Institute of Technology,

Nirma University.

M.Tech CASAD Semester I

CL1105 Advanced materials 2014-2015

Assignment I

Revision of Concrete Technology

Tejas M. PatilM. Tech. 1st Year

14MCLC22

Due date - 11th August 2014

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Question 1.2Discuss in brief the equipments used, the procedure for the evaluation of fol-lowing properties of cement along with their significance.Fineness, Standard consistency, Setting time, Compressive strength.Answer,-

1. Fineness test- The fineness of cement has an important bearing onthe rate of hydration and hence on the rate of gain of strength and alsoon the rate of evolution of heat. Finer cement offers a greater surfacearea for hydration and hence faster the development of strength. Dif-ferent cements are ground to different fineness. The disadvantages offine grinding is that it is susceptible to air-set and early deterioration.Hence optimum grinding should be chosen.

• Sieve Test- Weigh correctly 100 grams of cement and take it ona standard IS Sieve No. 9 (90 microns). Break down the air-setlumps in the sample with fingers. Continuously sieve the samplegiving circular and vertical motion for a period of 15 minutes.Weigh the residue left on the sieve. This weight shall not exceed10% for ordinary cement.

• Air Permeability Method- This method of test covers theprocedure for determining the fineness of cement as representedby specific surface expressed as total surface area in sq. cm/gm.of cement. The principle is based on the relation between the flowof air through the cement bed and the surface area of the particlescomprising the cement bed.From this the surface area per unitweight of the body material can be related to the permeability ofa bed of a given porosity.

2. Standard Consistency- The standard consistency of a cement pasteis defined as that consistency which will permit a Vicat plunger having10 mm diameter and 50 mm length to penetrate to a depth of 33-35mm from the top of the mould shown in Vicat Apparatus.For finding out initial setting time, final setting time and soundness ofcement, and strength a parameter known as standard consistency hasto be used.Procedure -

• Take about 400 gms of cement and prepare a paste with a weighedquantity of water for the first trial. The paste must be prepared

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Figure 1: Vicat’s Apparatus

in a standard manner and filled into the Vicat mould within 3-5minutes.After completely filling the mould, shake the mould toexpel air.

• Standard plunger, 10 mm diameter, 50 mm long is attached andbrought down to touch the surface of the paste in the test blockand quickly released allowing it to sink into the paste by its ownweight. Take the reading by noting the depth of penetration ofthe plunger.

• Conduct a 2nd trial. Similarly, conduct trials with different wa-ter/cement ratios till such time the plunger penetrates for a depthof 33-35 mm from the top.

3. Setting Time Test- Initial setting time is regarded as the timeelapsed between the moment that the water is added to the cement,to the time that the paste starts losing its plasticity(Usually 30 mins).The final setting time is the time elapsed between the moment thewater is added to the cement, and the time when the paste has com-pletely lost its plasticity and has attained sufficient firmness to resistcertain definite pressure(Usually 10 hrs).procedure-

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• Take 500 gm. of cement sample and guage it with 0.85 times thewater required to produce cement paste of standard consistency(0.85 P).

• The paste shall be guaged and filled into the Vicat mould inspecified manner within 3-5 minutes.

• Start the stop watch the moment water is added to the cement.

• The period elapsing between the time when water is added tothe cement and the time at which the needle penetrates the testblock to a depth equal to 33-35 mm from the top is taken asinitial setting time.

• Replace the needle of the Vicat apparatus by a circular attach-ment. The cement shall be considered as finally set when, upon,lowering the attachment gently cover the surface of the test block,the centre needle makes an impression, while the circular cuttingedge of the attachment fails to do so.

4. Soundness test- The testing of soundness of cement, is done to ensurethat the cement does not show any appreciable subsequent expansionis of prime importance.procedure-

Figure 2: Apparatus for Soundness Test

• The apparatus is shown in Fig. It consists of a small split cylinder.On either side of the split are attached two indicator arms.

