SEISMIC ASSESSMENT OF UNREINFORCED MASONRY BUILDINGS IN
BOSTON'S BACK BAY NEIGHBORHOOD
ARCHNES
by
MASSACHUSETTS U'
Emily D. Spencer
JUL 02 2015
B.S. Civil and Environmental Engineering
University of Houston, 2014
LIBRARIES
SUBMITTED TO THE DEPARTMENT OF CIVIL AND ENVIRONMENTAL
ENGINEERING IN PARTIAL FULFILLMENT OF THE REQUIREMENTS OF THE
DEGREE OF
MASTER OF ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
JUNE 2015
C 2015 Emily D. Spencer. All Rights Reserved.
The author hereby grants to MIT permission to reproduce
and to distribute publicly paper and electronic
copies of this thesis document in whole or in part
in any medium now known or hereafter created.
/
Signature of Author:
II
Signature redacted
Department of Civil a
nvir&115'ental Engieepn
May 11;
Certified by:
Signature redacted
r
John A. Q(fh'sendorf
Professor of Civil and Environmental Engineering and Architecture
Thesis Supervisor
Accepted by:
Signature redacted
IHeidi
Nepf
Donald and Martha Harleman Professor of Civil and EnvironmentAl Engineering
Chair, Department Committee for Graduate Students
TUTE
SEISMIC ASSESSMENT OF UNREINFORCED MASONRY BUILDINGS IN
BOSTON'S BACK BAY NEIGHBORHOOD
by
Emily D. Spencer
Submitted to the Department of Civil and Environmental Engineering
on May 11, 2015 in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering in
Civil and Environmental Engineering
ABSTRACT
This thesis presents a seismic evaluation of the unreinforced masonry buildings in Boston
Massachusetts's historical Back Bay neighborhood. This Boston district, famous for its rows of
Victorian brownstone residences is considered to be one of the best preserved examples of 1 9 'h
century urban design. There are a few specific reasons to speculate at the vulnerability of this
neighborhood to seismic events. First, in 1755, one hundred years before the Back Bay started to
be built, the most massive earthquake of New England's history occurred, damaging
unreinforced masonry structures in Boston. Approximately eighty percent of the Back Bay
neighborhood is now made up of unreinforced masonry structures. Second, seismic design was
not required in Boston until 1975, which means a staggering majority of the buildings in the
Back Bay were constructed without any kind of anti-seismic lateral system. The aim of this
thesis is to assess the structural response of the unreinforced masonry homes of the Back Bay to
seismic activity due to these issues. A case study of an unreinforced masonry building in the
neighborhood is assessed through structural analysis of its fagade and party walls. The
performance of this building is extrapolated to represent the state of the unreinforced masonry
buildings of the Back Bay.
Thesis Supervisor: John A. Ochsendorf
Title: Professor of Civil and Environmental Engineering and Architecture
3
Acknowledgement
I would like to thank a few people in particular that helped in the completion of this thesis.
First I would like to thank my advisor Professor John Ochsendorf for not only introducing me to
historical preservation engineering but also for his dedicated guidance and expertise through the
research and writing of this thesis.
I would also like to thank Post-Doctoral Student Ornella Iuorio for her leadership, insight,
friendship, and day to day assistance in this project.
Thank you to Professors Pierre Ghisbain and Jerome Connor for their incredible engineering
classes, knowledge, and advice.
Thank you to my friend Rosalie Bianquis, whose moral support during my time at MIT was
unprecedented and irreplaceable.
Especially, I would like to thank my parents, Bruce and Sandra, my brother Ian, and my sister
Samantha, for their love and encouragement during my years of school. I would also like to thank
my grandmother, Muriel Paschall, who always believed, more than I, how far I could go.
Finally I would like to thank all of my classmates in the Masters of Engineering program. I will
always remember their vehement support and friendship.
5
6
Table of Contents
Acknow ledgem ent ........................................................................................................................................
5
Table of Figures ............................................................................................................................................
9
Table of Tables ...........................................................................................................................................
11
1.0
Introduction.....................................................................................................................................13
1.1
Research M otivations and Objectives.....................................................................................
13
Classification of Unreinforced M asonry Structures...................................................................
15
Characteristics of URM buildings..........................................................................................
15
2.1.1 M asonry Walls ...........................................................................................................................
15
2.0
2.1
2.1.2 Flooring......................................................................................................................................16
2.1.3 Structural Behavior ....................................................................................................................
2.2
Failure M echanism s of URM Walls ...........................................................................................
17
17
2.2.1
In-Plane Failures .................................................................................................................
18
2.2.2
Out-of-Plane Failures.....................................................................................................
19
Earthquake Perform ance of URM W alls ....................................................................................
2.3
Earthquake H istory of Boston.....................................................................................................
3.0
20
21
H istorical Boston Earthquakes.................................................................................................
21
3.1.1
The Cape Ann Earthquake ..............................................................................................
21
3.1.2
Earthquake Risk in Boston..............................................................................................
23
3.1
3.2
Boston Geology ..........................................................................................................................
23
3.3
H istory of Boston Seism ic Building Codes ............................................................................
24
The Back Bay ..................................................................................................................................
4.0
25
4.1
History.........................................................................................................................................25
4.2
Neighborhood Building Typologies........................................................................................
26
4.2.1
Unreinforced M asonry .....................................................................................................
27
4.2.2
Transitional M asonry .....................................................................................................
27
4.2.3
M odem Construction ..........................................................................................................
28
M ethod of Structural Analysis .....................................................................................................
29
General M odel Inputs..................................................................................................................
29
5.0
5.1
5.1.1
Estim ated M aterial Properties..........................................................................................
29
5.1.2
Expected Ground M otion.................................................................................................
30
5.1.3
Estim ated Base Shear.....................................................................................................
30
Cantilever Beam M ethod ............................................................................................................
31
5.2
7
5.3
Finite Element M odel .................................................................................................................
32
5.4
Global Behavior Evaluation Criteria........................................................................................
35
5.5
Local Behavior Evaluation Criteria .........................................................................................
36
In Plan e ...............................................................................................................................................
36
O ut o f Plan e ........................................................................................................................................
37
6.0 Case Study Structural Analysis Results ............................................................................................
6.1
40
M odelling Considerations..............................................................................................................42
6.2 Cantilever Beam Results...................................................................................................................43
6.3 Finite Element M odel Results...........................................................................................................45
S cen ario 1............................................................................................................................................
45
S cen ario 2 ............................................................................................................................................
53
6.4 Local Elem ent Failure Results..........................................................................................................57
In-Plane Failure Results ......................................................................................................................
57
Out-of-Plane Failure Results...............................................................................................................63
6.5 Analysis M odel Conclusions..............................................................................................................
7.0
7.1
66
Conclusion......................................................................................................................................68
Areas of Future W ork .................................................................................................................
Documentation References .........................................................................................................................
Image References........................................................................................................................................71
8
69
70
Table of Figures
Figure 1 A brick masonry wall is made of multiple wythe layers of stretcher and header brick courses
15
(tp ub .co m )...................................................................................................................................................
16
Figure 2 Pier and spandrel elements define sections of a perforated masonry wall. ..............................
16
Figure 3 Pier and spandrel elements define sections of a perforated masonry wall. ..............................
Figure 4 Joist pockets in the masonry allow timber joists to transfer floor loads to load bearing walls.... 16
Figure 5 Joist pockets in the masonry allow timber joists to transfer floor loads to load bearing wallss.. 17
17
Figure 6 Pier and spandrel elements define sections of a perforated masonry wall. ..............................
Figure 7 Unreinforced masonry wall failures from varying ground accelerations where liquefaction was an
issue. (a) Damage from a quake in Nisqually, Washington with peak ground acceleration of 0.31g
(Washington Surveying and Rating Bureau) (b) Long Beach, CA full fagade failure with PGA of 0.22g
(Historical Society of Long Beach) (c) The famous Northridge earthquake caused corner failure due to a
PGA of 1.Og (Bruneau)(d) The Loma Preita, CA earthquake with a PGA of 0.16g causing out of plane
failure of a fagade wall (EERI) (e) Recent damage from the Napa Valley, CA earthquake with PGA of
0.35g causing this corner failure (ZFA Structural Engineers) (f) One of the strongest earthquakes in history,
the Christchurch earthquake caused this full facade failure with a PGA of 1.8g (USGS)......................20
Figure 8 Notable earthquakes affecting Boston from the 1 7 th century to the 2 1St century and their
21
ep icen ters. ...................................................................................................................................................
Figure 9 Historical drawings accounting the Cape Ann earthquake of 1755 (National Information Service
for E arthquake E ngineering).......................................................................................................................22
Figure 10 The Cape Ann earthquake of 1755 aligns with the facades of the Back Bay residences in
B oston , M assachu setts................................................................................................................................23
Figure 11 The Back Bay residences have a similar building organization and structure (Bunting)...........26
Figure 12 The Back Bay consists of four general building types: unreinforced masonry (yellow),
reinforced masonry (red), modern construction (blue), and churches (green)........................................27
Figure 13 The cantilever beam model lumps masses at the floor levels where portions of the base shear
31
are app lied ...................................................................................................................................................
32
Figure 14 Bad w all to w all connection ..................................................................................................
Figure 15 The four wall sections make up four different SAP2000 models to analyze.......................... 33
Figure 16 An example of the data collection process for the SAP2000 models. Proportional base shear
values are applied at the joints at floor level and deflection values are read from the joints on the right side
34
of the m odel also at floor level....................................................................................................................
Figure 17 SAP2000 models, from right, considering 10%, 50%, and 100% of the building acting together,
34
w ill be also necessary to analyze. ...............................................................................................................
37
Figure 18 Rigid block free-body diagram (DeJong)..............................................................................
40
Figure 19 Front and rear faqades of 37 Commonwealth........................................................................
Figure 20 Counterclockwise from left, interior brick courses, vaulted brick basement floor, and joist
41
pockets of 39 C omm onw ealth ....................................................................................................................
Figure 21 Original structural drawings of 37 Commonwealth (Boston Athenaeum N. Bradlee Collection).
. ...................................................................................................................................................................
Figure
Figure
Figure
Figure
Figure
Figure
Figure
22 Modeling simplifications for scenario 1................................................................................
23 Modeling simplification for scenario 2...................................................................................
24 Pushover curve for the cantilever beam hand calculations......................................................
25 Pushover curve from SAP2000 for scenario 1. .....................................................................
26 Base shear vs. interstory drift for the basement level............................................................
27 Base shear vs. interstory drift for the first floor......................................................................
28 Base shear vs. interstory drift for the second floor.................................................................49
9
41
42
43
43
45
47
48
Figure 29 Base shear vs. interstory drift for the third floor. ....................................................................
50
Figure 30 Base shear vs. interstory drift for the fourth floor. .................................................................
51
Figure 31 Base shear vs. interstory drift for the roof level. ....................................................................
52
Figure 32 Pushover curve from the cantilever beam hand calculations for scenario 2.......................... 53
Figure 33 Pushover curve from SAP2000 for scenario 2. ......................................................................
54
Figure 34 Base shear vs. interstory drift for the basement level............................................................
54
Figure 35 Base shear vs. interstory drift for the first floor.....................................................................
55
Figure 36 Base shear vs. interstory drift for the second floor ................................................................
55
Figure 37 Base shear vs. interstory drift for the third floor. ....................................................................
56
Figure 38 Base shear vs. interstory drift for the fourth floor. ..................................................................
56
Figure 39 Base shear vs. interstory drift for the roof level. ....................................................................
57
Figure 40 Most of the piers will fail from diagonal tension failure in the SAP2000 models. Bed joint
sliding is observed in the full wall and rocking is observed in the curved wall section. ........................ 58
Figure 41 Local shear failure examination for full wall. ........................................................................
59
Figure 42 Local shear failure examination for flat wall section. ...........................................................
60
Figure 43 Local shear failure examination for the curved wall section .................................................
61
Figure 44 Local shear failure examination for the long pier section of the fagade.................................62
Figure 45 C ase study chim ney ....................................................................................................................
64
10
Table of Tables
Table 1 Masonry properties used throughout all models and calculation methods in this thesis. .......... 29
Table 2 Ground motion and response spectrum values necessary to determine expected building base shear.
31
....................................................................................................................................................................
Table 3 FEMA 356 interstory drift limits for Collapse Prevention, Life Safety, and Immediate Occupancy
35
perform ance levels. .....................................................................................................................................
Table 4 To violate the FEMA 356 performance levels, these are the interstory distances that each floor is
allow ed to drift............................................................................................................................................36
Table 5 Expected base shear for wall sections in scenario 1 and corresponding max roof displacements. 44
Table 6 Expected base shear for wall sections in scenario 2 and corresponding max roof displacements. 44
Table 7 Base shear values necessary to exceed FEMA 356 performance levels for the overal pushover
46
cu rv e ............................................................................................................................................................
Table 8 Base shear values necessary to exceed FEMA 356 performance levels for basement level. ........ 47
Table 9 Base shear values necessary to exceed FEMA 356 performance levels for first floor..............48
49
Table 10 Base shear values necessary to exceed FEMA 356 performance levels for second floor. .....
Table 11 Base shear values necessary to exceed FEMA 356 performance levels for third floor...........50
Table 12 Base shear values necessary to exceed FEMA 356 performance levels for fourth floor......51
Table 13 Base shear values necessary to exceed FEMA 356 performance levels for roof level............52
Table 14 Terms needed for rigid block analysis of full fagade...............................................................63
63
Table 15 Stability results for full fagade rigid block calculation. ...........................................................
64
Table 16 Stability results of roof w all.....................................................................................................
Table 17 Stability analysis of chimney that is one wythe thick..............................................................65
65
Table 18 Shear capacities at different failure plane heights. .................................................................
66
.........................................
fagade
portions.
interstory
to
crack
Table 19 Minimum ground acceleration
11
12
1.0
Introduction
Low rise unreinforced masonry buildings are one of the most common structural types in use in
the United States. Typically built before the early twentieth century, unreinforced masonry
buildings are constructed as four load bearing multi-wythe brick walls with flexible diaphragm
timber floors. Inherently, earthquake resistance in these buildings comes from the massive gravity
load of the bearing walls, but a lack of lateral anti-seismic design condemns them to be one of the
most vulnerable building types to seismic damage.
