Simplified Performance Based Design Procedure of Wall Buildings
Simplified Performance Based Design Procedure of Wall Buildings
Simplified Performance Based Design Procedure of Wall Buildings
Key words: concrete buildings, rc structural walls, structural response, performance-based design.
Abstract: Buildings with reinforced concrete structural walls are frequently used. Wall-to-floor
ratio (at least in one direction) is usually high and although these walls were typically lightly
reinforced with simple reinforcement details, such structures exhibited well behavior during
previous earthquakes. Nevertheless, their analysis is usually very complicated and time consuming
at which end we find out that following minimum requirements were enough in the first place.
The basic goal of this research was to simplify design of structural wall buildings by
distinguishing between the domains where:
1. simple or no calculations are required;
2. more precise calculations are required;
3. performance based design is recommended rather then force based ones.
The derived procedure makes calculation simpler, establishes the minimum material requests that
correspond closer to reality and enable building of safer and less expensive structural wall
buildings. The desired performance levels correspond to demand and ideally this procedure
involves a minimum of design effort.
In order to establish this procedure, a parametric study has been done. The varied parameters
included maximum ground accelerations, number of stories, wall-to-floor ratio and wall length
and width. A set of model wall building structures were chosen and designed according to the EC8
code. Their nonlinear response to a set of ground motions was analyzed. Calculated nonlinear
response performance was correlated with model geometric and material parameters.
The benefits of such methodology will be in fundamentally improved understanding of the seismic
performance of buildings. Also, it should enhance the options for building owners in the
management of seismic risk in an effective and efficient way.
1. INTRODUCTION
Reinforced concrete walls are frequently used in Croatia. When walls are situated in advantageous
position in a building, they can form an efficient lateral-force-resisting system, while
simultaneously fulfilling other functional requirements. Buildings braced by structural walls are
invariably stiffer than framed structures, reducing the possibility of excessive deformations under
small earthquakes. The necessary strength to avoid structural damage under moderate earthquakes
can be achieved by properly detailed longitudinal and transverse reinforcement, and provided that
special detailing measures are adopted, dependable ductile response can be achieved under major
earthquakes. Wall-to-floor ratio (at least in one direction) is usually high and although these walls
were typically lightly reinforced with simple reinforced details, such structures exhibited well
behavior during previous earthquakes. Nevertheless, their analysis is usually very complicated and
time consuming at which end we find out that following minimum requirements were enough in
the first place.
The structural engineering procedures outlined in most buildings codes utilize a force-based
approach for the design of structures to resist earthquakes. It has been pointed out that this
equivalent-elastic forced-based method of seismic design is often not the most effective
approach. A primary reason for its inadequacy is the fact that the use of the capacity reduction
factor assumes that buildings constructed with similar lateral force resisting systems possess the
same ductility. This is clearly not the case, since ductility depends on several other factors such as
material strengths, geometry, axial load and reinforcing ratio. Also, there are tendencies of the
structural engineering profession toward performance-based design in order to accurately
determine the performance of buildings and structural components by calculating deformation-
based response parameters such as drift, rotation and strain under various levels of ground motion
intensity. It is therefore clear that new seismic design methodologies are required.
Current performance-based procedures typically involve nonlinear analyses. Consequently, they
are most easily performed by analyzing an existing structure and determining if selected
parameters meet the criteria for chosen performance levels. In order to develop a new design,
designer faces a few numbers of preliminary designs and risk iterations to determine the most
efficient structure. To some degree, this explains the persistence of traditional force-based design
procedures in the code design of new buildings. However, there are a number of simplified
methods for the displacement based design (mostly employing an equivalent single-degree-of-
freedom system) which allows the designer to incorporate ductility or deformation-based response
parameters into the initial phase of the design process in order to obtain a building that responds
more predictably to earthquakes of varying intensity.
Figure 1: Recommended minimum seismic performance design objectives for buildings [1]
Performance objectives typically include multiple goals for the performance of the constructed
building while its selection sets the acceptability criteria for the design. Design criteria are the
rules and guidelines that must be met to ensure that the usual three major objectives of the design
(performance of function, safety, economy) are satisfied. The performance levels are keyed to
limiting values of measurable structural response parameters, such as drift and ductility, structural
damage indexes, story drift indexes and rate of deformations. When the performance levels are
selected, the associated limiting values become the acceptability criteria to be verified in later
stages of the design.
b) Element and component acceptability limits. Each element (frame, wall, diaphragm or
foundation) must be checked to determine if its components respond within acceptable limits.
3. PARAMETRIC STUDY
Buildings with reinforced concrete structural walls are frequently used. Wall-to-floor ratio (at least
in one direction) is usually high and although these walls were typically lightly reinforced with
simple reinforcement details, such structures exhibited well behavior during previous earthquakes.
Nevertheless, their analysis is usually very complicated and time consuming at which end we find
out that following minimum requirements were enough in the first place. The basic goal of this
research was to simplify design of structural wall buildings by distinguishing between the domains
where simple or no calculations are required and walls are designed mainly according to minimum
requirements prescribed by codes, and where more precise calculations are required. In order to
establish this procedure, a parametric study has been done.
A w a ll
b
l
A
375cm
sto ry
l
Figure 2: Model wall building layout
Each of the model walls was designed following minimum requirements given by the code as well
as according to traditional force-based design procedures. Either way, the walls were carefully
detailed to ensure their flexural ductility and protect them against shear failure by capacity design
principles, in order to ensure that inelastic action will only occur in intended plastic hinges. Main
features of the code minimum requirements are summarized, as follows [2]:
- minimum vertical reinforcement ratio throughout the wall: 0,004
- maximum vertical reinforcement ratio throughout the wall: 0,04
- the thickness of the web: bw0 max{150mm, hs/20}
- minimum amount of web reinforcement: h,min = v,min = 0,002
- length of the confined boundary element: lc max{0,15lw, 1,50bw}
- minimum longitudinal reinforcement ratio in boundary element: 0,005.
