Average Depth of Precipitation Over an Area

The information on the average depth of precipitation (or rainfall) over a specified area on either the storm basis or seasonal basis or annual basis is often required in several types of hydrologic problems. The depth of rainfall measured by a rain gauge is valid for that rain gauge station and in its immediate vicinity. Over a large area like watershed (or catchment) of a stream, there will be several such stations and the average depth of rainfall over the entire area can be estimated by one of the following methods.

1) Arithmetic Mean Method

This is the simplest method in which average depth of rainfall is obtained by obtaining the sum of the depths of rainfall (say P1, P2, P3, P4 .... Pn) measured at stations 1, 2, 3…. n and dividing the sum by the total number of stations i.e. n. Thus, 

This method is suitable if the rain gauge stations are uniformly distributed over the entire area and the rainfall variation in the area is not large.

2) Theissen Polygon Method

The Theissen polygon method takes into account the non-uniform distribution of the gauges by assigning a weightage factor for each rain gauge. In this method, the enitre area is divided into number of triangular areas by joining adjacent rain gauge stations with straight lines, as shown in Fig. 1 (a and b). If a bisector is drawn on each of the lines joining adjacent rain gauge stations, there will be number of polygons and each polygon, within itself, will have only one rain gauge station. Assuming that rainfall Pi recorded at any station ‘i’ is representative rainfall of the area Ai of the polygon i within which rain gauge station is located, the weighted average depth of rainfall P-bar for the given area is given as

Here, Ai/ A is termed the weightage factor for i^th  rain gauge.

Fig. 1 Areal averaging of precipitation a) Rain gauge network, b) Theissen polygons, c) Isohyets

This method is, obviously, better than the arithmetic mean method since it assigns some weightage to all rain gauge stations on area basis. Also, the rain gauge stations outside the catchment can also be used effectively. Once the weightage factors for all the rain gauge stations are computed, the calculation of the average rainfall depth P-bar is relatively easy for a given network of stations.

While drawing Theissen polygons, one should first join all the outermost rain gauge stations. Thereafter, the remaining stations should be connected suitably to form quadrilaterals. The shorter diagonals of all these quadrilaterals are then drawn. The sides of all these triangles are then bisected and thus, Theissen polygons for all rain gauge stations are obtained.

3) Isohyetal Method

An isohyet is a contour of equal rainfall. Knowing the depths of rainfall at each rain gauge station of an area and assuming linear variation of rainfall between any two adjacent stations, one can draw a smooth curve passing through all points indicating the same value of rainfall, Fig. 1 (c). The area between two adjacent isohyets is measured with the help of a planimeter.

The average depth of rainfall P-bar for the entire area A is given as

Since this method considers actual spatial variation of rainfall, it is considered as the best method for computing average depth of rainfall.

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Measurement of Precipitation - Rain Gauges

Rainfall may be measured by a network of rain gauges which may either be of non-recording or recording type. Rainfall can be measured with a weather radar also.

Non-Recording Rain gauge

The non-recording rain gauge used in India is the Symon’s rain gauge (Fig. 1). It consists of a funnel with a circular rim of 12.7 cm diameter and a glass bottle as a receiver. The cylindrical metal casing is fixed vertically to the masonry foundation with the level rim 30.5 cm above the ground surface. The rain falling into the funnel is collected in the receiver and is measured in a special measuring glass graduated in mm of rainfall; when full it can measure 1.25 cm of rain. The rainfall is measured every day at 08.30 hours IST. The funnel shank is inserted in a bottle which receives the rainwater. The water collected in the bottle is measured by pouring it into a measuring cylinder which gives the depth of rainfall in mm.

Fig. 1 Symon’s Rain Gauge

During heavy rains, it must be measured three or four times in the day in which the receiver fill and overflow, but the last measurement should be at 08.30 hours IST and the sum total of all the measurements during the previous 24 hours entered as the rainfall of the day in the register. Usually, rainfall measurements are made at 08.30 hr IST and sometimes at 17.30 hr IST also. Thus the non-recording or the Symon’s rain gauge gives only the total depth of rainfall for the previous 24 hours (i.e., daily rainfall) and does not give the intensity and duration of rainfall during different time intervals of the day. It is often desirable to protect the gauge from being damaged by cattle and for this purpose a barbed wire fence may be erected around it.

Recording Rain Gauge

This is also called self-recording, automatic or integrating rain gauge. This type of rain gauge has an automatic mechanical arrangement consisting of a clockwork, a drum with a graph paper fixed around it and a pencil point, which draws the mass curve of rainfall. From this mass curve, the depth of rainfall in a given time, the rate or intensity of rainfall at any instant during a storm and time of onset and cessation of rainfall can be determined. The gauge is installed on a concrete or masonry platform 45 cm square in the observatory enclosure by the side of the ordinary rain gauge at a distance of 2-3 m from it. The gauge is so installed that the rim of the funnel is horizontal and at a height of exactly 75 cm above ground surface. The self-recording rain gauge is generally used in conjunction with an ordinary rain gauge exposed close by, for use as standard, by means of which the readings of the recording rain gauge can be checked and if necessary adjusted. There are three types of recording rain gauges—tipping bucket gauge, weighing gauge and float gauge.

1) Tipping Bucket Rain Gauge

This consists of a cylindrical receiver 30 cm diameter with a funnel inside (Fig. 2). Just below the funnel a pair of tipping buckets is pivoted such that when one of the bucket receives a rainfall of 0.25 mm it tips and empties into a tank below, while the other bucket takes its position and the process is repeated. The tipping of the bucket actuates on electric circuit which causes a pen to move on a chart wrapped round a drum which revolves by a clock mechanism. This type of rain gauge cannot record snowfall.

Fig. 2 Tipping Bucket Rain Gauge

2) Weighing Type Rain Gauge

In this type of rain-gauge, when a certain weight of rainfall is collected in a tank, which rests on a spring-lever balance, it makes a pen to move on a chart wrapped round a clock driven drum (Fig. 3). The rotation of the drum sets the time scale while the vertical motion of the pen records the cumulative precipitation. The record thus gives the accumulation of rainfall with time.

