the same amount of tensile force due to surface tension. As such on a hemispherical section of a soap bubble of radius r the tensile force due to surface tension is equal to 2σ (2πr). The pressure force acting on the hemispherical section of the soap bubble is same as in the case of a droplet and it is equal to p (πr²). Thus equating these two forces for equilibrium, we have

iii) Pressure Intensity Inside a Liquid Jet

Consider a jet of liquid of radius ‘r’, length ‘l’ and having internal pressure intensity ‘p’ in excess of the outside pressure intensity. If the jet is cut into two halves, then the forces acting on one half will be those due to pressure intensity p on the projected area (2rl) and the tensile force due to surface tension ‘σ’ acting along the two sides. These two forces will be equal and opposite for equilibrium and hence we have

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Viscosity of a Fluid

It is defined as the internal resistance offered by one layer of fluid to the adjacent layer. In case of liquids, main reason of the viscosity is molecular bonding or cohesion. In case of gases main reason of viscosity is molecular collision. In case of liquids, due to increase in temperature the viscosity will decrease due to breaking of cohesive bonds. In case of gases, the viscosity will increase with temperature because of molecular collision increases. All fluids offer resistance to any force tending to cause one layer to move over another. Viscosity is the fluid property responsible for this resistance. Since relative motion between layers requires the application of shearing forces, that is, forces parallel to the surfaces over which they act, the resisting forces must be in exactly the opposite direction to the applied shear forces and so they too are parallel to the surfaces.

It is a matter of common experience that, under particular conditions, one fluid offers greater resistance to flow than another. Such liquids as tar, treacle and glycerine cannot be rapidly poured or easily stirred and are commonly spoken of as thick; on the other hand, thin liquids such as water, petrol and paraffin flow much more readily. (Lubricating oils with small viscosity are sometimes referred to as light, and those with large viscosity as heavy; but viscosity is not related to density). Gases as well as liquids have viscosity, although the viscosity of gases is less evident in everyday life.

Quantitative Definition of Viscosity

Consider two plates sufficiently large (so that edge conditions may be neglected) placed a small distance Y apart, the space between them being filled with fluid as shown in Fig.1. The lower plate is assumed to be at rest, while the upper one is moved parallel to it with a velocity ‘V’ by the application of a force ‘F’, corresponding to area ‘A’, of the moving plate in contact with the fluid. Particles of the fluid in contact with each plate will adhere to it and if the distance Y and velocity V are not too great, the velocity v at a distance y from the lower plate will vary uniformly from zero at the lower plate which is at rest, to V at the upper moving plate. Experiments show that for a large variety of fluids,

Fig.1 Fluid motion between two parallel plates

It may be seen from similar triangles in Fig.1 that the ratio V/Y can be replaced by the velocity gradient (dv/dy), which is the rate of angular deformation of the fluid.

If a constant of proportionality 'μ' (Greek ‘mu’) be introduced, the shear stress 'τ' (Greek ‘tau’) equal to (F/A) between any two thin sheets of fluid may be expressed as 

This equation is called Newton’s law of viscosity, it states that, for the straight and parallel motion of a given fluid, the tangential stress between two adjoining layers is proportional to the velocity gradient in a direction perpendicular to the layers.

In the transposed form, it serves to define the proportionality constant. which is called the coefficient of viscosity, or the dynamic viscosity (since it involves force), or simply viscosity of the fluid. Thus the dynamic viscosity μ, may be defined as the shear stress required to produce unit rate of angular deformation. In SI units μ is expressed in N.s/m², or kg/m.s. The dynamic viscosity μ is a property of the fluid and a scalar quantity.

In the metric gravitational system of units, μ is expressed in kg(f)-sec/m². In the metric absolute system of units μ is expressed in dyne-sec/m² or gm(mass)/cm-sec which is also called ‘poise’ after Poiseuille. The ‘centipoise’ is one hundredth of a poise. The numerical conversion from one system to another is as follows.