The unreinforced masonry building type describes the majority of the structures in the historical
neighborhood of the Back Bay in Boston, Massachusetts. As one of the best examples of nineteenth
century urban design in the United States, this neighborhood is lined with beautiful irreplaceable
Victorian brownstone rowhouses.
The Back Bay is faced with several issues. In a region that is seemingly not susceptible to
earthquakes, seismic design was not required for new construction in Massachusetts law until
1975, which means virtually all of the unreinforced masonry homes in the neighborhood were
traditionally built without any kind of anti-seismic design. Although rare, Boston has been affected
by a handful of damaging earthquakes in the past, namely one of intensity VIII (MMI) off of the
coast of Cape Ann, Massachusetts in 1755. Also, the Back Bay was built on timber piles through
an infilled area of the Charles River that is susceptible to liquefaction. By considering these
structural issues, the building performance can be assessed to make an appropriate seismic
assessment of the neighborhood.
Research Motivations and Objectives
1.1
The aim of this thesis is to understand the structural performance of the unreinforced masonry
buildings in the Back Bay during imminent future earthquakes. The motivations for this thesis are
evident in the subsequent points.
1. Back Bay unreinforced masonry homes were built without anti-seismic design on infilled
land. Major earthquakes in the 1 71h and 18t centuries damaged the existing brick buildings.
It has been more than 250 years since an earthquake that had the intensity of Cape Ann's
and it is reasonable to think that Boston is overdue for an earthquake that can happen at
any time.
13
2. Politics has prevented a publically available study on the seismic vulnerability of the Back
Bay neighborhood as most of the residences are privately owned by the affluent or
landlords who choose either not to reveal structural analyses on their homes or are scared
to see the results of such a study.
3. Many engineers in the northeast don't believe in a seismic risk to Boston and the Back Bay
large enough to substantiate mandatory action. It is necessary to cogitate the long list of
risks facing the Back Bay to fully understand the earthquake vulnerability.
To honor these motivations, this thesis will focus on the following objectives:
*
Collect in one piece of literature the primary seismic issues facing the Back Bay
" Determine seismic performance of Back Bay structures to facilitate future retrofitting in
order to save money and lives
This thesis will begin with a classification of non-specific unreinforced masonry structures, their
failure modes, and observed earthquake performance. Structural analysis methods and evaluation
criteria for this type of building will be presented. A case study building in the Back Bay
neighborhood will then be analyzed through hand calculations and a finite element model.
Expected ground accelerations for the Back Bay area will be applied to the calculations. The
performance of the case study will be determined by global behaviors such as interstory drift and
local behaviors such as pier deterioration and chimney dislocation. The conclusion of this thesis
will extrapolate a basic seismic assessment for the Back Bay neighborhood.
14
2.0
Classification of Unreinforced Masonry Structures
Characteristics of URM buildings
2.1
Typically built before the early twentieth century when the utilization of steel frame design had
not become commonplace, an unreinforced masonry building is defined as a building whose walls
are constructed of stacked masonry units bonded by mortar without steel reinforcement. The type
of masonry used can consist of brick, hollow clay tiles, stone, concrete blocks, or adobe (FEMA
2009). This thesis will focus on unreinforced brick buildings. Defining characteristics of
unreinforced masonry buildings include: use of lime and sand mortar, lack of steel reinforcing,
vertically tapering wall thicknesses, perforated walls, decorative parapets and chimneys that
extend higher than the occupiable structure, timber floors, and an exterior masonry veneer. These
characteristics will be explained in detail.
2.1.1 Masonry Walls
The walls in unreinforced masonry buildings, regardless of masonry material, act as the main
vertical resistance system, supporting their own weight and dead and live loads emanating from
the floors and roof. These load bearing walls are considered to be engineered and not designed in
that they were designed empirically from tables published in local building laws that defined wall
thickness as a function of building height in order to maintain the compressive stress in the
masonry walls to be below the maximum allowed stress values, which inherently caused very
conservative factors of safety in the walls (Buntrock 2010).
In particular, unreinforced brick masonry buildings consist of walls made of a number of brick
wythes, which is a vertical layer of bricks. Typically, two or three layers of structural brick layers
reside behind a veneer exterior wythe, which is a layer of better looking brick. Every few layers
of the veneer brick layer,
there are header bricks which
STRETCHER
NEAM
are turned ninety degrees to
connect the outer wythe to
the inner wythes. Sometimes
there is a whole course of
header bricks, while at other
Figure 1 A brick masonry wall is made of multiple wythe layers of stretcher and header
brick courses (tpub.com).
15
times a brick course may have a header brick separated by a regular brick, or a stretcher. Header
bricks are one of the main characteristics to find when identifying an unreinforced masonry
building from the exterior (FEMA 2009). These terms are manifested in Figure 1.
Perforations, or holes for windows, are found in
most unreinforced brick structures and their
placement and size can dictate the structural
integrity of the wall, so their dimensions are
nowadays confined by codes. The perforations
SPAN
separate the walls into new building elements that
can be categorized further. A spandrel is a section
of a wall between perforations of different stories,
Figure 2 Pier and spandrel elements define sections of a
perforated masonry wall.
and a pier is the section of the wall between perforations on the same floor.
Parapets are a portion of the masonry wall that extends above the top floor of the building. Their
heights range from a few inches to a few feet. The purpose of the parapet is to protect the roofing
materials from wind, to act as a guardrail when the roof is occupied, and to make the building
appear taller. Chimneys, like parapets, extend higher than the roof and can be many feet tall. As
part of an unreinforced building, these elements are also unreinforced brick, which can make them
very vulnerable to failure (FEMA E-74).
2.1.2 Flooring
Joists and sheathing made of timber span between the masonry walls. The joists are usually a foot
in depth, a few inches thick, and are spaced one foot on center. If the masonry walls are vertically
tapered and reduce thickness with every floor,
there is a shelf for the joists to sit on. But if the
walls are not tapered, which is characteristic for
low-rise masonry buildings, instead of a shelf
there exists a joist pocket which is a rectangular
shaped hole in the masonry that the joist slides
Figure 3 Joist pockets of unreinforced masonry building (280
into. An example of a joist pocket is in Figure commonwealth).
16
3. In both of these cases the joist simply sits on
a masonry base creating a simply supported
condition, but in some situations the joist
pockets may be more confining which can
create a fixed condition at the joist end when the
timber floor deflects. On top of the joists is
timber sheathing which are sheets of plywood
Figure 4 Arched brick vaults separated by iron beams are
sometimes seen in unreinforced masonry buildings (Friedman).
one fourth to one half inches thick and can be in one or more layers. Some unreinforced masonry
buildings don't have bottom floors made out of timber, but of vaulted brick with iron beams, as
seen in Figure 4 (Friedman 1995).
2.1.3 Structural Behavior
As aforementioned, the masonry walls are load bearing and the codes that led to their construction
deem them to be able to withstand high vertical compressive stresses. The timber floors deflect
under live loads and transfer force to the adjoining walls, but depending on the boundary condition
it may be a bending stress or just a floor bearing load. Depending on the configuration of the
building, timber joists may only be transferring loads to the party walls if there are only joist
pockets in one direction. In this case, the force and deflection of the party walls will continue to
distribute force through the wall-to-wall corner connection, creating a box effect, assuming the
connection is uncracked, in good condition, and can transfer loads.
The walls of unreinforced masonry buildings were not designed to resist wind loads and
earthquake loads. The compressive stress of the walls generally compensates for lateral wind
forces and it is not common to observe building failures due to wind, but that is out of the scope
of this thesis. A more controversial aspect about the erection of these buildings is that they are
observed to have been built without earthquake design. Historic seismic events have proven that
the vertical compressive stress that may resist wind loads well are not enough to prevent the walls
from failing from earthquakes (Buntrock 2010).
Failure Mechanisms of URM Walls
2.2
Unreinforced masonry walls are highly indeterminate and because of this have been observed to
fail in a multitude of in-plane and out-of-plane modes. According to FEMA 306, for a perforated
wall with weak piers and strong spandrels, which is the condition assumed for this thesis, there are
17
four modes of in-plane and two out of plane failure mechanisms. For in-plane, these are flexural
rocking, bed joint sliding, diagonal tension cracking, and toe crushing. Pictorial examples of these
failures are in Figure 5. For out of plane there is one way bending and two way bending, depicted
in Figure 6. FEMA 306 provides a shear capacity equation for each failure mode. The failure
mode of wall elements is dictated by certain parameters and is typically governed by the lowest
shear value. It is observed that through calculation later in this document that the failure mode can
be said to be dictated by the pier height to width ratio and compressive stress caused by the
masonry above the pier.
2.2.1
1.
In-Plane Failures
Flexural Rocking
The flexural rocking mode is characterized by cracking at the top and bottom of a perforated wall's
piers. It is observed to occur when piers are slender, spandrels are strong, and the compressive
stress within the masonry is low. In this behavior mode, the piers rock and develop hairline
fractures at the top and bottom of the piers. Although cracking deformations can be large, this
failure is still considered to be stable since it can still handle vertical loads. If rocking continues,
the pier can degrade, overturn in-plane, or slowly 'walk' out-of-plane, causing instability.
2.
Bed Joint Sliding
The bed-joint sliding mode is characterized by cracking that occurs in the mortar bed-joints
between masonry units in the horizontal plane and in a stair-stepping pattern. This failure mode
occurs when the shear strength of the masonry is higher than that of the mortar.
3.
Toe Crushing
Toe-crushing occurs when shear stress is concentrated at the toe of a pier during rocking, causing
cracking and material spalling to occur. As the rocking mode degrades the pier, bed-joint sliding
occurs in the middle, and diagonal cracks form from the toe of the pier to the upper corners. Failure
by toe-crushing occurs when the toe of the wall has weakened to a point when the vertical load
carrying capacity of the pier has been compromised.
4.
Diagonal Tension Cracking
When a pier with strong mortar and weak masonry units is subjected to high compressive stress,
the diagonal tension cracking mode can be observed. This behavior is characterized by an 'X'
18
shape that develops through the masonry units, not around, in the pier. Sometimes, with strong
masonry units and weak mortar, this mechanism can occur but with cracking in a stair-stepping
shape, similar to that of bed-joint sliding, but in an 'X' shape. Diagonal tension cracking is
considered to be a failure more than the three aforementioned modes since it cannot handle vertical
loads after its initiation.
2.2.2
1.
Out-of-Plane Failures
One-way bending
In this failure mode, a wall
overturns in one direction,
such as a parapet, chimney, or
the top story wall of a
structure
cracking
at
the
penultimate floor diaphragm,
and falling to the ground.
2.
Figure 5 From top left, clockwise, examples of rocking failure (Javed), bed joint sliding
Two-way bending
Two-way bending is very
similar to one way bending in
(FEMA), diagonal tension cracking (FEMA), and toe crushing (FEMA).
terms of cause but occurs when the location of the crack development is at the central area of the
story wall, causing the two portions of the wall to burst outward at opposite rotation angles either
horizontally or vertically.
Figure 6 From the left, a one way bending parapet failure (Welliver), a one way bending fullfloor failure (FEMA), and a two way
bending failure of two floors (Bruneau).
19
Perforated walls with weak spandrels and strong piers have a similar method of failure mode
determination, but due to height to width ratios of the piers and the height of the spandrels of the
case study building analyzed in Chapter 5, this condition is out of the scope of this thesis.
2.3
Earthquake Performance of URM Walls
This section will parameterize unreinforced masonry earthquake damage in terms of ground
acceleration in order to visually imagine expected damage for the Back Bay. It is estimated that
the Cape Ann earthquake in 1755 had a ground acceleration of 0.18-0.21g (Whitman 1975). The
examples of damage in Figure 7 are all from sites with loose soil where liquefaction occurred,
which is estimated to be the conditions in the Back Bay.
(a)
(d)
Figure 7 Unreinforced masonry
wallfailures from varying
ground accelerations where
liquefaction was an issue.
(a) Damage from a quake in
Nisqually, Washington with
peak ground acceleration of
0.31g
(Washington Surveying
and Rating Bureau)
(b) Long Beach, CA fullfagade
failure with PGA of 0.22g
(Historical Society of Long
(b)
Beach)
(c) Thefamous Northridge
earthquake caused corner
failure due to a PGA of 1.Og
(Bruneau)
(d) The Loma Preita, CA
earthquake with a PGA of 0.16g
causing out of plane failure of a
fagade wall (EERI)
M)
(e) Recent damage from the
Napa Valley, CA earthquake
with PGA of 0.35g causing this
f)
"77
20
corner failure (ZFA Structural
Engineers)
(f) One of the strongest
earthquakes in history, the
Christchurch earthquake
caused this full fagadefailure
with a PGA of 1.8g (USGS)
3.0
Earthquake History of Boston
Historical Boston Earthquakes
3.1
Extensive records of seismic activity have been taken in the New England area since it was settled
in the early 1600s. Since 1602, nineteen earthquakes, of intensity 5 or greater, have occurred with
their epicenter in Massachusetts. Between the years of 1668 and 2007, there have been 355 total
earthquakes in Massachusetts. Many other moderate earthquakes, centered in Maine, New York,
New Hampshire, and Canada have affected Massachusetts in damaging ways. Figure 8 shows a
number of earthquakes with available information to have damaged Boston between the 1 7 th
century and twenty first century and their epicenters (USGS).
HISTORICAL EARTHQUAKES TO HAVE AFFECTED BOSTON, MA
12
100
zz
00
cc
z
-bX
160
65
10015
0 0
801
195200
4YEA
Figure 8 Notable earthquakes
affecting Boston from the 1 7(X century to the 21"~century and their epicenters.
3.1 .1 The Cape Ann Earthquake
The most destructive earthquake to have ever occurred in New England had a max intensity
(Modified Mercalli Intensity scale) of 8 centered 25 miles east of Cape Ann, Massachusetts on
November 18, 1755. Felt over 300,000 square miles, from Halifax, Nova Scotia to the north,
Winyah, South Carolina to the south, and even 250 miles out to sea, the earthquake caused a
tsunami in the West Indies. The area felt several aftershocks and tremors, notably north of Boston.
