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Download RCC DESIGN - musicmarkup.infoA musicmarkup.info Reinforced Concrete Design: Principles and Practice By N. Krishna Raju, R.N. of Mysore and M.E. degree in Structures from the University of Bangalore. reinforced concrete musicmarkup.info - Ebook download as PDF File .pdf) or view Design of Reinforced Concrete Structures m.l Gambhir
Krishna Raju. PDF The second edition of the book was long overdue and is now presented incorporating the various changes required in the text matter in most of the chapters conforming to the revised Indian Standard Code IS : The new revised Indian Standard Code emphasizes the importance of Limit State Design Philosophy for reinforced concrete structures while the traditional working stress design is incorporated in the Annexure-B of the revised code. Consequently the design examples are presented according to the limit state design procedure enshrined in the code. Most of the chapters have been completely revised with examples based on the limit state design procedure. In addition the use of SP: 16 design charts and tables for rapid design of rein- forced concrete structures generally required in the design offices by structural engineers is also included in some of the typical design examples.
These are loads that change with respect to time. Live or imposed loads include the loads due to people occupying the floor and those due to mate- Balcony Balconies not liable to over-crowding' for class 2 loading -.
The imposed floor and roof loads loading for other classes 3. Office Iloors other than entrance hall floors of light work 2. Floors of banking halls, office entrance halls and reading 3. The 4. Floors of warehouses, workshops, lactories and other 5.
Assembly floor space without fixed seating, public rooms in hotels, dance halls and wailing halls. Wind Load 'F' acting in 'a direction normal to the individual structural eontd. Where '. Cpe;;; external pressure coefficient. Structnres subjected to snow loads'have to be designed suitably by consid- ering the snow loads prevailing in the region and also the various load 2,1 CONCRETE combinations. Concrete is a composite material composing of cement, aggregate -respectivel y.
Cement reacts'in tile presence of water to produce complex compounds which gradually harden and bonds the e Earth Quake Loads aggregate comprising sand and coarse aggregate into a solid mass with - Seismic or earthquake forces have to 'be considered in the d"esign of struc- time. Fresh concrete exhibits plastiCity and flowability so that it can be lUreS located in seismic zones according to IS: The horizontal placed iIlto the mouids of required shape and compacted to form a dense seismic force Feq is computed as, mass.
Thp compacted and hardened concrete is cUl'ed in the presence of F,. Where ex;: For a detailed study of the type and properties of different types from 1. Dead load above the section considercd.
In concrete, aggregate volume is nearly 75 percent of the total volume. Hence, thc'structural behavior of concrete is significantly influenced by the type of aggregates uscd. Fine agg'reg-ate comprises of sand dug out from riverbeds and pits having particle sizes from 0. Crushed rock and gravel are generally used as coarse aggregates with maximum size of 10 mm, 20 and 40 mm. For reinforced concrete work 10 and 20 mm ,are commonly used.
For mass concrete works like dams, larger sizes of aggregates upto mm are used. Lightweight and heavy weight aggregates are also used in specific works. The various: No Type of Cement IS: Marine Structures. Indian Standard Code: Table-9 o' IS: The design mix uses the following parameters: For compuration of load factor against cracking, knowledge 7 Grade of concrete of the flexurai strength is required.
According to IS: A critical review of the Indian, British and Modulus of elasticity of concrete which is significantly influenced by the American methods of concrete mix design has been reported by Krishna type of the aggregates used, type of cement and mix proportions is an Reddy" and the author. UC- the American and British methods resulted in concrete having compressive tural concrete members which forms an important Hmit state in the design strength nearly equal to the desired character;'tic strength while the Indian of concrete mcmbers.
In the absence of tcst data, the modulus of e. For eXh. Water content in which not more than 5 percent of the test results are expected to fall. The concrete significantly affects the shrinkage. The IS: Code rec- concrete mix should be designed for the target strength computed as, ommends the total shrinkage strain as 0. Shrinkage deviation of concrete also influences the deflections of reinforced concrete members. For The inelastic time dependent strain developed in a concrete member under Reinforced concrete, the minimum grade of concrete to be used is M In the absence of reliable experimental data.
Age al Loading Creep coefficient 2. Higher creep coefficient results in larger Minimum Maximum Minlmu'm Maximum deflections. C time dependent deflections in reinforced concrete members. M The coefficient of thermal expansion of concrete.