Fig. 3 Weighing Type Rain Gauge

3) Float Type Rain Gauge

In this type, as the rain is collected in a float chamber, the float moves up which makes a pen to move on a chart wrapped round a clock driven drum. When the float chamber fills up, the water siphons out automatically through a siphon tube kept in an interconnected siphon chamber. The float rises with the rise of water level in the chamber and its movement is recorded on a chart through a suitable mechanism. The clockwork revolves the drum once in 24 hours. The clock mechanism needs rewinding once in a week when the chart wrapped round the drum is also replaced. A siphon arrangement is also provided to empty the chamber quickly whenever it becomes full. The weighing and float type rain gauges can store a moderate snow fall which the operator can weigh or melt and record the equivalent depth of rain.

Fig. 4 Float Type Rain Gauge

Bureau of Indian Standards has laid down the following guidelines for selecting the site for rain gauges (IS : 4897-1968).

• The rain gauge shall be placed on a level ground, not upon a slope or a terrace and never upon a wall or roof.
• On no account, the rain gauge shall be placed on a slope such that the ground falls away steeply in the direction of the prevailing wind.
• The distance of the rain gauge from any object shall not be less than twice the height of the object above the rim of the gauge.
• Great care shall be taken at mountain and coast stations so that the gauges are not unduly exposed to the sweep of the wind. A belt of trees or a wall on the side of the prevailing wind at a distance exceeding twice its height shall form an efficient shelter.
• In hills where it is difficult to find a level space, the site for the rain gauge shall be chosen where it is best shielded from high winds and where the wind does not cause eddies.
• The location of the gauge should not be changed without taking suitable precautions. Description of the site and surroundings should be made a matter of record.

Radar Measurement of Precipitation

In regions of difficult and inaccessible terrains, precipitation can be measured (within about 10% accuracy of the rain gauge measurements) with the help of a radar (radio detecting and ranging). A radar transmits a pulse of electromagnetic waves as a beam in a direction depending upon the position of the movable antenna. The wave travelling at a speed of light is partially reflected by cloud or precipitation particles and returns to the radar where it is received by the same antenna. The display of the magnitude of energy of the returned wave on the radarscope (i.e., radar screen) is called an echo and its brightness is termed echo intensity. The duration between the transmission of the pulse and appearance of the echo on the radarscope is a measure of the distance (i.e., range) of the target from the radar.
Direction of the target with respect to the radar is decided by the orientation of the antenna at the time the target signal is received. The echo is seen in polar coordinates. If there is no target (i.e., cloud or precipitation particles), the screen is dimly illuminated. A small target would appear as a bright point whereas an extended target (such as a rain shower) would appear as a bright patch. The radarscope being divided as per the coordinate system; the position of the target can be estimated. By having a proper calibration between the echo intensity and rainfall (or its intensity), one can estimate the rainfall (or rainfall intensity).

Satellite Measurement of Precipitation

It is a common experience that gauge network for measuring precipitation in a large and inaccessible area (such as in desert and hilly regions) is generally inadequate and non-existent in oceans. The satellite observation is the only effective way for continuous monitoring of precipitation events over a large or inaccessible area. Use of the meterological satellites for weather and water balance studies is, therefore, continuously increasing.

In satellite measurements, the precipitation is estimated by correlating the satellite- derived data and observed rainfall data. These relationships can be developed for a part of electromagnetic spectrum using cloud life history or cloud indexing approach. The first approach uses data from geo-stationary satellites that produce data at every half an hour interval. The second approach, based on cloud classification, does not require a series of consecutive observations of the same cloud system. Microwave remote sensing techniques that can directly monitor the rainfall characteristics have great potential in rainfall measurement.

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Types of Supports for Plane Structures

Supports are used to attach structures to the ground or other bodies, thereby restricting their movements under the action of applied loads. The loads tend to move the structures; but supports prevent the movements by exerting opposing forces or reactions to neutralize the effects of loads, thereby keeping the structures in equilibrium. The type of reaction a support exerts on a structure depends on the type of supporting device used and the type of movement it prevents. A support that prevents translation of the structure in a particular direction exerts a reaction force on the structure in that direction. Similarly, a support that prevents rotation of the structure about a particular axis exerts a reaction couple on the structure about that axis. The type of supports commonly used for plane structures are given below.

1) Fixed Support

A fixed support is the most rigid type of support or connection. It constrains the member in all translations and rotations (i.e. it cannot move or rotate in any direction). The easiest example of a fixed support would be a pole or column in concrete. The pole cannot twist, rotate or displace; it is basically restricted in all its movements at this connection. Fixed supports are extremely beneficial when you can only use a single support. The fixed support provides all the constraints necessary to ensure the structure is static. It is most widely used as the only support for a cantilever. The fixed support is also called rigid support. It provides greater stability to the structure as compared with all other supports. To provide good stability to the structure, at least one rigid support should be provided. Beam fixed in the wall is a good example of fixed support.

Fig. 1 Fixed Support

2) Pinned Support (Hinged Support)

The hinged support is also called pinned support. A pinned support is a very common type of support and is most commonly compared to a hinge in civil engineering. Like a hinge, a pinned support allows rotation to occur but no translation (i.e. it resists horizontal and vertical forces but not a moment). The horizontal and vertical components of the reaction can be determined using the equation of equilibrium. Pinned supports can be used in trusses. By linking multiple members joined by hinge connections, the members will push against each other; inducing an axial force within the member. The benefit of this is that the members contain no internal moment forces and can be designed according to their axial force only. Hinge support reduces sensitivity to an earthquake.