• Cement is gauged with 0.78 times the water required for standardconsistency (0.78 P), in a standard manner and filled into the

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mould kept on a glass plate. The mould is covered on the topwith another glass plate. The whole assembly is immersed inwater at a temperature of 27C 32C and kept there for 24 hours.

• Measure the distance between the indicator points. Submergethe mould again in water. Heat the water and bring to boilingpoint in about 25-30 minutes and keep it boiling for 3 hours.Remove the mould from the water, allow it to cool and measurethe distance between the indicator points. The difference betweenthese two measurements represents the expansion of cement. Thismust not exceed 10 mm for ordinary, rapid hardening and lowheat Portland cements. If in case the expansion is more than 10mm as tested above, the cement is said to be unsound.

5. Compressive strength - The compressive strength of hardened ce-ment is the most important of all the properties. cement is alwaystested for its strength at the laboratory before the cement is used inimportant works.Procedure,-

• Take 1:3 cement sand mixture in a non-porous enamel tray andmix them with a trowel for one minute, then add water of quantity(P/4 + 3.0) per cent of combined weight of cement and sandand mix the three ingredients thoroughly until the mixture is ofuniform colour.

• Until the mixture is of uniform colour. The time of mixing shouldnot be less than 3 minutes nor more than 4 minutes. Immediatelyafter mixing, the mortar is filled into a cube mould of size 7.06cm. The area of the face of the cube will be equal to 50 sq cm.

• Compact the mortar either by hand compaction in a standardspecified manner or on the vibrating equipment for 2 minutes.

• Keep the compacted cube in the mould at a temperature of 27C2C and at least 90 per cent relative humidity for 24 hours. After24 hours the cubes are removed from the mould and immersed inclean fresh water until taken out for testing.

• Three cubes are tested for compressive strength at the periods.he compressive strength shall be the average of the strengths ofthe three cubes for each period respectively.

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Question 1.3Discuss in detail the phenomenon of ’Hydration of cement’.Answer,-

• Hydration of cement- The chemical reactions that take place be-tween cement and water is called ’Hydration of Cement’. By the pro-cess of hydration, Portland cement when mixed with sand gravel andwater produces the synthetic rock we call concrete. The reaction withwater is termed ”hydration”. This involves many different reactions,often occurring at the same time. As the reactions proceed, the prod-ucts of the hydration process gradually bond together the individualsand and gravel particles, and other components of the concrete, toform a solid mass. These products are important because they havecementing or adhesive values. The hydration of cement can be ex-plained in two ways namely, ’through solution’ and ’solid state’ mech-anisms. In ’through solution’ mechanism, compounds dissolve to pro-duce supersaturated solution from which different hydrated productsget precipitated. During ’solid state’ mechanism, water attacks ce-ment compounds to produce hydrated products starting from surfaceand proceeding to interior of compounds with time. It is likely that,both mechanisms may occur during the course of hydration reactiondepending upon availability of water.

• Heat of Hydration- When water is added, the reactions which occurare mostly exothermic, that is, the reactions generate heat. We canget an indication of the rate at which the minerals are reacting bymonitoring the rate at which heat is evolved using a technique calledconduction calorimetry. On mixing cement with water, the rapid heatevolution occurs. It is mainly due to Aluminates and Sulphates andceases quickly due to Gypsum. The next heat evolution is becauseof ettrignite and partly due to reaction of C3S. Different compoundshydrate at different rates to produce different amount of heat. Figshows rate of hydration of different compounds. It is noticeable thatAluminate have very high rate of hydration but retarders, like Gyp-sum control their solubility. So, heat of hydration is mainly due tohydration of C3S.

