Tensile strength of concrete Three kind of tensile strength Direct tensile strength (fdir, 직접인장강도) Splitting tensile strength (fsp, 쪼갬인장강도) Flexural tensile strength (fr, 휨인장강도, modulus of rupture) Relation between tensile strength and compressive strength Tensile strength ∝ fcu2/3 (recent research) Direct tensile strength test is difficult ⇒ Splitting tensile strength test (KS F 2423) & Flexural tensile strength test(KS F 2408) Rupture modulus :

Tensile strength of concrete Splitting tensile strength test Calculation of splitting tensile strength where, P : maximum load d : diameter of specimen L : length of specimen Flexural tensile strength test <third-point loading> <center-point loading>

Tensile strength of concrete Differences of each tensile strength Stress distribution of each testing method Area of maximum tensile stress Weak(failure) point ? - maximum stress, defect(or crack) !!

Shear strength of concrete Shear strength is difficult to measure but 20%~80% of compressive strength Almost every failure of members is due to diagonal tension crack(사인장균열), not direct shear Shear strength of members is represented by tensile strength Strength (강도) : resistance capacity of material against load Stiffness (강성) : resistance capacity of member against deformation Stress (응력) : load per unit area <Shear failure of beam>

Stress-strain relation 2.3 Mechanical properties Stress-strain relation stress strain Almost straight line (in small stress), convex curve growing to maximum stress point Maximum stress point (strain : 2%), rupture strain is 0.3~0.4% in general compressive test : smaller plastic deformation than steel, polymer…, brittle material

by Hognestad Stress-strain relation 2.3 Mechanical properties Model code of stress-strain relation by Hognestad where, εu : rupture strain εp : strain at maximum stress

by Faffitis, Shah Stress-strain relation 2.3 Mechanical properties Model code of stress-strain relation by Faffitis, Shah where , , strain at maximum stress

by Kim, Lee Stress-strain relation 2.3 Mechanical properties Model code of stress-strain relation by Kim, Lee where, , ,

Stress-strain relation 2.3 Mechanical properties Affecting factors of stress-strain relation Strength of concrete Age high-strength 7 days 28 days 3 days 1 day 12 hours low-strength

Stress-strain relation 2.3 Mechanical properties Affecting factors of stress-strain relation Loading rate additional strain due to creep

fcu 0.75 fcu 0.5 fcu ft ft ≈ 1/10 fcu Stress-strain relation 100 2.3 Mechanical properties Applied load : Tensile strain : Stress-strain relation of compression & tension 0.75 fcu fcu 0.5 fcu Compressive failure Tensile failure 100 500~1000 ft ft ≈ 1/10 fcu

Elastic modulus Elastic modulus of aggregate, cement paste, concrete 2.3 Mechanical properties Elastic modulus of aggregate, cement paste, concrete

Elastic modulus Various modulus of elasticity 2.3 Mechanical properties Various modulus of elasticity secant modulus of elasticity (할선 탄성계수 ) tangential modulus of elasticity where, f1 : stress at 50μ strain ε2 : strain at 0.4fcu initial tangential modulus of elasticity initial tangential modulus of elasticity (초기 접선 탄성계수) initial slope of stress-strain curve relation with secant modulus secant modulus of elasticity

Elastic modulus (model code – korea) 2.3 Mechanical properties unit : MPa secant modulus of elasticity : unit weight (단위중량) of concrete ~ 30 MPa 30 MPa ~ Source: 콘크리트 구조설계기준 3장 initial tangential modulus of elasticity Source: 콘크리트 구조설계기준 식 2.2.19

Elastic modulus (model code – korea) 2.3 Mechanical properties Elastic modulus affected by age of concrete where, Source: 콘크리트 구조설계기준 식 2.2.19 Dynamic modulus of elasticity ultrasonic pulse test… Larger than static modulus by 20~40% Relation with static modulus (England)