SEISMIC UPGRADE OF AN EXISTING MASONRY BUILDING
A Project
Presented to the faculty of the Department of Civil Engineering
California State University, Sacramento
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
Civil Engineering
(Structural Engineering)
by
Joshua Johannes Plenert
SPRING
2014
© 2014
Joshua Johannes Plenert
ALL RIGHTS RESERVED
ii
SEISMIC UPGRADE OF AN EXISTING MASONRY BUILDING
A Project
by
Joshua Johannes Plenert
Approved by:
__________________________________, Committee Chair
Benjamin Fell, Ph.D., P.E.
____________________________
Date
iii
Student: Joshua Johannes Plenert
I certify that this student has met the requirements for format contained in the University format
manual, and that this project is suitable for shelving in the Library and credit is to be awarded for
the project.
________________________________, Graduate Coordinator ________________
Matthew Salveson, P.E.
Date
Department of Civil Engineering
iv
Abstract
of
SEISMIC UPGRADE OF AN EXISTING MASONRY BUILDING
by
Joshua Johannes Plenert
This report proposes a seismic retrofit strategy of a 1-story existing building with
reinforced masonry walls and a flexible wood diaphragm. Significant structural
deficiencies are identified from procedures described in ASCE 31 (2003) and include
diaphragm to shear wall connections, collector element, and out-of-plane anchorage for
the masonry shear walls. Equivalent lateral seismic loads are applied to the structure such
that all critical load paths are designed and detailed for a base shear using a seismic
response coefficient, R = 3.5, and an importance factor, I = 1.25. Capacity design and
retrofit checks followed procedures details in ASCE 7-10 and ASCE 41. Considering the
seismic deficiencies this structure has, the retrofit strategy and proposed details could be
applicable to a plethora of reinforced masonry structures in high, or moderate, seismic
regions.
_______________________, Committee Chair
Benjamin Fell, Ph.D., P.E.
_______________________
Date
v
TABLE OF CONTENTS
Page
List of Tables ........................................................................................................................ viii
List of Figures ........................................................................................................................... x
Chapter
1. INTRODUCTION ............................................................................................................... 1
1.1 Motivation.............................................................................................................. 1
1.2 Objective and Scope .............................................................................................. 3
1.3 Organization and Outline ....................................................................................... 5
2. STRUCTURAL OVERVIEW AND DESCRIPTIVE EVALUATION ............................. 6
2.1 Lateral Load Resisting Systems .............................................................................. 6
2.2 Site Hazards and Design Requirements ................................................................. 9
2.3 Identified Deficiencies ......................................................................................... 12
3. FLEXIBLE WOOD DIAPHRAGM AND ASSOCIATED COMPONENTS.................. 16
3.1 Diaphragm Shear Forces ...................................................................................... 17
3.2 Tensile Capacity of Diaphragm Chords ............................................................... 21
3.3 Tensile Capacity of Continuous Cross Ties ........................................................ 25
4. DIAPHRAGM TO SHEAR WALL LOAD TRANSFER ELEMENTS .......................... 29
4.1 Out-of-plane Force Resisting Elements ................................................................ 29
4.2 In-plane Force Resisting Elements ...................................................................... 34
4.3 Masonry Shear Wall Capacities ........................................................................... 36
5. SPECIAL CONDITIONS .................................................................................................. 41
5.1 Special Condition 1 .............................................................................................. 41
5.2 Special Condition 2 .............................................................................................. 43
vi
6. SUMMARY ....................................................................................................................... 45
Appendix................................................................................................................................. 46
References ............................................................................................................................... 67
vii
LIST OF TABLES
Page
Table 2.1
Structural Components at High Roof Areas ..................................................... 8
Table 2.2
Structural Components at Low Roof Areas ...................................................... 8
Table 2.3
Soils Information at Site under Consideration ................................................ 10
Table 2.4
Seismic Hazard Information ........................................................................... 11
Table 2.5
Windstorm Characterization ........................................................................... 12
Table 2.6
Identified Deficiencies Illustrated in Figure 2.5 ............................................. 15
Table 3.1
Diaphragm Seismic Demands, As-built Capacity and Retrofit Strategy ........ 20
Table 3.2
Chord Retrofit Strategies Identified in Figure 3.7 .......................................... 24
Table 4.1
Summary of Out-of-plane Anchorage Retrofit Strategy ................................. 32
Table 4.2
Summary of Shear Wall Stresses .................................................................... 39
Table A.1
Base Shear Summary ...................................................................................... 47
Table A.2
Diaphragm Shear Summary ............................................................................ 48
Table A.3
Chord Forces ................................................................................................... 49
Table A.4
Box A: Flexible Diaphragm Seismic Forces .................................................. 50
Table A.5
Box B: Flexible Diaphragm Seismic Forces ................................................... 51
Table A.6
Box C: Flexible Diaphragm Seismic Forces ................................................... 52
Table A.7
Box D: Flexible Diaphragm Seismic Forces .................................................. 53
Table A.8
Box E: Flexible Diaphragm Seismic Forces ................................................... 54
Table A.9
Box F: Flexible Diaphragm Seismic Forces ................................................... 55
Table A.10
Box G: Flexible Diaphragm Seismic Forces .................................................. 56
Table A.11
Box H: Flexible Diaphragm Seismic Forces .................................................. 57
viii
Table A.12
Box I: Flexible Diaphragm Seismic Forces .................................................... 58
Table A.13
Box J: Flexible Diaphragm Seismic Forces .................................................... 59
Table A.14
Box K: Flexible Diaphragm Seismic Forces .................................................. 60
Table A.15
Box L: Flexible Diaphragm Seismic Forces ................................................... 61
Table A.16
Box M: Flexible Diaphragm Seismic Forces .................................................. 62
Table A.17
Box N: Flexible Diaphragm Seismic Forces .................................................. 63
Table A.18
Box O: Flexible Diaphragm Seismic Forces .................................................. 64
Table A.19
Special Condition 1 RISA Results .................................................................. 66
ix
LIST OF FIGURES
Page
Figure 2.1
Three-dimensional Schematic View of Religious Meetinghouse in
Fremont, CA ..................................................................................................... 6
Figure 2.2
Architectural Floor Plan.................................................................................... 7
Figure 2.3
Architectural Roof Plan .................................................................................... 7
Figure 2.4
Re-entrant Corner Failure ............................................................................... 14
Figure 2.5
Locations of Deficiencies Listed in Table 2.6 ................................................ 15
Figure 3.1
Free Body Diagram of Forces Acting on Diaphragm and Diaphragm
Components .................................................................................................... 16
Figure 3.2
Layout Box and Grid Line Assignments for Diaphragm Analysis ................. 17
Figure 3.3
Diaphragm Seismic Upgrade Illustrating Deficient Areas Retrofitted with
Blocking or Plywood Sheathing ..................................................................... 20
Figure 3.4
Chord Force Illustration .................................................................................. 21
Figure 3.5
Chord Failure .................................................................................................. 22
Figure 3.6
Chord Retrofit Strategy ................................................................................... 23
Figure 3.7
Location of Chord Discontinuities Summarized in Table 3.2 ........................ 25
Figure 3.8
Cross Ties Example ........................................................................................ 26
Figure 3.9
Detail of Continuous Cross Tie Retrofit Strategy ........................................... 27
Figure 3.10
Plan Showing Low Roof Continuous Cross Tie and Chord Reinforcement
Locations......................................................................................................... 28
Figure 3.11
Plan Showing High Roof Continuous Cross Tie and Chord Reinforcement
Locations......................................................................................................... 28
x
Figure 4.1
Out-of-plane Anchorage Failure ..................................................................... 29
Figure 4.2
Results of Out-of-plane Pushover Analysis on Masonry Wall ....................... 30
Figure 4.3
Layout of Walls and Associated Seismic Weights ......................................... 31
Figure 4.4
Detail of Out-of-plane Anchorage Retrofit Strategy at Face of Perpendicular
Masonry Wall ................................................................................................. 32
Figure 4.5
Detail of Out-of-plane Anchorage Retrofit Strategy at Face of Parallel
Masonry Wall ................................................................................................. 33
Figure 4.6
Detail of Out-of-plane Anchorage Retrofit Strategy at top of Parallel CMU
Partition........................................................................................................... 33
Figure 4.7
Detail of Out-of-plane Anchorage Retrofit Strategy at top of Perpendicular
CMU Partition ................................................................................................ 34
Figure 4.8
Detail of In-plane and Out-of-plane Anchorage Retrofit Strategy at Joists .... 35
Figure 4.9
Detail of In-plane and Out-of-plane Anchorage Retrofit Strategy at Truss .... 36
Figure 4.10
Results of In-plane Pushover Analysis of Masonry Wall ............................... 37
Figure 4.11
Plan Identifying Shear Walls and Associated Weights and Equivalent
Thicknesses ..................................................................................................... 38
Figure 4.12
Discontinuous Shear Wall Upgrade Detail ..................................................... 40
Figure 5.1
Plan Showing Locations of Special Conditions .............................................. 41
Figure 5.2
Detail of Special Condition 1 Retrofit Strategy at Failed Connection ............ 43
Figure 5.3
Detail of Special Condition 1 Retrofit Strategy at Un-failed Connection ...... 43
Figure 5.4
Detail of Special Condition 2 Retrofit Strategy .............................................. 44
Figure A.1
Special Condition 1 RISA Results .................................................................. 65
xi
1
CHAPTER 1
INTRODUCTION
1.1
Motivation
Earthquakes pose a major threat to structures, human life, and economies in major urban
centers worldwide. According to the USGS 2009 Earthquake Probability Mapping tool, the Bay
Area of California has a 60-90% probability of experiencing an earthquake with a magnitude of
6.5 on the Richter scale within the next 50 years. On May 2, 1983, a magnitude 6.5 earthquake
occurred approximately 9 miles north-northeast of the City of Coalinga, CA. The next day a
damage survey team from the Earthquake Engineering Research Institute (EERI) arrived on-site
to perform a visual survey of the main commercial district of downtown Coalinga.
Approximately 20% of the 139 damaged buildings surveyed were reinforced masonry buildings
similar to the building analyzed in this report. The majority of the failures observed were out-ofplane failures, many of which occurred at connections from the walls to the roof. The EERI
reconnaissance team made the following sobering observation in the survey referenced at the end
of this report. “Coalinga is typical of many older California communities. One can find similar
construction material and structural types throughout the length of the state. What we saw in
Coalinga could happen in any older California community." The EERI reconnaissance team also
emphasized the importance of identifying potential failure modes in stating “the emphasis is not
on whether the construction is poor or not, but rather on knowing the kind of damage that can
occur” (Shah, 1983).
Analysis and design practices for earthquake engineering are continuously evolving as
our understanding of structural responses to seismic forces and the ability to predict seismic
forces improves. However, many of the older structures built in California were not adequately
2
built to resist seismic forces. For example, with the introduction of ASCE 7 (2010), seismic
design loads changed considerably from the previously used loads specified in ASCE 7 (2005).
The seismic design maps used to determine a risk-target maximum considered earthquake
(MCER) contained in Chapter 22 of ASCE 7 (2010), have replaced older maps in order to
incorporate four major advances in our understanding of seismic events. First, the new maps
incorporate current USGS source zone models, which have been improved using Next Generation
Attenuation (NGA) relationships. Second, uniform-hazard ground motion was replaced with a
risk-targeted ground motion in order to take into account site-to-site variability in the shape of
ground motion hazard curves (Luco, 2007). Third, a switch from “geo-mean” ground motions
(the mean ground motions of any two orthogonal directions) to maximum direction ground
motions has resulted in a 10% increase in short period ground motion and a 30% increase in longterm ground motion based on work by Whittaker (2014). Fourth, 84th percentile ground motions
(which is 180% of median ground motions) have replaced 150% ground motions. These changes
have resulted in lower short-period ground motions in areas of low seismicity and higher shortperiod ground motions in areas of high seismicity, thus allowing for design parameters to be less
uniform and more site specific.
Older reinforced masonry buildings have common deficiencies, the most common of
which is the out-of-plane anchorage from the roof system to the masonry walls. A typical
connection detail is a toenail between the joist or truss and a wood plate secured to the top of
masonry walls. Considering an approximate pull-out force of 55 lbs/nail which was calculated
using Table 11.2C and Section 11.5.4 of AWC (2012), this type of connection is not able to
ensure a positive connection between the diaphragm and shear wall. Considering that out-ofplane forces caused by large seismic events can be on the order of 0.12-0.56 kips for a lateral load
resisting system comprised of heavy partially grouted masonry walls, it is critical to design a
3
positive connection with adequate capacity to prevent out-of-plane failure between the joists or
trusses and the masonry shear wall. In-plane considerations for the masonry shear walls are also
important to consider as many older masonry structures have insufficient reinforcement, relative
to current seismic provisions. Without proper reinforcement, the shear walls will experience
significant diagonal shear failures at window and door openings. Unreinforced masonry (URM)
structures are common in older communities and pose a significant risk of collapse, due to their
inability to dissipate lateral seismic forces through large inelastic deformations the way a properly
reinforced masonry structure can (Bruneau, 1992).
This report will provide in-depth analyses and design procedures to propose retrofit
strategies for an existing masonry structure, which can be applicable to a wide-variety of masonry
structures in California.
Special attention is allotted to the out-of-plane anchorage issue
(discussed previously), diaphragm load path connections and the design of collector elements.
1.2
Objectives and Scope
The objective of this report is to provide a detailed explanation of the evaluation and
analysis of an existing masonry building and the procedures used to design upgrades to identified
structural deficiencies. The analyses and upgrade designs presented herein focus on elements of
the masonry structure that are common to many masonry buildings throughout California. The
procedures described in this report are intended to act as an example of common practices used in
the evaluation of existing masonry buildings.
