Save this PDF as: Download "Version 2 CE IIT, Kharagpur". Error: (a). Ths the loads shown Version CE IIT, Kharagr. 2 in Fig. (c) are the eqivalent joint. Version 2 CE IIT, Kharagpur notes for is made by best teachers who have written You can download Free Version 2 CE IIT, Kharagpur pdf from EduRev by. Syllabus · Lectures · Downloads; FAQ. Course Co-ordinated by: IIT Kharagpur Module Name, Download, Description, Download Size. Energy methods in structural analysis, General Introduction, PDF, kb. Energy methods in structural.

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Course Co-ordinated by: IIT Kharagpur Module Name, Download, Description, Download Size. Objectives and Methods of Analysis and Design, and Properties of Concrete and Steel, Objectives and Methods of Analysis and Design, PDF. (b)) members be oriented in any direction. In this case, there is no restriction of how loads are applied on the space frame. Version 2 CE IIT, Kharagpur. Module 6 MANAGEMENT OF WATER RESOURCES Version 2 CE IIT, Kharagpur LESSON 3 REMOTE SENSING AND GIS FOR WATER RESOURCE.

Strctre may be classified into rigid and deformable strctres deending on change in geometry of the strctre while sorting the load. Beams trsses and frames are examles of rigid strctres. Unlike rigid strctres, deformable strctres ndergo changes in their shae according to externally alied loads.

However, it shold be noted that deformations are still small. Cables and fabric strctres are deformable strctres. Cables are mainly sed to sort ssension roofs, bridges and cable car system. They are also sed in electrical transmission lines and for strctres sorting radio antennas. In the following sections, cables sbjected to concentrated load and cables sbjected to niform loads are considered.

Version CE IIT, Kharagr 63 The shae assmed by a roe or a chain with no stiffness nder the action of external loads when hng from two sorts is known as a fniclar shae.

Cable is a fniclar strctre. It is easy to visalize that a cable hng from two sorts sbjected to external load mst be in tension vide Fig.. Now let s modify or definition of cable. A cable may be defined as the strctre in re tension having the fniclar shae of the load. Cable sbjected to Concentrated oads As stated earlier, the cables are considered to be erfectly flexible no flexral stiffness and inextensible. As they are flexible they do not resist shear force and bending moment.

It is sbjected to axial tension only and it is always acting tangential to the cable at any oint along the length. If the weight of the cable is negligible as comared with the externally alied loads then its self weight is neglected in the analysis.

In the resent analysis self weight is not considered. The for reaction comonents at A andb, cable tensions in each of the for segments and three sag vales: a total of eleven nknown qantities are to be determined. For examle, if one of the sag is given then the roblem can be solved easily. Otherwise if the total length of the cable S is given then the reqired eqation may be written as hc hd hc hd he h he S.

Cable sbjected to niform load. Cables are sed to sort the dead weight and live loads of the bridge decks having long sans. The bridge decks are ssended from the cable sing the hangers. The stiffened deck revents the sorting cable from changing its shae by distribting the live load moving over it, for a longer length of cable.

In sch cases cable is assmed to be niformly loaded. Consider a free body diagram of the cable as shown in Fig. As the cable is niformly loaded, the tension in the cable changes continosly along the cable length.

The sloes of the cable at m and n are denoted by and resectively. Alying eqations of eqilibrim, we get Fy T sin T T sin q x. Integrating eqation. Hence, T sin q x. Now the tension in the cable may be evalated from eqations. De to niformly distribted load, the cable takes a arabolic shae. However de to its own dead weight it takes a shae of a catenary. However dead weight of the cable is neglected in the resent analysis. Determine reaction comonents at A and B, tension in the cable and the sag y B, andy E of the cable shown in Fig..

Neglect the self weight of the cable in the analysis.

• determine the shear force of two-way slabs subjected to uniformly

Now horizontal reaction H may be evalated taking moment abot oint forces left ofc. M B, we get Similarly, 8 y D. To determine the tension in the cable in the segmentab, consider the eqilibrim of joint A vide Fig.. The tension T ab F T cos H x ab ab.. See Fig..

