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Case Studies of Soft-Story Retrofits Using

Different Design Guidelines

SEAONC Special Projects Initiative Report By

Jonathan Buckalew, Bruce Maison, Brian McDonald,

Marko Schotanus, and David McCormick

December 2015

ABSTRACT San Francisco has passed a mandatory retrofit ordinance targeting multi-unit soft, weak, or

open front (SWOF) buildings. Ordinance 66-13 allows use of multiple guidelines. It is up to the

structural engineer to work with the building owner and decide which of these guidelines to

use. Unfortunately, it is not possible for a practicing engineer to evaluate the merits of each

guideline within the scope of a typical SWOF retrofit project. This may result in choosing a

guideline based on prior familiarity or perceived ease of use.

The goal of this study is to illustrate the outcomes of using these different guidelines on retrofit

case studies based on Ordinance 66-13. In this way engineers can be better informed when

advising their clients. First, the study retrofits two sample buildings to three of the

methodologies allowed by San Francisco’s Ordinance: ASCE 41-13, IEBC A4, and the recently

released FEMA P807. The second part of the project provides insight into the FEMA P807

guideline by evaluating the ASCE 41-13 and IEBC A4 retrofits using P807. Lastly, the retrofits are

analyzed by computer (SAPwood) and collapse fragility curves developed using incremental

dynamic analyses. These curves quantify how each retrofit reduces the sample building’s

probability of collapse.

While the different guidelines may satisfy the ordinance, this study found that they produce

retrofits that can vary significantly. For the two sample buildings, based on static push-over

curves, the lateral strength required by FEMA P807 is significantly smaller than that required by

ASCE 41-13 and IEBC A4.The ASCE 41 and IEBC A4 retrofits were not controlled by strength

checks alone, but required additional strength in order to meet certain demand-to-capacity

ratios (for ASCE-41: D/C < 3 to allow use of linear static procedures), and story drift

requirements (IEBC A4). However, it was found that even without these additional checks, the

retrofit strength required by P-807 was still significantly less than those from ASCE-41 and IEBC

A4. This study can be used to better understand the different guidelines and help select the one

that best suits their client’s objective.

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Contents

1. Acknowledgement and Disclaimer

2. Introduction

3. Special Projects Initiative Overview

4. Guideline Comparison

5. Analysis and Retrofit Assumptions

6. Building 1 Results

7. Building 2 Results

8. Incremental Dynamic Analyses

9. Conclusions

Appendix A – SAPwood Material Backbone Curves

Appendix B – SAPwood Pushover Curves

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1. ACKNOWLEDGEMENT AND DISCLAIMER

This study was undertaken as the 2013 Special Projects Initiative of the Structural Engineers

Association of Northern California (SEAONC). SEAONC’s Special Projects Initiative is intended to

provide financial support for innovative projects that will serve SEAONC and its members

through initiatives that improve and promote structural engineering practice.

All opinions and conclusions expressed herein are solely those of the authors. While the

information presented in this document is believed to be correct, neither the author, nor

SEAONC, its Board, committees, editors, or individuals who have contributed to this document

make any warranty, expressed or implied, or assume any legal liability or responsibility for the

use, application of, and/or reference to opinions, findings, conclusions, or recommendations

expressed herein. The material presented in this document should not be used or relied upon

for any specific application without competent examination and verification of its accuracy,

suitability, and applicability by qualified professionals. Users of information from this document

assume all liability arising from such use.

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2. INTRODUCTION

Soft, weak, or open front (SWOF) wood structures might pose a significant threat to public

safety. As cities and government organizations work to identify these buildings, structural

engineers must be ready to provide expertise on how to best mitigate these potentially

dangerous buildings. San Francisco has initiated a mandatory retrofit program that has three

methodologies that can be used.

The first is ASCE 41-13 “Seismic Evaluation and Retrofit of Existing Buildings” (ASCE 41-13). It is

a comprehensive standard for retrofitting buildings to meet various performance objectives,

but it is not written explicitly for SWOF structures (Ordinance 66-13 has modifications to ASCE

41 such as restricting upgrades to the first story only). The second is Appendix Chapter A4 of

the “2012 International Existing Building Code” (IEBC A4-12), which uses simplified procedures

that focus on eliminating the soft/weak story irregularity. IEBC A4 is not intended for evaluation

of the expected performance of an existing structure.

The last option that recently became available (published in 2012) to structural engineers is

FEMA P807/ ATC 71-1 – “Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings

with Weak First Stories” (FEMA P807). FEMA P807 does not require the designer to perform an

explicit structural analysis, but instead relies on regression equations created from thousands

of nonlinear response history analyses performed on (hypothetically) similar models. The

regression equations are intended to be used in lieu of a nonlinear analysis.

Motivation for this project comes from Ordinance 66-13 from San Francisco. Ordinance 66-13

allows use of multiple retrofit guidelines, each with their own design criteria and unique

performance objectives. It is up to the structural engineer and building owner to decide which

of these guidelines to use. Unfortunately, it is not possible for a practicing engineer to evaluate

the merits of each guideline within the scope of a typical SWOF retrofit project (e.g. performing

trial designs with each). This often results in choosing a guideline based on prior familiarity or

perceived ease of use.

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3. SPECIAL PROJECTS INITIATIVE OVERVIEW

The goal of this project is to assist engineers by providing a basis by which the guidelines can be

judged so as to best suit the client’s objectives. Two buildings are used for this project. Building

1 is a typical midblock SWOF building from the pre-war era (before 1930). It is a three-story

structure with retail on the ground floor and apartments on the top two floors. Building 2 is a

corner building similar to the corner buildings that failed in the Marina District of San Francisco

during the Loma Prieta Earthquake. It is a four-story building with parking on the first floor and

apartments on the upper three floors. The project is organized into three parts.

The first part is a retrofit comparison, where in each building was retrofitted to satisfy the

provisions of the three guidelines specified in Ordinance 66-13.

The second part is a benchmarking comparison, where each retrofit was evaluated using the

FEMA P807 guideline. FEMA P807 is a new guideline that has not yet been widely tested. This

benchmarking will establish where an ASCE41-13 and IEBC A4-12 retrofits fall on the FEMA

P807 spectrum. A quantitative comparison, based on a common evaluation method, can be

made from the results of this section.

The last part of the project evaluates each retrofit using nonlinear incremental dynamic analysis

(IDA). The retrofits were modeled using the NEES software Seismic Analysis Program for

Woodframe structures (SAPWood1). Results from the IDAs were used to create collapse fragility

curves. The performance of each retrofit was quantified based on building collapse, not

probability of exceeding a drift limit used in the FEMA P807 methodology.

It must be emphasized that all analyses necessitate numerous assumptions in the computer

models that have a direct influence on results. In particular, there is currently no industry

consensus on the load-drift (backbone) curves for many of the materials found in wood-frame

buildings. P-807, SAPWood, and ASCE 41-13 prescribe backbone curves that differ significantly,

and a recent review indicates all of these might be conservative2.

1 John van de Lindt; Shiling Pei (2010), "SAPWood," https://nees.org/resources/sapwood.

2 Maison, B., McDonald, B., McCormick, D., Schotanus, M., and Buckalew, J., 2014. Commentary on FEMA P-807 for

Retrofit of Wood-Frame Soft-Story Buildings, Earthquake Spectra, Vol. 30, No. 4, November.

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4. GUIDELINE COMPARISON

The following sections outline key differences between the three guidelines as used in this

study. All comparisons below are based on the linear static methods used to retrofit the sample

buildings. Both case study buildings had SWOF conditions in their first story. Note that

Ordinance 66-13 uses the terminology “target story” to identify the portion of the building that

requires evaluation or retrofit. For this report the terms “ground floor” or “first level” are used

in lieu of “target story”.

4.1 Guideline Overview

ASCE 41-13 ASCE 41-13 is a comprehensive standard used to evaluate and retrofit

existing structures. It is intended for all building sizes and type.

IEBC A4 IEBC A4-12 is a prescriptive retrofit code created specific for wood frame

structures with a soft, weak, or open front. A4 gives no credit to existing

vertical elements that are not sheathed with structural panels.

FEMA P807 FEMA P807 is a new retrofit guideline that utilizes a performance-based

engineering approach. It relies on results from numerous nonlinear analyses

as contained in regression equations to evaluate the strength of a soft story

building. P807 was not put through an industry consensus process like ASCE

41.

Table 4.1 – Ordinance 66-13 Guideline Overview

4.2 Performance Objectives

ASCE 41-13 Life safety in the BSE-1E event (20%/50yr earthquake). This results

in a short period spectral acceleration of about 85% of Sds or

0.57Sms ([2/3]*0.85 = 0.57) for San Francisco3. Sds and Sms per ASCE

7-10 definitions.

IEBC A4 Prescriptive retrofit based on 75% of current code forces for new

construction. This results in a short period spectral acceleration of

0.5*Sms ([2/3]*0.75 = 0.5).

FEMA P807 30% probability of exceedance at 0.5Sms. Probability of exceedance

refers to the chance the building story drift will exceed a drift limit

that might suggest collapse.

Table 4.2 – Ordinance 66-13 Guideline Performance Objectives

The performance objectives shown above are based on Ordinance 66-13. It is important to

recognize that each retrofit has different objectives, and thus they result in different retrofits

that are not equivalent in terms of seismic safety. The engineer should inform their clients of

this information to select a guideline to best fit their client’s objective.

