The normal behaviour was defined as follows:
Pressure-Overclosure: “Hard” Contact
Constraint enforcement method: Penalty (Standard)
Allow separation after contact
Contact stiffness behaviour: Linear
Stiffness value: Use default
Stiffness scale factor: 1
Clearance at which contact pressure is zero: 0
The “Hard” contact relationship means that two surfaces come into contact when the clearance
distance between them reduces to zero, and the surfaces separate when the contact pressure
reduces to zero. By using this pressure-overclosure relationship, the enforcement method is
typically “Penalty.” With this method, the contact force is proportional to the penetration
distance. Linear contact stiffness behaviour was chosen for the friction contact property since
this keeps the penalty stiffness constant; therefore the contact pressure and overclosure
relationship is linear. The default stiffness scale factor is 1, however it was suggested that a value
of 0.001 to 0.003 could be used for steel connection models (Daneshvar, 2013). A comparison of
models with the default stiffness scale factor and a reduced factor of 0.003 showed little
difference in the results (Figure 3.11). Finally, separation was allowed after contact, because the
loading may have caused some surfaces to deform away from others, or the bolts may have lost
contact to the bolt holes as bolt hole elongation occurred.
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Figure 3.11: Difference between Stiffness Scale Factor = 1 and = 0.003 for Test #8
The second contact property was the “Rollers” property which was used at the locations where
the actuators apply displacement to the beam (one near the connection and one near the tip). In
this case, the tangential behaviour was frictionless since the rollers were free to move. The
normal behaviour was identical to the “Friction” contact property.
To continue, all contact pairs were found and created in Abaqus; they have various parameters
which could be altered. These include:
Type: interaction or tie,
Sliding: finite or small,
Discretization: surface-to-surface,
Property: friction or rollers as defined previously,
Adjust interactions to remove overclosure,
Surface smoothing.
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To begin explaining interactions, master and slave surfaces must be defined. In general, the slave
surface is that which follows the movement of the master surface. Therefore it should be the
instance which is expected to see higher deformations. Following this logic, the slave surface
should have a smaller mesh density. If the two surfaces are not significantly different in mesh
size, the master surface should be the one with a coarser mesh or which is stiffer and therefore
is expected to experience less deformation.
If two elements cannot move with respect to one another, this is defined as a tie constraint. One
example of this is the two portions of the beam which were tied together since they were one
member in reality, and therefore the parts could not move relative to one another. All other
interactions represented elements in contact, with either friction between them or the rollers at
the locations of the actuators.
To continue, a finite sliding formulation was selected since this is the general formulation which
allows any motion of the surfaces. Small sliding allows large motions but minimal sliding between
the surfaces.
The discretization method was surface-to-surface rather than node-to-surface. The former
provides a more accurate stress distribution which is less sensitive to master and slave surface
designations. It considers the shape of both the master and the slave surface and enforces
contact conditions as an average nearby the slave nodes. In the node-to-surface contact
discretization, contact conditions are enforced only at individual slave nodes. Node-to-surface
discretization should be used when contact surface normals are not approximately normal to one
another. The node-to-surface method constrains the slave nodes not to penetrate into the
master surface but the nodes of the master surface can penetrate into the nodes of the slave
surface (SIMULIA, 2018).
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Next, interactions can be adjusted to remove overclosure. This moves the slave surface nodes to
be precisely in contact with the master surface without creating any initial strain in the model.
Abaqus requires all tied surfaces to use this feature but it can be toggled on or off for contact
interactions. Models with and without the adjustment to remove overclosure feature were
compared and the results showed no differences. The reason for this is the assembly was drawn
with all interaction locations in contact except for the bolts within the bolt holes. The bolts would
not be adjusted to remove overclosure since their separation distance is larger than the
tolerance. Therefore, no interactions were adjusted to remove overclosure.
Surface smoothing is important when curved surfaces are in contact in the assembly. In finite
element analysis, curved geometric surfaces are approximated as a connected group of element
faces. These faceted surfaces differ from the true surface geometry and can consequently lead
to contact stress inaccuracies. By applying surface smoothing, the noise created in the contact
pressure is reduced as compared to using the true geometry with no smoothing.
To continue, in the Interaction Module, contact controls can be specified. These include
automatic stabilization which helps to automatically control rigid body motion in static problems,
before contact closure and friction restrain such motion. This feature should be used when it is
clear that contact will be established but cannot necessarily be done in the modelling. Abaqus
activates viscous damping for relative motions of the contact pair at all slave nodes. If no contact
controls are specified, Abaqus uses a default contact control which is adequate for most analyses.
Models with and without defining an automatic stabilization contact control were analysed and
the results showed that the model without the defined controls yielded the most accurate
results. Therefore, default contact controls were used for all the shear tab models.
Finally, in the initial runs of the validation models, the load cell locations were assumed to have
some flexibility since, in the laboratory tests, they were connected to a backup frame and then
bolted to the strong floor (see Figure 3.5). These load cells were placed just offset from the
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column top and bottom. To accurately represent this flexibility, a SAP 2000 19 model of the
backup frame was created. This included the steel sections of the backup HSS column and
diagonals fixed to the ground. By applying a displacement to the SAP 2000 model, the resulting
force was measured to then calculate the stiffness at both load cell locations. Validation Test #5
was modelled using these stiffness values implemented as springs in Abaqus. The results proved
to differ slightly from the results using full restraints at the load cell locations in the U1 direction.
Since the differences between the models were deemed negligible, the springs were not used in
further models. Should they have been included, additional variables and uncertainties would be
introduced into the finite element models. Therefore using a full restraint simplified the models,
while maintaining sufficient accuracy and reliability. The force vs. absolute beam rotation curves
of Test #5 with and without springs are presented in Figure 3.12 for comparison.
Figure 3.12: Abaqus Results Showing Negligible Difference between Full Restraint and Springs at
Load Cell Locations for FE Models of Test #5
3.4.6 Load Module
First, the pretension in the bolts was applied in the “Preload” step and then modified in the
“Loading” step. The mechanical bolt load was applied to the cross-section of the bolt shaft where
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