Segment de T de The tension Tcd coscd. A cable of niform cross section is sed to san a distance of m as shown in Fig.. The left sort is below the right sort by m and the lowest oint on the cable C is located below left sort by m. Evalate the reactions and the maximm and minimm vales of tension in the cable.

Using eqation. From eqations and, one cold evalate the vale ofx. Ths, x x x. The maximm cable tension occrs at Band the minimm cable tension occrs dy atc where andtc H 7. A cable of niform cross section is sed to sort the loading shown in Fig..

Module 3. Irrigation Engineering Principles. Version 2 CE IIT, Kharagpur

Determine the reactions at two sorts and the nknown sag. Sbstitting the vale of y C in eqation , can be evalated. Hence, y C ay Smmary In this lesson, the cable is defined as the strctre in re tension having the fniclar shae of the load.

The rocedres to analyse cables carrying concentrated load and niformly distribted loads are develoed. A few nmerical examles are solved to show the alication of these methods to actal roblems. Define an arch.. Identify three-hinged, two-hinged and hingeless arches.. State advantages of arch constrction.. Analyse three-hinged arch.. Evalate horizontal thrst in three-hinged arch.. Introdction In case of beams sorting niformly distribted load, the maximm bending moment increases with the sqare of the san and hence they become neconomical for long san strctres.

In sch sitations arches cold be advantageosly emloyed, as they wold develo horizontal reactions, which in trn redce the design bending moment. For examle, in the case of a simly sorted beam shown in Fig.. Now consider a two hinged symmetrical arch of the same san and sbjected to similar loading as that of simly sorted beam.

The vertical reaction cold be calclated by eqations of statics. The horizontal reaction is determined by the method of least work. It is clear that the bending moment below the load is redced in the case of an arch as comared to a simly sorted beam. It is observed in the last lesson that, the cable takes the shae of the loading and this shae is termed as fniclar shae.

If an arch were constrcted in an inverted fniclar shae then it wold be sbjected to only comression for those loadings for which its shae is inverted fniclar. Since in ractice, the actal shae of the arch differs from the inverted fniclar shae or the loading differs from the one for which the arch is an inverted fniclar, arches are also sbjected to bending moment in addition to comression.

As arches are sbjected to comression, it mst be designed to resist bckling. Until the beginning of the th centry, arches and valts were commonly sed to san between walls, iers or other sorts. Now, arches are mainly sed in bridge constrction and doorways.

In earlier days arches were constrcted sing stones and bricks. In modern times they are being constrcted of reinforced concrete and steel. Arches sort load rimarily in comression. For examle in Fig. Conseqently bending moment is not redced.

It is imortant to areciate the oint that the definition of an arch is a strctral one, not geometrical.. Tye of arches There are mainly three tyes of arches that are commonly sed in ractice: three hinged arch, two-hinged arch and fixed-fixed arch. Two-hinged arch and fixed-fixed arch are statically indeterminate strctres. The indeterminate reactions are determined by the method of least work or by the flexibility matrix method.

In this lesson threehinged arch is discssed. Analysis of three-hinged arch In the case of three-hinged arch, we have three hinges: two at the sort and one at the crown ths making it statically determinate strctre. Consider a three hinged arch sbjected to a concentrated forcep as shown in Fig.. There are for reaction comonents in the three-hinged arch.

One more eqation is reqired in addition to three eqations of static eqilibrim for evalating the for reaction comonents. Taking moment abot the hinge of all the forces acting on either side of the hinge can set the reqired eqation. Taking moment of all the forces abot hingea, yields by P P.

P Fy ay. For a simly sorted beam of the same san and loading, moment nder the loading is given by, P M D. For the articlar case considered here, the arch constrction has redced the moment by.

A three-hinged arabolic arch of niform cross section has a san of m and a rise of m. Show that the bending moment is zero at any cross section of the arch.