3 Pekelnicky R., and Poland C, ASCE 41-13: Seismic Evaluation and Retrofit of Existing Buildings, SEAOC 2012

Convention Proceedings

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Note that ASCE 41-06 is also allowed by Ordinance 66-13, but is not one of the guidelines used

in this project.

4.3 Material Strengths

ASCE 41-13 was developed to cover a wide range of materials and building types. It contains

acceptance criteria and material strengths for all parts of the load path including diaphragms,

connections, lateral system elements, and foundations.

ASCE 41 states that the strength of dissimilar materials in wall assemblies shall not be combined

unless test data is available [ASCE 41-13, 12.4.1]. However, the commentary for the same

section refers to FEMA P807 for further information on the effects of combining dissimilar

materials. For this study, the commentary is interpreted to allow combinations of dissimilar

materials using the same procedures as FEMA P807.

IEBC A4-12 bases material strengths on code values for new construction. New retrofit

elements are designed and detailed using current code provisions for new construction. Unlike

the other guidelines, IEBC A4 does not permit the use of gypsum or plaster products to resist

lateral loads on the ground floor [IEBC A4-12, A403.9.1]. This is an important aspect for the case

study buildings since their lateral force resisting systems consists mostly of plaster-on-wood-

lath partition walls.

FEMA P807 allows use of and provides backbone curves for both wood structural panels and

gypsum/plaster walls. The backbone data is provided up to 5% drift (after this point all

materials are assumed to have no strength). P807 accounts for and encourages existing

materials to be used and combined with new retrofit elements. Guidelines for creating

composite load-drift curves are provided in P807 section 4.5.1.

FEMA P807 does not provide strength or stiffness properties for diaphragms, connections, or

foundations. The guideline recommends designing these elements to develop the strength of

the wall or moment frame used in the evaluation/retrofit analysis (FEMA P807, section 6.5.1).

For this study, the acceptance criteria for these elements come from ASCE 41-13 or the

International Building Code (IBC) depending on whether existing or new elements are being

utilized. See tables 4.3 and 4.3A for a summary of material strength assumptions used by each

of the guidelines.

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ASCE 41-13

Material tables provided for lateral system elements, diaphragms,

foundations, and connections. Dissimilar materials were combined

using FEMA P807 rules.

IEBC A4 Material strengths taken as those for new construction. Gypsum and

plaster products cannot be used to resist lateral loads in the story.

FEMA P807 Material tables provided for wall elements. No material tables

provided for diaphragms, connections, or foundations.

Table 4.3 – Material Strengths Summary

ASCE 41-131 IEBC A4 FEMA P807

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Plaster on wood lath 400 plf 0 plf 538 plf

Horizontal sheathing 80 plf 0 plf 171 plf

Stucco 350 plf 0 plf 333 plf

Gypsum wallboard 100 plf 0 plf 213 plf

Wood structural panel (WSP)

(10d @ 4” O.C.)

1530 plf2,4

1020 plf2 1496 plf

Table 4.3A – Wall Sheathing Material Strengths Used in Study5

Table 4.3A Notes:

1. Expected strengths for shear wall elements based on ASCE 41-13 Table 12-1. Per section 12.3.2.2.1 Strength

values for WSP obtained from National Design Specification for Wood Construction (NDS).

2. 1020 plf design strength for WSP obtained from Table 4.3A of NDS Special Design Provisions for Wind and

Seismic (assuming 15/32” thick Structural 1 panels with 10d@4” spacing).

3. Peak material strength values listed in table are obtained from load-drift curve data on Table 4-1 of FEMA P807.

Only peak strength values recorded above.

4. Expected strength values for deformation-controlled actions shall be permitted to be based on 1.5 times the

yield strength [1.5*1020plf = 1530plf] per section 12.3.2.2.1 of ASCE 41-13,

5. Values in Table 4.3A represent a single layer of sheathing for one side of a wall. These values are double when

both sides of the wall are sheathed.

4.4 Strength Design Checks

This study based ASCE-41-13 retrofits on Linear Static Procedures (LSPs) since this is the

approach expected to be used in design office practice for retrofit of wood buildings (rather

than non-linear or dynamic procedures). LSPs require two local strength checks. The first is a

standard demand capacity ratio (DCR) check (mkQCE > QUD) to ensure that individual elements

are not overstressed (ASCE 41-13, Section 7.5.2.2). The second strength check limits the DCR

(QUD/QCE) to 3.0 for a linear analysis where any structural irregularities are present [ASCE 41-13,

Section 7.3.1.1]. The intent of the provision is to limit the demand amplifying effects of the

structural irregularity that a linear analysis might not capture. Even if the soft story irregularity

is mitigated in the retrofit, an out-of-plane discontinuity may still exist. This structural

irregularity occurs when an element of the seismic force resisting system in one story is offset

out-of-plane relative to an element in an adjacent story. For typical SWOF buildings majority of

the interior walls of the second story do not continue to the foundation. It should be noted that

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ASCE 41-06 contains a similar provision except the DCR limit is capped to 2.0 [ASCE 41-06,

Section 2.4.1.1]

Two options are available when the DCR limit prevents a linear analysis from being used (i.e.

QUD/QCE >3.0). The first option is to use a nonlinear analysis, where there is no DCR limit based

on the presence of a structural irregularity. This option is consistent with the original intent of

the provision. The second option is to over-retrofit the ground floor to push the DCRs below 3.0

and validate the linear analysis. The second option is utilized in this study to keep the analysis

assumptions and computational requirements similar among the different guidelines. This

option, based on budgetary restraints, will likely reflect the expected practice in a design office.

IEBC A4 retrofits based on linear static analyses require one local strength check. This check is

based on new construction code acceptance criteria (φVn>Vu; φMn>Mu) and verifies that

individual elements are not overstressed.

FEMA P807 deviates from traditional design and does not perform stress checks individual

elements. It takes a more holistic approach by utilizing the ultimate strength of all the ground

floor elements to develop a capacity. This capacity is then compared to the earthquake demand

to determine if the building is adequate. Table 4.4 summarizes the different strength checks

required by the three guidelines.

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ASCE 41-13 (applied

only to the 1st

story)

Base shear: [ASCE 41-13, 7.4.1.3.1]

Vb= C1C2CmSaW

C1 = inelastic displacement modification factor

C2 = cyclic stiffness degradation modification factor

Cm = effective mass factor

Local strength check: [ASCE 41-13, 7.5.2.2.1]

mkQCE > QUD

m factor varies:

~3-4 for plywood, gypsum, wood sheathing [ASCE 41-13, Table 12-3]

6 for steel moment frame - Flexure [ASCE 41-13, Table 9-5]

Linear elastic analysis check: [ASCE 41-13, 7.3.1.1]

QUD/QCE < 3.0

IEBC A4-12

Base shear: [75% new code, IEBC A4-12, A403.3]

Vb = 0.75(SDS/[R/I])W

R = 6.5 [wood panel shear walls; ASCE 7-10, Table 12.2.1 only if the

extreme soft story irregularity is eliminated, otherwise the lowest

value for all floors would govern]

Local strength check:

φVn > Vu; φMn > Mu

FEMA P807

Global strength check: [FEMA P807, 5-6; AB-107, B1.2.6.1]

Sc>Sa, where Sc is the short period spectral capacity, and Sa is the

spectral demand taken as 0.5Sms per ASCE 7-10. This check is

deemed satisfied with a 30% probability of exceedance on drift

limits.

Table 4.4 – Strength Design Checks Summary

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4.5 Drift Design Checks

ASCE 41-13 retrofits do not require any checks on story drift.

IEBC A4 limits the inelastic drift of the first story to 2.5% of the story height [IEBC A4, section

A403.4]. This limit is calculated ignoring the existing plaster, gypboard, and stucco walls on the

ground floor.

FEMA P807 does not check drift explicitly, but drift limits are built into the methodology. The

performance objective is the probability of exceeding a drift limit representing onset of

strength loss. This limit ranges from 1.25% to 4% depending on the building materials. The

strength degradation ratio (Cd) determines the onset of strength loss drift limit. If Cd is equal to

0 then 1.25% will be the drift limit. If Cd is equal to 1.0 then 4% will be the strength limit. The

actual Cd for a building is determined by an interpolation between these two limiting cases

depending on upon the materials in the building.

ASCE 41-13 No explicit drift limit for linear static analysis

IEBC A4-12 2.5% maximum inelastic story drift

FEMA P807

No explicit drift check (drift limits from 1.25% to 4% implicit to

methodology). This implicit check is deemed satisfied with a 30%

probability of exceedance on drift limits (AB-107, B1.2.6.1).

Table 4.5 – Drift Design Checks Summary

4.6 Diaphragm Assumptions

Both ASCE 41-13 and IEBC A4-12 have similar checks to identify the diaphragm rigidity.

Typically, the diaphragm of the second floor for an existing SWOF building is classified as a rigid.

The soft story irregularity implies the deformations of the first story will be large with respect to

the deflections of the diaphragm.