A seismic evaluation of an existing building begins with a “Screening Phase” as
explained in Chapters 2 and 3 of ASCE 31 (2003). The screening phase begins with a review of
any available as-built drawings followed by a site visit intended to verify existing data, collect
additional data, and asses the general condition of the building. Checklists prescribed by ASCE
4
31 (2003), Table 3-2, assist in the identification of potential deficiencies. Necessary checklists
are identified based on the desired level of performance, the level of seismicity, and the building
type. The specific checklists used in this report are discussed in Section 2.3 of this report.
The desired level of performance will determine seismic demand as a percentage of the
Maximum Considered Earthquake (MCE) and is determined by the building owner in
consultation with the design professional and the local authority having jurisdiction. Typical
levels of performance used in the evaluation of existing buildings include Life Safety (LS) and
Immediate Occupancy (IO), both of which are defined in detail in Section 1.5 of FEMA (2000).
The performance level used in the evaluation of the building discussed in this report is defined in
Section 2.1 of this report. The level of seismicity is based on mapped response acceleration
values and site amplification factors, which are discussed in detail in Section 2.2 of this report.
The building type is based on the lateral-force-resisting system and the diaphragm type as defined
by Table 2-2 of ASCE 31-03. The building type for the evaluation presented in this report is
discussed in detail in Section 2.1 of this report.
Once potential deficiencies have been identified, further analysis is performed during
an “Evaluation Phase” as described in Chapter 4 of ASCE 31-03.
The analysis includes
calculating lateral forces to be distributed to lateral force resisting systems, calculating diaphragm
forces, and calculating forces in individual components of the lateral force resisting system. For
this building the diaphragm, the load path, and two special conditions are analyzed.
The diaphragm is analyzed for shear capacity and diaphragm components, which include
chords and ties, are analyzed for tensile capacity.
The load path is analyzed to determine forces
acting on out-of-plane connecting elements as well as in-plane connecting elements and shear
walls. Two special conditions are analyzed at locations that were identified as deficiencies but
are not typical.
5
1.3
Organization and Outline
Chapter 2 contains a description of the structure including identification of relevant
structural systems. Drawings of the structure were prepared based on as-built information. Onsite observations are presented in this chapter along with a discussion of relevant structural
information, such as shear walls and diaphragms.
Site hazards, design requirements, and
identified deficiencies are also discussed.
Chapter 3 presents the seismic retrofit approach and applicable analyses on the
diaphragm including the diaphragm shear capacities, chord (collector) capacities, and continuous
cross-tie capacities. Detailed drawings of possible upgrade measures at typical locations are
presented.
Chapter 4 presents the approach and results of an analysis of the load path from the
diaphragm to the foundation. The load path analysis considers the capacities of out-of-plane
lateral force resisting elements, in-plane lateral force resisting elements, and shear walls.
Detailed drawings of recommended seismic upgrades are presented and discussed.
Chapter 5 presents the approach and results of an analysis of atypical conditions
identified as potential deficiencies. The first special condition was a drag element constructed of
a steel wide flange girder. The second special condition analyzed was a location where trusses
are resting soley on a ledger, rather than the masonry shear wall.
Detailed drawings of
recommended seismic upgrades are presented and discussed to mitigate these atypical conditions.
6
CHAPTER 2
STRUCTURAL OVERVIEW AND DESCRIPTIVE EVALUATION
The structure evaluated in this report is a religious meetinghouse located in Fremont, CA.
The building is approximately 21,000 square feet and constructed primarily of reinforced,
partially grouted Concrete Masonry Units (CMU) with a flexible wood diaphragm. Built in 1956,
the structure has had two major additions in the years 1961 and 1969. The structure is primarily
one story, but does have a small section of second story over the foyer area. Figure 2.1 illustrates
a three-dimensional view of the building created from as-built plans and on-site observations.
Figure 2.1: Three-dimensional Schematic View of Religious Meetinghouse in Fremont, CA
2.1
Lateral Load Resisting System
Archive drawings of the original construction and site visits were used to obtain an
accurate evaluation of the building and its load resisting systems (vertical and lateral). The tables
and figures presented in this subsection provide some of the information acquired. Figure 2.2
illustrates a floor plan of the structure. Understanding the wall layout including door and window
locations is critical for determining seismic weights and load path, which are discussed in the
later chapters.
7
Figure 2.2: Architectural Floor Plan
Figure 2.3 illustrates the roof plan of the building. The high roof areas are identified with
darker lines in order distinguish between the high roof diaphragm and the low roof diaphragm
which are not continuous.
Figure 2.3: Roof Plan
Tables 2.1 and 2.2 describe the structural components of the building.
Structural
components of the walls and roof systems are described. This information is critical for proper
analysis of the diaphragm and load path.
8
Table 2.1: Structural Components at High Roof Areas
Horizontal Elements
Sheathing:
Diagonal 1x8 sheathing
Joists:
2x8 wood joists at 24” o.c.
Purlins:
None
Beams:
4x10 wood beams
Roof
Girders:
16” wide flange girders
Truss Type 1:
2x truss with split ring connections
Truss Type 2:
2x truss with split ring connections
Truss Type 3:
2x truss with split ring connections
Floors Type:
4” concrete slab on grad
Vertical Elements
Columns:
Pipe and reinforced concrete columns
Walls:
Partially grouted reinforced masonry block
Column Foundations:
Concrete square footings
Wall Foundations:
Concrete strip footings
*D-Structural Drawings, FO-Field Observation, T-Testing
Source*
D, FO
D, FO
D, FO
D, FO
D, FO
D, FO
D, FO
D, FO
D
D, FO
D, FO, T
D
D
Table 2.2: Structural Components at Low Roof Areas
Horizontal Elements
Sheathing:
Unblocked plywood sheathing
Joists:
2x6 wood joists at 24” o.c.
Roof
Purlins:
None
Beams:
4x10 wood beams
Floors Type:
4” concrete slab on grad
Vertical Elements
Columns:
Wood, pipe, and reinforced concrete columns
Walls:
Partially grouted reinforced masonry block
Column Foundations:
Concrete square footings
Wall Foundations:
Concrete strip footings
*D-Structural Drawings, FO-Field Observation, T-Testing
Source*
D, FO
D, FO
D, FO
D, FO
D
D, FO
D, FO, T
D
D
Based on the data collected and presented in this subsection, the building type has been
determined to be an RM1 (reinforced masonry bearing walls with flexible diaphragms) as defined
in Table 2-2 of ASCE 31 (2003). This determination is based on a lateral force resisting system
consisting of reinforced, partially grouted, Concrete Masonry Units (CMU) and a diaphragm
consisting of diagonal wood sheathing and plywood sheathing, which are flexible relative to the
9
walls. The RM1 building type identification will assist in determining which structural checklists
are required to be used in the identification of potential deficiencies. Structural checklists are
discussed further in Section 2.3 of this report.
2.2
Site Hazards and Design Requirements
An understanding of the natural hazards specific to the site at which the building is
located is essential for an accurate evaluation of the structure. Soil conditions, seismic hazards,
and windstorm characteristics all effect the structural evaluation and design requirements of a
building. The tables presented in this section identify the natural hazards specific to the site in
question.
Table 2.3 contains the soils information that applies to this site. Site classifications range
from A to F (A being hard rock and F being very plastic clay) and are determined based on the
average soil properties for the top 100 feet of soil. In the absence of a soils report, the site class is
assumed to be Class D as prescribed in ASCE 31 (2003), Section 3.5.2.3.1. Class D sites have a
shear wave velocity between 600 ft/sec and 1200 ft/sec. Shear wave velocity is the velocity at
which shear waves are able to be transmitted through the soil and range from less than 600 ft/sec
to as high as 5,000 ft/sec. Lower shear wave velocity values are associated with softer soils
which amplify ground shaking. Ground shaking is the primary cause of damage to man-made
structures and geologists have observed that areas with soft soils tend to repeatedly experience the
most damage to structures.
An example of a soft soil area is San Francisco where some
neighborhoods repeatedly experienced significant damage in both the 1906 and 1989 earthquakes.
The United States Geologic Survey (USGS) describes site Class D as consisting of “some
Quaternary muds (less than 1.8 million years old), sands, gravels, silts, and mud. Significant
amplification of shaking by these soils is generally expected.”
10
Table 2.3: Soils Information at Site Under Consideration
Description:
Stiff soil
Shear wave velocity:
600 ft/sec < Vs < 1200 ft/sec
Site class:
D (assumed per ASCE 31-03, section 3.5.2.3.1)
Soil stability:
Stiff soil
Reference:
ASCE 31-03, section 3.5.2.3.1
Comments: A soils investigation was not available for this site. Site class D is assumed as per
ASCE 31 (2003), section 3.5.2.3.1. The above description and shear wave velocity range are
those relating to the assumed site class D.
Table 2.4 contains the seismic hazard information relating to the building evaluated in
this report. The seismic hazard is based on the Risk-targeted Maximum Considered Earthquake
(MCER) ground motion response acceleration values for a short-period of 0.2 seconds and a longperiod of 1.0 second. General MCER values are determined as prescribed in Section 11.4.3 of
ASCE 7 (2010) and site specific MCER values are determined as prescribed in Sections 21.1 and
21.2. MCER values can also be determined using the USGS Ground Motion Parameter Software
(2014). The MCER ground motion response acceleration values are significant because they will
be used to determine the seismic response coefficient (discussed further in Section 3.1 of this
report) which will be multiplied by the seismic weight to determine design base shear values.
Higher MCER values will result in higher design base shear values.
A site visit and any other resources available determine site-specific vulnerabilities. In
this case, vulnerabilities were determined by researching data available through the Association
of Bay Area Governments, Earthquake and Hazards Program (2014). Fault rupture is a brittle
fracture at the ground surface and can be a complex phenomenon to predict (typically predicted
by experienced geologists). Fault ruptures can cause significant damage due to differential
displacements in the foundation. Slope failures include a wide range of landslides or landslips.
Potential for slope failures can be determined by site observations and consulting with an
experienced geologist. Slope failures pose a significant risk to structures due to displacement of
11
soils under the foundation and/or impact from nearby landslides. The distance to the nearest fault
can be determined using the USGS Quaternary Faults Web Mapping Application referenced
below. Site proximity to faults increases the risk of significant ground motion during a seismic
event which can result in an increase in structural damage to structures.
Table 2.4: Seismic Hazard Information
Hazard
Spectral Acceleration1
Vulnerability2
0.2 sec period:
1.0 sec period:
Fault rupture:
Slope failure:
Liquefaction:
MCER
2.499 g
0.953 g
None
None
High risk
1.27 miles
Distance to Nearest Fault3
References:
1. ASCE 7 (2010), Section 11.4
2. Association of Bay Area Governments, Earthquake and Hazards Program (2014)
3. USGS Quaternary Faults Web Mapping Application (20140
Table 2.5 contains windstorm characterization information relating the building
evaluated in this report. The design wind speed is determined by the local authority having
jurisdiction and the site exposure is determined based on ground surface roughness that is
determined by considering natural topography, vegetation, and constructed facilities. A site
surrounded by tall vegetation, buildings, and topography will deflect wind and reduce the
design wind values applied to the building. It is important to consider whether wind forces or
seismic forces will govern the evaluation and upgrade design of a facility in order to ensure
adequate resistance to the governing lateral force. In this case the building consists of heavy
partially grouted masonry walls and most of the building is relatively short compared to
surrounding buildings. Due to the high seismic weight of the structure, low design wind
speed, and high ground surface roughness, it was determined that seismic forces will govern
12
the analysis and design of upgrades to the lateral force resisting system of the building
evaluated in this report.
Table 2.5: Windstorm Characterization
Parameter
Wind speed (mph)1:
Site exposure category:
Site exposure description:
Description
85
B
Terrain with buildings, forest or surface
irregularities 20 feet or more in height covering
at least 20% of the area, extending one mile or
more from the site.
References:
1. City of Fremont
2.3
Identified Deficiencies
The seismic deficiencies identified using ASCE 31 (2003) and structural calculations
addressed in this report are listed in Table 2.6, and the locations of identified deficiencies are
illustrated in Figure 2.5. The significance of each deficiency is discussed in this section in the
same order listed in Table 2.6 and the upgrade design of the deficiencies are discussed in
Chapters 3, 4, and 5 of this report.
Deficiency S-1 is a major collector with a partially failed connection at one end. The
collector transfers shear forces from one shear wall to another. If the collector fails completely,
lateral forces will not be shared between shear walls and may result in one of the shear walls
being overstressed. The collector is also acting as a major girder and holds up 4.5’ of roof
trusses. If the connection were to fail completely, the trusses resting on the girder would be
unsupported at one end and would result in a collapse of the roof system. Although gravity forces
are unlikely to fail the connection completely, lateral forces resulting from a seismic event may
13
cause the partially failed connection to fail completely resulting in a major collapse of the high
roof section of the building.
Deficiency S-2 is a lack of in-plane force transfer elements between the diaphragm and
the shear walls. If the shear forces in the diaphragm are not transferred to the shear walls through
in-plane connection elements, the diaphragm may shear away from the tops of the walls resulting
in localized failures. As localized failures are compounded they may result in major failures due
to improperly supported walls.
Deficiency S-3 is a lack of sufficient out-of-plane wall anchorage from the diaphragm to
the tops of masonry shear walls. A lack of adequate out-of-plane wall anchorage may result in
the tops of masonry walls detaching from the diaphragm and deflecting toward the inside or
outside of the building. This type of deflection may result in collapse of masonry walls and
possible the collapse of the roof system Out-of-plane anchorage failures is one of the most
common types of failure according the Preliminary Survey of Damage to the Commercial District
referenced at the end of this report.