Fig. 2 Pinned Support

3) Roller Support

It is a support that is free to rotate and translate along the surface on which they rest. The surface on which the roller supports are installed may be horizontal, vertical and inclined to any angle. Roller supports can resist a vertical force but not a horizontal force. The roller supports has only one reaction, this reaction acts perpendicular to the surface and away from it. A roller support or connection is free to move horizontally as there is nothing constraining it. The most common use of a roller support is in a bridge. In civil engineering, a bridge will typically contain a roller support at one end to account for vertical displacement and expansion from changes in temperature. This is required to prevent the expansion causing damage to a pinned support. This type of support does not resist any horizontal forces. This obviously has limitations in itself as it means the structure will require another support to resist this type of force.

Fig. 3 Roller Support

4) Simple Support

A simple support is basically just where the member rests on an external structure. They are quite similar to roller supports in the sense that they are able to restrain vertical forces but not horizontal forces. The member simply rests on an external structure to which the force is transferred to. An example is a plank of wood resting on two concrete blocks. The plank can support any downward (vertical) force but if you apply a horizontal force, the plank will simply slide off the concrete blocks.

Fig. 4 Simple Support

5) Rocker Support

Rocker support is similar to roller support. It also resists vertical force and allows horizontal translation and rotation. But in this case, horizontal movement is due to the curved surface provided at the bottom as shown in Fig. 5. So, the amount of horizontal movement is limited in this case.

Fig. 5 Rocker Support

6) Link Support

A link has two hinges, one at each end. The link is supported and allows rotation and translation perpendicular to the direction of the link only. It does not allow translation in the direction of the link. It has a single linear resultant force component in the direction of the link which can be resolved into vertical and horizontal components. In other words, the reaction force of a link is in the direction of the link, along its longitudinal axis.

Fig. 6 Link Support

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Equilibrium of Structures

A structure is considered to be in equilibrium if, initially at rest, it remains at rest when subjected to a system of forces and couples. If a structure is in equilibrium, then all its members and parts are also in equilibrium. In order for a structure to be in equilibrium, all the forces and couples (including support reactions) acting on it must balance each other and there must neither be a resultant force nor a resultant couple acting on the structure. For a space (three-dimensional) structure subjected to three-dimensional systems of forces and couples (Fig. 1), the conditions of zero resultant force and zero resultant couple can be expressed in a Cartesian coordinate system (xyz) as

     Σ Fx = 0, Σ Fy = 0, Σ Fz = 0

     Σ Mx = 0, Σ My = 0, Σ Mz = 0

These six equations are called the equations of equilibrium of space structures and are the necessary and sufficient conditions for equilibrium. The first three equations ensure that there is no resultant force acting on the structure and the last three equations express the fact that there is no resultant couple acting on the structure.

Fig. 1 Space Structure Subjected to Three-Dimensional Systems of Forces and Couples

Fig. 2 Plane Structure Subjected to a Coplanar System of Forces and Couples

For a plane structure lying in the 𝑥y plane and subjected to a coplanar system of forces and couples (Fig. 2), the necessary and sufficient conditions for equilibrium can be expressed as

      Σ Fx = 0, Σ Fy = 0, Σ Mz = 0

These three equations are referred to as the equations of equilibrium of plane structures. The first two of the three equilibrium equations express that the algebraic sums of the 𝑥 components and y components of all the forces are zero, thereby indicating that the resultant force acting on the structure is zero. The third equation indicates that the algebraic sum of the moments of all the forces about any point in the plane of the structure and the moments of any couples acting on the structure is zero, thereby indicating that the resultant couple acting on the structure is zero. All the equilibrium equations must be satisfied simultaneously for the structure to be in equilibrium.

It should be realized that if a structure (e.g., an aerospace vehicle) initially in motion is subjected to forces that satisfy the equilibrium equations, it will maintain its motion with a constant velocity, since the forces cannot accelerate it. Such structures may also be considered to be in equilibrium. However, the term equilibrium is commonly used to refer to the state of rest of structures and is used in this context herein.

Concurrent Force Systems

When a structure is in equilibrium under the action of a concurrent force system; that is, the lines of action of all the forces intersect at a single point - the moment equilibrium equations are automatically satisfied and only the force equilibrium equations need to be considered. Therefore, for a space structure subjected to a concurrent three-dimensional force system, the equations of equilibrium are

      Σ Fx = 0, Σ Fy = 0, Σ Fz = 0

Similarly, for a plane structure subjected to a concurrent coplanar force system, the equilibrium equations can be expressed as

      Σ Fx = 0, Σ Fy = 0

• If a structure is in equilibrium under the action of only two forces, the forces must be equal, opposite and collinear.
• If a structure is in equilibrium under the action of only three forces, the forces must be either concurrent or parallel.

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Analytical Models

An analytical model is a simplified representation or an ideal of a real structure for the purpose of analysis. The objective of the model is to simplify the analysis of a complicated structure. The analytical model represents the behavioural characteristics of the structure of interest to the analyst, while discarding much of the detail about the members, connections and so on, that is expected to have little effect on the desired characteristics. Establishment of the analytical model is one of the most important steps of the analysis process; it requires experience and knowledge of design practices in addition to a thorough understanding of the behaviour of structures. Remember that the structural response predicted from the analysis of the model is valid only to the extent that the model represents the actual structure. Development of the analytical model generally involves consideration of the following factors.

Plane and Space Structure

If all the members of a structure as well as the applied loads lie in a single plane, the structure is called a plane structure. The analysis of plane or two-dimensional structures is considerably simpler than the analysis of space or three-dimensional structures. Many actual three-dimensional structures can be subdivided into plane structures for analysis.

As an example, consider the framing system of a bridge shown in Fig. 1. The main members of the system designed to support vertical loads are shown by solid lines whereas the secondary bracing members which is necessary to resist lateral wind loads and to provide stability are represented by dashed lines. The deck of the bridge rests on beams called stringers; these beams are supported by floor beams, which in turn are connected at their ends to the joints on the bottom panels of the two longitudinal trusses. Thus the weight of the traffic deck, stringers and floor beams is transmitted by the floor beams to the supporting trusses at their joints; the trusses, in turn transmit the load to the foundation. Because this applied loading acts on each truss in its own plane the trusses can be treated as plane structures.