• Hydration of silicates-

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Figure 3: Rate of liberation of heat

2C3S + 6H2O →(CaO)3(SiO)2(H2O)3 + 3CaOH

2C2S + 4H2O →(CaO)3(SiO)2(H2O)3 + CaOH

1. Both, C2S and C3S produce C-S-H and Ca(OH)2 as reactionproducts.

2. C2S Produces less Ca(OH)2. (important for durability in sulfaterich environments).

3. More heat is evolved during C3S hydration.

Figure 4: Rate of Hydration of pure compounds

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4. C3S Hydration is more rapid, contributing to early age strength(2-3h to 14 days).

5. C2S Hydration occurs more slowly to contributing to strengthafter 14 days.

• C-S-H

1. Known as Calcium silicate hydrate.

2. C/S ratio varies between 1.5− 2.

3. H2O is even more variable.

4. Structure ranges from poorly crystalline to amorphous - highlyvariable and poorly understood.

5. Occupies 50-60 % of the solid volume of the hydrated cementpaste (hcp).

6. Huge surface area (100-700 m2/g)

7. Strength due to covalent/ionic bonding (65%) and Van der Waalsbonding (35%) within the complex structure.

8. Primary strength-giving phase in portland cement concrete.

• Calcium Hydroxide

1. Calcium hydroxide or Ca(OH)2.

2. Definite stoichiometry.

3. Large, hexagonal prism morphology.

4. Size of the crystals depends on the amount of space available.

5. Occupies 20-25% of the solid volume in the hcp.

6. Much lower surface area than C-S-H.

7. Does not contribute much to strength.

8. Keeps the pore solution alkaline (pH 12.4-13.5).

• Hydration of the Calcium Aluminates

C3A + 3(CaO)(SiO2)(H2O)2 + 26(H2O)→(CaO)6(Al2O3)(SiO2)3(H2O)32

When more C3A remains

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(CaO)6(Al2O3)(SiO2)3(H2O)32 + 2(C3A) + 4(H2O)→ 3(CaO)4(Al2O3)(SiO2)(H2O)12

Reaction of C4AF occurs more slowly

C4AF + 2CaOH2 + 14(H2O)→(CaO)4((Al2O3), (Fe2O3))(H2O)13+ (Al2O3)(Fe2O3))(H2O)3

1. Reaction of C3A with water occurs very quickly and liberatesmuch heat - Flash Set.

2. Gypsum is added to the cement to control the hydration of C3A

• Calcium Aluminates and Calcium Sulfoaluminates

1. Includes ettringite, monosulfate hydration, calcium aluminate hy-drates, and ferric-aluminum hydroxide gels.

2. Comprise 15-20% of solid volume of hcp.

3. Do not contribute much to strength.

4. Formation of ettringite, in particular, does influence setting time.

5. High heat of hydration for C3A can be favorable or unfavorable,depending upon application.

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Question 1.8Discuss in detail the various stages in manufacturing of concrete.Answer,-Bad concrete and good concrete, are both made of essentially the samematerials or ingredients. The only thing most often separates them is, thecare taken during at each stage of manufacturing of concrete. The variousstages of manufacturing of concrete are as follows.

1. batchingbatching of concrete is nothing but the measurement of concrete.

• Volume batching-

(a) In this method, measurement is done in volume.

(b) Since it is very difficult to measure granular material in termsof volume,this method is not preffered for batching.

(c) Gauge boxes are used for measuring the fine and coarse ag-gregates. Usually, The volume of the box is made equal tothe volume of one bag of cement. i.e., 35 liters.

(d) in India volume batching is adopted even for large concretingoperations.

(e) Correction to the effect of bulking should be made to caterfor bulking of fine aggregate, when the fine aggregate is moistand volume batching is adopted.

• Weigh batching-

(a) Measurement is done by weight.

(b) Since measurement of weight provides accuracy, flexibilityand simplicity to operation, Weigh batching is the more pre-cise and correct method of measuring than Volume batching.

(c) in smaller works, the weighing arrangement consists of twoweighing buckets, each connected through a system of leversto spring-loaded dials which indicate the load. On large worksites, the weigh bucket type of weighing equipments are used.The weighing is done through a lever-arm system and twointerlinked beams and jockey weights the materials.