Deficiency S-4 is a lack of continuity in cross diaphragm cross ties. The tops of parallel
shear walls are supported by the continuity of cross tie members which develop out-of-plane
forces into the diaphragm. Cross tie members in flexible wood diaphragms typically consist of 2x
wood members incorporated into the trusses and joists of the roof system. Lateral forces can
cause separation to occur at discontinuities in cross ties resulting in a weekend diaphragm.
Discontinuities were identified at ridge locations and at locations where outriggers at gabled ends
meet perpendicular to trusses or joists. These connections are typically performed using toenails
or hangers, which are not designed to transfer lateral forces.
Deficiency S-5 is the lack of seismic strapping at diaphragm re-entrant corners. Tension
forces in chords can be concentrated at re-entrant corners. Without seismic strapping to develop
14
chord forces into the diaphragm, separation of the diaphragm and perpendicular shear walls may
occur as illustrated in Figure 2.4.
Figure 2.4: Re-entrant Corner Failure [from ASCE 31 (2003)]
Deficiency S-6 is the insufficient capacity of the wood diaphragm. The diagonal 1x
sheathing and the unblocked plywood sheathing do not have sufficient shear capacity in multiple
locations. The diaphragm distributes lateral forces to lateral force resisting shear walls. Shear
failure of the diaphragm can reduce the structure’s ability distribute lateral forces adequately.
Deficiency S-7 is the discontinuity of diaphragm chords. Diaphragm chords consist of
horizontal reinforcement in shear walls used to resist tensile forces induced when the flexible
diaphragm deflects. Discontinuities in diaphragm chords exist at gabled ends and at entry ways.
Discontinuities in diaphragm chords may result in separation of shear walls due to inadequate
tensile capacities.
The ASCE 31 (2003) checklists used in this evaluation identified other non-structural
deficiencies that will not be discussed in this report. It is important to recognize, however, that a
complete evaluation of a building per ASCE 31 (2003) may include a significant number of nonstructural deficiencies. For additional information on typical nonstructural seismic deficiencies,
see the non-structural checklists in Section 3.7 of ASCE 31 (2003).
15
Table 2.6: Identified Deficiencies Illustrated in Figure 2.5
No.
S-1
S-2
S-3
S-4
S-5
Item
16” wide
flange girder:
Shear transfer:
Out-of-plane
anchorage:
Cross ties:
Description
The 16” wide flange girder between the chapel and cultural
hall has broken loose from the wall at the north end
Load path does not exist to transfer diaphragm shear to
interior or exterior shear walls
Out-of-plane wall anchors are insufficient or do not exist
Type*
EQ, G
Continuous cross ties are missing or are insufficient to
transfer out-of-plane anchorage loads into the diaphragm
Strapping has not been provided at re-entrant corners
EQ
Re-entrant
corners:
S-6
Wood
The capacity of the unblocked roof sheathing is not adequate
diaphragms:
to resist seismic forces
S-7
Diaphragm
Some diaphragm chords are not continuous at breaks in
chords:
walls
*EQ-Earthquake deficiency, G-Gravity deficiency
Figure 2.5: Locations of Deficiencies Listed in Table 2.6
EQ
EQ
EQ
EQ
EQ
16
CHAPTER 3
FLEXIBLE WOOD DIAPHRAGM AND ASSOCIATED COMPONENTS
The building uses a flexible wood diaphragm to distribute seismic forces to vertical
lateral-force-resisting elements. The diaphragm is flexible and consists of two different wood
systems.
At the low roof areas, the diaphragm system consists of unblocked ½” plywood
sheathing. At the high roof areas, the diaphragm system consists of unblocked 1x8(nominal)
diagonal sheathing. Flexible diaphragms are typically analyzed using a beam analogy. The
sheathing is treated like the web of a wide flange beam and the chords are treated like the flanges.
Figure 3.1 shows the free-body diagram typically used for diaphragm analysis. The “load” shown
in Figure 3.1 represents the lateral earthquake force and “v” represents the resulting base shear at
the shear walls resisting the seismic force.
Figure 3.1 demonstrates how shear forces are
developed in “web” or diaphragm of the building while tension and compression forces are
developed in the “chords”.
Figure 3.1: Free-body Diagram of Forces Acting on Diaphragm and Diaphragm Components
17
3.1
Diaphragm Shear Forces
The diaphragm upgrade design is performed by dividing the diaphragm into boxes and
analyzing each box individually while taking to account any shared seismic weights at box
boundaries and shared resulting values such as diaphragm shear and chord forces.
Box
boundaries should lie on shear walls and length to width aspect ratios of boxes should not exceed
those prescribed in Table 4.2.4 of the American Wood Council’s Special Design Provisions for
Wind and Seismic referenced at the end of this report. Grid lines are also defined at box
boundaries in order to assist in evaluating the capacities of lines of shear walls that span multiple
boxes. In this analysis, the diaphragm was divided up into boxes as demonstrated in Figure 3.2.
Figure 3.2: Layout Box and Grid Line Assignments for Diaphragm Analysis
18
To analyze the diaphragm of each box illustrated in Figure 3.2, the seismic base shear is
calculated with Equations 3.1-3.4 below.
𝑉 = 𝐶𝑠 𝑊
Eq. 3.1
Where W is the seismic weight tributary to the diaphragm of each box, taken as the unfactored
dead load for this structure, and ranging from 4 – 35 kips. The seismic response coefficient, Cs, is
calculated using the following equations from section 12.8.1.1 of ASCE 7 (2010) –
𝐶𝑠 =
𝑆𝐷𝑆
𝑅
𝐼𝑒
( )
Eq. 3.2
Where SDS is the design spectral response acceleration parameter in the short period range and is
equal to 1.28g for this site. The response modification factor, R, is equal to 3.5 for this retrofit
and the importance factor, I = 1.25. Furthermore, the value of Cs is not required to be greater than
–
𝐶𝑠 =
𝑆𝐷1
𝑅
𝐼𝑒
𝑇( )
Eq. 3.3
Where SD1 = 0.74g is the design spectra response acceleration parameter at a period of 1.0 second
and T = 0.19s is the fundamental period of the structure. Finally, the response coefficient must be
greater than –
𝐶𝑠 = 0.044𝑆𝐷𝑆 𝐼𝑒 ≥ 0.01
Eq. 3.4
Since the structure is one story, the base shear is also equal to the diaphragm shear force.
The diaphragm shear force of each box was compared to the nominal unit shear capacities, which
are found in Table 4.2A, 4.2B, 4.2C, and 4.2D of AWC (2008), of the diaphragm at that box to
determine which areas of the diaphragm need to be upgraded. Table 3.1 compares the seismic
demand applied to the diaphragm, Vdiaphragm, and the nominal shear capacity, Vcapacity, at grid lines
for each section of Figure 3.2 where there was a shear capacity deficiency.
19
The analysis of the existing diaphragm determined that the diagonal straight 1x8
sheathing should have ½” plywood sheathing added on top of it. All of the high roof and much of
the low roof diaphragm also required blocking. Adding blocking to plywood edges increases the
shear capacity of the diaphragm and is typically needed at locations where diaphragm shear
forces are concentrated such as at major shear walls. Often blocking is required at major shear
walls but is not needed further away from major shear walls because diaphragm shear forces are
distributed throughout the diaphragm as they move further away from locations of high
concentrations. Figure 3.3 identifies areas of the diaphragm that would need to be upgraded by
adding plywood sheathing and blocking to plywood panel edges (indicated in blue) or simply by
adding blocking to the existing plywood (indicated in red).
20
Table 3.1: Diaphragm Seismic Demands, As-built Capacity and Retrofit Strategy
Box
Grids
Box A
Box B
Box C
1, 2
2, 3
3, 5
A, C
7, 10
D, E
2, 3
D, E
D, E
C, E
7, 10
2, 3
3, 5
E, G
5, 8
8, 12
E, G
6, 9
G, H
Box E
Box G
Box H
Box I
Box J
Box K
Box L
Box M
Box N
Box O
Vdiaphragm
(lb/ft)
369
413
491
132
1030
424
298
346
435
663
318
427
510
525
406
705
292
1914
361
Vcapacity
(lb/ft )
255
255
255
100
100
255
255
255
255
100
100
255
255
100
100
100
100
255
255
Retrofit Strategy
Add blocking
Add blocking
Add blocking
Add plywood and blocking
Add plywood and blocking
Add blocking
Add blocking
Add blocking
Add blocking
Add plywood and blocking
Add plywood and blocking
Add blocking
Add blocking
Add plywood and blocking
Add plywood and blocking
Add plywood and blocking
Add plywood and blocking
Add blocking
Add blocking
Figure 3.3: Diaphragm seismic upgrade illustrating deficient areas retrofitted with blocking or
plywood sheathing
21
3.2
Tensile Capacity of Diaphragm Chords
Chords are a diaphragm boundary element designed to resist the tension or compression
resulting from the diaphragm moment created as the flexible diaphragm deflects between shear
walls.
Chords must be designed to resist both tensile forces and compressive forces.
As
mentioned previously, chords can be analyzed in a manner similar to the flanges of a simply
supported wide flange beam with a uniformly distributed load. Figure 3.4, from Hsiao and
Tezcan (2012), illustrates how chords correspond to the flanges of a wide flange beam.
Figure 3.4: Chord Force Illustration [from Hsiao and Tezcan, 2012]
The maximum bending moment occurring at the midspan of the diaphragm can be
2
calculated as 𝑤𝑙 ⁄8, where w is the distributed seismic load and l is the unsupported length.
22
From this, the chord force is the bending moment divided by the distance between the tension and
2
compression chord, 𝑤𝑙 ⁄8𝑑.
The chords of many older masonry building do not have adequate capacity to resist the
tensile and compressive forces experienced during a seismic event. Inadequate chord capacities
can result tension cracks in the masonry as illustrated in Figure 3.5.
Figure 3.5: Chord Failure [from Hsiao and Tezcan, 2012]
The Handbook for the Seismic Rehabilitation of Existing Buildings published by the
Federal Emergency Management Agency (1992) provides details for common chord
reinforcement techniques as illustrated in Figure 3.6. In this detail, a continuous steel angle us
bolted to the masonry shear wall at the diaphragm in order to increase the tensile capacity of the
chord. Steel straps are welded to the angel and nailed to blocking under the plywood sheathing in
order develop out-of-plane forces in to diaphragm.
23
Figure 3.6: Chord Retrofit Strategy [adapted from FEMA 1992]
The allowable tensile strength for yielding of steel chord reinforcing elements can be
calculated as demonstrated Equation 3.8 from the American Institute of Steel Construction
(2011).
𝑃𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 =
𝐹𝑦 𝐴𝑔
Ω𝑡
Eq. 3.5
Where Fy is the specified minimum yield stress of the steel element, typically 40 ksi for
rebar, Ag is the gross area of steel cross section, and Ωt is is the safety factor, 1.67 for limit states
involving yielding. The allowable compressive strength of the masonry wall that will resist
compressive chord forces can be calculated using Equation 3.9 from the Building Code
Requirements for Masonry Structures.
𝐹𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 =
2
𝑓′𝑚
ℎ
−(
) ]
[1
4
140𝑟
𝑓𝑜𝑟
ℎ
𝑟
≤ 99
Eq. 3.6
24
Where f’m is the compressive strength of the masonry, typically 1,500 psi for normal
weight CMU block, h is the effective laterally unsupported length of the wall, and r is the radius
of gyration of the wall
The chords in the building evaluated in this report consist of horizontal reinforcement
running along the tops of masonry walls.
At 12” masonry walls the horizontal chord
reinforcement consists of 4 #5 rebar, at 8” masonry walls the horizontal chord reinforcement
consists of 4 #4 rebar, and at 6” masonry walls the horizontal chord reinforcement consists of 2
#4 rebar. Although the existing chords were not identified as potential deficiencies during the
evaluation of the structure due to tension or compression resisting capacities, the chords were
found to be discontinuous at multiple locations including gabled ends and building entryways.
Discontinuities in chords are common and should be considered during site visits. Discontinuities
can be corrected by adding reinforcement as illustrated in Figure 3.6 at locations where breaks in
the chords exist. Figure 3.7 illustrates the locations where chord discontinuities were observed
and Table 3.2 summarizes the chord forces at discontinuous locations and retrofit strategies are
listed based on Simpson Strong-tie published capacities.
Table 3.2: Chord Retrofit Strategies Identified in Figure 3.7
Chord
C1
C2
C3
C4
C5
C6
C7
Chord
Force
(lbs)
773
659
13645
1202
3704
12425
9391
Retrofit
Capacity
(lbs)
845
845
18430
12980
4585
12980
12980
Retrofit strategy
(1) Simpson CS22 Strap
(1) Simpson CS22 Strap
(2) Simpson CMST12 Straps
(2) Simpson CMST14 Straps
(1) Simpaon CMSTC16 Strap
(2) Simpson CMST14 Straps
(2) Simpson CMST14 Straps
25
Figure 3.7: Location of Chord Discontinuities Summarized in Table 3.2
3.3
Tensile Capacity of Continuous Cross Ties
Diaphragms are required to be provided with tension ties between the chords that develop
out-of-plane forces into the diaphragm. Figure 3.8 illustrates a simplified example of how cross
ties are typically oriented in a building.
