ConcreteConcreteAn artificially built-up stone An artificially built-up stone resulting from hardening of resulting from hardening of a mixture of cement, a mixture of cement, aggregates and water with aggregates and water with or without a suitable or without a suitable admixture, is generally admixture, is generally known as ‘Concrete’.known as ‘Concrete’.

2. Grades of Concretes : As per IS : 456 -2000, the concrete mixes have been

designated as follows

Group Group Grade Grade DesignationDesignation

Specified Charactering Specified Charactering Compressive Strength of Compressive Strength of 150mm Cube at 28 days in 150mm Cube at 28 days in

N/mm2N/mm2

(1)(1) (2)(2) (3)(3)

OrdinaryOrdinary

ConcreteConcreteM10M10 1010

M15M15 1515

M20M20 2020

StandardStandard

ConcreteConcreteM25M25 2525

M30M30 3030

M35M35 3535

Group Group Grade Grade DesignatioDesignationn

Specified Charactering Specified Charactering Compressive Strength of Compressive Strength of 150mm Cube at 28 days in 150mm Cube at 28 days in

N/mm2N/mm2

(1)(1) (2)(2) (3)(3)

StandardStandard

ConcreteConcreteM40M40 4040

M45M45 4545

M50M50 5050

M55M55 5555

Group Group Grade Grade DesignationDesignation

Specified Charactering Specified Charactering Compressive Strength of Compressive Strength of 150mm Cube at 28 days in 150mm Cube at 28 days in

N/mm2N/mm2

(1)(1) (2)(2) (3)(3)

High High StrengthStrength

ConcreteConcrete

M60M60 6060

M65M65 6565

M70M70 7070

M75M75 7575

M80M80 8080

NOTES : 1. In the designation of concrete mix M refers to the mix and the number to the specified compressive strength of 150 mm size cube at 28 days, expressed in N/mm2

2. For Concrete of compressive strength greater than M 55, design parameters given in the standard may not be applicable and the values may be obtained from specialized literatures and experimental results.

. CHARACTERISTIC STRENGTH

I.S. 456-2000 defines the characteristic value of material strength as below. The term ‘characteristic strength of a material means the value of the strength of the material below which not more than 5% of the test results are expected to fall. __

fck = f (1 – 1.65 m)fck = characteristic strength of materialf = mean strength of material m = variation coefficient of the

particular material under consideration.

Water Cement RatioThe ration of water and cement by weight in

a concrete mix, is known as water cement ratio. Dutt Abrahames (1918), after carrying out a number of experiments a relationship between water and cement, which is known as water cement ratio law.

It states, “With given concrete materials and conditions of test, the quantity of mixing water used per bag of cement determines the strength of the concrete so long as the mix is of a workable plasticity.

Workability It may be defined as the

property of concrete which determines the amount of internal work, necessary to produce full compaction i.e. work ability is the amount of energy to overcome friction while consolidation

Factors affecting the work ability are :(i) Water Content (ii) Size of aggregates(iii) Shape of the aggregates(iv) Surface texture of the aggregates(v) Porosity and absorption of aggregates(vi) Grading of aggregates(vii) Air entraining agents (viii) Temperature.

Methods of determining the workability of concrete

1. Slump test

2. Compaction factor test

3. Vee – bee consistometer test.

SEGREGATIONThis is the separation of the constituent

materials of concrete. In a good concrete all the ingredients are properly distributed to make a homogeneous mixture. If a sample exhibits a tendency for separation, for example , coarse aggregate from the rest of the ingredients then that sample is said to be showing the tendency for segregation. Such a concrete will be weak and be lacking in homogeneity and will be inducting all undesirable properties in the hardened concrete.

Segregation is of 3 typesi) Coarse aggregate separating out or settling down from the rest of the matrix.ii) The paste or matrix separating away from coarse aggregate andiii) water separating out from the rest of the material.

