BETONARME 1 Ders1

REINFORCED CONCRETE 10423522

Dr. Murat Serdar Kırçıl

İNM 1-024

www.yildiz.edu.tr/~kircil

Reinforced Concrete 1 Lecture Notes

Dr.Murat Serdar Kırçıl

Outline of the course

Brief history

Basic information on ingredients of reinforced concrete: Cement, sand-aggregate, water

Mechanical properties of concrete

The fundamentals of the design of reinforced concrete structures: Methods and assumptions

Design of reinforced concrete elementsFlexural designShear design, shear & torsion Members subjected to axial force onlyMembers subjected to axial force and flexure

Serviceability

Bond and anchorage

WHAT IS STRUCTURAL ENGINEERING?

STRUCTURAL ENGINEERING IS

THE ART OF USING MATERIALSthat have properties which can only be estimated

TO BUILD REAL STRUCTURESthat can only be approximately analyzed

TO WITHSTAND FORCESthat are not accurately known

Edward L. Wilson,

(Three Dimensional Static and Dynamic Analysis of Structures)



REINFORCED CONCRETE

Concrete is a structural material that has high compressivestrength while its tensile strength is low. It is produced bymixing sand-aggregate, cement and water. Some admixturesmay be added to concrete if they are required.

Reinforcement steel is used to compensate the tensilestrength deficiency of concrete.

The material as a combination of concrete and reinforcementsteel is called REINFORCED CONCRETE (R/C).

The compressive force is sustained by the compressivezone of the R/C sections.

The tensile forces is sustained by reinforcement steel barswhich are placed on the tension side of the RC sections.



HISTORYIn ancient period, the human-being was used stones as a structuralmaterial since its compressive strength is high. Some Hellenistic andRoman templates were constructed by using such massive stones.



Betonarme 1 Ders Notları


However, the span of the stones were limited since stone’stensile strength is pretty low and because of the absence ofbinder. The longer span requires larger section height andheavier stone; and those heavy stones cause some operationaldifficulties.

To overcome this difficulty, the human-being developed newstructural forms which all sections are under the effect ofcompression such as arch and dome.

HISTORY


Yrd.Doç.Dr.Murat Serdar Kırçıl

The Assyrians and Babylonians used clay as a binder, andEgyptians made further progress by the discovery of limeand gypsum mortar as the binding agent for monumentalstructures, such as pyramids.

HISTORY

The Romans developed a cement by mixing slaked limeand volcanic ash. The volcanic ash was obtained fromMount Vesuvius and called Pozzolona.



During the middle ages the art of making cement was lost.

HISTORY

The first hydraulic cement that hardens under water wasdiscovered by an English engineer John Smaeton in 1756.This product is still known today as hydraulic cement.

In 1824 Joseph Aspdin, a brick layer in England, patentedportland cement, as much superior product. The productionand usage of portland cement became widespread in manycountries in the second half of 19th century.



In 1849, J.Louis Lambot used the reinforced concrete at thefirst time for the production of RC boat that was floated on riverSen. He used iron wires as reinforcement.

HISTORY



W.Wilkinson constructed a building with reinforcedconcrete slabs, as the first production of reinforcedconcrete in building type structures, in 1854. Heconctructed a two storey cottage with reinforced concreteslabs. He used iron bars and wires as the reinforcement steel.

HISTORY



Reinforced concrete was patented first time in 1855 by Coignet andthen in 1857 by Monier. Monier produced huge RC flowerpots for thegarden of Versaille Palace and led the today’s RC circular water tanksby using circular wires as tensile reinforcement.

HISTORY



One of the important RC building structure was constructed in 1875by an American engineer, William E. Ward. He noted all the problemshe had got and the solutions he had developed. He published hisstudies in 1883 with an article titled as Beton in Combination with IronAs a Building Material (American Society of Mechanical Engineers).

