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BSSC SDC B E: Accidental Torsion Studies E-1
Appendix E
Evaluation of the Accidental Torsion Requirement in ASCE 7 by the FEMA P695 Methodology
E.1 Overview
The purpose of this study is to evaluate the significance of the accidental
torsion requirement in Section 12.8.4.2 of ASCE 7-10 for buildings in SDC
B. The accidental torsion provisions require application of a +/-5% offset of
the center of mass in each of two orthogonal directions to compute a
torsional moment, thereby increasing the design seismic base shear. The
primary goal of this study is to quantitatively examine the possible
elimination or revision of the accidental torsion requirement for SDC B
buildings designed according to the newly proposed stand-alone code
document. To this end, the study quantifies the effect of the accidental
torsion design requirement in terms of building collapse capacity and
collapse risk for a variety of SDC B buildings in order to determine the
consequences, or lack thereof, of removing or revising the accidental torsion
requirements.
Seismic ground motions may induce torsional response in buildings. Some of
this torsion is created by asymmetrical building geometry, hereafter referred
to as “inherent” torsion. In contrast, accidental torsion is unexpected and
may occur for a variety of reasons including: asymmetric distribution of
lateral ground motions across the plan of the building, asymmetric stiffness
contributions from the gravity system or nonstructural elements not
accounted for in design, uneven live-load distribution, or changes in the
center of rigidity due to nonlinear behavior. To account for all of these
potential sources of accidental torsion, ASCE 7 defines an accidental
torsional design moment to be considered in buildings with rigid diaphragms,
in addition to any inherent torsion that may exist. The additional accidental
torsional moment is equivalent to the torsion due to applying the seismic load
at a distance from the center of mass equal to 5% of the building dimension
perpendicular to the applied lateral load (Section 12.8.4.2 of ASCE 7-10).
These provisions have the effect of increasing the design base shear in the
frames and walls that resist lateral forces.
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E-2 E: Accidental Torsion Studies BSSC SDC B
E 1.1 Literature Review on Accidental Torsion
Significant research on accidental and inherent torsion in buildings has been
conducted in the past, producing varying results (Stathopoulos et al. 2009;
De Stefano and Pintucchi 2007). However, those that have specifically
addressed the issue of accidental torsion in design codes have all concluded
that it is not needed for most ‘regular’ buildings; ‘regular’ loosely refers to
buildings that are not particularly torsionally flexible or irregular, although
the exact definition varies from study to study (Stathopoulos et al. 2005,
Chang et. al 2009).
Some of the key findings of the past research are outlined here. De Stefano
and Pintucchi (2007) provide a more complete summary and assessment of
recent research on torsion in buildings. This section summarizes selected past
research of torsional seismic response of buildings, based on three main
categories of models: 1) linear models, 2) simplified single-story shear-
spring models and 3) lumped plasticity nonlinear frame models.
Results from linear models have shown that design accidental torsion is not a
significant factor for building performance under earthquake excitation for
many buildings (Chopra 1992. A strength of the linear models is that they
represent realistic building geometries, such as multi-story space frames,
very accurately. However, the linear models cannot accurately simulate post
yielding behavior and collapse and, more recently, detailed nonlinear models
have been used to evaluate torsional response.
Some of the first nonlinear models used for studying torsion in buildings
were models that represented the aggregated behavior of lateral force
resisting systems with bilinear shear springs in a single-story. These models
have the advantage of being able to simulate behavior beyond the linear
range. Anagnostopoulos et al. (2009) showed that the procedures for
calibrating such simplified models is crucial for obtaining accurate results.
They demonstrated that by calibrating single story shear spring models to
more high end lumped plasticity models using pushover analysis, they could
obtain results that qualitatively agreed with the results from the more
sophisticated nonlinear frame models with lumped plasticity elements. The
results of the single-story simplified models even with agreed lumped
plasticity models having more than one story (based on 3 and 5 story
models).
However, Anagnostopoulos et al. (2009) recommends that strong caution be
taken when calibrating simplified shear spring models. For example, some
researchers have scaled building strength of the simplified models based on
design loads, without modifying the stiffness. Increasing strength
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BSSC SDC B E: Accidental Torsion Studies E-3
independently of stiffness in bilinear models leads to inaccurate measures of
initial stiffness, but also artificially increases the yield displacement. Since
much of the early work on torsion with nonlinear models used ductility
demand as a performance measure, artificially increasing the yield
displacement of a lateral force resisting system artificially increased its
performance; this phenomenon has been addressed quite specifically by Tso
and Smith (1999). Anagnostopoulos et al. (2009) showed that carefully
calibrated simplified shear-spring models predict greater ductility demand on
the flexible side of irregular buildings, which is in agreement with linear
models and lumped plasticity models. However, increasing strength
independently of stiffness in simplified models leads to the exact opposite
prediction; ductility demand is increased in the stiff side elements. Since
they used ductility demand as a main performance measure, the calibration of
the simplified models made the difference between being qualitatively right
or qualitatively wrong in their predictions.
More recent work using nonlinear models of frame structures includes
Stathopoulos and Anagnostopoulos (2009) and Chang et al. (2009).
Stathopoulos and Anagnostopoulos (2009) used one, three and five story RC
space frames with lumped plasticity models of beam and column elements to
assess the importance of design accidental torsion, concluding that it is
insignificant for the building heights and torsional rigidities studied and
ought to be re-examined. A similar study by Chang et al. (2009) examined
six and twenty-story steel space frames and reached the same conclusion;
design accidental torsion requirements are not significantly beneficial, for the
building types they studied. Both of these studies used ductility demand as
the main measure of performance.
This study will expand on past work by considering a wider variety of
torsional flexibility and irregularity in buildings, focusing on collapse
capacity as the primary performance metric. To our knowledge, no studies
of accidental torsion have used collapse as a performance measure, as we do
here, but instead have relied mostly on ductility demands to quantify the
impacts of accidental torsion (De Stefano and Pintucchi 2007). The building
designs considered here have base shear levels consistent with SDC B, in
contrast to most previous studies that considered SDC D ground motion
levels, and consider a broad range of torsional flexibilities.
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E-4 E: Accidental Torsion Studies BSSC SDC B
E.1.2 Methodology
In this study, we consider the effects of accidental torsion code provisions on
a set of archetype nonlinear building models, which include torsionally stiff
and torsionally flexible structures, and have ductility, mass, and strength
characteristics of SDC B buildings. Since a main purpose of seismic codes is
to reduce the likelihood of earthquake-induced collapse, accidental torsion
requirements are evaluated with regard to seismic collapse risk.
FEMA P695 proposes a methodology for systemically evaluating the seismic
design provisions of new seismic resisting lateral systems on the basis of
ensuring an acceptably low probability of collapse. The method uses
building collapse capacity as a metric for determining appropriate response
coefficients R, Cd, and Ω0 for newly proposed systems. The process for
implementing the FEMA P695 methodology is illustrated in Figure E-1.
Figure E-1 Flow chart schematic of FEMA P695 methodology
(FEMA 2009)
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BSSC SDC B E: Accidental Torsion Studies E-5
In this study, the FEMA P695 method has been adapted to evaluate a
particular code provision, namely the 5% offset requirement to account for
accidental torsion, rather than a specific Seismic Force Resisting System
(SFRS), but the main concepts have not changed. Rather than focus on a
specific system, the method has been used to evaluate the collapse
performance of a set of typical SDC B buildings designed with and without
the accidental torsion requirement. To this end, an archetype design space is
developed, analytical models created and analyzed, and their collapse
performance is evaluated. The difference in collapse risk with and without
accidental torsion provides quantitative information as to the importance of
including accidental torsion requirements in SDC B. Each of these steps is
documented in detail in the following sections.
E.2 Archetype Design Space
The objective of this study is to quantify the effect of the accidental torsion
requirement on the design and safety of buildings in SDC B. Therefore, it is
important to identify a range of archetype designs that encompass as many
SDC B buildings as possible, with special emphasis on those buildings that
may be most affected by accidental torsion requirements. This section
discusses building characteristics that may affect the influence of accidental
torsion requirements in design and how these characteristics were considered
in developing a representative set of buildings. Table E-3 and
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E-6 E: Accidental Torsion Studies BSSC SDC B
Table E-4, at the end of this section, summarize the suite of archetype
designs that are analyzed. Every archetype building is designed in two
versions: one with and one without the accidental torsion design requirement
considered, to provide a direct assessment of the impacts of accidental
torsion design requirements on building collapse performance. The archetype
design models were created by calibrating their linear and nonlinear
properties to a set subset of baseline ‘high end’ OMF frame models.
E.2.1 Seismic Force Resisting System (SFRS)
Building systems most commonly used in SDC B are less ductile than those
used in higher seismic design categories. In fact, most have values of R, the
response modification coefficient, of around 3. Due to the infeasibility of
analyzing every available SFRS for SDC B, the models in this study are
based on the design and behavior of reinforced concrete Ordinary Moment
Frame (OMF) models. The choice of OMFs to represent SDC B buildings
more generally is justified by this study’s focus on measuring the effect of
designing for accidental torsion on collapse capacity and collapse risk, not
comparing specific systems. Reinforced concrete OMFs are used because
they are non-ductile, their nonlinear behavior is fairly well documented and
modelable, and they are commonly used in SDC B. In addition, the most
important properties pertaining to collapse capacity such as ductility,
overstrength, and deformation capacity are fairly similar to many other
systems used in SDC B.
E.2.2 Building Height
Three different building heights are used in this study in order to capture the
effects of designing for accidental torsion: 1, 4, and 10 stories. The height of
10 stories (132 ft.) was chosen as the tallest archetype structure because it is
tall enough to adequately capture the effects of higher modes in tall
buildings. Past studies by Chang et al. (2009) and Stathopoulos and
Anagnostopoulos (2009) have suggested that accidental torsion requirements
are less beneficial for taller buildings (5, 6, and 20 stories) than single story
buildings.
E.2.3 Building Weight
Since gravity loads can play a major role in the design of SDC B buildings, a
range of building weights are considered. The ‘low’ and ‘high’ gravity
scenarios in this study are 100 psf and 200 psf of un-factored dead weight,
respectively, for all stories except the roof level. ‘Low’ and ‘high’ roof
weights are 80 psf and 160 psf, respectively, and are used for the single-story
buildings. These values are intended to represent a reasonable range of
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BSSC SDC B E: Accidental Torsion Studies E-7 S2
S1=2S2
L2=100'
Frame 3
Frame 2 Frame 4
weights of buildings, but are not linked to any particular floor system or
occupancy. Live load was taken to be 20 psf at the roof level and 50 psf for
all other stories, and live load reductions were made according to section 4.7
of ASCE 7-10 Past research has shown that gravity load levels can
significantly affect system ductility, overstrength, and collapse performance
(FEMA 2009).
Only the high gravity load level was used for the 10-story archetype designs
because the 1-story and 4-story archetypes showed that high gravity
buildings performed worse overall and had more significant improvements
from design accidental torsion than their low gravity counterparts .
E.2.4 Building Plan Layout
Most of the archetype building layouts considered in this study are
symmetric (rectangular layouts). Past research (Llera and Chopra 1995,
Stathopoulos and Anognostopoulos 2005), have shown that accidental
torsion requirements have a larger effect on the performance of symmetric
buildings than asymmetric buildings, because the relative increase in
torsional design forces due to accidental torsion increases as inherent torsion
decreases. In addition, we consider buildings with different torsional
rigidities because the torsional period or frequency affects response to
earthquake excitation.
The rectangular building plans follow the schematic in Figure E-2Error! Not
a valid bookmark self-reference., with overall building dimensions 200 ft.
x 100 ft. and relative frame spacing of S/L=S1/L1=S2/L2= 1.0, 0.75, 0.5, and
0.25. This configuration is used for all of the rectangular buildings in this
study. (In the context of this study, the term “frame” refers to any frame or
wall line that is part of the lateral force resisting system). The extent to which
designing for accidental torsion increases the design base shear in frame lines
depends on the relative torsional stiffness of a structure and its frame-line
spacing. This effect is illustrated using the building plan that is illustrated in
Figure E-2. The building has plan dimensions L1 and L2 and frames are
spaced at distances S1 and S2 apart. All frames are considered to have equal
stiffness k. Taking a normalized design base shear of 1 in each frame and
then computing the additional shear due to accidental torsion produces the
results shown in Table E-1. In general, as relative frame spacing decreases,
torsional rigidity decreases and the contribution of accidental torsion to the
design base shear in frames increases.
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E-8 E: Accidental Torsion Studies BSSC SDC B
Figure E-2 Plan view of a symmetric archetype structure with a
rectangular frame layout
Table ETable ETable ETable E----1111 Increase in Increase in Increase in Increase in BBBBase ase ase ase SSSShear hear hear hear DDDDue to ue to ue to ue to the the the the 5% 5% 5% 5% OOOOffset ffset ffset ffset AAAAccidental ccidental ccidental ccidental
TTTTorsion orsion orsion orsion RRRRequirementequirementequirementequirement for Building for Building for Building for Building Layout Layout Layout Layout shown in shown in shown in shown in
Figure EFigure EFigure EFigure E----2222
S/L
Frames 1&3 Frames 2&4
Design Base
Shear
(Normalized)
Total Design Base
Shear, Accounting for
Accidental Torsion
Design Base
Shear
(Normalized)
Total Design Base
Shear, Accounting
for
Accidental Torsion
1
(Perimeter) 1 1.02 1 1.08
0.75 1 1.03 1 1.11
0.5 1 1.04 1 1.16
0.25 1 1.08 1 1.32
In addition to the rectangular frame layout that was used most for most of the
archetypes analyzed, a subset of archetypes with an ‘I-shaped’ frame layout
was also analyzed. I-shaped or similar frame layouts are common in parking
garages and other structures.
L2=100'
S1
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BSSC SDC B E: Accidental Torsion Studies E-9
Figure E-3 ‘I-shaped’ frame layout
E.2.5 Building Plans with Inherent Torsion
A few selected archetype buildings were analyzed with asymmetric building
plan layouts, as depicted in Figure E-4. Two different inherent torsion plan
layouts were used: one with S/L=S1/L1=S2/L2=0.5 and one with
S/L=S1/L1=S2/L2=0.25. For each of these layouts, two of the frames are
located at the building’s edge and the other two are inset according to the
prescribed relative frame spacing. Eccentricities in each direction are labeled
as e1 and e2. Both of the archetype building geometries used to represent
buildings with inherent torsion are classified as having horizontal irregularity
type 1b (extreme torsional irregularity) according to ASCE 7-10.
Figure E-4 ‘Inherent torsion’ frame layout
E.2.6 Natural Accidental Torsion
We use the term “natural accidental torsion” to describe the effective offset
between center of mass and center of stiffness, accounting for the many
sources of ‘accidental torsion’ that may exist. Levels of natural accidental
torsion were systematically introduced in the model, but not the design, by
offsetting the center of mass (CM) of the models from the design CM along
L1=2L
2=200'
L2=100'
S2
S1=2S
2
CM X
e1
e2 CR X
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E-10 E: Accidental Torsion Studies BSSC SDC B
the diagonal of the building. Center of mass offset distances of 0%, 5%, and
10% of the total diagonal length of the building were used.
