Principal Investigator(s) and
Institution(s)
Zach Liang and George C. Lee, University at Buffalo
Objective
The application of earthquake protective systems for bridges currently consists of the
addition of devices such as dampers and base isolators which can significantly increase
the overall damping of the bridge system. It is generally believed that, concurrent with
an increase in energy dissipation capability, structural responses will be reduced. This
may not always be true however. In some cases, high damping will also cause higher damping
proportionality, which in turn results in a higher chance of energy transfer among
vibration modes, thereby magnifying responses. The phenomenon of modal cross-effect can be
further magnified when a bridge is irregularly shaped; e.g., due to the effects of
geometry or stiffness. These kinds of cross-effects can sometimes be large under multiple
directional ground motions. In order to quantify the magnitude of cross-effects, the
bridge/device/system (highly damped) should be modeled as a multi-degree-of-freedom (MDOF)
system, as will be addressed under this task.
Several earthquake engineering researchers and practitioners have suggested that the
dynamic behavior of bridges with high damping may significantly differ from that with low
damping. However, the differences have not been quantified in the open literature. The
objective of this task is therefore to review and address these issues on the basis of
three-dimensional nonlinear time history analyses validated by a large-scale model test.
Approach
The use of seismic protective systems is a relatively new approach in bridge design, and
can be cost-effective in many situations. At the same time, it also brings in
uncertainties in structural response reductions. Although cross/orthogonal effects have
been observed in real cases, they need to be properly quantified based on appropriate
models.
Conventionally, to quantify the dynamic behavior of a bridge, a single-degree-of-freedom
(SDOF) model is often used. The more sophisticated MDOF method employs proportionally
damped models, which can be modally decoupled into SDOF modes. Mathematically speaking, by
using these models, cross effects among modes cannot be described, nor can orthogonal
effects among perpendicular directions be quantified.
This 2-year task will consist of three subtasks, as follows:
Subtask 1 - Numerical studies will be performed to examine quantitatively the
cross/orthogonal effects on several common types of highway bridges. This examination will
initially focus on three kinds of protective systems: base isolation for short-span
bridges, passive fluid dampers for long-span bridges, and variable passive fluid devices
on critical bridges for fail-safe protections.
Subtask 2 - Experimental studies and verifications will be performed, based on the
numerical simulations and generally damped MDOF model bridges. This task will be done by
using a 3-directional shaking table with large velocity and displacement testing capacity.
The main effort will be limited to the base-isolation type of protective systems.
Subtask 3 - More accurate yet not too complicated mathematical models will be established.
With the help of this formulation, one should be able to model most common types of
bridges. In addition, quantitative results on both cross/orthogonal effects and more
accurate response computations will be obtained. It is important that the corresponding
computation should not be too complex for bridge engineers to apply, nor too complicated
resulting in increased cost of design.
These three subtasks will be accomplished by:
establishing accurate and applicable dynamic models for bridges with highly damped
earthquake protective systems by: (a) comparing dynamic responses of isolated bridges
based on conventional SDOF (including proportionally damped MDOF) models with generally
damped MDOF models based on theoretical formulations and numerical simulations; and (b)
experimentally verifying the numerical results by using 3-D shaking tables in a
cooperative project with the Taiwan Earthquake Engineering Research Center; and
quantifying cross (orthogonal) effects for typical highway bridges by: (a) establishing
engineering definitions of the cross (orthogonal) effects; (b) quantifying the effects
caused by damping; and (c) quantifying the effects caused by stiffness.
Anticipated Start Date and Duration
January 1, 1999 - 24 months
9/23/99 |