Factors that influence the tensile strength

The quality of the concrete is influenced by its plastic character behavior near breaking. The concretes of inferior quality behave with a pronounced plastic character, and the stresses from the tensioned zone are distributed quite uniformly; in the concretes of superior quantity, having a pronounced elastic behavior, the distributions of the stresses are linear. Consequently, this factor will influence much more the value of the strength for the concrete subjected to bending tension, while the strength of the concrete subjected to riving tension is less influenced.

The form and the size of the test samples. The tensile strength of the concrete is influenced by the size of the test sample, its value decreasing with the increase of the cross section. One cause is attributed to the concrete shrinkage that creates an initial state of stress, reducing the tensile strength.

• To the big size elements, the shrinkage is not uniform on the element surface and the stresses produced by the shrinkage are bigger, which leads to a decreasing of Rt.

• The strength Rti is influenced by the depth of the cross section: when depth is bigger, then Rti is smaller, because the plasticity of the tensioned zone is smaller when the depth is bigger.

• The quality of cement and the cement dosage, influence though the quality of the cement stone that assures the bond between aggregates. The superior quality cements from concretes with bigger tensile strength.

• The increase of the cement dosage influence more significantly the compressive strength than the tensile strength; in some cases, the increase of the cement dosage can produce a diminish of the tensile strength.

• The ratio W/C does not significantly influence the tensile strength.

• The aggregates influence though the nature of surface, granulosity and mineralogical nature. A concrete prepared with crushed stone has a bigger tensile strength, because of their better adherence to the cement stone.

• When the fine parts have a large volume, the tensile strength is smaller.

• The mineralogical nature influences though the adherence realized on the surface aggregate-cement stone.

• The tensile strength is more significantly influenced by the protection of the concrete after pouring; if this protection is not realized, the tensile strength will be smaller. Also, the homogeneity of the concrete, the compaction technology and the admixtures which diminish the quantity of water, have a good influence on the tensile strength.

• The keeping environment influences very much the tensile strength, especially by its humidity. In the first stages of its hardening, the concrete must be kept in favorable conditions. The concrete kept in wet environment has bigger tensile strength. To the concretes that harden in dry environment, initial stresses of shrinkage occur, these reducing the tensile strength. The water evaporation from the concrete, at a short time from its pouring, depends on the wind speed, that produce the air change on the concrete surface. An increase of the protection temperature of the concrete hurries the chemical hydration reactions and has a good influence on the early strength of the concrete, without any dangerous effect on the later strength. But a higher temperature during the pouring and the hardening, can unfavorably influence the strength after 7 days.

Shear strength of the concrete

• In reinforced concrete elements, the pure shear strain is very seldom met. Usually the shear forces are accompanied by bending moments, which result in simultaneous unit shear stresses and normal stresses . The direct determination of shear strength or is a difficult operation, having in view the great number of test samples Fig. 3.12.

Fig. 3.12 Types of test samples

• Taking into account that in the failure state the distribution of the unit stresses is modified and the concrete is a brittle material, the failure can be considered to take place under the action of principal unit tension stresses , the breaking being produced by wresting:

• For calculation, we can admit:

bR3,0...........2,0R

tiR6,1R

Breaking of the concrete subjected to torsion

• The torsion test of some test samples showed that oblique cracks appear on lateral surfaces at 45° from the ax of the bar, disposed on propeller-type direction, (Fig.3.13), the same with that of the principal unit compressive stresses, thus showing that the breaking is caused by the principal unit tension stresses .

• Only unit shear stresses occur on the cross section of the test samples tested to torsion. If the moments of torsion are not too big and the unit stresses do not exceed the micro-cracking value of the unit tensile stress, the concrete behaves like an elastic material, in cases of short time loading.

Fig. 3.13. The cracking of torsion elements

For a cylindrical test sample, supposing that the material is elastic we can write:

te

ttt W

MR

tM is the torsion moment

teW is the torsion resistance modulus

2

r

r2

r

r

IW

34p

te

pI is a polar inertia moment of the cross section.

• Approximate methods are used in the case of bars with cross sections other than circular.