E.2.8 Design Assumptions and Methodology for OMF Models
A subset of the archetype buildings was designed as reinforced concrete
OMF’s according to ASCE 7-10 and ACI 318-10 and are listed in Table E-2.
Each archetype building was designed for dead, live, and seismic loads using
all applicable load combinations; additional loading from snow and wind
were not considered. The design short period and one-second spectral
accelerations were taken as the maximum allowable values for SDC B:
SDS=0.33(g) and SD1=0.133(g).
The buildings were designed as space frames with 2-way slabs, having spans
of 30 ft., and story heights of 15 ft. and 13 ft. in the first story and all other
stories, respectively. For design, they were modeled as 2D portal frames with
SAP2000, using the Equivalent Lateral Force Procedure (ELFP) to determine
design loads, story forces and drifts. The design of all members was force
controlled, with the exception of the ten story archetypes whose lowest six
stories were governed by the stability (P-∆∆∆∆) requirements of Section 12.8.7 in
ASCE 7. Columns of the one-story buildings were modeled pinned at the
base, whereas all other designs used a fixed foundation assumption for
design, to be consistent with common design practice.
Each OMF design depended on the number of stories and gravity loads and
had two versions, which are summarized in Table E-2. The first version was
designed as a space frame with 30 ft. bays and 30 ft. of tributary width and
an equivalent tributary seismic mass. Space frame OMFs were selected
because they are common and have nonlinear behavior that we believe is
representative of many SDC B type buildings. This design ignores accidental
torsion effects, i.e. it is designed only for the base shear calculated according
to the equivalent lateral force method. These are later referred to as the ‘low
base shear’ models because they have the lowest design base shear of all
designs for their particular height and gravity load levels. In Table E-2, the
low base shear designs are the odd numbered designs. The second version
was designed with the same geometry and loads, except with larger design
base shear due to the consideration of 5% accidental torsion (later referred to
as the ‘high base shear’ models). For symmetric archetypes, the increase was
32%, which was due to the base shear increase from accidental torsion when
relative wall spacing (S/L) is 0.25 in a building with the geometry shown in
Figure E-2. Frames with extreme values of design base shear were selected
for design (even numbered designs in Table E-2), because simplified models
are later calibrated by interpolation of properties between ‘high end’ OMF
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-11
models. In addition, for select archetypes with inherent torsion, additional
‘high end’ OMF frames were designed and modeled considering more
extreme changes in design base shear.
The high-end OMF models are designed as space frames with 30 ft. of
tributary width, but the 3D frame layouts have just two frame lines in each
direction and plan dimensions of 200 ft. x 100 ft., as shown in Figure E-2.
Note that these simplified models have only two frame lines in each
orthogonal direction to more easily capture a wide range of torsional
flexibilities, creating a discrepancy with the original OMF space frame
design. The discrepancy between the two building plans was reconciled by
adjusting the mass and weight of the 3D models to reflect the correct
building mass and weight tributary to just two of the OMF frames.
Since gravity loads contribute significantly to the frame element design
moments and forces, much care was taken to design the two versions of each
frame consistently. For each OMF, the lower base shear version was
designed first. Columns were designed to be as small as possible while
keeping the longitudinal reinforcement ratio below about 4.5%. Beams were
designed as T-beams, but with smaller longitudinal reinforcement ratios
(2.5%-3%) than columns. The beam longitudinal reinforcement ratios were
often governed by maximum reinforcement requirements (which limit
reinforcement and promote steel yielding before concrete crushing).
Transverse shear reinforcement was designed with bar sizes ranging from #3
to #5, and bar size was kept consistent for all columns and for all beams
throughout each building; in every case, rebar size was determined such that
the maximum allowable spacing could be used for all or the elements of the
frame, reflecting common engineering practice.
After designing the frame with the lower base shear, the high base shear
version of the same frame was designed. Starting with the first design,
element sizes and reinforcement were increased to accommodate the larger
loads. We aimed to keep reinforcement ratios as similar as possible by
increasing the reinforcement and element sizes concurrently.
Table ETable ETable ETable E----2222 Matrix of Matrix of Matrix of Matrix of OMFOMFOMFOMF DDDDesignsesignsesignsesigns ((((BBBBaseline aseline aseline aseline MMMModels)odels)odels)odels)
Design
#
Building
Height
(stories)
Lateral
System
Gravity
(Story
Weight)
Relative
Frame
Spacing
(S/L)
Inherent
torsion
Design
Accidental
Torsion
1 1
Concrete
OMF 80 psf
1* None
None
2 0.25 5%
41.86% Draft
E-12 E: Accidental Torsion Studies BSSC SDC B
Design
#
Building
Height
(stories)
Lateral
System
Gravity
(Story
Weight)
Relative
Frame
Spacing
(S/L)
Inherent
torsion
Design
Accidental
Torsion
3 160 psf
1* None
4 0.25 5%
5
4
100 psf 1* None
6 0.25 5%
7 200 psf
1* None
8 0.25 5%
9 10 200 psf
1* None
10 0.25 5%
*Frame spacing does not matter if the building is symmetric and accidental torsion is
not considered
E.2.8 Design Assumptions and Methodology for Simplified Frame Models
Simplified models have been constructed such that the design lateral
earthquake force in each frame, without considering accidental torsion, is
exactly the same as the baseline case for the corresponding ‘high end’ OMF
model, so that their nonlinear properties can be matched directly. For
simplified archetypes designed for accidental torsion, the earthquake forces
are increased and frame properties are obtained by interpolation between the
low and high base shear versions of the ‘high end’ OMF frames. This
process is described in more detail in section E.4.
E.2.9 Archetype Design Space Tables
Table E-3 summarizes key properties of the archetype design space that has
been used for this study.
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BSSC SDC B E: Accidental Torsion Studies E-13
Table E-4 lists all the buildings and design properties considered in the study,
including a total of 196 archetypical models.
Table ETable ETable ETable E----3333 Summary of Summary of Summary of Summary of Archetype Design SpaceArchetype Design SpaceArchetype Design SpaceArchetype Design Space
Design #
Building
Height
(stories)
Lateral
System
Gravity
(Story
Weight)
Relative
Frame
Spacing
(S/L)
Configuration Inherent
Torsion
Design
Accidental
Torsion
Natural
Accidental
Torsion
196 Total
Archetypes
1
4
10
Concrete
OMF
Low
High
1
0.75
0.5
0.25
*0.45
*0.4
*0.35
*0.3
Rectangular
Frame
Layout
*I-Shaped
Frame
Layout
None
(Torsionally
Symmetric)
*25%
0%
5%
0%
5%
10%
*Properties only represented by selected subgroups of the archetype design space
41.86% Draft
E-14 E: Accidental Torsion Studies BSSC SDC B
Table ETable ETable ETable E----4444 Full Archetype Design SpaceFull Archetype Design SpaceFull Archetype Design SpaceFull Archetype Design Space
Building
Height
(stories)
Gravity
(Story
Weight)
Relative
Frame
spacing
(S/L)
LRFS
Configuration
Inherent
Torsion
Design for
Accidental
Torsion
Natural
Eccentricity
(Offset of
CM)
1
80 psf
1
Rectangular
Frame Layout
None
(Symmetric)
No
0
0.75
0.5
0.25
1
Yes 0.75
0.5
0.25
1
No
*0
0.75
0.5
0.25
1
Yes 0.75
0.5
0.25
1
No
5%
0.75
0.5
0.25
1
Yes 0.75
0.5
0.25
1
No
10%
0.75
0.5
0.25
1
Yes 0.75
0.5
0.25
1
160 psf
1 Rectangular
Frame Layout
None
(Symmetric)
No
0
0.75
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BSSC SDC B E: Accidental Torsion Studies E-15
Building
Height
(stories)
Gravity
(Story
Weight)
Relative
Frame
spacing
(S/L)
LRFS
Configuration
Inherent
Torsion
Design for
Accidental
Torsion
Natural
Eccentricity
(Offset of
CM)
1
160 psf
0.5
Rectangular
Frame Layout
None
(Symmetric)
No
0
0.25
1
Yes 0.75
0.5
0.25
1
No
*0
0.75
0.5
0.45
0.4
0.35
0.3
0.25
1
Yes
0.75
0.5
0.45
0.4
0.35
0.3
0.25
1
No
5%
0.75
0.5
0.45
0.4
0.35
0.3
0.25
1
Yes
0.75
0.5
0.45
0.4
0.35
0.3
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E-16 E: Accidental Torsion Studies BSSC SDC B
Building
Height
(stories)
Gravity
(Story
Weight)
Relative
Frame
spacing
(S/L)
LRFS
Configuration
Inherent
Torsion
Design for
Accidental
Torsion
Natural
Eccentricity
(Offset of
CM)
1
160 psf
0.25
Rectangular
Frame Layout
None
(Symmetric)
Yes 5%
1
No
10%
0.75
0.5
0.25
1
Yes 0.75
0.5
0.25
1
160 psf
0.5
I- shape
None
(symmetric)
No
*0
0.45
0.4
0.35
0.3
0.25
0.5
Yes
0.45
0.4
0.35
0.3
0.25
0.5
No
5%
0.45
0.4
0.35
0.3
0.25
0.5
Yes
0.45
0.4
0.35
0.3
0.25
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BSSC SDC B E: Accidental Torsion Studies E-17
Building
Height
(stories)
Gravity
(Story
Weight)
Relative
Frame
spacing
(S/L)
LRFS
Configuration
Inherent
Torsion
Design for
Accidental
Torsion
Natural
Eccentricity
(Offset of
CM)
1 160 psf
0.5
Rectangular
High Inherent
Torsion
(Extremely
Asymmetric)
No
*0 0.25
0.5 Yes
0.25
0.5 No
+5% 0.25
0.5 Yes
0.25
0.5 No
+10% 0.25
0.5 Yes
0.25
0.5 No
-5% 0.25
0.5 Yes
0.25
0.5 No
-10% 0.25
0.5 Yes
0.25
4
100 psf
1
Rectangular
None
(symmetric)
No
*0
0.75
0.5
0.25
1
Yes 0.75
0.5
0.25
1
No
5%
0.75
0.5
0.25
1
Yes 0.75
0.5
0.25
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E-18 E: Accidental Torsion Studies BSSC SDC B
Building
Height
(stories)
Gravity
(Story
Weight)
Relative
Frame
spacing
(S/L)
LRFS
Configuration
Inherent
Torsion
Design for
Accidental
Torsion
Natural
Eccentricity
(Offset of
CM)
4
100 psf
1
Rectangular
None
(symmetric)
No
10%
0.75
0.5
0.25
1
Yes 0.75
0.5
0.25
4 200 psf
1
Rectangular None
(symmetric)
No
*0
0.75
0.5
0.25
1
Yes 0.75
0.5
0.25
1
No
5%
0.75
0.5
0.25
1
Yes 0.75
0.5
0.25
1
No
10%
0.75
0.5
0.25
1
Yes 0.75
0.5
0.25
10
200 psf
1
Rectangular
None
(symmetric)
No
*0
0.75
0.5
0.25
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BSSC SDC B E: Accidental Torsion Studies E-19
Building
Height
(stories)
Gravity
(Story
Weight)
Relative
Frame
spacing
(S/L)
LRFS
Configuration
Inherent
Torsion
Design for
Accidental
Torsion
Natural
Eccentricity
(Offset of
CM)
10
200 psf
1
Rectangular
None
(symmetric)
Yes
*0 0.75
0.5
0.25
1
No
5%
0.75
0.5
0.25
1
Yes 0.75
0.5
0.25
1
No
10%
0.75
0.5
0.25
1
Yes 0.75
0.5
0.25
* The natural eccentricity is zero, but small amounts of torsion are introduced due to
the nature of the simplified frame models (this occurs for any kind of frame in 3
dimensions)2.
E3 Analysis Procedure
E3.1 Ground Motions
This study uses a set of 22 pairs of far-field strong ground motions selected
by the FEMA P695 project. These motions are recorded from large
magnitude events at moderate fault rupture distances. Although there are no
ground motions in the far-field set from SDC B-like environments, the
FEMA P695 strong ground motion set is used without modification because
it: (1) provides a consistent ground motion record set through which to
examine relative changes in collapse capacity due to accidental torsion
requirements, and (2) contains broadband frequency content, which is
41.86% Draft
E-20 E: Accidental Torsion Studies BSSC SDC B
important for obtaining unbiased results for multiple buildings with varying
lateral and torsional periods.
In incremental dynamic analysis of the two-dimensional models, each
component of each of the 22 ground motions was applied, leading to a total
of 44 records scaled until collapse occurs. Ground motions were applied bi-
directionally and simultaneously to the three-dimensional models. Each
analysis was repeated twice for each of the 22 pairs of ground motions: once
with the north-south (NS) component acting along the x-axis of the building
and the east-west (EW) component acting along the y-axis, then again with
the components switched so that the NS and EW components acted along the
y-axis and x-axis, respectively. All of the results from the 44 cases were
used for computing collapse statistics, per FEMA P695.
E3.2 Incremental Dynamic Analysis
Ground motions are scaled to increasing intensities until collapse occurs for
incremental dynamic analysis. In this study, ground motion scaling is based
on the geometric mean1 of the spectral acceleration of the two components at
a specific building period, i.e. Sa(T1). The fundamental period of the model,
obtained from eigenvalue analysis, was used for scaling ground motions for
all two-dimensional models. Periods of the three-dimensional designs and
models vary slightly (10% or less) depending on how much the design base
shear is increased to account for accidental torsion; however, it is desirable to
use the same period for scaling ground motions such that results can be
directly compared to one another. Therefore, one representative period has
been selected to scale ground motions for each combination of height and
gravity load level that is used.
Once incremental dynamic analysis is performed, two statistical measures of
collapse performance are used: the Adjusted Collapse Margin Ratio (ACMR)
and probability of collapse given the maximum considered earthquake
(MCE) ground motion intensity level, denoted P(Collapse|MCE).
The maximum considered earthquake ground motion intensity (MCE) in
ASCE 7-10 is based on a target risk of 1% probability of collapse in 50
years. At many locations, the risk-targeted MCE is similar to a ground
motion intensity whose likelihood of occurrence corresponds to a 2%
probability of occurring in a 50 year time period (approximately a 2500 year
return period) at a site.
1 This scaling procedure is slightly different than the FEMA P695 method, which
scales a set of pre-normalized records together, but the end result of either method, in
terms of the assessed margin against earthquake-induced collapse, is expected to be
indistinguishable from the other (FEMA P695).
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-21
To compute the ACMR of a building, the Collapse Margin Ratio (CMR)
must be computed first, based on the ratio of the median collapse capacity, or
spectral acceleration causing collapse in incremental dynamic analysis, to the
MCE spectral acceleration at the site of interest as in:
CMR = Sacollapse,median(T1)/SaMCE (T1) (E.1)
In addition, Baker and Cornell (2006) have shown that rare ground motions
tend to have a different spectral shape than the ASCE code-defined design
spectrum; in fact, the spectra tend to have peaks at the period of interest.