Fig. 1 Framing System of Bridge

As another example, the framing system of a multi-story building is shown in Fig. 2. At each story, the floor slab rests on floor beams which transfer any load applied to the floor, the weight of the slab and their own weight to the girders of the supporting rigid frames. This applied loading acts on each frame in its own plane, so each frame can be analyzed as a plane structure. The loads thus transferred to each frame are further transmitted from the girders to the columns and then finally to the foundation.

Fig. 2 Framing System of Multi-storeyed Building

Although a great majority of actual three-dimensional structural systems can be subdivided into plane structures for the purpose of analysis, some structures such as latticed domes, aerospace structures and transmission towers cannot be subdivided into planar components due to their shape, arrangement of members or applied loading. Such structures, called space structures are analyzed as three-dimensional bodies subjected to three-dimensional force systems.

Line Diagram

The analytical model of the two or three-dimensional body selected for analysis is represented by a line diagram. On this diagram, each member of the structure is represented by a line coinciding with its centroidal axis. The dimensions of the members and the size of the connections are not shown on the diagram. The line diagrams of the bridge truss of Fig. 1 and the rigid frame of Fig. 2 are shown in Fig. 4 and 5 respectively.

Fig. 3 Line Diagram of Bridge and Connection

Fig. 4 Line Diagram of Multi-storeyed Building

Connections

Two types of connections are commonly used to join members of structures: rigid connections and flexible or hinged connections. A rigid connection or joint prevents relative translations and rotations of the member ends connected to it; that is, all member ends connected to a rigid joint have the same translation and rotation. In other words, the original angles between the members intersecting at a rigid joint are maintained after the structure has deformed under the action of loads. Such joints are capable of transmitting forces as well as moments between the connected members. Rigid joints are usually represented by points at the intersections of members on the line diagram of the structure, as shown in Fig. 3.

A hinged connection or joint prevents only relative translations of member ends connected to it; that is, all member ends connected to a hinged joint have the same translation but may have different rotations. Such joints are thus capable of transmitting forces but not moments between the connected members. Hinged joints are usually depicted by small circles at the intersections of members on the line diagram of the structure.

The perfectly rigid connections and the perfectly flexible frictionless hinges used in the analysis are merely idealizations of the actual connections, which are seldom perfectly rigid or perfectly flexible. However, actual bolted or welded connections are purposely designed to behave like the idealized cases. For example, the connections of trusses are designed with the centroidal axes of the members concurrent at a point to avoid eccentricities that may cause bending of members. For such cases, the analysis based on the idealized connections and supports generally yields satisfactory results.

Supports

Supports for plane structures are commonly idealized as either fixed supports- which do not allow any movement; hinged supports - which can prevent translation but permit rotation; roller or link - supports which can prevent translation in only one direction.

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Tests on Bricks

I) Field Tests on Bricks

The field test on bricks gives an idea about its basic quality based on its shape, size and colour at first observation without any big appliances. They are very common and easiest way to check the quality of brick. Field tests of brick are very helpful on the site. Some very common tests of brick that is followed to find if brick is good at first observation are as follows.

1) Shape and Size

The clay bricks should have a uniform rectangular plane surface, as per standard size and sharp straight edges. BIS recommends the standard size of brick is 190 x 90 x 90 mm and constructional size is 200 x 100 x 100 mm.

2) Visual Inspection

In this test, bricks are closely inspected for its shape. The bricks of good quality should be uniform in shape and should have truly rectangular shape with sharp edges.

3) Hardness

The clay bricks should be sufficiently hard when scratched by a finger-nail and no impression should be left on the brick surface.

4) Colour

The clay bricks should have a uniform deep red colour throughout. It indicates the uniformity of chemical composition and the quality of burning of the bricks.

5) Texture and Compactness

The surfaces should not be so smooth to cause skidding of mortar. The clay brick should have a pre-compact, homogeneous and uniform texture. A broken surface should be free form cracks, holes grits or lumps of lime.

6) Soundness

When two clay bricks are stuck together, a metallic ringing sound should come.

7) Structure

A brick is broken and its structure is examined. It should be homogeneous, compact and free from any defects such as holes, lumps etc.

8) Basic Strength

When dropped flat on the hard ground from a height of about one meter, clay bricks should not break.

II) Laboratory Tests on Bricks

Laboratory tests on brick determine the mechanical properties of brick and give a scientific approach to ensure the quality of bricks. It is essential while purchasing the brick and examine the properties for the quality of construction. Followings brick tests are performed in the laboratory to determine the quality of brick.

1) Water Absorption of Brick

The brick is porous by nature and Porosity is the ability to release and absorb moisture. Therefore, it tends to absorb the water or moisture. It’s an important and useful property of brick. But if brick absorbs more water than the recommended result, then it affects the strength of brick as well as durability of the structure and will damage plaster and paint over walls. Dry bricks are put in an oven at a temperature of 105° to 115°C till these attain constant mass. The weight (W1) of the bricks is recorded after cooling them to room temperature. The bricks are then immersed in water at a temperature of 27° ± 2°C for 24 hours. The specimens are then taken out of water and wiped with a damp cloth. Three minutes later it is weighed again and recorded as W2.

Water absorption test is performed to know the percentage of water absorption of bricks. Water absorption of bricks should not more than 20% by its dry weight. If brick fails in the water absorption test, possible reasons are like manufacturing error, insufficient burning, error in clay composition etc. If brick fails in water absorption as well as efflorescence than never use those bricks because it will cause in permanent problems and it will be very difficult to solve them. Water bath, weight balance and oven are required for performing this test.

2. Compressive Strength of Brick

The compressive strength of the brick is the most essential property of the bricks because in the construction, bricks are widely used in masonry and it also plays a significant role as a load bearing component. When bricks are used in any structure, the bottom-most layer of the brick will be subjected to the highest compressive stress. Therefore, it is essential to know that any particular brick will be able to withstand that load or not. This test is performed to know the strength of bricks because it affects the overall structure in the way of quality, durability and serviceability.

