Quantitative Evaluation of Code Provisions for Vertically

2018 SEAOC CONVENTION PROCEEDINGS

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Quantitative Evaluation of Code Provisions for Vertically Irregular Frame Buildings

Katherine Wade, Haselton Baker Risk Group, LLC

D. Jared DeBock, California State University, Chico Haselton Baker Risk Group, LLC

Dustin Cook, Colorado State University, Boulder Curt Haselton, California State University, Chico

Haselton Baker Risk Group, LLC Michael Valley, Magnusson Klemencic Associates

Thomas Sabol, Englekirk Structural Engineers University of California, Los Angeles

Abstract Vertically irregular buildings are addressed in building codes

by imposing design requirements and limitations on buildings

with the intention of maintaining acceptable seismic

performance. However, relatively few studies have

quantitatively evaluated the treatment of vertical irregularities

in design codes. This study assesses the collapse

performance of a variety of vertically irregular buildings as

well as their treatment in building codes and standards

(primarily ASCE/SEI 7-16) using the FEMA P695

Methodology.

The following vertical irregularities are examined in this

study: Soft Story Irregularity, Mass Irregularity, and Weak

Story Irregularity; also explored are thresholds for strong-

column/weak-beam (SCWB) requirements and the effect of

gravity-induced lateral loads on collapse potential. These

irregularities were analyzed in OpenSees using non-linear

building frame models ranging from 3 to 20 stories located in

both high and low seismicity regions.

Preliminary results suggest that the ASCE/SEI 7-16 seismic

design provisions generally provide adequate collapse

resistance for regular and vertically irregular buildings.

However, caution is recommended when “optimizing” a

building design by reducing member sizes to the point that

code requirements are barely met throughout the structure; this

may dangerously reduce collapse resistance. It is a further

early conclusion of this work that prohibition of the Equivalent

Lateral Force (ELF) method for some vertical irregularities,

such as Mass Irregularity, is unnecessary, because the ELF

design procedure generally results in equivalent or better

collapse resistance than the Modal Response Spectrum

Analysis (MRSA) procedure (even when the MRSA base shear

is scaled up to 100% of the ELF value, as required in

ASCE/SEI 7-16).

Introduction

This study investigates the performance of vertically irregular

frame buildings for two purposes:

1. Assess the adequacy of current ASCE/SEI 7-16

(ASCE, 2016) provisions for vertical irregularities in

terms of collapse performance.

2. Consider whether additional provisions should

extend the treatment of vertical irregularities in

ASCE/SEI 7-16.

The irregularities and configurations that are examined

include:

Mass/Weight Irregularity

Soft/Weak Story Irregularity

Strong-Column/Weak-Beam Provisions

Gravity-Induced Lateral Demand Irregularity

This paper is an extension of a previous publication (DeBock

et al., 2018) which provided information on the methods used

in this study and preliminary results. The methods of the study

are replicated in this paper and extended with the final results

and conclusions on the collapse performance of vertically

irregular buildings.

Method

The methods and modeling details of this study originally

presented in (DeBock, et. al., 2018) are presented in this and


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the following sections. The performance of archetype

buildings with vertical irregularities is compared to baseline

archetypes that are not irregular, using collapse resistance as

the metric. Collapse resistance is computed using the FEMA

P695 process (FEMA, 2009). The median spectral

acceleration for which side-sway collapse occurs is computed

by performing incremental dynamic analysis (IDA,

Vamvatsikos & Cornell, 2002) with the FEMA P695 far-field

ground motion set. The median collapse intensity is then

divided by the maximum considered earthquake (MCE)

intensity to compute a collapse margin ratio (CMR) and

adjusted collapse margin ratio (ACMR). FEMA P695 uses

ACMR to compute probability of collapse, given MCE; this

study focuses on changes to the ACMR caused by vertical

irregularities. If a vertical irregularity does not significantly

reduce collapse resistance relative to the baseline (regular)

building, then we conclude that the design procedures used to

account for that irregularity are adequate.

Baseline Archetypes

A set of baseline concrete and steel perimeter moment frame

designs are developed, ranging from three to twenty stories.

The archetypes are designed according to ASCE/SEI 7-16 for

seismic design category (SDC) Dmax and Bmax (i.e. the highest

possible demands for SDC D and SDC B) and referenced

design standards for steel (AISC, 2010a & 2010b) and concrete

(ACI, 2015). The Equivalent Lateral Force procedure (ELF)

and Modal Response Spectrum Analysis (MRSA) from

ASCE/SEI 7-16 Chapter 12 are both used for design. All

frames are designed as Risk Category II structures meeting a

2% design drift limit.