• If the concrete would haven elastic behavior up to its breaking:

ttete R.WM Actually, if the torsion moment exceeds a certain limit value, the stresses produce the microcraking of the Concrete.

Further on its behavior is elastic-plastic. Experimental researches showed that for usual concretes the plasticity is complete or near complete before the failure.

Relation between compressive and tensile strengths

•The compressive strength of concrete is considered the most important property and it is used for structural design especially in civil engineering.•For some purposes the tensile strength is used for designing, for example in the case of the design of highway and air field slabs, shear strength, resistance to cracking.

ttpt R.WM

tpW is the torsion resistance modulus in the plastic stage.

• In hydraulic construction the concrete is characterized by the split tensile strength and flexural strength, near the compressive strength at 90 days.

• The road concrete is characterized by the flexural strength.

• The two types of strength are related, but there is no direct proportionality. As the compressive strength fc increases, the tensile strength, ft also increases but at a decreasing rate.

• A number of factors affect the relation between the two strengths, such as: type and grading of aggregates, age, type of tests, curing, compaction, etc

• A number of empirical formulae connecting tensile strength ft and compressive strength fc have been suggested, many of them of the type:

nct fkf

where: k and n are coefficients.The best relation is given by the expression:

3/2ct f3.0f

where: ft is the splitting strength in MPa fc is the compressive strength on cylinders.

The above expression was suggested by Raphael [1].A modification was given by Oluokun:

7,02,0 ct ff

• A relation given in British Code of Practice BS 8007:1987 is:

• Where the compressive strength is determined on cubes (MPa) and ft represents the direct tensile strength

• The mean strength to axial tension, fctm can be computed from the average value of compressive strength, fcm with relation [2]:

7,012,0 ct ff

cmo

cmnctmoctm f

f1lff

MPa10f

MPa12.2f

cmo

ctmo

where:

Breaking of the concrete subjected to fatigue

• One of the most important elements that influences the breaking resistances of the concrete subjected to different loads, is the time element, consisting in the speed of test and the period of maintaining under charge.

• If the loading speed increases, the compression strength of the concrete also increases. The explanation consists in the occurrence and increase of the micro-cracking process. At great loading speeds, the developing of the micro cracking is not complete, thus the breaking occurs at bigger stresses. If loading has a permanent or a long-term duration character and its intensity is situated over the micro-cracking limit, the micro-cracks develop in the whole mass of the concrete and the breaking takes place in time, at smaller loads than in the case of testing under short-term duration.

• The minimum value of the unit stress to which the breaking takes place is named duration mechanical strength or statistic fatigue strength.

• The constructions placed in seismic zones can be subjected to repeated major loads during earthquakes.

• The phenomenon of fatigue appears even if the number of cycles during the earthquake is not too big (this phenomenon is known as “low-cycle fatigue”).

• In many structures, however, repeated loading is applied. Typical of these are offshore structures subjected to wave and wind loading, bridges, road and railway sleepers (ties); a number of cycles of loading applied during the life of the structure may be as high as 10 million, and occasionally even 50 million.

• The concrete solicited at high speed until the value of the statically breaking force is reached, does not attain the critical state off degradation from the first cycle.

• Only after some cycles the volume of degradations increases and can produce the breaking. If the maximum load gradually diminishes with every cycle, the chances of survival increase.

• If during the loading cycle the load intensity does not very much exceed the micro-cracking limit, the micro-cracks can develop only after a great number of loading-unloading cycles (this is dynamic fatigue). The number of cycles is much bigger if the load produces stresses with values near the micro-cracking limit. The number of cycles to which the fatigue occurs depends on the amplitude of the loading oscillation, that is the ratio between the minimum and maximum stress , also named lop-sided coefficient.

• When a material fails under a number of repeated loads, each smaller than the static compressive strength, failure in fatigue is said to take place.

• One considers a concrete specimen subjected to alternations of compressive stresses. The stress-strain curve varies with the number of load repetition, changing from concave towards the strain axis (with a hysteresis loop on unloading) to the straight line, and eventually becomes concave towards the stress axis. The degree of this latter concavity is an indication of how near the concrete is to failure. Failure will however, take place only above a certain limiting value, known as “fatigue limit” or “endurance limit”.

