Design of singly reinforced rectangular section for flexure
Singly reinforced Beam

Design of singly reinforced rectangular section for flexure

Learn : Design of singly reinforced rectangular section for flexure, factored moment, ultimate moment of resistance, limiting moment of resistance factor, fixing dimension of the section, Area of tension steel.   Design of singly reinforced rectangular section for flexure The design problem is generally of determining dimensions (cross-sectional) of a beam (b X D) and the area of steel for a known moment or load. The basic requirement for safety at the limit of collapse (flexure) is that the factored moment Msbecause of loads should not exceed the ultimate moment of resistance Mulim of the section and the failure should be ductile. 2188ed6a96dad6de04b0dfb5853df1bee74e3d92 therefore \[M_{u}\leq M_{u lim}\] Taking equality \[M_{u}= M_{u lim}\] \[=0.36f_{ck}.\frac {x_{umax}}{d}\left ( 1-\frac {0.42 x_{u max}}{d} \right )bd^{2}\] \[M_{u}=R_{u}bd^{2}\] For the given material i.e., grade of concrete and type of steel, Ru is constant and is called as limiting moment of resistance factor. \[R_{u}=0.36f_{ck}\frac {x_{u max}}{d}\left (…

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Basic rules for design of beams
Beam Design

Basic rules for design of beams

Learn About design of beams, effective span, effective depth, reinforcement, nominal cover to reinforcement, curtailment of tension reinforcement  BASIC RULES FOR DESIGN OF BEAMS While designing R.C.C. beams, following important rules must be kept in mind: Effective Span (CI. 22.2, IS 456) The effective span of the beams are taken as follows : (a) Simply Supported Beam or Slab The effective span of a simply supported beam or slab is taken as least of the following: (i) Clear span plus the effective depth of beam or slab. (ii)Centre to centre distance between supports. (b) Continuous Beam or Slab In case of continuous beam or slab if the width of the supports is less than \[\frac {1}{12} \]of the clear span, the effective span is taken as in (a). If the width of the support is greater than \[\frac {1}{12}\] of the clear span or 600 mm whichever is less, the…

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Density Index and relative compaction

Learn Density Index, relative compaction, density index and void ratio relationship,charectristics of granular soils in dense and loose states,Relative density Density Index The term density index ID or relative density or degree of density is used to express the relative compactness (or degree of compaction) of a natural cohesionless soil deposit. The density index is defined as the ratio of the difference between the voids ratio of the soil in its loosest state emax and its natural voids ratio e to the difference between the voids ratios in the loosest and densest states: \[I_{D} = \frac{e_{max}-e}{e_{max}-e_{min}}.                  (1)\] where emax = voids ratio in the loosest state emin = voids ratio in the densest state e = natural voids ratio of the deposit. This term is used for cohesionless soil only. This term is not applicable to cohesive soil because of uncertaintities in…

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Voids ratio porosity degree of saturation

Learn voids ratio, porosity, degree of saturation, percentage air voids, Air content Voids ratio. Voids ratio e of a given soil sample is the ratio of the volume of voids to the volume of soil solids in the given soil mass. \[e= \frac{V_{v}}{V_{s}}\] Porosity. The porosity n of a given soil sample is the ratio of the volume of voids to the total volume of the given soil mass \[n = \frac{V_{v}}{V}\] The voids ratio e is generally expressed as a fraction, while the porosity n is expressed as a percentage and is, therefore, also referred to as percentage voids. Figure (a) shows the soil element in terms of voids ratio e. If the volume of voids is taken equal to e, the volume of solids, by definition equation would be equal to 1, and the total volume equal to (1 + e). Similarly, if the volume of the voids…

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Absolute or true specific gravity

Learn specific gravity, Absolute or true specific gravity, Table of specific gravity of soil constituent Specific gravity  Specific gravity is defined as the ratio of the weight of a given volume of soil solids at a given temperature to the weight of an equal volume of distilled water at that temperature, both weights being taken in air. In other words, it is the ratio of the unit weight of soil solids to that of water. \[G = \frac{\gamma_{s}}{\gamma_{w}}\] The Indian Standard specifies 27°C as the standard temperature for reporting the specific gravity. Some qualifying words like: true, absolute, apparent, bulk or mass, etc., are sometimes added to the term ‘specific gravity’. These qualifying words modify the sense of specific gravity as to whether it refers to soil particles or to soil mass. The soil solids have permeable and impermeable voids inside them, the permeable voids being capable of getting filled with…