For testing bricks for compressive strength from a sample the two bed faces of bricks are ground to provide smooth, even and parallel faces. The bricks are then immersed in water at room temperature for 24 hours. These are then taken out of water and surplus water on the surfaces is wiped off with cotton or a moist cloth. The frog of the brick is flushed level with cement mortar and the brick is stored under damp jute bags for 24 hours followed by its immersion in water at room temperature for three days. The specimen is placed in the compression testing machine with flat faces horizontal and mortar filled face being upwards. Load is applied at a uniform rate of 14 N/m² per minute till failure. The maximum load at failure divided by the average area of bed face gives the compressive strength.

Recommended Result of Compressive Strength Test of Brick

Test result recommendations are as follows.

• For first class bricks, it should not less than 10 N/mm² (102 kg/cm²).
• For second class bricks, it should not less than 7 N/mm² (71 kg/cm²).
• For third class bricks, it should not less than 3.5 N/mm² (36 kg/cm²).

In India, the northern and the eastern region produce bricks having good compressive strength than the western region because the western region has black cotton soil, while the soil is good in Gangetic region. If the test result is not as per recommendation, there are many reasons behind it such as the clay composition, degree of burning like over burning or insufficient burning, error in the testing appliance or testing procedure etc. If bricks fail in strength as well as water absorption test, then do not use it. If bricks are irregular in some minor shape/size than it can be corrected with mortar.

3) Efflorescence Test

This test should be conducted in a well-ventilated room. The brick is placed vertically in a dish 30 x 20 cm approximately in size with 2.5 cm immersed in distilled water. The whole water is allowed to be absorbed by the brick and evaporated through it. After the bricks appear dry, a similar quantity of water is placed in the dish and the water is allowed to evaporate as before. The brick is to be examined after the second evaporation and reported as follows.

• Nil : When there is no perceptible deposit of salt
• Slight : When not more than 10% of the area of brick is covered with salt
• Moderate : When there is heavy deposit covering 50% of the area of the brick but unaccompanied by powdering or flaking of the surface.
• Heavy : When there is heavy deposit covering more than 50% of the area of the brick accompanied by powdering or flaking of the surface.
• Serious : When there is heavy deposit of salts accompanied by powdering and/or flaking of the surface and this deposition tends to increase in the repeated wetting of the specimen.

Bricks for general construction should not have more than slight to moderate efflorescence.

4) Dimension Tolerance

Twenty bricks are selected at random to check measurement of length, width and height. These dimensions are to be measured in one or two lots of ten each as shown in Fig. 1. Variation in dimensions is allowed only within narrow limits, ±3% for class one and ±8% for other classes.

Fig. 1

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Classification of Structures

The most important decision made by a structural engineer in implementing an engineering project is the selection of the type of structure to be used for supporting or transmitting loads. Commonly used structures can be classified into five basic categories, depending on the type of primary stresses that may develop in their members under major design loads. It should be realized that any two or more of the basic structural types described in the following may be combined in a single structure, such as a building or a bridge, to meet the structure’s functional requirements. The different type of structures is given below.

1) Tension Structures

The members of tension structures are subjected to pure tension under the action of external loads. Because the tensile stress is distributed uniformly over the cross-sectional areas of members, the material of such a structure is utilized in the most efficient manner. Tension structures composed of flexible steel cables are frequently employed to support bridges and long- span roofs. Because of their flexibility, cables have negligible bending stiffness and can develop only tension. Thus, under external loads, a cable adopts a shape that enables it to support the load by tensile forces alone. In other words, the shape of a cable changes as the loads acting on it change. As an example, the shapes that a single cable may assume under two different loading conditions are shown in Fig. 1.

Fig. 1

Fig. 2 shows the cable structure of the suspension bridge. In a suspension bridge, the roadway is suspended from two main cables by means of vertical hangers. The main cables pass over a pair of towers and are anchored into solid rock or a concrete foundation at their ends. Because suspension bridges and other cable structures lack stiffness in lateral directions, they are susceptible to wind-induced oscillations. Bracing or stiffening systems are therefore provided to reduce such oscillations. Besides cable structures, other examples of tension structures include vertical rods used as hangers (for example, to support balconies or tanks) and membrane structures such as tents and roofs of large-span domes.

Fig. 2 Suspension Bridge

2) Compression Structures

Compression structures develop mainly compressive stresses under the action of external loads. Two common examples of such structures are columns and arches (Fig. 3). Columns are straight members subjected to axially compressive loads, as shown in Fig. 3. When a straight member is subjected to lateral loads and/or moments in addition to axial loads, it is called a beam-column.

Fig. 3 Column

An arch is a curved structure, with a shape similar to that of an inverted cable, as shown in Fig. 4. Such structures are frequently used to support bridges and long-span roofs. Arches develop mainly compressive stresses when subjected to loads and are usually designed so that they will develop only compression under a major design loading. However, because arches are rigid and cannot change their shapes as can cable, other loading conditions usually produce secondary bending and shear stresses in these structures, which should be considered in their designs. Because compression structures are susceptible to buckling or instability, the possibility of such a failure should be considered in their designs; if necessary, adequate bracing must be provided to avoid such failures.

Fig. 4 Arch

3) Trusses

Trusses are composed of straight members connected at their ends by hinged connections to form a stable configuration (Fig. 5). When the loads are applied to a truss only at the joints, its members either elongate or shorten. Thus, the members of an ideal truss are always either in uniform tension or in uniform compression. Real trusses are usually constructed by connecting members to gusset plates by bolted or welded connections. Although the rigid joints thus formed cause some bending in the members of a truss when it is loaded, in most cases such secondary bending stresses are small and the assumption of hinged joints yields satisfactory designs.

Because of their light weight and high strength, trusses are the most commonly used types of structures. Such structures are used in a variety of applications, ranging from supporting roofs of buildings to serving as support structures in space stations and sports arenas.