• The change in strain with the number of cycles of loading can be described as consisting of three phases. In phase 1, that is, the initiation phase, strain increases rapidly, but a progressively decreasing rate, with the number of cycles of loading. In phase 2, which represents the stable state, strain increases approximately linearly with the number, of cycles. In phase 3, which represents instability, strain increases at a progressively increasing rate until failure in fatigue take place.

• The strain at failure in fatigue is much larger than in static failure.

• The elastic strain also increases progressively with cycling.

• Strictly speaking, concrete does not appear to have a fatigue limit, i.e. a fatigue strength at an infinite number of cycles.

• Generally speaking, the ratio of fatigue strength to static strength is not independent of the water cement ratio, the cement content type of aggregate, and age at loading because these factors affect both the static and fatigue strength in the same manner.

• As strength increases with age, fatigue strength both in compression and in flexure also increases. The important point is that, at a given number of cycles, fatigue failure occurs at the same fraction of ultimate strength, and is thus independent of the magnitude of this strength and of the age of concrete. It can thus be seen that a single parameter is critical in fatigue failure. It was exposed the view that the deterioration of bond between the hydrated cement paste and aggregate is responsible for this failure.

• It should also be noted that, for a given maximum stress in the cycle, as the amplitude of stress decreases, we are no longer dealing with fatigue but rather with sustained loading which leads to creep failure.

The duration of cycling becomes therefore important. Expressions taking this into account were developed by Hsu, who considers that separate equation for fatigue life are needed for low-cycle loading of the type caused by earthquakes.

• About the fatigue behavior of reinforced and pre-stressed concrete, it should note that fatigue cracks in concrete act as stress-raisers thus magnifying the vulnerability of the steel to fatigue failure.

• Another observation relevant to reinforced concrete is that the fatigue strength of bond of concrete with the reinforcement is the governing factor in reinforced concrete subjected to cyclic loading.

The fatigue strength depends on the age and the quality of the concrete, increasing with them.The fatigue tensile strength represents 0,6 of static tensile strength.

Breaking theories of concrete

• The breaking process of the concrete develops by the interaction of lot phenomena that occur behind and during breaking. It is very difficult to establish only one theory (or mechanism) that could take into account all complex phenomena that are developed in the concrete structure.

• In the course of time, many theories have appeared. They can by classified as follows:

• - phenomenological (or classical) theories;• - statistical theories;• - structural theories.

Phenomenological theories• These theories admit the following assumptions:• - the concrete is an homogeneous, elastic,

isotropic and continuous material;• - the breaking force is not influenced by the time

and the speed loading;• - the breaking behaviors does not depend on the

loads applying order.• Having in view the fact that these theories want to

establish the rules after which the breaking is produced, when the member subjected to a complex stress state, I the case when its behavior to simple solicitation is known.

• In this case, the six compounds can be replaced by the unit principal stresses, on three directions ,

• between these the following relation is admitted:321 , ,

• The maximum unit stresses theory admits that the breaking is produced when the maximum unit stress exceeds the breaking strength of material, and in this case, one can write:

321

cr3,2,1

where cr represents the compressive strength or the tensile strength.

•The maximum specific deformation theory considers that the breaking is produced when the maximum specific deformation exceeds the limit specific deformation:

• where b,t are the limit specific deformations to compression and tension, respectively.

• c) The theory of the maximum unit tangential stresses supposes that the breaking appears when the maximum unit tangential stress exceeds a critical value.

• The theories that refer to the physical phenomenon of the breaking consider that the concrete is a homogeneous material, and, in reality, the concrete is a material with elastic-viscous-plastic properties.

• Hence, other theories tried to explain the breaking phenomenon though the plastic criteria.

tbmax ,

• d) The theory of the specific mechanical work of from modification, or the plasticity criterion, considers that the breaking is produced when the specific mechanical work of form modification is exceeded for an element

subjected to compression or tension.