Therefore, analysis using broadband sets of ground motions, such as the
FEMA P695 far-field set, which do not have the expected peaks and valleys
in the response spectra, yield conservative estimates of median ground
motion intensity at which collapse occurs. To account for the frequency
content of the ground motion set, the FEMA P695 methodology uses a
spectral shape factor (SSF) to adjust the CMR. The spectral shape factor is
based on the site hazard of interest and a building’s period and ductility and
ranges between 1.1 and 1.2 for the SDC B structures in this study. These
factors have been calibrated to adjust the CMR to the value that would be
obtained if ground motions with the appropriate spectral shape were selected
specifically for the building, rather than using a general set. The equation for
ACMR of 3-dimensional buildings is:
ACMR = 1.2 x SSF x CMR (E.2)
Tables of SSF values and a more detailed description of how to compute SSF
and ACMR can be found in Chapter 7 of FEMA P695. The 1.2 factor adjusts
three-dimensional model results to a two-dimensional equivalent collapse
capacity, as described in FEMA P695.
Since ACMR corresponds to a median collapse value that is scaled by MCE,
a collapse cumulative distribution can be constructed if the dispersion in the
spectral intensity at which collapse occurs is known. Chapter 7 of the FEMA
P695 report gives a detailed explanation of important factors such as
uncertainty in design and modeling properties that contribute to total collapse
dispersion, as well as how to combine them to obtain total collapse
dispersion (βTOT), quantified by the logarithmic standard deviation. Several
tables of pre-computed dispersion values for different combinations of model
quality, quality of design requirements, and quality of system test data are
also presented in FEMA P695, Chapter 7. Values of βTOT can vary from
0.275 to 0.95, but are mostly between 0.45 and 0.7. For this study, a typical
value of the total dispersion βTOT was assumed to be 0.65, based on the tables
in chapter 7 of FEMA P695. It should be noted, however, that factors such
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E-22 E: Accidental Torsion Studies BSSC SDC B
as model quality and quality of design requirements are subjective, and
therefore, our selection of βTOT =0.65 was somewhat subjective as well.
The probability of collapse given MCE is computed from cumulative
distribution function that is defined by the adjusted collapse margin ratio
(ACMR) and the total logarithmic dispersion (βTOT) as follows:
P(Collaspe|MCE)=LognormalCDF(1,ACMR, βTOT) (E.3)
E.4 Nonlinear Modeling
E.4.1 Overview of Modeling Approach
The majority of the analysis for this study of accidental torsion relies on
simplified models, which have been calibrated to the fully designed OMF
buildings and models. The following steps outline the general method used
for building simplified models: 1) Build and analyze ‘high end’ OMF 2D
models of archetypes in Table E-2, 2) Calibrate simplified models to match
the 2D OMF behavior, and 3) Build simplified 3D models for all archetypes
in Table E-4 using the 2D frames. Each of these steps is discussed in more
detail in the following sections.
E.4.2 ‘High End’ OMF Models
Each of the fully designed OMFs (listed in Table E-2) was modeled as a
moment frame in OpenSEES (Open Source Earthquake Engineering
Software). Columns and beams were modeled using a lumped plasticity
approach, with plastic hinge properties of beams and columns computed
according to empirical relationships developed by Haselton et al. (2008).
These relationships are based on the design properties of the beams and
columns (i.e. concrete compression strength, element dimensions, axial load
ratio, and reinforcement detailing) and are therefore capable of representing
the influence of changes in design on the element modeling. Plastic hinges
were modeled using the ‘Ibarra Material’ in OpenSEES developed by Ibarra
et. al (2005). The Ibarra hinge materials have tri-linear monotonic backbones
and incorporate cyclic and in-cycle deterioration, which are important for
modeling collapse.
Shear failure is not modeled directly in the ‘high end’ models. However,
shear failure has been accounted for by means of a non-simulated collapse
mechanism. The non-simulated collapse mechanism is triggered by post-
processing of dynamic analysis results and depends on the column deflection.
Physically, the non-simulated collapse mode represents the loss of vertical
load carrying capacity in at least one column due to shear failure. Non-
simulated collapse modes are described in more detail in section E.4.5.
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-23
Beam/Column
P-∆ Truss
Beam/Column Plastic Hinge
Nonlinear Joint
In addition to plastic hinges in the beams and columns, nonlinear joint
behavior was modeled using 2D shear panels with an Ibarra pinching
material. Nonlinear joint properties were obtained from Lowes and
Altoontash (Altoontash 2004; Lowes et al. 2004). The primary factors
affecting joint strength and/or ductility are confinement, joint area, and
column axial load ratio. Many of the outer joints of the ‘high end’ models
failed during analysis, but failure of the interior joints was prevented, which
is what we expect in interior space frames, due to the high level of
confinement of interior joints.
Distributed gravity loads were applied to the beams, and all remaining dead
loads were applied to P-∆ columns, connected to the frame by rigid truss
elements. Building mass was lumped at the joints and foundation
connectivity was modeled as pinned in the 1-story models and fixed for the
others. (Since 4-story fixed and grade-beam foundation models resulted
nearly identical computed CMRs, these foundation fixities were judged to be
reasonable.)
The ‘high end’ OMFs were analyzed using Incremental Dynamic Analysis
(IDA) and static pushover analysis, and the results of each were used to
calibrate simplified models.
Figure E-5 Schematic of a four-story OMF model
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E-24 E: Accidental Torsion Studies BSSC SDC B
E.4.3 Simplified Model Calibration Procedure
For each ‘high end’ OMF model, a simplified 2D model was made that
matched its properties as exactly as possible. The simplified models are
single bay x-braced frames with nonlinear braces, as shown in Figure E-6.
The braces are truss elements with hysteretic material properties defined by
the nonlinear Ibarra material. Like the nonlinear hinge materials in the ‘high
end’ models, the brace materials are characterized by a tri-linear monotonic
backbone and different modes of cyclic and in-cycle deterioration properties.
The properties of the tri-linear backbones were calibrated to the ‘high end’
models, as described in the following paragraphs. The columns of the
simplified models are rigid beam/columns; multi-story simplified models
have elastoplastic hinges in columns between the stories to allow for story-
story interaction to occur as it would in a moment frame structure. P-∆ loads
for the 2D simplified models were applied directly to the columns.
Figure E-6 Schematic of a four-story simplified model
The first step for calibrating the simplified 2D models was to match the static
pushover properties of the corresponding ‘high end’ 2D models, with P-∆
effects included in the analysis. This calibration was achieved by modifying
the brace properties, specifically initial stiffness, strength, hardening
stiffness, capping displacement and negative post-capping slope, until the
pushover analysis results of each story of the simplified and ‘high end’ OMF
models matched as nearly as possible. After matching the story by story
pushover analysis results, the pushover results of the building as a whole, as
well as modal periods, were checked to ensure that the overall static behavior
of the simplified models matched the behavior of the ‘high end’ OMF
models as closely as possible. Figure E-7 illustrates the pushover calibration
Rigid Beam/Column Element
Rigid Truss Element
Nonlinear Truss Element
Elastoplastic Hinge
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-25
comparison for the 2D, 4-story, high gravity archetype designed without
accidental torsion.
All of the simplified model properties except for cyclic deterioration
parameters were calibrated using static pushover. Lastly, the cyclic
deterioration properties of the simplified models were adjusted until the IDA
results matched the IDA results of the corresponding ‘high end’ model. Table
E-5 illustrates the IDA comparison between the two models.
One difficulty with calibrating simplified braced frame models to represent
the ‘high end’ OMF models was the inherent lack of story-to-story
interaction in the simplified models. If all column and beam elements are
modeled as truss elements, each story of the simplified braced frame
assemblies behaves independently of the stories above and below. Two
major problems arise from this behavior: higher mode periods are much
different for the simplified models than the high end models, and damage
concentrates in just one story during pushover and dynamic analysis, rather
than distributing to multiple stories. This problem has been remedied by
making the columns flexurally rigid and adding plastic hinges between
stories to simulate the story-to-story interaction that occurs in the OMF
frames. Plastic hinge properties in the simplified models are based on beam
and column properties in the corresponding OMF frames. As a result, higher
modes of the simplified models matched those of the ‘high end’ models and
earthquake damage was distributed to multiple stories in a similar manner as
well. Table E-5 shows a comparison of the first 3 modal periods for the
‘high end’ and simplified versions of the 4-story high gravity OMF
archetype.
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E-26 E: Accidental Torsion Studies BSSC SDC B
Figure E-7 Static pushover results for the 2D, 4-story high gravity
model designed without accidental torsion and
analyzed using a triangular loading pattern with P-∆
effects considered
Table ETable ETable ETable E----5555 IDA IDA IDA IDA RRRResults for esults for esults for esults for the 2D, the 2D, the 2D, the 2D, 4444----storystorystorystory High Gravity High Gravity High Gravity High Gravity
Archetypical Model Designed without Accidental Archetypical Model Designed without Accidental Archetypical Model Designed without Accidental Archetypical Model Designed without Accidental
TorsionTorsionTorsionTorsion
Measure OMF Simplified Difference
Period (sec) 2.36 2.36 0.1%
Median Sacollapse (g) 0.189 0.191 1.3%
βtotal 0.65 0.65 NA
CMR 2.2 2.3 1.3%
ACMR 2.7 2.7 1.3%
P(Collapse|MCE) 0.064 0.062 -3.7%
Table ETable ETable ETable E----6666 Modal Periods of the 4Modal Periods of the 4Modal Periods of the 4Modal Periods of the 4----story High Gravity OMF story High Gravity OMF story High Gravity OMF story High Gravity OMF
Archetype without Accidental Torsion ConsideredArchetype without Accidental Torsion ConsideredArchetype without Accidental Torsion ConsideredArchetype without Accidental Torsion Considered
Mode Period (s)
Difference 'High end' Simplified
1 2.36 2.36 0.0%
0 5 10 15 20 25 300
50
100
150
200
250
Roof Displacement (in)
To
tal
Ba
se
Sh
ea
r (k
ips
)
OMF
Simplif ied
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BSSC SDC B E: Accidental Torsion Studies E-27
Mode Period (s)
Difference 'High end' Simplified
2 0.86 0.84 -2.2%
3 0.50 0.52 3.4%
4 0.32 0.36 11.6%
Once the 2D behavior of the simplified models was calibrated to the ‘high
end’ 2D OMF models, 3D simplified models were created. These models
reflect the design plan dimensions of 200ft. x 100ft. There are two frame
lines in each orthogonal direction of the simplified models and one leaning
column in the center of each quadrant of the building to transmit P-∆ forces
to the rigid diaphragm. The P-∆ columns in the 3D models are not a part of
the frames like they are in the simplified 2D models; the reason for this
difference is because real buildings typically have gravity carrying elements
that are distributied fairly evenly throughout the building, not just in the
lateral system. Therefore, P-∆ columns have been placed at the center of
each quadrant in order for P-∆ forces to have an appropriate lever arm for
impacting torsional response. The thick black lines in Figure E-8 represent
the frame lines of a sample 3D model (each frame is modeled as shown in
Figure E-6, except that they no longer carry P-∆ loads) and the squares
indicate P-∆ columns.
Figure E-8 Plan layout of a 3D simplified model
Determination of the 3D brace frame properties was based on the design base
shear of the structure. For cases where the frames in the 3D models had
exactly the same design base shear as the frames in the 2D model, the
modeled frames were identical. For cases where the design base shear due to
accidental torsion was different, because of the building of interest did not
fall in the subset of archetypes fully designed as 2D frames OMFs, the
properties of the braces (and plastic hinge elements between stories for multi-
L1=2L
2=200'
L2=100' X CM, CR
X CM +10%
41.86% Draft
E-28 E: Accidental Torsion Studies BSSC SDC B
story buildings) were computed using linear interpolation between the high
and low base shear versions of the 2D frames. Model strength, stiffness and
cyclic deterioration parameters were interpolated based on the design base
shear of the frames. Such interpolations were only performed between
frames that had the same gravity load and number of stories.
Using interpolation to compute the frame properties meant that several
archetype buildings could be modeled in 3-D using only two fully designed
baseline archetypes for each combination of height and gravity load level. It
should be noted that the capping displacement of the calibrated 2D simplified
models was always determined such that no interpolation would be needed to
compute capping displacement for intermediate models. In other words, the
capping displacement of the high base shear version of a given archetype was
kept the same as the capping displacement of the low base shear version.
The reason that capping displacement was kept constant for each archetype is
because we believe that system ductility should be independent of design
base shear. Therefore, linking capping displacement to design base shear
would introduce error into the experiment by calibrating intermediate models
to design idiosyncrasies, rather than meaningful system properties.
Additionally, the capping displacemt for the high and low base shear
versions of each ‘high end’ OMF frame in this study were extremely similar
(consistantly less than10% different), which confirmed our decision to keep
it constant during calibration. An example of the interpolation of simplified
frame properties is shown below in Figure E-9. The interpolation of cyclic
deterioration properties is not presented in the figure, but is based on design
base shear just as the monotonic backbone properties have been.
Figure E-9 Example interpolation of nonlinear monotonic
backbone properties for the second story of the 4-
story, high gravity archetype (P-∆ effects not included)
0
50
100
150
200
250
300
0 2 4 6 8 10 12 14 16 18 20
Sto
ry
Sh
ea
r (
kip
s)
Displacement (in)
Low Base Shear (factor of 1.0)
High Base Shear (factor of
1.32)
Interpolated Intermediate
Model (base shear factor of
1.16)
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BSSC SDC B E: Accidental Torsion Studies E-29
E.4.4 Non-Simulated Collapse Modes
Collapse is defined in a number of different ways for this study. For IDA, a
building is considered to collapse when the maximum interstory drift ratio
begins to increase rapidly, without any significant increase in ground motion
intensity (side-sway collapse). However, two other forms of collapse are
considered in addition to sideway collapse: 1) Failure of the (unmodeled)
gravity system and 2) Loss of vertical load carrying capacity of the lateral
system, due to shear failure of a column and its subsequent loss of ability to
carry gravity loads.
Neither shear failure modes nor gravity system failure are simulated by the
simplified or OMF frame models, so these failure modes are assessed
through non-simulated methods. These failure modes are of interest because
both result in structural members no longer having the capacity to withstand
vertical loads, which can lead to building collapse.
No gravity systems are design or modeled in this study, but it is still
important to acknowledge the fact that collapse in real buildings can result
due to failure of gravity elements, even if the lateral system is still in tact.
Assessing non-simulated collapse due to failure of the gravity system is
achieved in this study by setting a threshold interstory drift, beyond which
the gravity system is assumed to fail. If the maximum interstory drift in any
story of a building exceeds that threshold, then the building is assumed to
collapse. Thresholds of 3% and 6% were used for assessing non-simulated
collapse due to failure of the gravity system. These thresholds were chosen to
represent the range in ductility in gravity-load bearing systems possible in
SDC B.
Design standards for OMF’s do not require capacity design, so, as a result,
transverse reinforcement may be inadequate for carrying loads associated
with plastic hinging of the columns, resulting in brittle shear failure. This
specific type of brittle failure only applies to SDC B reinforced concrete
columns, but it is still relevant to include when we are trying to use OMF’s to
represent a SDC B lateral systems in general, because several other systems
with low R-factors are prone to brittle failure as well (joint shear failure and
weld failure in steel frames for example).