Fig. 5 Plane Truss

4) Shear Structures

Shear structures, such as reinforced concrete shear walls (Fig. 6), are used in multistory buildings to reduce lateral movements due to wind loads and earthquake excitations. Shear structures develop mainly in-plane shear, with relatively small bending stresses under the action of external loads.

Fig. 6 Shear Wall

5) Bending Structures

Bending structures develop mainly bending stresses under the action of external loads. In some structures, the shear stresses associated with the changes in bending moments may also be significant and should be considered in their designs. Some of the most commonly used structures such as beams, rigid frames, slabs and plates, can be classified as bending structures. A beam is a straight member that is loaded perpendicular to its longitudinal a𝑥is. The bending (normal) stress varies linearly over the depth of a beam from the maximum compressive stress at the fiber farthest from the neutral axis on the concave side of the bent beam to the maximum tensile stress at the outermost fiber on the convex side.

For example, in the case of a horizontal beam subjected to a vertically downward load, as shown in Fig. 7, the bending stress varies from the maximum compressive stress at the top edge to the maximum tensile stress at the bottom edge of the beam. To utilize the material of a beam cross section most efficiently under this varying stress distribution, the cross sections of beams are often I-shaped, with most of the material in the top and bottom flanges. The I-shaped cross sections are most effective in resisting bending moments.

Fig. 7 Beam

Rigid frames are composed of straight members connected together either by rigid (moment-resisting) connections or by hinged connections to form stable configurations. Unlike trusses, which are subjected only to joint loads, the external loads on frames may be applied on the members as well as on the joints. The members of a rigid frame are subjected to bending moment, shear and axial compression or tension under the action of external loads. The design of horizontal members or beams of rectangular frames is often governed by bending and shear stresses only, since the axial forces in such members are usually small.

Frames, like trusses, are among the most commonly used types of structures. Structural steel and reinforced concrete frames are commonly used in multistory buildings, bridges and industrial plants. Frames are also used as supporting structures in airplanes, ships, aerospace vehicles and other aerospace and mechanical applications. The generic term framed structure is frequently used to refer to any structure composed of straight members, including a truss.

Fig. 8 Rigid Frame

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Manufacturing of Bricks

The following operations are involved in the manufacturing of brick.

I) Preparation of Clay

The preparation of clay involves following operations.

a) Unsoiling

The soil used for making building bricks should be processed so as to be free of gravel, coarse sand (practical size more than 2 mm), lime and kankar particles, organic matter, etc. About 20 cm of the top layer of the earth, normally containing stones, pebbles, gravel, roots, etc. is removed after clearing the trees and vegetation.

b) Digging

Clay dug out from ground is spread on level ground about 60 to 120 cm heaps. After removing the top layer of the earth, proportions of additives such as fly ash, sandy loam, rice husk ash, stone dust etc. should be spread over the plane ground surface on volume basis. The soil mass is then manually excavated, puddled, watered and left over for weathering and subsequent processing. The digging operation should be done before rains.

c) Cleaning

Stones, pebbles, vegetable matter etc. should be removed from soil.

d) Weathering

Clay is exposed to atmosphere from few weeks to full season. Stones, gravels, pebbles, roots, etc. are removed from the dug earth and the soil is heaped on level ground in layers of 60 -120 cm. The soil is left in heaps and exposed to weather for at least one month in cases where such weathering is considered necessary for the soil. This is done to develop homogeneity in the mass of soil, particularly if they are from different sources and also to eliminate the impurities which get oxidized. Soluble salts in the clay would also be eroded by rain to some extent, which otherwise could have caused scumming at the time of burning of the bricks in the kiln. The soil should be turned over at least twice and it should be ensured that the entire soil is wet throughout the period of weathering. In order to keep it wet, water may be sprayed as often as necessary. The plasticity and strength of the clay are improved by exposing the clay to weather.

e) Blending

Clay is made loose and any ingredient to be added to it is spread out at top and turning it up and down in vertical direction. The earth is mixed with sandy earth and calcareous earth in suitable proportions to modify the composition of soil. Moderate amount of water is mixed so as to obtain the right consistency for moulding. The mass is then mixed uniformly with spades. Addition of water to the soil at the dumps is necessary for the easy mixing and workability, but the addition of water should be controlled in such a way that it may not create a problem in moulding and drying. Excessive moisture content may affect the size and shape of the finished brick.

f) Tempering

Clay is brought to a proper degree of hardness, then water is added to clay and whole mass is kneaded or pressed under the feet of men or cattle for large scale. Tempering is usually done in pug mill. Tempering consists of kneading the earth with feet so as to make the mass stiff and plastic (plasticity means the property which wet clay has of being permanently deformed without cracking). It should preferably be carried out by storing the soil in a cool place in layers of about 30 cm thickness for not less than 36 hours. This will ensure homogeneity in the mass of clay for subsequent processing.

Pug mill consists of a conical iron tube as shown in Fig. 1. The mill is sunk 60 cm into the earth. A vertical shaft, with a number of horizontal arms fitted with knives, is provided at the centre of the tube. This central shaft is rotated with the help of bullocks yoked at the end of long arms. Steam, diesel or electric power may be used for this purpose. Blended earth along with required water, is fed into the pug mill from the top. The knives cut through the clay and break all the clods or lump clays when the shaft rotates. The thoroughly pugged clay is then taken out from opening provided in the side near the bottom. The yield from a pug mill is about 1500 bricks.

Fig. 1 Pug Mill

II) Moulding

Clay, which is prepared form pug mill is sent for the next operation of moulding. It is a process of giving a required shape to the brick from the prepared brick earth. Moulding may be carried out by hand or by machines. The process of moulding of bricks may be the soft-mud (hand moulding), the stiff-mud (machine moulding) or the dry-press process (moulding using maximum 10 per cent water and forming bricks at higher pressures). Fire-brick is made by the soft mud process. Roofing, floor and wall tiles are made by dry-press method. The stiff-mud process is used for making all the structural clay products.