Bulking of sand :It may be defined as an increase

in the bulk volume of the quantity of and (fine aggregate) in a moist condition over the volume of the same quantity dry or completely inundated. The ratio of the volume of moist sand to the volume of sand when dry, is called bulking factor. Fine sands bulk more than coarse sand.

When water is added to dry and loose sand, a thin film if water is formed around the sand particles. Interlocking of air in between the sand particles and the film of water tends to push the particles apart due to surface tension and thus increase the volume in fully saturated sand the water films are broken and the volume becomes equal to that of dry sand.

Controlled Concrete The concrete in which preliminary tests

are performed for designing the mix, is called controlled concrete. the controlled is used for all the seven types of grades i.e.,

M10, M15, M20, M25, M30, M35, M40, M45, M50, M55

The controlled concrete is designed for producing the required workability and characteristic strengths.

Why Steel as reinforcing material ?The steel is commonly used as reinforcing

material due to its following qualities .1. It Possesses high tensile strength and elasticity.2. Its thermal coefficient is nearly equal to that of concrete i.e. 11.7 x 10-6/C0 and 9.9 x 10-6/C0 respectfully.3. It develops good bond with concrete.4. It is cheaply and easily available in bulk.5. It is economical comparing all the aspects.

Assumption for Design of MembersIn the methods based on elastic theory, the following

assumption shall be made.a) At any cross section, plane sections before bending

remain plane after bending.b) All tensile stresses are taken up by reinforcement

and none by concrete, except as other used specifically permitted.c)The stress strain relationship of steel and concrete,

under working stress is a straight line.d)The modular ration ‘m’ has the value 280

-------- 3 o cbc

c is the permissible which o c bcompressive stress due to bending in concrete is

N /mm 2

Bond When a reinforcing bar is

embedded in concrete, the concrete adheres to its surface and resists any force that tries to cause slippage of the bar relative so the surrounding concrete. This achieved by the development of a shear at the interface of bar and concrete and is known as bond stress.

Shear A vast majority of structural

elements in reinforced concrete are subjected to shearing forces. It generally acts in combination with flexure. The behaviour of concrete elements in shear is not so well understood as that inflexure. This is because of the complexity of the behaviour of concrete elements in shear and inadequacy of get result

METHODS OF DESIGN

The Working Stress Method The conventional working stress design

method is based on the behaviour of the structure at working load. The stress distribution of

concrete at working load is assumed to be linear. Hence the section of the member is design by assuming linear stress strain relationship and

ensuring that the stress in concrete and steel do not exceed the allowable working stresses at service loads the method ensures satisfactory

behaviour of structure at working load but give no indication of actual margin of safety again

collapse, as the ultimate load carrying capacity cannot be predicted accurately.

Ultimate Load Design Method

After a good amount of research, the behaviour of a structure at ultimate load is quite well understood and the difference of elastic theory of design have become evident. The ultimate strength design of the section based on the behaviour at ultimate load provides a more relastic assessment on the degree of safety. However the design based in ultimate strength method loads to a condition adversely affecting the serviceability of the structure.

The Limit State Design Method

Neither the working stress design method (which ensures satisfactory behaviour at working loads and assumes to possess adequate safety against collapse) not the ultimate strength design method (which ensures adequate safety against its final collapse and assumes to behave satisfactorily at working loads) ensures satisfactory behaviour both at working and ultimate loads

The design method which ensures adequate safety of the structure against collapse and serviceability at working loads is known as limit state design method. The two principal limit states are the ultimate limit state and the serviceability limit state. Ultimate limit state is reached when the structure collapses. Serviceability limit states are those of excessive objection and cracking.

Types of reinforced beams :

1. Singly reinforced The Main reinforcing steel is

provided only at the tensile Zone is called singly reinforced beam.