If the diaphragm deflects more than twice the first story drift, then the diaphragm is flexible. If

the diaphragm deflects less than half the first story drift, then the diaphragm is rigid. Anywhere

in between the diaphragm is considered stiff [ASCE 41-13, section 7.2.9.1]. If a diaphragm is

rigid, then additional torsion amplification factors need to be checked [ASCE 41-13, section

7.2.3.2.2; ASCE 7-10, section 12.8.4].

FEMA P807 assumes the diaphragm is rigid and does not require the engineer to check the

rigidity of the diaphragm. The background analyses used to derive the regression equations

assumed a rigid diaphragm.

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5. ANALYSIS AND RETROFIT ASSUMPTIONS

5.1 Analysis Assumptions

The sample buildings were assumed to be located in San Francisco on stiff soil (site class D) with

an MCE spectral acceleration of 1.5g. While the buildings are located near adjacent structures,

the effects of pounding were not included in the analyses.4 The buildings are assumed to be on

a flat site (partially embedded structures sometimes cannot be evaluated using P807 due to the

presence of concrete retaining walls.) The following table summarizes the loads assumed for

each building.

Floor and Roof Dead Load 20 psf (horizontal area)

Interior Partitions Dead Load 20 psf (horizontal area)

Exterior Wall Self Weight 20 psf (vertical area)

Live Load (not used in P-delta) 40 psf (horizontal area)

Table 5.1 – Building Load Assumptions

The calculations were performed in EXCEL spreadsheets. The analyses for ASCE 41-13 and IEBC

A4-12 retrofits assumed LSPs. The LSP was chosen for several reasons. This type of analysis

would be consistent with what a typical engineer would use given the scope of the first story

retrofit. It also simplifies comparisons between different retrofits and identifying what

controlled each retrofit. LSP made the computational effort involved of ASCE 41-13 and IEBC

A4-12 more comparable to FEMA P807. Note that other analysis types (linear dynamic,

nonlinear static, and nonlinear dynamic) are also viable options for ASCE 41-13.

The second floor diaphragm is assumed to be rigid across all of the guidelines. This is a built into

the FEMA P807 methodology and was also used for ASCE 41-13 and IEBC A4-12 retrofits. The

additional loads due to accidental (e.g. artificial 5% mass offsets) and inherent (actual) torsion

were considered in the ASCE 41-13 and IEBC A4-12 retrofit [ASCE 41-13, Section 7.2.3.2.1; ASCE

07-10, Section 12.8.4.2]. Only inherent torsion is considered in FEMA P807. Based on the

calculations, the increase in demand due to combined torsion (inherent and accidental) is on

the order of 5-7%.

P-delta effects were considered in the ASCE 41-13 and IEBC A4-12 retrofits. To avoid analysis

iterations (since P-delta lateral forces depend on story drifts), a simplified factor was used

based on the IEBC A4-12 drift limit of 2.5%. For the EXCEL calculations, the global base shear

demand was increased by 0.025W to account for P-delta effects. This assumes the first story

reaches 2.5% drift and imposes an additional lateral load equal to 0.025 times the gravity load.

Note that this is conservative where the final story drifts are less than 2.5%.

4 For further information regarding the effects of pounding between adjacent structures see Maison, McDonald,

and Schotanus, Pounding of San Francisco-Type Midblock Buildings, Earthquake Spectra, Vol. 29, No. 3, Aug. 2013.

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5.2 Retrofit Assumptions

In order to perform the project within the time and budget constraints, only the first floor

retrofits from different guidelines were compared. Other parts of the load path were not

checked. It was assumed that the diaphragm, connections, collectors, and foundation elements

could develop the full capacity of the first floor lateral elements.

Retrofits were designed assuming wood shear walls (10d@4”) and steel special moment frames

pinned at the base. The retrofit elements are located to maintain the existing wall layout and

openings. It was also assumed that existing conditions would not restrict placement or sizing of

new elements. In actual buildings, aspects such as ceiling space, wall cavity size, space above

garage doors, and location of utility meters could influence the retrofit design. Note that the

decision to use special moment frames versus intermediate, ordinary moment frames, or

cantilever columns will dramatically impact the ASCE 41-13 and IEBC A4-12 retrofits by reducing

the ‘R’ and ‘m’ factors.

The existing wall elements were assumed to be of good quality construction and not having

environmental deterioration (e.g. rot). No ASCE 41-13 reduction factors were applied to

material strengths specified in the different guidelines (i.e. ASCE 41 knowledge factor, kappa =

1.0). Note that the knowledge factor for ASCE 41-13 varies from 0.75 to 1.0 depending on how

much data from the existing building has been collected (drawings, field investigations and

testing, etc.). See ASCE 41-13 section 6.2.4 for more information on knowledge factors.

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6. MID-BLOCK BUILDING RESULTS

Building 1 Overview

Building 1 represents a mid-block building in San Francisco. The first floor has two retail spaces

that extend the length of the building, (Figure 6.1). The front of the building consists of doors

and large windows facing the street that create the open front that Ordinance 66-13 targets.

Each upper floor contains four apartment units for a total of eight units in the building (Figure

6.3). Fundamental periods of the building varied from 0.65 sec (unretrofitted) to 0.29 sec (when

retrofitted).

Figure 6.1 – Building 1 Street Side Elevation

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Figure 6.2 – Building 1 First Floor Plan

Figure 6.3 – Building 1 2nd

and 3rd

Floor Plans

Building 1 Retrofits (Part 1)

The following retrofits were created using the Ordinance 66-13 performance objectives

outlined in Table 4.2. Each retrofit that follows shows a plan layout identifying the location of

the retrofit elements and what percent of existing walls have a single layer of wood structural

panel (WSP). This percentage is calculated assuming that each side of the wall can have a layer

of sheathing. For example a wall with sheathing along one side will only have 50% of the wall

sheathed. See Figure 6.4 for a layout of the existing walls. There are 386 ft of walls in the X-

direction and 118 ft in the Y-direction (i.e., there are 386 ft of X-direction walls, so there is 772

ft of wall that can be sheathed with a single layer of WSP [2x386’]). Note that window and door

openings shown as dashed lines below are included in the total wall length. The moment

frames are not included in the % wall sheathed calculation.

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Figure 6.4 – Building 1 Existing Wall Layout in First Story

A retrofit satisfying FEMA P807 is shown in Figure 6.5. Note that other retrofit layouts for the Y

direction are possible. No retrofit was required in the X direction due to large number of

existing walls; hence 0% of the walls were sheathed. Note for FEMA P807, as well as ASCE 41, it

is necessary to check existing anchorage to the foundation for existing walls that are assumed

to be part of the lateral system. This could result in substantially more scope than shown

below. The Y direction required a single moment frame along the open front and 23% of the

walls sheathed with new WSP (54 ft of 236 ft). In the Y-direction the global DCR (ultimate

strength ratio) for the retrofit is 0.92.

Figure 6.5 – Building 1 FEMA P807 Retrofit in First Story

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A retrofit satisfying IEBC A4-12 is shown in Figure 6.6. IEBC A4-12 does not permit the use of

gypsum, stucco, or plaster to resist lateral loads. The retrofit is designed relying only on new

elements. 13% of the walls required WSP sheathing in the X direction (99 ft of 772 ft) and 53%

of the total walls were sheathed in the Y direction with new WSP (124 ft of 236 ft). Most of the

walls in the Y direction are narrow and the 2.5% drift limit controlled the design of the retrofit.

The design (not ultimate) strength DCRs of the retrofitted structure are approximately 0.80 in

the X direction. This implies about 25% strength was added to limit drift.

Figure 6.6 – Building 1 IEBC A4 Retrofit

A retrofit satisfying ASCE 41-13 is shown in Figure 6.7. 4% of the walls require sheathing in the X

direction (34 ft of 772 ft) and 51% of the total walls are sheathed in the Y direction with new

WSP. The retrofit is controlled by the DCR limit for linear analyses (see section 4.4 for

explanation). The ultimate strength DCRs (including m factors) were around 0.80 in the X

direction. This implies about 25% extra ultimate strength was added to the retrofit to justify the

use of LSP.

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Figure 6.7 – Building 1 ASCE 41-13 Retrofit in First Story

See Table 6.1 for a summary of the different retrofits. The total length of WSP is based on a

single layer of sheathing (double layered WSP walls will be counted for twice its length). Note

that the ASCE 41-13 and IEBC A4-12 retrofits were over-strengthened to meet analysis and drift

limitations, respectively.

The strength DCRs for the ASCE 41-13 and IEBC A4-12 retrofits were on the order of 0.80,

implying about 25% additional strength added to the ground floor to meet other guideline

criteria (note that ASCE 41-13 DCR uses ultimate values and IEBC A4-12 uses design values). To

see what the retrofits would look like without the additional criteria multiply the % of wall

sheathed in the Y-direction by 0.75 (the reduction would bring the strength DCRs closer to 1.0).

This results in around 40% of the walls still require sheathing. Even without these additional

criteria, the FEMA P807 retrofit is still less extensive than ASCE 41-13 and IEBC A4-12 (24%

versus 40% of wall lengths).

Y - Direction X - Direction

Guideline % Walls

(Y-Dir.)

Total Length of

WSP (Y-Dir.)

MF

Beam

MF

Column

% Walls

(X-Dir.)

Total Length of

WSP (X-Dir.)

