Page 158 - Riem-Vol6_nº3

503 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
F.M. ALMEIDA FILHO | M. K. EL DEBS | A.L.H.C. EL DEBS
tained by tests in cylindrical specimens (10x20cm). Figure 5 shows
the experimental behavior of SCC and OC, for each series, and the
steel bar behavior assumed in numerical study.
As shown at Figure 5, both concretes behavior were practically the
same. However, there was an absence of the descending branch
of the post-peak of its behavior, which could be achieved by using
Popovics’ formulation [19], shown below (Eq. 1 to 3).
(1)
(2)
(3)
This formulation takes into account the variation of the concrete
compressive strength in the post-peak branch. According to Popo-
vics’ theory, the relation between the initial modulus of elasticity
(Ec ) and the secant modulus of elasticity (Ecs) can vary until 4.0 for
normal strength concretes and in 1.3 for high strength concretes.
3.2 Mesh, load and finite elements
Figure 6 shows the used mesh for the numerical models; due to
the symmetry, only a quarter of the beam model was studied.
Experimental investigation of the bond stress response was
Figure 4 – Beams during tests
Figure 5 – Stress vs. strain behavior of steel and concrete
-1 0 1 2 3 4 5
-5
0
5
10
15
20
25
30
35
St re ss ( MPa)
Strain (‰)
OC1
SCC1
Popovics (1973)
-0,5 0,0 0,5 1,0 1,5 2,0 2,5
-10
0
10
20
30
40
50
60
70
Ec(CAA) = 32,73 GPa
Ec(CC) = 32,61 GPa
S tr ess (M Pa)
Strain (‰)
OC2
SCC2
0 2 4 6 8 10
0
100
200
300
400
500
600
700
Es (10 mm) = 207.05 GPa
Es (16 mm) = 209.18 GPa
S tr ess (M Pa)
Strain (‰)
10 mm steel bar
16 mm steel bar