26
Figure 3.8: Cross Ties Example [from ASCE 31 (2003)]
If cross ties are not continuous, the tension in the ties will be concentrated into the
flexible diaphragm at the location of the discontinuity which could result in a separation of the
diaphragm at that point and a decrease in out-of-plane support for the masonry walls. Ties must
be designed to resist an axial tension determined by the following equation.
𝐹𝑝 = 0.4𝑆𝐷𝑆 𝑊
Eq. 3.7
Where Fp is the axial tension the tie must be designed to resist, SDS=1.28 is the spectral
response acceleration, and W is the seismic weight tributary to tie. The diaphragm ties for the
building evaluated in this report consist of 2x wood members. Although the ties were determined
to have the capacity necessary to resist tensile forces, the ties are not continuous at multiple
locations. Discontinuities in cross ties are commonly found at locations where outriggers attach
to roof trusses along gabled ends and at diaphragm ridges. In order to reinforce the ties and make
them continuous, seismic strapping with the capacity to resist the same tensile forces are added to
27
the ties. It was determined from out-of-plan anchorage calculations summarized in Table 4.1 that
the highest out-of-plane force that the cross ties will be required to transfer is 2005lbs. It is
recommended that all straps used to make cross ties continues be Simpson CS14 straps with a 2ft
end length. Simpson CS14 straps have a tensile capacity of 2490lbs and will be adequate in all
locations. Figure 3.9 illustrates a location where a discontinuity in the cross tie exists and details
how the discontinuity could be upgraded using a seismic strap on top of the plywood sheathing.
Out-of-plane anchorage is also detailed to support the tops of masonry walls.
Figure 3.9: Detail of Continuous Cross Tie Retrofit Strategy
Figures 3.10 and 3.11 identify the locations on the low roof and high roof where seismic
strapping is needed to make the existing cross ties continuous. The seismic straps would be
installed on top of the diaphragm over joists, truss top chords, and/or blocking as demonstrated in
Figure 3.9.
28
Figure 3.10: Plan Showing Low Roof Continuous Cross Tie and Chord Reinforcement Locations
Figure 3.11: Plan Showing High Roof Continuous Cross Tie and Chord Reinforcement Locations
29
CHAPTER 4
DIAPHRAGM TO SHEAR WALL LOAD TRANSFER ELEMENTS
Seismic forces must be transferred from the diaphragm to the shear walls in all directions.
To ensure that load transfer elements can resist seismic forces in principle directions, the
elements are analyzed for out-of-plane forces as well as in-plane forces.
4.1
Out-of-plane Force Resisting Elements
Out-of-plane anchorage is a very common deficiency in many masonry buildings and is a
common location where failures can occur during seismic events. When proper out-of-lane
anchorage does not exist, masonry walls can separate from the diaphragm resulting in a loss of
support at the top of the wall which could lead to a collapse of the wall as illustrated in Figure
4.1.
Figure 4.1: Out-of-plane Anchorage Failure [from Hsiao and Tezcan 2012]
When out-of-plane anchorage fails the masonry wall is deflected by seismic forces in a
cantilevered fashion and excessive stresses result at the fixed end of the wall near the foundation.
Figure 4.2 is the result of an out-of-plane pushover analysis performed on a masonry wall of a
30
synagogue in San Francisco. The red shown in the figure are areas of high stress which are most
likely to experience cracking during a seismic event do to the loss of out-of-plane anchorage at
the top of the wall.
Figure 4.2: Results of Out-of-plane Pushover Analysis on Masonry Wall [from Paret, Freeman,
Searer, Hachem, and Gilmartin, 2007]
This section presents the design of the out-of-plane upgrade using ASCE 7-10, section
12.11.2.1. The out-of-plane force is calculated using the following equation:
𝐹𝑝 = 0.4𝑆𝐷𝑆 𝑘𝑎 𝐼𝑒 𝑊𝑝
Eq. 4.1
Where Fp is the design force in the individual anchors and SDS=1.28 and is the design
spectral response acceleration parameter at short periods. ka = 1.0 + Lf/100 where Lf is the span
in feet of a flexible diaphragm that provides the lateral support for the wall, Ie=1.25 and is the
seismic importance factor, and Wp is the weight of the wall tributary to the anchor.
The out-of-plane anchorage force is calculated for three different scenarios: high 12”
masonry wall, low 8” masonry wall, and low 6” masonry wall. The following figure presents the
wall types that the out-of-plane force connections are designed to resist using an anchor spacing
of 2ft on center. Wall weights are listed and identified by color. Wall weights at box boundaries
31
as well as partitions within boxes contribute to the seismic weight that the load path must be
designed to resist.
Figure 4.3: Layout of Walls and Associated Seismic Weights
The out-of-plane anchorage forces at the top of walls are resisted by bolting a large steel
angle to the side of the truss using through bolts and one threaded rod epoxied into to the top of
the wall.
At the face of the wall, the out-of-plane forces are resisted using a horizontal
installation of a Simpson HTT or similar hardware. Table 4.1 summarizes out-of-plane forces at
typical walls. The anchors are recommended to be installed at every truss or joist so the
calculations summarized in Table 4.1 are based on a 2ft anchor spacing. The ¾” rod and HTT4
capacities are based on an installation using Simpson SET Epoxy.
32
Table 4.1: Summary of Out-of-plane Anchorage Retrofit Strategy
Wall Type
12" CMU Top
12" CMU Face
8" CMU Top
6" CMU Top
Wall
Height (ft)
18
14
9
9
Total
Weight
(psf)
124
124
71
55
Out-ofplane
force
(lbs/2ft)
2005
1559
898
898
Anchor
Capacity
(lbs)
2710
3610
1355
1355
Upgrade
Anchor Type
(2) 3/4" Rods
HTT4
(1) 3/4" Rod
(1) 3/4" Rod
Figure 4.2 is a detail of out-of-plane anchorage attaching diaphragm cross ties to the face
of a CMU wall. This detail applies to locations where the roof joists are perpendicular to the
wall.
Figure 4.4: Detail of Out-of-plane Anchorage Retrofit Strategy at Face of Perpendicular Masonry
Wall
Figure 4.3 is a detail of out-of-plane anchorage attaching the diaphragm to the face of a
CMU wall using blocking and a Simpson HTT. This detail applies to locations where the roof
joists are parallel to the wall.
33
Figure 4.5: Detail of Out-of-plane Anchorage Retrofit Strategy at Face of Parallel Masonry Wall
Out-of-plane anchorage is also required at interior non-loadbearing CMU walls. Figures
4.4 and 4.5 are details of out-of-plane anchorage at interior CMU partitions. Figure 4.4 is
detailed for locations where the partition is parallel to joists and/or trusses. Figure 4.5 is detailed
for locations where the partition is perpendicular to joists and/or trusses.
Figure 4.6: Detail of Out-of-plane Anchorage Retrofit Strategy at Top of Parallel CMU Partition
34
Figure 4.7: Detail of Out-of-plane Anchorage Retrofit Strategy at Top of Perpendicular CMU
Partition
Additional out-of-plane conditions are detailed in conjunction with in-plane shear transfer
elements detailed in subsection 4.2.
4.2
In-plane Force Resisting Elements
Shear forces are required to be transferred from the diaphragm to the shear walls. If
shear forces are not transferred to shear walls the flexible diaphragm may break loose from the
shear walls thus preventing diaphragm shear forces to be transferred into the lateral force resisting
shear walls. Loss of this type of connection can result in localized failures of the diaphragm and
possibly collapse of masonry walls.
The minimum shear force that needs to be resisted by shear transfer elements at
diaphragm boundaries is calculated by the lesser of the following equations.
𝑉𝑑 = 1.25𝑆𝐷1 𝐶𝑝 𝑊𝑑
Eq. 4.7
𝑉𝑑 = 𝑣𝑢 𝐷
Eq. 4.8
35
Where SD1=0.74 and is the design spectral response acceleration parameter, Wd is the
total seismic dead load tributary to the diaphragm, vu is the unit shear strength of diaphragm, D is
the depth of diaphragm, and Cp is the horizontal force factor (0.50 for straight or diagonal
sheathing and tongue and groove decking, 0.75 for blocked panels or multiple panel systems).
Shear forces are transferred at the top of walls using full height blocking, boundary
nailing, and Simpson A35 and HGA10 framing clips.
Figure 4.6 details in-plane shear transfer elements in conjunction with out-of-plane
anchorage at joist locations at exterior walls. The in-plane load path is plywood diaphragm to
boundary nailing to full height blocking to Simpson framing clip to top of shear wall. The out-ofplane anchorage load path is cross tie (joist) to through bolts to steel angle to epoxy anchor at top
of shear wall.
Figure 4.8: Detail of In-plane and Out-of-plane Anchorage Retrofit Strategy at Joists
36
Figure 4.7 is a condition similar to figure 3.6 but involves a truss heal at high roof
locations. The in-plane and out-of-plane load paths are the same as those of figure 4.6. The truss
heal connection is a split ring connection and many of the connections are splitting. Plywood
gusset reinforcement has been detailed at the truss heals in addition to the in-plane and out-ofplane anchorage. Seismic strapping has also been detailed to act as chord reinforcement at gabled
ends where the chord (reinforced bond beam) is not continuous. Plywood sheathing has also been
detailed to be added on top of the 1x8 diagonal sheathing.
Figure 4.9: Detail of In-plane and Out-of-plane Anchorage Retrofit Strategy at Truss
4.3
Masonry Shear Wall Capacities
Masonry shear walls are the vertical elements of the lateral force resisting system and are
essential for keeping the building from tipping over during a seismic event. If masonry shear
walls are overstressed, concentrations of shear stresses can build up at door and window openings
37
as illustrated in Figure 4.10. This figure is the result of an in-plane pushover analysis performed
on a masonry synagogue in San Francisco. Areas indicated in red are locations of concentrated
stresses which may result in cracking of the masonry.
Figure 4.10: Results of In-plane Pushover Analysis for Masonry Wall [from Paret, Freeman,
Searer, Hachem, and Gilmartin, 2007]
In order to identify potential shear wall deficiencies, preliminary calculations were
performed according to section 3.5.3.3 of ASCE 31 (2003). The average stress in shear walls was
calculated using the following equation.
𝑎𝑣𝑔
𝑣𝑗
=
1 𝑉𝑗
( )
𝑚 𝐴𝑤
Eq. 4.9
Where Vj is the story shear at level j, Aw is the summation of the horizontal crosssectional area of the shear walls in the direction of loading, and m is the component modification
factor. The locations and compositions of shear walls are presented in the following figure.
38
Figure 4.11: Plan Identifying Shear Walls and Associated Weights and Equivalent Thicknesses
Although preliminary calculations did not identify any of the shear walls as potential
deficiencies, during the site visit it was observed that some of the shear walls were not continuous
through the attic space to the diaphragm. Table 4.2 summarizes the analysis of the shear walls
indicating that all shear walls are sufficient. The following figure details a potential upgrade
measure to a discontinuous shear wall. Out-of-plane anchorage is detailed in addition to the
discontinuous shear wall detail.
39
Table 4.2: Summary of Shear Wall Stresses
Grids
1 Low
10 High
10 Low
11 Low
12 High
2 Low
3 Low
4 Low
5 High
5 Low
6 High
7 High
7 Low
8 High
9 High
A High
B Low
C High
D Low
E High
E Low
F Low
G High
H High
Base
Shear
(kips)
76.0
574.5
41.6
44.9
311.9
379.8
479.0
125.4
186.9
323.4
112.6
419.5
138.9
317.2
112.6
266.3
343.2
443.3
547.3
681.8
447.5
187.2
664.0
186.4
Equivalent
Solid
Thickness
Wall
(in)
4.6
6.5
4.6
4.6
6.5
4.6
4.6
4.6
6.5
4.6
6.5
6.5
4.6
6.5
6.5
6.5
4.6
6.5
4.6
4.6
6.5
4.6
4.6
4.6
Shear
Stress
(psi)
14.0
28.8
12.6
14.0
25.6
21.6
11.4
37.9
20.7
25.0
45.1
19.8
12.2
15.4
45.1
16.1
12.8
35.5
12.2
36.8
8.9
11.2
40.6
60.3
Allowable
Stress
Unity Check
(psi)
(Actual/Allow.)
70.0
0.20
70.0
0.41
70.0
0.18
70.0
0.20
70.0
0.37
70.0
0.31
70.0
0.16
70.0
0.54
70.0
0.30
70.0
0.36
70.0
0.64
70.0
0.28
70.0
0.17
70.0
0.22
70.0
0.64
70.0
0.23
70.0
0.18
70.0
0.51
70.0
0.17
70.0
0.53
70.0
0.13
70.0
0.16
70.0
0.58
70.0
0.86
40
Figure 4.12: Discontinuous Shear Wall Upgrade Detail
41
CHAPTER 5
SPECIAL CONDITIONS
This chapter analyzes two special conditions that were identified as deficiencies during
the site visit. The locations of the special conditions are identified in Figure 5.1.
Figure 5.1: Plan Showing Locations of Special Conditions
5.1
Special Condition 1
The first special condition is a 21x62 steel wide flange girder. The girder was identified
as a deficiency because the connection of the girder to the CMU wall at one end has broken loose.
The girder is holding up 43.5ft of roof trusses and also acts as a collector to drag seismic forces
into the CMU shear walls at each end.
If the girder connection fails completely it could result in
the collapse of the 43.5ft roof section resting on the girder at one end. The existing partial failure
appears to be due to lateral forces possible from a past seismic event. A future seismic event
42
could cause the connection to fail completely suggesting that an upgrade of the connection from
the wide flange collector to the shear wall is critical.
The design of the wide flange girder is guided by section 12.10.2 of ASCE 7 (2010). The
load combination applied at this condition is the following.