HISTORY



The first book, titled as Das System Monier, which defines theprinciples and design methods have been written by Wayss andpublished in 1887.

HISTORY



The first RC arch bridge was concstructed in New South Wales in 1900 by using Monier System.

HISTORY



In Turkey, the first multistorey RC building have been constructed in 1918 by Mimar Kemaleddin. (Merit Antique Hotel in Laleli)

HISTORY



French engineer François Coignet carried out many beam andcolumn experiments and led the design methods of modern RCbuilding systems. He published a book with Napoleon De Tedesco onthe basis of knowledge obtained from the afromentioned experiments.

They developed straight line theory which based on the elastic behaviour of concrete and reinforcement steel.

HISTORY



The first code has been published in 1904 and 1906 in Germany andFrance, respectively.

The German code was used in Turkey until 1953. In 1953 the firstTurkish code for RC structures was published by Turkish Associationfor Bridge and Structural Engineering (Türkiye Köprü ve İnşaatCemiyeti). It was revised in 1962.

In 1969, TS500 has been published by Turkish Standards Institution (TS500 – Betonarme Yapıların Hesap ve Yapım Kuralları)

In 1984, it was revised and Ultimate Srength Design has beenintroduced.

The last revision was made in 2000 and elastic theory has been repealed.

There are some international codes those effect the national codes. The most importants are ACI-318 (published by American Concrete Institute), CEB (published by Europen Concrete Committee), and Eurocode 2 (code for Europen Union countries).

HISTORY



ADVANTAGES OF REINFORCED CONCRETE

• It is economic for short and mid-span lenghts (L<8~10m) comparingto other materials.

• It is a viscous material and can be shaped easily.

• Production of concrete is easy. High qualified workmanship is notrequired.

• Maintenance of reinforced concrete is easier than that of steelstructures. Furthermore, it is more durable against the harmful effectlike water or some chemicals.

• It is durable to fire and high temparature.



• Construction defects, especially made with reinforcement, can not berealized after concreting; until the observation of deformations andcracks in structural elements.

• Retrofitting and strengthing of RC structures is not quite easy sincediffuculties in providing compatibility of new and existing concrete.

• The quality of concrete is completely depends on the site conditions ifit’s not ready-mixed.

• It is not economic anymore with increasing span length (L>10-12 m)

DISADVANTAGES OF REINFORCED CONCRETE



REINFORCED CONCRETE STRUCTURES

Frame with shear wall

Shear wall / perde

Column / kolon Beam

kiriş

FOTOĞRAFLAR PROF.DR.AHMET TOPÇU’NUN DERS NOTLARINDAN ALINMIŞTIR. http://mmf2.ogu.edu.tr/atopcu/

Column

Beam

Shear wall



FOTOĞRAF İNŞ. MÜH. MUTLU ÖZTÜRK’ÜN ALBÜMÜNDEN ALINMIŞTIR.

Frame with shear wall




Shear building





Frame structures


Column

Beam




CONCRETE

It starts to harden as soon as molded and its strength increases withtime.


Concrete is a material as the mixture of cement, sand, aggregateand water. If it is prepared using the proper portion of theafromentioned ingridients then a plastic material, which can bemolded into a predetermined shape, is obtained.



CEMENT

Cement is a pulverized material which consists of clay and limestone.Those materials are mixed, fused and then pulverized in rotary kilns.It is called ‘hydraulic bind’ since it becomes plastic when it interactswith water.



There are several types of cement with different ingredients andproduction type. The most widely-used one is Portland Cement.TS19 is the Turkish Standard which gives the minimum specificationsof portland cement. The portland cement is classified by itscompressive strength; PÇ 32.5, PÇ 42.5 and PÇ 52.5 havecompressive strength of 32.5 MPa, 42.5 MPa and 52.5 MPa,respectively. It reaches its specified strength in 28 days.

Some other types of cements are Portland Blast Furnace Cementand Puzzoloniz Cements .