FEMA P807 24% 56 ft W12x35 W12x35 0% 0 ft

IEBC A4-12 53% 124 ft W16x50 W14x61 13% 99 ft

ASCE 41-13 51% 120 ft W14x53 W12x58 4% 34 ft

Table 6.1 – Building 1 Retrofit Summary

Building 1 FEMA P807 Comparison (Part 2)

This section evaluates the different Building 1 retrofits described above using the FEMA P807

methodology. The original material strength assumptions made for the ASCE 41-13 and IEBC

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A4-12 were changed to the ultimate values as defined in FEMA P807 to provide a consistent

comparison. The most notable difference will be that the existing nonconforming walls of

plaster/gypsum were included in the evaluation of the IEBC A4-12 retrofit.

Figure 6.8 shows the FEMA P807 push over curves for the X direction using the three different

criteria5. The push over curves were created via EXCEL spreadsheet calculations as the sum of

the individual component backbone curves. Note that the P-delta effect is not reflected in the

graphs (including the P-delta would progressively reduce the curves with increasing drift ratio).

The existing building and FEMA P807 retrofit lines coincide because there was no retrofit

required in this direction. The IEBC A4-12 retrofit produced the strongest retrofit in this

direction. This makes sense because the original IEBC A4 retrofit was checked ignoring the

existing walls and now is being evaluated using the existing materials. The light blue dashed line

shows 1.3 times the strength of the second story. This line represents the “need-not-exceed”

cap that was added to Ordinance 66-13 (P807 also has a cap in the form of an equation that

typically yields a value of 1.3) to make all three methodologies similar and prevent over

strengthening the first floor. For this direction an engineer using IEBC A4-12 to develop the

retrofit could take advantage of this need-not-exceed limit.

Figure 6.8 – FEMA P807 X direction pushover curves

Figure 6.9 shows the FEMA P807 push over curves for the Y direction of Building 1 using the

three different criteria. In this direction the existing structure is clearly identified as being

inadequate. It is useful to note the existing structure has zero strength at 2% drift. For each

retrofit this means that any strength beyond 2% drift will come from the retrofitted elements.

5 The push-over curves show limited ductility by having rapid drop-off in load at about 6 inch roof level

displacement (1.5% drift). There is evidence that the P807 material backbone curves are conservative. See

footnote 2 for discussion.

20

For Building 1 there is a significant gap between FEMA P807 and the other two retrofits. Both

ASCE 41-13 and IEBC A4-12 retrofits have more than twice the first story strength of the FEMA

P807 retrofit. It is important to remember that the ASCE 41-13 and IEBC A4-12 retrofit designs

were not controlled by strength. They both were over strengthened to meet other

requirements. However, even without the over-strengthening, the P807 retrofit has lower

strength versus those using ASCE 41-13 or IEBC A4-12.

Figure 6.9 – FEMA P807 Y direction pushover curves

21

Table 6.2 summarizes the important FEMA P807 parameters to help interpret the push over

curves above. The percent of wall sheathed values are repeated from Part 1 here for reference

purposes. Sc is the spectral capacity and is calculated from the regression equations in FEMA

P807. This value should be compared with the spectral acceleration of the site to validate if the

structure is adequate. The strength degradation ratio (Cd) is a measurement of ductility and is

included to better understand which drift limit corresponding to onset of strength loss, see

section 4.5 for more information about Cd. Lastly, V1 is the peak first story ultimate strength

using FEMA P807 material values. FEMA P807 has a cap on the first story strength to prevent

over strengthening the ground floor thereby pushing the failure to the second floor. This value

is around 1.25 to 1.3 times the strength of the second story. For Building 1 the cap is set at 312

kips in the X-direction and 226 kips in the Y-direction. The values underlined below exceed

these limits. The engineer could potentially “take advantage” of the 1.3V2 need-not-exceed

limit that is included in Ordinance 66-13. According to P807, not limiting the first story retrofit

strength means that the building safety is controlled by an upper story failure so that further

strengthening of the first story does not increase the safety of the building – the building safety

is controlled by the upper stories.

X - Direction Y - Direction

% WallsX Sc,x Cd,x V1,x % WallsY Sc,y Cd,y V1,y

Existing 0% 0.90g 0.16 272k 0% 0.21g 0.13 47k

FEMA P807 0% 0.90g 0.16 272k 24% 0.82g 0.98 100k

IEBC A4-12 13% 1.45g 0.56 354k 53% 2.03g 1.00 268k

ASCE 41-13 5% 1.14g 0.32 300k 51% 1.91g 1.00 242k

Notes: 1) Underlined text indicates where the shear strength provided exceeds the need not exceed limits of FEMA

P807 and Ordinance 66-13. This corresponds to 312 k and 226 k in the x and y direction, respectively.

Table 6.2 – FEMA P807 Evaluation Summary

22

7. CORNER BUILDING RESULTS

Building 2 Overview

Building 2 represents a typical corner building for San Francisco (Figure 7.1). The first floor

consists of two large garages and a lobby, see Figure 7.2. The top three stories contain

apartments, see Figure 7.3. The fundamental periods of the building varied from 0.55 sec

(unretrofitted) to 0.34 sec (when retrofitted).

Figure 7.1 – Building 2 Elevation

Figure 7.2 – Building 2 First Floor Plan

23

Figure 7.3 – Building 2 Typical Upper Floor Plans

Building 2 Retrofits (Part 1)

The following retrofits were created using the performance objectives outlined in Ordinance

66-13 (see section 4.1 and 4.2). Each retrofit that follows shows a plan layout identifying the

location of the retrofit elements and what percent of existing walls have a single layer of WSP.

As for Building 1, this percentage is calculated assuming that each side of the wall can have a

layer or sheathing. For example a wall with sheathing along one side will only have 50% of the

wall sheathed. See Figure 7.4 for a layout of the existing walls. There are 149 ft of walls in the X-

direction and 181 ft in the Y-direction. (i.e., there are 149 ft of X-direction walls, so there is 298

ft of walls that can be sheathed with a single layer of WSP [2x149’]). Note window and door

openings shown as dashed lines below are included in the total wall length. The moment

frames are not included in the % wall sheathed calculation. Note that a nominal moment frame

was added below a discontinuous wall along the east side of the building. The same moment

frame (W12x26 beam and column) were used for all the Building 2 retrofits.

Figure 7.4 – Building 2 Existing Wall Layout

24

The retrofit satisfying FEMA P807 is shown in Figure 7.5. The X direction required two moment

frames along the open front and 22% of the walls sheathed (81 ft of 362 ft). The Y direction

required 13% of the walls to be sheathed with new WSP (40 ft of 298 ft). The global DCR

(ultimate strength ratios) for the retrofit varied from 0.96 to 0.99.

Figure 7.5 – Building 2 FEMA P807 Retrofit

A retrofit satisfying IEBC A4-12 is shown in Figure 7.6. IEBC A4-12 does not permit the use of

gypsum or plaster materials to resist lateral loads. The retrofit is designed relying only on new

elements. 30% of the walls required sheathing in the X direction (88 ft of 298 ft) and 45% of the

total walls were sheathed with WSP in the Y direction (161 ft of 362 ft). Most of the walls in

Building 2 are significantly longer than those in Building 1. The longer walls are much stiffer

than the short ones from Building 1 and the retrofit is controlled by the strength of the walls,

not their deflection. The design strength (not ultimate) DCRs for the WSP walls in this retrofit

range from 0.87 to 1.00

25

Figure 7.6 – Building 2 IEBC A4-12 Retrofit

A retrofit satisfying ASCE 41-13 is shown in Figure 7.7. In the X direction, 51% of the walls

required sheathing (152 ft of 298 ft) and 60% of the total walls required sheathing in the Y

direction (220 ft of 362 ft). Similar to Building 1, the retrofit is controlled by the DCR limit for

linear analyses (see Section 4.4 for more information). The ultimate strength DCRs (including m

factors) were around 0.75. This implies there is about 30% extra ultimate strength was added to

the retrofit to justify the use of LSP.

Figure 7.7 – Building 2 ASCE 41-13 retrofit

26

See Table 7.1 for a summary of the different retrofits. Note that the ASCE41-13 retrofit was

over-strengthened to meet analysis requirements.

Similar to Building 1, the ultimate strength DCRs for the ASCE 41-13 retrofit were on the order

of 0.75, implying about 25% additional strength added to the first story to meet other guideline

criteria. To see what the retrofit would look like without the additional criteria multiply the % of

wall sheathed by 0.75 (the reduction would bring the strength DCRs closer to 1.0). This results

in 46% and 38% of the walls still require sheathing for the Y and X direction respectively. Even

without these additional criteria, the FEMA P807 retrofit is still less extensive than the ASCE 41-

13 retrofit.

Y – Direction X - Direction

Guideline % Walls

(Y-Dir.)

Total Length of

WSP (Y-Dir.)

% Walls

(X-Dir.)

Total Length of

WSP (X-Dir.)

MF

Beam

MF

Column

FEMA P807 22% 81 ft 13% 40 ft W12x30 W12x30

IEBC A4-12 45% 161 ft 30% 88 ft W16x50 W14x68

ASCE41-13 61% 220 ft 51% 152 ft W16x50 W14x61

Table 7.1 – Building 2 Retrofit Summary

Building 2 FEMA P807 Comparison (Part 2)

This section evaluates the different Building 2 retrofits described above using the FEMA P807

methodology. The original material strength assumptions made for the ASCE 41-13 and IEBC

A4-12 will be changed to the ultimate strength values as defined in FEMA P807. The most

notable difference will be that the existing walls (having nonconforming plaster and gypsum

materials) will be included in the evaluation of the IEBC A4-12 retrofit.