21
Seventeen days before, on November 1, Lisbon, Portugal was devastated by a massive earthquake
and tsunami. It is believed, however not proven, that it triggered the Cape Ann earthquake (USGS).
It is important to note that the majority of the damage was concentrated in the small Boston harbor
areas that had been infilled, as the Back Bay neighborhood is now. Having said that, a lot of
damage still occurred on the natural land portions of the city, which is concerning since most of
Boston now is built on non-engineered fill. It was recorded in Boston that approximately 1500
chimneys were damaged, stone walls and fences collapsed, and roofs were damaged (Ebel 2006).
An account from a Bostonian named John Hyde in 1755 stated, "Many chimnies.. .not fewer than
12 or 1500 are shattered, and thrown down in part; so that in some places, especially on the low
loose ground, are dislocated, or broken several feet from the top.. .the streets are almost covered
with the bricks that have fallen...the roofs of some houses are quite broken in by the fall of the
chimnies" (Philisophical Transactions). An account from John Adams, future President of the
United States, stated of the quake, "The house[s] seemed to rock and reel and crack as if it would
fall in ruins..." (Adams 1856).
Figure 9 Historical drawings accounting the Cape Ann earthquake of 1755 (National Information Service for Earthquake
Engineering)
Modern analysis of the Cape Ann earthquake suggests that based on masonry chimney damage,
the ground acceleration might have been as large as 0.18-0.21g (Whitman). It is estimated that
these ground motions equate to 2% chance of exceedance every 50 years (USGS). Small
earthquakes continue to occur in a cluster in this area and are believed to be very late aftershocks
to the 1755 quake (Ebel 2006).
The earthquake epicenter was about 30 miles east off the coast of Cape Ann. If it is assumed that
ground motion emanates radially from that location, it approaches the Back Bay neighborhood at
an angle of sixty degrees, if lines of latitude constitute as zero degrees. The neighborhood is also
22
oriented along the Charles River at an angle very close to sixty degrees. This means that for
structural analysis done in Chapter 6, applying the earthquake load in-plane with the fagade is
acceptable. Figure 10 displays this finding.
CAPE ANN
EPICENTER
BACK BAY
37 COMMONWEALTH
Figure 10 The Cape Ann earthquake of 1755 aligns with the facades of the Back Bay residences in
Boston, Massachusetts.
3.1.2 Earthquake Risk in Boston
Although Boston and Massachusetts in general do not lie on major active tectonic boundaries like
California or Japan, they do lie on ancient faults that formed hundreds of millions of years ago and
are now considered to be geological zones of weakness. It is believed that these zones of weakness
are areas that stresses from present day faulting action can be released, reactivating the ancient
faults and causing intraplate earthquakes.
It is near impossible to predict where, when, and how strong the next earthquake in Boston will
be. There is a general correlation between the locations of earthquake epicenters in New England
from 1602-2014, and it is expected that there is a 2% chance that in any given period of 50 years
an earthquake will occur that is potentially damaging (Kafka).
3.2
Boston Geology
Boston geology can be simplified into two strata. First, the bedrock is made up of a rock formation
called Cambridge Argillite, which is a typically weak rock that is slightly metamorphic (USGS).
Second, a great majority of the Boston landmass is made up of non-engineered, cohesionless,
23
saturated infill. These two weak layers can be the cause of ground failure during seismic activity.
A geologic phenomenon called liquefaction occurs when the strength and stiffness of a soil
deteriorates from seismic shaking and begins to behave like a liquid. Devastating ground failure
can results from liquefaction (USGS). Of the historic earthquakes that have had epicenters near
Boston, four had ground accelerations that had the potential to cause liquefaction (1638, 1663,
1727, and 1755). Further analysis of the effects of liquefaction are out of the scope of this thesis,
but it is important to note its potentiality when considering seismic risk for the Back Bay.
History of Boston Seismic Building Codes
3.3
In the United States, the first provisions made for seismic design were first seen in the appendix
to the 1927 Uniform Building Code (UBC). The first national seismic zone hazard map was seen
in the UBC in 1949. By the 1950s, cities in California had begun to adopt their own seismic
resistant design measures. After the San Fernando earthquake in 1971, many revisions were made
to the UBC in 1973 (FEMA 1998). In 1975 Massachusetts became the first state in the east to
implement seismic design provisions that were particular for the state. A study entitled 'Seismic
Design Decision Analysis' done by Robert Whitman of MIT determined that the maximum
intensity of earthquake that was probable for the state was similar to the UBC's Zone 3
classification in California (instead of the current Zone 2A classification), but with lower return
periods (Nordenson). The zoning classification is vestige of the old UBC building code. Zone 2A
corresponds to a potential peak ground acceleration of 0.1 5g and Zone 3 corresponds to 0.30g. A
committee of engineers used the MIT study as justification to recommend the 1975 provisions,
which included seismic design requirements for new construction. It wasn't until 1980 that
rehabilitation requirements were made for existing buildings.
24
4.0
The Back Bay
4.1
History
of the Back Bay neighborhood came about not long after Boston, Massachusetts
institution
The
decided to transform itself from a harbor town to a more prosperous, lively city. To do this the city
decided that they needed start harnessing energy from the surrounding rivers in Boston in order to
become a boom town like certain cities in California and Texas (Bunting 1967). From the year
1818 to 1821, the construction of the Mill Dam took place. As one of Boston's greatest engineering
achievements, this dam project's intent was to increase Boston's water power and industrial
prowess and to provide a toll road to and from the city. Because the Charles River becomes nothing
more than a slow flowing estuary that rose and fell with the tides, the Mill Dam did not end up
producing the expected amount of water power that was predicted. Even though a great feat of
engineering, the Mill Dam was a huge failure. The course of the Mill Dam confined a bay next
to Boston, named the Back Bay. After being dammed up for years, the bay turned into a stagnant
lagoon of raw sewage and trash that didn't allow much inflow and outflow to dilute the waste. In
1849 the Health Department demanded that the bay be filled in for public health reasons.
Meanwhile, early 1 9 th century Boston saw a substantial rise in population. In fact, the single decade
of the 1840s saw a population increase of 33 percent. Due to a need to cover up the environmental
hazard that the Back Bay waters were becoming and the need for more housing developments, it
was decided that the Back Bay waters would be filled in (Creating Land in Boston's Back Bay).
In 1857, the Back Bay began to be infilled with glacial granite from West Needham,
Massachusetts. This ice-age gravel was transported on train tracks built especially for the project
that are part of the present day Green Line in Boston and Commonwealth Avenue in the Back Bay
neighborhood. The Mill Dam was covered completely by the gravel and resides under present day
Beacon Street. By the start of the Civil War, the bay had been infilled as far west as Clarendon
Street. It was around this time that investors built the first brownstone houses. As more land was
filled in, more houses were built. War prosperity caused an acceleration in the infilling process
and home construction. By 1870, the infill was complete through Dartmouth Street up to Exeter
Street. In 1872, a large fire destroyed 65 acres of Boston, delaying construction and causing
required fire escapes in the newly constructed homes. By the late 1880s, the infill project was
complete up to the Fens. In the decade following, the remainder of the Back Bay was filled in. At
the end of the project 450 acres were added to the original 783 acres of Boston (Bunting 1967).
25
4.2
Neighborhood Building Typologies
Back Bay structures have defining characteristics. A Back Bay house is considered to be a Type
II structure according to the Boston Building Department. A Type II structure has exterior walls
made of masonry and interior floors and partitions made of wood. The high quality seasoned timber
floor joists are overdesigned by modem standards and are typically 3"x 12" spaced 1 foot on center.
Brick party walls describe the longer walls perpendicular to the road and are engaged by the
transverse floor loads. The facade and rear elevations, parallel to the road, are only susceptible to
gravity loads, out of plane loading, and roof loads. Each fagade and rear elevation is represented
by multiple, tall windows. A typical foundation is comprised of wooden piles ranging from 20-35
feet deep, spaced from 1.5-3 feet on center, that are positioned under the stone foundation walls,
which are in turn atop granite leveling blocks (Bunting 1967). Figure 11 shows these typical
properties.
Figure 11 The Back Bay residences have a similar building organization and structure (Bunting).
Three typologies, specified in Figure 12 for each residence, specifically describe the majority of
the buildings of the Back Bay: unreinforced masonry, transitional masonry, and modem
construction buildings. The materials, construction technique, and structural behavior of the
buildings are dictated by these categories.
26
4.2.1 Unreinforced Masonry
The unreinforced masonry typology encompasses about eighty percent of the Back Bay
neighborhood. Built approximately between the years of 1860 and 1910, these buildings are
typically three to five stories in height. During this time there were city ordinances limiting the
height of the neighborhood buildings to keep the fagade looking continuous. The masonry walls,
typically 16 inches thick at street level and decreasing in size with increasing floor number, are
made out of layered brick wythes. Two or three wythes reside behind an ornamental wythe of
better looking brick. These thick, heavy walls represent the main vertical structural resistant
system. The horizontal floors are timber joists. Joist-pockets in the masonry walls allow the
insertion of the transverse joists so that they may transfer loads to the walls. It has been observed
that the floor between the basement and first floor are not wooden joists, but vaulted brick flooring
with iron beams. The roofs are flat with tar and gravel or slanted wooden mansards roofs.
4.2.2 Transitional Masonry
Transitional masonry describes a generation of buildings that present a combination of old and
new building materials and were built in the Back Bay beginning in the twentieth century until
about the year 1970. Structural steel was introduced to building construction and allowed the
buildings in the neighborhood to realize heights of seven to ten stories. Each building comprises
of steel frames with masonry infilled multi-wythe walls. Flooring materials have been observed to
0
lo
Or'-w
r
I
~ ~
~
TYCCG
-
Lrm3@!tdM
Figure 12 The Back Bay consists offour general building types: unreinforced masonry (yellow), reinforced masonry (red), modern
construction (blue), and churches (green).
27
be timber joists or concrete. The joist to wall connection in transitional masonry is no longer a joist
pocket situation but instead a more modem connection exists where the joists connect to the
horizontal steel beams. The roofs are also flat or wooden mansard.
4.2.3
Modem Construction
Modem construction in the Back Bay is represented by structures containing reinforced concrete
that rise higher than about ten stories. Further, the modem construction typology can be separated
into two categories: those built before the implementation of the Boston seismic code in 1970 and
those after, to the new code. However, the majority of the modem construction buildings were
constructed before the advent of the code.
28
5.0
Method of Structural Analysis
There are many assumptions and means of approach for the structural analysis of unreinforced
masonry buildings under lateral loading, which causes them to be incredibly complex. Therefore
there is not one accepted analysis method. Some codes, such as those from FEMA, suggest
ignoring out of plane wall stiffness when analyzing the URM building response and only
considering wall mass, while some codes deem it necessary to include out of plane stiffness
especially if the out of plane walls carry most of the diaphragm load (Park 2009). This thesis will
explore different analysis methods to evaluate the seismic response of the unreinforced masonry
buildings of the Back Bay.
General Model Inputs
5.1
First, all geometries and measurements used in hand calculations and finite element models were
taken straight from the original structural drawings by N. Bradlee from the Boston Athenaeum.
Pictures were taken of the drawings and by using a few key dimensions, scaled CAD drawings
were able to be made. Every dimension used for this thesis was taken from those scaled drawings.
5.1.1 Estimated Material Properties
It is incredibly difficult to choose correctly the properties of existing masonry buildings, especially
those that are over 150 years old. Structural properties cannot be inferred solely from age and can
be determined by material testing or code default values (FEMA 1997). Since the case study
property is a private residence, under no circumstance would it have been possible to carry out
invasive or even non-invasive measures in order to obtain material samples to determine material
properties from. Therefore it was necessary to use default values suggested by the FEMA 356 and
ASCE 41 codes which are essentially one and the same. Table 1 summarizes the estimated material
properties and their sources.
Table 1 Masonry properties used throughout all models and calculation methods in this thesis.
Source
Notes
Value
Units
Compressive Strength of Brick (f'm)
780
psi
FEMA 356 Table 7-1 & 7-2 Assume Fair Condition
Elastic Modulus in Compression (E)
429000
psi
FEMA 356 Table 7-1 & 7-2 Assume Fair Condition
Property
Flexural & Diagonal Tensile Strength
(f'dt)
13
psi
FEMA 356 Table 7-1& 7-2 Assume Fair Condition
Shear Strength of Masonry Bed Joint
(Vie)
26
psi
FEMA 356 Table 7-1 & 7-2 Assume Fair Condition
120
lb/ft3
-
Masonry Specific Gravity (y)
Poisson's Ratio for Masonry (v)
0.25
29
-
-
In accepted range for property
Accepted mid-range value
5.1.2 Expected Ground Motion
The peak ground acceleration values for the Back Bay area are estimated from maps and equations
presented in Chapters 11 and 22 of the ASCE 7-10 code. By reading the typological lines on the
maps, the expected ground acceleration is determined to be 14.32% the force of gravity for soil
class B. But the Back Bay is built on infilled land and can be assumed to be of soil class D (accepted
default value when conditions unknown), which increases the peak ground acceleration to a value
of 22.92% the force of gravity. The exact value of 0.2292g is provided by ASCE 7-10 for the Back
Bay zip code 02116 and soil class D and is directly used in the hand calculations for the cantilever
beam method. A paper written by Robert Whitman, a former professor of MIT, well before ASCE
7-10 determined these values, suggests that it is likely that the Cape Ann earthquake had a ground
acceleration of 0.18-0.21g. In this thesis the ground acceleration of 0.2292g will be used due to
the support of Whitman's hypothetical ground accelerations.