CEMENT



WATERMixing water for concrete may be taken from any supply suitable fordrink. Natural waters also can be used for mixture. Waters whichcontain clay, acid, organic materials and industrial wastes can not beused as mixing water. Sea water either can not be used since itcontains high amount of salt that causes corrosion.



AGGREGATEAggregate is used in concrete mainly to reduce the amount ofcement paste. It also limits volume change of concrete and makesmore durable as compared to cement paste. Aggregate should beclean, hard, strong and durable. Aggregate containing considerableamount of silt or clay should not be used in concrete unless it iswashed.

Fine aggregate (sand) < 7mmCoarse aggregate’s diameter varies from 7 mm to 70 mm



CONCRETE

KUM

ÇAKIL

ÇİMENTO

+ SU BETON

It starts to get hardener as soon as it’s molded into a prescribed shape.It reaches its characteristic srength in 28 days.

Concrete is a material as the mixture of sand, aggregate, cementand water. It gets harder with time.



The most important property of concrete is its compressivestrength. Furthermore, durability became an another importantproperty in recent years.

Concrete mixture must be designed mainly to obtain the requiredstrength and workability. Slump test is a widely used method to test theworkability of concrete.

CONCRETE



CONCRETE / Slump TestSlump test is a widely used test to check the workability of the freshconcrete.


The test is carried out using a mould known as a slump cone orAbrams cone. This cone is filled with fresh concrete in three stages,each time it is tamped using a rod of standard dimensions (Ø12,l=60cm). At the end of the third stage, the cone is carefully liftedvertically upwards, so as not to disturb the concrete cone. Concretesubsides. This subsidence is termed as slump.



It is expected to have slump 50-100mm. The concretewill be used for foundations must have slump between30 mm and 80 mm. For the concrete will be placed withvibration, drier concrete with slump 0-50 mm isacceptable.

CONCRETE / Slump Test



Mechanical properties of concrete(Compressive strength)

FOTOĞRAF YRD.DOÇ.DR.HAYRİ ÜN’ÜN DERS NOTLARINDAN ALINMIŞTIR.

Concrete is a typical brittle, nonlinear and nonhomogeneous material with high compressive strength while its tensile strength is very low.

The compressive strength is defined as the strength of 28 days old specimen tested under the monotonic uniaxial compression. The universal standard test specimen is cylindrical specimen with diameter of 150 mm and height 300 mm.



FOTOĞRAF MUTLU ÖZTÜRK’ÜN ALBÜMÜNDEN ALINMIŞTIR.

Sometimes cube specimens can be used instead of cylindirical one. The cube specimen’s edge length is 200mm.




FOTOĞRAF MUTLU ÖZTÜRK’ÜN ALBÜMÜNDEN ALINMIŞTIR.

The ratio between strength values obtained using cylindir and cube specimen is averagely 0.8-0.85. 0.80, 0.85 and 0.90 values are proper for normal strength concrete, high strength concrete and very high strength concrete, ( Ersoy, U., Özcebe, G., Betonarme, Evrim Yayınevi).




Concrete gets harder with time. Hardening is very fast during the first 7 days and its strength rises up to %70 percent; then, hardining speed decreases.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 100 200 300 400

Gün

Day

anım

28 days old strength

Strength at 1 year

Strength after 3 months

7 days old strength

3 days old strength




Characteristic strength of concrete is defined as the 28 days oldstrength by all national and international codes. TS500 defines theconcrete with strength between 16 Mpa and 50 Mpa as normal strengthconcrete.