Structural Modeling of the Archetype Buildings

General Modeling Considerations

Nonlinear models of the moment frame archetype buildings

are constructed in OpenSEES (PEER, 2016) using the lumped

plasticity method. The lumped plasticity models consist of

linear elastic beam and column elements, joined by nonlinear

elements where plastic deformations are expected to

concentrate, as depicted in Figure 1. Nonlinear behavior is

simulated with plastic hinges at the ends of beams and columns

and with nonlinear joint panel zone elements.

Gravity loads are applied to the frames and also to a leaning

column. Per FEMA P695, the load combination representing

expected gravity loads, 1.05D + 0.25L, is used to compute the

vertical load effects. Gravity loads directly carried by the

frames are distributed on the beams. The remaining gravity

load, which is carried by the building’s gravity system, is

applied to the leaning P-Delta column. Building mass tributary

to the walls is lumped at the wall nodes. For analysis, an

expected mass of 1.05 times the dead weight is considered.

Steel Moment Frame Modeling

Nonlinear beam and column hinges are modeled with the

Modified Ibarra-Medina-Krawinkler deterioration model with

bilinear hysteretic response (Ibarra & Krawinkler, 2005) in

OpenSEES. Initial backbone properties are calculated with the

equations recommended by (NIST, 2017) and cyclic

deterioration parameters are computed from (Lignos &

Krawinkler, 2010). For calculating the nonlinear properties of

the beams and columns, the actual yield strength of the steel is

assumed to be 10% higher than the nominal yield strength (per

NIST, 2017). Although composite action is not considered for

the design of the frame beams, it is considered in the nonlinear

analysis, because steel moment frames are commonly

connected to a diaphragm. The controlling mechanism for

composite action of the slabs is yielding of the shear studs,

which are assumed be ¾” diameter, 75 ksi steel, placed at 12

inches on center. Panel zones are modeled with the Joint2D

element in OpenSEES with nonlinear behavior idealized as

trilinear without cyclic deterioration, based on Chapter 8 of

(NIST, 2017) and (Gupta & Krawinkler, 1999).

Concrete Moment Frame Modeling

Nonlinear beam and column hinges are idealized with trilinear

backbones having peak-oriented hysteretic response and cyclic

deterioration (Ibarra, Medina, & Krawlinker, 2005). The

backbone and hysteretic properties of the nonlinear beam-

column hinges are computed from empirical relationships

developed by (Haselton, et. al., 2008) based on the design

properties of the beams and columns (i.e. concrete strength,

element dimensions, axial load ratio, and reinforcement

detailing). RC OMF joints are calibrated according to

(Altoontash, 2004) & (Lowes, Mitra, Altoontash, 2004) and

are modeled with the Ibarra material model (Ibarra, Medina, &

Krawlinker, 2005) with pinched cyclic response. Joint

strength and rotation capacity depend on joint size,

confinement, concrete strength, and axial load ratio. RC

special moment frame (SMF) joints are not expected to fail, so

they are modeled with elastic elements.

Results

The performance of archetype buildings is gauged by dividing

their ACMR by the ACMR of the baseline to get collapse

resistance relative to the baseline (regular) building—relative

collapse resistance less than 1.0 corresponds to a reduction in

collapse resistance. In some cases, the performance of

buildings designed with the MRSA method are contrasted with


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Figure 1. Schematic of a lumped plasticity nonlinear frame model (FEMA, 2018).

ELF designed buildings. Baseline and irregular archetypes

designed by the ELF procedure achieve equivalent or higher

collapse resistance than the MRSA designed buildings (even

with ELF and MRSA scaled to the same base shear). This

observation indicates that some limitations on ELF,

particularly the prohibition of ELF for mass irregular

buildings, may be unnecessary.

Weight (Mass) Irregularity

Irregularity

According to ASCE/SEI 7-16 Table 12.3-2, “Weight (mass)

irregularity is defined to exist where the effective mass of any

story is more than 150% of the effective mass of an adjacent

story. A roof that is lighter than the floor below need not be

considered.” Where a mass irregularity exists, ELF design is

prohibited for SDC D and above.

Mass irregularities are examined in both steel and RC SMF

frames between 3 and 20 stories by placing excess mass at

different locations in the building. Only SMF buildings are

tested because limitations on mass irregularities are only

applicable in SDC D and above, and OMF buildings are

unusual in these regions. Buildings designed using MRSA and

ELF are tested. The mass ratios tested relative to the next

adjacent story are between 1.5 and 3.0. Each variant tested

trigger strength and drift checks and, if necessary, are re-

designed.

