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IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 1
Concrete compressive characteristic strength analysis of pile caps with three piles
The increase in the concrete compressive strength (f
ck
) caused a
reduction in the cracking intensity, as shown in Table 7, due to the
increase in the concrete tensile strength. It is worth noting that the
cracking process begins in the region where the structure reaches
the ultimate tensile strength, thus beginning a microcracking process,
which leads to stress reduction until the material reaches the critical
opening crack (w
c
) – Figure 4a –, when a complete separation of the
crack sides takes place. Therefore, the higher the concrete’s ultimate
tensile strength, the higher the pile cap’s cracking resistance.
Having mentioned that, in Table 8 a correlation between the pile
cap’s crack intensity reduction according to the concrete tensile
strength increase is presented. From model 1 to model 3 there
was an increase of 21,32% (from 2,58 MPa to 3,12 MPa) in the
concrete tensile stress and a reduction around 30% in the crack
opening intensity.
3.3 Compressive struts stresses
In all three pile caps analyzed compressive struts were developed
with equal divisions of the stress flow at the bottom of the column’s
cross-section in direction to the piles, as shown in Figure 8.
In addition, in all models struts compressive stresses were con-
centrated in the piles superior cross-section region closer to the
column, corroborating Delalibera’s [6] statement that in the inferior
nodal zones the struts stresses are not uniformly distributed.
The concrete compressive strength led to a proportional in-
crease in the struts compressive stresses, as demonstrated in
Table 9. The concrete’s compressive strength increase from 30
MPa to 40 MPa (+33,33) generated an increase of 38,09% in
the struts stresses.
Notwithstanding, as shown in Figure 8, pile caps stress flow did not
have a perceptible modification.
In all models, the inferior nodal zones stresses were higher than
the concrete compressive strength (f
ck
), indicating concrete col-
lapse, as shown in Table 10.
There was also the development of tensile stresses in the nodal
zones and along the struts which reached values higher than the
concrete tensile strength, as can be seen in Table 11, demonstrat-
ing the concrete splitting.
3.4 Ties tension stresses
Tie bars yielded in the ultimate load in all three models. Moreover,
in the inferior nodal zones an abrupt reduction in the ties tensile
stresses occurred due to the positive action of the compressive
struts in the steel bars.
From figures 9 to 11, it is possible to observe that, in the pile cap’s
span, reinforcement tensile stresses were practically constant with
values around 590 MPa. Nonetheless, at the beginning of the nod-
al zones, tensile stresses were greatly reduced, reaching very low
values, around 5 MPa in the borders of the bars and in the hooks.
These results prove that tie hooks are not necessary, since tie bars
anchorage is made almost totally in the inferior nodal zones which
receive the positive influence of the compressive struts.
Ties tensile stresses in the inferior nodal zones and at the bars bor-
ders were not altered by the increase in the concrete compressive
strength, as shown in the Figures 9, 10 and 11.
Figure 7 – Pile caps load
versus
displacement graphic
Table 7 – Opening cracks values
Load values
(kN)
F=920
F=1.840 F=2.750
Maximum
opening
crack on
the pile
cap’s
surface (mm)
Model 1
0,022
1,52
3,88
Model 2
0,019
1,27
3,33
Model 3
0,015
0,97
3,20
Table 8 – Opening cracks variation (
) in relation to the concrete tensile strength
f
tk
f
tk
F=920
F=1.840
F=2.750
Opening cracks
variation (%)
Model 1
2,58 MPa
-
-
-
-
Model 2
2,83 MPa
+9,69%
-13,63%
-16,45%
-14,17%
Model 3
3,13 MPa
+10,60%
-21,05%
-23,62%
-4,00%