The shear force at the mid san is zero. Bending moment The bending moment at any section x from the left end is, x Mx ayxhay Version CE IIT, Kharagr 84 The eqation of the three-hinged arabolic arch is y x x M x x x x x x x x x In other words a three hinged arabolic arch sbjected to niformly distribted load is not sbjected to bending moment at any cross section. It sorts the load in re comression. Can yo exlain why the moment is zero at all oints in a three-hinged arabolic arch?

A three-hinged semicirclar arch of niform cross section is loaded as shown in Fig. Calclate the location and magnitde of maximm bending moment in the arch. D and it can be calclated M 8H. A three-hinged arabolic arch is loaded as shown in Fig. Draw bending moment diagram. Soltion: eactions: Taking A as the origin, the eqation of the three-hinged arabolic arch is given by, y 8 8 x x Taking moment of all the forces abot hinge B leads to, ay 8 kn Version CE IIT, Kharagr 87 Fy by kn Now making se of the condition that, the moment at hinge C of all the forces left of hingec is zero gives, M c ay H 8 a H a 8 kn 8 Considering the horizontal eqilibrim of the arch gives, H kn b ocation of maximm bending moment Consider a section x from endb.

Moment at sectionx in art CB of the arch is given by lease note that B has been taken as the origin for this calclation , 8 8 Mx x x x x According to calcls, the necessary condition for extremm maximm or M minimm is that x.

Deisgn of 2 Way Slab NPTEL

Sbstitting the vale of x in eqation , the maximm bending moment is obtained. A three-hinged arabolic arch of constant cross section is sbjected to a niformly distribted load over a art of its san and a concentrated load of kn, as shown in Fig.. The dimensions of the arch are shown in the figre. Evalate the horizontal thrst and the maximm bending moment in the arch. The notations Mx, My, w, lx and ly are the same as mentioned below Eqs.

The detailing of reinforcing bars for the respective moments is explained in sec.

However, the effective span to effective depth ratio is different from those of one-way slabs. Accordingly, this item for the two-way slabs is explained below.

Effective span to effective depth ratio cl. While the bending moments and shear forces are computed from the coefficients given in Tables 12 and 13 cl. Further, the restrained two-way slabs need adequate torsional reinforcing bars at the corners to prevent them from lifting.

There are three types of corners having three different requirements. Accordingly, the determination of torsional reinforcement is discussed in Step 7, as all the other six steps are common for the one and two-way slabs.

The amount of reinforcement in each of the four layers shall be 75 per cent of the area required for the maximum mid- span moment in the slab. This provision is given in cl. Version 2 CE IIT, Kharagpur b At corner C2 contained by edges over one of which is continuous, the torsional reinforcement shall be half of the amount of a above. As mentioned in sec. The two methods are i employing Eq. Thereafter, Step 7 of sec. The detailing of torsional reinforcing bars is explained in Step 7 of sec.

In the following, the detailings of reinforcing bars for i restrained slabs and ii simply supported slabs are discussed separately for the bars either for the maximum positive or negative bending moments or to satisfy the requirement of minimum amount of steel. The maximum positive and negative moments per unit width of the slab calculated by employing Eqs. There shall be no redistribution of these moments.

The reinforcing bars so calculated from the maximum moments are to be placed satisfying the following stipulations of IS Bars marked as T1 and T4 in Figs. The bottom and top bars of the edge strips are explained below. The detailing of torsion bars at corners C1 and C2 is explained in Fig. The above explanation reveals that there are eighteen bars altogether comprising eight bottom bars B1 to B8 and ten top bars T1 to T Tables 8. For easy understanding, plan views in a and b of Fig.

Two sections and , however, present the bars shown in the two plans. Torsional reinforcements are not included in Tables 8. Table 8. Bars Into Along Resisting Cl. Clause D The remaining fifty per cent should extend to within 0. The spans shown in figure are effective spans. The corners of the slab are prevented from lifting. Solution of Problem 8. The total depth D is thus mm. However, this value needs to be modified by multiplying with k of cl.