Statistical theoriesThe statistical theories consider that a process of

occurrence and development of micro-cracks that are normally

orientated on the direction of maximum tensile stresses precede the breaking process.Also, these theories consider that the concrete is not

homogeneous, and near the defects, stresses concentrations occur.

• The reparation of the structure defects is considered to be done under a statistical rule, fact that is not real, because the defects distribution depends on the technological factors, and on the keeping of the concrete after its pouring.

• These theories neglect some specifically characteristics of the concrete, (the gradual breaking character, the influence of preparing, pouring and keeping conditions).

Structural theories

These theories consider that the concrete breaking is produced by wresting on the maximum elongation direction, and the breaking is gradually produced.

• Hence, four stages of breaking were observed:- an incubation period;- a breaking period of deformations;- an uniform development of deformations;- a self-accelerated period of deformation development,

that precede the breaking.• The researches made by Graff, Skramtaev, L’Hermite,

Gvozdev, Seikin, Slate, Sturman, Berg, etc., for discovering the breaking process to axial compression had shown that:

- the concrete breaking is produced by traction (wresting) on the maximum elongation direction, at the contact surface aggregate-matrix, though the matrix, or even though aggregates.

- in the charged concrete structure micro-cracks are developed; these micro-cracks gradually unite and form macro-cracks;

- the unit stress under that the first micro-cracks occurs is in direct ratio to the concrete grade;

- for a stress that exceeds a certain value, depending on the concrete grade the concrete breaking can be produced by statically fatigue.

• The occurrence of micro-cracks in the concrete is favored by some factors, such as:

- the existence of the stress concentrations to the top of defects;

- the different properties of matrix and aggregates;- the stress states produced by shrinkage, swelling, etc.

• The breaking of the concrete to compression is produced as a result of the occurrence of micro-cracks in the concrete structure; these micro-cracks can develop or can stop. This is the first stage. In this stage, the consolidation process is stronger than the destruction one, and this fact leads to a damping of the breaking process in time. The micro-cracks occur when the unit stresses attain the micro-cracking limit R0.

• The second stage in the concrete behavior is represented by the moment when the stress attains the critic stress Rcr, over which the breaking begins to produce in an accelerated rhythm. When ,

the destruction process is continued, and in time appears an intense degradation of the concrete structure, that will lead to the breaking.

crb R

3.8. Characteristics and design strength of the concrete

ConcreteThe following clauses give principles and rules for normal and high strength concrete. StrengthThe compressive strength of concrete is denoted by concrete strength classes which relate to the characteristic (5%) cylinder strength fck, or the cube strength fck,cube, in accordance with EN 206-1.The strength classes in this code are based on the characteristic cylinder strength fck determined at 28 days with a maximum value of Cmax.The recommended value is C90/105.

The characteristic strengths for fck and the corresponding mechanical characteristics necessary for design, are given in Table 3.1. In certain situations (e.g. prestressing) it may be appropriate to assess the compressive strength for concrete before or after 28 days, on the basis of test specimens stored under other conditions than prescribed in EN 12390.•If the concrete strength is determined at an age t > 28 days the values αcc and αct defined in 3.1.6 (1)P and 3.1.6 (2)P should be reduced by a factor kt. The recommended value is 0,85.•(5) It may be required to specify the concrete compressive strength, fck(t), at time t for a number of stages (e.g. demoulding, transfer of prestress), where

fck(t) = fcm(t) - 8 (MPa) for 3 < t < 28 days.fck(t) = fck for t .> 28 days

• (6) The compressive strength of concrete at an age t depends on the type of cement, temperature and curing conditions. For a mean temperature of 20°C and curing in accordance

• with EN 12390 the compressive strength of concrete at various ages fcm(t) may be estimated from Expressions (3.1) and (3.2).