(d) Addition of water by graduated bucket in terms of liters willnot be accurate enough for the reason of spillage of water etc.It is usual to have the water measured in a horizontal tankor vertical tank fitted to the mixer.

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2. Mixing- Mixing is essential to ensure that the mass becomes homo-geneous, uniform in colour and consistency. There are two methods ofmixing.

• Hand Mixing-

(a) Hand mixing is practiced for small scale unimportant con-crete works.

(b) The measured quantity of coarse aggregate and fine aggre-gate are spread in alternate layers. The cement is poured onthe top of it, and mixed dry by shovel, turning the mixtureover and over again until uniformity of colour is achieved.Water is taken in a water-can fitted with a rose-head andsprinkled over the mixture and simultaneously turned over.This operation is continued till such time a good uniform,homogeneous concrete is obtained.

• Machine Mixing-

(a) Mixing of concrete is carried out by machine, for reinforcedconcrete work and for medium or large scale mass concretework.

(b) Many types of mixers are available for mixing concrete. Theycan be classified as batch-mixers and continuous mixers.

(c) Machine mixing is efficient and economical, especially in largeplants.

(d) As per I.S. 17911985, concrete mixers are designated by anumber representing its nominal mixed batch capacity inliters. The following are the standardized sizes of three types:Tilting( 85 T, 100 T, 140 T, 200 T), Non-Tilting( 200 NT,280 NT, 375 NT, 500 NT, 1000 NT), Reversing( 200 R, 280R, 375 R, 500 R and 1000 R). The letters T, NT, R denotetilting, non-tilting and reversing respectively.

3. Transporting Concrete- Main objective of transporting concrete isthat homogeneity obtained at the time of mixing should be maintainedwhile being transported to the final place of deposition.

(a) Motar Pan. Use of mortar pan for transportation of concreteis labour intensive, and one of the common methods adopted inIndia.

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(b) Wheel Barrow, Hand cart. This method is employed forhauling concrete for comparatively longer distance as in the caseof concrete road construction.

(c) Crane, Bucket and Rope way. Cranes are fast and versatile tomove concrete horizontally as well as vertically along the boomand allows the placement of concrete at the exact point. Thisquality makes them one of the right equipment for transportingconcrete above ground level.Rope way and bucket of various sizes are used for transportingconcrete to a place, where simple method of transporting concreteis found not feasible. exa, Valley, Dam.

(d) Truck Mixer and Dumper. For large concrete works particu-larly for concrete to be placed at ground level for longer distances,trucks and dumpers or ordinary open steel-body tipping lorriescan be used.

(e) Belt conveyors. Conveyors can place large volumes of concretequickly where access is limited. There are portable belt conveyorsused for short distances or lifts.

(f) Chute. Chutes are generally provided for transporting concretefrom ground level to a lower level. The lay-out is made in such away that the concrete will slide evenly under effect of gravity ina compact mass without any separation or segregation.

(g) Skip and Hoist. This is one of the widely adopted methodsfor transporting concrete vertically up for multistorey buildingconstruction.

(h) Tansit Mixer. Transit mixer is one of the most popular equip-ments for transporting concrete over a long distance particularlyin Ready Mixed Concrete plant.

(i) Pump and Pipe Line. Pump and pipe line are adopted fortransportation of pumpable concrete.

4. Placing- It is important to ensure that concrete is placed in system-atically to yield optimum results.

• Form work: Form work shall be designed and constructed soas to remain sufficiently rigid during placing and compaction ofconcrete. Formwork should not be removed until the concrete hasdeveloped a strength of at least twice the stress to which concretemay be subjected at the time of removal of formwork.

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• Underwater concrete: Concrete is often required to be placedunderwater or in a trench filled with the bentonite slurry. In suchcases, use of bottom dump bucket or tremie pipe is made use of.In the bottom dump bucket concrete is taken through the waterin a water-tight box or bucket and on reaching the final place ofdeposition the bottom is made to open by some mechanism andthe whole concrete is dumped slowly.