Figure 7.8 shows the FEMA P807 push over curves for the X direction of Building 2. The push

over curves were created via EXCEL spreadsheet calculation as the sum of the individual

component backbone curves. Note that the P-delta effect is not reflected in the graphs

(including P-delta would progressively reduce the curves with increasing drift ratio). The ASCE

41-13 retrofit produced the strongest retrofit in this direction. The original IEBC A4-12 retrofit

was checked ignoring the existing walls and now is being evaluated using the existing materials.

The light blue dashed line shows 1.3 times the strength of the second story. This line represents

the “need-not-exceed” cap that was added to the ordinance to prevent over strengthening the

first floor. For this direction an engineer using ASCE 41-13 to develop the retrofit could take

advantage of this need-not-exceed limit. However, note that limiting the first story retrofit

strength per P807 and Ordinance 66-13 means that the building safety is controlled by an upper

story failure so that further strengthening of the first story does not increase the safety of the

building – the building safety is controlled by the upper stories.

27

Figure 7.8 – FEMA P807 X direction pushover curves

Figure 7.9 shows the FEMA P807 push over curves for the Y direction of Building 2. In this

direction the existing structure is clearly identified as being inadequate. It is useful to note the

existing structure has zero strength at 2% drift. For each retrofit this means that any strength

beyond 2% drift will come from entirely the retrofitted elements.

Figure 7.9 – FEMA P807 Y direction pushover curves

Table 7.2 summarizes the important FEMA P807 parameters to help interpret the push over

curves above. The percent of wall sheathed values are repeated from Part 1 here for reference

purposes. The spectral capacity, Sc, is calculated from the regression equations in FEMA P807.

This value should be compared with the spectral acceleration specified by the Ordinance to

28

validate if the structure is adequate. The strength degradation ratio (Cd) is a measurement of

ductility and is included to better understand which drift limit corresponding to onset of

strength loss, see Section 4.5 for more information about Cd. Lastly, V1 is the peak first story

ultimate strength FEMA P807 material values. FEMA P807 has a built in cap on the first story

strength to prevent over strengthening the ground floor and pushing the failure to the second

floor. This value is around 1.25 to 1.3 times the strength of the second story. For Building 2 to

cap is set at 338 kips in the X-direction and 311 kips in the Y-direction. The values highlighted in

red below exceed these limits and could potentially take advantage of the 1.3V2 need-not-

exceed limit that is included in Ordinance 66-13.

X - Direction Y - Direction

% WallsX Sc,x Cd,x V1,x % WallsY Sc,y Cd,y V1,y

Existing 0% 0.23g 0.00 93k 0% 0.30g 0.00 127k

P807 15% 0.79g 0.94 160k 22% 0.77g 0.77 206k

IEBC A4 30% 1.28g 0.98 288k 45% 1.30g 0.94 306k

ASCE 41 60% 1.83g 1.00 419k 61% 1.68g 0.98 376k

Notes: 1) Underline text indicates where the shear strength provided exceeds the need not exceed limits of FEMA

P807. This corresponds to 338 k and 311 k in the x and y direction, respectively.

Table 7.2 – FEMA P807 Evaluation Summary

29

8. Incremental Dynamic Analyses

Incremental dynamic analysis (IDA) is a parametric study used to better understand how a

particular building performs under dynamic loading. An IDA is typically defined using two

properties; intensity measure and damage measure. The intensity measure is the variable that

will be scaled for each analysis. For this project the intensity measure is the short period

spectral acceleration. The damage measure is a variable that can be identified in the analysis

results. This measure varies depending on the goal of the particular analysis and examples

include base shear, node rotations, and peak inter-story drifts. For this project inter-story drift

was chosen to better understand the difference between onset of strength loss limits assumed

by FEMA P807 and collapse as predicted by the analytical model.

The goal of the IDAs is to develop a collapse fragility curve for a particular building. This curve

quantifies the probability of exceeding the damage measure (collapse) for different intensity

levels (short period acceleration). Probability of collapse is approximated as the number of

ground motions that cause the structural model to collapse. For example, if 3 of 22 ground

motions result in collapse at a particular spectral acceleration a 14% probability of collapse can

be inferred. Collapse fragility curves will be used to better understand the different retrofits

produced by each of the three guidelines. This will provide a way to measure how each retrofit

improved building performance. The IDAs will also be used to identify how close the onset of

strength loss drift limit from FEMA P807 is to collapse.

IDA Assumptions

The building retrofits were modeled and analyzed using SAPwood6. SAPwood is a structural

analysis program developed as part of the NEESWood program to better understand the

seismic performance of wood frame structures. The retrofits were analyzed using a bi-

directional model that assumes 3 degrees of freedom and a rigid diaphragm per level (two

translational and one rotational). 22 pairs of “far-field” ground motions from ATC 63 were

chosen for this project (44 total records). These records were chosen because FEMA P807 was

developed using the same ground motions.

There are two different ways to scale ground motions for IDAs. The first is to scale the

individual ground motions until the average response spectrum matches the target spectrum

(FEMA P807 used this approach in its development). This procedure results in an average

response spectrum that matches the target spectrum, but does not guarantee the same

spectral acceleration at a particular period for each ground motion record. The second way is to

scale the individual ground motions to a specific spectral acceleration at the period of the

undamaged structure. This procedure will ensure that all the ground motions will be scaled to a

single spectral acceleration value, but the average of the ground records will not match a code

response spectrum. For this project the second procedure was primarily used because

SAPwood is set up to scale the individual ground motions in this way. It probably does not

6 John van de Lindt; Shiling Pei (2010), "SAPWood," https://nees.org/resources/sapwood.

30

matter much which approach is used since relative comparisons are made across the different

retrofit designs. Four spring models are available in SAPwood: linear spring model, bilinear

spring model, SAWS-type 10-parameter hysteretic model, and a 16-parameter evolutionary

parameter hysteretic model. See Table 8.1 for a summary of which spring models were used for

each element.

Existing materials 10-parameter hysteretic model

Plywood shear walls 16-parameter hysteretic model

Steel moment frames Bilinear model

P-delta column Bilinear model

Table 8.1 – SAPwood element model summary

The backbone curve parameters in the SAPwood model were adjusted to match curves

provided in FEMA P807 (but had more ductility assigned, see Appendix A). The curves have the

same strength peak strength as the FEMA P807 curves. The one modification made was to

provide additional ductility to the curves. Instead of having zero strength at 2% (non-ductile

materials) or 5% (ductile materials) drift, the curves were extended to be more realistic per the

judgment of the authors. However, they still may be conservative, see footnote 2 for more

discussion on this aspect. See Appendix A for the backbone curves used in the SAPwood

analysis. P-delta affects were accounted for by using an elastic spring with negative stiffness in

each story. The stiffness was calculated by taking the weight of the floors above and dividing it

by the story height. Collapse is defined as a lateral instability occurring in any of the stories. This

was signaled by a very large story drift in either building principle direction or failure to

converge in an analysis run.

IDA Results

ASCE 7-10 defines the performance of a code building as having a 10% chance of collapse for an

MCE event (Sa = 1.5g). In the past, existing buildings were often retrofitted using 75% of code

level forces. Currently there is no codified probabilistic performance objective for retrofits. For

the purposes of this project a 75% code fragility curve was developed by targeting a 10%

chance of collapse at 75% of MCE (assumed here as having Sa = 1.125g) event. See Figure 8.1 for

code collapse curves. A beta value of 0.4 was used to develop to curves in Figure 8.1. This value

was comparable to the beta values observed in the SAPwood results that considered only the

earthquake record-to-record uncertainty (as opposed to a beta reflecting the total collapse

uncertainty including aspects such as design requirements and modeling uncertainties). The

following curves were developed based on material strengths as defined in FEMA P807. Using

other material property assumptions could dramatically impact the results.

