1. 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 :

2. 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>

3. 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) !!

4. 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>

5. 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

6. 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

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

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

9. 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

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

11. 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

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

13. 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

14. 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

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