(1.2 + 0.2𝑆𝐷𝑆 )𝐷 + Ω𝐸 𝑄𝐸 + 0.2𝑆
Eq. 4.1
Where SDS is the design spectral response acceleration parameter at short periods, D is the
dead load tributary to the girder, ΩE the overstrength factor assigned in Table 12.2-1 of ASCEb7
(2010), QE is the effect of horizontal seismic forces.
At this location QE is determined by the diaphragm shear force tributary to the wide
flange collector at Grid Line E due to Box J and Box N which was determined to be 59.3 k. D is
determined to be 0.475k per foot, SDS was determined to be 1.283, and ΩE was determined to be
2.5 from table 12.2-1 of ASCE 7 (2010). The girder was analyzed in Risa 3D and found to be
adequate. The reaction force at each end of the girder was used to design a new connection from
the girder/collector to the CMU wall. Figure 5.2 details the potential upgrade measure at the end
of the beam that had the failed connection. The failed CMU wall is detailed to be removed and
replaced with reinforced concrete and a ¼”x8” steel plate is used to drag the force from the
collector into the CMU shear wall. Figure 5.3 details the connection at the un-failed end of the
collector where a similar steel plate is used to drag the force from the wide flange into the CMU
wall.
43
Figure 5.2: Detail of Special Condition 1 Retrofit Strategy at Failed Connection
Figure 5.3: Detail of Special Condition 1 Retrofit Strategy at Un-failed Connection
5.2
Special Condition 2
The second special condition is a location were roof trusses are resting on a ledger. This
condition was identified as a deficiency during the site visit due to a lack of out-of-plane
anchorage. Without out-of-plane anchorage, a seismic event could cause lateral forces to shake
the masonry wall and possibly cause the roof trusses to slip off of the ledger resulting in the
44
collapse of the roof section resting on the ledger. Due to the risk of caollapse during a seismic
event, an upgrade at this location is considered critical.
The out-of-plane design forces were determined in the manner describe in subsection 4.1.
Elements intended to transfer in-plane shear forces are also design as described in subsection 4.2
and detailed below. The overstressed split ring connection at the truss heal is also detailed to be
reinforced with plywood gussets. Figure 5.4 details the potential upgrade measures described for
this condition.
Figure 5.4: Detail of Special Condition 2 Retrofit Strategy
45
CHAPTER 6
SUMMARY
This report follows a typical approach to analyzing and upgrading existing structures.
Potential deficiencies were identified as directed in ASCE 31 (2003) by reviewing as-built
drawings, performing site observations, and performing preliminary calculations. After potential
deficiencies were identified, further analysis of deficient structural systems was performed using
ASCE 7 (2010) and ASCE 41 (2006).
The deficiencies identified in this report are typical for buildings constructed of CMU
walls and flexible diaphragms. During seismic events, the most common failures occur at the
connection from the walls to the diaphragm. The load path is often lacking sufficient strength to
resist in-plane and out-of-plane forces. Cross ties often lack continuity resulting in separation of
the diaphragm at discontinuities and diaphragms often lack proper shear capacity due to
insufficient blocking.
Upgrading weaknesses in structural systems reduces the risk of potential failure during a
seismic event.
When individual elements of a structure are prevented from failing, the
redundancy of the system is maintained.
46
APPENDIX
This appendix contains a summary of the spreadsheets used to perform the structural
analysis. Base shears, diaphragm shears, and chord forces are summarized for the grid lines and
boxes illustrated in figure 3.2. The information gathered for each box are also summarized. This
appendix also contains a summary of the Risa 3D analysis performed at special condition 1.
47
Table A.1: Base Shear Summary
Base Shear Summary
Code Ref.: Current IBC/CBC
SDS = 1.283
Cs =
0.458
R = 3.5
Ie = 1.25
Seismic Weight * Cs or Base Shear
Diaphragm
Level
Grids
High
High
High
High
High
High
High
High
High
High
High
High
High
High
High
High
High
High
High
High
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
5
6
7
7
8
8
9
10
10
12
A
C
C
E
E
E
G
G
G
H
1
2
2
2
2
3
3
3
3
3
3
4
5
5
5
5
7
7
10
11
B
B
B
B
B
D
D
D
D
D
D
D
D
E
E
E
E
E
F
F
ASD Base
Shear
Along Grid
kips
36
22
27
54
25
36
22
27
83
60
51
28
57
57
26
48
38
67
23
36
15
12
13
33
16
13
15
25
16
11
13
24
15
6
22
20
8
19
8
9
14
16
19
9
8
14
11
13
5
8
25
17
13
25
17
16
12
16
17
19
Box I.D.
Box M
Box O
Box E
Box J
Box M
Box N
Box O
Box E
Box J
Box N
Box E
Box E
Box J
Box J
Box M
Box N
Box M
Box N
Box O
Box O
Box A
Box A
Box B
Box G
Box K
Box B
Box C
Box G
Box H
Box K
Box L
Box H
Box C
Box D
Box I
Box L
Box D
Box I
Box F
Box F
Box A
Box B
Box C
Box D
Box F
Box A
Box B
Box C
Box D
Box F
Box G
Box H
Box I
Box G
Box H
Box I
Box K
Box L
Box K
Box L
Length of
Wall
Along Grid
(ft)
29.0
8.0
15.0
53.0
33.0
33.0
8.0
15.0
49.0
39.0
53.0
20.0
20.0
24.5
19.0
40.5
14.0
46.0
14.0
14.0
24.5
15.0
15.0
38.5
11.0
15.0
15.0
62.0
62.0
18.5
18.5
15.0
0.0
0.0
40.0
18.5
15.5
36.0
15.0
14.5
30.0
27.0
34.0
13.0
17.0
22.5
35.0
45.0
8.0
20.0
34.5
31.0
8.0
40.5
25.0
18.0
40.5
37.0
33.0
43.0
48
Table A.2: Diaphragm Shear Summary
Di a phra gm Shea r Summa ry
Code Ref.: Current IBC/CBC
Di a phra gm Cs = 0.458
Di a phra gm Shea r * Cs
Unbl ocked Di a phra gm Ca pa ci ti es (pl f):
Wa l l s
perp. to
di recti on
ASD
of l oa d
Di a ph.
s hown
Wei ght
bel ow to
Tri buta ry
determi ne
Di a phra gm
to Box
req'd bl k'g
Level
Gri ds
Gri d
Box I.D. di s ta nces
(ki ps )
(ft)
Hi gh
5
16
Box M
28.5
Hi gh
6
15
Box O
30
Hi gh
7
20
Box E
53
Hi gh
7
24
Box J
53
Hi gh
8
16
Box M
28.5
Hi gh
8
27
Box N
62
Hi gh
9
15
Box O
30
Hi gh
10
20
Box E
53
Hi gh
10
24
Box J
53
Hi gh
12
27
Box N
62
Hi gh
A
7
Box E
19
Hi gh
C
7
Box E
19
Hi gh
C
35
Box J
75
Hi gh
E
35
Box J
75
Hi gh
E
15
Box M
39
Hi gh
E
18
Box N
39
Hi gh
G
15
Box M
39
Hi gh
G
18
Box N
39
Hi gh
G
11
Box O
8
Hi gh
H
11
Box O
8
Low
1
9
Box A
42.5
Low
2
9
Box A
42.5
Low
2
10
Box B
51
Low
2
19
Box G
47.5
Low
2
10
Box K
51
Low
3
10
Box B
51
Low
3
12
Box C
59
Low
3
19
Box G
47.5
Low
3
10
Box H
39
Low
3
10
Box K
51
Low
3
12
Box L
59
Low
4
10
Box H
39
Low
5
12
Box C
59
Low
5
4
Box D
21
Low
5
8
Box I
29
Low
5
12
Box L
59
Low
7
4
Box D
21
Low
7
8
Box I
29
Low
10
4
Box F
20
Low
11
4
Box F
20
Low
B
6
Box A
24.5
Low
B
6
Box B
24.5
Low
B
7
Box C
24.5
Low
B
4
Box D
24.5
Low
B
4
Box F
24.5
Low
D
6
Box A
24.5
Low
D
6
Box B
24.5
Low
D
7
Box C
24.5
Low
D
4
Box D
24.5
Low
D
4
Box F
24.5
Low
D
20
Box G
62.5
Low
D
13
Box H
62.5
Low
D
13
Box I
66
Low
E
20
Box G
62.5
Low
E
13
Box H
62.5
Low
E
13
Box I
66
Low
E
6
Box K
24.5
Low
E
7
Box L
24.5
Low
F
6
Box K
24.5
Low
F
7
Box L
24.5
ASD
Shea r
Loa d
Al ong
Gri d
(pl f)
405.6
1913.7
1029.8
317.6
405.6
704.7
1913.7
1029.8
317.6
704.7
132.2
132.2
662.7
662.7
524.7
292.3
524.7
292.3
361.2
361.2
369.2
369.2
413.2
298.5
427.0
413.2
491.4
298.5
158.6
427.0
509.7
158.6
491.4
148.1
114.2
509.7
148.1
114.2
147.8
147.8
133.0
108.0
117.3
209.8
196.2
133.0
108.0
117.3
209.8
196.2
423.6
345.7
435.1
423.6
345.7
435.1
126.4
119.4
126.4
119.4
Ca s e 1
255
Di s t. from
the edge
of the
di a ph. to
Tota l
the poi nt
Di a ph.
a t whi ch
Wei ght bl k'g i s no
Tri buta ry
l onger
to Gri d
req'd.
(ki ps )
(ft)
16
5.3
15
13.0
20
19.9
24
5.2
16
5.3
27
19.8
15
13.0
20
19.9
24
5.2
27
19.8
7
Not Req'd
7
Not Req'd
35
23.1
35
23.1
15
10.0
18
2.5
15
10.0
18
2.5
11
1.2
11
1.2
9
6.6
9
6.6
10
9.8
19
3.5
10
10.3
10
9.8
12
14.2
19
3.5
10
Not Req'd
10
10.3
12
14.7
10
Not Req'd
12
14.2
4
Not Req'd
8
Not Req'd
12
14.7
4
Not Req'd
8
Not Req'd
4
Not Req'd
4
Not Req'd
6
Not Req'd
6
Not Req'd
7
Not Req'd
4
Not Req'd
4
Not Req'd
6
Not Req'd
6
Not Req'd
7
Not Req'd
4
Not Req'd
4
Not Req'd
20
12.4
13
8.2
13
13.7
20
12.4
13
8.2
13
13.7
6
Not Req'd
7
Not Req'd
6
Not Req'd
7
Not Req'd
Ca s e 3
190
Di s t. from
the edge
of the
di a ph. to
the poi nt
a t whi ch
bl k'g i s no
l onger
req'd.
(ft)
7.6
13.5
21.6
10.6
7.6
22.6
13.5
21.6
10.6
22.6
Not Req'd
Not Req'd
26.7
26.7
12.4
6.8
12.4
6.8
1.9
1.9
10.3
10.3
13.8
8.6
14.2
13.8
18.1
8.6
Not Req'd
14.2
18.5
Not Req'd
18.1
Not Req'd
Not Req'd
18.5
Not Req'd
Not Req'd
Not Req'd
Not Req'd
Not Req'd
Not Req'd
Not Req'd
1.2
0.4
Not Req'd
Not Req'd
Not Req'd
1.2
0.4
17.2
14.1
18.6
17.2
14.1
18.6
Not Req'd
Not Req'd
Not Req'd
Not Req'd
49
Table A.3: Chord Forces
Chord Forces
Code Ref.:
Current IBC/CBC
Diaphragm
Level
Grids
ASD Chord
Force Along
Grid
High
High
High
High
High
High
High
High
High
High
High
High
High
High
High
High
High
High
High
High
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
5
6
7
7
8
8
9
10
10
12
A
C
C
E
E
E
G
G
G
H
1
2
2
2
2
3
3
3
3
3
3
4
5
5
5
5
7
7
10
11
B
B
B
B
B
D
D
D
D
D
D
D
D
E
E
E
E
E
F
F
3,704
263
628
12,425
3,704
2,849
263
628
12,425
2,849
13,645
13,645
4,208
4,208
2,204
10,923
2,204
10,923
9,391
9,391
773
773
632
4,830
659
632
612
4,830
5,199
659
680
5,199
612
984
7,109
680
984
7,109
1,202
1,202
3,337
4,126
5,521
600
739
3,337
4,126
5,521
600
739
2,272
1,467
786
2,272
1,467
786
4,126
6,027
4,126
6,027
Box I.D.
(lbs)
Box M
Box O
Box E
Box J
Box M
Box N
Box O
Box E
Box J
Box N
Box E
Box E
Box J
Box J
Box M
Box N
Box M
Box N
Box O
Box O
Box A
Box A
Box B
Box G
Box K
Box B
Box C
Box G
Box H
Box K
Box L
Box H
Box C
Box D
Box I
Box L
Box D
Box I
Box F
Box F
Box A
Box B
Box C
Box D
Box F
Box A
Box B
Box C
Box D
Box F
Box G
Box H
Box I
Box G
Box H
Box I
Box K
Box L
Box K
Box L
Summary of
Chord types
Chord
chord types
Unity check
& their
Capacities
as indicated
for chord
capacities
as Defined
in each Box
capacity
defined
on the Right
Analysis
below :
(lbs)
Type.