Results

At first look, it appears that steel buildings are more negatively

affected by mass irregularity than concrete buildings (see

Figure 2 and Figure 3), but this observation is an artifact of the

archetype designs, and is not expected it to be true in general.

The negative trend seen in Figure 3 is caused by the baseline

steel variants having much higher design overstrength than

some of the irregular variants; the static overstrength of mass

irregular steel models decreases by as much as 30% relative to

the baseline; for comparison the mass-irregular concrete

models maintain static overstrengths values within 2% of the

baseline. In the case of the three-story MRSA designed steel

frame variants with mass irregularity at the second story, the

member sizes in the steel buildings did not change when the

mass irregularity are introduced, even though the design base

shear increased substantially (as much as a 60% increase for

mass ratio = 3.0 for the three-story building). Therefore, the

decline in collapse resistance in the steel buildings is attributed

to a reduction in “overdesign;” when the overdesign of each

member remains nearly the same, as in the RC SMF archetypes

shown in Figure 2, no significant declines in collapse

resistance are observed.

Lea

nin

g (

P-Δ

)

colu

mn

Elastic beam/

column

Nonlinear

plastic hinge Nonlinear joint

element


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In some of the RC frame buildings, the performance of the re-

designed mass irregular buildings even improves relative to the

baseline design. In all cases (including where the collapse

performance diminishes with increasing mass ratio), the ELF

designed buildings perform better than the MRSA designed

buildings. This is an interesting finding because mass

irregularity triggers a MRSA design in ASCE/SEI 7-16.

Figure 2. RC SMF V2 mass irregularity (FEMA, 2018).

Figure 3. Steel SMF V2 mass irregularity (FEMA, 2018).

The performance of the ELF and MRSA designed buildings

can be further investigated by examining the design demands

produced by each method. The story shears and overturning

moments using ELF are generally larger than those using

MRSA. Figure 4 and Figure 5 exemplify this finding,

presenting the design forces for an RC frame building with a

mass irregularity at the 3rd story. The MRSA design picks up

the increased force demand at the mass irregular third story,

however overall, the ELF designed building will be equally

strong at the irregular story and stronger than the MRSA

building in the floors above.

Figure 4. Comparison of ELF and MRSA design forces in

a mass irregular building (FEMA, 2018).

Figure 5. Comparison of ELF and MRSA story shear

forces in a mass irregular building (FEMA, 2018).

Conclusion and Recommendations

Based upon the superior collapse performance of ELF

designed buildings relative to MRSA designed buildings, it is

recommended that the prohibition on ELF design for mass

irregular buildings be removed from ASCE/SEI 7-16. It is

interesting to note that mass irregularities are examined in

this study by adjusting the mass ratio at a single story at a

time. A future study examining the effect of increased mass

over multiple stories on collapse may be valuable.

Soft and Weak Story Irregularities

Irregularity

According to ASCE/SEI 7-16 Table 12.3-2, a soft story

irregularity exists where there is “a story in which the lateral

stiffness is less than 70% of that in the story above or less

than 80% of the average stiffness of the three stories above.”

If the story stiffness is less than 60% of the story above or


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less than 70% of the average of the three stories above, then it

has an extreme soft story irregularity.

Weak story irregularity exists where, “the story lateral

strength is less than 80% of that in the story above. The story

lateral strength is the total lateral strength of all seismic-

resisting elements sharing the story shear for the direction

under consideration.” An extreme weak story irregularity

occurs when the strength of a story is less than 65% of the

strength of the story above.

Where soft story irregularities exist, the ELF method is

prohibited (similar to the mass irregularity) for SDC D and

above. Weak story irregularities and extreme soft story

irregularities are prohibited in SDC E and F. Extreme weak

story irregularities are prohibited for SDC D and above, and

limited to 2 stories or 30 feet in SDC B and C.

Soft/weak story irregularities and extreme irregularities are

examined in RC SMF and OMF buildings between 4 and 20

stories tall. All of these buildings are designed using the ELF

procedure.

Soft and weak story irregularities are investigated using RC

SMF and OMF frames for target strength ratios between 0.6

and 0.8, and stiffness ratios between 0.6 and 0.9 relative to the

story above. Soft and weak story irregularities are achieved by

increasing the story height. Weak story irregularities are also

achieved with an alternative approach—increasing the strength

of the story above.