. Doubly Reinforced BeamsThe beam reinforced in which main steel is

provided on both sides i.e. on tension as well as on the compression side, is called a doubly reinforced section.In following situations, doubly reinforced beams are generally preferred to :1. When it is necessary to restrict the size i.e. depth and breadth of the section due to architectural reasons.2. When bending moment due to external loading is too much. the moment of resistance of a section cannot be increased by 25 % more than a balanced section.

3. The provide head room as in the case of basement floors or under stair cases.4. When the beams are subjected to reversible loading conditions due to which bending moment reverses.5. When members are subjected to eccentric loads or either side of its axis such as columns subjected to wind pressures.6. When a member is subjected to accidental lateral loads, shocks or impact i.e. rail track sleepers.7. When the beam is a continuous one, the tension occurs at the top near the supports, hence a section of the beam, near supports is always designed as double reinforced section.

Balanced section :

The section reinforced with such an amount of steel that, when distant concrete fibre in compression zone, attains allowable stress in compression, the tensile stress in the reinforcement reaches the allowable stress in steel, is called a balance or economic or critical section. The neutral axis corresponding to this condition, is called the critical neutral axis.

The moment of resistance of a balanced section is obtained by multiplying the lever arm with either compressive force or tensile force

Under reinforced section :

The section in which the amount of reinforcement provided, is less than what is required for a balanced section, is called an under reinforced section. In such section when steel attains its maximum permissible stress, the corresponding compressive stress in concrete remains less than that its maximum allowable limit. In an under reinforced section, the position of actual N.A. shifts above the critical neutral axis.

M. R = Ast (d – n/3)

Over reinforced section :The section in which amount of steel

provided is more than what is required for a balanced section, is called an over – reinforced section. In such sections when the stress in concrete reaches its permissible limit, the corresponding stress in steel remains less than its allowable limit. In over reinforced section, the position of actual N.A. remains below the critical N.A.M. R = b x N x C x (d – n/3)

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HOOKS LAW:HOOKS LAW:

Stress is directly proportional to strain Stress is directly proportional to strain within elastic limit. within elastic limit.

Any ductile metal such as mild steel, when Any ductile metal such as mild steel, when subjected to a gradually increasing subjected to a gradually increasing tension, experiences strain both tension, experiences strain both longitudinally and laterally. The curve longitudinally and laterally. The curve which represents the relation between which represents the relation between tensile stress and strain is called stress-tensile stress and strain is called stress-strain diagram.strain diagram.

On gradually increasing the load on On gradually increasing the load on the bar, it goes on straining the bar, it goes on straining proportionally. The point A on the curve proportionally. The point A on the curve which shows the limit of proportionately which shows the limit of proportionately and upto this stage, the material obeys and upto this stage, the material obeys Hook’s low, is called limit of Hook’s low, is called limit of proportionately. The curve OA is a proportionately. The curve OA is a straight line. During the limit of straight line. During the limit of proportionately, the material is fully proportionately, the material is fully elastic i.e. it regains its original length if elastic i.e. it regains its original length if the load is removed.the load is removed.

The stress developed at the limit of The stress developed at the limit of proportionality is called elastic limit. The proportionality is called elastic limit. The elastic limit may be defined as the elastic limit may be defined as the maximum stress upto which no permanent maximum stress upto which no permanent deformation occurs.deformation occurs.

On increasing the load beyond elastic On increasing the load beyond elastic limit, the strain increases slightly more limit, the strain increases slightly more than stress upto yield point B. The curve than stress upto yield point B. The curve between A and B is slightly curved. between A and B is slightly curved. Beyond yield point B the strain increaseBeyond yield point B the strain increase

More quickly than the stress producing More quickly than the stress producing it till the stage C is reached. Between B it till the stage C is reached. Between B and C, the extension takes place without an and C, the extension takes place without an increase of the load. This phenomenon of increase of the load. This phenomenon of slow growth of strain is generally called slow growth of strain is generally called ‘creeping’. At C, the stress is maximum, ‘creeping’. At C, the stress is maximum, and is know as ultimate strength. Beyond and is know as ultimate strength. Beyond C, the bar elongates rapidly even with less C, the bar elongates rapidly even with less stress and finally fails at E where are of stress and finally fails at E where are of section becomes leastsection becomes least

Pre – Stressed Concrete

1. Definition

The member of concrete in which internal stresses are intentionally induced in a planned manner such that the stresses resulting from the superimposed loads get counteracted to a desired degree, is called a prestressed concrete member.

