1 1 Material Behavior

Chapter 1

Material BehaviorMaterial Behavior

Stress Strain Characteristics of ConcreteStress-Strain Characteristics of Concrete Subjected to Uniaxial Compression

The stress-strainThe stress strain properties of concrete depend on many variables yamong which, (a) strength of concrete and (b) ( )confinement and (c) rate of loading are the most important ones.



Stress-Strain Characteristics of Concrete under Repeated Compressive Loading

Tests by a) Sinha, Gersle and Tulin, and b)Karsan and Jirsa

Modeling the Uniaxial Stress-Strain Curve of Concrete under Compression

Hognestad Model

Modeling the Uniaxial Stress-Strain Curve of Concrete under Repeated Compressive Loading

Envelop curveEnvelop curve

Stre

ss

StrainStrainThompson and Park Model

Tensile Strength and σ−ε Properties of Concrete in Tension

Direct tension test: σ = P/A


M d l f R t T tModulus of Rupture Test

IyMfctf

⋅=I

Tensile Strength and σ−ε Properties of Concrete in TensionSplit Cylinder TestSplit Cylinder Test

dP2fctslπ

=dlπ


cf35.0Direct tensile strength (fct is in MPa)

cf50.0

f70

Split tensile strength (fcts is in MPa)

Flexural tensile strength (f is in MPa) cf7.0

cf64.0

Flexural tensile strength (fctf is in MPa)

Flexural tensile strength (fctf is in MPa) cctf(Single load at mid span)


After Rüsch

Shear Strength and Modulus of ElasticityShear Strength and Modulus of Elasticity

Shear strength of concrete is higher than its tensile strengthg g gfs = 35 percent to 80 percent of fc

Modulus of ElasticityModulus of Elasticity

Pauw cj5.1

cj f)1362(wE =

ACI cjcj f4750E = cjcj

EUROCODE 2 3/1)8f(9500E +=EUROCODE 2 cjcj )8f(9500E +=

TS500 14000f3250E cjcj +=

Bearing StrengthBearing Strength

f2ff

In case of point loads

I f t i l d

cccl f2Rff ≤=

In case of strip loads

cc

cl f5.1bff ≤′

= ccl b5.1 ′

The ratio of total area to the loaded area is R.b and b' are the widths of the member and the loaded area, respectively

Shear Modulus, Poisson’s Ratio and Coefficient of Thermal Expansion

Coefficient of thermal expansion for concrete can be taken as 1×10-5 mm/mm/C0

which happens to be same with that of steel In case of point loads

Tests made at METU have revealed that the Poisson's ratioh i ifi tl ith thchanges significantly with the

load level.

At t l l f /f 0 3 0 7At stress levels of σc/fc=0.3-0.7, the Poisson’s ratio is approximately0.15-0.25. In and TS-500, it is specified as 0.20

Shear Modulus, Poisson’s Ratio and Coefficient of Thermal Expansion

Shear modulus also varies as a function of the load level. Various values have beenrecommended based on Ec and μc values found experimentally using the followingelasticity equationelasticity equation.

( )c

c 12E

Gμ+

=

In 1967, an extensive research program was carried at METU to study the relationship between G and E It was intended to determine G from two

( )c12 μ+

relationship between Gc and Ec. It was intended to determine Gc from two independent tests in which the same concrete would be used.

E40G = cc E4.0G =

In TS-500, above is recommended to compute the shear modulus.

Behavior under Multiaxial StressesBehavior under Multiaxial Stresses

Concrete Under Biaxial Stresses

Rüsch, H., und Hilsdorf, H., “Verformungseigenschaften von Beton unterZentrischen Zugspannangen” Materialprüfungsamt für das Bauwesen derZentrischen Zugspannangen , Materialprüfungsamt für das Bauwesen derTechnischen Hochschule München, Rep. No .44, 1963.


Concrete Under Triaxial Stresses

Richart, F.E., Brandtzaeg, A., and Brown, R.L., “A Study of the Failure ofConcrete Under Combined Compressive Stresses” University of IllinoisConcrete Under Combined Compressive Stresses , University of IllinoisEng. Exp. Sta. Bull. No. 185, 1928.


Cowan H J “The Strength of Plain Reinforced and Prestressed ConcreteCowan, H.J., The Strength of Plain Reinforced and Prestressed Concreteunder the Action of Combined Stresses, With Particular Reference to theCombined Bending and Torsion”, Magazine of Concrete Research, V.5,Dec 1953Dec. 1953.

04ff 2ccl 0.4ff σ+=

Behavior of Reinforcing Steel under Monotonic Loading

Behavior of Reinforcing Steel under Monotonic Loading

Es = 200 000 MPa

Behavior of Reinforcing Steel under Repeated and Reversed Loading

Bauschinger Effect

Repeated loading - unloading Repeated reverse cyclic loading

Modeling the Uniaxial Stress-Strain Curve of Steel under Monotonic Loading

εsy= f y /Es

0 01εsp= 0.01

εsu= 0.10-0.20

fsu = ~1.5f y

T ili d lTrilinear model

Modeling the Uniaxial Stress-Strain Curve of Steel under Reverse Cyclic Loading

Aktan, A.E., Karlsson, B.I., and Sözen, M., “Stress-Strain Relationshipof Reinforcing Bars Subjected to Large Strain Reversals”, CivilE i i St di St t l R h S i N 397 U i f

oi

1 Kσ775σ775K

−±−±=

Engineering Studies, Structural Research Series, No. 397. Univ. ofIllinois, June 1973. K0 = 8,000 MPa

nσ775±

Akt K l d S M d lAktan, Karlsson and Sozen Model

Tension StiffeninggAs early as 1899, it was known that a bar embedded into concrete block carries more load than that of a bare bar. Considėre tested smallblock carries more load than that of a bare bar. Considėre tested small mortar prisms reinforced with steel wires. When he subject the prism to tension he observed that their load-deformation response was almost parallel to the bare steel wire response but remained well above itparallel to the bare steel wire response but remained well above it.

Tension Stiffeningg

In 1908, Mörsch explained this phenomenon as follows:In 1908, Mörsch explained this phenomenon as follows:“Because the friction against the reinforcement, and the tensile strength which still exists in the pieces lying between the cracks, even cracked concrete decreases to some extent the stretch of reinforcement.”

This effect came to be called “tension stiffening.”

Tension StiffeningTension Stiffening

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1 1 Material Behavior