• Slip form technique: Slip-forming of vertical construction is aproven method of concrete construction generally adopted for tallstructures. In this method, concrete is continuously placed, com-pacted and formwork is pulled up by number of hydraulic Jacks,giving reaction, against jack rods or main reinforcements.The rateof slipping the formwork will vary depending upon the tempera-ture and strength development of concrete to withstand withoutthe support of formwork.

5. Compaction- Compaction of concrete is the process adopted for ex-pelling the entrapped air from the concrete. The following methodsare adopted for compacting the concrete:

• Hand Compaction. Hand compaction of concrete is adoptedin case of unimportant concrete work of small magnitude. Itinvolves mainly -

(a) Rodding

(b) Ramming

(c) Tamping

• Vibration. Where high strength is required, it is necessary thatstiff concrete, with low water/cement ratio be used. To compactsuch concrete, mechanically operated vibratory equipment, mustbe used. Also,Re-vibration is delayed vibration of concrete thathas already been placed and compacted. It may occur whileplacing successive layers of concrete, when vibrations in the upperlayer of fresh concrete are transmitted to the underlaying layerwhich has partially hardened or may be done intentionally toachieve certain advantages. it can be classified on the basis oftype of vibrator used. mainly-

(a) Internal vibrator (Needle vibrator)

(b) Formwork vibrator (External vibrator)

(c) Table vibrator

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(d) Platform vibrator

(e) Surface vibrator (Screed vibrator)

(f) Vibratory Roller

• Compaction by Pressure and Jolting.

• Compaction by Spinning.

6. Curing- Water used in concrete evaporates and water available is notoften sufficient. If the hydration is to continue unbated, extra watermust be added to replenish the loss of water on account of absorptionand evaporation. Alternatively, some measures must be taken by wayof provision of impervious covering or application of curing compoundsto prevent the loss of water from the surface of the concrete. Therefore,the curing can be considered as creation of a favourable environmentduring the early period for uninterrupted hydration. Curing methodsmay be divided broadly into four categories:

• Water Curing This method is preferred in most cases as it satis-fies all criteria of curing mainly, promotion of hydration, elimina-tion of shrinkage and absorption of the heat of hydration. Watercuring can be done in following ways:

(a) Immersion concrete items are normally immersed in curingtanks for a certain duration.

(b) Ponding Pavement slabs, roof slab etc. are covered underwater by making small ponds.

(c) Spraying Vertical retaining wall or plastered surfaces or con-crete columns etc. are cured by spraying water.

(d) Wet covering wet coverings such as wet gunny bags, hes-sian cloth, jute matting, straw etc., are wrapped to verticalsurface for keeping the concrete wet.

• Membrane curing concrete could be covered with membranewhich will effectively seal off the evaporation of water from con-crete. It is found that the application of membrane or a sealingcompound, after a short spell of water curing for one or two daysis sometimes beneficial. Membrane curing is a good method ofmaintaining a satisfactory state of wetness in the body of concreteto promote continuous hydration when original water/cement ra-tio used is not less than 0.5.

• Application of heat When concrete is subjected to higher tem-perature it accelerates the hydration process resulting in faster

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development of strength. Therefore, subjecting the concrete tohigher temperature and maintaining the required wetness can beachieved by subjecting the concrete to steam curing.The expo-sure of concrete to higher temperature is done in the followingmanner:

(a) Steam curing at ordinary pressure.

(b) Steam curing at high pressure.

(c) Curing by Infra-red radiation.

(d) Electrical curing

• Miscellaneous

(a) Calcium chloride is used either as a surface coating or as anadmixture. It can be used as curing medium since it absorbsmoisture from atmoshpere and retains at surface.

(b) Formwork prevents escaping of moisture from the concrete,particularly, in the case of beams and columns. Keeping theformwork intact and sealing the joint with wax or any othersealing compound prevents the evaporation of moisture fromthe concrete. This can also be seen as method of curing.

