Page 111 - Riem-Vol6_nº2

282 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 2
Experimental and numerical analysis of reinforced concrete mushroom slabs
(11) f f f c cm   '
Where:
Gf0 is the basic value of fracture energy determined as a function
of the aggregate size;
fcm is the average compressive strength of concrete (Equation 11);
fcm0 is assumed as 10 MPa.
The load was considered as a 50 mm displacement applied at 100
mm from the edges of the slab into 160 load steps. The equilibrium
between external and internal force vectors was verified using the
Newton-Raphson method, which is an incremental iterative pro-
cedure. An energy based convergence criterion was used with a
tolerance value of 1∙10−3. The concrete compressive behavior was
described with a parabolic hardening and softening relationship
proposed by Feenstra[18]. The unconfined uniaxial tensile stress–
strain diagram was assumed to be linear in tension until cracking.
After cracking it was assumed that the tensile stress decreases
exponentially as a function of strain in the direction normal to the
crack. More details are available in Lima Neto [19].
4.1 Slab without column capital
A parametric investigation was performed in order to establish
the ideal refinement for the finite elements mesh, for the tensile
strength of concrete (fct) and for the shear retention factor (βc).
Figure 11 presents the optimal finite elements mesh used in the
computational models of tested slabs. For the tensile strength of
concrete and the shear retention factor were used values of 1.85
MPa and 0.12, respectively. Figure 12a presents the load-displace-
ment curves for experimental and computational models. As ex-
pected, the computational models were stiffer in terms of flexural
response but the ultimate punching shear strength for both models
were similar. The ultimate strength of experimental model was 327
kN and the computational failed with 309 kN (difference of 5.5% as
shown in Table 3). The distribution of the normal stresses of Figure
13a show the formation of 2 strut compressed, the most significant
being that may have generated the tensile stresses which allowed
the opening of the rupture surface. Just as concentrated compres-
sive stresses near the binding slab-column value above the com-
pressive strength of the concrete, that may have generated the
crushing of concrete at this point and thus made ​possible rupture
by punching. Note also that the approximated radius to appear-
ance of rupture supposed cone on the upper face of the slab, from
the face of the column would be close to that found experimentally
(2.8·d).
Figure 14a shows radial tangential cracks in 3 different areas of the
slab. The first crack is in the projection of the column edges and
is formed in the early load stages mainly due to stresses caused
by flexure. The second tangential crack appears in advanced load
stages and is supposed to be formed by flexure and shear stress-
es. This crack develops towards the column edges and may even-
tually divide the original fan strut into two mains prism struts. The
third radial crack was observed immediately after the peak load
during the computational analysis and may indicate the formation
of the critical shear cracks that leads to a punching shear failure.
Assuming that this third radial crack represents the failure surface,
it is possible to see that it would form a 24º angle with the horizon-
tal, similar to inclination of the failure surface observed after test,
which was of 23º.
Figure 15a and 15b present comparisons between computational
and experimental results for strains in the concrete surface of slab
LC1. It is possible to observe that in case of tangential strains there
is consistency between computational (C1N and C2N) and experi-
mental (C1 and C2) results. However, for the case of radial strains,
computational (C3N and C4N) and experimental results (C3 and
C4) were consistent only for initial load stages but differed signifi-
cantly for the ultimate load stage. In experimental tests radial strain
gauges registered tensile strains, what in fact was not observed in
the computational analyzes.
4.2 Slabs with column capitals
The finite elements mesh was refined for analyzes of slabs with
column capitals as shown in Figure 11. Minor changes in the ad-
opted values of the tensile strength of concrete and of the shear
retention factor were also necessary in order to improve the quality
of computational results. Therefore, for slab LC2 were adopted fct =
1.75 MPa and βc = 0.15. For slab LC3 were adopted fct = 1.72 MPa
and βc = 0.16 and for the slab LC4 were used fct = 1.85 MPa and
βc = 0.15.Computational models of slabs with column capitals also
showed a stiffer load-displacement response if compared to ex-
perimental results. However, peak loads of computational models
were similar to failure loads observed on tests as show in Table 3.
The LC3 slab, with a slope of 1:3, showed a rupture of 518.5 kN
experimental and numerical analysis model of a loading capacity
of 456.5 kN, namely, a difference of 12%, but with proper behavior
and rupture mode close to what was observed in laboratory. It also
highlights that there was a gain in load capacity compared to previ-
ous slabs, provided by the increase of the capital, and was also
observed a surface of rupture inside the capital, as happened with
the slabs tested. The loading to slab LC4 was 513.5 kN experi-
mental and numerical of 457.3 kN, namely, the strength capacity of
the slab shaped was 11% lower than experimental. Note that the
slab with a 1:4 slope capital did not present improvement in load
capacity when compared with the slab slope of 1:3 (LC3), as was
observed experimentally.
In Figure 13b it is observed to the slab LC2 in the last step load,
forming a compressed strut, starting from the outer edge of the
capital on the underside of the slab to the top surface of the same.
Probably this strut compressed generated tensile stresses which
enable the opening of the collapse cone, since the underside of
the slab, the edge of the slab with capital realizes a compressive
stress values ​above the compressive strength of the concrete ad-
opted for the slab. Thus, there is an indication that this rupture, as
was observed in the laboratory, has been starting at outside edge
of the capital with the slab. Figures 13c and 13d is perceived, as
in the previous model, which models of the slabs LC3 and LC4
present the development of a strut compressed with tensile stress
on your back.
However unlike of LC2, it is noted that these models which high
concentration of compressive stresses are spread from the exter-
nal limit of the capital, with slightly higher stress, up to this con-
nection with the column. Because of this fact, it is possible be con-
sidered that the surface rupture passed the limit of the capital and