Within the context of force-based design, current codes suggest the use of an approximation of the
first mode response of the wall, with a correction for higher mode effect (equivalent lateral force
method). It has been done by distribution of moments along the height of the wall following an
envelope of the calculated bending moment diagram, vertically displaced by a distance equal to the
height of the critical region of the wall. As for the shear force envelope, it was obtained using the
magnification factor depending on the ductility class of the structure. As an alternative, and
presumably more accurate method to determine the seismic response, a multi-mode analysis was
investigated in this study. Comparison with the equivalent lateral force method as well as with the
time history analyses was made.
lc lc
L
4. ANALYSIS RESULTS
The nonlinear response of each model has been calculated for every ground motion record.
Comparing the maximum roof level displacement, relative story displacement, places of the hinge
openings and their plastic rotations, evaluation of the structural performance has been done.
Structural behavior criteria were evaluated according to the Functional and Life Safe performance
objectives. Here are the main observations regarding the results of walls nonlinear analysis:
- For the moderate seismic intensity, all the model walls responded well with the elastic response
or by yielding of the flexural reinforcement in the plastic regions at the base of the wall
consistently with capacity design approach.
- In the regions with high seismic intensity, a few problems occurred: plastic regions in 5-story
walls extended from the base of the wall up to the first floor, while in the 10- and 15-story
buildings, there was a significant influence of the higher modes resulting in yielding of the flexural
reinforcement in the upper half of the wall (Figure 5). These shortcomings could be avoided using
modified modal superposition for shear and moments manly by recognizing that ductility primarily
acts to limit first mode response, but has comparatively little effect in modifying the response in
higher modes.
- There were a few cases with the shear demand at the base at the higher design intensity
exceeding the amplified design shear profile, mainly by influence of the second mode. This could
be avoided by modified modal superposition as well by increasing the amount of horizontal
reinforcement through the critical height of the wall.
FBD FBD F BD
5 Capacity 10 Capacity 15 Capacity
Petrovac Petrovac 14 Petrovac
9
Bar Bar 13 Bar
4 Centro 8 Centro 12 Centro
11
7
10
3 6 9
S to ry
S to ry
S to ry
8
5
7
2 4 6
5
3
4
1
2 3
2
1
1
0
0 0
0 1000 2000 3000 4000
0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000 7000
Moment (kNm)
Moment (kNm) Moment (kNm)
Figure 5: Moments envelope along the heights for time history dynamic analysis
- The achieved performance levels expressed in terms of mean drift ratios, interstory drift ratios
and plastic hinge rotations, confirmed our introductory statement about very favorable seismic
response of wall buildings (Figure 6). Namely, almost all cases analyzed for moderate seismic
intensity achieved the requirements of Immediate Occupancy structural level. For higher levels of
seismic intensity, wall response parameters corresponded to Damage control structural range often
approaching towards Immediate Occupancy level.
5 10 15
14
9
13
4 8 12
11
7
10
3 6 9
S to r y
S to r y
S to r y
8
5
7
2 4 6
5
3
4
1 2 3
2
1
1
0 0 0
0,00 0,50 1,00 1,50 0,00 0,50 1,00 0,00 0,50 1,00
Mean Drift Ratio (%) Mean Drif t Ratio (%) Mean Drif t Ratio (%)
Figure 6: Mean drift ratio profiles for time history dynamic analysis
1 0 s to ry 1 0 s to ry
2% 2%
1 5 s to ry
15
st
or
y
2 0 s to ry
3% 3%
20
st
or
y
A W /A S (% ) A W /A S (% )
Dam age D am age
c o n tro l c o n tro l
LS IO LS IO
The structural response limits are given by means of acceptability diagrams obtained through
various model wall buildings nonlinear response to a set of ground motions (Figure 7). This
methodology tends to be transparent, i.e. based on well-established fundamental principles of
structural dynamics, mechanical behavior of real buildings and in compliance with the worldwide-
accepted philosophy for seismic design. The benefits of such methodology will be in
fundamentally improved understanding of the seismic performance of buildings. Also, it should
enhance the options for building owners in the management of seismic risk in an effective and
efficient way.
REFERENCES
[1] ATC-40 Report. 1996. Seismic Evaluation and Retrofit of Concrete Buildings. Applied
Technology Council Report No. SSc 96-01, Redwood City, California.
[2] EUROCODE 8. 2003. Design of Structures for Earthquake Resistance. Part 1: General Rules,
Seismic Actions and Rules for Buildings. Draft No.6, European Committee for Standardization
CEN, Brussels.
[3] LOPEZ,R.; SOZEN,M.A. 1992. A Guide to Data Preparation for LARZWD Computer
Programs for Nonlinear Analysis of Planar Reinforced Concrete Structures Incorporating
Frames and Walls. University of Illinois, Urbana, USA.
[4] PAULAY,T.; PRIESTLEY,M.J.N. 1992. Seismic Design of Reinforced Concrete and Masonry
Buildings. John Wiley & Sons, New York, USA.
[5] SIGMUND,V.; GULJA,I; MATOEVI,. 2000. CAMUS 3 INTERNATIONAL
BENCHMARK, Report on Numerical Modeling. Combescure,D, CEA, Commissariat a
LEnergie Atomique, p.215-230, Saclay, Paris.
[6] STANI,A.; SIGMUND,V.; GULJA,I. 2003. Behavior of the Walls under In-plane Horizontal
Loadings. Fyb-Symposium: Concrete Structures in Seismic Regions, Athens, Greece.