The values recommended in IS: Table 2. C;U '--'VI' Minimum grade for PCC under mild exposure conditions not speci- Aggregates com. Depending upon the ratio concentration of sulphate expressed as SO, ,different types of cements are.
The minimum cement content and the corresponding maximum free slag cement or 0. Many codes have provided for minimum cover requirements in. It is important to note the thickness of clear cOver and the phate resisting density of concrete in the protection to steel against corrosion and fire portland cement.
Portland pozzo- Super sulphated 0. In cement with pro- mineral acids, down to pH 3. ContreteDesign 4 The cerilent contents given in class 2 are tlie minimum recommended. Alternatively, a blend of ordinary Portland cement Resistance and slag may also be used provided sufficient information is available Beams Floors Ribs Columns on performance of such blended cements in these conditions. The Hours 0. In the 45 35 40 2. In the case. For footings of columns where the footing slab is in contact Over the years, Pllenomenar progress has been acnieved to produce con- with soil, the mihimum cover shall be 50 mm.
In , concrete grades specified periods of fire resistance varying from 0.
The dawn of 21st century has wit- in Table 2. Recent developments in' ditions, whi'ih include simply supported or continuous members. Fig 2. E various types of rolled steel sections. BuiJdhlgs and Materials 0'0!: J 20 strain percent Table 2. The modnlus of elasticity of steel of all grades is taken- as Monlreal Chicago Lake store Drive ,kNfmm'.
In general. Slabs IS: The maximum area of tension reinforcement shall not exceed 0. The compression reinforcement in beams shall be enclosed by stirrups IS: Beams IS: The maximum spacing of shear reinforcement should not exceed 'O. Columns with helical ties, at least six main longitudinal rein- for vertical 'stirrups and 'd' for inclined stirrups at where'd' is the forcements have to be provided within the helical.
The effective depth. The maximum spacing is restricted to mm. The pitch of helical reinforcement is Jimilcd 10 a maximum value of 75 mm and a minimum of 25 mm.. Helically reinforced Fig. Reinforced concrete columns are generally of square; rectangular. The working stress m'ethod is based 4 Diameter of Bars: Columns IS: By solving Eq. From the above relation we get Neutral axis depth factor. The neutral axis depth factor 'k' depends only on the permissible stresses Further when the section is subjected to external loading, resisting in concrete and steel 'ache and OS!
Moment of Resistance of the section is given by the relation. Hence, we have Substituting m. Elastic Theory ofR;! Equation worked out on the basis of mild steel conforming to Grade I ofIS: The permissible stresses in steel and concrete according to IS: Table 4. The values shown Tabte-2I orIS: Sleel IS: Bars Accordfngly the permissiole values of stresses in I iv Compression In bars In a beam or slab where the compressive Half the guaranteed yield I steel are obtained by applying a factor of safety of 1.
The revised Indian standard b Over 20mm code IS: For Design office use, it is convenient to use the values of design coef- I For high yield strength deformed bars of Grade Fe, the permissi- ficients 'j' and 'Q' to check the depth of the section and to compute the ble stress in direct tension and flexural tension shall be 0.
The area of reinforcements required to resist the working moment 1M' using permissible stresses for shear and compression reinforcement shall be equations 3 and 4. The values of design coefficients are compiled in as for Grade Fe III reinforced concrete sections, the depth of neutral axis generally deter- mines the type of section.
Referring to the Fig. Solving this quadratic equation. Under reinfol"ced section. N A rr d f-O"cbc-f-. The moment of resistance is computeq from tension side with steel reaching the maximum permissible stress O'st and the moment of resistance is computed from Fig. Hence percentage steel reinforcement in the balanced section is given by.
Typical values of the design constants Ptb and Qb for Where Mrb ; IQnr- o o 0 Lrt:: Vol '. Ol Ol T,l os::! A singly reinforced concrete beam with an effective span of 4m has a rect- J,,7. The beam is reinforced with 3 bars of 10 mm diameter Fe' HYSD bars at an effective depth of mm. Calculate the maximu. Assume M grade concrete. M q ; Live load moment; [ A reinforced concrete beam of rectangular section mm wide by mm over all depth is reinforced with 4 bars of 32 mm diameter at an effec M,; 0.
Moment of Resistance;;; M r M Grade Concrete. CJ'cbc ;:: If na ;:: M,; Q. I J'l. I d Moment of Resistance Provided, d; - 40 ; mm. Design suitable dimensions and reinforce- The cross section of an RC.
