Page 148 - Riem-Vol6_nº2

319 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 2
D. L. ARAÚJO | A. R. DANIN | M. B. MELO | P. F. RODRIGUES
model with bonding length equal to 10φ , it can be noted that the
fibers do not influence the bonding strength.
Figure 11 shows the tensile stresses distribution along the bar at
the moment the numerical maximum strength was reached. The
crosshatched part represents the bonding region between steel
and concrete. The bonding stress between bar and concrete can
be determined by means of the equilibrium of the reinforced con-
crete element illustrated in Figure 12. For a steel bar with diameter
φ, we have:
(11)     dx A d A ds s c c
If we neglect the contribution of the tensioned concrete and sub-
stitute the steel area by the value of the circular section, we get:
(12)
4 dx
d s 
Starting from Equation (12) and from the profiles shown in Figure 11,
the average numerical bonding stress (fb,n), shown in Table 6, was
determined. As well as the maximum numerical strength, this bond-
ing stress represented approximately 70% of the average bonding
stress determined in the tests. In this figure, it can be seen that the
stresses distribution for the model with bonding length equal to 5φ
presents a decay that is approximately linear, which proves that the
Figure 11 – Tensile stress distribution in the bars of 10 mm diameter
Model without fibers, bonding length equal
to 10 - stresses in
Model without fibers, bonding length equal
to 5 – stresses in MPa
A B
Figure 12 – Steel-concrete bonding stress