C 20

Concrete 28 days old characteristic compressive strength (MPa)

fck=20 N/mm2




Concrete

class

Characteristic

compressive

strength

Equivalent

cube

strength

(150mm)

Characteristi

c tensile

strength

28 days old

modulus of

elasticity

MPa Mpa MPa MPa

C16 16 20 1.4 27000

C18 18 22 1.5 27500

C20 20 25 1.6 28000

C25 25 30 1.8 30000

C30 30 37 1.9 32000

C35 35 45 2.1 33000

C40 40 50 2.2 34000

C45 45 55 2.3 36000

C50 50 60 2.5 37000

Concrete grades and strengths defined by TS500/2000





Obtained with uniaxial load

Strain = Axial shortening

fc

εεεεcoεεεεcu

Stress (σ)

Strain(ε)

FA

ε

A

F=σ

Sress-strain curve (uniaxially loaded)



Typical stress-strain relationship for concrete

The curve is almost linear at the level of low stress values.

fc


Stress (σ)

Şekil değiştirme (ε)

It becomes parabola with increasing load and strain

The top of the curve shows the strength of concrete (fc)

It is crushed when the failure (crushing) strain is reached (εcu). The stress corresponding to crushing is lower than maximum stress (compressive strength).


Beyond this point, strain increase achived decreasing stress.




fc


σ

ε

Is the shape of stress-strain curve same

always?

?


Typical stress-strain relationship for concrete




Tek eksenli basınç etkisinde beton silindirler için gerilme-şekil değiştirme eğrileri (Ersoy, U., Özcebe, G., Betonarme)

The initial slope of curves increases with the increasing strength

Deformation corresponding to maximum stress is almost always 0.002 and not effected by compressive strength.


It is not possible to find a unique curve.




Tek eksenli basınç etkisinde beton silindirler için gerilme-şekil değiştirme eğrileri (Ersoy, U., Özcebe, G., Betonarme)

It’s not possible to define a stress-strain curve with one equation since it has different characteristics at different stress levels. It’s linear at low stress levels while it becomes parabola with increasing stress.

The top point of the curve becomes evident with increasing strength.

Ductility decreases with increasing strength

DUCTILE

BRITTLE

Mechanical properties of concreteSress-strain curve (uniaxially loaded)



What can we use stress-strain curve of concrete (uniaxial

stress) for?

?




This part of section is elongating since it is loaded by tensile force.(Tension side)

This part of section is under the effect of compressive force and it is shortening. (Compression side)

+



M

+

M

FC FC

FT FT



FC

FT

ASSUMPTION: The stress distribution of concrete in compression is assumed to be same as the σ-Ɛ curve obtained experimentally from uniaxially loaded specimen.

σσσσ

εεεε

0.85fcd

0.002 0.003

Streess-strain curve given by TS500/2000.

1/1



REDISTRIBUTION (Yeniden dağılım)

N.A

FC

σ

ε

σ

ε

σ

ε

σ

ε

At a certain stage of loading, extreme compression fiber reaches maximumstress and relevant strain level. Failure is not observed at this stage althoughmaximum stress is reached since adjacent fibers are not fully stressed.These adjacent fibers help the fully stressed extreme fiber and preventfailure. The fully stressed extreme fiber has greater deformation capacity than��but a loss of stress. Finally failure is occurred when the extreme fiberreaches ultimate strain ( ��). This behavior of concrete is calledredistribution.

fc


σ

ε



Is loading rate effective on

stress-strain?

?




Yükleme hızının gerilme-şekil değiştirme eğrisine etkisi (Berktay, İ., Betonarme 1, İMO İst. Şubesi)

Concrete is a material which deforms with time. This figure showsthe curves obtained from the experiments carried out in Munich Tech.University under the supervision of Prof.Rüsch.

Loading rate is low

Loading rate is high

Low loading rate is decreasing strength as it’s increasing theductility

Mechanical properties of concreteSress-strain curve (loading rate)



Modulus of elasticity (Elastisite modülü)

Inıtal modulus is the slope of tangent to the curve at the origin. It is realistic if the stress level is low.

σ

ε

fc

Tangent modulus

Secant modulusInıitial

modulus




Tangent modulus is the slope of the tangent to the σ-Ɛ curve at a given stress.