Column shear failure has been shown to depend on a combination of
displacement demand and shear force demand (Aslani 2005, and Elwood
2004). Therefore, the second non-simulated collapse mode, loss of vertical
load carrying capacity, is also assessed using interstory drift thresholds.
However, the drift thresholds are story specific, because the expected column
drift for which shear failure occurs depends on multiple parameters such as
41.86% Draft
E-30 E: Accidental Torsion Studies BSSC SDC B
column dimensions, axial load ratio, and reinforcement detailing. Using
those parameters, Aslani (2005) and Elwood (2004) have developed
empirical methods for predicting the probabilities of shear failure and
subsequent loss of gravity-load bearing capacity in reinforced concrete
columns.
In this study, column drifts corresponding to a 50% probability of loss
vertical load carrying capacity are computed according to the methods of
Aslani (2005) and Elwood (2004) and interpreted as non-simulated collapse
related to column shear failure. These column drifts are then mapped to total
interstory drifts using results from static pushover analysis, accounting for
drift contributions from column, beam, and joint rotations. Collapse occurs if
the drift in any column exceeds the collapse interstory drift threshold. For
example, the loss of vertical load carrying capacity drift threshold for a
second story interior column in the 4-story, high gravity, archetype is 1.80%,
but the interstory drift threshold for non-simulated collapse for the second
story is taken to be 2.35%, due to the portion of the drift resulting from beam
and joint rotations.
The adjusted collapse margin ratio for each archetype varies significantly
with varying methods of assessing non-simulated collapse, however, the
relative improvement gained from designing for accidental torsion in this
study is mostly independent of which, if any, non-simulated collapse
mechanism is implemented. Therefore, all of the results figures combine the
results from each of the non-simulated collapse modes considered in addition
to the results obtained without non-simulated collapse, unless otherwise
specified. Complete results are provided in the subsequent section, E.5.
E.5 Sensitivity of Collapse Risk Assessments to Designing for Accidental Torsion
Results of the assessments, in terms of the change in collapse risk due to
designing SDC B buildings with and without accidental torsion, and the
absolute collapse risk (ACMR or probability of collapse), are presented in
this section. The following figures and paragraphs describe the main trends
observed in this study. These trends include:
Trends specifically relevant to the scope of the study:
• Torsionally flexible buildings benefit more from being designed for
accidental torsion than torsionally stiff buildings. As a result, the
relative frame spacing parameter (S/L) is an excellent predictor of
the effectiveness of designing accidental torsion for all building
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-31
types studied. In addition, torsionally flexible buildings perform
much worse overall, with greater absolute collapse probabilities.
• Inherent torsion had little or no impact on the effectiveness of
designing for accidental torsion, but it does lower absolute collapse
capacity significantly.
• The torsional irregularity ratio that is computed in Table 12.3-1 of
ASCE 7 is a good, but sometimes conservative predictor, of the
effectiveness of designing for accidental torsion. Collapse capacity
decreases as torsional irregularity ratio increases.
Other Trends:
• Buildings with intermediate torsional flexibility perform moderately
better than torsionally stiff buildings and much better than torsionally
flexible buildings, when measured in terms of absolute collapse risk.
• Lightweight buildings perform better than heavy buildings.
• Short buildings perform better than tall buildings for the range of
building heights used in the study.
E.5.1 Trends Specifically Relevant to the Scope of this Study
E.5.1.1 Torsional Stiffness Measured by Relative Frame Spacing
Designing for accidental torsion in archetypes with moderate to high
torsional stiffness (0.5≤S/L≤1.0) makes very little difference in their collapse
performance, as shown in Figure E-10. The relative improvements in ACMR
due to including accidental torsion in the design are less than 10% for the
majority of cases and 2.1% on average. In this range, improvements due to
designing for accidental torsion are fairly constant regardless of the relative
frame spacing. In contrast, torsionally flexible (i.e. S/L<0.5) archetypes see
significant improvements in collapse capacity when they are designed for
accidental torsion. Each line in
Figure E-13 represents average relative improvement of collapse capacity
for each archetypical building as relative frame spacing (S/L) is varied. The
trend is virtually flat when 0.5≤S/L≤1.0, but steep (showing increasingly
pernicious consequences from not designing for accidental torsion) when
S/L<0.5.
The influence of relative frame spacing (S/L) on the effectiveness of design
accidental torsion was quantitatively compared to the influence of the other
design/modeling parameters by means if a binary regression tree, Figure E-
0.25 0.3 0.35 0.4 0.45 0.5 0.75 1-0.05
0
0.05
0.1
Relative Frame Spacing (S/L)
Re
lati
ve
Im
pro
ve
me
nt
of
AC
MR
Inherent Tors
Mean of Control Cases
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E-32 E: Accidental Torsion Studies BSSC SDC B
10. The other parameters are: plan configuration, inherent torsion (yes/no),
number of stories, gravity load level, and center of mass offset. The
following binary regression tree was obtained by splitting the data into
optimal binary categories such that the total variance of the categorized data
was minimized.
Figure E-10 Binary regression tree for relative improvements of
ACMR
The regression tree of Figure E-10 shows that the most significant portion
of the variance in the data is captured by relative frame spacing (S/L). When
the results are categorized as (S/L)>0.425 and (S/L)<0.425, the expected
values of ACMR improvements for the two categories are 2.7% and 10.7%,
respectively.
Cross-validated error estimates are computed for each split of the binary
regression tree in Figure E-10 and are shown in Figure E-11. The results
show that only the first split, which is based on relative frame spacing (S/L),
is appropriate for this data set, because any additional splits do not lower the
error total error from cross-validated estimation. In other words, relative
frame spacing (S/L) is the single most influential factor for predicting the
effect of design accidental torsion, for this particular data set. The pruned
regression tree for relative improvement of ACMR is presented in Figure E-
12.
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BSSC SDC B E: Accidental Torsion Studies E-33
Figure E-11 Relative error obtained thru cross-validation vs.
number of splits for the binary regression tree of
relative ACMR improvement due to design accidental
torsion. Only the first split decreased the error
significantly.
41.86% Draft
E-34 E: Accidental Torsion Studies BSSC SDC B
Figure E-12 Pruned binary regression tree for relative
improvements of ACMR
Figure E-13 Average relative improvement of ACMR for subgroups
of buildings due to design accidental torsion, as a
function of relative frame spacing
A modified version of a statistical method called change-point analysis was
used to try to pin-point the exact location where the influence of design
accidental torsion on collapse capacity begins to really kick in. By visual
inspection of Figure E-13, it can be observed that the slope of the lines must
change somewhere in the range 0.25<(S/L)<0.5, but data within that range
has only been obtained for the 1-story high gravity case.
The essence of change-point analysis is to detect jumps in a data set by
fitting local polynomial regressions to data only on one side of each point
and then only to the other side. A jump in the data is indicated when the
squared difference of the value of the two local regression lines at a point
(one local polynomial fitted to the data on each side of the point) is large in
comparison to other points. However, we are concerned with a sudden
change in slope, not an actual jump, so the method has been refined to
compare slopes of local polynomials rather than values (hereafter referred to
as ‘change-slope’ analysis).
0.25 0.3 0.35 0.4 0.45 0.5 0.75 1-0.05
0
0.05
0.1
0.15
0.2
Relative Frame Spacing (S/L)
Re
lati
ve
Im
pro
ve
me
nt
of
AC
MR
10-Story High Grav
4-Story Low Grav
4-Story High Grav
1-Story Low Grav
1-Story High Grav
I-shape
Inherent Tors
Mean of Control Cases
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-35
0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Ch
an
ge
-Slo
pe
Va
lue
fro
m L
oc
al
Po
lyn
om
ial
An
aly
sis
Ninetieth Quantile
Median
Tenth Quantile
In local polynomial regression, the two main parameters that control the way
the regression is fit are the portion of neighboring data points used (alpha)
and the degree of the polynomial. Alpha values of 0.5-0.9 in increments of
0.05 with polynomial degree equal to 1.0 were used for performing the
change-slope analysis (9 combinations).
Due to the relatively large dispersion of the data, fitting the left-side local
polynomial to at small relative frame spacing was difficult. This difficulty
has been overcome by simulating data and doing multiple iterations. Data
was simulated using local polynomials of degree one with alpha values
ranging from 0.6 to 9 in increments of 0.05 (7 combinations). For each
combination of polynomial degree and alpha, three hundred data points were
simulated from the original data, and a change-slope analysis was performed
at each point. This process was repeated 100 times for each combination of
data simulation parameters and change-slope parameters for a total number
of 9x7=63 combinations. For each of the 63 combinations, the median
change-slope values were retained at each point.
Due to the sensitivity of the change slope analysis to data variance at small
values of relative frame spacing (S/L), some of the change-slope analysis
gave bogus results at the left side. This problem was remedied by looking at
the range 0.325<(S/L)<0.7 and rejecting any analysis that showed a
maximum change-slope at (S/L)=0.325. From the remaining analyses, an
envelope of change slope values was created and is shown in
Figure E-14.
41.86% Draft
E-36 E: Accidental Torsion Studies BSSC SDC B
0.2 0.4 0.6 0.8 1−0.1
−0.05
0
0.05
0.1
0.15
0.2
0.25
Relative Frame Spacing (S/L)
Rel
ativ
e A
CM
R Im
prov
emen
t and
S
cale
d C
hang
e−P
oint
Val
ues
(uni
tless
)
DataLocal Poly FitMean−stdErrorMean+stdErrorChange−Point Result
Figure E-14 Envelope of successful change-slope analyses (57 of
63 analyses were considered successful)
The envelope above indicates that the location of the most sudden change in
slope likely occurs at a relative frame spacing (S/L) of approximately 0.45.
In addition to the envelope of change-slope analyses results, a t-distribution
of peak points of each successful analysis was formed, for which the 90%
confidence range was 0.36<(S/L)<0.53 with a mean of 0.45. A sample of the
change-slope analysis results from 100 iterations of a single combination of
parameter values is shown in Figure E-15.
Figure E-15 Example of a single change-slope analysis result
obtained from 80 iterations with a local polynomial of
degree 1 and alpha=0.7 for simulating data and
alpha=0.65 for doing change-slope analysis. The
circles are the original data. The red line and dashed
black lines represent the local polynomial parameters
for simulating the data, and the blue line is the scaled
change-slope analysis result.
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-37
Results also show that torsionally flexible buildings (relative frame spacing
(S/L) <0.5) have much lower absolute collapse capacities than their
torsionally stiff counterparts. Figure E-16 shows that collapse capacity
increases as relative frame spacing increases for every archetype group when
relative frame spacing (S/L) is less than 0.5, but plateaus when S/L≥0.5.
Figure E-16 Average absolute ACMR vs. relative frame spacing.
Non-simulated collapse modes not considered. Thin
lines represent cases where accidental torsion is
considered in design
A pruned binary regression tree has also been constructed for absolute
ACMR and is presented in Figure E-17. Binary regression analysis shows
that gravity load level, relative frame spacing (S/L), and number of stories
are the most influential factors for collapse capacity, in that order. For the
case of absolute collapse capacity, relative frame spacing is still a significant
contributor, but it is not the only important factor, nor is it the most
important.
It can also be observed that none of the splits on the pruned regression tree
for ACMR are for design accidental torsion, which indicates that its
contribution to collapse capacity in this study is much smaller than the
contributions from gravity load, relative frame spacing, and number of
stories. For an ideal case in which building code requirements and the design
0.25 0.3 0.35 0.4 0.45 0.5 0.75 11
1.5
2
2.5
3
3.5
Relative Frame Spacing (S/L)
AC
MR
10-Story High Grav
4-Story Low Grav
4-Story High Grav
1-Story Low Grav
1-Story High Grav
I-shape
Inherent Tors
41.86% Draft
E-38 E: Accidental Torsion Studies BSSC SDC B
0.1
0.12
0.14
0.16
0.18
0.2
Re
lati
ve
Im
pro
ve
me
nt
of
AC
MR
S/L=0.5
S/L=0.25
of our archetypes are both perfect, design accidental torsion would be the
single most important factor for predicting collapse capacity for two reasons:
1) code requirements are supposed to make collapse capacity independent of
building factors such as weight and height and 2) the design accidental
torsion requirement is supposed to make building collapse capacity
independent of torsional flexibility.
Figure E-17 Pruned binary regression tree for absolute ACMR (non-
simulated collapse modes omitted)
E.5.1.2 Effects of Inherent Torsion
The presence of inherent torsion in an archetype building did not
significantly influence the effect of designing for accidental torsion in this
study.
Figure E-18 shows the average relative improvements of collapse capacity
for the 1-story high gravity archetypes with relative frame spacing (S/L) of
0.5 and 0.25. Two of the archetypes shown have inherent torsion (high
levels of the torsional irregularity ratio) and the other two are regular. The
slopes of the lines are virtually flat, indicating that inherent torsion is not a
determining factor for the effect of designing for accidental torsion. The
torsional irregularity ratio is discussed in more detail in the next section.
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-39
Figure E-18 Effect of inherent torsion on collapse capacity for the
1-story high gravity archetype
However, it is important to note that the absolute collapse capacity of
buildings with inherent torsion is much lower than their symmetric
counterparts. Note that in Figure E-16, all blue lines represent 1-story high
gravity archetypes. In absolute terms, the collapse capacities of the
symmetric archetypes (labeled ‘1-Story High Grav’ and ‘I-shape’) are much
higher, in an absolute sense, than the collapse capacity of the 1-story high
gravity archetype that has inherent torsion.
E.5.1.3 Torsional Irregularity Ratio
Since relative frame spacing (S/L) is not a practical metric for categorizing
buildings with more than two frame lines in each orthogonal direction, the
results have been recast in terms of torsional irregularity ratio, which is
computed according to Table 12.3-1 of ASCE 7-10, by completing the
following steps:
• Apply a lateral load which is offset from the center of mass perpendicular to
the direction of loading by a distance 5% of the buildings longest dimension
perpendicular to the direction of loading
• Take a ratio of the largest displacement parallel to the applied load at any
point in the plan of the building to the average displacement parallel to the
applied load
• Repeat with 5% offset in the opposite direction
• Repeat for each main orthogonal direction
• Take the largest of the computed displacement ratios
Contributions to torsional irregularity can come from either inherent torsion
or torsional flexibility (torsional flexibility contributes to torsional
41.86% Draft
E-40 E: Accidental Torsion Studies BSSC SDC B
irregularity because a 5% offset for accidental torsion must be considered
when the torsional irregularity ratio is computed). For symmetric buildings
(i.e. those without inherent torsion), the torsional irregularity ratio is a good
predictor of the effectiveness of designing for accidental torsion, as shown in
Figure E-19, because it is directly related to relative frame spacing.
