Fecha de vencimiento y amortización de los valores

Once the finite element analyses were completed, the numerical results were compared with the experimental data and analytical estimations presented in Chapter 3, respectively Chapter 4.

5.3.6.1. Flexural behavior

Foremost, the predicted general flexural behavior of the four M2 hybrid beam specimens was validated. The obtained load-midspan deflection curves are presented adjacently, in Figure 5.21.

Figure 5.21: Numerically predicted global flexural responses of M2 hybrid beams versus experimental curves and analytical

As observed, the advanced finite element model is capable of reproducing the main nonlinear features that were associated with the experimental general bending behavior of the GFRP-concrete beams. There are, however, slight dissimilarities for the structural members tested under three-point bending, M2-HB1 and M2-HB2, where the severe stiffness degradation of the concrete slab near the ultimate load was underestimated. Compared to the analytical model with partial shear interaction formulation, the numerical model predicted better the load-deflection response especially after the shear bolt connectors began to yield.

The deflection results along the bottom flange of the beams are plotted in the Figure 5.22 for an intermediate total load of 50 kN. The charts show that the numerical distributions fit well with the experimental deflections regardless of the bending scheme applied.

Figure 5.22: Numerically predicted deflection profiles versus experimental curves and analytical estimations, at an

intermediate load of 50 kN.

The exact determined midspan deflection values at the intermediate and ultimate load are summarized in Table 5.5 next to the laboratory and analytical results. Computed bending moments at the serviceability limit state are also presented in the table. Percentile differences of the estimated results were computed against the corresponding experimental values.

Table 5.5: Comparison between experimental results and analytical and numerical estimates for serviceability bending

moments (𝑴𝑺𝑳𝑺) and midspan deflections (𝒘) measured at an intermediate load of 50 kN and at the ultimate failure load. Beam 𝑀𝑆𝐿𝑆 (kNm) diff. a (%) 𝑤50 (mm) diff. a (%) 𝑤𝑢 (mm) diff. a (%)

EXP ANA FEA EXP ANA FEA EXP ANA FEA

M2-HB1 10.7 10.5 10.6 -2 -1 21.0 21.6 21.7 +3 +3 52.5 35.2 44.6 -33 -15 M2-HB2 9.4 10.5 10.7 +12 +14 20.7 20.8 21.6 ±0 +4 51.7 31.4 42.1 -39 -19 M2-HB3 8.8 8.8 8.4 ±0 -5 12.8 15.6 13.8 +23 +8 35.2 27.5 34.8 -22 -1 M2-HB4 8.7 8.9 8.5 +2 -2 12.5 15.0 13.6 +20 +9 33.6 26.3 35.5 -22 +6 a _{Percentile differences computed between analytical (ANA) or numerical (FEA) predictions and experimental (EXP)} results.

The calculated differences reveal the prevalence of the nonlinear finite element model in estimating deflections, notably at higher loads. Nonetheless, the elastic analytical model shares rather similar differences with the FE analyses in terms of predicted serviceability bending moments.

5.3.6.2. Stress and strain distributions

Axial stress and strain distributions produced by the simulations were first analyzed and validated. Figure 5.23 illustrates with banded isolines, on a mirrored complete model, the longitudinal normal stress distributions at failure for a representative specimen of each test setup. Since the stresses and strains are computed at an element level, the displayed results were averaged for viewing reasons.

Figure 5.23: Longitudinal normal stress distributions at the ultimate load, for hybrid beams M2-HB1 and M2-HB3 (MPa).

The axial strain variations at section S1 (near or at the midspan) and along the bottom flange of the GFRP profile were validated against the experimental curves, and rendered in Figure 5.24, respectively Figure 5.25. The strain values were probed at unique nodal points matching the installed strain gauge positions, and essentially represent the extrapolated output values from the corresponding element integration points.

Figure 5.24: Numerical (solid line) versus experimental (dotted line) axial strain variations in section S1.

As noticed from the previous batches of figures, the numerically predicted axial strains are in good agreement with the experimental values for all four hybrid GFRP-concrete specimens. Furthermore, the finite element model reflects appropriately in the results the change in concrete composition and applied loading scheme, without any preference for a specific configuration. Opposed to the linear elastic analytical model, the nonlinearity of the actual registered responses is replicated well in both tension and compression, particularly for the GFRP members. Concrete compressive strains were predicted properly, but in exchange, the tensile strains on the bottom side of the slab were mismatched due to the localization of cracks in the experiments. Minor divergences were also detected near the ultimate load for M2-HB2 which failed due to web transverse crushing, and along the bottom flange, close to the concrete-jacketed support.

The numerical axial strain distributions at section S1 were plotted in Figure 5.26 for the four specimens, in function of the beam’s depth and for an intermediate total load of 50 kN, alongside the experimental and analytical corresponding strain distributions. The finite element analysis estimates with remarkable precision the laboratory data, in both structural components of the hybrid beams. In addition, the output values were closer than the ones obtained from the analytical model with partial shear interaction. Bottom slab axial strains in the M2-HB1 and M2-HB2 beams loaded with a concentrated midspan force were farther from the experimental observations, as explained before.

Figure 5.26: Experimental, analytical and numerical axial strain distributions of hybrid beams M2 in section S1, at an

A comparative analysis between the estimated and registered axial strains and stresses for the hybrid beams are shown in Table 5.6 for an intermediate load of 50 kN, and in Table 5.7 for the ultimate failure load, together with computed percentile differences. The concrete compressive strain at section S1 and the maximum tensile strain and stress in the profile were analyzed.