5.1.3 Estimated Base Shear
The ASCE 7-10 code provides a method to estimate the base shear values that will be applied to
the base of the four wall sections. First the section's fundamental period must be estimated:
T = Ctho(1)
Where Ct and x are period parameters taken from Table 12.8-2 of ASCE 7-10 under the category
of 'All other structural systems' and are 0.02 and 0.75, respectively. The term htot is the total height
of the wall section. This value for the period has to be compared to TL, which is the long term
period in order to determine which equation to use next. The long term period for the Boston area
is 6 seconds. For the height of the case study building, the estimated period will never reach above
6 seconds, so the seismic response coefficient needed will be calculated as:
CS=
(2)
sS
And not to exceed:
Cs,max
-
D1
(3)
Where T is the fundamental period calculated in Equation 3, R is a response modification factor
found in Table 12.14-1 of ASCE 7-10 and is assumed as 1.5 for the unreinforced masonry
typology, and Iis an Importance Factor taken from Table 11.5-1 in ASCE 7-10 and is assumed as
1. Table 2 below shows the necessary values needed to calculate SDs and SDI.
30
Table
2 Ground motion
and response spectrum
expected building base shear.
values necessary to deterinine
Label
Term Description
Source
Value
Fa
0.214
1.2
ASCE 7-10 Figure 22-1
ASCE 7-10 Table 11.4-1
SMS
0.324
Sms=FaSs
SDS
0.2292
Spectral Acceleration of MCE at Is period
Site coefficient for Soil Class D
Spectral Response Acceleration Is period
Si
F,
0.069
2.4
ASCE 7-10 Figure 22-2
ASCE 7-10 Table 11.4-2
SMI
0.167
Smi=FSi
Design Earthquake Response Acceleration at Is period
SDI
0.110
SDI=( 2/ 3 )SMI
Spectral Acceleration of MCE at short periods
Site coefficient for Soil Class D
Spectral Response Acceleration for MCE at short periods
Design Earthquake Response Acceleration at short periods
S,
SDS=( 2/ 3 )SMs
Finally, the base shear can be calculated by:
(4)
Fb = CsW
Where W is the weight of the building section in kips. This estimated base shear value will be
useful for both the cantilever beam and finite element model to have a basis for comparison even
though higher base shear values will be applied in these methods for pushover analysis.
Cantilever Beam Method
5.2
A conservative method to estimating max
P6
roof displacements and interstory drifts of an
M6
-
P6
- .
h6
P5
unreinforced masonry building is to assume
-5
-
the building as a solid cantilever beam with a
P4 ---
m,
fixed base boundary condition, visualized in
Figure 13 and theorized in the textbook
h3
Structural Motion Engineering by Jerome
P-
Connor. In this model, incremental lateral
Sh,
'-
loads are applied to each floor as portions of
the expected base shear dictated by ASCE 710 and in the shape of the fundamental mode.
Equation 1 determines the proportional value
of the base shear for the ith floor:
Pi=
nmq
j=1j
jj
Fb
Fb
Fb
Figure 13 The con tilever beam model lumps masses at the floor
levels where portions of the base shear are applied.
(5)
31
Where Fb is the base shear calculated from ASCE 7-10 provisions, mi is the lumped mass of the
story, and P is the mode shape term for the ith or jth floor. The value of mi will be the weight of
the interstory building portion. The value of Pi is used in Equation 2, which calculate deflection
considering shear and bending:
AROOF
Zj
(6)
hi4Pi1 + Z.JPhi1
EA
Where hi is the height of the ith floor, Pi is the proportional base shear calculated in Equation 1, E
is the modulus of elasticity of masonry, I is the moment of inertia of the cross-section of the wall
in the bending direction, and A is the shear area of the wall.
Finite Element Model
5.3
The finite element program SAP2000 version 17.1.0 was used to model the four wall sections for
two reasonable scenarios. The first scenario assumes that the facade is not connected well to the
party wall due to mortar degradation and general wear. A broad example of this is in Figure 14.
The second scenario considers portions of the party wall and floors to act with the facade. The
distinctions between these scenarios will be explored further in Chapter 6.
A few assumptions had to be made for the finite element
model, just as for the cantilever beam model. Default material
properties (Young's Modulus, Shear Modulus) from FEMA
356 and accepted values (Density, Poisson's Ratio, Thermal
Coefficient) defined the inputted masonry material. Masonry
values and the directional properties are unknown for the
-
is anisotropic, but since the material is developed from default
Young's Modulus, Shear Modulus, Thermal Coefficient, and
Poisson's Ratio, it was chosen to be isotropic in SAP2000.
There are a few particulars about the model's geometry,
section properties, and restraints that were assumed in order to
Figure 14 Bad wall to wall connection
approach accurate results:
1. To simulate a fixed foundation condition, moment restraints are modeled to line the bottom
of the wall sections.
2. Perforations in the wall sections come from case study geometry.
32
3. Frame elements were given no section property, making them just constraints for the
masonry panels.
4. The frame elements are chosen to allow load transfer from area objects.
5. Masonry panels are defined as a thick shell area section and is given the thickness of the
wall from the case study.
6. Rectangular areas were drawn as piers and spandrels between the window perforations and
were given the masonry area section and material properties.
7. During analysis, the masonry area sections automatically mesh into smaller sections to get
more accurate deflections.
8. The mass source comes from the defined elements, not an applied dead load.
Figure 15 shows the geometry of the four SAP2000 models done for the four wall sections for the
first scenario of the facade acting alone apart from the party walls and floor.
Pier - Worst Case
Curved Wall Section
Flat Wall Section
Full Wall - Best Case
Figure 15 The four wall sections make up four different SAP2000 models to analyze.
Analysis cases are set up for the self-weight dead load, applied live load (proportional base shear
values calculated for the cantilever beam model), and response spectrum earthquake load.
Deflection values are read off at each floor level, as exemplified in Figure 16 and evaluated per
the criteria in the next section.
33
Figure 16 An example of the data collection process for the SAP2000 models. Proportional
base shear values are applied at the joints at floor level and deflection values are read
from the joints on the right side of the model also at floor level.
The second scenario that considers certain percentages of the party wall to act with the fagade is
represented by the finite element model in Figure 17. Forces will be applied at the same level as
in the first scenario but as a uniformly distributed line load. Only in-plane analysis will be studied
in scenario 2 since this condition assumes exceptional fagade to party wall connections.
Figure 17 SAP2000 models, from right, considering 10%, 50%, and 100% of the building acting together, will be also necessary to
analyze.
34
Global Behavior Evaluation Criteria
5.4
The global performance of the four parameterized wall sections will be evaluated by their
interstory drift ratios, which is the difference between the deflection of one story and the one below
it, divided by the height between the points where the deflection was measured. Many codes
provide interstory drift ratio limits to evaluate unreinforced masonry buildings and it is necessary
to choose one that is right for these calculations and case study. There is a challenge in choosing
the right code to go by since it is unclear as to where they measure their story drifts from. This
thesis will measure drifts by measuring the deflection at the estimated location of the timber floor,
subtracting the deflection at the timber floor below it, and dividing by the distance between the
timber floors. It is suggested in the paper by Park, who also measure interstory drifts this way for
low rise unreinforced masonry buildings, to use the interstory drift ratios provided by the FEMA
356 document. FEMA 356 has determined specific interstory drifts for three different performance
levels including Immediate Occupancy (10), Life Safety (LS), and Collapse Prevention (CP).
Table 3 summarizes the interstory drift limits.
Table 3 FEAIA 356 interstorv drift limits
for Collapse Prevention,
Li/i Sa/e'ty, and Immediaie Occupancy periWrmance Ievels.
Damage Levels
Drift Ratio []1.00
0i
0.60
immediate Occupancy
(10)
0.30
When the drift limit for 10 is met, there is expected to be minor cracking of veneer bricks, minor
spalling at corner openings, and no observable out-of-plane offsets. When the drift limit for LS is
met, there is expected to be extensive cracking, noticeable in-plane offsets, and minor out-of-plane
offsets. Finally, when the drift limit for CP is met, there is also expected to be extensive cracking,
but it is also expected that the brick face course and veneer may begin to peel back from the inner
wythes of the building, and there is noticeable in-plane and out-of-plane offsets (Park, et al). It is
important to note that even though 10 is defined by light damage, small brick failures can cause
property damage and loss of life from falling brick pieces.
The Back Bay case study interstory building heights are applied to the FEMA 356 drift ratios.
Table 4 shows the distance that each story has to drift in order to be categorized in the three
performance levels. The last line of the table shows the maximum interstory distance that the full
35
building can stand. These values are the main criteria that will evaluate the global performance of
the four wall sections.
Table 4 To violate
the FEAIA
356 perfrnance levels, these are the interstorv distances that each loor is alloiwed to drult.
Immediate
Occupancy
Damage Leves
10
jS
0.432
0.402
0.452
0.487
Basement [in]
Floor 1 [in]
Floor 2 [in]
Floor 3 [in]
1.440
1.340
1.508
1.622
0.864
0.804
0.905
0.973
Floor 4 [in]
1.412
0.847
0.424
Roof [in]
Full Building Height
[in]
1.606
0.963
0.482
8.928
5.357
2.678
5.5
Local Behavior Evaluation Criteria
In Plane
This section will provide an overview of the equations used to calculate the shear capacities of the
pier elements of the full fagade, which will act as the failure criteria of the in-plane four failure
mechanisms (flexural rocking, bed joint sliding, toe crushing, and diagonal tension cracking).
When these stress values, or yield stresses, are met within the pier elements, they will be
considered to fail by the corresponding mechanism.
Von Mises shear stresses taken from the finite element model will be compared to each of the pier
yield stresses. A Von Mises stress is the combination of the three dimensional principle stresses,
taken from Mohr's Circle, within a material to create an equivalent stress (CSI 2014). As a measure
of distotional stresses within the material, it is assumed in this thesis that reading Von Mises shear
stresses from the finite element model will be an adequate representation of the stresses within the
masonry piers. By comparing the acquired Von Mises stresses to the masonry piers' shear capacity,
it will be possible to determine if the piers will fail at a reasonable application of base shear. These
results are in Chapter 6.
Flexural rocking failure of the fagade piers is calculated in Equation 7:
Vr = 0. 9 aPCE(L/heff)
36
(7)
Where a is a factor that is 0.5 for a fixed-free cantilever and 1.0 for a fixed-free pier, PCE is the
expected vertical axial compressive force acting upon the pier, L is the length of the wall, and heff
is the effective height of the pier. The shear to cause bed-joint sliding in a facade pier is calculated
in Equations 8 and 9:
VbJs1 =
Vbjs2
(8)
VmeAn
= VfrictionAn =
0 . 5 PCE
(9)
Where VbjsJ is bed joint sliding shear considering mortar bond and friction, Vbjs2 is bed joint sliding
shear considering only friction, vine is the shear strength of the unreinforced masonry components
assumed as the default value 27psi for bed joints in good condition per FEMA 273, and A, is the
area of the net mortared section. Toe crushing in the fagade piers is calculated from the shear
Equation 10:
Vic = aPCE (L/heff)(
-
(10)
fae/ 0. 7f'me)
Where fae is the expected vertical axial compressive strength also known as PCE, and f'me is the
expected masonry compressive strength. Finally, the shear to cause diagonal cracking in the facade
piers will use Equation 11:
Vdt = f'dtAnf3(1 + fac/f'dt)1/2
Wheref'dt is the diagonal tension strength and p is 0.67 for L/heff<0.67, L/heffwhen 0.67>L/he)Yl .0,
and 1.0 when L/hegf>1 (FEMA 1998).
Out of Plane
The elements that will be evaluated for out-of-plane behavior are chimneys, full facade, and partial
fagade. Masonry chimneys are considered to be the most vulnerable
element of an unreinforced masonry building and damage to them are one
of the ways that seismologists determine the Modified Mercalli Intensity
(MMI) after an earthquake. Failure of chimneys are is crucial because
bricks falling from such a height can damage other parts of the building
and injure people below. The global out of plane behavior for the case
study will be evaluated using the basic rocking rigid block method.
b
0
Y"
Figure 18 Rigid block
free-body diagram
(Dejong).
37
A facade or a chimney can be reimagined as Housner's rigid block theory. For the simplified rigid
block calculations it is assumed that the connections of these blocks to the roof, other parts of the
wall, the ground, etc. are flexible between two rigid bodies. At certain forces (ground acceleration,
wind load), the block can then overcome its overturning moment at a critical angle of rotation and
rock, or it can overcome friction at the base and slide.
Figure 18 shows the free body diagram of a rigid block. By summing the moments about the point
0, a parameter to calculate the minimum ground acceleration to overturn the block can be
determined:
-gmin
=
-
tan a
9
Where A is a dimensionless uplift parameter,
Uginin
(12)
is the minimum ground acceleration for
overturn, g is the force of gravity, and a is the critical angle. Rocking motion will be triggered if {
is greater than tan(a). Therefore the inception of rocking in this case is completely dependent on
the block's geometry (DeJong). In Chapter 6, the rigid block method will be applied to the case
study chimney and fagade. Additionally, if there is no overturn of the present conditions, then the
failure state will be calculated.
As will be seen in Chapter 6, the rigid block theory is slightly inconclusive for chimney analysis.
Therefore, the chimney will also be analyzed locally for shear failure instead of complete overturn.
This method is suggested by Alan Darrell Ho, a student of Robert Whitman and also author of
"Determination of Earthquake Intensities from Chimney Damage Reports". This paper analyzes
the chimney capacities of those during the Cape Ann earthquake of 1755.
There are a few assumptions when considering a simple analysis of shear failure. First, the bond
stress at the failure location is zero, and second, the shear resistance is due to friction developing
at the horizontal failure plane between the brick and mortar. The equation for shear failure is:
V = PW
(13)
Where p is the coefficient of friction, assumed as 0.7 which is seen in literature, and W is the total
weight of the chimney above the failure location. When applied forces exceed V, the friction force,
the bricks will slide and be considered to fail (Ho 1979). The longer wall of the chimney will be
analyzed with this method since its out of plane bending will be bending about the weak axis.
38
Another form of out of plane failure is when the brick wall between two floors cracks at the floor
interfaces and in the middle of the masonry panel and bursts outward. There is a method in a paper
presented by the University of Canterbury of calculating the minimum ground acceleration that
would be necessary to crack this portion of a wall in the middle. The moment required to crack the
unreinforced masonry wall is:
(14)
Mcr =
Where t is the thickness of the wall and R is sum of the compressive force from the wall portion
above and half of the wall at hand's weight. The next two equations are combined to simplify to
Equation 17.