Although buildings with inherent torsion have higher torsional irregularity
ratios than their symmetric counterparts that have the same relative frame
spacing (S/L), they see similar improvements from designing for accidental
torsion. Therefore, using torsional irregularity as an indicator for the
importance of accidental torsion in design penalizes buildings with inherent
torsion more readily than those without inherent torsion. The conservatism
of using torsional irregularity ratio to predict the benefits of design accidental
torsion in buildings with inherent torsion can be observed by examining
Figure E-13 and Figure E-19. Note that in
Figure E-13, where relative frame spacing is on the x-axis, all of the blue
lines follow the same basic trend. However, in Figure E-19 below, the dotted
blue line that represents the 1-story high gravity case with inherent torsion is
far below the other blue lines. Using the torsional irregularity ratio as a
trigger to require accidental torsion therefore identifies buildings with
inherent torsion as candidates for being designed with accidental torsion
more readily than symmetric buildings, despite the observation that the
degree of inherent torsion is not highly related to the importance of
accidental torsion.
0.25 0.3 0.35 0.4 0.45 0.5 0.75 1-0.05
0
0.05
Relative Frame Spacing (S/L)
Re
lati
ve
Im
pro
ve
me
nt
of
AC
MR
Mean of Control Cases
0.25 0.3 0.35 0.4 0.45 0.5 0.75 1-0.05
Relative Frame Spacing (S/L)
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-41
Figure E-19 Relative improvement of collapse capacity due to
designing for accidental torsion vs. torsional
irregularity ratio
Binary regression analysis also confirms the observation that torsional
irregularity ratio is strong factor for relative ACMR improvement due to
design accidental torsion requirements. When torsional irregularity ratio is
substituted for the combination relative frame spacing, plan configuration,
and inherent torsion, the result is very similar to that obtained using relative
wall spacing as a parameter.
1 1.5 2 2.5 3 3.5 4 -0.05
0
0.05
0.1
0.15
0.2
Torsional Irregularity Ratio
Re
lati
ve
Im
pro
ve
me
nt
of
AC
MR
10-Story High Grav
4-Story Low Grav
4-Story High Grav
1-Story Low Grav
1-Story High Grav
I-shape
Inherent Tors
41.86% Draft
E-42 E: Accidental Torsion Studies BSSC SDC B
1 1.5 2 2.5 3 3.5 4 1
1.5
2
2.5
3
3.5
Torsional Irregularity Ratio
AC
MR
10-Story High Grav
4-Story Low Grav
4-Story High Grav
1-Story Low Grav
1-Story High Grav
I-shape
Inherent Tors
Figure E-20 Pruned binary regression tree for relative
improvements of ACMR, using torsional irregularity
ratio
An additional change-slope analysis of the results from using torsional
irregularity ratio was not done, because the torsional irregularity ratios can be
computed directly from the relative frame spacing values for the 1-story high
gravity building results. When t-test results from section E5.1.1 are
converted to torsional irregularity ratios, the 90% confidence range for the
‘kink’ in the data is 1.29<torsional irregularity ratio<1.58, with an expected
value of 1.40.
Torsional irregularity ratio is also good predictor for absolute collapse
capacity, as can be seen in Figure E-21. Note that the thick dotted blue line
that represents the 1-story high gravity building with inherent torsion
coincides with the thick blue lines representing the symmetric 1-story high
gravity buildings, which can be contrasted to the results that are based on
relative wall spacing (S/L) in Figure E-16. Therefore, torsional irregularity
ratio is an equal or better predictor than relative wall spacing for absolute
collapse capacity.
Figure E-21 Absolute capacity vs. torsional irregularity ratio (non-
simulated collapse modes omitted)
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-43
It should be noted that, although Figure E-21 shows a strong correlation
between torsional irregularity ratio and collapse capacity, there are other
significant factors in this study that affect collapse capacity as well. The
pruned regression tree of ACMR in Figure E-22 shows that gravity load level
and number of stories are also important factors, just like when relative frame
spacing was used.
Figure E-22 Pruned binary regression tree of ACMR using torsional
irregularity ratio (non-simulated collapse modes
omitted)
E.5.2 Other Trends
E.5.2.1 Better Performance in Buildings with Intermediate Torsional Flexibility
An unexpected trend observed in Figure E-16 is a slight increase in collapse
capacity when buildings transition from being torsionally stiff (S/L~1.0) to
moderately torsionally stiff (S/L~0.5), even though the structure’s torsional
resistance is decreasing. It seems logical that greater torsional flexibility
would lead to greater deformations and, therefore, lower collapse capacity.
This observation is true in general, but there is a minor increase in collapse
capacity when torsional stiffness reduces from very stiff to moderately stiff.
This slight increase occurs because as the fundamental torsional period
increases with increased torsional flexibility, the building falls into a
frequency range for which the earthquake records have much less spectral
energy. This effect partly counterbalances the larger displacements that occur
41.86% Draft
E-44 E: Accidental Torsion Studies BSSC SDC B
due to the increased torsional flexibility. As an illustrative example, the first
seven modal periods for the 3D 4-story high gravity archetype are shown
below in Table E-7 (torsional periods are highlighted in grey) along with a
spectral acceleration plot of the FEMA P695 far-field ground motion set
(Figure E-23). Note that spectral acceleration is highest for short periods and
decreases steadily as the fundamental period increases beyond 0.5 seconds,
which means that buildings with short torsional periods (i.e. torsionally stiff
buildings), will experience the greatest torsional accelerations and torsional
flexible buildings experience relatively less demand.
Table ETable ETable ETable E----7777 Summary of Summary of Summary of Summary of MMMModal odal odal odal PPPPeriods for the 4eriods for the 4eriods for the 4eriods for the 4----SSSStory tory tory tory HHHHigh igh igh igh GGGGravity ravity ravity ravity
AAAArchetyperchetyperchetyperchetype
4-story High Gravity
Mode
S/L = 1 S/L = 0.75 S/L = 0.5 S/L = 0.25
Period
(s)
Torsional
or
Lateral
Period
(s)
Torsional
or
Lateral
Period
(s)
Torsional
or
Lateral
Period
(s)
Torsional
or
Lateral
1 2.34 lat 2.34 lat 2.70 tors 6.78 tors
2 2.34 lat 2.34 lat 2.34 lat 2.34 lat
3 1.30 tors 1.75 tors 2.34 lat 2.34 lat
4 0.83 lat 0.83 lat 0.96 tors 2.21 tors
5 0.83 lat 0.83 lat 0.83 lat 1.32 tors
6 0.51 lat 0.63 tors 0.83 lat 0.91 tors
7 0.51 lat 0.51 lat 0.59 tors 0.83 lat
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BSSC SDC B E: Accidental Torsion Studies E-45
Figure E-23 Acceleration spectrum of the FEMA P695 ground
motion set (FEMA P695 Report)
E.5.2.2 Lightweight vs. Heavy Buildings
Gravity load level is also a major contributor to building collapse
performance as is illustrated by the regression trees in Figure E-17 and
Figure E-22. Figure E-24 also illustrates the effects of gravity loads on
collapse performance for the one and four story archetypes; heavier buildings
(red) tended to perform worse than lightweight buildings (black) in this
study. However, the relative improvement from designing for accidental
torsion is fairly similar between high and low gravity archetypes (note that
the red line trends are similar to black line trends in Figure E-25 and also the
binary regression tree in Figure E-10).
A major contributor to the difference in absolute collapse capacity between
the high and low gravity archetypes is the fact that transverse reinforcement
spacing was typically controlled by the maximum allowable spacing, rather
than by design loads. Since the high gravity frames have larger sections,
their maximum allowable spacing for transverse reinforcement is also larger,
lead to less ductile beam and column elements and overall worse
performance.
41.86% Draft
E-46 E: Accidental Torsion Studies BSSC SDC B
0.25 0.3 0.35 0.4 0.45 0.5 0.75 12
Relative Frame Spacing (S/L)
4-Story Low Grav
1-Story Low Grav
4-Story High Grav
1-Story High Grav
Figure E-24 Influence of gravity load level and building height on
absolute collapse capacity. Non-simulated collapse
modes not considered.
Figure E-25 Influence of gravity load level and building height on
the effect of design accidental torsion on collapse
capacity.
E.5.2.3 Effect of Building Height on Collapse Performance
Taller buildings tend to perform worse than shorter buildings in this study.
The tallest building analyzed is 10 stories (132 ft.), and its absolute collapse
capacity is the lowest of all the archetypes (see Figure E-16 and Figure E-
21). Additionally, Figure E-24 shows that the 4-story buildings (dashed
lines) performed worse than their 1-story counterparts (solid lines). After
about 10 stories, equation 12.8.5 of ASCE 7-10, which defines a minimum
value of 0.01g for the base shear coefficient Cs, is triggered, reducing the
effect of building height in the design. One significant contributor to the
greater performance of the shorter buildings, which is specific the building
types in this study, but not necessarily in general, is the of the OMF design
requirements for maximum transverse reinforcement spacing. Due to
maximum shear spacing requirements, the shorter buildings in this study tend
to be more ductile. For example, the design shear in the columns of the 1-
story OMF’s is so low that transverse reinforcement is almost not even
needed for resisting shear forces. However, since the design of transverse
0.25 0.3 0.35 0.4 0.45 0.5 0.75 10
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Relative Frame Spacing (S/L)
Re
lati
ve
Im
pro
ve
me
nt
of
AC
MR
4-Story Low Grav
1-Story Low Grav
4-Story High Grav
1-Story High Grav
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-47
reinforcement is controlled by maxim spacing requirements, the columns are
‘over-designed’ for shear forces. The transverse reinforcement spacing is so
low, in fact, that the columns exceed capacity design standards, which makes
them very ductile, even though capacity design is not required for OMF’s.
E.6 Conclusions and Recommendations
E.6.1 Revision of Section 12.8.4.2 in ASCE 7
According to the results of this study, the single most significant predictor for
the improvement of building collapse capacity due to designing for
accidental torsion is relative frame spacing (S/L). Buildings with relative
frame spacing (S/L) greater than 0.45 tend see very little improvement in
their collapse capacities when designed for accidental torsion (see
Figure E-13,Figure E-12, and Figure E-14); therefore, we recommend that
such buildings need not adhere to the accidental torsion requirement of
ASCE 7-10. However, computing an ‘equivalent S/L relative frame spacing’
for buildings with multiple frame lines is burdensome and prone to
misinterpretation.
As a result, an alternative method, using torsional irregularity ratio, is
suggested, because ASCE 7-10 already requires that quantity to be
computed. As shown above, the torsional irregularity ratio is a good
predictor of relative improvement of collapse capacity (see section E.5.1.3
and Figure E-19), and buildings with torsional irregularity ratio less than 1.4
gain very little, in terms of collapse capacity, from design accidental torsion.
A torsional irregularity ratio of 1.4 is also the cut-off or torsional irregularity
type 1b, therefore, we recommend that buildings designed for SDC B,
which do not have type 1b torsional irregularity, need not adhere to the
accidental torsion requirement of section 12.8.4.2 of ASCE 7-10. Since
our results indicate that torsional flexibility, rather than inherent torsion, is
critical in determining the effect of designing for accidental torsion on
collapse capacity (see
Figure E-18), this recommendation conservatively affects buildings with
inherent torsion. However, buildings with inherent torsion perform more
poorly in general than their symmetric counterparts in terms of absolute
collapse capacity (see Figure E-16), such that higher levels of conservatism
in design may be appropriate.
0.25 0.3 0.35 0.4 0.45 0.5 0.75 1-0.05
0
Relative Frame Spacing (S/L)
Re
lati
ve
Im
pro
ve
me
nt
of
AC
MR
41.86% Draft
E-48 E: Accidental Torsion Studies BSSC SDC B
E.6.2 Future Research
It is desirable for buildings of all levels of torsional irregularity due to
torsional flexibility or inherent torsion to have similar collapse capacities; if
this were the case, the lines in Figure E-21 would be flat, indicating that
collapse capacity is independent of torsional irregularity ratio. However, as
shown in Figure E-21 the collapse capacity declines rapidly after the
torsional irregularity ratio increases past 1.4 and has decreased 20-50% by
the time the torsional irregularity ratio is approximately 2.3. Therefore, an
amplification factor for torsionally flexible buildings in SDC B that would
increase their collapse capacities to a level comparable to the collapse level
when torsional irregularity ratio is less than 1.4 is suggested for future
research.
Additionally, the authors recommend a similar future study to examine the
effects of design accidental torsion in SDC D. Such a study would have at
least two benefits:
• A better knowledge of whether the torsion amplification factor, Ax,
in ASCE 7-10 is accomplishing its intended purpose of making
seismic collapse capacity independent of the level of torsional
irregularity or flexibility.
• Possible elimination of the accidental torsion design requirement for
buildings in high seismic regions that are not categorized as having
torsional irregularity type 1a or 1b.
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-49
E.7 Exhaustive Results Summary
E.7.1 All Archetype Collapse Results
Table ETable ETable ETable E----8888 Collapse Results for the Collapse Results for the Collapse Results for the Collapse Results for the 1111----Story, Story, Story, Story, Low Low Low Low GravityGravityGravityGravity, , , ,
Symmetric Symmetric Symmetric Symmetric ArchetypesArchetypesArchetypesArchetypes
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3011100 1 0.37 3.43 0.03 0.37 3.40 0.03 0.20 1.79 0.18
3011200 0.75 0.37 3.43 0.03 0.37 3.40 0.03 0.20 1.79 0.18
3011300 0.5 0.37 3.43 0.03 0.37 3.40 0.03 0.20 1.79 0.18
3011400 0.25 0.37 3.43 0.03 0.37 3.40 0.03 0.20 1.79 0.18
3011110 1 0.38 3.46 0.03 1% 0.37 3.41 0.03 0% 0.20 1.86 0.17 4%
3011210 0.75 0.38 3.49 0.03 2% 0.38 3.44 0.03 1% 0.20 1.88 0.17 5%
3011310 0.5 0.39 3.54 0.03 3% 0.38 3.45 0.03 2% 0.21 1.93 0.16 7%
3011410 0.25 0.38 3.52 0.03 2% 0.37 3.44 0.03 1% 0.21 1.92 0.16 7%
3011100 1 0.37 3.43 0.03 0.37 3.40 0.03 0.20 1.79 0.18
3011200 0.75 0.38 3.46 0.03 0.37 3.42 0.03 0.20 1.79 0.18
3011300 0.5 0.37 3.44 0.03 0.37 3.41 0.03 0.20 1.79 0.18
3011400 0.25 0.31 2.82 0.06 0.29 2.68 0.06 0.19 1.75 0.19
3011110 1 0.38 3.45 0.03 0% 0.37 3.41 0.03 0% 0.20 1.86 0.17 4%
3011210 0.75 0.38 3.48 0.03 1% 0.37 3.43 0.03 0% 0.20 1.88 0.17 5%
3011310 0.5 0.38 3.52 0.03 2% 0.38 3.45 0.03 1% 0.21 1.93 0.16 7%
3011410 0.25 0.33 2.99 0.05 6% 0.30 2.71 0.06 1% 0.21 1.91 0.16 9%
3011101 1 0.33 3.05 0.04 0.32 2.96 0.05 0.16 1.43 0.29
3011201 0.75 0.34 3.14 0.04 0.33 3.06 0.04 0.15 1.39 0.31
3011301 0.5 0.36 3.34 0.03 0.34 3.15 0.04 0.14 1.29 0.35
3011401 0.25 0.27 2.52 0.08 0.23 2.14 0.12 0.14 1.25 0.36
3011111 1 0.34 3.10 0.04 1% 0.33 3.02 0.04 2% 0.17 1.52 0.26 7%
3011211 0.75 0.35 3.18 0.04 1% 0.33 3.02 0.04 -1% 0.15 1.41 0.30 1%
3011311 0.5 0.37 3.38 0.03 1% 0.36 3.28 0.03 4% 0.14 1.31 0.34 1%
3011411 0.25 0.30 2.74 0.06 9% 0.26 2.41 0.09 13% 0.13 1.21 0.39 -4%
3011102 1 0.33 3.04 0.04 0.33 3.00 0.05 0.15 1.41 0.30
3011202 0.75 0.35 3.17 0.04 0.33 3.02 0.04 0.15 1.38 0.31
3011302 0.5 0.36 3.30 0.03 0.33 3.03 0.04 0.12 1.13 0.42
3011402 0.25 0.26 2.40 0.09 0.20 1.86 0.17 0.10 0.96 0.52
3011112 1 0.33 2.99 0.05 -2% 0.32 2.94 0.05 -2% 0.15 1.36 0.32 -4%
3011212 0.75 0.35 3.21 0.04 1% 0.34 3.08 0.04 2% 0.16 1.44 0.29 5%
3011312 0.5 0.37 3.38 0.03 2% 0.34 3.10 0.04 2% 0.12 1.06 0.47 -7%
3011412 0.25 0.30 2.71 0.06 13% 0.23 2.10 0.13 13% 0.11 1.01 0.49 5%
No
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No
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Yes
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Yes
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No
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mu
late
d
Co
lla
pse
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
6%
No
no
nsi
mu
late
d
Co
lla
pse
Mo
de
s
ID
Sto
rie
s
Gra
vit
y
Re
lati
ve
Fra
me
Sp
aci
ng
(S
/L)
De
sig
n f
or
Acc
ide
nta
l T
ors
ion
Na
tura
l E
cce
ntr
icit
y (
Off
set
of
CM
)
41.86% Draft
E-50 E: Accidental Torsion Studies BSSC SDC B
*Total logarithmic dispersion (b) is assumed to be 0.65 for computing
P(Collapse|MCE).