σ

ε

fc

Tangent modulus

Secant modulusInitial

modulus

Modulus of elasticity (Elastisite modülü)Mechanical properties of concrete



Secant modulus is the slope of the secant at a given stress

σ

ε

fc

Tangent modulus

Secant modulusInitial

modulus




TS500/2000 gives the secant modulus relevant to 0.4fc and it is calculated with the given equation below.

σ

ε

fc

Secant modulus

Ec = 3250 (fck)0.5 + 14000 (N/mm2)

0.4fcEc




ACI318 equation for modulus of elasticity

Ec = 9500 (fck + 8)1/3 (N/mm2)

Ec = 4750 (fck)0.5 (N/mm2)

Eurocode2 equation for modulus of elasticity

For fc = 20 N/mm2

TS500 Ec = 28534

ACI318 Ec = 21243

Eurocode Ec = 28848




Poission ratio, Shear modulus and Coefficent of thermalexpansion

Poission ratio given by TS500/2000 is 0.20

Shear modulus can be taken as

Ec40.0c

G =

Coefficient of thermal expansion given by TS500/2000 is 10-5 1/oC




Tensile strength (Çekme dayanımı)As mentioned before concrete has a very low tensile strengthcomparing to its compressive strength (approximately %10 of thecompressive strength). There are different methods to determine tensilestrength of concrete; Direct Tension Test, Modulus of Rupture Test(flexure test) and Split Cylinder Test. Each method may yield differentresult. TS500/2000 gives the tensile strength obtained from DirectTension Test. For the computation of tensile strength, the equation shownbelow is given by TS500.

fctk= 0.35 (fck)0.5 (N/mm2)

ACI318 gives the tensile strength obtained from Modulus of RuptureTest with the equation shown below.

fctf = 0.63 (fck)0.5

Eurocode 2 gives the tensile strength determined with Direct TensionTest.

fct = 0.21 (fck)2/3




Time dependent deformation of concreteShrinkage (büzülme)

The water necessary for the hydration of concrete is 25% of cement byweight (Ersoy U., Özcebe G., Betonarme). However, water used forconcrete mix is more so that workability is provided. The excess water thatnot used for hydration evaporates after placing the concrete in the forms.The volume of concrete decreases as it evaporates. This behavior ofconcrete is called shrinkage.

Shrinkage(ε)

Time (t)t0

t0 = time concrete starts to harden

Betonda büzülme şekil değiştirmesi - zaman ilişkisi, (Berktay, İ., Betonarme 1, İMO İst. Şubesi)



Shrinkage is almost completely reversible. Concrete that has undergone to shrinkage in a dry environment can expand and return its original shape if it is placed in water again.

If a concrete member is restrained by other members then shrinkage cracksare observed on the member. The amount of shrinkage depends ontemperature, humidity, area of exposed surface and the water content ofconcrete mix.

Time dependent deformation of concreteShrinkage (büzülme)



CREEP (Sünme)Creep is the shortening of a concrete element under the effect of a long-term and constant compressive load.

All factors which effect shrinkage is also effective on creep. In addition toaforementioned factors, the age of concrete is effective on the creep ofconcrete. For younger concrete creep is more.

Time dependent deformation of concrete

If the sustained load on the concrete specimen is removed there is somerecovery on in the deformations.



This figure shows the creep behavior of a reinforced concrete element.

Sabit eksenel basınç altında zaman bağlı tipik sünme eğrisi, (Ersoy, U., Özcebe, G., Betonarme)

The portion OA (∆i) shows the instantaneous deformation occured assoon as the concrete element is loaded. The deformation increasesbetween AB, although load is kept constant on the specimen.

CREEP (Sünme)




The difference between the deformations at A and B shows the time-dependent deformation (∆t) of concrete (shrinkage + creep) since there isno change in the load between those points.

