1 Introduction
2 Position of the Problem: Hypothesis
3 Modeling of the Circular Section
3.1 Discretization of the Concrete Section
3.2 Definition of the Position of the Bars
4 Calculation of Internal Forces
5 Practical Calculation of Internal Forces
5.1 In the Concrete and the Fiber Concrete
5.2 In the Reinforcing Bar
6 Establishment of Loading Curves
-
The first one, it’s about to find a N value (axial force), and for any Mi value; deformations balancing efforts (N, Mi). Then the loading curve M = f(δw) is deducted.
-
The second is to find a M value (bending moment), and for any Ni value; the deformations balancing efforts (Ni, M). Then the loading curve N = f(δu) is deducted. The Flowchart method is given in Fig. 4.×
7 Establishment of the Interaction Curve
7.1 Theoretical Explanations
7.2 Calculation Algorithm
8 Application to the Reinforced Concrete
8.1 Influence of the Steel Bars Number
f
cj
(MPa) |
f
tj
(MPa) |
E
bo
(MPa) | Parameter of the Sargin law |
ε
rt
|
ε
0
|
ε
cu
| |
---|---|---|---|---|---|---|---|
K
b
|
\( k_{{b}}^{{^{\prime } }} \)
| ||||||
25 | 2.1 | 32,164 | 2.316 | 1.316 | −0.05 | 0.018 | 0.0035 |
50 | 3.6 | 40,524 | 1.378 | 0.378 | −0.05 | 0.017 | 0.0035 |
E
a
(MPa) |
σ
e
(MPa) |
ε
u
|
σ
r
(MPa) |
---|---|---|---|
200,000 | 400 | 0.01 | 400 |
8.2 Influence of Concrete Strength Characteristics
8.3 Influence of the Steel Yield Stress
8.4 Influence of the Tense Concrete Participation
8.5 Comparing the Behavior According to the Conventional Relationships (BAEL)
9 Application to Steel Fibers Reinforced Concrete
9.1 Confrontation with Experimental Results
f
cj
(MPa) |
f
tj
(MPa) |
E
bo
(MPa) |
ε
rt
|
ε
0
|
ε
cu
| |
---|---|---|---|---|---|---|
BFAC | 47.6 | 2.94 | 38,180 | −0.05 | 0.0021 | 0.0035 |
BFON | 47.7 | 2.94 | 38,180 | −0.05 | 0.0021 | 0.0035 |
L
f
(mm) |
w (%) | Diameter (mm) |
E
a
(MPa) |
ε
u
| Configuration | |
---|---|---|---|---|---|---|
BFAC | 60 | 0.31 | 1 | 200,000 | 0.074 | Hooked fibers |
BFON | 60 | 0.31 | 1 | 200,000 | 0.074 | Undulated fibers |
9.2 Confrontation Between Reinforced and Steel Fibers Concrete
L
f
(mm) |
w (%) | Diameter (mm) |
E
a
(MPa) |
σ
e
(MPa) |
ε
u
| Configuration |
---|---|---|---|---|---|---|
30, 50 | 0.5, 1, 1.5 | 1 | 200,000 | 1100 | 0.074 | With hook |