**The natural eccentricity is zero, but 2small amounts of torsion are
introduced due to the nature of the simplified frames.
2 Unless the rotational degrees of freedom of floor diaphragms are fixed in
the OpenSees models, small amounts of torsion are introduced in the 3D
models due to geometric nonlinearities. This effect occurs due to the
configuration of the simplified models. When a frame or wall resists a lateral
load, it must be stabilized in the out-of-plane direction to prevent it from
twisting. Taking framed systems as an example, when out-of-plane
deflections are present, compression forces in the columns are destabilizing
and push the frame farther out of plane. If there is any lateral load acting
along the plane of the frame, there will be more compression in the columns
of one side than the other, cause varying destabilizing forces at each end,
which results in a moment; thus, ‘accidental torsion’ is introduced. A similar
phenomenon occurs from the braces as well; tension braces tend to pull one
end of the top of the frame back to its vertical in-plane position, while
compression braces tend to push the top of frames at the opposite end farther
out plane. The extent to which geometric nonlinearities contribute to natural
accidental torsion in the simplified models can be observed in the 1-story
rows of Table E-8 and Table E-9 in which the perfectly symmetric 1-story
archetypes have been analyzed with and without the rigid diaphragm being
allowed to rotate. For cases where S/L is greater than or equal to 0.5 (i.e. the
building was not extremely torsionally flexible), these geometric
nonlinearities contribute very little to natural accidental torsion.
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-51
Me
dia
n C
oll
ap
se S
a(1
.3s)
(g)
Ad
just
ed
Co
lla
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rgin
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tio
*P
(Co
lla
pse
|M
CE
)
Imp
rov
em
en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
Me
dia
n C
oll
ap
se S
a(1
.3s)
(g)
Ad
just
ed
Co
lla
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Ma
rgin
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tio
*P
(Co
lla
pse
|M
CE
)
Imp
rov
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en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
Me
dia
n C
oll
ap
se S
a(1
.48
s)(g
)
Ad
just
ed
Co
lla
pse
Ma
rgin
Ra
tio
*P
(Co
lla
pse
|M
CE
)
Imp
rov
em
en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
3012100 1 0.28 2.85 0.05 0.28 2.80 0.06 0.21 2.07 0.13
3012200 0.75 0.28 2.85 0.05 0.28 2.80 0.06 0.20 2.03 0.14
3012300 0.5 0.28 2.85 0.05 0.28 2.80 0.06 0.20 2.03 0.14
3012400 0.25 0.28 2.85 0.05 0.28 2.80 0.06 0.20 2.03 0.14
3012110 1 0.29 2.94 0.05 3% 0.29 2.88 0.05 3% 0.21 2.10 0.13 2%
3012210 0.75 0.30 2.97 0.05 4% 0.29 2.94 0.05 5% 0.21 2.16 0.12 6%
3012310 0.5 0.31 3.08 0.04 8% 0.30 3.00 0.05 7% 0.22 2.17 0.12 7%
3012410 0.25 0.32 3.16 0.04 11% 0.31 3.12 0.04 11% 0.21 2.15 0.12 6%
3012100 1 0.28 2.85 0.05 0.28 2.80 0.06 0.20 2.03 0.14
3012200 0.75 0.28 2.85 0.05 0.28 2.80 0.06 0.20 2.03 0.14
3012300 0.5 0.28 2.85 0.05 0.28 2.80 0.06 0.20 2.03 0.14
3012500 0.45 0.28 2.85 0.05 0.28 2.80 0.06 0.16 1.58 0.24
3012600 0.4 0.28 2.84 0.05 0.28 2.78 0.06 0.16 1.58 0.24
3012700 0.35 0.28 2.79 0.06 0.27 2.73 0.06 0.16 1.56 0.25
3012800 0.3 0.26 2.65 0.07 0.25 2.46 0.08 0.15 1.54 0.25
3012400 0.25 0.23 2.33 0.10 0.22 2.20 0.11 0.18 1.84 0.18
3012110 1 0.29 2.93 0.05 3% 0.29 2.88 0.05 3% 0.21 2.13 0.12 5%
3012210 0.75 0.29 2.96 0.05 4% 0.29 2.94 0.05 5% 0.21 2.16 0.12 6%
3012310 0.5 0.31 3.07 0.04 8% 0.30 3.00 0.05 7% 0.22 2.16 0.12 6%
3012510 0.45 0.31 3.07 0.04 8% 0.30 3.01 0.05 7% 0.15 1.55 0.25 -2%
3012610 0.4 0.30 3.04 0.04 7% 0.30 2.98 0.05 7% 0.16 1.62 0.23 3%
3012710 0.35 0.30 3.06 0.04 10% 0.29 2.90 0.05 6% 0.16 1.64 0.22 5%
3012810 0.3 0.29 2.95 0.05 12% 0.28 2.81 0.06 14% 0.16 1.64 0.22 6%
3012410 0.25 0.27 2.71 0.06 16% 0.26 2.60 0.07 18% 0.22 2.17 0.12 18%
3012101 1 0.25 2.47 0.08 0.24 2.45 0.08 0.16 1.63 0.23
3012201 0.75 0.25 2.56 0.07 0.25 2.53 0.08 0.15 1.52 0.26
3012301 0.5 0.28 2.77 0.06 0.27 2.70 0.06 0.14 1.43 0.29
3012501 0.45 0.27 2.73 0.06 0.27 2.69 0.06 0.16 1.59 0.24
3012601 0.4 0.27 2.75 0.06 0.26 2.63 0.07 0.15 1.54 0.25
3012701 0.35 0.26 2.66 0.07 0.25 2.55 0.07 0.15 1.46 0.28
3012801 0.3 0.25 2.50 0.08 0.21 2.16 0.12 0.15 1.47 0.28
3012401 0.25 0.21 2.10 0.13 0.17 1.70 0.21 0.12 1.25 0.37
3012111 1 0.26 2.63 0.07 7% 0.26 2.58 0.07 5% 0.17 1.67 0.22 2%
3012211 0.75 0.27 2.72 0.06 6% 0.27 2.68 0.06 6% 0.16 1.60 0.23 6%
3012311 0.5 0.30 2.98 0.05 8% 0.28 2.84 0.05 5% 0.14 1.43 0.29 0%
3012511 0.45 0.30 3.04 0.04 12% 0.29 2.87 0.05 7% 0.14 1.43 0.29 -10%
3012611 0.4 0.30 3.00 0.05 9% 0.28 2.83 0.05 7% 0.17 1.66 0.22 8%
3012711 0.35 0.30 2.99 0.05 13% 0.26 2.60 0.07 2% 0.16 1.60 0.24 9%
3012811 0.3 0.28 2.81 0.06 12% 0.24 2.45 0.08 14% 0.16 1.57 0.24 7%
3012411 0.25 0.25 2.50 0.08 19% 0.20 1.99 0.15 17% 0.14 1.39 0.31 11%
3012102 1 0.24 2.42 0.09 0.24 2.40 0.09 0.15 1.47 0.28
3012202 0.75 0.26 2.65 0.07 0.25 2.56 0.07 0.14 1.42 0.29
3012302 0.5 0.27 2.76 0.06 0.26 2.62 0.07 0.13 1.26 0.36
3012402 0.25 0.20 2.01 0.14 0.15 1.52 0.26 0.11 1.05 0.47
3012112 1 0.25 2.55 0.07 5% 0.25 2.47 0.08 3% 0.14 1.46 0.28 -1%
3012212 0.75 0.28 2.78 0.06 5% 0.26 2.63 0.07 3% 0.15 1.52 0.26 6%
3012312 0.5 0.29 2.87 0.05 4% 0.27 2.71 0.06 3% 0.12 1.23 0.38 -2%
3012412 0.25 0.23 2.34 0.10 16% 0.18 1.76 0.19 16% 0.11 1.14 0.42 8%
Na
tura
l E
cce
ntr
icit
y (
Off
set
of
CM
)
ID
Sto
rie
s
Gra
vit
y
Re
lati
ve
Fra
me
Sp
aci
ng
(S
/L)
De
sig
n f
or
Acc
ide
nta
l T
ors
ion
No
no
nsi
mu
late
d
Co
lla
pse
Mo
de
s
No
nsi
mu
late
d
Co
lla
pse
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
6%
No
nsi
mu
late
d
Co
lla
pse
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
3.5
%
1 160 psf
No
0
Yes
No
**0
Yes
No
5%
Yes
No
10%
Yes
Table ETable ETable ETable E----9999 Collapse Results for the 1Collapse Results for the 1Collapse Results for the 1Collapse Results for the 1----Story, High Gravity, Story, High Gravity, Story, High Gravity, Story, High Gravity,
Symmetric ArchetypesSymmetric ArchetypesSymmetric ArchetypesSymmetric Archetypes
41.86% Draft
E-52 E: Accidental Torsion Studies BSSC SDC B
Me
dia
n C
oll
ap
se S
a(1
.3s)
(g)
Ad
just
ed
Co
lla
pse
Ma
rgin
Ra
tio
*P
(Co
lla
pse
|M
CE
)
Imp
rov
em
en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
Me
dia
n C
oll
ap
se S
a(1
.3s)
(g)
Ad
just
ed
Co
lla
pse
Ma
rgin
Ra
tio
*P
(Co
lla
pse
|M
CE
)
Imp
rov
em
en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
Me
dia
n C
oll
ap
se S
a(1
.3s)
(g)
Ad
just
ed
Co
lla
pse
Ma
rgin
Ra
tio
*P
(Co
lla
pse
|M
CE
)
Imp
rov
em
en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
4012300 0.5 0.28 2.83 0.05 0.28 2.78 0.06 0.16 1.58 0.24
4012500 0.45 0.28 2.79 0.06 0.27 2.75 0.06 0.16 1.58 0.24
4012600 0.4 0.27 2.73 0.06 0.27 2.68 0.06 0.16 1.56 0.25
4012700 0.35 0.26 2.59 0.07 0.24 2.45 0.08 0.15 1.52 0.26
4012800 0.3 0.24 2.42 0.09 0.23 2.31 0.10 0.15 1.53 0.26
4012400 0.25 0.20 2.03 0.14 0.18 1.85 0.17 0.15 1.47 0.28
4012310 0.5 0.30 2.99 0.05 6% 0.29 2.96 0.05 6% 0.16 1.61 0.23 2%
4012510 0.45 0.30 3.01 0.05 8% 0.29 2.91 0.05 6% 0.16 1.62 0.23 3%
4012610 0.4 0.30 2.98 0.05 9% 0.29 2.93 0.05 9% 0.16 1.63 0.23 4%
4012710 0.35 0.29 2.92 0.05 13% 0.28 2.80 0.06 14% 0.16 1.65 0.22 8%
4012810 0.3 0.28 2.80 0.06 16% 0.27 2.67 0.07 16% 0.17 1.67 0.21 10%
4012410 0.25 0.26 2.57 0.07 27% 0.23 2.29 0.10 24% 0.16 1.56 0.25 6%
4012301 0.5 0.28 2.76 0.06 0.26 2.62 0.07 0.11 1.08 0.46
4012501 0.45 0.27 2.71 0.06 0.25 2.55 0.08 0.11 1.08 0.45
4012601 0.4 0.26 2.60 0.07 0.24 2.40 0.09 0.11 1.11 0.44
4012701 0.35 0.25 2.48 0.08 0.22 2.22 0.11 0.11 1.12 0.43
4012801 0.3 0.22 2.17 0.12 0.19 1.95 0.15 0.11 1.10 0.44
4012401 0.25 0.17 1.72 0.20 0.15 1.52 0.26 0.11 1.11 0.44
4012311 0.5 0.30 2.98 0.05 8% 0.28 2.85 0.05 9% 0.11 1.11 0.43 3%
4012511 0.45 0.29 2.94 0.05 9% 0.26 2.65 0.07 4% 0.12 1.17 0.40 8%
4012611 0.4 0.28 2.85 0.05 10% 0.26 2.59 0.07 8% 0.12 1.22 0.38 10%
4012711 0.35 0.27 2.75 0.06 11% 0.25 2.55 0.07 15% 0.12 1.19 0.40 6%
4012811 0.3 0.26 2.58 0.07 19% 0.22 2.18 0.11 12% 0.12 1.16 0.41 5%
4012411 0.25 0.23 2.31 0.10 34% 0.18 1.83 0.18 21% 0.12 1.18 0.40 7%
ID
Sto
rie
s
Gra
vit
y
Re
lati
ve
Fra
me
Sp
aci
ng
(S
/L)
1 160 psf
No
**None
yes
No
5%
Yes
De
sig
n f
or
Acc
ide
nta
l T
ors
ion
Na
tura
l E
cce
ntr
icit
y (
Off
set
of
CM
)
No
no
nsi
mu
late
d
Co
lla
pse
Mo
de
s
No
nsi
mu
late
d
Co
lla
pse
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
6%
No
nsi
mu
late
d
Co
lla
pse
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
3%
Table ETable ETable ETable E----10101010 Collapse Results for the 1Collapse Results for the 1Collapse Results for the 1Collapse Results for the 1----Story, High Gravity, ‘IStory, High Gravity, ‘IStory, High Gravity, ‘IStory, High Gravity, ‘I----
ShapShapShapShaped’ Archetypesed’ Archetypesed’ Archetypesed’ Archetypes
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-53
Me
dia
n C
oll
ap
se S
a(1
.3s)
(g)
Ad
just
ed
Co
lla
pse
Ma
rgin
Ra
tio
*P
(Co
lla
pse
|M
CE
)
Imp
rov
em
en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
Me
dia
n C
oll
ap
se S
a(1
.3s)
(g)
Ad
just
ed
Co
lla
pse
Ma
rgin
Ra
tio
*P
(Co
lla
pse
|M
CE
)
Imp
rov
em
en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
Me
dia
n C
oll
ap
se S
a(1
.3s)
(g)
Ad
just
ed
Co
lla
pse
Ma
rgin
Ra
tio
*P
(Co
lla
pse
|M
CE
)
Imp
rov
em
en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
5012300 0.5 0.22 2.25 0.11 0.22 2.18 0.12 0.11 1.06 0.46
5012400 0.25 0.16 1.64 0.22 0.15 1.51 0.26 0.10 0.98 0.51
5012310 0.5 0.24 2.41 0.09 7% 0.23 2.32 0.10 6% 0.11 1.11 0.44 5%
5012410 0.25 0.20 1.96 0.15 19% 0.17 1.68 0.21 11% 0.11 1.14 0.42 16%
5012301 0.5 0.21 2.13 0.12 0.20 2.01 0.14 0.10 1.02 0.49
5012401 0.25 0.16 1.56 0.25 0.14 1.42 0.30 0.09 0.85 0.60
5012311 0.5 0.21 2.12 0.12 0% 0.19 1.94 0.15 -3% 0.11 1.14 0.42 12%
5012411 0.25 0.18 1.85 0.17 19% 0.16 1.64 0.22 16% 0.09 0.94 0.54 10%