The value of k for the total depth of slab as mm is 1. Step 5: Determination of areas of steel The respective areas of steel in middle and edge strips are to be determined employing Eq. However, in Problem 8. Accordingly, the areas of steel for this problem are computed from the respective Tables 40 and 41 of SP and presented in Table 8.

Table 40 of SP is for the effective depth of mm, while Table 41 of SP is for the effective depth of mm. Thus the characteristics of the reflectance of various earth features for different electromagnetic wavelength bands is used to identify different earth objects and are hence also known as Spectral Signatures.

A study of the spectral reflectance characteristics of natural earth surface features shows that the broad features are normally separable. In the following paragraphs, we discuss the spectral signatures of certain typical earth features, natural and artificial. Vegetation The spectral signature or reflectance of healthy green vegetation is as given in Figure 6.

In the visible range of electromagnetic wavelength spectrum, it has an absorption band in the blue and red parts because of the presence of chlorophyll. Even within the green part of the spectrum, only 10 to 15 percent of the incident light is reflected. The reflectance peak is seen to be at 0.

The reflectance property of healthy vegetation is seen to be much larger 40 percent or more in the infrared portion of the spectrum and is nearly constant from 0. In this range of electromagnetic spectrum, the reflectance variation is different for different plants and also between healthy vegetation and stressed vegetation. Hence, a reflectance measurement in this range permits one to discriminate between different species of vegetation, though this differentiation is not very apparent in the visible range of the spectrum.

Beyond 1. Soil The spectral signature of soil is simpler in soils compared to that by vegetation since all the incoming radiation is either reflected or absorbed due to very little transmittance. A typical reflectance curve for soil shows increase in wavelength in the visible and near- infrared regions Figure 6. The reflectance property of soil varies with soil moisture content, texture that is, the relative content of sand silt and clay that makes up the soil , surface roughness, colour, content of organic matter, presence of sesquioxides, etc.

In the visible portion of the spectrum, there is a distinct decrease in reflectance as moisture content increases, since more moisture in soil makes a soil appear darker causing less reflectance. Soil texture influences the spectral reflectance by the way of difference in moisture holding capacity and due to difference in the size of the particles.

Soils with higher organic matter appears as light brown to grayish in colour. The reflectance characteristics in the visible region of the electromagnetic spectrum has been observed to be inversely proportional to the organic matter content. The presence of iron oxide in soil also significantly reduces the reflectance, at least in the visible wavelength. Water For water resources engineer, locating areal extent of water bodies like lakes, rivers, ponds, etc.

The spectral response from a water body is complex, as water in any quantity is a medium that is semi-transparent to electromagnetic radiation. Electromagnetic radiation incident on water may be absorbed, scattered and transmitted.

The spectral response also varies according to the wavelength, the nature of the water surface calm or wavy , the angle of illumination and observation of reflected radiation from the surface and bottom of shallow water bodies. Pure clear water has a relatively high reflectance in the visible wavelength bands between 0. Thus clear water appears dark on an infrared image. Therefore, location and delineation of water bodies from remotely sensed data in the higher wave bands can be done very accurately.

Man-made structures Sometimes it is required to identify artificial structures that is useful to an engineer. For example roads, paved surfaces, canals, and even dams and barrages can be identified from remotely sensed images by their reflectance characteristics. Many of these, especially linear features, are clearly discernible in the visible waveband of electromagnetic spectrum.

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One of these, the Passive System, records the reflected electromagnetic energy of the earth, the source of the energy being the radiation of the Sun. The other, called the Active System, employs its self-generated pulses and records the reflected pulse. These two systems may be compared to taking photographs in sunlight and with flashlight respectively. The active remote sensing systems mostly use radars that emit radiation in the microwave band of the electromagnetic spectrum.

This system is useful in cases where passive systems do not give sufficient information. For example, images of flood inundated areas are important to a Water Resources Engineer. However, most of these images taken by the passive systems are blocked by cloud cover since incidents of floods are most common during the monsoons and are almost coincident with heavy cloudy days.

Radar based systems, on the other hand, are able to penetrate the cloud cover and give a clear picture of the flood inundation extent.