The Principle of pre-stressing

The main principle of pre-stressing a concrete member consists of including sufficient compressive stress in concrete before a member is subjected to loads, in the zones which develops tensile stress due to applied load. the pre – induced compressive stress in concrete neutralises the tensile stress developed due to the external loads. hence, the zone ultimately will be free from any stress. In a pre-stressed member, the entire cross section becomes effective for resisting bending and the danger of cracking, is minimised or even avoided.

Reasons for high strength concrete .1. To resist large prestressing forces

applied to the member by the tension and also to provide proper anchorages at the ends.2. To resist the bursting stresses liable to be at be ends of the beams.3. To provide high bond stress for transferring the stresses to the concrete.4. To minimise the chances of developing shrinkage cracks in concrete.5. To provide high modules of elasticity so as to have very little elastic and creep strains and thus minimise loss of prestress in the steel reinforcement.

Reason for high strength steel

The yield point for mild steel generally used in ordinary reinforced concrete. occurs at a stress 2000 kg/cm2 to 3000 kg/cm2. when such a mild steel is prestressed to the order of 2000 kg/cm2, the steel will be having hardly any capacity to bear tensile stress. In case of high tension steel the ultimate strength in 21000 kg/cm2. Hence, even if it is prestressed say 10,000 kg/cm2, it will be able to bear large stress in the reinforcement after making suitable deduction for loss of prestress.

Methods of pretressing

(a)The prestressed concrete members are classified according to their method of design, construction and application of prestress.

1. Externally and internally prestressed members

2. Linear or circular prestressing

3. Pre – tensioning and post tensioning

Pre – tensioning

In pretensioning, he tendons are stressed prior to pouring of concrete.

Examples : Slender members like beams, posts, PSC sleepers etc.,

Post tensioning

In postensioning the tendons are stressed to the required level after hardening of concrete.

Example :

Box girder and I – Girders etc.,

Losses of prestressed concrete

The prestressing force induced in a member does not remain constant but there is gradual reduction in prestressing force. the amount of force lost after prestressing is known as loss of prestress and its value generally varies from 15 to 20%.

1. Loss of prestress during tensioning due to friction

(i) Loss due to length effect.(ii) Loss due to curvature effect(iii) Loss due to combined effect of the

length and the curvature 2. Loss of prestress at the anchoring stage.3. Loss pf prestress subsequent to prestressing

(i) Due to shrinkage of concrete(ii) Due to creep of concrete(iii) Due to elastic shortening of concrete.(iv) Due to creep in steel.

Grade of Grade of Concrete Concrete & Steel & Steel

Permissible Permissible Stressess in Stressess in Concrete & Concrete &

Steel Steel

ZZ RR

M20 , Fe M20 , Fe 415 415

7,230 N/mm2 7,230 N/mm2 0.9d 0.9d 0.91bd20.91bd2

M25 , Fe M25 , Fe 415 415

8.5, 230 8.5, 230 N/mm2 N/mm2

0.9d 0.9d 1.11bd2 1.11bd2

Z = jd Z = (d-0.40d) (Mild Steel) 3

Z= (d – x) Z = 0.87 d

3

Z = (d – 0.29d) (RTS) 3

Z = 0.9d

MR = b x 0.29d x 7 (d – 0.29d) 2 3

MR = 0.91 bd2/1.11 bd2

Ld = Ø x Permissible stress in steel-----------------------------------

4x Bond stress

Where,

Ø – dia. of reinforcing steel in mm.