Fig. 2 Details of Mould

1) Hand Moulding

Moulds are rectangular boxes of wood or steel, which are open at top and bottom. Steel moulds are more durable and used for manufacturing bricks on large scale. Bricks prepared by hand moulding are of two types.

a) Ground Moulding

In this process, the ground is levelled and sand is sprinkled on it. The moulded bricks are left on the ground for drying. Such bricks do not have frog and the lower brick surface becomes too rough. To overcome these defects, moulding blocks or boards are used at the base of the mould. The process consists of shaping in hands a lump of well pugged earth, slightly more than that of the brick volume. It is then rolled into the sand and with a jerk it is dashed into the mould. The moulder then gives blows with his fists and presses the earth properly in the corners of the mould with his thumb. The surplus clay on the top surface is removed with a sharp edge metal plate called strike or with a thin wire stretched over the mould. After this the mould is given a gentle slope and is lifted leaving the brick on the ground to dry.

This method is adopted when a large and level land is available. To prevent the moulded brick from sticking to the side of the mould, sand is sprinkled on the inner sides of the mould, or the mould may be dipped in water every time before moulding is done. The bricks so produced are respectively called sand moulded and slop moulded bricks, the former being better since they provide sufficient rough surface necessary for achieving a good bond between bricks and mortar.

Fig. 3 Type of Strikes

b) Table Moulding

The bricks are moulded on stock boards nailed on the moulding table. Process of moulding these bricks is just similar to ground bricks on a table of size about 2m x 1m. Stock boards have the projection for forming the frog. The process of filling clay in the mould is the same as explained above. After this, a thin board called pallet is placed over the mould. The mould containing the brick is then smartly lifted off the stock board and inverted so that the moulded clay along with the mould rests on the pallet. The mould is then removed as explained before and the brick is carried to the drying site.

Fig. 4 Table Moulding

Fig. 6 Stock Board

2) Machine Moulding

This method proves to be economical when bricks in huge quantity are to be manufactured at the same spot. It is also helpful for moulding hard and string clay. These machines are broadly classified in two categories.

a) Plastic Clay Machines

This machine containing rectangular opening of size equal to length and width of a brick. Pugged clay is placed in the machine and as it comes out through the opening, it is cut into strips by wires fixed in frames, so these bricks are called wire cut bricks. This is a quick and economical process.

b) Dry Clay Machines

In these machines, strong clay is first converted into powder form and then water is added to form a stiff plastic paste. Such paste is placed in mould and pressed by machine to form hard and well-shaped bricks. These bricks have well behaviour than ordinary hand moulded bricks. They carry distinct frogs and exhibit uniform texture. These are burnt carefully as they are likely to crack.

III) Drying

Green bricks contain about 7–30% moisture depending upon the method of manufacture. The object of drying is to remove the moisture to control the shrinkage and save fuel and time during burning. The drying shrinkage is dependent upon pore spaces within the clay and the mixing water. The addition of sand or ground burnt clay reduces shrinkage, increases porosity and facilities drying. The moisture content is brought down to about 3 percent under exposed conditions within three to four days. Thus, the strength of the green bricks is increased and the bricks can be handled safely.

Clay products can be dried in open air driers or in artificial driers. The artificial driers are of two types, the hot floor drier and the tunnel drier. In the former, heat is applied by a furnance placed at one end of the drier or by exhaust steam from the engine used to furnish power and is used for fire bricks, clay pipes and terracotta. Tunnel driers are heated by fuels underneath, by steam pipes or by hot air from cooling kilns. They are more economical than floor driers. In artificial driers, temperature rarely exceeds 120°C. The time varies from one to three days. In developing countries, bricks are normally dried in natural open air driers. They are stacked on raised ground and are protected from bad weather and direct sunlight. A gap of about 1.0 m is left in the adjacent layers of the stacks so as to allow free movement for the workers. The drying of brick is by the following means.

i) Natural Drying – usually about 3 to 10 days to bricks to become dry under sunlight.

ii) Artificial Drying – drying by tunnels usually 120⁰C about 1 to 3 days.

Fig. 7 Method of Drying Bricks

IV) Burning

This is very important operation in the manufacturing of bricks to impart hardness, strength and makes them dense and durable. The burning of clay may be divided into three main stages.

a) Dehydration (400 – 650ºC)

This is also known as water smoking stage. During dehydration,

• The water which has been retained in the pores of the clay after drying is driven off and the clay loses its plasticity
• Some of the carbonaceous matter is burnt
• A portion of sulphur is distilled from pyrites
• Hydrous minerals like ferric hydroxide are dehydrated
• The carbonate minerals are more or less decarbonated

Too rapid heating causes cracking or bursting of the bricks. On the other hand, if alkali is contained in the clay or sulphur is present in large amount in the coal, too slow heating of clay produces a scum on the surface of the bricks.

b) Oxidation Period (650 – 900ºC)

During the oxidation period, remainder of carbon is eliminated and the ferrous iron is oxidized to the ferric form. The removal of sulphur is completed only after the carbon has been eliminated. Sulphur on account of its affinity for oxygen, also holds back the oxidation of iron. Consequently, in order to avoid black or spongy cores, oxidation must proceed at such a rate which will allow these changes to occur before the heat becomes sufficient to soften the clay and close its pore. Sand is often added to the raw clay to produce a more open structure and thus provide escape of gases generated in burning.

c) Vitrification

To convert the mass into glass like substance, the temperature ranges from 900 – 1100°C for low melting clay and 1000 – 1250°C for high melting clay. Great care is required in cooling the bricks below the cherry red heat in order to avoid checking and cracking. Vitrification period may further be divided into

i) Incipient Vitrification

It is the stage at which the clay has softened sufficiently to cause adherence but not enough to close the pores or cause loss of space—on cooling the material cannot be scratched by the knife.

ii) Complete Vitrification

The stage at which more or less well-marked by maximum shrinkage.

iii) Viscous Vitrification

This stage produced by a further increase in temperature which results in a soft molten mass, a gradual loss in shape, and a glassy structure after cooling. Generally, clay products are vitrified to the point of viscosity. However, paving bricks are burnt to the stage of complete vitrification to achieve maximum hardness as well as toughness.