31

Figure 8.1 – Building Code Collapse Fragility Curves

The following results are based on the computer analyses results from SAPwood. The code

fragility curves from Figure 8.1 are repeated in Figure 8.2 for reference. The four new curves

shown on Figure 8.2 are the collapse fragility curves for each of the four models (Existing, FEMA

P807, ASCE 41-13, and IEBC A4-12). The curves were computed as follows. At each short period

spectral value, 22 earthquake analyses were performed (using both X and Y-direction

earthquake components), and the number of runs having collapsed was used to compute the

collapse probability. A fragility curve was then fitted to the data across the various spectral

values. Based on these curves there is a dramatic improvement in the seismic performance of

Building 1, as seen by how far the retrofit curves lie to the right side of the existing building

curve. For example, at Sa = 1g the probability of collapse was reduced from 85% to 35% (FEMA

P807) or 15% (ASCE 41-13 and IEBC A4-12). While the performance is improved from the

existing condition, they retrofits fall short of the 75% code line.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3 3.5 4

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Short Period Spectral Acceleration

Probability of Collapse Curves

75% Code at Sms=1.5

Code at Sms=1.5

32

Figure 8.2 – Building 1 Collapse Fragility Curves

The curves shown on Figure 8.2 identify the probability of collapse, but do not distinguish which

direction or floor caused the structure to collapse. Tables 8.2 and 8.2a identifies the collapse

direction and floor for each of the earthquakes for the retrofitted models (each earthquake is

scaled until it produced collapse). The existing building collapses in the Y-direction of the first

floor for all ground motions (consistent with the SWOF deficiency) and is not included in the

table below. For Building 1, all of the FEMA P807 models failed at the first floor. The ASCE 41-13

and IEBC A4-12 models had more than half of their failures occur in the second floor. These

results suggest the first floor of ASCE 41-13 and IEBC A4-12 retrofits did not reach their full

strength before the second floor failed. Note that the ASCE 41-13 and IEBC A4-12 retrofits do

not take advantage of the Ordinance 66-13 provision that the first story retrofit strength need

not exceed 1.3 times the strength of the second story.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.5 1 1.5 2 2.5 3 3.5 4

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Short Period Spectral Acceleration

Building 1, Collapse Fragility Curves

ASCE 41-13

Existing

FEMA P807

IEBC A4-12

75% Code at Sms=1.5

Code at Sms=1.5

33

Earthquake FEMA P807

Retrofit

ASCE 41-13

Retrofit

IEBC A4-12

Retrofit

1 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

2 1st

Floor (X) 1st

Floor (X) 1st

Floor (X)

3 1st

Floor (Y) 1st

Floor (Y) 2nd

Floor (Y)

4 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

5 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

6 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

7 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

8 1st

Floor (X) 2nd

Floor (Y) 2nd

Floor (Y)

9 1st

Floor (Y) 1st

Floor (X) 2nd

Floor (Y)

10 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

11 1st

Floor (X) 1st

Floor (X) 1st

Floor (X)

12 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

13 1st

Floor (X) 2nd

Floor (Y) 2nd

Floor (Y)

14 1st

Floor (Y) 1st

Floor (Y) 1st

Floor (Y)

15 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

16 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

17 1st

Floor (X) 2nd

Floor (Y) 1st

Floor (X)

18 1st

Floor (X) 1st

Floor (X) 1st

Floor (X)

19 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

20 1st

Floor (Y) 1st

Floor (Y) 1st

Floor (Y)

21 1st

Floor (X) 1st

Floor (X) 2nd

Floor (Y)

22 1st

Floor (Y) 1st

Floor (Y) 1st

Floor (Y)

Table 8.2 – Building 1 Collapse Locations

Failure

Location

FEMA P807

Retrofit

ASCE 41-13

Retrofit

IEBC A4-12

Retrofit

1st

Floor (Y) 15 4 3

1st

Floor (X) 7 5 4

2nd

Floor (Y) 0 13 15

2nd

Floor (X) 0 0 0

Table 8.2a – Building 1 Collapse Summary

The FEMA P807 guidelines have a provision to prevent over-strengthening the ground floor

thereby moving the failure to the second floor. Based on the previous pushover plots, the ASCE

41-13 and IEBC A4-12 retrofits exceeded this maximum first story strength, suggesting that the

second story could be at risk for excessive damage. Based on the SAPwood analysis, this

occurred for several of the ASCE 41-13 and IEBC A4-12 models. It should be noted that some of

the earthquakes did result in a first story failure for the ASCE 14-13 and IEBC A4-12 models. This

suggests that the designs are near the “tipping point” that provides just enough strength to the

first story before pushing failures to the second story.

34

To better understand the strength of the first story without a second story failure a separate set

of retrofit models were analyzed. These additional models added very stiff elements to the

second, third and fourth floor of Building 1. The addition of these elements isolates the

strength of the first stories and will result in collapse fragility curves based on the first story

strength alone (similar to how the retrofits were designed).

Figure 8.3 – Building 1 Collapse Fragility Curves with Rigid Upper Stories

Figure 8.3 shows the collapse fragility curves for the models with rigid upper stories. All of the

models showed an improvement in seismic performance when the upper stories were made

rigid. Part of this increase in strength is due to the reduced effects of P-delta. The upper floors

do not drift relative to the floor below and the negative stiffness spring does not increase

demands on the first story. The other reason for the increased strength lies in the location of

the failure. The original ASCE 31-14 and IEBC A4-12 models for Building 1 had over half of the

earthquakes cause failure in the second level, not allowing the first floor to reach its full

strength. With the second story failure removed, the models showed an increase in strength.

Also note that the ASCE 41-13 and IEBC A4-12 retrofits shifted to the right of the 75% code

curve. When the first floor is taken in isolation of the upper floors it can meet the current

standard for retrofitting existing buildings (75% of current code). For example, at Sa = 1g, the

probability of collapse was reduced from 60% to 15% (FEMA P807) or 4% (ASCE 41-13 and IEBC

A4-12). The 75% code has a 6% probability of collapse.

Table 8.3 compares the retrofits in terms of their median short period spectral acceleration

capacities. The median is the spectral value (at the building’s fundamental period) of the scaled

earthquake suite that results in collapse for 50% of the analysis runs (11 out of 22 earthquake

runs). Comparisons at the median are independent of the beta uncertainty parameter. Retrofits

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

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Short Period Spectral Acceleration

Building 1 (Rigid Upper Stories),

Probability of Collapse Curves

Existing

FEMA P807

ASCE 41-13

IEBC A4-12

75% Code at Sms=1.5

Code at Sms=1.5

35

based on ASCE 41-13 and IEBC A4-12 have similar capacities about 20 to 30% greater than that

for the FEMA P807 retrofit.

Case Collapse in Any

Story Permitted1

Collapse Restricted

to First Story2

Existing As-Built 0.60g 0.88g

FEMA P807 1.18g 1.69g

ASCE 41-13 1.54g 2.08g

IEBC A4-12 1.56g 2.15g

Notes:

Median spectral acceleration is the value that results with 50% of

the scaled earthquake records having collapse. 1Analyses with computer models having the ability to collapse in

any story. 2Analyses with the upper stories modeled as strong and rigid so

that collapse could occur only in the first story.

Table 8.3: Building 1 median short period spectral accelerations for collapse.

Similar to Figure 8.2, Figure 8.4 shows the collapse fragility curves for Building 2. All three

retrofits greatly decreased the probability of collapse. For example at Sa = 1g the probability of

collapse was reduced from 85% to 35% (ASCE 41-13) or 20% (FEMA P807 and IEBC A4-12).

These probabilities are larger than that from 75% code (6%).

Note that, unlike Building 1, Building 2 shows an inverse relationship between push over curve

strength and collapse probability. Figures 7.8 and 7.9 of this report identified the ASCE 41-13

retrofit as having the strongest retrofit as measured by a FEMA P807 pushover curve. The IEBC

A4-12 retrofit was the second strongest, followed by the FEMA P807 retrofit. This order is

reversed on the collapse fragility curves shown in Figure 8.4. The FEMA P807 retrofit has then

best performance of the three retrofits, followed by IEBC A4-12 and ASCE 41-13.

36

Figure 8.4 – Building 2 Collapse Fragility Curves

The reason for this inverse relationship between the push over curve and the collapse

probability plot can be found in the location of the building failure. For Building 2, the FEMA

P807 retrofit collapse mechanism is in the first story. For the ASCE 41-13 and IEBC A4-12

retrofits the second story failed before the first story could reach its peak strength. The collapse

locations are noted in Table 8.4 and 8.4a below. The results support the FEMA P807 philosophy

that over strengthening the first floor could negatively impact the overall building performance.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.5 1 1.5 2 2.5 3 3.5 4

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Short Period Spectral Acceleration

Building 2 Collapse Fragility Curves

ASCE 41-13

Existing

FEMA P807

IEBC A4-12

75% Code at Sms=1.5

Code at Sms=1.5

37

Earthquake FEMA P807

Retrofit

ASCE 41-13

Retrofit

IEBC A4-12

Retrofit

1 1st

Floor (Y) 2nd

Floor (X) 2nd

Floor (X)

2 1st

Floor (X) 2nd

Floor (X) 2nd

Floor (X)

3 1st

Floor (Y) 2nd

Floor (Y) 1st

Floor (Y)

4 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

5 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

6 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

7 1st

Floor (X) 2nd

Floor (Y) 2nd

Floor (Y)

8 1st

Floor (X) 2nd

Floor (X) 2nd

Floor (X)

9 1st

Floor (Y) 2nd

Floor (X) 2nd

Floor (Y)

10 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

11 1st

Floor (X) 2nd

Floor (X) 2nd

Floor (X)

12 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

13 1st

Floor (X) 2nd

Floor (Y) 2nd

Floor (Y)

14 1st

Floor (Y) 2nd

Floor (Y) 1st

Floor (Y)

15 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

16 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

17 1st

Floor (X) 2nd

Floor (X) 2nd

Floor (X)

18 1st

Floor (X) 2nd

Floor (X) 2nd

Floor (X)

19 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (Y)

20 1st

Floor (Y) 2nd

Floor (Y) 1st

Floor (Y)

21 1st

Floor (X) 2nd

Floor (X) 2nd

Floor (X)

22 1st

Floor (Y) 2nd

Floor (Y) 2nd

Floor (X)

Table 8.4 – Building 2 Collapse Locations

Failure

Location

FEMA P807

Retrofit

ASCE 41-13

Retrofit

IEBC A4-12

Retrofit

1st

Floor (Y) 14 0 3

1st

Floor (X) 8 0 0

2nd

Floor (Y) 0 14 11

2nd

Floor (X) 0 8 8

Table 8.4a – Building 2 Collapse Summary

Similar to Building 1, a second set of models are analyzed with rigid elements in the upper

stories. This will isolate the effects of the over strengthening that occurred in the ASCE 41-13

and IEBC A4-12 retrofits. See figure 8.4 for the collapse fragility curves generated by the second

set of models with rigid upper stories.