8
MCr
win =
ain =
m
(15)
(16)
Where win is the mass per unit area of wall surface, h, is the interstory wall height, m is the mass
of the wall section, and ain is ground acceleration.
4Rt
a=n =
(17)
The calculated acceleration is the minimum acceleration required to crack the wall mid-span
(Priestley 1985). Results for this calculation are in Chapter 6.
39
6.0 Case Study Structural Analysis Results
Structural assessment results of an unreinforced masonry case
study building in the Back Bay neighborhood will be presented.
The case study building, 37 Commonwealth Avenue, is one of
several residences in all of the Back Bay that original structural
drawings were acquired. This availability as well as the midblock location of the residence, and its similar building typology
to most homes in the neighborhood, led to its selection.
Before any analysis began, all available information about 37
Commonwealth was found. This included original structural
drawings found at the Boston Athenmum, and long form
building permits from the City of Boston, which provided
information on building construction over the years and building
materials. Site visits to similar buildings and 39 Commonwealth
in the Back Bay led to the understanding of certain building
components and connections.
The residence of 37 Commonwealth is located in a block
confined by Berkeley Street, Clarendon Street, Public Alley
423, and Commonwealth Avenue. Constructed in 1872 by
architect N.J. Bradlee, who built 39 Commonwealth at the same
time, this five story unreinforced masonry building is 74 feet
from the bottom of the basement to the highest point of the roof,
the facade is approximately 30 feet wide, and the party walls are
approximately 75 feet long. The thickness of the external walls
is 16 inches, the floors are made of wood, and the foundation is
Figure 19 Front and rearfagades of 37
Commonwealth
40
granite. Figures 20 shows some of the original structural drawings of 37 Commonwealth and
Figure 21 shows the wall brick course, vaulted basement flooring, and joist pocket holes of sister
structure 39 Commonwealth.
Figure 21 Original structural drawings of 37 Commonwealth (Boston Athenaeum N. Bradlee Collection).
Figure 20 Counterclockwise from left, interior brick courses, vaulted brick basement floor, and joist pockets of 39 Commonwealth
41
6.1 Modelling Considerations
It is assumed in the structural analysis of 37 Commonwealth that the building acts independently
of its surrounding buildings. The aggregation of the housing block is predicted to stiffen the
internal buildings under lateral loads and to not allow them to deflect as much as will be shown in
this chapter. Since complex finite element models take a long time to run, the behavior of the
unreinforced masonry buildings as an aggregate block is therefore out of the scope of this thesis
for ease of calculation.
Further, in order to explore how and if portions of the building act together, two behavior scenarios
will be explored. The first scenario is to model the facade as if it was acting on its own, assuming
that the wall to wall connection is in a bad condition and doesn't transfer lateral loads. Within the
fagade analysis is a parametric study that will examine how different sections on the wall will
behave if acting on their own due to possible masonry connection deterioration within the fagade.
Four wall sections will be analyzed for their individual behavior including: the full facade (best
case), a partial curved section of facade, a partial flat section of fagade, and a pier section through
the windows (worst case). The 37 Commonwealth building has a complex fagade geometry and
for calculations and will be simplified to act on one plane. The four parameters will be modeled
similarly. A summary of this modeling simplification is in Figure 22.
Pier - Worst Case
Flat Wall Section
Curved Wall Section
Wall Plan View
Simplification Used For Calculations
Figure 22 Modeling simplificotions for scenario 1.
42
Full Wall - Best Case
The second scenario is to model a certain percentage of the party wall and floor
diaphragms as acting together with the fagade, assuming that the wall to wall
Wall Plan
connection is in excellent condition and is creating a box effect. This scenario
is only applicable for the best case, full wall parameter in Figure 23 since the
Simplification
U
other parameters don't have party wall connections. This application will not
take into account the stiffness of the floor, just the weight.
6.2 Cantilever Beam Results
The cantilever beam method described in Chapter 4 was applied to the four
scenarios presented in the previous section. For the first scenario of the fagade
Figure 23 Modeling
simplification for
scenario 2.
acting apart from the party walls, of the four isolated wall sections only the pier section violated
the FEMA 356 performance levels. The most conclusive results for the cantilever beam model
come from graphing base shear vs. max roof displacement over total building height. The drift
results are depicted in Figure 24. The FEMA 356 drift limits are represented on the graph as the
vertical differently colored lines corresponding to their colors in Table 4.
PUSHOVER CURVE (CANTILEVER BEAM METHOD)
140 0
I
I
I
I
I
I
I
I
I
120 0
I
100 0
k
800
-*-Full Wall
Curved
-Ar- Flat
-
Pier
I
(A
LU
I
60 0
(A
La
I
40 0
I
I
I
I
20 0
0
0.000
0.002
0.010
0.008
0.006
0.004
MAX ROOF DISPLACEMENT/TOTAL HEIGHT [IN/IN]
Figure 24 Pushover curve for the cantilever beam hand calculations.
43
0.012
0.014
The pier section, when acting on its own, will violate all of FEMA 356's drift ratio limits at
approximately 172 kips for 10, 354 kips for LS, and 596 kips for CP. It is important to notice,
however, that the magnitude of the base shear values on the y axis compared to the expected base
shear values of the four parameters in Table 5, which were calculated from ASCE 7-10 provisions.
Tai/c 5 Expecctcd base sharJor wall scctions in scenarioI
Parameter
and corresponldingi max ivaf dicmns
ASCE 7 Expected Base Shear [kips]
Max Roof Displacement [in]
40.74
17.60
20.71
7.50
0.004
0.010
0.013
0.112
Full Facade
Curved Section
Flat Section
Pier
Varying percentages of the party wall and floor load from zero to fifty percent were chosen to act
in accordance with the fagade. To account for this, estimated floor weights were added to the
weight of the masonry stories and the cross-sectional area and moment of inertia represented the
'C' shape. The whole building was represented as the one hundred percent value. The results of
considering these varying percentages are in Table 6.
Tailc 6 Expected base shcar bor wall sections in scepnario 2 and correspondingmax ra!
dmspacmena.
Percentage
10
20
ASCE 7 Expected Base Shear [kips]
87.23
119.47
Max Roof Displacement [in]
0.0021
0.0029
30
151.72
183.97
216.21
377.47
0.0036
0.0044
0.0052
0.0090
40
50
100
Max roof displacement for the full fagade and expected base shear increased as more of the
building was taken into account. The interstory drifts in this scenario were nowhere near the 10
performance level and are not shown.
Although the cantilever beam model represents the displacement behavior of the case study
building and shows that the pier section in the first scenario, when acting on its own, will violate
all of FEMA 356's performance levels, it is necessary to continue with the finite element results
44
in order to represent better the perforated quality of the fagade and the structural nature of the
masonry.
6.3 Finite Element Model Results
Scenario 1
Again, the building facade was modeled as four different sections, assuming that there is a
possibility that portions of the wall can be acting on their own due to bad wall to wall connections.
These four models are considered to be a worst case scenario situation because when percentages
of the party walls are added in scenario 2, the interstory drifts are smaller.
Overall, when force was applied to the floors of the four facade sections, proportional to increasing
base shear values whose calculation were outlined earlier, the building deflected more, which is
expected and inherent. The most important takeaway from the finite element analysis is
determining at what base shear values the wall sections violate the interstory drift limits from
FEMA 356. If this happens at realistic base shear values, the building will be considered to be at
risk. For all of the following graphs, the expected base shear for the sections are represented by a
colored single data point on each of the curves.
PUSHOVER CURVE (SCENARIO 1)
450
I-
400
Full
-
350
Curved
Flat
Pier
300
20
200
co
150
100
50
0
0.0000000
0.0020000
0.0080000
0.0060000
0.0040000
MAX ROOF DISPLACEMENT/TOTAL HEIGHT [IN/IN]
Figure 25 Pushovercurve f-om SA P2000/brscenario 1.
45
0.0100000
Figure 25 begins with a broad observation of the sections' behavior. The max roof displacement
at increasing values of base shear is graphed. This observation considers the interstory distance to
be the full height of the building. The model was run until each wall section violated all of the
interstory drift limits. Table 7 provides a detailed reading of Figure 25 and documents at what base
shear each interstory drift limit will be met.
Table 7 Base shear va/ue.s ncessarv ro exceed FEMA 356 perfiurmance Ieve/s for
the uveral pushover curve.
Base Shear at
CP [kips]
1400
Full Facade
40.74
417
Base Shear at
LS [kips]
860
Curved Section
17.60
41.8
83.2
138
Flat Section
20.71
44.7
88.6
147
Pier
7.50
1.8
3.5
6
Parameter
ASCE 7 Expected Base
Shear [kips]
Base Shear at
10 [kips]
If the pier is acting alone, it is likely that it will meet all of the drift limits. The other wall sections
have expected base shear values that are fairly far off from the shear values needed to violate even
the immediate occupancy drift limit.
It is necessary to analyze what is happening at each floor rather than the global building drift
since wall perforations and amount of compressive stress on the wall section can affect how
much a story can drift.
46
BASEMENT INTERSTORY DRIFTS (SCENARIO 1)
600
500
400
300
IFull
IU
Wall
<--Curved
-
200
Flat
Pier
100
0
0
0.2
0.6
0.4
1
0.8
1.2
1.4
1.6
1.8
2
INTERSTORY DRIFT [IN]
Figure .6 Base shear vs. interstorv driftfor the basement level.
Figure 26 shows the interstory drifts between the ground and the basement floor with increasing
values of base shear. The base shear value that each drift limit will be met for the four wall sections
of the basement is in Table 8.
Table 8 Base shear valiues necessarv to exceed FEMA 356 perjbrmance levels f.r basement level.
Base Shear at
LS [kips]
>2000
Base Shear at
CP [kips]
>2000
Full Facade
40.74
Base Shear at
10 [kips]
1200
Curved Section
17.60
190
377
620
Flat Section
20.71
143
321
550
Pier
7.50
6.2
13
21.9
Parameter
ASCE 7 Expected Base
Shear [kips]
If the pier acts on its own, the shear values for the drift limits are reasonably close to the expected
base shear for the expected earthquake event.
47
FLOOR 1 INTERSTORY DRIFTS (SCENARIO 1)
500
450
400
Full Wall
Curved
-Flat
Pier
---
350
300
250
L
200
150
100
50
0
0
0.5
1
1.5
3
2.5
2
INTERSTORY DRIFT [IN]
3.5
4
Figure 27 Base shear vs. interstorv drift for the first floor.
Figure 27 shows the interstory between the basement and first floor with increasing base shear.
The drift limits are exceeded at much lower base shear values compared to the basement drift,
which is expected since the basement is confined underground, it has no perforations, and is
substantially heavier than the first floor masonry wall panel. Also, the basement has the
compressive force of five stories above it whereas the first floor has only 4. The base shear value
that each drift limit will be met for the four wall sections of the first floor is in Table 9.
Table 9 Base shear values necessary to exceed FEAMA 356 per/brmance levels brfirst floor.
ASCE 7 Expected Base
Base Shear at
Base Shear at
Base Shear at
10 [kips]
420
LS [kips]
800
CP [kips]
1438
Curved Section
17.60
60
122
202
Flat Section
20.71
54
110
183
Pier
7.50
2.8
5
8.3
Parameter
Full Facade
Shear [kips]
40.74
Once again, if the pier acts on its own, the shear values for the drift limits are reasonably close to
the expected base shear for the expected earthquake event.
48
FLOOR 2 INTERSTORY DRIFTS (SCENARIO 1)
500
450
400
I
I
350
S300
L
250
Wall
Curved
Ln---Full
V 200
-Flat
Pier
-
150
100
50
0
0
1
0.5
2
1.5
3
2.5
4
3.5
INTERSTORY DRIFTS [IN]
Figure 28 Base shear vs. interstorV drift for the second floor
Figure 28 shows the interstory drifts between the first and second floor with increasing base shear.
Compared to the first floor, the drift limits have been exceeded at lower base shears, especially the
full wall section which has previously been violating the drift limits at base shear values that would
never realistically happen. The base shear value that each drift limit will be met for the four wall
sections of the second floor is in Table 10.
Table 10 Base shear values necessarY to exceed FEMA 356 perfbmzance levelsfbr second floor.
Base Shear at
LS [kips]
645
Base Shear at
CP [kips]
1165
Full Facade
40.74
Base Shear at
IO [kips]
340
Curved Section
17.60
38
81.1
130
Flat Section
20.71
41
85
141
Pier
7.50
2
3.8
6
Parameter
ASCE 7 Expected Base
Shear [kips]
The flat and curved wall sections are approaching reasonable base shear values at which they
violate the drift limits. The pier section is approaching incredibly low base shear values that it is
considered to 'fail' at.
49
FLOOR 3 INTERSTORY DRIFTS (SCENARIO 1)
500
450
400
I-I
350
30
300II
-
Full Wall
---
Curved
-
Flat
--
Pier
250
CA
200
150
100
50
0
0.5
1
2
1.5
3
2.5
4
3.5
INTERSTORY DRIFT [IN]
Figure29 Base shear is. interstory drift Jbr the third floor
Figure 29 shows the interstory drifts between the second and third floor with increasing base shear.
The results don't change much from the second floor for the full wall section, but the flat, pier,
and curved sections were affected by the story change. The base shear value that each drift limit
will be met for the four wall sections of the third floor is in Table 11.
Table II Base shear values necessary to exceed FEMA 356 perbrmance levels for third floor.
Base Shear at
LS [kips]
770
Base Shear at
CP [kips]
1280
Full Facade
40.74
Base Shear at
10 [kips]
360
Curved Section
17.60
33
70
113
Flat Section
20.71
36
74
120
Pier
7.50
0.6
3
5
Parameter
ASCE 7 Expected Base
Shear [kips]
The curved and flat sections continue to have drift limit shear values that are closer to the expected
base shear as higher floors are analyzed. The pier reaches immediate occupancy at a staggering
600 pounds of force.
50
FLOOR 4 INTERSTORY DRIFTS (SCENARIO 1)
500
450
Full Wall
Curved
Flat
--Pier
-
400
350
300
S250
Z200
150
100
50
0
0
0.5
1
1.5
3
2.5
2
INTERSTORY DRIFT [IN]
4
3.5
Figure 30 Base shear vs. interstory drift fbr the fourth floor
Figure 30 shows the interstory drifts between the third and fourth floor with increasing base shear.