1 Ns/m² = 10 poise

In many problems involving viscosity, there frequently appears a term dynamic viscosity ‘μ’ divided by mass density ‘ρ’. The ratio of the dynamic viscosity μ and the mass density ρ is known as Kinematic viscosity and is denoted by the symbol ‘υ’ (Greek ‘nu’) so that

On analyzing the dimensions of the kinematic viscosity it will be observed that it involves only the magnitudes of length and time. The name kinematic viscosity has been given to the ratio (μ/ρ) because kinematics is defined as the study of motion without regard to the cause of the motion and hence it is concerned with length and time only.

In SI units υ is expressed in m²/s. In the metric system of units υ is expressed in cm²/sec or m²/sec. The unit cm²/sec is termed as ‘stoke’ after G.G. Stokes and its one-hundredth part is called ‘centistoke’. In the English system of units it is expressed in ft2/sec. The numerical conversion from one system to another is as follows.

1 m²/s = 10⁴ stokes

The dynamic viscosity μ of either a liquid or a gas is practically independent of the pressure for the range that is ordinarily encountered in practice. However, it varies widely with temperature. For gases, viscosity increases with increase in temperature while for liquids it decreases with increase in temperature. This is so because of their fundamentally different intermolecular characteristics. In liquids the viscosity is governed by the cohesive forces between the molecules of the liquid, whereas in gases the molecular activity plays a dominant role. The kinematic viscosity of liquids and of gases at a given pressure, is essentially a function of temperature.

Common fluids such as air, water, glycerine, kerosene etc., follow Newton’s law of viscosity. There are certain fluids which, however, do not follow Newton’s law of viscosity. Accordingly, fluids may be classified as Newtonian fluids and non-Newtonian fluids. In a Newtonian fluid there is a linear relation between the magnitude of shear stress and the resulting rate of deformation i.e., the constant of proportionality μ in the equation does not change with rate of deformation. In a non-Newtonian fluid there is a non-linear relation between the magnitude of the applied shear stress and the rate of angular deformation. In the case of a plastic substance which is a non-Newtonian fluid an initial yield stress is to be exceeded to cause a continuous deformation. An ideal plastic has a definite yield stress and a constant linear relation between shear stress and the rate of angular deformation. A thixotropic substance, which is a non-Newtonian fluid, has a non-linear relationship between the shear stress and the rate of angular deformation, beyond an initial yield stress. The printer’s ink is an example of a thixotropic liquid.

Fig. 2 Variation of shear stress with velocity gradient

An ideal fluid is defined as that having zero viscosity or in other words shear stress is always zero regardless of the motion of the fluid. Thus an ideal fluid is represented by the horizontal axis (τ = 0) in Fig. 2, which gives a diagrammatic representation of the Newtonian, non-Newtonian, plastic, thixotropic and ideal fluids. A true elastic solid may be represented by the vertical axis of the diagram. The fluids with which engineers most often have to deal are Newtonian, that is, their viscosity is not dependent on the rate of angular deformation, and the term ‘fluid-mechanics’ generally refers only to Newtonian fluids. The study of non-Newtonian fluids is termed as ‘rheology’.

Causes of Viscosity

For one possible cause of viscosity we may consider is the forces of attraction between molecules. Yet there is evidently also some other explanation, because gases have by no means negligible viscosity although their molecules are in general so far apart that no appreciable inter-molecular force exists. The individual molecules of a fluid are continuously in motion and this motion makes possible a process of exchange of momentum between different layers of the fluid.

In gases this interchange of molecules forms the principal cause of viscosity and the kinetic theory of gases (which deals with the random motions of the molecules) allows the predictions – borne out by experimental observations is that

1. The viscosity of a gas is independent of its pressure (except at very high or very low pressure) 
2. Because of the molecular motion increases with a rise of temperature, the viscosity also increases with a rise of temperature (unless the gas is so highly compressed that the kinetic theory is invalid).

The process of momentum exchange also occurs in liquids. There is, however, a second mechanism at play. The molecules of a liquid are sufficiently close together for there to be appreciable forces between them. Relative movement of layers in a liquid modifies these inter-molecular forces, thereby causing a net shear force which resists the relative movement. Consequently, the viscosity of a liquid is the resultant of two mechanisms, each of which depends on temperature, and so the variation of viscosity with temperature is much more complex than for a gas. The viscosity of nearly all liquids decreases with rise of temperature, but the rate of decrease also falls. Except at very high pressures, however, the viscosity of a liquid is independent of pressure.