C beam of rectangular section is to be. I A" The beam section is reinforced with tension and com- Solving, n. Critical neutral axis depth is given by the relation pression reinforcement.
The section is also reinforced with 2 bars of 25 mm diameter on-the compression side at an. So mOl on the iension side. The self weight of the beam together with the moment "and the stresses in steel "and concrete corresponding to this dead load is 3. Adopting M. HYSD bais estimate. Calculate the neutral axis depth and estimate the safe moment of resistance of the seCtion adopting M grade' concrete and Fe-4l5 HYSD bars.
If the beam spans over 5 m, estimate the safe permissible live load on the beam. Assuming the width of the beam as half the effective depth. Limit state design is a method of designing structures based on a Inadequacy ot the method' - Serviceability statistical concept of safety and the', associated statistical probability of aspects such as deflection and cracking at fuilure. In concrete structures, this state may be ,.
Evolution of Limit State Design Method forcement etc. Limit state design philosophy'" For a real structure, there will in general be many types of loads and many modes of failure, nonhally with complex correlations between 5. Applications of classicaJ.. At such low levels, the probability of failure is very sensitive to the exact shape of the normal distributiop curves. To determine exact,' "A structure may become unfit for its intended purpoSe in a number of ways shapes of normal distribut10n curves, we require very large numbers of iillenns of either Safety or,Serviceability.
The prominent limit states are: I' as a result of static, sustained, pulsating or dynamic loading ,or 19ss of Since the materials in the structur""re likely to differ in quality from overall stability disintegration due to fire or frost. The proposed values for the partial safety factors are as.
The structure may exhibit excessive deflections or displacements adversely given in Table 5. In contrast the ACI Code'" provides for these variations in material affecting the' finishes causing discomfort' to the users. Also the structure strengths and workmanship in the form of capacity reduction factors. The initial idea 'of referring to a single Table 5.
With this concept the local or the overall behaviour in all Steel 1. In the limit: Concrete, 1. Due to the number of variables involved, a rational determination of the Characteristic loads are expressed as the safety of a structure, based on probability theory is not yet practical in the design office. For the immediate future, the characteristic , loads can not be assessed in this way'due to lack of statistical information on the structure.
The variation in the properties of concrete ancl steel are expressed as char- dead, imposed or live and wind load. In addition, loads resulting from the effects of creep, shrinkage or temperature ate also considered if their effect I. Many of the national o ' des As such the desigidoads are obtained by enhancing the characteristic loads including the Indian standard code IS: Table 5. Note ,.. I While considering eanhquake effects, sub"ilule EL for WL 2 For the Limit slates of serviceability, the valu,es of Yr given in this Table are applicable for shan-term effects.
While assessing the Long-. Effect of loads ,, f. Fm Flc. I Plane sectionsnormal to the axis remain plane after bending. The recommended" stress-strain curve' is shown in Fig. Reinforced concrete slabs are primarily subjected to flexure and shear 0. Columns ,are primarily I I designed.
The composite action of steel Vi , a'ri"d concrete is mainly dUff to bond and anchorage. However practical Fig. I6", by the Bnreau of Indian Standards. Area of stress block is the sum of rectangular and parabolic portion and is computed as. Por design purposes the partial safety factor Ym equal to 1. Area of tension reinforcement. Hence it is preferable to design beams as underreinforced si. Where p is the percentage of steel. Substituting for A" I bel from the From proportionality of strains, we have the relation, above expression in Eq.
Th,s IS presented in I. Publication SP: The design tables I to 4 in SP: The moment of resistance of a concrete section can also be determined in terms of concrete' 6. A constant. Table 6.
A,, ,, 0. Based on. Equations 6. Since x,ld is constant for a given value of! If p, "I. For different grades of steel, the reinforcement index and the limiting 3 Charts 1 to 18 present the moment of resistance per metre width for moment of resistance for singly reinforced rectangular sections are com,;, varying depths 5 to 80 cm and varying percentage of steel and for piled in Table 6.
Nfmm'j equations. Nlmm2 Mjbrf fy. From Annexure G IS: Limiting value Of ;;J for Fe- ,grade steel is 0. Referring to Table 6. Method-2 Using SP: Hence the section is over reinforced. Method-I using IS': A,,] b Neutral AxIs Depth d 0. A,,] [ 0. Interpolating For Fe grade steel and! The effective span oflhe beam is 7m, If! Adopt M- 20 grade concrete and Fe Grade the reqUired parameter. HYSD bars. Method-I Using IS: Referring to Table- D of sr: The stress blocks are separately shown for the rectangu- The flexural stre'ngth of flanged beams Tee and L-beams depends upon lar portion and the flange portion.