38

Figure 8.4 – Building 2 Collapse Fragility Curves with Rigid Upper Stories

When the second floor failures are removed from the possible failure mechanisms the results

become similar to that of Building 1. The best seismic performance comes from ASCE 41-13,

followed by IEBC A4-12 and FEMA P807. This pattern is consistent with the push-over curves

noted earlier in the report (Figures 7.8 and 7.9). Interestingly, once the second floor is removed

from the equation, all three retrofits essentially meet or exceed the 75% code curve that was

developed to represent the standard practice for retrofitting existing structures.

Table 8.5 compares the retrofits in terms of their median short period spectral acceleration

capacities. When collapse is permitted in any story, FEMA P807 has the largest capacity that is

about 10 to 25% greater than those from ASCE 41-13 and IEBC A4-12. However, when collapse

is restricted to the first story, the trend is reversed with ASCE 41-13 and IEBC A4-12 having

capacities that are about 10 to 25% greater than that for FEMA P807. This reversal is due to

collapses occurring in the upper stories for the ASCE 41-13 and IEBC A4-12 retrofits.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Pro

ba

bil

ity

of

Co

lla

pse

Short Period Spectral Acceleration

Building 2 (Rigid Upper Stories),

Collapse Fragility Curves

Existing

FEMA P807

ASCE 41-13

IEBC A4-12

75% Code at Sms=1.5

Code at Sms=1.5

39

Case Collapse in Any

Story Permitted1

Collapse Restricted

to First Story2

Existing As-Built 0.61g 0.76g

FEMA P807 1.45g 1.83g

ASCE 41-13 1.16g 2.30g

IEBC A4-12 1.36g 2.06g

Notes:

Median spectral acceleration is the value that results with 50% of

the scaled earthquake records having collapse. 1Analyses with computer models having the ability to collapse in

any story. 2Analyses with the upper stories modeled as strong and rigid so

that collapse could occur only in the first story.

Table 8.5: Building 2 median short period spectral accelerations for collapse.

IDA Discussions

The fragility curves showed that the seismic performance of each retrofit varied between the

two buildings. For Building 1, the results of the collapse fragility curve are similar to the FEMA

P807 pushover curves where the IEBC A4-12 retrofit had the largest first story strength

followed by ASCE 41-13 and FEMA P807. Building 2, on the other hand, showed an inverse

relationship between the pushover curve strength and seismic performance (as measured by

the collapse fragility curves). For Building 2 the FEMA P807 retrofit had the best seismic

performance, while having the lowest strength as measured by the pushover curve. The cause

of this relationship is related to the collapse mechanism of the building.

Looking at the Building 2 ASCE 41 and IEBC A4 retrofits, the majority of the collapses occurred

in the second floor of the building. This is due to the strength and ductility of the upper stories

relative to those for the first story. Progressively increasing the strength and ductility of the first

story eventually results with the second story becoming the weak link in the building. When this

occurs, collapse in the upper story happens before the first story reaches its full retrofit

strength. This concept of over strengthening the first floor and increasing damage in the second

floor is part of the FEMA P807 methodology.

To better understand this phenomenon, a second set of models analyzed in SAPwood that

isolated the first story of each retrofit by adding rigid elements to the upper floors. This

eliminated the chance of a second story failure that was observed in the ASCE 41-13 and IEBC

A4-12 retrofits for Building 2. Once the upper story failure modes were removed, the seismic

performance of the ASCE 41-13 and IEBC A4-12 Building 2 retrofits significantly improved and

surpassed the performance of the FEMA P807 retrofit.

It is not clear that having a restriction on over-strengthening the first story is an appropriate

design consideration. The value of this restriction depends on how accurate the actual

40

capacities (strength and ductility) of the first and second stories can be calculated. Currently,

there is no industry consensus on the backbone curves for many of the materials found in

wood-frame buildings, and this is especially true for the older non-conforming material types

(e.g., lath-and-plaster partitions) that dominate the upper stories in the case study buildings.

ASCE 41-13, SAPwood and P807 all prescribe backbone curves that can differ significantly. It is

relevant to note that FEMA P807 admits that their backbone curves for their low-displacement

capacity materials (e.g., lath-and-plaster partitions) are difficult to imagine as reflecting reality,

and that more testing is needed (P-807 Section E.2.4). Should the upper story strength be

underestimated thereby placing an artificial limit on the first story retrofit strength, then the

overall seismic safety of the building is compromised (versus a retrofit not having an over-

strengthening restriction).

To illustrate the above conundrum, consider the median spectral accelerations for Building 2

(Table 8.6). A first story “over-strengthening restriction” might limit the upgrade to the values

in column (a) of Table 8.6 since the second story is perceived to be the weak link. However, if

the actual upper story strength was underestimated, then it is possible the first story could be

retrofitted so that the values in column (b) apply. The over-strengthening restriction could

result in a retrofitted building having about one-half the capacity when comparing columns (a)

and (b). The trade-off involves the possible savings in retrofit cost offered by having an over-

strengthening restriction versus the possible increased collapse risk by limiting the first story

upgrade.

Case (a) Collapse in Any

Story Permitted

(b) Collapse Restricted

to First Story

(a) divided by (b)

ASCE 41-13 1.16g 2.30g 0.50

IEBC A4-12 1.36g 2.06g 0.66

Table 8.6: Building 2 median short period spectral accelerations for collapse (from Table 8.5).

It is the authors’ experience that there are few instances of upper story failures occurring in

actual earthquakes, and this is especially true for wood-frame buildings. Prediction of upper

story collapse is highly dependent on the modeling assumptions and material strength

properties. There is not a clear consensus on which material strength curves are “correct” and

properties vary between different guidelines. Note that the material strengths used in the

analysis are based on the FEMA P807 material properties (but has more ductility assigned, see

Appendix A).

Overall, the fragility curves for the various retrofits fell short of 75% of code level. Based on the

material strengths from FEMA P807 with modified ductility and the buildings chosen for this

project it appears that 75% code cannot be achieved by a first story only retrofit. When more

retrofit elements are added to the first story for Building 2 (as illustrated by going from a P807

retrofit to the ASCE 41-13 retrofit), collapse risk is not reduced. The second floor is driving the

collapse of the building. It should be noted that the collapse risk for both buildings were

dramatically reduced, even if they fell short of the 75% of code retrofit standard for existing

buildings.

41

9. CONCLUSION

San Francisco’s mandatory retrofit ordinance allows use of different approaches for retrofit

design that includes ASCE 41-13, IEBC A4-12, and FEMA P807. It should be noted that other

performance objectives do exist that go beyond those specified in the ordinance.

Based on the assumptions made in this project, ASCE 41-13 required the most extensive

retrofit, followed by IEBC A4-12 and FEMA P807. IEBC A4-12 and ASCE 41-13 have additional

provisions related to building drift and analysis limitations that need to be satisfied and these

can result with additional strengthening in the first floor. However, even without these

additional criteria, the retrofits satisfying ASCE 41-13 and IEBC A4-12 guidelines were still more

extensive than those based on FEMA P807.

Results from the SAPwood incremental dynamic analysis (IDA) for the collapse performance of

the two buildings were mixed. Building 1 showed that the ASCE 41-13 retrofit recorded the

largest first story push over strength and had the best seismic performance. Building 2 showed

that the ASCE 41-13 retrofit recorded the largest first story push over curve strength, but had

the least favorable IDA performance of the three retrofits. This resulted from the second story

of Building 2 collapsing before the first story can reach its peak retrofit strength. Once the

second floor was removed as a possible failure mechanism, the ASCE 41-13 retrofit for Building

2 outperformed the other two retrofits (IEBC A4-12 and FEMA P807) in IDA. More thought

should be given to the appropriateness of the FEMA P807 concept that limits the first story

retrofit depending on the calculated capacity of the upper stories since this has great

uncertainty due to industry current lack of knowledge. Further studies should be performed to

validate the FEMA P807 philosophy that over strengthening the first floor can decrease seismic

performance and if certain building layouts/sizes are more susceptible to this phenomenon.

Based on FEMA P807 material assumptions, the SAPwood results of the two sample buildings

suggest a first story retrofit will likely not be able to reach the 75% of current code standard for

existing building retrofits. When additional strength was added to the ASCE 41-13 and IEBC A4-

12 retrofits for Building 2 (without strengthening the upper floors), a second story collapse

mechanism occurred and reduced the overall seismic performance of the building. While falling

short of the 75% current code fragility curve, all of the retrofits greatly reduced the collapse risk

of the buildings. Note that these results are based on the material strength curves provided by

FEMA P807. Other guidelines (ASCE 41-13 and IEBC A4-12) have different assumptions for

material strength, as noted in section 4, and could produce different results.