Where:

cmcctcm ftf )()(

where:fcm(t) is the mean concrete compressive strength at an age of t days

2/

)(

281exp

t

tcc ts

• fcm is the mean compressive strength at 28 days according to Table 3.1

• βcc(t) is a coefficient which depends on the age of the concrete t

• t is the age of the concrete in days• s is a coefficient which depends on the type of

cement:= 0,20 for cement of strength Classes CEM 42,5 R,

CEM 52,5 N and CEM 52,5 R(Class R)= 0,25 for cement of strength Classes CEM 32,5 R,

CEM 42,5 N (Class N)= 0,38 for cement of strength Classes CEM 32,5 N

(Class S)• Note: exp{ } has the same meaning as e( )

• Where the tensile strength is determined as the splitting tensile strength, fct,sp, an approximate value of the axial tensile strength, fct, may be taken as:

fct = 0,9fct,sp (3.3)

The development of tensile strength with time is strongly influenced by curing and drying conditions as well as by the dimensions of the structural members. As a first approximation it may be assumed that the tensile strength fctm(t) is equal to:

ctmcctctm ftf )()(

where βcc(t) follows from Expression (3.2) andα = 1 for t < 28α = 2/3 for t ¡Ý 28. The values for fctm are given in Table 3.1.Note: Where the development of the tensile strength with time is important it is recommended that tests arecarried out taking into account the exposure conditions and the dimensions of the structural member.

05,0,ctkf

95,0,ctkf

ctmf

Characteristic strength to axial tension with fractil of 5%,

noted respectively with fractil 95% noted

the médium value is obtained function

the mean value with following relations:

ctmctk ff 7,005,0,

ctmctk ff 3,195,0,

• Design strengths in compression and in tension are established with relations:

(fcd)(fctd)

c

ckcccd

ff

c

ctkctctd

ff

05,0,

ccctWhere: and

Are coefficients that take into consideration the long term and unfavourable effects resulted from the loads aplication.

The partial safety coefficient for concrete

• for design situations permanent and transitory;

• for accidental situations.• Coefficient is between 0,8 and1,0. In

EC2 the reccomended value for and for is 1,0.

• The values of strengths are given in Table 1.

c

5,1c

2,1c

cccc

ct

Confined concrete

Confinement of concrete results in a modification of the effective stress-strain relationship:higher strength and higher critical strains are achieved. The other basic material characteristicsmay be considered as unaffected for design. In the absence of more precise data, the stress-strain relation shown in Figure 3.6 (compressive strain shown positive) may be used, with increased characteristic strength and strains according to:

strains according to:fck,c = fck (1,000 + 5,0 σ2/fck) for σ2 < 0,05fck

fck,c = fck (1,125 + 2,50 σ2/fck) for σ2 > 0,05fck

εc2,c = εc2 (fck,c/fck)2εcu2,c = εcu2 + 0,2 σ2/fck

where σ2 (= σ3) is the effective lateral compressive stress at the ULS due to confinement and εc2 and εcu2 follow from Table 3.1. Confinement can be generated by adequately closed links or cross-ties, which reach the plastic condition due to lateral extension of the concrete.

Figure 3.6: Stress-strain relationship for confined concrete

Transversal reinforcing with spiral

The confinement effect on increasing the concrete compressive strength is important in the case of columns with circular cross section subjected to compression.

Conclusions

EC2 STAS 10107/90

• fcm -> fck (cylinders) Rb ->Rbk cubes (28 days)

• Characteristic strengths

fck Rck=(0.87-0.002Rbk)Rbk

fctm=0.3(fck)2/3 Rtk=0.22(Rck)2/3

• Design strengths:

• fcd=(fck/c) Rc=mbcRck/bc

=1 Rt=mbtRtk/bt

mbc=mbt=1

c=1.5 FG bc=1.35

=1.3 AC bt=1.5

FG-fundamental group of loadsAC accidental combination of loads is partial safety coefficient for

concrete

Table 3.1 Mechanical characteristics of concrete (MPa)

Concrete

grade

C12/15 C16/20 C20/25 C25/30 C30/37 C35/45 C40/50

ckf 12 16 20 25 30 35 40

cubckf , 15 20 25 30 37 45 50

cmf 20 24 28 33 38 43 48

ctmf 1,6 1,9 2,2 2,6 2.9 3,2 3,5

05,0,ctkf

1,1 1,3 1,5 1,8 2,0 2,2 2,5

95,0,ctkf

2,0 2,5 2,9 3,3 3,8 4,2 4,6