7. Finishing- Concrete is often dubbed as a drab material, incapable ofoffering pleasant architectural appearance and finish. This shortcom-ing of concrete is being rectified and concretes these days are made toexhibit pleasant surface by process of finishing. Surface finishes maybe grouped as under:

• Formwork Finishes. Concrete obeys the shape of formworki.e., centering work. By judiciously assembling the formwork,pleasant finishing can be achieved.

• Surface Treatment. This is one of the methods of giving goodlook to the concrete surface.

• Applied Finishes. The term applied finish is used to denote theapplication of rendering to the exteriors of concrete structures.

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Question 1.9Explain in detail the what you mean by ’Shrinkage, Creep and Modulus ofElasticity of concrete.Answer,-

1. Shrinkage is a reduction in volume, and in concrete, it is mainlycaused by the loss of water. In most cases, shrinkage is measured bymonitoring longitudinal strain. When tensile stresses due to restrainedvolume contraction exceed the tensile strength of concrete, the shrink-age leads to cracking, which is called shrinkage cracking. Shrinkageis classified based on the causes of volume change and the state ofconcrete.

• Plastic shrinkage is the shrinkage that occurs due to loss ofmoisture from fresh concrete. This loss may in be in form of sur-face evaporation or moisture loss to the subgrade, for slabs on theground. The loss of moisture leads to the formation of menisci.These menisci generate negative capillary pressures, which causea volume reduction in the cement paste (Mindess, Young, andDarwin 2003). Because the loss of moisture is concentrated at theexposed surfaces, the volume contraction is uneven. Differentialvolume changes produce tensile stresses in concrete, which mayresult in the formation of cracks in the plastic concrete. This typeof cracking generally appears in random patterns and is shallow.

• Autogenous Shrinkage (also known as chemical shrinkage) isa volume change that occurs without moisture loss to the sur-rounding environment. It occurs when water in cement paste isconsumed by the hydration reactions, and results due to self des-iccation of the concrete. This type of shrinkage mainly occursin the mixes with low water-cement (w/c) ratios and may be in-creased by the use of reactive pozzolans. For the concretes withw/c ratios of 0.42 and greater, autogenous shrinkage is normallysmall and can be considered as a part of drying shrinkage.

• Drying shrinkage occurs due to the loss of moisture from hard-ened concrete. Among the different types of shrinkage, dryingshrinkage usually results in the largest volume change. Moistureloss causes volume changes based on three mechanisms that resultin changes in capillary stress, disjoining pressure, and surface freeenergy. Capillary stress occurs between relative humidity of 45

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and 95 percent, when a meniscus forms in the pore water withinpores in cement paste. The meniscus is under hydrostatic tension,and adopts a curved surface. The water exerts the correspondingcompression on the solid skeleton, reducing the size of the pores.Disjoining pressure is the pressure caused by adsorbed water con-fined within the small spaces of capillary pores. In this narrowspace, water exerts pressure on the adjacent cement surfaces.When the adsorbed water is lost, the disjoining pressure is re-duced and the cement particles are drawn closer together, whichresults in shrinkage.shrinkage also can be explained by changes in surface energy. Asthe most strongly adsorbed water surrounding the cement par-ticles is removed, the free surface energy of the solid increasessignificantly. This water has high surface tension and exerts acompressive pressure on cement particle, causing a reduction involume.Drying shrinkage is by far the most common cause of shrinkage.Drying shrinkage occurs in hardened concrete as a result of wa-ter movement. The reaction of cement and water results in theformation of a calcium silicate hydrate gel (C-S-H) with water-filled space. The size of the pores in the water-filled space variesfrom large capillary pores to smaller voids in the C-S-H gel thatare filled with adsorbed water (0.5-2.5 nm). As drying occurs,disjoining pressure removes adsorbed water from these pores andhydrostatic forces (capillary stresses) form a meniscus that exertsstresses on the C-S-H skeleton causing the cement paste to shrink.One of the most substantial factors influencing free shrinkage isthe water-to cement ratio (w/c). The w/c required for completehydration is typically assumed to be approximately 0.42 depend-ing on the amount of gel porosity that is assumed. The amountof water has a direct influence on the size and magnitude of theporosity (i.e. Higher w/c pastes have higher porosity). Therefore,specimens with a lower w/c have a lower amount of pore waterand consequently exhibit lower drying shrinkage. It should benoted that recently the use of high-range water-reducing admix-tures (HRWRA) hassled to increased workability for lower w/cmixtures. Other factors that influence shrinkage include chemicaladmixtures, mineral admixtures, and cement composition, sincethey typically alter the reaction products, porosity, and mechan-ical stiffness.