Version 2 CE IIT, Kharagpur The images recorded by a remote sensing sensor is a digital map of the scene that comprises of a regular grid array of squares, called pixels, with an unique value attached to each Figure 8. The value of each pixel is proportional to some property, like average reflectance, recorded by the sensor for the equivalent area on the ground. The pixel values normally range from 0 to For example, images recorded in the visible spectrum are usually a combination of three values for each pixel, one each for blue, green and red colours.

For each colour, the pixel has a value ranging from 0 to A pixel that records the image of a pure white area, will have the pixel values of all the three bands as For a pure black region, the three individual bands would have values of 0.

A blue looking area shall have the value for the image that records the blue colour, and 0 for green and red. Version 2 CE IIT, Kharagpur Similarly, sensors record pixel values in the infrared areas of the electromagnetic spectrum in passive systems and in the microwave areas in the active systems. The Indian Remote Sensing IRS satellites are, till now, equipped with active sensors that record images in four wave bands and others that record in a single wave band.

There are three sensors in these satellites, and each has its own characteristics, as given below.

This medium resolution sensor that records data in four spectral bands: Two in visible range 0. The spatial resolution, that is, the pixel size of the images are 23m for the first three bands and 69m in the last band. This is a high resolution 5. This is a coarse resolution m sensor operating in two bands: visible 0. Hence, primarily, the earth features have to be identified from MSS images based on the Spectral Reflectance characteristics or signatures of various objects as discussed in Section 6.

An MSS data of a region comprises of two or more images of the same area that has been scanned by the remote sensing sensor. For example, the LISS-III sensor shall give four images of the area corresponding to the four spectral bands in which the data is collected.

The DN varies from 0 to , and hence, each image may be printed or discussed in a gray-scale.

However, all the four images for a region printed or displayed in gray-tone may not be useful individually. Hence, a combined image is produced, called the False Colour Composite FCC image, which combines the characteristics of the images of all the four bands. An FCC image which simulates a colour infrared image, the visual interpretability of features is better than that from image of each band taken separately. Digital interpretation Visual image interpretation requires the person to have thorough knowledge of the features being identified and their spectral reflectance characteristics.

The technique is subject to human limitation. Hence, another technique — the Digital method of image interpretation — is often used in identifying earth surface features from remotely sensed images.

Infact, this comprises of a very important area, the details of which may be obtained in standard textbooks on Remote Sensing and Image Processing. Here only a brief account of the process is given below. Primarily, this is possible due to the fact that an image actually comprises of a number of pixels, each being assigned a Digital Number DN according to the average reflectance of the corresponding ground area in the particular spectral band.

Thus, an image is nothing but a matrix of DNs.

Computer algorithms are available in Image Processing Software Packages that make use of these numbers to identify the feature of land corresponding to each pixel. The numerical operations carried out on these digital images are grouped as follows: 1. Pre-processing: Removal of flawed data, correction of image.

Image enhancement: Improving images or image patches that suffer from low contrast between pixel DN values.Similarly and resectively are dislacements of ends k ' ' z y x,,,, j and k of the member in global co-ordinate system. A blue looking area shall have the value for the image that records the blue colour, and 0 for green and red. Using eqation. The Indian Remote Sensing IRS satellites are, till now, equipped with active sensors that record images in four wave bands and others that record in a single wave band.

During preliminary calculations, however, the weight of the foundationand backfill may be taken as 10 to 15 per cent of the total axial load on thefooting, subjected to verification afterwards. Alternatively, Annex D of IS can be employed to determine the bending moments in the two directions for two types of slabs: i restrained slabs, and ii simply supported slabs.

Further the height of the fall has to be decided, since it is possible to provide larger falls at longer intervals or smaller falls at shorter intervals. However, one cold se directly the eqation 7.

However,all types of soil get compressed significantly and cause the structure to settle. Version 2 CE IIT, Kharagpur Most of the sensors in remote sensing systems also operate in the wavelength regions in which the reflected energy predominates and thus the reflectance property of surfaces is very important.

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