Cap., (lbs)
Check
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
4
4
2
4
4
2
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
4
2
2
1
2
2
2
2
29,760
29,760
29,760
29,760
19,200
19,200
29,760
29,760
29,760
29,760
29,760
29,760
29,760
19,200
29,760
29,760
29,760
29,760
29,760
29,760
19,200
19,200
19,200
19,200
19,200
19,200
19,200
19,200
19,200
3,020
3,020
19,200
3,020
3,020
19,200
29,760
29,760
29,760
29,760
19,200
19,200
19,200
19,200
19,200
19,200
19,200
19,200
19,200
19,200
19,200
19,200
19,200
3,020
19,200
19,200
29,760
19,200
19,200
19,200
19,200
0.1
0.0
0.0
0.4
0.2
0.1
0.0
0.0
0.4
0.1
0.5
0.5
0.1
0.2
0.1
0.4
0.1
0.4
0.3
0.3
0.0
0.0
0.0
0.3
0.0
0.0
0.0
0.3
0.3
0.2
0.2
0.3
0.2
0.3
0.4
0.0
0.0
0.2
0.0
0.1
0.2
0.2
0.3
0.0
0.0
0.2
0.2
0.3
0.0
0.0
0.1
0.1
0.3
0.1
0.1
0.0
0.2
0.3
0.2
0.3
Type
1
12" CMU
w / (4) #5
29,760
Type
2
8" CMU
w / (4) #4
19,200
Type
3
6" CMU
w / (2) #4
9,600
Type
4
Double
Top Plate
3,020
50
Table A.4: Box A Flexible Diaphragm Seismic Forces
Box A: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
Low
Wt Factors
Code
Cs
Final
L (Horiz.):
42.5
ft
ASD
0.7
0.46
0.32
W (Vert.):
24.5
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
30
Exterior Walls
Hor'z
22.5
24.5
15
ft
Summary of Weights
Vert.
Diaph. =
20,825
lbs
Trans wall =
35,582
lbs
Longwall =
14,411
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
56,407
lbs
Longto tal =
35,236
lbs
ft
Wtrans =
1,327
plf
0
ft
Wlo ng =
1,438
plf
0
0
psf
Wtrans =
1,129
plf
27,158
17,395
7,828
lbs
Wlo ng =
1,365
plf
Top
Btm
Left
Right
Grid ID:
B
D
1
2
na
Length:
42.5
42.5
24.5
24.5
ft
Height:
9.0
9.0
10.0
4.5
ft
Wall Unit w t.:
71
71
71
71
psf
Chord Type:
2
2
2
2
H Parapet:
0
0
0
0
Length Par.:
0
0
0
Par. Unit w t.:
0
0
Wall Trib w t:
27,158
Concentrated Load On Diaphragm
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
ΔV Right
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
0
0
0
0
0
0
0
0
0
0
0
Interior Walls
Hor'z
Vert.
Grid Loads
B
D
1
2
Manual
lbs
lbs
lbs
lbs
Diaph. :
17618
17618
28203
28203
Length:
24
40
ft
Spec. Load:
0
0
0
0
Height:
9
9
ft
In Plane w t :
27158
27158
17395
7828
Wall w t.:
78
10
psf
Tot.Trib.Wt :
44776
44776
45598
36031
H Parapet:
0
0
ft
ASD Load:
14,355
14,355
14,619
11,552
Unit w t.:
0
0
psf
ULT Load:
20,507
20,507
20,884
16,502
Wlo ng
Diaphragm
B
D
15
1
2
4
Forces
V
V
T Chord
V
V
T Chord
Wtrans
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
Tot.Trib.Wt :
17,618
17,618
10,404
28,203
28,203
2,409
1129
1365
ASD Load:
5,651
5,651
3,337
9,046
9,046
773
362
438
ULT Load:
8,073
8,073
4,767
12,923
12,923
1,104
517
625
51
Table A.5: Box B Flexible Diaphragm Seismic Forces
Box B: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
Low
Wt Factors
Code
Cs
Final
L (Horiz.):
51
ft
ASD
0.7
0.46
0.32
W (Vert.):
24.5
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
27
Exterior Walls
Hor'z
35
15
15
ft
Summary of Weights
Vert.
Diaph. =
24,990
lbs
Trans wall =
38,131
lbs
Longwall =
9,358
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
63,121
lbs
Longto tal =
34,348
lbs
ft
Wtrans =
1,238
plf
0
ft
Wlo ng =
1,402
plf
0
0
psf
Wtrans =
969
plf
16,295
7,828
7,828
lbs
Wlo ng =
1,340
plf
Top
Btm
Left
Right
Grid ID:
B
D
2
3
na
Length:
51
51
24.5
24.5
ft
Height:
9.0
4.5
4.5
4.5
ft
Wall Unit w t.:
71
71
71
71
psf
Chord Type:
2
2
2
2
H Parapet:
0
0
0
0
Length Par.:
0
0
0
Par. Unit w t.:
0
0
Wall Trib w t:
32,589
Concentrated Load On Diaphragm
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
ΔV Right
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
0
0
0
0
0
0
0
0
0
0
0
Interior Walls
Hor'z
Vert.
Grid Loads
B
D
2
3
Manual
lbs
lbs
lbs
lbs
Diaph. :
17174
17174
31560
31560
Length:
39
34
ft
Spec. Load:
0
0
0
0
Height:
9
9
ft
In Plane w t :
32589
16295
7828
7828
Wall w t.:
78
10
psf
Tot.Trib.Wt :
49763
33468
39388
39388
H Parapet:
0
0
ft
ASD Load:
15,954
10,730
12,628
12,628
Unit w t.:
0
0
psf
ULT Load:
22,791
15,329
18,040
18,040
Wlo ng
Diaphragm
B
D
19
2
3
3
Forces
V
V
T Chord
V
V
T Chord
Wtrans
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
Tot.Trib.Wt :
17,174
17,174
12,862
31,560
31,560
1,971
969
1340
ASD Load:
5,509
5,509
4,126
10,123
10,123
632
311
430
ULT Load:
7,869
7,869
5,894
14,461
14,461
903
444
614
52
Table A.6: Box C Flexible Diaphragm Seismic Forces
Box C: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
Low
Wt Factors
Code
Cs
Final
L (Horiz.):
59
ft
ASD
0.7
0.46
0.32
W (Vert.):
24.5
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
34
Exterior Walls
Hor'z
45
15
0
ft
Summary of Weights
Vert.
Diaph. =
28,910
lbs
Trans wall =
46,163
lbs
Longwall =
14,254
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
75,073
lbs
Longto tal =
43,164
lbs
ft
Wtrans =
1,272
plf
0
ft
Wlo ng =
1,762
plf
0
0
psf
Wtrans =
969
plf
18,851
7,828
7,828
lbs
Wlo ng =
1,500
plf
Top
Btm
Left
Right
Grid ID:
B
D
3
5
na
Length:
59
59
24.5
24.5
ft
Height:
9.0
4.5
4.5
4.5
ft
Wall Unit w t.:
71
71
71
71
psf
Chord Type:
2
2
2
4
H Parapet:
0
0
0
0
Length Par.:
0
0
0
Par. Unit w t.:
0
0
Wall Trib w t:
37,701
Concentrated Load On Diaphragm
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
ΔV Right
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
0
0
0
0
0
0
0
0
0
0
0
Interior Walls
Hor'z
Vert.
Grid Loads
B
D
3
5
Manual
lbs
lbs
lbs
lbs
Diaph. :
21582
21582
37537
37537
Length:
75
34
ft
Spec. Load:
0
0
0
0
Height:
9
9
ft
In Plane w t :
37701
18851
7828
7828
Wall w t.:
53
42
psf
Tot.Trib.Wt :
59283
40432
45364
45364
H Parapet:
0
0
ft
ASD Load:
19,006
12,963
14,544
14,544
Unit w t.:
0
0
psf
ULT Load:
27,152
18,518
20,777
20,777
Wlo ng
Diaphragm
B
D
25
3
5
3
Forces
V
V
T Chord
V
V
T Chord
Wtrans
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
Tot.Trib.Wt :
21,582
21,582
17,214
37,537
37,537
1,907
969
1500
ASD Load:
6,922
6,922
5,521
12,040
12,040
612
311
481
ULT Load:
9,889
9,889
7,888
17,200
17,200
874
444
687
53
Table A.7: Box D Flexible Diaphragm Seismic Forces
Box D: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
Low
Wt Factors
Code
Cs
Final
L (Horiz.):
21
ft
ASD
0.7
0.46
0.32
W (Vert.):
24.5
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
13
Exterior Walls
Hor'z
8
0
15.5
ft
Summary of Weights
Vert.
Diaph. =
10,290
lbs
Trans wall =
12,330
lbs
Longwall =
17,175
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
22,620
lbs
Longto tal =
27,465
lbs
ft
Wtrans =
1,077
plf
0
ft
Wlo ng =
1,121
plf
0
0
psf
Wtrans =
832
plf
945
7,828
13,671
lbs
Wlo ng =
859
plf
Top
Btm
Left
Right
Grid ID:
B
D
5
7
na
Length:
21
21
24.5
24.5
ft
Height:
9.0
4.5
4.5
4.5
ft
Wall Unit w t.:
71
10
71
124
psf
Chord Type:
2
2
4
1
H Parapet:
0
0
0
0
Length Par.:
0
0
0
Par. Unit w t.:
0
0
Wall Trib w t:
13,419
Concentrated Load On Diaphragm
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
ΔV Right
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
0
0
0
0
0
0
0
0
0
0
0
Interior Walls
Hor'z
Vert.
Grid Loads
B
D
5
7
Manual
lbs
lbs
lbs
lbs
Diaph. :
13733
13733
11310
11310
Length:
26
34
ft
Spec. Load:
0
0
0
0
Height:
9
9
ft
In Plane w t :
13419
945
7828
13671
Wall w t.:
44
42
psf
Tot.Trib.Wt :
27152
14678
19138
24981
H Parapet:
0
0
ft
ASD Load:
8,705
4,706
6,136
8,009
Unit w t.:
0
0
psf
ULT Load:
12,435
6,722
8,765
11,441
Wlo ng
Diaphragm
B
D
3
5
7
5
Forces
V
V
T Chord
V
V
T Chord
Wtrans
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
Tot.Trib.Wt :
13,733
13,733
1,872
11,310
11,310
3,068
832
859
ASD Load:
4,405
4,405
600
3,628
3,628
984
267
275
ULT Load:
6,293
6,293
858
5,182
5,182
1,406
381
393
54
Table A.8: Box E Flexible Diaphragm Seismic Forces
Box E: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
High
Wt Factors
Code
Cs
Final
L (Horiz.):
53
ft
ASD
0.7
0.46
0.32
W (Vert.):
19
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
53
Exterior Walls
Hor'z
20
15
15
ft
Summary of Weights
Vert.
Diaph. =
20,140
lbs
Trans wall =
101,866
lbs
Longwall =
23,560
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
122,006
lbs
Longto tal =
43,700
lbs
ft
Wtrans =
2,302
plf
0
ft
Wlo ng =
2,300
plf
0
0
psf
Wtrans =
2,302
plf
65,720
23,560
23,560
lbs
Wlo ng =
2,300
plf
Top
Btm
Left
Right
Grid ID:
A
C
7
10
na
Length:
53
53
19
19
ft
Height:
21.0
10.0
10.0
10.0
ft
Wall Unit w t.:
124
124
124
124
psf
Chord Type:
1
1
1
1
H Parapet:
0
0
0
0
Length Par.:
0
0
0
Par. Unit w t.:
0
0
Wall Trib w t:
138,012
Concentrated Load On Diaphragm
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
ΔV Right
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
0
0
0
0
0
0
0
0
0
0
0
Interior Walls
Hor'z
Vert.
Grid Loads
A
C
7
10
Manual
lbs
lbs
lbs
lbs
Diaph. :
21850
21850
61003
61003
Length:
0
0
ft
Spec. Load:
0
0
0
0
Height:
0
0
ft
In Plane w t :
138012
65720
23560
23560
Wall w t.:
0
0
psf
Tot.Trib.Wt :
159862
87570
84563
84563
H Parapet:
0
0
ft
ASD Load:
51,252
28,075
27,111
27,111
Unit w t.:
0
0
psf
ULT Load:
73,217
40,107
38,730
38,730
Wlo ng
Diaphragm
A
C
61
7
10
3
Forces
V
V
T Chord
V
V
T Chord
Wtrans
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
21,850
21,850
42,542
61,003
61,003
1,958
2302
2300
Tot.Trib.Wt :
ASD Load:
7,008
7,008
13,645
19,567
19,567
628
738
738
ULT Load:
10,012
10,012
19,493
27,952
27,952
897
1,055
1,054
55
Table A.9: Box F Flexible Diaphragm Seismic Forces
Box F: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
Low
Wt Factors
Code
Cs
Final
L (Horiz.):
20
ft
ASD
0.7
0.46
0.32
W (Vert.):
24.5
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
17
Exterior Walls
Hor'z
20
15
14.5
ft
Summary of Weights
Vert.
Diaph. =
9,800
lbs
Trans wall =
12,780
lbs
Longwall =
14,663
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
22,580
lbs
Longto tal =
24,463
lbs
ft
Wtrans =
1,129
plf
0
ft
Wlo ng =
999
plf
0
0
psf
Wtrans =
1,129
plf
12,780
13,671
15,656
lbs
Wlo ng =
999
plf
Top
Btm
Left
Right
Grid ID:
B
D
10
11
na
Length:
20
20
24.5
24.5
ft
Height:
9.0
9.0
4.5
9.0
ft
Wall Unit w t.:
71
71
124
71
psf
Chord Type:
2
2
1
2
H Parapet:
0
0
0
0
Length Par.:
0
0
0
Par. Unit w t.:
0
0
Wall Trib w t:
12,780
Concentrated Load On Diaphragm
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
ΔV Right
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
0
0
0
0
0
0
0
0
0
0
0
Interior Walls
Hor'z
Vert.