Table 5.6: Concrete compressive strain (𝜺𝟏,𝒖′ – section S1) and bottom flange maximum axial strain (𝜺𝒇,𝒎𝒂𝒙,𝒖) and stress (𝝈𝒇,𝒎𝒂𝒙,𝒖) at an intermediate load of 50 kN.

Beam 𝜀1,50′ (%) diff. a (%) 𝜀𝑓,𝑚𝑎𝑥,50 (%) diff. a (%) 𝜎𝑓,𝑚𝑎𝑥,50 (MPa) diff. a (%) EXP ANA FEA EXP ANA FEA EXP ANA FEA

M2-HB1 -0.15 -0.13 -0.15 -18 -4 0.52 0.46 0.54 -12 +3 203 180 210 -12 +3 M2-HB2 -0.13 -0.12 -0.13 -7 +4 0.54 0.45 0.54 -17 ±0 212 176 215 -17 +2 M2-HB3 -0.06 -0.07 -0.06 +18 +3 0.30 0.27 0.28 -10 -8 117 106 110 -10 -6 M2-HB4 -0.06 -0.07 -0.06 +10 -1 0.29 0.27 0.27 -8 -5 113 104 109 -8 -3

Table 5.7: Concrete compressive strain (𝜺𝟏,𝒖′ – section S1) and bottom flange maximum axial strain (𝜺𝒇,𝒎𝒂𝒙,𝒖) and stress (𝝈𝒇,𝒎𝒂𝒙,𝒖) at failure load.

Beam 𝜀1,𝑢′ (%) diff. a (%) 𝜀𝑓,𝑚𝑎𝑥,𝑢 (%) diff. a (%) 𝜎𝑓,𝑚𝑎𝑥,𝑢 (MPa) diff. a (%) EXP ANA FEA EXP ANA FEA EXP ANA FEA

M2-HB1 -0.19 -0.20 -0.26 +6 +42 1.04 0.72 0.95 -31 -8 406 281 376 -31 -7 M2-HB2 -0.18 -0.18 -0.23 -1 +25 1.06 0.68 0.91 -36 -14 415 265 364 -36 -12 M2-HB3 -0.14 -0.13 -0.14 -6 -4 0.65 0.49 0.58 -26 -11 256 191 231 -26 -10 M2-HB4 -0.12 -0.13 -0.14 +8 +14 0.64 0.49 0.59 -24 -7 250 191 235 -24 -6 a _{Percentile differences computed between analytical (ANA) or numerical (FEA) predictions and experimental (EXP)} results.

The tabular data demonstrate that the advanced nonlinear finite element model is a powerful tool in obtaining reliable axial stress and strain results, with errors as small as 4% for the intermediate load and with acceptable differences up to 14% for the ultimate load. The percentile difference at 50 kN did not indicate a tendency of overestimating or underestimating the response; however, the results at failure were slightly undervalued because of the pronounced nonlinear behavior of concrete at high compressive and tensile plastic strain rates. Analytical errors were regarded as acceptable for the initial part of flexural behavior, and on the other hand, firmly unconservative at the failure load by as much as 36% for the GFRP profile. Possibly due to the localized damage in the concretes slab at failure, the total compressive strains were overestimated by the finite element analyses, in particular for the beams subjected to three-point bending.

Numerical distributions of the top concrete strain across the slab, at section S1, are plotted in Figure 5.27 and Figure 5.28, for one specimen from each test setup. The distributions were extracted for an intermediate load level of 50 kN and for the ultimate load (Pmax). The charts show a relatively uniform cross-section variation at the first step, with higher strain concentrations in the proximity of the top

flange at the moment of failure. Moreover, concentrations are more extensive, as expected, in the case of M2-HB1 which was loaded with a midpoint concentrated force.

Figure 5.27: Concrete slab axial compressive strain at

section S1 for hybrid beam M2-HB1 (load in kN).

Figure 5.28: Concrete slab axial compressive strain at

section S1 for hybrid beam M2-HB3 (load in kN).

For the particular case of hybrid beam M2-HB2 which had a different failure mode than the rest, an analysis was performed regarding the transverse normal stress distribution at the midspan that most probably determined the collapse. Figure 5.29 illustrates with color-coded isolines the aforementioned stress distribution along the entire hybrid beam model, while Figure 5.30 and Figure 5.31 depict the distribution at the central cross-section level.

Figure 5.29: Transverse normal stress distribution at the ultimate load, for hybrid beam M2-HB2 (MPa).

Figure 5.30: Midspan sectional transverse normal stress

distribution at failure, for hybrid beam M2-HB2 (MPa).

Figure 5.31: Transverse compressive stress in the GFRP

The finite element analysis proved that the maximum transverse compressive stress occurred right under the position of the concentrated load, in the upper web region of the composite profile. The actual stress distribution at failure shown in Figure 5.31 was certainly higher as the constitutive GFRP elastic model did not capture the nonlinear stress-strain relationship recorded by the characterization tests, which validates the hypothesis that the compressive transverse strength of the material was reached.

Additionally, the finite element analysis is able to anticipate the location of the tensile concrete cracks and potential crushing areas, and to simulate the relative slip of the mechanical connection. The experimentally detected cracks were overlaid in Figure 5.32 on the computed maximum principal plastic strains monitored on the bottom face of the four investigated M2 hybrid beams.