28-01-2013, 03:54 PM
PUSHOVER ANALYSIS OF A 19 STORY CONCRETE SHEAR WALL BUILDING
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INTRODUCTION
Design of civil engineering structures is typically based on prescriptive methods of building codes.
Normally, loads on these structures are low and result in elastic structural behavior. However, under a
strong seismic event, a structure may actually be subjected to forces beyond its elastic limit. Although
building codes can provide reliable indication of actual performance of individual structural elements, it is
out of their scope to describe the expected performance of a designed structure as a whole, under large
forces. Several industries such as automotive and aviation, routinely build full-scale prototypes and
perform extensive testing, before manufacturing thousands of identical structures, that have been
analyzed and designed with consideration of test results. Unfortunately, this option is not available to
building industry as due to the uniqueness of typical individual buildings, economy of large-scale
production is unachievable.
With the availability of fast computers, so-called performance based seismic engineering (PBSE), where
inelastic structural analysis is combined with seismic hazard assessment to calculate expected seismic
performance of a structure, has become increasingly feasible. With the help of this tool, structural
engineers too, although on a computer and not in a lab, can observe expected performance of any
structure under large forces and modify design accordingly. Nonlinear response history analysis is a
possible method to calculate structural response under a strong seismic event. However, due to the large
amount of data generated in such analysis, it is not considered practical and PBSE usually involves
nonlinear static analysis, also known as pushover analysis. From research viewpoint, while PBSE is still
in developmental stage where improved analysis techniques are being researched (Gupta [1].
BUILDING DESCRIPTION AND MOTIVATION FOR PUSHOVER ANALYSIS
Building analyzed is a nineteen story (18 story + basement), 240 feet tall slender concrete tower located
in San Francisco with a gross area of 430,000 square feet. Unique features of the slender concrete tower
presented challenges for seismic design. Typically, a 240 feet tall concrete building in seismic zone 4
would have a lateral system that combines shear walls and moment frames. However, two architectural
features made the use of moment frames difficult. First, the 60 feet long open bays limited the number of
possible moment frames. Second, on the southeast side two of the perimeter columns are discontinued at
the 6th story and six new columns are introduced that slope for the lowest six stories at an angle of about
20 degrees from vertical. These sloped columns connect to transverse walls through horizontal transfer
elements at the 6th story and put considerable gravity-induced horizontal loads on the lateral system at that
level. Due to limited number of available columns and large horizontal loads from the sloped columns,
the moment frames were abandoned.
MODELING AND ANALYSIS TECHNIQUES
As seen from the floor plan, due to shape of middle core walls, separate pushover analysis in positive and
negative transverse direction is needed. Transverse walls at the 6th story and below in eastern half of the
building are thicker, thereby requiring separate pushover analysis in positive and negative longitudinal
direction as well. Due to the slender shape of floor plan, consideration of mass eccentricity is important
for transverse pushover cases. With these considerations in mind, 8 separate pushover analyses were
performed as shown in Fig. 4. Uniform lateral load pattern was used where lateral load at each floor is
proportional to total floor mass. Software SAP2000 version 7 [13] and ETABS version 7 [14] were used
for analysis. SAP2000 was used to perform pushover analysis and ETABS was used to calculate hinge
properties of shear wall and elastic analysis. For all lateral elements, cracked section was assumed with
an effective stiffness equal to 50% of gross section. Additional modeling techniques of different type of
elements are described in the following.
Verification of pushover analysis model
In pushover analysis model, as shear walls were modeled by frames rather than shell elements, it was
considered important to verify that pushover analysis model is a good representation of the building. For
this purpose, pushover analysis model was compared with linear analysis model where shear walls were
modeled by shell elements. A comparison of modal periods of the two models is given in Table 1. It can
be seen from the table that a good match is achieved between the two models. Although not presented
here, mode shapes were also compared and found to be similar.
RESULTS
Strengthening requirements
Upon performing the various pushover runs as shown in Fig. 4, shear hinges were found to develop at a
few wall and spandrel locations which was considered undesirable for the performance objective. By
performing trial runs with arbitrarily increased shear strength of the shear hinges at these locations, shear
strengthening requirement was quantified as a factor of original shear strength. These requirements are
listed for walls and spandrels in Table 2 and 3, respectively.
Performance of strengthened building
After strengthening the building in shear as listed in Table 2 and 3, capacity curves obtained from
pushover analysis of the building were found to meet the demand curve. At the performance points thus
obtained, several flexural hinges were formed in the building. However, the plastic rotations of the
hinges developed, as calculated by SAP2000, were checked and found to be within the limits suggested
by FEMA and ATC guidelines for the intended design objective of Life Safety. For illustration, Fig. 7
shows capacity curves and performance points for two of the pushover runs. Figure 8 shows the
deformed shape and hinges developed in the building at the performance point for these runs. It has been
indicated by Chopra [3] that pushover analysis may be inherently limited in accurately computing hinge
plastic rotations. Therefore story drift may be a more relevant indicator of building performance.
Average story drift at performance point of different pushover runs is shown in Table 4. Average of story
drift from different pushover runs was found to be below the value recommended by the FEMA
guidelines.
CONCLUSION
Pushover analysis is a useful tool of Performance Based Seismic Engineering to study post-yield behavior
of a structure. It is more complex than traditional linear analysis, but it requires less effort and deals with
much less amount of data than a nonlinear response history analysis. Pushover analysis was performed
on a nineteen story concrete building with shear wall lateral system and certain unique design features.
Utilizing the results from this analysis, some modifications were made to the original code-based design
so that the design objective of Life Safety performance is expected to be achieved under design
earthquake.