It is challenging to compare the performance of each of the retrofits, because it is dependent

on the analysis assumptions. The building code allows the use of four different analyses (linear

static, linear dynamic, non-linear static, and non-linear dynamic). Each of these options will

produce different designs that all meet the performance objective of the code. Likewise the

three guidelines used in this study produced different retrofits based on different assumptions.

ASCE 41-13 is intended to cover all building types, ages, and materials. It is a comprehensive

tool to be used for first floor retrofits of wood frame buildings and it is not surprising that it

42

appears to be the most conservative of the three. FEMA P807, on the other hand, is a very

specific tool that was developed to target a small subset of the housing stock. It is not surprising

that these documents produced different results.

It is important to recognize that the retrofits and associated conclusions made in this study are

highly dependent on the analysis and design assumptions. Regarding analysis modeling, there is

currently no consensus on the load-drift (backbone) curves for many of the materials found in

wood-frame buildings. P807 and ASCE 41-13 prescribe backbone curves that differ significantly,

and a recent review indicates all of these might be conservative (see footnote 2 on page 5 for

discussion). Regarding design aspects, if the IEBC A4-12 Building 1 retrofit used WSP with

10d@2” O.C., instead of 10d@4” O.C., then drift might not have controlled the design. Also,

fixing the base of the moment frame could sufficiently stiffen the ground floor and require a

flexible diaphragm assumption. Using a special versus an ordinary moment frame will also

impact the design loads depending on which guideline is used. Varying the retrofit elements,

analysis assumptions, and location of retrofit elements could change the results presented in

this study. Note that other parts of the building load path not checked in this study

(diaphragms, connections, hold downs, and foundations) could significantly impact the results

of the study.

This study is intended to help provide a basis by which the engineer can judge which guideline

would best suit their client’s goals. The authors trust this study can be used to better

understand the different guidelines and select the one that best suits the client’s needs.

43

Appendix A – SAPwood Material Backbone Curves

The following figures are provided to illustrate the material curve assumptions made for the

SAPwood IDA analyses. The curves used for the SAPwood analyses are based on the FEMA P807

curves. FEMA P807’s assumption of zero residual strength at 1.25% and 5% drift for non-ductile

and ductile materials respectively is very conservative. Additional ductility was added to each

material based on the judgment of the authors (however, these still may be conservative, see

footnote 2 on page 5 for discussion).

Figure A.1 – Single layer of 10d@4” O.C.

-30000

-20000

-10000

0

10000

20000

30000

-10 -5 0 5 10

Str

en

gth

(lb

s)

% Drift

(1) 10d@4" Plywood Wall

Hysteresis Loop

SAPwood Curve

P807 curve

44

Figure A.2 – Double layer of 10d@4” O.C.

Figure A.3 – One Layer of Wood Lathe on Plaster, One layer of Horizontal Sheathing

-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

-10 -5 0 5 10

Str

en

gth

(lb

s)

% Drift

(2) 10d@4" Plywood Wall

Hysteresis Loop

SAPwood Curve

P807 curve

-10000

-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

10000

-10 -5 0 5 10

Str

en

gth

(lb

s)

% Drift

(1) wood lath (1) horz. sheathing

Sample Hysteresis Loop

SAPwood Curve

P807 curve

45

Figure A.4 – Two Layers of Wood Lathe of Plaster

Figure A.5 – Steel Moment Frame

-80000

-60000

-40000

-20000

0

20000

40000

60000

80000

-10 -5 0 5 10

Str

en

gth

(lb

s)

% Drift

(2) wood lath

Sample Hysteresis Loop

SAPwood Curve

P807 curve

-150000

-100000

-50000

0

50000

100000

150000

-10 -5 0 5 10

Str

en

gth

(lb

s)

% Drift

Moment Frame

Sample Hysteresis Loop

SAPwood Curve

46

Appendix B – SAPwood Pushover Curves

The following figures show the first story pushover curves produced from the SAPwood models.

The loading pattern monotonically displaced the second floor of each building to a 7% drift. The

loading protocol was applied to each direction independently. The SAPwood curve includes P-

delta. For simplicity an average overturning factor was used for the wall input into SAPwood, as

opposed to having an individual factor for each wall. This averaging, in tandem with the added

P-delta effects, creates small discrepancies between the two curves. A single averaged

overturning factor is used across the different retrofits for each building in both directions. The

resulting discrepancy occurs across the different retrofits. For example, building 1 in the X-

direction shows the P807 curve slightly higher for all four models. The P807 pushover curves

from part 2 of the project are also included for reference.

Figure B.1 – Building One No Retrofit (Y-Direction) Pushover Curves

-50000

-40000

-30000

-20000

-10000

0

10000

20000

30000

40000

50000

60000

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B1 (E) - Pushover Curve (Y-Dir)

SAP wood

P807 (E Bldg)

47

Figure B.2 – Building One No Retrofit (X-Direction) Pushover Curves

-50000

0

50000

100000

150000

200000

250000

300000

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B1 (E) - Pushover Curve (X-Dir)

SAP wood

P807 (E Bldg)

48

Figure B.3 – Building One FEMA P807 Retrofit (Y-Direction) Pushover Curves

Figure B.4 – Building One FEMA P807 Retrofit (X-Direction) Pushover Curves

0

20000

40000

60000

80000

100000

120000

0.0 2.0 4.0 6.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B1 (P807) - Pushover Curve (Y-Dir)

SAP wood

P807 (P807 Retrofit)

-100000

-50000

0

50000

100000

150000

200000

250000

300000

0.0 2.0 4.0 6.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B1 (P807) - Pushover Curve (X-Dir)

SAP wood

P807 (P807 Retrofit)

49

Figure B.5 – Building One ASCE 41-13 Retrofit (Y-Direction) Pushover Curves

Figure B.6 – Building One ASCE 41-13 Retrofit (X-Direction) Pushover Curves

0

50000

100000

150000

200000

250000

300000

0.0 2.0 4.0 6.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B1 (ASCE 41) - Pushover Curve (Y-Dir)

SAP wood

P807 (ASCE 41 Retrofit)

-50000

0

50000

100000

150000

200000

250000

300000

350000

0.0 2.0 4.0 6.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B1 (ASCE 41) - Pushover Curve (X-Dir)

SAP wood

P807 (ASCE 41 Retrofit)

50

Figure B.7 – Building One IEBC A4-12 Retrofit (Y-Direction) Pushover Curves

Figure B.8 – Building One IEBC A4-12 Retrofit (X-Direction) Pushover Curves

0

50000

100000

150000

200000

250000

300000

350000

0.0 2.0 4.0 6.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B1 (IEBC A4) - Pushover Curve (Y-Dir)

SAP wood

P807 (IEBC A4 Retrofit)

-50000

0

50000

100000

150000

200000

250000

300000

350000

400000

0.0 2.0 4.0 6.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B1 (IEBC A4) - Pushover Curve (X-Dir)

SAP wood

P807 (IEBC A4 Retrofit)

51

Figure B.9 – Building Two No Retrofit (Y-Direction) Pushover Curves

Figure B.10 – Building Two No Retrofit (X-Direction) Pushover Curves

-100000

-50000

0

50000

100000

150000

200000

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B2 (E) - Pushover Curve (Y-Dir)

SAP wood

P807 (E Bldg)

-60000

-40000

-20000

0

20000

40000

60000

80000

100000

120000

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B2 (E) - Pushover Curve (X-Dir)

SAP wood

P807 (E Bldg)

52

Figure B.11 – Building Two FEMA P807 Retrofit (Y-Direction) Pushover Curves

Figure B.12 – Building Two FEMA P807 Retrofit (X-Direction) Pushover Curves

0

50000

100000

150000

200000

250000

300000

0.0 2.0 4.0 6.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B2 (P807) - Pushover Curve (Y-Dir)

SAP wood

P807 (P807 Retrofit)

0

50000

100000

150000

200000

250000

0.0 2.0 4.0 6.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B2 (P807) - Pushover Curve (X-Dir)

SAP wood

P807 (P807 Retrofit)

53

Figure B.13 – Building Two ASCE 41-13 Retrofit (Y-Direction) Pushover Curves

Figure B.14 – Building Two ASCE 41-13 Retrofit (X-Direction) Pushover Curves

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

500000

0.0 2.0 4.0 6.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B2 (ASCE 41) - Pushover Curve (Y-Dir)

SAP wood

P807 (ASCE 41 Retrofit)

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

500000

0.0 2.0 4.0 6.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B2 (ASCE 41) - Pushover Curve (X-Dir)

SAP wood

P807 (ASCE 41 Retrofit)

54

Figure B.15 – Building Two IEBC A4-12 Retrofit (Y-Direction) Pushover Curves

Figure A.16 – Building Two IEBC A4-12 Retrofit (X-Direction) Pushover Curves

0

50000

100000

150000

200000

250000

300000

350000

0.0 2.0 4.0 6.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B2 (IEBC A4) - Pushover Curve (Y-Dir)

SAP wood

P807 (IEBC A4 Retrofit)

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

0.0 2.0 4.0 6.0 8.0

Sto

ry S

he

ar

(lb

s)

Building Drift (%H)

B2 (IEBC A4) - Pushover Curve (X-Dir)

SAP wood

P807 (IEBC A4 Retrofit)