Results

The first method (increased story height) of creating the

irregularity does not produce clear trends in the RC SMF or

OMF collapse performance. As seen in Figure 6 and Figure 7,

the collapse performance does not tend to drop below

approximately 85% of the baseline model performance. In

part, this is because increasing the story height does not always

result in a decrease in story strength, particularly for OMF

variants whose columns are governed by lateral force demands

rather than strong-column-weak-beam ratio requirements.

Similar observations are made when collapse resistance is

plotted against relative stiffness, rather than relative strength.

The second method for achieving a weak story—increasing the

strength of the story directly above the “weak” story—tends to

result in collapse resistance somewhat higher for extreme weak

story ratios than for moderate weak story ratios (see Figure 8

and Figure 9). Haselton, et. al., 2010, showed that a weak story

irregularity caused by strengthening upper stories, similar to

this study, does not reduce collapse performance of RC

moment frames. The reason is a “weak” story irregularity in

code-conforming buildings really means the adjacent story is

strong—so collapse resistance is not compromised.

Figure 6. Soft/Weak story irregular RC SMF (FEMA,

2018).

Figure 7. Soft/Weak story irregular RC OMF (FEMA,

2018).

Figure 8. Weak story irregular RC SMF (FEMA, 2018).


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Figure 9. Weak story irregular RC OMF (FEMA, 2018).

Conclusions and Recommendations

Based upon the acceptable collapse performance of the

soft/weak story archetypes (i.e. their collapse resistance does

not drop substantially below that of the baseline), it is

concluded that weak and soft story irregularities in code

conforming buildings are acceptable. This conclusion is

largely due to the fact that code conforming soft stories must

still meet drift requirements and “weak story” really means

“strong adjacent story.” These results suggest that the

prohibition of extreme weak story irregularities in SDC D and

the height limitation on extreme weak story irregularities in

SDC B and C may be overly conservative. More study would

be required to comment on the prohibition of weak and

extreme soft story irregularities in SDC E and F.

Strong-Column/Weak-Beam (SCWB)

Congifuration

Though strong-column/weak-beam (SCWB) is not a building

irregularity, it is a component of building configuration that

affects the collapse performance of the building. SCWB ratio

is currently addressed in material standards (ACI, 2015 &

AISC, 2010) and not ASCE/SEI 7-16.

The effect of SCWB ratios is examined in both steel and RC

SMF and OMF buildings (RC frames presented in this paper).

SCWB ratios between 0.5 and 2.0, and 0.4 and 1.0 for the SMF

and OMF buildings respectively are examined. “Realistic”

designs are created by setting a minimum SCWB ratio and

allowing the ratio to exceed the minimum where other design

factors control. “Exact” designs are created by exactly

matching the target SCWB ratio at each joint in the building

by allowing other design requirements to be violated.

Results

Overall, the collapse performance improves with increasing

SCWB ratio (see Figures 10-11). This is due to the damage

spreading out over the height of the building as the SCWB ratio

increases. It is also observed that the variants with SCWB

ratios below the material standard baseline (1.2 for RC frames)

tend to perform less favorably.

It is interesting to note that the way in which the SCWB ratio

is achieved affects the collapse performance of the building.

In some cases where the beam sizes are increased to reduce the

SCWB ratio, the collapse performance actually improves.

A further study (not examined in detail in this paper) is

designed to determine whether the enhanced performance of

increased SCWB ratio requirements might be achieved

economically by placing the highest SCWB ratio requirements

at the base of the building and allowing the requirements to

step down along the height of the building. It is determined

that this method of varying the SCWB target along the height

of the building has the potential to maintain or even increase

collapse performance in a cost-effective manner as long as the

minimum SCWB target at the top of the building does not drop

below the current material standard requirements.

Figure 10. SCWB RC SMF (FEMA, 2018).

Figure 11. SCWB RC OMF (FEMA, 2018).


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Conclusion

There is no need to consider SCWB in ASCE/SEI 7-16 at this

time. Increasing the SCWB ratio beyond the material

standards generally increases collapse performance. There are

also preliminary results that suggest that stepping the target

SCWB ratio along the height of the building may be an

economic way to benefit from increasing the SCWB

requirements, however more study is required to make a

specific recommendation for how prescriptive requirements

could be structured to achieve this enhanced performance.

Gravity-Induced Lateral Demand (GILD)

Irregularity

Gravity-induced lateral demand (GILD) is not currently

recognized in ASCE/SEI 7-16 as a vertical irregularity.

However, recent studies (Dupuis, et. al., 2014 and Shorka, et.

al., 2014) have recommended that the National Building Code

of Canada recognize and restrict GILD irregular buildings due

to ratcheting behavior, increased inelastic drifts, and decreased

collapse capacity.

