Gusset plate connections under monotonic and cyclic loading

Walbridge et al. 989
Fig. 13. Finite element model of the gusset plate – brace member subassembly.
iour of the bolt slip model for an entire cycle. Some iteration
was necessary in the selection of appropriate values for the
bolt slip load and the assumed amount of slip. Due to the tediousness
of the spring superposition procedure (which required
stopping the analysis and modifying the model after
each half cycle), only a few load cycles were modelled of
the tests on specimens A1 and A3.
Results
Figure 11 shows axial load versus displacement plots for
specimens A1 to A4 from Rabinovitch and Cheng (1993),
along with the hysteresis plots predicted using the corresponding
finite element models. Comparing the hysteresis
plots for specimen A2 and A4, for which several load cycles
were applied in the analysis, it can be seen that the finite element
model predicts the buckling load and subsequent decay
of the post-buckling load resistance under cyclic loading
quite well. The load resistance of the gusset plate in tension
is also matched closely by the numerical model.
A comparison of specimens A3 and A4, which had edge
stiffeners, with A1 and A2 (with no edge stiffener) indicates
that the effect of gusset plate edge stiffeners appears to be a
reduction in the rate of decay of the post-buckling load. This
corresponds well with the test results. Looking at the hysteresis
plots for specimens A1 and A3, it can be seen that using
the bolt slip model shown in Figs. 9 and 10, the finite element
model is also able to predict the behaviour observed in
these tests reasonably well considering the highly random
nature of the bolt-slip phenomenon and the relatively simplistic
nature of the modelling approach employed.
A comparison of cumulative energy dissipation for specimens
A2 and A4 is presented in Fig. 12. The energy dissipated
was determined by calculating the area enclosed by
the hysteresis loop for each cycle. The amount of dissipated
energy predicted by the finite element model is slightly
higher than the test values for both specimens. This is likely
because the elasto-plastic material model was used in the cyclic
loading study. Although a study of the effect of strain
hardening on buckling load showed only a small difference
between material models, the effect of this parameter on the
stiffness of the model once yielding had started was found to
be significant. For specimen A2 especially, it was found that
larger displacements had to be imposed on the compression
side to cause buckling to occur as observed during the test.
This meant that more energy was dissipated in this portion
of each cycle. The cumulative energy dissipation curves for
specimen A2 indicate that most of the difference between
the two curves occurs in cycles 3, 4, and 5. In these cycles,
higher displacements had to be imposed on the compression
side to cause the gusset plate model to buckle during the
same cycle as the test specimen. In subsequent cycles, the
energy dissipated (per cycle) matches quite well.
Parametric study
For the parametric study presented in this section, the gusset
plate model validated in the previous sections was modified
to include a brace member. The model of the gusset
plate and brace member is presented in Fig. 13. The objective
of the parametric study was to expand the experimental
investigation performed by Yam and Cheng (1993) and
Rabinovitch and Cheng (1993) to include the effect of gusset
plate – brace member interaction and load sequence.
Using the modified model, three different load sequences
were investigated. The first, designated LS1, consisted of a
series of cycles of increasing displacement amplitude, starting
with a tension cycle. The increase in the displacement
amplitude with each cycle was taken as the yield displacement,
δy, obtained from a monotonic load analysis of the
gusset plate (based on the recommendations of the Applied
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