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Modes of Transport

The term ‘mode of transport’ refers to numerous methods of moving people, objects or both. The various modes of transportation include air, water and land transportation, which includes trains, highways and off-road travel. There are also other modes, including pipelines, cable transmission and space flight etc. The different modes of transport are shown below.

Fig.1 Modes of Transport

Advantage and Disadvantage Different Modes of Transport

1) Road Transport

Advantages	Disadvantages
Less capital outlay	Seasonal nature
Door to door service	Accidents and breakdowns
Service in rural areas	Unsuitable for long distance and bulky traffic
Flexible service	Slow speed
Suitable for short distance	Lack of organization
Lesser risk of damage in transit
Saving in packing cost
Rapid speed
Less cost
Private owned vehicles
Feeder to other modes of transport

2) Railway Transport

Advantages	Disadvantages
Dependable	Huge capital outlay
Better organized	Lack of flexibility
High speed over long distances	Lack of door to door service
Suitable for bulky and heavy goods	Monopoly
Cheaper transport	Unsuitable for short distance and small loads
Larger capacity	Booking formalities
Public welfare	No rural service
Administrative facilities of Government	Under-utilized capacity
Employment opportunities	Centralized administration
Safety

3) Air Transport

Advantages	Disadvantages
High speed	Very costly
Comfortable and quick services	Small carrying capacity
No investment in construction of track	Uncertain and unreliable
No physical barriers	Breakdowns and accidents
Easy access	Large investment
Emergency services	Specialized skill
Quick clearance	Unsuitable for cheap and bulky goods
Most suitable for carrying light goods of       high value	Legal restrictions
National defense
Space exploration

Elements of Transport

The movement of goods or passenger traffic, through rail, sea, air or road transport requires adequate infrastructure facilities for the free flow from the place of origin to the place of destination. Irrespective of modes, every transport system has some common elements. These elements influence the effectiveness of different modes of transport and their utility to users.

1) Vehicle or Carrier to Carry Passenger or Goods

The dimension of vehicles, its capacity and type are some of the factors, which influence the selection of a transport system for movement of goods from one place to the other.

2) Route or Path for Movement of Carriers

Routes play an important role in movement of carriers from one point to another point. It may be surface roads, navigable waterways and roadways. Availability of well-designed and planned routes without any obstacle for movement of transport vehicles in specific routes, is a vital necessity for smooth flow of traffic.

3) Terminal Facilities for Loading and Unloading of Goods and Passengers from Carriers

The objective of transportation can’t be fulfilled unless proper facilities are available for loading and unloading of goods or entry and exit of passengers from carrier. Terminal facilities are to be provided for loading and unloading of trucks, wagons etc. on a continuous basis.

4) Prime Mover

The power utilized for moving of vehicles for transportation of cargo from one place to another is another important aspect of the total movement system.

5) Transit Time and Cost

Transportation involve time and cost. The time element is a valid factor for determining the effectiveness of a particular mode of transport. The transit time of available system of transportation largely determines production and consumption pattern of perishable goods in an economy.

6) Cargo

Transportation basically involves movement of cargo from one place to another. Hence, nature and size of cargo constitute the basis of any goods transport system.

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Phases of Structural Engineering Projects

Structural engineering is the science and art of planning, designing and constructing safe and economical structures that will serve their intended purposes. Structural analysis is an integral part of any structural engineering project, its function being the prediction of the performance of the proposed structure. A flowchart showing the various phases of a typical structural engineering project is presented in Fig. 1.

Fig. 1 Phases of a Typical Structural Engineering Project

The process is an iterative one, and it generally consists of the following steps.

1) Planning Phase

The planning phase usually involves the establishment of the functional requirements of the proposed structure, the general layout and dimensions of the structure, consideration of the possible types of structures (e.g. rigid frame or truss) that may be feasible and the types of materials to be used (e.g., structural steel or reinforced concrete). This phase may also involve consideration of non-structural factors, such as aesthetics, environmental impact of the structure etc.