Sabit eksenel basınç altında zaman bağlı tipik sünme eğrisi, (Ersoy, U., Özcebe, G., Betonarme)

There will be immediate recovery when the load is removed at point B whichis called elastic recovery (portion B-C, ∆re). Some more recovery isobserved with time (portion C-D, ∆rc) which is called creep recovery. Thedeformation which is marked ∆p is never recovered (permanentdeformation). This deformation is usually greater than initial instantaneousdeformation (OA).

CREEP (Sünme)




Reinforcement steel (donatı çeliği / donatı)


The reinforcement steel, that is placed in the tensile zone of the section, isused to compensate the weakness of concrete in tension. Reinforcementbars are designated with their diameter in mm. The reinforcement steel usedin concrete may either plain bars or deformed bars. The deformed bars havesmall projections (nervür) to engage the concrete so that slipping betweenreinforcement bar and concrete can be prevented.

Plain barDeformedbar



Designation Diameter (mm) Weight (kg/m) Cross-sectional

area(mm2)

∅∅∅∅6 6 0.22 28

∅∅∅∅8 8 0.40 50

∅∅∅∅10 10 0.62 79

∅∅∅∅12 12 0.89 113

∅∅∅∅14 14 1.21 154

∅∅∅∅16 16 1.58 201

∅∅∅∅18 18 2.00 254

∅∅∅∅20 20 2.47 314

∅∅∅∅22 22 2.95 380

∅∅∅∅24 24 3.55 452

∅∅∅∅26 26 4.17 531

∅∅∅∅28 28 4.83 616

∅∅∅∅30 30 5.55 707

∅∅∅∅32 32 6.31 804

∅∅∅∅34 34 7.13 908

∅∅∅∅36 36 8.00 1018

∅∅∅∅38 38 8.90 1134

∅∅∅∅40 40 9.87 1257



S420aS420bS500aS500b


S220a

Widely used

Not widely used

(maybe as transverse reinforcement)






420S aSteel

Yield strength (MPa)

Manufacturing process

Hot rolled steel reinforcement with the characteristic yieldstrength of 420 MPa





Characteristic yielding strength is denoted with fyk

Hot rolled steel reinforcement with the characteristic yieldstrength of 420 MPa

420S aSteel

Yield strength (MPa)

Manufacturing process




The reinforcing bars can be grouped in 2 classes depending on their manufacturing process

Hot rolled: S220a, S420a, S500a

Cold worked (soğukta işlenmiş): S420b, S500b

Hot rolled steel is manufactured in the plant. Some is used directlywhile some is added metals (nickel, silisium, manganese, crom etc.) toincrease their strength.

In cold working process, steel is drawn or twisted under normaltemperatures. The molecules are rearranged and strength increasesbut strain limit and ductility decreases.





R.150.250.8.5 R.150.150.8.8

Welded wire fabric reinforcement




The figure shows the σ – ε curves of both hot rolled (a) and cold worked (b) reinforcement steel, respectively.

Çelik için gerilme-şekil değiştirme eğrileri(Ersoy, U., Özcebe, G., Betonarme)




Hot rolled steel has a definite yield point and yield plateau. Up to the this point stress-strain relationship is linear. Strain hardening starts at the end of the yield plateau. It keeps elongating until its maximum strain capacity.

However, the cold worked steel (curve b) does not have a definite yield point and yield plateau. The yield strength is defined as the stress corresponding to a permanent strain of 0.002

Çelik için gerilme-şekil değiştirme eğrileri(Ersoy,

U., Özcebe, G., Betonarme)




However, the cold worked steel (curve b) does not have a definiteyield point and yield plateau. The yield strength is defined as the stresscorresponding to a permanent strain of 0.002.

A line is drawn parallel to the initial slope of the σ – ε curve. Thehorizontal projection of the intersection point is defined yield strength.




Steel grades and their mechanical properties in TS500


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BETONARME 1 Ders1