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• Carbonation shrinkage occurs as the result of chemical reac-tions between hardened cement paste and carbon dioxide. It isbelieved that CO2 reacts with calcium silicate hydrate (C-S-H)inducing a decrease in its calcium-silica (C/S) ratio with a con-comitant water loss. Carbonation shrinkage is a function of rela-tive humidity and is greatest around 50 percent relative humidity.Carbonation shrinkage, although not very significant itself, canadd to the effect of drying shrinkage and thereby lead to cracking.

2. Creep- The degree of curvature of the stress-strain relationship de-pends upon many factors amongst which the intensity of stress andtime for which the load is acting are of significant interest. Therefore,it clearly shows that the relation between stress and strain for concreteis a function of time. The gradual increase in strain, without increasein stress, with the time is due to creep. Creep can also be defined asthe increase in strain under sustained stress.One of the explanations given to the mechanics of creeps is basedon the theory that the colloidal particles slide against each other tore-adjust their position displacing the water held in gel pores and cap-illary cavities. This flow of gel and the consequent displacement ofwater is responsible for complex deformation behaviour and creep ofconcrete.

• Measurement of Creep- it is generally assumed that the creepcontinues to assume a limiting value after an infinite time underload. It is estimated that 26 per cent of the 20 year creep occursin 2 weeks. 55 per cent of 20 year creep occurs in 3 months and76 per cent of 20 year creep occurs in one year. If creep after oneyear is taken as unity, then the average value of creep at laterages are:1.14 after 2 years1.20 after 5 years1.26 after 10 years1.33 after 20 years and1.36 after 30 yearsThere are many expressions to give the magnitude of ultimatecreep in concrete member. Ross suggested the relation betweenspecific creep (creep strain per unit stress)c and time under loadt in the form -

c = ta+bt

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• Creep is influenced by changes in Aggregates, Mix proportioning,and Age.

3. Modulus of Elasticity-

• In view of the peculiar and complex behaviour of stress-strainrelationship, the modulus of elasticity of concrete is defined insomewhat arbitrary manner. The term Youngs modulus of elas-ticity can strictly be applied only to the straight part of stress-strain curve. In the case of concrete, since no part of the graphis straight, the modulus of elasticity is found out with referenceto the tangent drawn to the curve at the origin. The modulusfound from this tangent is referred as initial tangent modulus.This gives satisfactory results only at low stress value.

• The modulus of elasticity most commonly used in practice is se-cant modulus. There is no standard method of determining thesecant modulus. Sometime it is measured at stresses ranging from3 to 14 MPa and sometime the secant is drawn to point repre-senting a stress level of 15, 25, 33, or 50 per cent of ultimatestrength.

• Modulus of elasticity may be measured in tension, compressionor shear. The modulus in tension is usually equal to the modulusin compression.

• Relation between Modulus of Elasticity and StrengthModulus of elasticity of concrete increases approximately withthe square root of the strength. The IS 456 of 2000 gives theModulus of elasticity as, -

Ec = 5000√fck

where Ec is the short term static modulus of elasticity in N/mm2.

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