GILD is examined in this study predominately in 20 story steel

SMF and OMF buildings. The irregularity is achieved by

sloping all of the columns at a single story. The GILD

irregularity is quantified as the GILD ratio, which is defined as

the gravity-induced lateral demand normalized by the story

shear capacity. The tested GILD ratio values range from 0 to

0.5.

Results

When the building is designed for GILD, the collapse capacity

generally remains within 15% of the baseline, even increasing

with GILD ratio in some cases. Though collapse performance

is the main metric for performance used in this study, the drift

demands are also tracked for the GILD irregular buildings and

it is found that these demands amplified in the GILD irregular

buildings relative to regular buildings. This finding is in

keeping with an earlier study (Shorka, et. al., 2014), which

found that applying GILD over the entire height of the building

may have a negative effect on collapse performance, although

GILD at a single story tends to result in smaller amplification

in displacement demands.

Naturally, the archetype set of buildings tested in this study is

limited. These buildings are subjected to only the horizontal

components of far-field crustal ground motions and P-Delta

effects are simulated using the “Pdelta” transformation in

OpenSees. A few small tests are used to examine the effects

of (1) vertical ground motions on ratcheting behavior and

collapse performance, and (2) the effect of the linear

transformation method. The addition of vertical ground

motions are found to reduce the predicted ACMR by ~6%, a

relatively minimal effect. The “exact” transformation

(corotational) also has a minimal effect on the collapse

performance, reducing ACMR by ~3%.

The GILD demands are considered in the design of the

archetype buildings. To determine how GILD could affect

buildings designed without consideration for the additional

lateral demands, additional archetypes are created that do not

account for GILD in the proportioning of their members.

Figure 14 shows that the collapse performance can diminish

significantly when GILD is not considered in the design,

showing reductions in ACMR as great as ~50%.

Figure 12. GILD Steel SMF (FEMA, 2018).

Figure 13. GILD Steel OMF (FEMA, 2018).

Conclusion

Based upon this study, there is not a clear need for GILD

irregularities to be addressed in ASCE/SEI 7-16. However, it

is very important that designers do not neglect GILD in the

proportioning of the lateral system. Further study is

recommended to examine how GILD applied over the height

of the building, and other factors such as subduction ground

motions, or other methods for achieving GILD (as have been

tested in other studies) may affect collapse performance.


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Figure 14. GILD Steel SMF (not designed for GILD),

(FEMA, 2018).

Conclusions and Recommendations

In general, this study has found that the ASCE/SEI 7-16

treatment of vertical irregularities results in satisfactory

collapse performance in code-conforming buildings. None of

the code-conforming irregular buildings examined in this

study presented unacceptable collapse performance.

In the case of Mass Irregularities, it is recommended that

Equivalent Later Force (ELF) method design be allowed.

This recommendation is based upon the favorable collapse

performance of ELF designed mass irregular buildings

relative to Modal Response Spectrum Analysis (MRSA)

buildings, even when the MRSA base shear is scaled to 100%

of the ELF base shear.

Weak and soft stories do not appear to cause a problem; due

predominately to the fact that code conforming weak and soft

stories must still meet drift and strength requirements. Weak

stories in code-conforming buildings may really be thought of

as strong upper story irregularities. These results suggest that

the prohibition of extreme weak story irregularities in SDC D

and the height limitation on extreme weak story irregularities

in SDC B and C may be overly conservative. More study

would be required to comment on the prohibition of weak and

extreme soft story irregularities in SDC E and F.

Increased strong-column/weak-beam (SCWB) ratio above

material standard requirements does generally improve

collapse performance. There is also preliminary evidence

that stepping the SCWB target down along the height of the

building may enhance collapse performance in an economic

manner.

Finally, this study of gravity-induced lateral demand (GILD)

does not indicate that GILD should be incorporated into

ASCE/SEI 7-16 as an irregularity at this time. Though GILD

that is not designed for can have very significant negative

effects on collapse performance. Further study is

recommended to determine the effect of GILD on different

building configurations, sites, and ground motion types.

Acknowledgments

The study is part of a project managed by the Applied

Technology Council (ATC) under FEMA contract HSFE60-

12-D-0242 task order HSFE60-16-J-0223, entitled “ATC-123:

Improving Seismic Design of Buildings with Configuration

Irregularities.” Any opinions contained in this article represent

those of the authors and do not necessarily represent the

opinions of ATC or FEMA. The authors gratefully

acknowledge the ATC-123 working group members, technical

committee, and project review panel for their valuable

feedback and contributions.

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Documents

Quantitative Evaluation of Code Provisions for Vertically