5012302 0.5 0.20 2.02 0.14 0.19 1.88 0.17 0.11 1.06 0.46
5012402 0.25 0.14 1.43 0.29 0.13 1.27 0.36 0.07 0.74 0.68
5012312 0.5 0.22 2.21 0.11 9% 0.21 2.13 0.12 13% 0.11 1.07 0.46 1%
5012412 0.25 0.18 1.83 0.18 28% 0.15 1.52 0.26 20% 0.09 0.89 0.57 20%
5012303 0.5 0.25 2.50 0.08 0.23 2.29 0.10 0.11 1.07 0.46
5012403 0.25 0.18 1.85 0.17 0.17 1.68 0.21 0.12 1.23 0.37
5012313 0.5 0.26 2.63 0.07 5% 0.25 2.46 0.08 7% 0.11 1.11 0.44 3%
5012413 0.25 0.21 2.11 0.13 14% 0.19 1.87 0.17 11% 0.12 1.25 0.36 2%
5012304 0.5 0.27 2.72 0.06 0.25 2.54 0.08 0.12 1.19 0.39
5012404 0.25 0.19 1.93 0.16 0.17 1.69 0.21 0.11 1.08 0.45
5012314 0.5 0.28 2.83 0.05 4% 0.25 2.53 0.08 0% 0.12 1.24 0.37 4%
5012414 0.25 0.22 2.25 0.11 17% 0.18 1.77 0.19 5% 0.12 1.19 0.40 10%
ID
Sto
rie
s
Gra
vit
y
Re
lati
ve
Fra
me
Sp
aci
ng
(S
/L)
De
sig
n f
or
Acc
ide
nta
l T
ors
ion
No
no
nsi
mu
late
d
Co
lla
pse
Mo
de
s
No
nsi
mu
late
d
Co
lla
pse
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
6%
No
nsi
mu
late
d
Co
lla
pse
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
3%
No
None
yes
Na
tura
l E
cce
ntr
icit
y (
Off
set
of
CM
)
No
-10%
yes
160 psf1
Yes
No
+10%
yes
No
-5%
Yes
No
+5%
Table ETable ETable ETable E----11111111 Collapse Results for the 1Collapse Results for the 1Collapse Results for the 1Collapse Results for the 1----Story, High Gravity, Story, High Gravity, Story, High Gravity, Story, High Gravity,
Archetypes with Inherent TorsionArchetypes with Inherent TorsionArchetypes with Inherent TorsionArchetypes with Inherent Torsion
41.86% Draft
E-54 E: Accidental Torsion Studies BSSC SDC B
Me
dia
n C
oll
ap
se S
a(2
.19
s)(g
)
Ad
just
ed
Co
lla
pse
Ma
rgin
Ra
tio
*P
(Co
lla
pse
|M
CE
)
Imp
rov
em
en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
Me
dia
n C
oll
ap
se S
a(2
.19
s)(g
)
Ad
just
ed
Co
lla
pse
Ma
rgin
Ra
tio
*P
(Co
lla
pse
|M
CE
)
Imp
rov
em
en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
Me
dia
n C
oll
ap
se S
a(2
.19
s)(g
)
Ad
just
ed
Co
lla
pse
Ma
rgin
Ra
tio
*P
(Co
lla
pse
|M
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)
Imp
rov
em
en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
Me
dia
n C
oll
ap
se S
a(2
.19
s)(g
)
Ad
just
ed
Co
lla
pse
Ma
rgin
Ra
tio
*P
(Co
lla
pse
|M
CE
)
Imp
rov
em
en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
Me
dia
n C
oll
ap
se S
a(2
.19
s)(g
)
Ad
just
ed
Co
lla
pse
Ma
rgin
Ra
tio
*P
(Co
lla
pse
|M
CE
)
Imp
rov
em
en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
3041100 1 0.20 3.24 0.04 0.18 2.82 0.06 0.20 3.09 0.04 0.20 3.24 0.04 0.12 1.91 0.16
3041200 0.75 0.20 3.24 0.04 0.18 2.82 0.06 0.20 3.09 0.04 0.20 3.24 0.04 0.12 1.91 0.16
3041300 0.5 0.20 3.24 0.04 0.18 2.82 0.06 0.20 3.09 0.04 0.20 3.24 0.04 0.12 1.91 0.16
3041400 0.25 0.16 2.59 0.07 0.14 2.25 0.11 0.15 2.41 0.09 0.15 2.43 0.09 0.11 1.69 0.21
3041110 1 0.21 3.30 0.03 2% 0.18 2.87 0.05 2% 0.21 3.25 0.03 5% 0.21 3.30 0.03 2% 0.12 1.97 0.15 3%
3041210 0.75 0.21 3.30 0.03 2% 0.18 2.89 0.05 3% 0.21 3.26 0.03 5% 0.21 3.27 0.03 1% 0.12 1.98 0.15 3%
3041310 0.5 0.21 3.36 0.03 4% 0.18 2.93 0.05 4% 0.21 3.27 0.03 6% 0.21 3.28 0.03 1% 0.13 1.99 0.14 4%
3041410 0.25 0.18 2.82 0.06 9% 0.15 2.41 0.09 7% 0.16 2.52 0.08 4% 0.16 2.56 0.07 5% 0.11 1.77 0.19 5%
3041101 1 0.20 3.17 0.04 0.17 2.71 0.06 0.19 3.04 0.04 0.20 3.12 0.04 0.11 1.76 0.19
3041201 0.75 0.20 3.14 0.04 0.17 2.65 0.07 0.19 2.98 0.05 0.20 3.09 0.04 0.11 1.72 0.20
3041301 0.5 0.20 3.21 0.04 0.17 2.72 0.06 0.20 3.10 0.04 0.20 3.12 0.04 0.11 1.70 0.21
3041401 0.25 0.13 2.13 0.12 0.10 1.62 0.23 0.11 1.82 0.18 0.11 1.77 0.19 0.08 1.28 0.35
3041111 1 0.20 3.16 0.04 0% 0.17 2.66 0.07 -2% 0.19 3.05 0.04 1% 0.19 3.04 0.04 -3% 0.11 1.80 0.18 2%
3041211 0.75 0.20 3.22 0.04 2% 0.17 2.68 0.06 1% 0.20 3.12 0.04 5% 0.20 3.09 0.04 0% 0.11 1.76 0.19 2%
3041311 0.5 0.21 3.34 0.03 4% 0.18 2.77 0.06 2% 0.20 3.18 0.04 3% 0.21 3.30 0.03 6% 0.11 1.70 0.21 0%
3041411 0.25 0.16 2.47 0.08 16% 0.12 1.83 0.18 12% 0.12 1.96 0.15 8% 0.12 1.85 0.17 4% 0.08 1.30 0.34 2%
3041102 1 0.20 3.15 0.04 0.16 2.60 0.07 0.19 3.00 0.05 0.20 3.09 0.04 0.11 1.71 0.20
3041202 0.75 0.20 3.18 0.04 0.16 2.54 0.08 0.19 2.96 0.05 0.19 3.00 0.05 0.10 1.54 0.25
3041302 0.5 0.20 3.20 0.04 0.16 2.52 0.08 0.19 2.99 0.05 0.19 3.05 0.04 0.10 1.52 0.26
3041402 0.25 0.13 2.03 0.14 0.09 1.40 0.30 0.11 1.75 0.20 0.11 1.68 0.21 0.07 1.09 0.45
3041112 1 0.20 3.19 0.04 2% 0.16 2.56 0.07 -1% 0.19 3.02 0.04 1% 0.20 3.09 0.04 0% 0.11 1.70 0.21 -1%
3041212 0.75 0.20 3.19 0.04 0% 0.16 2.58 0.07 1% 0.19 3.04 0.04 3% 0.20 3.15 0.04 5% 0.10 1.59 0.24 3%
3041312 0.5 0.21 3.28 0.03 3% 0.16 2.55 0.07 1% 0.19 3.08 0.04 3% 0.19 3.04 0.04 0% 0.09 1.44 0.29 -5%
3041412 0.25 0.15 2.39 0.09 18% 0.10 1.63 0.23 17% 0.12 1.97 0.15 13% 0.11 1.81 0.18 7% 0.07 1.10 0.44 1%
4 100 psf
No
**0
No
10%
Yes
No
no
nsi
mu
late
d C
oll
ap
se
Mo
de
s
No
nsi
mu
late
d C
oll
ap
se
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
LVC
C (
LVC
C
dri
fts
com
pu
ted
usi
ng
inte
rio
r co
lum
n a
xia
l lo
ad
s)
No
nsi
mu
late
d C
oll
ap
se
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
3%
Yes
No
5%
Yes
No
nsi
mu
late
d C
oll
ap
se
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
6%
No
nsi
mu
late
d C
oll
ap
se
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
LVC
C (
LVC
C
dri
fts
com
pu
ted
usi
ng
ex
teri
or
colu
mn
ax
ial
loa
ds)
Na
tura
l E
cce
ntr
icit
y (
Off
set
of
CM
)
ID
Sto
rie
s
Gra
vit
y
Re
lati
ve
Fra
me
Sp
aci
ng
(S
/L)
De
sig
n f
or
Acc
ide
nta
l T
ors
ion
Table ETable ETable ETable E----12121212 Collapse Results for the 4Collapse Results for the 4Collapse Results for the 4Collapse Results for the 4----Story, Low Gravity, Story, Low Gravity, Story, Low Gravity, Story, Low Gravity,
Symmetric ArchetypesSymmetric ArchetypesSymmetric ArchetypesSymmetric Archetypes
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-55
Me
dia
n C
oll
ap
se S
a(2
.19
s)(g
)
Ad
just
ed
Co
lla
pse
Ma
rgin
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(Co
lla
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Imp
rov
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t o
f A
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sig
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Acc
ide
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ion
Me
dia
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.19
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Acc
ide
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Me
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Acc
ide
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Me
dia
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Ad
just
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(Co
lla
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Imp
rov
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en
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f A
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De
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Acc
ide
nta
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Me
dia
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Ad
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Ma
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(Co
lla
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Imp
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em
en
t o
f A
CM
R f
rom
De
sig
nin
g f
or
Acc
ide
nta
l T
ors
ion
3042100 1 0.17 2.70 0.06 0.14 2.13 0.12 0.16 2.48 0.08 0.17 2.70 0.06 0.12 1.83 0.18
3042200 0.75 0.17 2.70 0.06 0.14 2.13 0.12 0.16 2.50 0.08 0.17 2.70 0.06 0.12 1.83 0.18
3042300 0.5 0.17 2.70 0.06 0.14 2.13 0.12 0.16 2.50 0.08 0.17 2.70 0.06 0.12 1.83 0.18
3042400 0.25 0.15 2.39 0.09 0.13 1.98 0.15 0.14 2.17 0.12 0.14 2.23 0.11 0.11 1.68 0.21
3042110 1 0.18 2.78 0.06 3% 0.14 2.23 0.11 5% 0.16 2.57 0.07 3% 0.18 2.78 0.06 3% 0.12 1.84 0.17 1%
3042210 0.75 0.18 2.84 0.05 5% 0.14 2.24 0.11 5% 0.17 2.63 0.07 5% 0.18 2.81 0.06 4% 0.12 1.83 0.18 0%
3042310 0.5 0.18 2.80 0.06 4% 0.14 2.20 0.11 3% 0.16 2.58 0.07 3% 0.18 2.75 0.06 2% 0.12 1.83 0.18 0%
3042410 0.25 0.17 2.67 0.07 12% 0.14 2.12 0.12 7% 0.15 2.33 0.10 7% 0.15 2.42 0.09 8% 0.11 1.78 0.19 6%
3042101 1 0.16 2.56 0.07 0.12 1.82 0.18 0.15 2.30 0.10 0.15 2.42 0.09 0.10 1.51 0.26
3042201 0.75 0.17 2.63 0.07 0.11 1.76 0.19 0.14 2.26 0.10 0.15 2.43 0.09 0.09 1.37 0.31
3042301 0.5 0.17 2.67 0.07 0.11 1.80 0.18 0.15 2.36 0.09 0.16 2.52 0.08 0.10 1.59 0.24
3042401 0.25 0.13 2.10 0.13 0.09 1.34 0.32 0.10 1.63 0.23 0.11 1.74 0.20 0.08 1.23 0.38
3042111 1 0.16 2.57 0.07 0% 0.12 1.88 0.16 4% 0.15 2.28 0.10 -1% 0.15 2.39 0.09 -1% 0.10 1.58 0.24 4%
3042211 0.75 0.17 2.71 0.06 3% 0.11 1.78 0.19 1% 0.14 2.26 0.10 0% 0.16 2.56 0.07 5% 0.09 1.42 0.29 4%
3042311 0.5 0.18 2.81 0.06 5% 0.12 1.82 0.18 1% 0.15 2.35 0.09 0% 0.16 2.50 0.08 -1% 0.09 1.49 0.27 -7%
3042411 0.25 0.15 2.38 0.09 14% 0.10 1.51 0.26 13% 0.12 1.92 0.16 18% 0.13 2.05 0.13 18% 0.08 1.29 0.35 5%
3042102 1 0.16 2.53 0.08 0.11 1.76 0.19 0.14 2.27 0.10 0.15 2.34 0.10 0.09 1.49 0.27
3042202 0.75 0.16 2.50 0.08 0.10 1.58 0.24 0.14 2.20 0.11 0.14 2.24 0.11 0.09 1.38 0.31
3042302 0.5 0.16 2.54 0.08 0.10 1.54 0.25 0.14 2.18 0.11 0.15 2.29 0.10 0.08 1.23 0.38
3042402 0.25 0.13 1.98 0.15 0.07 1.09 0.45 0.10 1.50 0.27 0.10 1.61 0.23 0.06 0.97 0.52
3042112 1 0.16 2.58 0.07 2% 0.11 1.77 0.19 0% 0.15 2.28 0.10 0% 0.15 2.32 0.10 -1% 0.10 1.55 0.25 4%
3042212 0.75 0.17 2.68 0.06 7% 0.11 1.67 0.21 6% 0.15 2.36 0.09 7% 0.15 2.43 0.09 8% 0.09 1.40 0.30 2%
3042312 0.5 0.17 2.64 0.07 4% 0.10 1.51 0.26 -2% 0.14 2.23 0.11 2% 0.15 2.33 0.10 2% 0.08 1.20 0.39 -3%
3042412 0.25 0.15 2.35 0.09 18% 0.07 1.11 0.44 2% 0.10 1.62 0.23 8% 0.12 1.86 0.17 15% 0.07 1.03 0.48 6%
4 200 psf
No
**0
Yes
No
5%
Yes
No
10%N
on
sim
ula
ted
Co
lla
pse
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
3%
Yes
No
no
nsi
mu
late
d C
oll
ap
se
Mo
de
s
No
nsi
mu
late
d C
oll
ap
se
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
LVC
C (
LVC
C
dri
fts
com
pu
ted
usi
ng