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unit weight of soil, bulk unit weight, dry unit weight, unit weight of solids

Learn unit weight of soil, bulk unit weight, dry unit weight, unit weight of solids, unit weight Unit weight of soil The unit weight of a soil mass is defined as its weight per unit volume. Bulk unit weight. The bulk weight or moist unit weight is the total weight W of a soil mass per unit of its total volume V.  \[\gamma = \frac{W}{V}\]  Dry unit weight. The dry unit weight is the weight of solids per unit of its total volume (prior to drying) of the soil mass: \[\gamma_{d} = \frac{W}{V_{d}}\] Unit weight of solids. The unit weight of soil solids is the weight of soil solids Wd per unit volume of solids (Vs): \[\gamma_{s} = \frac{W_{d}}{V_{s}} \] Thus, when the dry weight is reckoned with reference to the total original volume V, it is called the dry unit weight and when it is reckoned with reference to…

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Density of soil solids
Density of soil

Density of soil solids

Learn Density of soil, density of soil formula, density of soil definition, density of soil meaning, density of soil solids, bulk density, dry density, density of solids, saturated density, submerged density. Density of soil solids. The density of soil is defined as the mass of the soil per unit volume.  Bulk density. The bulk density or moist density is the total mass M of the soil per unit volume \[\rho = \frac {M}{V}\] It is expressed in terms of g/cm3 or kg/m3. Dry density The dry density is the mass of solids per unit of total volume (prior to drying) of the soil mass: \[\rho_{d} = \frac {M_{d}}{V}\] Density of solids  The density of soil solids is the mass of soil solids (Md) per unit of volume of solids (Vs): \[\rho_{s} = \frac {M_{d}}{V_{s}}\] Saturated density When the soil mass is saturated, its bulk density is called saturated density. Thus,…

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Water content formula of soil
soil as a three phase system

Water content formula of soil

Learn water content formula in a given mass of a soil  Water content formula . The water content formula w, also called the moisture content, is defined as the ratio of weight of water Ww to the weight of solids (Ws or Wd) in a given mass of soil. The water content  formula w is generally expressed as a percentage. However, when used in the formulae giving relationship between certain quantities, it may be expressed as a fraction   The usual procedure to find the natural water content is to take a mass of about 20 g to 30 g of soil sample in a container and determine its mass M very accurately. The soil sample is then kept in an oven (105°C–110°C) for about 24 hours so that it becomes perfectly dry. Its dry mass Md is then determined and the water content is calculated from the relation  …

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Soil as a three phase system
soil as a three phase system

Soil as a three phase system

A soil  as a three phase system consisting of solid particles (called soil grains), water and air. The void space between the soil grains is filled partly with water and partly with air. However, if we take a dry soil mass, the voids are filled with air only. In case of a perfectly saturated soil, the voids are filled completely with water. In general, the soil mass has three constituents which do not occupy separate spaces but are blended together forming a complex material [Fig.a)], the properties of which depend upon the relative percentages of these constituents, their arrangement and a variety of other factors. For calculation purposes, it is always more convenient to show these constituents occupying separate spaces, as shown in Fig.(b)(i) and Fig. (b)(ii). As shown in Fig.(b) (i), the total volume V of the soil mass consists of (i) volume of air Va, (ii) volume of water…

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The Term Soil
the term soil

The Term Soil

The Term Soil The term ‘Soil’ has various meanings, depending upon the general professional field in which it is being considered. To an agriculturist, soil is the substance existing on the earth’s surface, which grows and develops plant life. To the geologist also, soil is the material in the relatively thin surface zone within which roots occur, and all the rest of the crust is grouped under the term rock irrespective of its hardness. To an engineer, soil is the unaggregated or uncemented deposits of mineral and/or organic particles or fragments covering large portion of the earth’s crust. It includes widely different materials like boulders, sands, gravels, clays and silts, and the range in the particle sizes in a soil may extend from grains only a fraction of a micron (10–4 cm) in diameter up to large size boulders. Soil engineering, Soil Mechanics or Geotechnique is one of the youngest…

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