**Project Title:**- Nonlinear Static and Dynamic Analysis of Canoga Park Towers with Feap-Struct
**Sub-contractors:**- Filip C. Filippou, University of California, Berkeley
**Project Summary:**- The lateral load resisting system of Canoga Park Towers consists of four independant
frames, on on each side of the building. The following models of the lateral load
resisting system were generated. Two dinensional models of frames A and B. Frame A is
characteristic of the lateral load resistance of the structure in the East-West direction,
while frame B is characteristic of the lateral load of resistance in the North-South
direction. In addition, two three dimensional models of the structure were prepared.
The simpler three dimensional model only represents the four lateral load resisting
frames and the rigid slabs that connect them with a rigid floor diaphragm assumption.
The complete three-dimensional model represents, in addition to the lateral load resisting
frames, the gravity load system of the building. This model will permit the accurate
assessment of the effect of gravity loads, in particular, their actual distribution, the
effect of vertical ground acceleration on the dynamic response of the building, and the
effect of any strength or stiffness of simple connections on the lateral resistance. The
brevity of the project and the complexity of both three-dimensional models did not allow
for any nonlinear static or dynamic analyses.
- All structural models were assumed rigid at the base, which might not be very realistic, in
view of the deep pile foundations and their likely significant effect on the response. Gravity
loads were applied as vertical concentrated loads at the nodes. Even though FEAP-STRUC elements
include the effect of element loads on the distribution of moments and curvatures in the
member, this option was not activated in the following analyses. The two dimensional models
were subjected to one component of ground acceleration at the base, while the three-dimensional
models will be subjected to the simultanious action of two horizontal accelerations in the
follow-up studies.
- The girders and columns of the lateral load resisting system were modeled with frame
elements. The frame element in FEAP-Struc is a flexibility based, distributed inelasticity
element. In a distributed inelasticity frame element the member response is monitored at a
number of control sections along the member. This modeling approach has the advantage of
directly obtaining curvatures along the member. End rotations can then be determined by
integration of the curvature distribution. Strain values at the top and bottom flange of
girders can also be readily obtained from the curvature at the corresponding section.
Consequently, the occurrence of fracturing can be assessed on the basis of strain rather that
"hinge" rotation. The latter measure requires ad-hoc assumptions about plastic hinge length
and section dimensions. The former depends on material properties, such as the strain hardening
ratio of the steel stress-strain relation, and on the shear force at the corresponding end of the
member. These features are automatically included in a distributed inelasticity element.
- The hysteretic behavior of the frame member is derived by integration of the hysteretic
behavior of the control sections of the element. Two types of section model have been incorporated
into the frame element of FEAP-STRUC. In the first and simpler model, subsequently called
"Hysteretic" model, a hysteretic moment-curvature relation is ascribed to each control section.
The hysteretic model in FEAP-STRUC is based on a trilinear envelope curve complemented by a set
of rules for loading and unloading that permit the description of a variety of characteristic
hysteretic behaviors, such as "pinching", stiffness and strength degradation. The trilinear envelope
curve can be conveniently used in the simulation of fracturing by specifying a negative stiffness
when a critical curvature value is exceeded in either positive and negative moment can be
independently specified, it is possible to specify fracture in only one bending direction
(e.g. bottom flange in tension).
- A more refined model of the hysteretic behavior of the cross section can be obtained by
subdividing each control section into layers for uniaxial bending or fibers for biaxial
bending and axial load. Each fiber can be assigned an appropiate stress-strain relation. It is,
therefore, possible to simulate the fracture of the bottom flange by assigning to the
corresponding layers a uniaxial stress-strain relation with a trilinear curve in tension that
includes fracturing at a critical strain value, but does not lose strength in compression on
account of the fact that the crack closes and compression stresses can be transferred by
contact. By assigning a typical nonlinear stress-strain relation for steel which accounts for
hardening and Bauschinger effect to the layers of the web and flange, it is possible to obtain
the hysteretic section response as follows: once the bottom flange fractures, the section loses
most but not all of its strength under positive bending moment, while it retains its original
load carrying capacity once the crack closes under negative bending moment. Since the section
behavior can be independently assigned to control sections of a given frame element in FEAP-STRUC,
one can readily assign the fracturing hysteretic behavior to the other section. It is, thus,
possible to develop an element that is well suitable to model the observed behavior in steel
beam-to-column connections. This element is used in the following nonlinear dynamic response
studies and the results are compared with those of a typical steel element that does not account
for fracturing.
- Conclusions:
- Nonlinear Static Load-to-Collapse (Push-Over) Analyses are by themselves of questionable
value in the seismic evaluation of high-rise, and thus flexible, frames with a significant
contribution of higher modes in the dynamic response unless the lateral load distribution is
significantly modified from the distribution that is stipulated in present codes of practice.
- Linear Elastic Dynamic Analyses also proved of questionable use in the presence of
localization of damage in the 18-story high-rise steel frame of the Canoga Park Towers. While
Demand/Capacity ratios under representative ground motions are almost uniformly distributed
over the height of the building, leading to a comment on the "randomness of weld fractures",
the nonlinear dynamic analyses reavealed a concentratin of inelastic
deformations in the upper stories of the frames. The agreement with the observed weld fracture
damage was excellent for the case of the N-S component of the Sylmar ground motion leading to the
suggestion that the building might have experienced a stronger ground excitation than implied
by the Canoga Park record, which is the closest available to the site. This
concentration of damage in the upper stories of the frame was much more pronounced with the
use of a special girder/connection model with weld fracture that was specifically developed
for this project. The brevity of the study did not permit a thorough evaluation of this
fracture model on the dynamic response of the frame. This should be an important future task
of the SAC project, since the use of such a realistic model will permit the assessment of the
remaining safety of many high-rise buildings under future strong earthquakes.
- The viscous damping ratio does not play an important role in the first ten seconds of
the dynamic response where most damage seems to have taken place, since the viscous energy
dissipation "builds up" after several cycles, in contrast, to the hysteretic energy dissipation,
which depends on the inelastic excursions of the frame members.
- The accurate modeling of gravity loads as distributed element loads and the related effect of vertical ground accelerations might have a significant effect on the response and should be an important future task of the SAC project. The brevity of this study did not permit the assessment of this effect, even though the distributed plasticity frame element in FEAP-STRUC is ideally suited for the purpose, In any case, axial loads due to gravity play an important role in the response of flexible, high-rise steel frames in conjunction with second order effects of instability. In this respect the leaning effect of the gravity load system on the lateral load resisting system should be carefully assessed in future studies.

SAC Steel Project

c/o Earthquake Engineering Research Center

1301 South 46th Street

Richmond, CA 94804

(510) 231-9477

FAX: (510) 231-5664

sacsteel@sacsteel.org - Nonlinear Static Load-to-Collapse (Push-Over) Analyses are by themselves of questionable
value in the seismic evaluation of high-rise, and thus flexible, frames with a significant
contribution of higher modes in the dynamic response unless the lateral load distribution is
significantly modified from the distribution that is stipulated in present codes of practice.