These results are close to those for the third floor. The pier base shear for the drift limits did not
decrease again but instead increased, albeit to values that are still incredibly low. The base shear
value that each drift limit will be met for the four wall sections of the fourth floor is in Table 12.
Table 12 Base shear values necessary to exceed FEMA 356 pertormance levels fbrJburthfloor.
Base Shear at
LS [kips]
745
Base Shear at
CP [kips]
1255
Ful Facade
40.74
Base Shear at
10 [kips]
372
Curved Section
17.60
30.2
62
102
Flat Section
20.71
34.3
69.5
112
Pier
7.50
1.1
2.3
4
Parameter
ASCE 7 Expected Base
Shear [kips]
The curved and flat sections continue to have drift limit base shears that are decreasing as floor
height increases. It becomes more reasonable to say that these sections are likely to 'fail' to a
certain degree closer to the roof which the pier section is likely to 'fail' to a certain degree at any
floor.
51
ROOF INTERSTORY DRIFTS (SCENARIO 1)
500
450
400
-
Full Wall
350
-
Curved
Flat
Pier
300
250
200
150
100
50
0
0
0.5
1
2
1.5
2.5
3
3.5
4
INTERSTORY DRIFT [IN]
Figure 31 Base shear vs. interstorv drift fbr the roof level.
Figure 31 shows the interstory drifts between the roof and the fourth floor with increasing base
shear. Compared to all floors below, the roof level has the largest interstory drifts at the lowest
values of base shear. The full wall section still doesn't 'fail' at a reasonable value, but the pier
section does especially. It is reasonable to predict that the flat and curved sections have the
possibility of producing a low level of failure at the roof level. Again, it is important to remember
that even very small pieces of wall that fail can cost a lot of money to repair and also injuries to
people. The base shear value that each drift limit will be met for the four wall sections of the roof
floor is in Table 13.
Table 13 Base shear values necessary to exceed FEMA 356 performance levels for roof
level.
ASCE 7 Expected Base
Shear [kips]
40.74
Base Shear at
10 [kips]
340
Base Shear at LS
[kips]
680
Base Shear at
CP [kips]
1175
Curved Section
17.60
33.6
67
102
Flat Section
20.71
30
60
113
Pier
7.50
0.7
1.2
4.1
Parameter
Full Facade
52
Scenario 2
When considering portions of the party walls and floors to act in accordance with the fagade, the
expected base shear is higher and the deflections are less. Three models were analyzed considering
different percentages of the full building acting with the fagade including 10%, 50%, and the full
100%. It is less common in this scenario for the FEMA 356 interstory drifts to be surpassed. The
results for this scenario will not go into detail as much as the first scenario did since most of the
graphs are very similar and tell the same story about interstory drifts. In Figure 32 the overall
behavior of the three percentages is shown when the interstory height is the full height of the
building using the cantilever beam hand calculation method. It is observed that in this method,
none of the interstory drift limits are even close to being met at reasonable or high base shear
values.
2)
PUSHOVER CURVE (CANTILEVER BEAM SCENARIO
3000
2500
2000
-100%
1500
-50%
< 1000
500
0
0
0.00005
0.0002
0.00015
0.0001
IN/IN]
HEIGHT
MAX ROOF DISPLACEMENT/TOTAL
0.00025
Figure 32 Pushover curve from the cantileverbeam hand calculationsfbr scenario 2.
Figure 33 displays the same type of information (base shear vs. interstory height/total height) but
from the finite element model that is a more accurate representation of the structural behavior of
brick masonry panels. The Immediate Occupancy drift limit is met, but for very highly unexpected
base shear values.
53
PUSHOVER CURVE (SAP2000 SCENARIO 2)
3000
2500
2000
1500
LU
--
100%
50%
--
10%
-
< 1000
500
0
0.006
0.005
0.004
0.003
0.002
MAX ROOF DISPLACEMENT/TOTAL HEIGHT [IN/IN]
0.001
0
Figure 33 Pushover curve from SAP2000 /br scenario 2.
Figure 34 begins the floor by floor analysis. Between the ground and the basement ceiling, the
interstory drift limits are met for the 10% and 50% models at very high base shears.
BASEMENT INTERSTORY DRIFTS (SCENARIO 2)
3000
2500
2000
u 1500
< 1000
--
500
100%
50%
-10%
0
0
0.05
0.1
0.15
0.3
0.25
0.2
INTERSTORY DRIFT [IN]
0.35
0.4
0.45
0.5
Figure 34 Base shear vs. interstory drift for the basement level.
Figure 35 shows that slowly, as higher floors are analyzed, the interstory drifts get larger. In this
case for the drift between the basement and the first floor, the Immediate Occupancy limit is met
for the 10%, 50% and 100% models. The Life Safety limit would have been met if higher shear
values were inputted, but since they are deemed unrealistic it is determined that the Life Safety
limit won't be met.
54
FLOOR 1 INTERSTORY DRIFTS (SCENARIO 2)
3000
2500
2000
1500
LU
100%
-
< 1000
ca--50%
-10%
500
0
0.2
0.1
0
0.3
0.6
0.5
0.4
INTERSTORY DRIFT [IN]
0.8
0.7
0.9
1
Figure 35 Base shear vs. interstor drift/fbr the firstfloor.
The results for the drift between the first and second floor, in Figure 36, are very similar to the
above results in Figure 35. However, the Life Safety limit is met at a lower value of base shear for
the 10% model and all of the models surpass the Immediate Occupancy limit under a base shear
of 2500 kips.
FLOOR 2 INTERSTORY DRIFTS (SCENARIO 2)
3000
2500
I
2000
2 1500
< 1000
c---100%
500
-10%
0
0
0.1
0.2
0.3
0.5
0.4
0.6
0.7
0.8
0.9
1
INTERSTORY DRIFT [IN]
Figure 36 Base shear vs. interstorv drift/brthe second floor
As in scenario 1, the drifts between the second and third floors are not as much as the drifts between
the first and second floors, which is due to a combination of vertical compressive stress and
perforation amounts. Figure 37 displays this decrease in the interstory drifts.
55
FLOOR 3 INTERSTORY DRIFTS (SCENARIO 2)
3000
2500
_
2000
1500
M
---
< 1000
100%
--- 50%
--
10%
500
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
INTERSTORY DRIFT [IN]
Figure 37 Base shear vs. interstory drift/for the thirdfloor.
The interstory drifts for the next story are larger, however, as seen in Figure 38. Even though this
is true, the base shear values that it takes to violate the drift limits would be incredibly difficult to
achieve in real life.
FLOOR 4 INTERSTORY DRIFTS (SCENARIO 2)
3000
2500
0
2000
1500
< 1000
co---100%
050%
-10%
500
0
0
0.1
0.2
0.3
0.4
0.5
0.6
INTERSTORY DRIFT [IN]
0.7
0.8
0.9
1
Figure 38 Base shear vs. inlerstory driftfor the fnirth floor.
Unlike the drifts between the roof and the fourth floor for the first scenario where the fagade is
acting on its own and the pier section fails at very low base shear values at the roof, the results for
the second scenario suggest that at the roof level it is very unrealistic for the FEMA 356 limits to
be broken. Figure 39 shows this.
56
ROOF INTERSTORY DRIFTS (SCENARIO 2)
3000
-100%
2500
a.
---
50%
10%
2000
1500
< 1000
500
0
0
Figure 39 Base shear vs.
0.2
0.6
0.4
0.8
1
INTERSTORY DRIFT [IN]
interstorvdrift jbr the roof level.
6.4 Local Element Failure Results
In-Plane Failure Results
As introduced in Chapter 3, unreinforced masonry typically fails in four different ways. Three of
these failure mechanisms (flexural rocking, bed-joint sliding, and toe crushing) are not really
considered to be failures since they still allow vertical loads to transfer throughout the facade. The
diagonal cracking failure mechanism however does not allow vertical loads to transfer after its
inception and is considered to be a failure. The case study of 37 Commonwealth was analyzed to
see which in-plane local failure mechanisms would occur in the faqade's pier elements. It is
assumed that this building exhibits a weak pier, strong spandrel condition due to the pier and
spandrel geometries and therefore the failures are expected to occur in the piers.
57
Figure 40 Most of the piers willfailfrom diagonal tension failure in the SAP2000 models. Bed joint sliding is observed
in the full wall and rocking is observed in the curved wall section.
The expected failure mechanisms of the facade piers using the equations in Chapter 5 are seen in
Figure 40 and are determined from provisions in FEMA 306, which typically takes the smallest
shear value from the equations to be the failing shear mechanism. In Figure 40, the green represents
diagonal tension failure, red represents bed-joint sliding failure, and the blue represents rocking
failure. These results rely heavily on pier length to effective height ratios, vertical compressive
stress, and strength of mortar joints. Diagonal tension failure appears to be the most frequently
occurring failure mechanism for many of the piers with small length to height ratios (L/heff). The
larger piers, with length to height ratios closer to one are predicted to fail first from bed joint
sliding. One pier is expected to fail from flexural rocking.
Now that the shear capacities of the piers are known, it will be determined whether these shear
values are met during the various applications of base shear loads. The Von Mises shear stresses
observed in the full rear fagade will be compared to the shear capacities to determine at what value
of base shear the wall elements will be expected to fail.
58
Results for this section will only focus on scenario 1, where the fagade is disconnected from the
party walls and is acting on its own. This is because it is considered to be the worst case scenario.
First the Von Mises shear stresses were found for the full fagade. In Figure 41, along the x axis are
the pier numbers that were designated in Figure 40. The data points above the pier numbers
represent the Von Mises shear stress values read from the finite element model caused by the
application of the expected base shear and increasing base shear values. The black diamond shaped
data point represents the shear stress capacity of the pier element. The red dotted line represents
the compressive strength of the brick. When this value is exceeded the brick fails.
VON MISES INTERNAL SHEAR STRESS OF PIERS - FULL WALL
1200
X
1000
0-
.
LU
800
COMPRESSIVE.........
STRENGTH OF BRICK=78OPSI
.................................................
.......
V
...................................
x
X
600
400
2 400x
0
X
x
200
X
x
x
x
X
6
7
x
X
13
14
x
x
Xxx
X
X
X
X
X
x
0
0
1
2
3
4
5
9
8
10
11
12
15
16
17
18
19
20
21
22
DESIGNATED PIER NUMBER
APPLIED BASE SHEARS
A Expected Base Shear=40.74 kips
X50 kips
X 100 kips
X250 kips
X500 kips *Shear
Failure
Figure 41 Local shearfJilure examination for fidl wall.
The pier elements numbered 16 and 21 are the first to exceed their shear stress capacity and fail,
around 175 kips of applied base shear. This is expected because the piers are compressed
significantly as the building bends. At 250 kips base shear, piers 16 and 21 are still the only ones
to have failed, but when that value is doubled to 500 kips, piers 12, 15, 17, 18, and 20 fail. By the
time 1500 kips base shear is applied, all but piers 2, 4, and 6 have failed. Even though the piers are
59
considered to fail at these points, the applied base shears are still significantly higher than the
expected base shear. The data points for 1000 and 1500 kips base shear were removed for graph
clarity and can be found in the Appendix. Internal shear stresses for the flat wall section are in
Figure 42. The piers were not renumbered and are the same as for the full wall section, just with
some of the piers missing since they aren't included in the flat wall section.
VON MISES INTERNAL SHEAR STRESS OF PIERS - FLAT SECTION
1000
900
X
800
COMPRESSIVE STRENGTH OF BRICK=780PSI
700
u-i
x
600
u-
x
500
U)
L/)
400
z
0
300
x
200
x
x
I
I
5
6
100
0
0
1
2
3
4
A
x
X
X
x
X
X
X
X
A
X
X
A
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
DESIGNATED PIER NUMBER
APPLIED BASE SHEARS
*Shear Failure X 10 kips A Expected Base Shear=21 kips X 50 kips X 60 kips X 80 kips X 90 kips
100 kips
Figure 42 Local shear failure examination for flat wall section.
The first pier element to fail is pier 19, which exceeds its shear stress capacity at the expected base
shear value, just barely. It is the only pier to fail until the application of 100 kips base shear when
piers 17 and 18 are seen to have failed. At 175 kips application, piers 13 and 14 have failed, though
by interpolating from the data given in the Appendix, they fail somewhere between 100 and 175
kips. By the time 250 kips is applied, pier 9 has also failed. Even though the piers are considered
to fail at these points, the applied base shears are still significantly higher than the expected base
shear. The data points for 175 and 250 kips are not represented in Figure 42 but are found in the
Appendix.
60
Internal Von Mises shear stresses for the curved wall section are in Figure 43. Just as with the flat
wall section, the piers were not renumbered, some were simply excluded.
VON MISES INTERNAL SHEAR STRESS OF PIERS - CURVED SECTION
1200.00
x
X
1000.00
x
V-)
800.00
COMPRESSIVE STRENGTH OF BRICK=780PSI
xx
VI)
LU
Ln
x
x
x
xX
600.00
x
W
x
x
x
x
x
0j
x
x
400.00
x
x
A
20
21
A
6x
200.00
x
A
A
A
+
A
0
1
2
3
4
5
6
7
8
9
10
A
A
A
0.00
11
12
13
14
15
16
17
18
19
22
DESIGNATED PIER NUMBER
APPLIED BASE SHEARS
* Shear Failure A Expected Base Shear=17.6 kips X 50 kips X 60 kips X 80 kips X 90 kips X 100 kips
Figure 43 Local shearfiilure examinationfor the curved wall section.
The first pier failure, occurs between the application of the expected base shear and 50 kips,
approximately halfway at 34 kips, which is about double the expected base shear. The piers to fail
around this point are 11, 16, 19, and 21. It is not until 90 kips base shear that piers 14 and 20 fail.
Once again, even though the piers are considered to fail at these points, the base shears that are
causing pier failures are still significantly higher than the expected base shear.
Last, internal Von Mises shear stresses for the long pier section of the wall (not to be confused
with the pier element denotation), considered to be the worst case, are in Figure 44.