Burning of bricks is done either in clamps or in kilns. Clamps are temporary structures and they are adopted to manufacture bricks on small scale. Kilns are permanent structures and they are adopted to manufacture bricks on a large scale.

a) Burning in Clamp ox Pazawah

A typical clamp is shown in Fig. 8. The bricks and fuel are placed in alternate layers. The amount of fuel is reduced successively in the top layers. Each brick tier consists of 4–5 layers of bricks. Some space is left between bricks for free circulation of hot gasses. The total height of clamp in alternate layers of brick is about 3 to 4 m. After 30 per cent loading of the clamp, the fuel in the lowest layer is fired and the remaining loading of bricks and fuel is carried out hurriedly. The top and sides of the clamp are plastered with mud. Then a coat of cow dung is given, which prevents the escape of heat. The production of bricks is 2–3 lacs and the process is completed in six months. This process yields about 60 per cent first class bricks.

Fig. 8 Clamp

Advantages

• The bricks produced are tough and strong because burning and cooling are gradual
• Burning in clamps proves to be cheap and economical
• No skilled labour and supervision are required for the construction of clamps
• There is considerable saving of clamps fuel

Disadvantages

• Bricks are not of required shape
• It is very slow process
• It is not possible to regulate fire in a clamp
• Quality of brick is not uniform

b) Kiln Burning

The kiln used for burning bricks may be underground, e.g. Bull’s trench kiln or overground, e.g. Hoffman’s kiln. These may be rectangular, circular or oval in shape. When the process of burning bricks is continuous, the kiln is known as continuous kiln, e.g. Bull’s trench and Hoffman’s kilns. On the other hand, if the process of burning bricks is discontinuous, the kiln is known as intermittent kiln. The different types of kiln are explained below.

i) Intermittent kiln

The example of this type of an over ground and rectangular kiln. After loading the kiln, it is fired, cooled and unloaded and then the next loading is done. Since the walls and sides get cooled during reloading and are to be heated again during next firing, there is wastage of fuel. Bricks manufactured by intermittent up drought kilns are better than those prepared by clamps. But, bricks burnt by this process is not uniform. Intermittent kiln is of two types.

Fig. 9 Intermittent Kiln

a) Intermittent Up-Draught Kiln

This is in the form of rectangular with thick outside walls. Wide doors are provided at each end for loading and unloading of kilns. A temporary roof may be installed to protect from rain and it is removed after kiln is fired. Flues are provided to carry flames or hot gases through the body of kiln. The stages are given below.

1. Raw bricks are laid in row of thickness equal to 2 to 3 bricks and height 6 to 8 bricks with 2 bricks spacing between rows
2. Fuels are filled with brush wood which takes up a fire easily
3. Loading of kiln with raw bricks with top course is finished with flat bricks and other courses are formed by placing bricks on edges
4. Each door is built up with dry bricks and are covered with mud or clay
5. The kiln is then fired for a period of 48 to 60 hours draught rises in the upward direction from bottom of kiln and brings about the burning of bricks.
6. Kiln is allowed to cool down and bricks are then taken out
7. Same procedure is repeated for the next burning

b) Intermittent Down-Draught Kiln

These kilns are rectangular or circular in shape. They are provided with permanent walls and closed tight roof. Floor of the kiln has opening which are connected to a common chimney stack through flues. Working is same as up-draught kiln. But it is so arranged in this kiln that hot gases are carried through vertical flues upto the level of roof and they are then released. These hot gases move downward by the chimney draught and in doing so, they burn the bricks.

ii) Continuous Kiln

These kilns are continuous in operations. This means that loading, firing, cooling and unloading are carried out simultaneously in these kilns. The examples of continuous kiln are Hoffman’s kiln and Bull’s trench kiln. In a continuous kiln, bricks are stacked in various chambers wherein the bricks undergo different treatments at the same time. When the bricks in one of the chambers is fired, the bricks in the next set of chambers are dried and preheated while bricks in the other set of chambers are loaded and in the last are cooled. There are three types of continuous kilns.

a) Bull’s Trench Kiln

This kiln may be of rectangular, circular or oval shape in the plan as shown in Fig 10. It is constructed in a trench excavated in ground either fully underground or partially projecting above ground openings is provided in the outer walls to act as flue holes. Dampers are in the form of iron plates and they are used to divide the kilns in suitable sections and it is the most widely used kiln in India.

The bricks are arranged in such a way that flues are formed. Fuel is placed in flues and it is ignited through flue holes after covering top surface with earth and ashes to prevent the escape of heat. Usually, two movable iron chimneys are employed to form draught. These chimneys are placed in advance of section being fired. Hence, hot gases leaving the chimney warm up the bricks in next section. Each section requires about one day to burn. The tentative arrangement for different sections as shown in Fig. 10 may be as follows

   Section 1 – Loading

   Section 2 – Emptying

   Section 3 – Unloading

   Section 4 – Cooling

   Section 5 – Burning

   Section 6 – Heating

Fig 10 Bull’s Trench Kiln

b) Hoffman’s Kiln

This kiln is constructed over ground and hence, it is sometimes known as flame kiln. Its shape is circular to plan and it is divided into a number of compartments or chambers. A permanent roof is provided; the kiln can even function during rainy season. Fig.11 shows plan and section of Hoffman’s kiln with 12 chambers

   Chamber 1 - Loading

   Chamber 2 to 5 – Drying and Pre-Heating

   Chambers 6 and 7 - Burning

   Chambers 8 to 11 - Cooling

   Chamber 12 – Unloading

The initial cost in stalling this kiln is high. The advantages of Hoffman’s kiln are given below.

• Good quality of bricks are produced
• It is possible to regulate heat inside the chambers through fuel holes
• Supply of bricks is continuous and regular
• There is considerable saving in fuel due to pre heating of raw bricks by flue gases

Fig.11 Hoffman’s Kiln

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