The moment of resistance of the section the position of neutral axis. Referring to Fig. Let br: Equivalent Stress BI! Hence, the 6. Knowing the value of Xu. The constants A and B are solved by specifying the following two condi- tions to be satisfied by this equation. Xw] Similar h. AMW -L 0. Spe- cial publk'llion SP: For Singly Reinforced T-Beams. Did b,Ib,. Old I 1. The section can be considered as a a Data rectangular section with b ;;:: Ultimate Strength ofReinforced Concrete Sections. The Neutral axis falls is computed by replacing Xu by x Assuming Dr.
Effective depth mm. Heace we have x. If M concrete and Fe, Method-l Using IS: As such value of C, will change. Yf Method 2 using SP: Hence, according to Clause-G. I Refer Fig. S code provisions. Assuming neutral axis to fall within the flange thickness, we have, M.
Method-1 Using IS: S ,-'f FlJ.
Mclhod -Itl'sing IS: Method-1 [Using IS: Tables 58 and 59 of SP: J4et MlI A'st2 A,,, X 0. Hence, we have 0. Code Formula " compression reinforcement.
I As a first trial, assume XII We have the stress in mild steel as, is equal to 0. The reinforcements. The moment of resistance of a doubly reinforced section can be Method-2 expressed in the form,. I Determine the ultimate moment of resistance of a doubly reinforced chose another trial value of x.
WIth 5 bars of 25 mm diameter at an effective depth of mm. The 10 The ultimate 'moment of resistance is computed by taking compression. Q15 0. Hence, the two methods yield nearly the same moment capacity of the d Cheek for nentral axis depth section.
I A rectangular reinforced concrete beam of width 40Qmm and,effec- 0 Compute parameters to be used in SP: The limiting moment of resi'stance of singly reinforced section is 2 Design the reinforcements for a doubly reinforced concrete beam sec- tion to support a factored moment of kN. Mu,um '. V; M,. The four different types of shear failure modes depend upon the The reinforcement values are nearly the same as those obtained by ratio 'of shear span to effective depth.
The transverse shear force in a method-I. Investigations over the years have shown that there are two major modes 47 4 The shear resistance Vs developed in the shear cinforcement.
Near suppo. As concreteis weak in tension, if the without web reinforcement, inclined cracks from supports develop trans- tensile stresses developed exceed the low tensile strength of concrete, forming the beam into a tied arch which.
Hence, nal reinforcement or d. In such beams the failure may be due to bars should be designed to resist the large shear forces. Limit state design a Crushing of reduced concrete section above the progressing diagonal of reinforced concrete beams comprises of the design for flexure at centre tension crack under combined shear and compression.
The major types of sh,ear failure modes encountered in reinforced concrete beams are identified under the following groups: The limiting aid ratio above which flexural failure is certain is dependent upon the area of tension rein- forcement and the. In beams with aid ratio between 2. If web reinforcement is provided, the shear strength of such beams can be considerably enhanced.
In the case of I-beams with thin webs, failure due to. For the sake of simplicity the nominal shear stress across the cross section- of a beams is computed as the average shear stress on the section and evaluated as fol- 1 lows: Table of IS: For smaller depth R. Slabs , the strength is larger as I I given in clause Table oflS: Concrele Grade Table 6. Beyond these values, diagonal compression is prevalent even ifthe I 1. According to SP: X' the section should be redesigned by enhancing the croSS se,: The various types of reinforcements used to resist shear can be classified , under the following two groups: The, typical arrangement of these types is shown in Fig.
At the Limit state of collapse in shear, the forces are resisted by the , combined action of concrete and steel. If V,; total Shear Force. V,; ; Let Asv ; N; diS, Eq. IY ;[Shearcarrkd by Depth 10 em. This Hence, the spacing of vertical stirrups is given by the relation, table is reproduced as Table 6.
The spacing of stirrups can be directly read out for ,a given shearldepth ratio. This table which is useful in designing.
This equation 6. Hence if section is considered near The minimum shear reinforcements to be provided in all the beams is the support, it is customary to enhance the shear strength capacity, the computed by the relation, common examples being the design of brackets,.
Hence, the design shear strength is different when beams are supported on members,: Other Useful Links.
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