61
VON MISES INTERNAL SHEAR STRESS OF PIERS - LONG PIER
2000
X
1800
1600
1400
x
Ln
LU
1200
C:
3
X
1000
I
(A
Z
0
80
800
x
COMPRESSIVE STRENGTH OF BRICK=780PSI
......
..........
X........................................
0.....................................................
x
600
X
x
400
*
X
A
200
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
DESIGNATED PIER NUMBER
APPLIED BASE SHEARS
*
Shear Failure
X 10 kips
X 15 kips X 20 kips X 40 kips A Expected Base Shear=7.5 kips
Figure 44 Local shearfailure examinationJbr the long pier section of the fiiade.
A pier element does not fail at the expected base shear of 7.5 kips, although pier 20 is very close,
a mere 15 psi away. Increasing to applying 10 kips base shear, pier 20 definitely fails. At 15 kips,
pier 15 is seen to have failed although it failed somewhere in-between 10 and 15 kips around 11
kips. By 20 kips, pier 11 fails and by 40 kips, pier 7 fails. The base shear values that causes shear
failure within the elements is higher than the expected base shear, but not by much. Therefore it is
possible that if the pier is acting on its own due to load paths and bad masonry connections, it is
likely to fail locally except for the pier element in the roof level.
62
Out-of-Plane Failure Results
The rigid block method is first applied to the full fagade. This situation assumes that the fagade is
disconnected from the party walls and floors, as speculated in the aforementioned scenario 1. Table
14 shows the parameters required from Figure 18.
Tab/c 14 Terns necded for rigid block analvis
olidln/Igade.
Height [ft]
74.23
Length Ift]
29.46
tw [ft]
1.33
a [radians]
a [degrees]
R
W [lb]
W [kips]
Stabilizing Moment [kip-ft]
0.018
1.03
37.12
221311.12
221.31
147171.89
Table 15 applies Equation 12 to examine at which ground acceleration the block will overturn at.
Table I5 Stability results for ./id
afi ade rigid block calculation.
REAR FACADE
ing,min [g]
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.15
0.17
0.175
0.178
0.18
X
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.010
0.015
0.017
0.018
0.0181
0.0183
tan(a)
Stability
0.018
0.018
0.018
0.018
0.018
0.018
0.018
0.018
0.018
0.018
0.018
0.018
0.018
0.018
0.018
STABLE
STABLE
STABLE
STABLE
STABLE
STABLE
STABLE
STABLE
STABLE
STABLE
STABLE
STABLE
STABLE
OVERTURN
OVERTURN
63
This method shows that for the full fagade to overturn it would take a ground acceleration of
0.1 78g, which is less than the force of gravity expected for the Back Bay. If the facade becomes
cracks between the floors, the smaller portion can overturn as well. The interstory wall section
between the roof and fourth floor is 13.4 feet high. Table 16 shows what it takes for this section to
overturn.
Table 6 Stability results ofroof wall.
ROOF LEVEL FACADE
fig,min
[g]
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.975
1
X
0.010
0.020
0.030
0.041
0.051
0.061
0.071
0.082
0.092
0.099
0.102
tan(a)
Stability
0.099
0.099
0.099
0.099
0.099
0.099
0.099
0.099
0.099
0.099
0.099
STABLE
STABLE
STABLE
STABLE
STABLE
STABLE
STABLE
STABLE
STABLE
OVERTURN
OVERTURN
The calculation suggests that it would take a little less than on e time the force of gravity to overturn
the shorter wall. The smaller the angle of a, the harder it is
for a wall to overturn. Therefore if this method is used for
parapet analysis it will only show that a parapet will overturn
at larger ground accelerations. It is acceptable then to also
examine the seismic vulnerability of the interstory wall
sections in terms of mortar strength and subsequent cracking.
The chimneys will find a similar result if the actual thickness
of the chimney is used, as seen in Figure 45. By using this
method and assuming that the height of the chimney is 15
feet, the chimney is expected to overturn at 0.87g. But the
chimney is hollow, so if it is speculated that the mortar to
masonry connections are in a bad condition, it is possible that
Figure 45 Case study chimney
64
the walls of the chimney can act alone. In this case, the thickness of the wall is one wythe of bricks
(Ho 1979). The bricks in the case study are 3.63 inches thick each and the chimney is 15 feet high.
Table 17 shows the results for this condition.
Table
17 Stability analysis o/chinnev that is one
ythC thick.
CHIMNEY WEAK AXIS
fir,min [g]
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.010194
0.012232
0.014271
0.01631
0.018349
0.020387
0.022426
tan(a)
Stability
0.0201
0.0201
0.0201
0.0201
0.0201
0.0201
0.0201
STABLE
STABLE
STABLE
STABLE
STABLE
OVERTURN
OV RTURN
If the chimney is one wythe thick, is expected to overturn around 0.22g, which is smaller than the
also be
expected acceleration of 0.2292g. As with the facade section, the out of plane failure will
analyzed by estimating local shear failures as outlined in Chapter 5.
Values of shear failure and corresponding ground acceleration in terms of g at different distances
from the top of the chimney are in Table 18.
Table
18
Shear capacities at dieflirent failure plane heighls.
Distance From Top of Chimney
Ift]
0.5
Shear Failure
[lb]
160.62
Acceleration to Fail
[g]
0.023
1.0
321.25
0.047
1.5
481.87
0.070
2.0
642.50
0.093
2.5
803.12
0.117
3.0
963.74
0.140
3.5
1124.37
0.163
4.0
1284.99
4.5
1445.61
0.210
5.0
10.0
15.0
1606.24
3212.48
4818.71
0.233
0.467
0.700
65
This analysis determined that the top third of the chimney will fail in shear if the maximum
considered earthquake (0.2292g) occurs.
The minimum ground acceleration to crack interstory fagade portions, whose method is presented
by Priestley, are displayed in Table 19. Note that this behavior does not take into account wall
perforations but the calculated interstory mass does.
Table / 9 Aiinimuni ground accelerationto crack interstorv fagade portions.
Wall Thickness [ft]
Roof
1.33
Floor 4
1.33
Floor 3
1.33
Floor 2
1.33
Floor 1
1.33
Interstory Height [ft]
Wall Length [ft]
Interstory Mass [ft]
R [ki s]
13.38
29.46
50.42
25.21
11.77
29.46
43.01
46.72
13.52
29.46
49.49
71.46
12.56
29.46
44.97
93.95
11.14
29.46
35.95
111.92
To middle of the wall between the fourth floor and roof will start cracking at a mere ground
acceleration of 0.25g. The expected peak ground acceleration for the soil type in the Back Bay is
0.2292g. It is incredibly reasonable that during the maximum considered earthquake that this wall
section can crack. Although wall cracking is not considered a failure because it can still transfer
vertical loads, continued ground motion can cause the cracked section to start crushing at the floor
interfaces from continuous rocking and eventually steps out of plane. In the event of the maximum
considered earthquake, if this crack occurs and is not fixed, an aftershock or additional earthquake
won't have to exert force to cause the cracking and brick crushing at the floor interfaces will begin
immediately.
6.5 Analysis Model Conclusions
There are a few major conclusions that can be made from the analysis model results:
For the condition when the building's faqade to party wall connection is bad (scenario 1):
*
If the full wall is acting on its own, it is within the performance drift limits for the expected
base shear and is not expected to fail globally.
*
If the curved and flat wall sections are acting on their own, they are within the performance
drift limits for the expected base shear and are not expected to fail globally.
66
*
If the long pier section is action on its own, it is expected to globally fail according to the
performance drift limits for the expected base shear for the section.
For the condition when the building's fagade to party wall connection is good and the walls act as
one (scenario 2), the building is so stiff that none of the wall sections are expected to fail globally
or locally.
For local shear behavior, none of the stresses read from the piers in the finite element model surpass
the shear capacities calculated for those elements. The closest this comes to happening is when the
long pier wall section is considered to be acting on its own, but even still the capacity is not met.
Overturn of the chimneys are expected at ground accelerations lower than the maximum
considered earthquake. Out of plane shear failure and dislocation of the top third of the chimneys
is guaranteed for the maximum considered earthquake. This is the biggest immediate threat to the
Back Bay residences. Dislocated brick from the chimneys can plunge through roofs or fall to the
street below, injuring people and property.
67
7.0
Conclusion
A severe earthquake in Boston will happen. It is not a matter of if it will happen because history
has proven that it is only a matter of time. If the Cape Ann earthquake of intensity VIII can happen
once, it most definitely will happen again. The Back Bay buildings were built without seismic
design and sit upon infilled land that will be susceptible to liquefaction during the next significant
earthquake. This is a deadly combination for these historical unreinforced masonry buildings and
it is naive to believe that the Back Bay is not at risk.
The intent of this thesis was to gain understanding of the seismic performance of a typical
unreinforced masonry building in Boston's Back Bay neighborhood. This was done by analyzing
global and local behaviors in terms of accepted in-plane and out-of-plane failure mechanisms of
unreinforced masonry walls from the application of the maximum considered earthquake for the
Boston area. It is important to note that even though the results presented in this thesis are based
on this earthquake scenario that does not mean that a larger earthquake cannot happen. Another
important point is to realize that the results of this thesis do not take into account potential
liquefaction ground failures. The influence from liquefaction may just be what the wall sections
that are not expected to fail need to surpass performance levels.
However, the results based on the current building without considering liquefaction or an
earthquake larger than the expected one suggest that when good masonry to masonry connections
exist, which means that the facade does not act on its own and the load paths are clear, under the
maximum considered earthquake only minimal local failures may happen. This is evident when
looking at the results of scenario 2.
Contrarily, if cracks in the masonry and mortar degradation exist, load paths within the walls are
unclear. The age of the masonry and mortar make this a real possibility if they are unmaintained.
Even though the exterior wythe may appear in good condition, the interior wythes may not be.
This situation can cause wall elements, such as the curved, flat, or long pier sections, to act on their
own. The results show that if this is the case, damage under the maximum considered earthquake
can be significant in the global and local spheres. This is evident when looking at the interstory
results of the long pier section for scenario 1 and the results of local element shear failures.
68
Regardless of pre-existing conditions, certain intensities and complete overturn of chimney
failures are guaranteed at ground accelerations below the maximum considered earthquake. These
failures like this can be devastating since they can cause roof damage from impact, and severe
injury to people below.
Overall, the case study building is just on the edge of being considered vulnerable or not
vulnerable. Some results don't have the scenarios violating the performance levels, but in some
cases if the base shear was just a little higher, or the applied seismic force was slightly more intense
the performance levels would be surpassed. Additionally, the performance levels are just
guidelines and failures can happen before Immediate Occupancy, shear capacity, or overturning
moment is met.
7.1
Areas of Future Work
This study would benefit from a future analysis of how multiple buildings in the Back Bay respond
to seismic activity together. The case study in this thesis was analyzed as acting alone, so the
building-building interaction would be interesting for a few reasons. If the buildings are connected,
they might act together as one stiff building or there might be differential movement which could
cause shear failures. If the buildings are not connected, during seismic activity pounding may
occur. Analyzing how this would affect the out of plane failure for walls at the end of the block
would also be necessary to fully understanding a more accurate behavior of the neighborhood.
Many of the calculation methods in this thesis that yielded conclusive results that were highly
dependent on the facade geometry. The size and frequency of the perforations were very
influential. A simple vulnerability of the buildings could then be analyzed in a parametric study of
only the fagades.
Future research in this subject should also focus on creating more detailed finite element models
that better represent the nonlinear behavior of masonry.
69
Documentation References
Adams, Charles Francis. "The Works of John Adams, Second President of the United States."
1856. Google Books.
ASCE (2010). Minimum Design Loads for Buildings and Other Structures, ASCE 7-10. Reston,
VA: ASCE. Print.
ASCE/SEI (2010). Seismic Rehabilitation of Existing Buildings, ASCE/SEI Standard 41-10.
Reston, VA: ASCE/SEI. Print.
Bunting, Bainbridge (1967). Houses of Boston's Back Bay. Print.
Buntrock, Rebecca (2010). Structural Performance of Early 2 0 th Century Masonry High Rise
Buildings. Massachusetts Institute of Technology. Thesis.
"Creating Land in Boston's Back Bay." Boston Geology. Web.
CSI (2014) SAP2000 Version 17.1.1, Integrated software for structural analysis and design.
Computers and Structures Inc., Berkeley, CA.
DeJong, Matthew J. "Dynamically Equivalent Rocking Structures." Wiley Online Library. N.p.,
10 Feb. 2014. Web.
Ebel, John E. "Seismological Research Letters." The Cape Ann, Massachusetts Earthquake of
1755: A 250th Anniversary Perspective. Seismological Society of America, 2006. Web.
FEMA (2000). Prestandard and Commentary for the Seismic Rehabilitation of Buildings. FEMA
356. Washington, D.C.: Federal Emergency Management Agency, 2000. Web.
http://fema.gov/library
FEMA (1998). Evaluation of Earthquake Damaged Concrete and Masonry Wall Buildings.
FEMA 306. Washington, D.C.: Federal Emergency Management Agency. Web.
http://fema.gov/library
FEMA (1998). Promoting the Adoption and Enforcement of Seismic Building Codes: A
Guidebook for State Earthquake and Mitigation Managers. FEMA 313. Washinton, D.C.:
Federal Emergency Management Agency. Web. http://fema.gov/library
FEMA (1997). NEHRP Guidelies for the Seismic Rehabiitation of Buildings. FEMA 273.
Washington, D.C.: Federal Emergency Management Agency. Web.
http://fema.gov/library
FEMA E-74 Example 6.3.5.1 Unreinforced Masonry Parapets." FEMA, 24 June 2014. Web.
FEMA (2009). Unreinforced Masonry Buildings and Earthquakes: Developing Successful Risk
Reduction Programs. FEMA P-774. Washington, D.D.: Federal Emergency Management
Agency, 2009. Web. http://fema.gov/library
Friedman, D. (1995). HistoricalBuilding Construction:Design, Materials, and Technology.
New York: W.W. Norton & Company. Print.
70
"Geology of Boston." Boston Geology. N.p., n.d. Web. 10 Feb. 2015.
http://www.bostongeology.com/boston/geology/geology.htm.