ex
teri
or
colu
mn
ax
ial
loa
ds)
No
nsi
mu
late
d C
oll
ap
se
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
6%
No
nsi
mu
late
d C
oll
ap
se
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
LVC
C (
LVC
C
dri
fts
com
pu
ted
usi
ng
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rio
r co
lum
n a
xia
l
loa
ds)
Na
tura
l E
cce
ntr
icit
y (
Off
set
of
CM
)
ID
Sto
rie
s
Gra
vit
y
Re
lati
ve
Fra
me
Sp
aci
ng
(S
/L)
De
sig
n f
or
Acc
ide
nta
l T
ors
ion
Table ETable ETable ETable E----13131313 Collapse Results for the 4Collapse Results for the 4Collapse Results for the 4Collapse Results for the 4----Story, High Gravity, Story, High Gravity, Story, High Gravity, Story, High Gravity,
Symmetric ArchetypesSymmetric ArchetypesSymmetric ArchetypesSymmetric Archetypes
41.86% Draft
E-56 E: Accidental Torsion Studies BSSC SDC B
Me
dia
n C
oll
ap
se S
a(4
.16
s)(g
)
Ad
just
ed
Co
lla
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Ma
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Imp
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Acc
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Me
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Me
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Me
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Acc
ide
nta
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ors
ion
3102100 1 0.07 2.18 0.11 0.06 1.98 0.15 0.07 2.17 0.12 0.05 1.48 0.27
3102200 0.75 0.07 2.17 0.12 0.06 1.93 0.16 0.07 2.17 0.12 0.05 1.48 0.27
3102300 0.5 0.07 2.17 0.12 0.06 1.94 0.15 0.07 2.17 0.12 0.05 1.48 0.27
3102400 0.25 0.04 1.38 0.31 0.04 1.15 0.42 0.04 1.22 0.38 0.03 1.02 0.49
3102110 1 0.07 2.23 0.11 2% 0.06 1.91 0.16 -3% 0.07 2.18 0.11 1% 0.05 1.42 0.29 -3%
3102210 0.75 0.07 2.22 0.11 2% 0.06 1.90 0.16 -2% 0.07 2.17 0.12 0% 0.04 1.38 0.31 -6%
3102310 0.5 0.07 2.29 0.10 6% 0.06 1.94 0.15 0% 0.07 2.20 0.11 2% 0.04 1.38 0.31 -7%
3102410 0.25 0.05 1.47 0.28 6% 0.04 1.26 0.36 10% 0.04 1.35 0.32 11% 0.04 1.11 0.43 9%
3102101 1 0.07 2.02 0.14 0.05 1.46 0.28 0.06 1.91 0.16 0.04 1.11 0.43
3102201 0.75 0.07 2.21 0.11 0.05 1.52 0.26 0.07 2.01 0.14 0.03 0.96 0.53
3102301 0.5 0.07 2.20 0.11 0.04 1.35 0.32 0.07 2.02 0.14 0.03 1.00 0.50
3102401 0.25 0.04 1.17 0.41 0.03 0.93 0.54 0.03 1.03 0.48 0.03 0.83 0.61
3102111 1 0.07 2.09 0.13 3% 0.05 1.46 0.28 0% 0.06 1.95 0.15 2% 0.04 1.10 0.44 -1%
3102211 0.75 0.07 2.27 0.10 3% 0.05 1.45 0.29 -5% 0.06 1.96 0.15 -3% 0.03 1.02 0.49 6%
3102311 0.5 0.07 2.21 0.11 1% 0.04 1.31 0.34 -3% 0.07 2.04 0.14 1% 0.03 0.93 0.55 -7%
3102411 0.25 0.04 1.33 0.33 14% 0.03 0.94 0.54 1% 0.04 1.15 0.42 11% 0.03 0.86 0.59 4%
3102102 1 0.07 2.04 0.14 0.05 1.40 0.30 0.06 1.89 0.16 0.03 1.06 0.47
3102202 0.75 0.07 2.24 0.11 0.04 1.38 0.31 0.06 2.00 0.14 0.03 1.01 0.49
3102302 0.5 0.07 2.18 0.12 0.03 0.97 0.52 0.06 1.75 0.19 0.03 0.82 0.62
3102402 0.25 0.04 1.15 0.41 0.02 0.72 0.69 0.03 0.99 0.50 0.02 0.70 0.71
3102112 1 0.07 2.05 0.13 1% 0.04 1.38 0.31 -1% 0.06 1.91 0.16 1% 0.04 1.08 0.45 2%
3102212 0.75 0.07 2.24 0.11 0% 0.05 1.40 0.30 1% 0.06 1.97 0.15 -2% 0.03 1.02 0.49 1%
3102312 0.5 0.07 2.28 0.10 5% 0.03 0.94 0.54 -3% 0.06 1.85 0.17 6% 0.03 0.84 0.60 2%
3102412 0.25 0.04 1.24 0.37 8% 0.02 0.68 0.72 -6% 0.03 1.04 0.48 5% 0.02 0.72 0.69 3%
10 200 psf
No
nsi
mu
late
d C
oll
ap
se
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
3%
Yes
No
no
nsi
mu
late
d
Co
lla
pse
Mo
de
s
No
nsi
mu
late
d C
oll
ap
se
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
6%
No
nsi
mu
late
d C
oll
ap
se
Occ
urs
if
IDR
at
Bu
ild
ing
Ed
ge
Ex
cee
ds
LVC
C
(LV
CC
dri
fts
com
pu
ted
usi
ng
in
teri
or
colu
mn
ax
ial
loa
ds)
No
**0
Yes
No
Na
tura
l E
cce
ntr
icit
y (
Off
set
of
CM
)
5%
Yes
No
10%
ID
Sto
rie
s
Gra
vit
y
Re
lati
ve
Fra
me
Sp
aci
ng
(S
/L)
De
sig
n f
or
Acc
ide
nta
l T
ors
ion
Table ETable ETable ETable E----14141414 Collapse Results for the 10Collapse Results for the 10Collapse Results for the 10Collapse Results for the 10----Story, High Gravity, Story, High Gravity, Story, High Gravity, Story, High Gravity,
Symmetric ArchetypesSymmetric ArchetypesSymmetric ArchetypesSymmetric Archetypes
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-57
Table ETable ETable ETable E----15151515 Modal Periods of the 1Modal Periods of the 1Modal Periods of the 1Modal Periods of the 1----Story, Low Gravity, Symmetric Story, Low Gravity, Symmetric Story, Low Gravity, Symmetric Story, Low Gravity, Symmetric
Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not
Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)
Mode
S/L = 1 S/L = 0.75 S/L = 0.5 S/L = 0.25
Period
(s)
Torsional
or
Lateral
Period
(s)
Torsional
or
Lateral
Period
(s)
Torsional
or
Lateral
Period
(s)
Torsional
or
Lateral
1 1.40 lat 1.40 lat 1.62 tors 3.98 tors
2 1.40 lat 1.40 lat 1.40 lat 1.40 lat
3 0.78 tors 1.05 tors 1.40 lat 1.40 lat
Table ETable ETable ETable E----16161616 Modal Periods of the 1Modal Periods of the 1Modal Periods of the 1Modal Periods of the 1----Story, High Gravity, Symmetric Story, High Gravity, Symmetric Story, High Gravity, Symmetric Story, High Gravity, Symmetric
Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not
Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)
Mod
e
S/L = 1 S/L = 0.75 S/L = 0.5 S/L = 0.25
Perio
d (s)
Torsion
al or
Lateral
Perio
d (s)
Torsion
al or
Lateral
Perio
d (s)
Torsion
al or
Lateral
Perio
d (s)
Torsion
al or
Lateral
1 1.52 lat 1.52 lat 1.76 tors 4.49 tors
2 1.52 lat 1.52 lat 1.52 lat 1.52 lat
3 0.84 tors 1.13 tors 1.52 lat 1.52 lat
Table ETable ETable ETable E----17171717 Modal Periods of the 1Modal Periods of the 1Modal Periods of the 1Modal Periods of the 1----Story, High Gravity, Story, High Gravity, Story, High Gravity, Story, High Gravity, ‘I‘I‘I‘I----Shaped’Shaped’Shaped’Shaped’
Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not
Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)
Mode
S/L = 0.5 S/L = 0.45 S/L = 0.4
Period
(s)
Torsional
or
Lateral
Period
(s)
Torsional
or
Lateral
Period
(s)
Torsional
or
Lateral
1 2.00 tors 2.26 tors 2.62 tors
2 1.52 lat 1.52 lat 1.52 lat
3 1.52 lat 1.52 lat 1.52 lat
Mode S/L = 0.35 S/L = 0.3 S/L = 0.25
1 3.14 tors 3.97 tors 5.65 tors
2 1.52 lat 1.52 lat 1.52 lat
3 1.52 lat 1.52 lat 1.52 lat
41.86% Draft
E-58 E: Accidental Torsion Studies BSSC SDC B
Table ETable ETable ETable E----18181818 Modal Periods of the 1Modal Periods of the 1Modal Periods of the 1Modal Periods of the 1----Story, High Gravity Archetypes Story, High Gravity Archetypes Story, High Gravity Archetypes Story, High Gravity Archetypes
with Inherent Torsion for which Accidental Torsion was with Inherent Torsion for which Accidental Torsion was with Inherent Torsion for which Accidental Torsion was with Inherent Torsion for which Accidental Torsion was
not Considered in Design (Torsional Modes in Grey)not Considered in Design (Torsional Modes in Grey)not Considered in Design (Torsional Modes in Grey)not Considered in Design (Torsional Modes in Grey)
Mode
S/L = 0.5 S/L = 0.25
Period
(s)
Torsional
or
Lateral
Period
(s)
Torsional
or
Lateral
1 2.28 tors 5.94 tors
2 1.42 lat 1.43 lat
3 1.22 lat 1.33 lat
Table ETable ETable ETable E----19191919 Modal Periods of the 4Modal Periods of the 4Modal Periods of the 4Modal Periods of the 4----Story, Low Gravity Symmetric Story, Low Gravity Symmetric Story, Low Gravity Symmetric Story, Low Gravity Symmetric
Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not
Considered in Design Considered in Design Considered in Design Considered in Design (Torsional Modes in Grey)(Torsional Modes in Grey)(Torsional Modes in Grey)(Torsional Modes in Grey)
Mod
e
S/L = 1 S/L = 0.75 S/L = 0.5 S/L = 0.25
Perio
d (s)
Torsion
al or
Lateral
Perio
d (s)
Torsion
al or
Lateral
Perio
d (s)
Torsion
al or
Lateral
Perio
d (s)
Torsion
al or
Lateral
1 2.34 lat 2.34 lat 2.70 tors 6.99 tors
2 2.34 lat 2.34 lat 2.34 lat 2.34 lat
3 1.29 tors 1.74 tors 2.34 lat 2.34 lat
4 0.80 lat 0.80 lat 0.93 tors 2.14 tors
5 0.80 lat 0.80 lat 0.80 lat 1.25 tors
6 0.49 lat 0.61 tors 0.80 lat 0.89 tors
7 0.49 lat 0.49 lat 0.56 tors 0.80 lat
Table ETable ETable ETable E----20202020 Modal Periods of the 4Modal Periods of the 4Modal Periods of the 4Modal Periods of the 4----Story, High Gravity Symmetric Story, High Gravity Symmetric Story, High Gravity Symmetric Story, High Gravity Symmetric
Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not
Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)
Mod
e
S/L = 1 S/L = 0.75 S/L = 0.5 S/L = 0.25
Perio
d (s)
Torsion
al or
Lateral
Perio
d (s)
Torsion
al or
Lateral
Perio
d (s)
Torsion
al or
Lateral
Perio
d (s)
Torsion
al or
Lateral
1 2.34 lat 2.34 lat 2.70 tors 6.78 tors
2 2.34 lat 2.34 lat 2.34 lat 2.34 lat
3 1.30 tors 1.75 tors 2.34 lat 2.34 lat
4 0.83 lat 0.83 lat 0.96 tors 2.21 tors
5 0.83 lat 0.83 lat 0.83 lat 1.32 tors
6 0.51 lat 0.63 tors 0.83 lat 0.91 tors
7 0.51 lat 0.51 lat 0.59 tors 0.83 lat
50% Draft
BSSC SDC B E: Accidental Torsion Studies E-59
Table ETable ETable ETable E----21212121 Modal Periods of the 10Modal Periods of the 10Modal Periods of the 10Modal Periods of the 10----Story, High Gravity Symmetric Story, High Gravity Symmetric Story, High Gravity Symmetric Story, High Gravity Symmetric
Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not Archetypes for which Accidental Torsion was not
Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)Considered in Design (Torsional Modes in Grey)
Mod
e
S/L = 1 S/L = 0.75 S/L = 0.5 S/L = 0.25
Perio
d (s)
Torsion
al or
Lateral
Perio
d (s)
Torsion
al or
Lateral
Perio
d (s)
Torsion
al or
Lateral
Perio
d (s)
Torsion
al or
Lateral
1 4.28 lat 4.28 lat 4.95 tors 14.6
8 tors
2 4.28 lat 4.28 lat 4.28 lat 5.24 tors
3 2.32 tors 3.14 tors 4.28 lat 4.28 lat
4 1.67 lat 1.67 lat 1.93 tors 4.28 lat
5 1.67 lat 1.67 lat 1.67 lat 2.90 tors
6 0.98 lat 1.23 tors 1.67 lat 1.89 tors
7 0.98 lat 0.98 lat 1.13 tors 1.67 lat
41.86% Draft
E-60 E: Accidental Torsion Studies BSSC SDC B
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