Grid Loads
B
D
10
11
Manual
lbs
lbs
lbs
lbs
Diaph. :
12232
12232
11290
11290
Length:
0
0
ft
Spec. Load:
0
0
0
0
Height:
0
0
ft
In Plane w t :
12780
12780
13671
15656
Wall w t.:
0
0
psf
Tot.Trib.Wt :
25012
25012
24961
26946
H Parapet:
0
0
ft
ASD Load:
8,019
8,019
8,002
8,639
Unit w t.:
0
0
psf
ULT Load:
11,455
11,455
11,432
12,341
Wlo ng
Diaphragm
B
D
4
10
11
6
Forces
V
V
T Chord
V
V
T Chord
Wtrans
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
Tot.Trib.Wt :
12,232
12,232
2,304
11,290
11,290
3,746
1129
999
ASD Load:
3,923
3,923
739
3,621
3,621
1,202
362
320
ULT Load:
5,605
5,605
1,056
5,173
5,173
1,716
517
458
56
Table A.10: Box G Flexible Diaphragm Seismic Forces
Box G: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
Low
Wt Factors
Code
Cs
Final
L (Horiz.):
47.5
ft
ASD
0.7
0.46
0.32
W (Vert.):
62.5
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
34.5
Exterior Walls
Hor'z
40.5
38.5
62
ft
Summary of Weights
Vert.
Diaph. =
59,375
lbs
Trans wall =
56,936
lbs
Longwall =
66,102
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
116,311
lbs
Longto tal =
125,477
lbs
Wtrans =
2,449
plf
ft
Wlo ng =
2,008
plf
0
psf
Wtrans =
1,570
plf
44,375
19,969
lbs
Wlo ng =
1,465
plf
Top
Btm
Left
Right
Grid ID:
D
E
2
3
na
Length:
47.5
47.5
62.5
62.5
ft
Height:
4.5
4.5
10.0
4.5
ft
Wall Unit w t.:
71
71
71
71
psf
Chord Type:
2
2
2
2
H Parapet:
0
0
0
0
ft
Length Par.:
0
0
0
0
Par. Unit w t.:
0
0
0
Wall Trib w t:
15,176
15,176
Concentrated Load On Diaphragm
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
ΔV Right
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
0
0
0
0
0
0
0
0
0
0
0
Interior Walls
Hor'z
Vert.
Grid Loads
D
E
2
3
Manual
lbs
lbs
lbs
lbs
Diaph. :
62738
62738
58156
58156
Length:
160
130
ft
Spec. Load:
0
0
0
0
Height:
9
9
ft
In Plane w t :
15176
15176
44375
19969
Wall w t.:
58
58
psf
Tot.Trib.Wt :
77915
77915
102531
78124
H Parapet:
0
0
ft
ASD Load:
24,979
24,979
32,871
25,047
Unit w t.:
0
0
psf
ULT Load:
35,685
35,685
46,959
35,781
Wlo ng
Diaphragm
D
E
11
2
3
22
Forces
V
V
T Chord
V
V
T Chord
Wtrans
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
Tot.Trib.Wt :
62,738
62,738
7,082
58,156
58,156
15,057
1570
1465
ASD Load:
20,123
20,123
2,272
18,653
18,653
4,830
503
470
ULT Load:
28,748
28,748
3,245
26,648
26,648
6,899
719
671
57
Table A.11: Box H Flexible Diaphragm Seismic Forces
Box H: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
Low
Wt Factors
Code
Cs
Final
L (Horiz.):
39
ft
ASD
0.7
0.46
0.32
W (Vert.):
62.5
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
31
Exterior Walls
Hor'z
25
62
15
ft
Summary of Weights
Vert.
Diaph. =
48,750
lbs
Trans wall =
13,055
lbs
Longwall =
35,322
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
61,805
lbs
Longto tal =
84,072
lbs
ft
Wtrans =
1,585
plf
0
ft
Wlo ng =
1,345
plf
0
0
psf
Wtrans =
1,504
plf
9,905
19,969
44,375
lbs
Wlo ng =
1,295
plf
Top
Btm
Left
Right
Grid ID:
D
E
3
4
na
Length:
31
31
62.5
62.5
ft
Height:
4.5
4.5
4.5
10.0
ft
Wall Unit w t.:
71
71
71
71
Chord Type:
2
2
2
2
H Parapet:
0
0
0
0
Length Par.:
0
0
0
Par. Unit w t.:
0
0
Wall Trib w t:
9,905
Concentrated Load On Diaphragm
psf
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
ΔV Right
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
0
0
0
0
0
0
0
0
0
0
0
Interior Walls
Hor'z
Vert.
Grid Loads
D
E
3
4
Manual
lbs
lbs
lbs
lbs
Diaph. :
42036
42036
30902
30902
Length:
70
70
ft
Spec. Load:
0
0
0
0
Height:
9
9
ft
In Plane w t :
9905
9905
19969
44375
Wall w t.:
10
10
psf
Tot.Trib.Wt :
51940
51940
50871
75277
H Parapet:
0
0
ft
ASD Load:
16,652
16,652
16,309
24,134
Unit w t.:
0
0
psf
ULT Load:
23,789
23,789
23,299
34,477
Wlo ng
Diaphragm
D
E
7
3
4
24
Forces
V
V
T Chord
V
V
T Chord
Wtrans
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
Tot.Trib.Wt :
42,036
42,036
4,575
30,902
30,902
16,210
1504
1295
ASD Load:
13,483
13,483
1,467
9,912
9,912
5,199
482
415
ULT Load:
19,261
19,261
2,096
14,160
14,160
7,428
689
593
58
Table A.12: Box I Flexible Diaphragm Seismic Forces
Box I: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
Low
Wt Factors
Code
Cs
Final
L (Horiz.):
29
ft
ASD
0.7
0.46
0.32
W (Vert.):
66
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
8
Exterior Walls
Hor'z
18
40
36
ft
Summary of Weights
Vert.
Diaph. =
38,280
lbs
Trans wall =
8,717
lbs
Longwall =
40,390
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
46,997
lbs
Longto tal =
78,670
lbs
ft
Wtrans =
1,621
plf
0
ft
Wlo ng =
1,192
plf
0
0
psf
Wtrans =
1,538
plf
11,718
44,375
34,875
lbs
Wlo ng =
1,180
plf
Top
Btm
Left
Right
Grid ID:
D
E
5
7
na
Length:
21
21
62.5
62.5
ft
Height:
4.5
4.5
10.0
4.5
ft
Wall Unit w t.:
10
124
71
124
psf
Chord Type:
4
1
2
1
H Parapet:
0
0
0
0
Length Par.:
0
0
0
Par. Unit w t.:
0
0
Wall Trib w t:
945
Concentrated Load On Diaphragm
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
ΔV Right
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
0
0
0
0
0
0
0
0
0
0
0
Interior Walls
Hor'z
Vert.
Grid Loads
D
E
5
7
Manual
lbs
lbs
lbs
lbs
Diaph. :
39335
39335
23498
23498
Length:
53
17
ft
Spec. Load:
0
0
0
0
Height:
9
9
ft
In Plane w t :
945
11718
44375
34875
Wall w t.:
10
10
psf
Tot.Trib.Wt :
40280
51053
67873
58373
H Parapet:
0
0
ft
ASD Load:
12,914
16,368
21,760
18,714
Unit w t.:
0
0
psf
ULT Load:
18,448
23,382
31,086
26,735
Wlo ng
Diaphragm
D
E
4
5
7
32
Forces
V
V
T Chord
V
V
T Chord
Wtrans
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
Tot.Trib.Wt :
39,335
39,335
2,450
23,498
23,498
22,163
1538
1180
ASD Load:
12,617
12,617
786
7,537
7,537
7,109
493
379
ULT Load:
18,024
18,024
1,123
10,767
10,767
10,155
705
541
59
Table A.13: Box J Flexible Diaphragm Seismic Forces
Box J: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
High
Wt Factors
Code
Cs
Final
L (Horiz.):
53
ft
ASD
0.7
0.46
0.32
W (Vert.):
75
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
20
Exterior Walls
Hor'z
24.5
53
49
ft
Summary of Weights
Vert.
Diaph. =
79,500
lbs
Trans wall =
69,006
lbs
Longwall =
139,500
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
148,506
lbs
Longto tal =
219,000
lbs
Wtrans =
2,802
plf
ft
Wlo ng =
2,920
plf
0
psf
Wtrans =
2,802
plf
93,000
186,000
lbs
Wlo ng =
2,920
plf
Top
Btm
Left
Right
Grid ID:
C
E
7
10
na
Length:
53
53
75
75
ft
Height:
10.5
10.5
10.0
20.0
ft
Wall Unit w t.:
124
124
124
124
psf
Chord Type:
1
2
1
1
H Parapet:
0
0
0
0
ft
Length Par.:
0
0
0
0
Par. Unit w t.:
0
0
0
Wall Trib w t:
69,006
69,006
Concentrated Load On Diaphragm
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
ΔV Right
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
0
0
0
0
0
0
0
0
0
0
0
Interior Walls
Hor'z
Vert.
Grid Loads
C
E
7
10
Manual
lbs
lbs
lbs
lbs
Diaph. :
109500
109500
74253
74253
Length:
0
0
ft
Spec. Load:
0
0
0
0
Height:
0
0
ft
In Plane w t :
69006
69006
93000
186000
Wall w t.:
0
0
psf
Tot.Trib.Wt :
178506
178506
167253
260253
H Parapet:
0
0
ft
ASD Load:
57,229
57,229
53,621
83,437
Unit w t.:
0
0
psf
ULT Load:
81,756
81,756
76,602
119,196
Wlo ng
Diaphragm
C
E
19
7
10
56
Forces
V
V
T Chord
V
V
T Chord
Wtrans
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
Tot.Trib.Wt :
109,500
109,500
13,118
74,253
74,253
38,738
2802
2920
ASD Load:
35,122
35,122
4,208
23,817
23,817
12,425
899
937
ULT Load:
50,174
50,174
6,011
34,024
34,024
17,750
1,284
1,338
60
Table A.14: Box K Flexible Diaphragm Seismic Forces
Box K: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
Low
Wt Factors
Code
Cs
Final
L (Horiz.):
51
ft
ASD
0.7
0.46
0.32
W (Vert.):
24.5
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
40.5
Exterior Walls
Hor'z
33
11
18.5
ft
Summary of Weights
Vert.
Diaph. =
24,990
lbs
Trans wall =
40,237
lbs
Longwall =
15,216
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
65,227
lbs
Longto tal =
40,206
lbs
ft
Wtrans =
1,279
plf
0
ft
Wlo ng =
1,641
plf
0
0
psf
Wtrans =
969
plf
32,589
17,395
1,103
lbs
Wlo ng =
1,398
plf
Top
Btm
Left
Right
Grid ID:
E
F
2
3
na
Length:
51
51
24.5
24.5
ft
Height:
4.5
9.0
10.0
4.5
ft
Wall Unit w t.:
71
71
71
10
psf
Chord Type:
2
2
2
4
H Parapet:
0
0
0
0
Length Par.:
0
0
0
Par. Unit w t.:
0
0
Wall Trib w t:
16,295
Concentrated Load On Diaphragm
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
ΔV Right
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
0
0
0
0
0
0
0
0
0
0
0
Interior Walls
Hor'z
Vert.
Grid Loads
E
F
2
3
Manual
lbs
lbs
lbs
lbs
Diaph. :
20103
20103
32613
32613
Length:
45
17
ft
Spec. Load:
0
0
0
0
Height:
9
9
ft
In Plane w t :
16295
32589
17395
1103
Wall w t.:
78
78
psf
Tot.Trib.Wt :
36397
52692
50008
33716
H Parapet:
0
0
ft
ASD Load:
11,669
16,893
16,033
10,809
Unit w t.:
0
0
psf
ULT Load:
16,670
24,133
22,904
15,442
Wlo ng
Diaphragm
E
F
19
2
3
3
Forces
V
V
T Chord
V
V
T Chord
Wtrans
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
Tot.Trib.Wt :
20,103
20,103
12,862
32,613
32,613
2,056
969
1398
ASD Load:
6,448
6,448
4,126
10,461
10,461
659
311
448
ULT Load:
9,211
9,211
5,894
14,944
14,944
942
444
640
61
Table A.15: Box L Flexible Diaphragm Seismic Forces
Box L: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
Low
Wt Factors
Code
Cs
Final
L (Horiz.):
59
ft
ASD
0.7
0.46
0.32
W (Vert.):
24.5
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
37
Exterior Walls
Hor'z
43
18.5
18.5
ft
Summary of Weights
Vert.
Diaph. =
28,910
lbs
Trans wall =
48,956
lbs
Longwall =
15,004
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
77,866
lbs
Longto tal =
43,914
lbs
ft
Wtrans =
1,320
plf
0
ft
Wlo ng =
1,792
plf
0
0
psf
Wtrans =
1,058
plf
37,701
1,103
22,785
lbs
Wlo ng =
1,668
plf
Top
Btm
Left
Right
Grid ID:
E
F
3
5
na
Length:
59
59
24.5
24.5
ft
Height:
7.0
9.0
4.5
7.5
ft
Wall Unit w t.:
71
71
10
124
psf
Chord Type:
2
2
4
1
H Parapet:
0
0
0
0
Length Par.:
0
0
0
Par. Unit w t.:
0
0
Wall Trib w t:
29,323
Concentrated Load On Diaphragm
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
ΔV Right
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
0
0
0
0
0
0
0
0
0
0
0
Interior Walls
Hor'z
Vert.