The outcome of this phase is usually a structural system that meets the functional requirements and is expected to be the most economical. This phase is perhaps the most crucial one of the entire project and requires experience and knowledge of construction practices in addition to a thorough understanding of the behavior of structures.

2) Preliminary Structural Design

In the preliminary structural design phase, the sizes of the various members of the structural system selected in the planning phase are estimated based on approximate analysis, past experience and code requirements. The member sizes thus selected are used in the next phase to estimate the weight of the structure.

3) Estimation of Loads

Estimation of loads involves determination of all the loads that can be expected to act on the structure.

4) Structural Analysis

In structural analysis, the values of the loads are used to carry out an analysis of the structure in order to determine the stresses or stress resultants in the members and the deflections at various points of the structure.

5) Safety and Serviceability Checks

The results of the analysis are used to determine whether or not the structure satisfies the safety and serviceability requirements of the design codes. If these requirements are satisfied, then the design drawings and the construction specifications are prepared, and the construction phase begins.

6) Revised Structural Design

If the code requirements are not satisfied, then the member sizes are revised and phases 3 through are repeated until all the safety and serviceability requirements are satisfied.

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Volumetric Strain (εv)

When a member is subjected to stresses, it undergoes deformation in all directions. Hence, there will be change in volume. The ratio of the change in volume to original volume is called volumetric strain.

Thus,

Where,

           εv = Volumetric strain 

          δV = Change in volume

           V = Original volume

It can be shown that volumetric strain is sum of strains in three mutually perpendicular directions.

For example consider a bar of length L, breadth b and depth d as shown in Fig. 1.

Fig. 1 Rectangular Bar

Now,

Volume, V = L b d

Since volume is function of L, b and d, by using product rule (The derivative of the product of two differentiable functions is equal to the addition of the first function multiplied by the derivative of the second, and the second function multiplied by the derivative of the first function.) we may write as;

Consider a circular rod of length ‘L’ and diameter ‘d’ as shown in Fig. 2.

Fig. 2 Circular Rod

Volume of the bar

                                                                                         (Since V is function of d and L)

Dividing the equation by V

In general for any shape volumetric strain may be taken as sum of strains in three mutually perpendicular directions.

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Hooke’s Law and Poisson’s Ratio

Hooke’s Law

Robert Hooke, an English mathematician conducted several experiments and concluded that stress is proportional to strain up to elastic limit. This is called Hooke’s law. Thus Hooke’s law states that ‘stress is proportional to strain up to elastic limit.’

σ ∝ ϵ

where ′σ′ is stress and ′ϵ′ is strain

Hence,

σ = E ϵ

Where ‘E’ is the constant of proportionality of the material, known as Modulus of Elasticity or Young’s modulus, named after the English scientist Thomas Young (1773–1829). 

The present day sophisticated experiments have shown that for mild steel the Hooke’s law holds good up to the proportionality limit which is very close to the elastic limit. For other materials, Hooke’s law does not hold good. However, in the range of working stresses, assuming Hooke’s law to hold good, the relationship does not deviate considerably from actual behaviour. Accepting Hooke’s law to hold good, simplifies the analysis and design procedure considerably. Hence Hooke’s law is widely accepted. The analysis procedure accepting Hooke’s law is known as Linear Analysis and the design procedure is known as the working stress method.

Poisson’s Ratio (μ)

When a material undergoes changes in length, it undergoes changes of opposite nature in lateral directions. For example, if a rectangular bar is subjected to direct tension in its axial direction it elongates and at the same time its sides contract as shown in Fig.1.

Fig. 1 Changes in Axial and Lateral Directions due to Tensile Force

If we define the ratio of change in axial direction to original length as linear strain and change in lateral direction to the original lateral dimension as lateral strain, it is found that within elastic limit there is a constant ratio between lateral strain and linear strain. This constant ratio is called Poisson’s ratio. 

Thus,

It is denoted by 1/m or μ.

For most of metals its value is between 0.25 to 0.33. Its value for steel is 0.3 and for concrete 0.15.

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