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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 ConcreteStress-Strain Characteristics of Concrete Subjected to Uniaxial Compression
Stress Strain Characteristics of ConcreteStress-Strain Characteristics of Concrete Subjected to Uniaxial Compression
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
Tensile Strength and σ−ε Properties of Concrete in Tension
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
Tensile Strength and σ−ε Properties of Concrete in Tension
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)
Tensile Strength and σ−ε Properties of Concrete in Tension
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.
Behavior under Multiaxial StressesBehavior under Multiaxial Stresses
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.
Behavior under Multiaxial StressesBehavior under Multiaxial Stresses
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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