Grid Loads
E
F
3
5
Manual
lbs
lbs
lbs
lbs
Diaph. :
21957
21957
38933
38933
Length:
44
68
ft
Spec. Load:
0
0
0
0
Height:
9
9
ft
In Plane w t :
29323
37701
1103
22785
Wall w t.:
78
10
psf
Tot.Trib.Wt :
51280
59658
40036
61718
H Parapet:
0
0
ft
ASD Load:
16,440
19,126
12,835
19,787
Unit w t.:
0
0
psf
ULT Load:
23,486
27,323
18,336
28,267
Wlo ng
Diaphragm
E
F
27
3
5
4
Forces
V
V
T Chord
V
V
T Chord
Wtrans
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
21,957
21,957
18,790
38,933
38,933
2,121
1058
1668
Tot.Trib.Wt :
ASD Load:
7,043
7,043
6,027
12,488
12,488
680
339
535
ULT Load:
10,061
10,061
8,610
17,840
17,840
972
485
764
62
Table A.16: Box M Flexible Diaphragm Seismic Forces
Box M: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
High
Wt Factors
Code
Cs
Final
L (Horiz.):
28.5
ft
ASD
0.7
0.46
0.32
W (Vert.):
39
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
19
Exterior Walls
Hor'z
14
29
33
ft
Summary of Weights
Vert.
Diaph. =
22,230
lbs
Trans wall =
76,410
lbs
Longwall =
71,019
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
98,640
lbs
Longto tal =
93,249
lbs
ft
Wtrans =
3,461
plf
0
ft
Wlo ng =
2,391
plf
0
0
psf
Wtrans =
2,640
plf
70,680
62,868
27,690
lbs
Wlo ng =
1,731
plf
Top
Btm
Left
Right
Grid ID:
E
G
5
8
na
Length:
28.5
28.5
39
39
ft
Height:
10.0
20.0
13.0
10.0
ft
Wall Unit w t.:
124
124
124
71
Chord Type:
1
1
1
2
H Parapet:
0
0
0
0
Length Par.:
0
0
0
Par. Unit w t.:
0
0
Wall Trib w t:
35,340
Concentrated Load On Diaphragm
psf
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
ΔV Right
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
0
0
0
0
0
0
0
0
0
0
0
Interior Walls
Hor'z
Vert.
Grid Loads
E
G
5
8
Manual
lbs
lbs
lbs
lbs
Diaph. :
46625
46625
49320
49320
Length:
30
33
ft
Spec. Load:
0
0
0
0
Height:
20
20
ft
In Plane w t :
35340
70680
62868
27690
Wall w t.:
78
78
psf
Tot.Trib.Wt :
81965
117305
112188
77010
H Parapet:
0
0
ft
ASD Load:
26,278
37,608
35,967
24,689
Unit w t.:
0
0
psf
ULT Load:
37,540
53,725
51,382
35,271
Diaphragm
E
G
10
5
8
17
Forces
V
V
T Chord
V
V
T Chord
Wtrans
Wlo ng
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
Tot.Trib.Wt :
46,625
46,625
6,873
49,320
49,320
11,548
2640
1731
ASD Load:
14,955
14,955
2,204
15,819
15,819
3,704
847
555
ULT Load:
21,364
21,364
3,149
22,599
22,599
5,291
1,210
793
63
Table A.17: Box N Flexible Diaphragm Seismic Forces
Box N: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
High
Wt Factors
Code
Cs
Final
L (Horiz.):
62
ft
ASD
0.7
0.46
0.32
W (Vert.):
39
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
40.5
Exterior Walls
Hor'z
46
33
39
ft
Summary of Weights
Vert.
Diaph. =
48,360
lbs
Trans wall =
123,008
lbs
Longwall =
64,623
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
171,368
lbs
Longto tal =
112,983
lbs
Wtrans =
2,764
plf
ft
Wlo ng =
2,897
plf
0
psf
Wtrans =
2,764
plf
27,690
101,556
lbs
Wlo ng =
2,897
plf
Top
Btm
Left
Right
Grid ID:
E
G
8
12
na
Length:
62
62
39
39
ft
Height:
12.0
20.0
10.0
21.0
ft
Wall Unit w t.:
124
124
71
124
psf
Chord Type:
1
1
2
1
H Parapet:
0
0
0
0
ft
Length Par.:
0
0
0
0
Par. Unit w t.:
0
0
0
Wall Trib w t:
92,256
153,760
Concentrated Load On Diaphragm
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
ΔV Right
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
0
0
0
0
0
0
0
0
0
0
0
Interior Walls
Hor'z
Vert.
Grid Loads
E
G
8
12
Manual
lbs
lbs
lbs
lbs
Diaph. :
56492
56492
85684
85684
Length:
0
0
ft
Spec. Load:
0
0
0
0
Height:
0
0
ft
In Plane w t :
92256
153760
27690
101556
Wall w t.:
0
0
psf
Tot.Trib.Wt :
148748
210252
113374
187240
H Parapet:
0
0
ft
ASD Load:
47,688
67,407
36,348
60,029
Unit w t.:
0
0
psf
ULT Load:
68,126
96,295
51,925
85,756
Diaphragm
E
G
49
8
12
13
Forces
V
V
T Chord
V
V
T Chord
Wtrans
Wlo ng
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
Tot.Trib.Wt :
56,492
56,492
34,054
85,684
85,684
8,884
2764
2897
ASD Load:
18,120
18,120
10,923
27,483
27,483
2,849
887
929
ULT Load:
25,885
25,885
15,604
39,262
39,262
4,071
1,267
1,327
64
Table A.18: Box O Flexible Diaphragm Seismic Forces
Box O: Flexible Diaphragm Seismic Forces
Code Ref.: Current IBC/CBC
Redundancy Factor:
ρ=
1.3
Diaphragm Input
Location:
High
Wt Factors
Code
Cs
Final
L (Horiz.):
30
ft
ASD
0.7
0.46
0.32
W (Vert.):
8
ft
ULT
1.0
0.46
0.46
Bldg. Elev.:
66
ft
Roof DL:
20
psf
Roof SL:
0
psf
Roof T DL:
20.0
psf
Wall Lengths at Base of Wall:
Length @ B ase:
14
Exterior Walls
Hor'z
14
8
8
ft
Summary of Weights
Vert.
Diaph. =
4,800
lbs
Trans wall =
57,660
lbs
Longwall =
29,760
lbs
Trans special=
0
lbs
Longspecial=
0
lbs
Trans to tal =
62,460
lbs
Longto tal =
34,560
lbs
ft
Wtrans =
2,082
plf
0
ft
Wlo ng =
4,320
plf
0
0
psf
Wtrans =
2,082
plf
78,120
19,840
19,840
lbs
Wlo ng =
3,080
plf
Top
Btm
Left
Right
Grid ID:
G
H
6
9
na
Length:
30
30
8
8
ft
Height:
10.0
21.0
20.0
20.0
ft
Wall Unit w t.:
124
124
124
124
psf
Chord Type:
1
1
1
1
H Parapet:
0
0
0
0
Length Par.:
0
0
0
Par. Unit w t.:
0
0
Wall Trib w t:
37,200
Concentrated Load On Diaphragm
Horiz Loading
Vert Loading
Load
Weight
x
y
ΔV Top
ΔV Btm
ΔV Left
Number
(lbs)
(ft)
(ft)
(lbs)
(lbs)
(lbs)
(lbs)
1
33000
15
4
16,500
16,500
16,500
16,500
16,500
16,500
16,500
16,500
Grid Loads
G
H
6
9
Manual
lbs
lbs
lbs
lbs
Diaph. :
Interior Walls
ΔV Right
Hor'z
Vert.
33780
33780
47730
47730
Length:
0
8
ft
Spec. Load:
0
0
0
0
Height:
0
20
ft
In Plane w t :
37200
78120
19840
19840
Wall w t.:
0
124
psf
Tot.Trib.Wt :
70980
111900
67570
67570
H Parapet:
0
0
ft
ASD Load:
22,756
35,875
21,663
21,663
Unit w t.:
0
0
psf
ULT Load:
32,509
51,250
30,947
30,947
Wlo ng
Diaphragm
G
H
42
6
9
2
Forces
V
V
T Chord
V
V
T Chord
Wtrans
lbs
lbs
lbs
lbs
lbs
lbs
lbs
lbs
Tot.Trib.Wt :
33,780
33,780
29,278
47,730
47,730
821
2082
3080
ASD Load:
10,835
10,835
9,391
15,309
15,309
263
668
988
ULT Load:
15,478
15,478
13,416
21,871
21,871
376
954
1,411
65
Figure A.1: Special Condition 1 RISA Results
66
Table A.19: Special Condition 1 RISA Results
Basic Load Cases
BLC Desciption
1
D
2
EQ
Category
DL
EL
Joint
Load Combinations
Description
1
D+EQ
2
D
3
EQ
BLC
Y
Y
Y
Factor
-1
-1
-1
BLC
1
1
2
Joint Coordinates
Label
1
N1
2
N2
X (ft)
0
43.5
Y (ft)
0
0
Z (ft)
0
0
Y
Reaction
Reaction
Z
Reaction
Joint Boundary Conditions
Joint Label
X
1
N1
Reaction
2
N2
Distributed
1
1
Factor
1.457
1.457
2.5
BLC
2
Factor
2.5
X-Rot
Fixed
Fixed
Y-Rot
Fixed
Fixed
Z-Rot
Member Distributed Loads
1
Member Label
M1
Direction
Y
Magnitude
(k/in)
-0.475
Direction
X
Magnitude
(k)
59.3
Shape
W21x62
Material
A36 Gr.36
Joint Loads
1
Joint Label
N2
Member Data
1
Label
M1
ASD Steel Code Checks
Member
1
M1
Unity Check
0.989
Joint Reactions
Joint Label
1
N1
2
N2
3
Totals:
4
COG (ft):
X (ft)
-148.25
0
-148.25
X: 21.75
Y (ft)
16.403
16.403
32.806
Y: 0
Type
Length (ft)
WF Beam
43.5
Z (ft)
0
0
0
Z: 0
Mx (k-ft) My (k-ft) Mz (k-ft)
NC
NC
0
NC
NC
0
67
REFERENCES
Amrhein, J.E. (1998). “Reinforced Masonry Engineering Handbook”. Masonry Institute of
America, Boca Raton, NY.
American Concrete Institute. (2005). Building Code Requirements for Masonry Structures,
Farmington Hills, MI.
American Institute of Steel Construction (AISC). (2011). Steel Construction Manual, Chicago,
IL.
American Society of Civil Engineering (ASCE). (2003). Seismic Evaluation of Existing
Buildings, Reston, VA.
American Society of Civil Engineering (ASCE). (2010). Minimum Design Loads for Buildings
and Other Structures, Reston, VA.
American Society of Civil Engineering (ASCE). (2006). Seismic Rehabilitation of Existing
Buildings, Reston, VA.
Association of Bay Area Governments. Earthquake and Hazards Program. Association of Bay
Area Governments, January 25, 2014. <http://quake.abag.ca.gov>
American Wood Council (AWC). (2012). National Design Specifications for Wood
Construction, Leesburg, VA.
American Wood Council (AWC). (2008). Special Design Provisions for Wind and Seismic,
Leesburg, VA.
Bruneau, Michel (1992). “State-of-the-art Report on Seismic Performance of Unreinforced
Masonry Buildings”. J. Struct. Eng. 120:230-251.
Federal Emergency Management Agency (FEMA). (2000). Prestandard and Commentary for
the Seismic Rehabilitation of Buildings, Washington, DC.
68
Federal Emergency Management Agency (FEMA). (1992). Techniques for the Seismic
Rehabilitation of Existing Buildings, Washington, DC.
Hsiao, K and Tezcan, J. (2012). “Seismic Retrofitting of Chord Reinforcement for Unreinforced
Masonry Historic Buildings with Flexible Diaphragms”. American Society of Civil
Engineering, Reston, VA.
Luco, N., Ellingwod, B., Hamburger, R., Hooper, J., Kimball, J., and Kircher, C. (2007). “RiskTargeted Versus Current Seismic Design Maps for the Conterminous United States”.
Structural Engineering Association of California, Sacramento, CA.
Paret, T., Freeman, S., Searer, G., Hachem, M., and Gilmartin, U. (2007). “Using Traditional
and Innovative Approaches in the Seismic Evaluation and Strengthening of a Historic
Unreinforced Masonry Synagogue”. Wiss, Janney, Elstner Associates, Inc. Emeryville,
CA.
Shah, H., Gere, J., Krawinkler, H., Rojahan, C., and Zsutty, T. (1983). “A Preliminary Survey of
Damage to the Commercial District”. Earthquake Engineering Research Institute.
Oakland, CA.
S.K. Gosh Associates Inc. (2012). “Changes Between ASCE 7-05 and ASCE 7-10”. S.K. Gosh
Associates Inc., Palatine, IL.
United States Geologic Survey (USGS). (2009). “Earthquake Probability Mapping Tool”.
usgs.gov. April 29, 2014.
United States Geologic Survey (USGS). (2014). “Ground Motion Parameter Software, version
5.1.0”. usgs.gov. January 25, 2014.
United States Geologic Survey (USGS). (2014). “Soil Type and Shaking Hazard in the San
Francisco Ba Area”. usgs.gov. April 29, 2014.
69
United States Geologic Survey (USGS). (2014). “Quaternary Faults Web Mapping
Application”. usgs.gov. January 25, 2014.
Whittaker, A., Huang, Y., and Luco, N. (2014). “Maximum Direction Ground Motions”.
www.nibs.org. National Institute of Building Sciences. Washington, DC.