Hess, Richard L. (2008). Unreinforced Masonry (URM) Buildings. United States Geological
Survey.
"History of Earthquakes in New England." Underground Town Hall. Web. 30 Jan. 2015.
Ho, Alan Darrell. (1979). Determination of Earthquake Intensities from Chimney Damage
Reports. Massachusetts Institute of Technology. Thesis.
Ingham, Jason. Seismic Assessment and Retrofit of Unreinforced Masonry Buildings. University
of Auckland, New Zealand. PowerPoint presentation.
Kafka, Alan L. "Why Does the Earth Quake in New England?" www2.bc.edu. Boston College,
15 Feb. 2014. Web.
Korini, Oltion, and Bilgin, Huseyin. A new modeling approach in the pushover analysis of
masonry structures. International Students Conference of Civil Engineering. Epoka
University, Albania. 2012.
"Massachusetts Earthquake History." USGS. United States Geological Survey. Web. 30 Jan.
2015.
Maxwell, Kenneth. Lisbon 1755: The First 'Modern' Disaster (but If Modern, How Is It So?)
Harvard University. Web. http://www.mod-langs.ox.ac.uk/files/windsor/5_maxwell.pdf
Miller, Jeremy. "Boston's Earthquake Problem." Boston.com. The New York Times, 28 May
2006. Web. 31 Jan. 2015.
Nordenson, Guy J P, and Glenn R. Bell. Seismic Design Requirements for Regions of Moderate
Seismicity. www.iitk.ac.in. Web.
Park, Joonam et al. Seismic Fragiit analysis of low-rise unreinforced masonry structures.
Engineering Structures 31 (2009): 125-137. Web.
Philosophical Transactions, Giving Some Account of the Present Undertakings, Studies, and
Labours of the Ingenious, in Many Considerable Parts of the World." Google Books.
Web.
Priestley, M. J. N. "Seismic Behaviour of Unreinforced Masonry Walls." Bulletin of the New
Zealand National Society for Earthquake Engineering 18.2 (1985): 191-205. Web.
Whitman, Robert. Seismic Design Decision Analysis. American Society of Civil Engineers.
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Image References
Boston Athenaeum. N. Bradlee Collection. Jan 2015.
Bruneau, Michel. "Performance of Masonry Structures during the 1994 Northridge (Los Angeles)
Earthquake." Canadian Journal of Civil Engineering 22 (1995): 378-402. University of
Buffalo. Web.
71
Masonry Terms. Digital Image. http://www.tpub.com/engbas/7-32.htm
Costa, Costa A., Antonio Arede, Andrea Penna, and Anibal Costa. "Free Rocking Response of a
Regular Stone Masonry Wall Withequivalent Block Approa Ch: Experimental and
Analytical Evaluation." Earthquake Engineering & Structural Dynamics 42 (2013): 2297319. Print.
Figure 5(a):Javed, M., Khan, A. N., and Magenes, G., 2008. Performance of masonry structures
during earthquake-2005 in Kashmir, Mehran University Research Journal of Engineering
& Technology 27, 271-282.
Figure 5(b) Bed-joint sliding. FEMA.
Figure 5(c) Christchurch earthquake damage. Digital Image. FEMA.
Figure 5(d) Christchurch earthquake damage. Digital Image. FEMA.
Figure 6(a) Parapet damage. Barry Welliver.
Figure 6(b) Christchurch earthquake damage. Digital Image. FEMA.
Figure 6(c) Northridge earthquake damage. Michel Bruneau.
Figure 7(a) "The Modified Mercalli Intensity Scale for Insurance Underwriting." The
Washington Surveying and Rating Bureau. N.p., 12 June 2012. Web.
Figure 7(b) Long Beach earthquake damage. Historical Society of Long Beach.
Figure 7(c) Northridge earthquake damage. Michel Bruneau.
Figure 7(d) Loma Prieta earthquake damage. Digital Image. EERI Reconnaissance Team.
Figure 7(e) Napa Valley earthquake damage. Digital Image. ZFA Structural Engineers.
Figure 7(f) Christchurch earthquake damage. Digital Image. USGS PAGER Team.
Figure 9(a & b) National Information Service for Earthquake Engineering, University of
California, Berkeley
Figure 1 1(a & b) Bunting, Bainbridge. (1967) Houses of Boston's Back Bay. Print.
All uncited images are the property of myself or Ornella Iuorio.
72
Appendix A
Cantilever Beam Hand Calculations
73
Constants and Base Shear Calculation for Scenario 1 wall elements.
**Scenario 2 done in the same manner, but with different Total Wall Weight
Full Wall Section
Constants
Base Shear Calculation
E
429
120
S161.
Building Dimensions
Curved Wall Section
Base Shear Calculation
Building Dimensions
Total Height [ft]
74.23
05
-0.18
0145
17.595
74
Flat Wall Section
Building Dimensions
Base Shear Calculation
7ft}
13.583
142.50
Total Width [ft)
77
1
Total Height [ft]
74.23
1.5
Total .ength
0.506
0.02
0.75
0.18
0.145
20.706
Pier Wall Section
Base Shear Calculation
Building Dimensions
Total Length [ft)
Total Width ftl
4.33
77
Total Height {ft)
74.23
51.55
1
1.5
0.506
0.02
0.75
0.18
0.145
7.490
75
Response Spectrum
By using the method outlined in Chapter 5, the response spectrum can be calculated. This spectrum
represents the response for the zip code of 02116, which contains the Back Bay. It is also assumed
that the soil is of Soil Class D, which represents infilled land and is also the default value used
when no reliable information is provided. The spectrum below shows that the peak ground
acceleration is 0.2292g.
Response Spectrum
0.25
0.2
0.15
0
CU
0.1
0.05
0
0
1
2
3
5
4
Period
76
6
[s]
7
8
9
10
Full Wall Section
144
278.00
428.75
591.00
732.25
892.81
I 12
0.99
1.53
1.98
1.91
2.48
A An1l
0.0002
0.0004
0.0007
0.0008
0.0011
5656
5656
5656
5656
5656
5656
A AA0i11
0.00009
0.00022
0.00024
0.00012
0.00030
58898854
58898854
58898854
58898854
58898854
58898854
167
1.48
2.30
2.97
2.87
3.72
0.402
0.558
0.693
0.814
0.906
1.000
0.000165
0.000294
0.000628
0.000994
0.001180
0.001628
5b.b
U.56
U.UUUU6
u.uuuu6
35.9
45.0
49.5
43.0
50.4
Base Shear
0.49
0.77
0.99
0.96
1.24
0.00010
0.00021
0.00033
0.00039
0.00054
0.00004
0.00011
0.00012
0.00006
0.00015
Max Roof Disp
Max Roof Disp/Total H
0.00054
5
0.000165
2.23
0.000129
0.000334
0.000366
0.000186
0.000449
1.97
3.06
3.96
3.83
4.95
15
20
0.001086
0.001628
0.002171
1.21584E-06
1.82376E-06
2.43168E-06
10
2.79
2.46
3.83
4.94
4.78
6.19
0.000275
0.000490
0.001047
0.001656
0.001966
0.002714
0.000275
0.000214
0.000557
0.000609
0.000310
0.000748
5.58
4.93
7.65
9.89
9.57
12.38
0.000551
0.000979
0.002093
0.003312
0.003932
0.005428
0.000551
0.000428
0.001114
0.001219
0.000620
0.001496
_
_ i
6.07919E-07
11.16
9.85
15.31
19.78
19.13
24.77
25
50
100
0.002714
0.0054276
0.0108552
3.03959E-06
0.0000061
1.21584E-05
0.000220
0.000392
0.000837
0.001325
0.001573
0.002171
0.000220
0.000171
0.000446
0.000487
0.000248
0.000598
0.001102
0.001959
0.004186
0.006623
0.007864
0.010855
0.001102
0.000857
0.002228
0.002437
0.001241
0.002991
27.89
24.63
38.27
49.45
47.84
0.002754
0.004896
0.010466
0.016558
0.019660
0.002754
0.002142
0.005569
0.006093
0.003101
61.92
0.027138
0.007478
44.63
39.41
61.24
79.12
76.54
99.07
0.004407
0.007834
0.016745
0.026493
0.031456
0.043421
0.004407
0.003428
0.008911
0.009748
0.004962
0.011965
55.79
49.26
76.55
98.89
95.67
123.84
0.005508
0.004284
0.011139
0.012185
0.006203
0.014956
0.013220
0.010283
0.026733
500
250
400
0.0271379
0.0434206
0.0542758
4.86335E-05
6.07919E-05
3.03959E-05
0.005508
0.009793
0.020932
0.033117
0.039320
0.054276
89.26
78.82
122.47
0.008814
0.015669
0.033491
0.008814
0.006855
0.017822
111.58
98.53
153.09
0.011017
0.019586
0.041863
0.011017
0.008569
0.022277
133.89
118.23
183.71
0.013220
0.023503
0.050236
158.23
0.052987
0.019496
197.79
0.066234
0.024370
237.35
0.079480
0.029244
153.08
198.14
800
0.0868413
0.062911
0.086841
0.009924
0.023930
191.35
247.67
1000
0.1085516
0.078639
0.108552
0.012405
0.029913
229.62
297.20
1200
0.1302619
0.094367
0.130262
0.014887
0.035895
9.7267E-05
0.000145901
0.000121584
78
1
223.15
0.022034
ntrtr
0.022034
167.37
0.016525
nesry
0.016525
147.79
0.029379
0.012853
197.05
0.039172
0.017138
229.64
0.062795
0.033416
306.18
0.083726
0.044555
296.68
0.099350
0.036556
395.58
0.132467
0.048741
287.02
0.117959
0.018608
382.69
0.157278
0.024811
371.51
0.162827
0.044869
495.34
0.217103
0.059825
P9
1500
2000
0.1628274
0.000182376
0.2171032
0.000243168
Curved Wall Section
144
278.00
428.75
591.00
732.25
892.81
2668
2668
2668
2668
2668
2668
6180991
6180991
6180991
6180991
6180991
6180991
0.402
0.558
0.693
0.814
0.906
1.000
79
26.68
16.23
18.44
20.57
17.86
21.32
Base Shear
Max Roof Disp
0.62
0.0003
U.UU0I
0.52
0.74
0.96
0.93
1.23
5
0.002853
0.0005
0.0010
0.0017
0.0020
0.0029
0.0008
0.0017
0.0023
0.0013
0.0029
Max Roof Disp/Total H
3.19604E-05
1.23
1.04
1.47
1.93
1.86
2.46
0.001
0.001
0.002
0.003
0.004
0.006
0.000619
0.000438
0.000959
0.001309
0.000759
0.001623
1.85
1.57
2.21
2.89
2.80
3.69
10
0.0009
0.0016
0.0030
0.0050
0.0061
0.0086
2.47
2.09
2.94
3.86
3.73
4.91
0.000928
0.000657
0.001439
0.001963
0.001138
0.002434
15
0.005707
0.008560
0.011414
9.58811E-06
1.27841E-05
0.002
0.003
0.005
0.008
0.010
0.014
0.001547
0.001095
0.002399
0.003272
0.001897
0.004057
11.11
9.39
13.25
17.36
16.77
22.11
0.001238
0.000876
0.001919
0.002618
0.001518
0.003246
20
6.39207E-06
3.09
2.61
3.68
4.82
4.66
6.14
0.0012
0.0021
0.0040
0.0067
0.0082
0.0114
0.005569
0.009511
0.018146
0.029926
0.036756
0.051362
0.005569
0.003942
0.008635
0.011780
0.006831
0.014606
21.61
18.27
25.77
33.75
32.62
42.99
25
90
175
0.014267
0.0513624
1.59802E-05
0.0000575
0.0998712
0.000111861
80
0.010830
0.018494
0.035284
0.058189
0.071470
0.099871
0.010830
0.007665
0.016790
0.022905
0.013282
0.028401
30.87
26.10
36.81
48.21
46.60
61.42
250
0.015471
0.026420
0.050405
0.083126
0.102101
0.142673
0.015471
0.010950
0.023985
0.032721
0.018974
0.040573
0.000511366
0.024753
0.042272
0.080648
0.133002
0.163361
0.228277
0.024753
0.017519
0.038376
0.052354
0.030358
0.064916
0.049506
0.084545
0.161297
0.266005
0.326722
0.456554
0.049506
0.035039
0.076752
0.104708
0.060717
0.129833
0.061883
0.105681
0.201621
0.332506
0.408402
0.570693
123.47
104.39
147.24
192.85
186.38
245.67
1000
0.5706928
0.000639207
74.08
62.63
88.35
115.71
111.83
147.40
600
0.037130
0.063409
0.120973
0.199504
0.245041
0.342416
0.037130
0.026279
0.057564
0.078531
0.045538
0.097374
0.074259
0.126817
0.241945
0.399007
0.490082
0.684831
0.074259
0.052558
0.115128
0.157062
0.091075
0.194749
0.3424157
0.000383524
0.2282771
0.000255683
0.1426732
0.000159802
98.78
83.51
117.79
154.28
149.10
196.53
800
0.4565543
49.39
41.75
58.90
77.14
74.55
98.27
400
0.061883
0.043798
0.095940
0.130885
0.075896
0.162291
148.17
125.26
176.69
231.42
223.66
294.80
1200
0.6848314
0.000767049
1
81
185.21
156.58
220.87
289.27
279.57
368.50
0.092824
0.158522
0.302432
0.498759
0.092824
0.065697
0.143910
0.196327
0.612603
0.856039
0.113844
0.243436
246.95
208.77
294.49
385.70
372.76
0.123766
0.211362
0.403242
0.665012
0.816804
0.123766
0.087596
0.191880
0.261769
0.151792
491.33
1.141386
0.324582
1500
2000
0.8560393
1.1413857
0.000958811
0.001278415
Flat Wall Section
144
2608
5773904
0.402
U.UU.L1J.U
0U.0.L13
2608
5773904
0.558
26.08
18.62
2.UI7
278.00
2.062
0.002018
0.000915
428.75
2608
5773904
0.693
24.34
3.35
0.004278
0.002261
591.00
732.25
2608
2608
5773904
5773904
0.814
0.906
25.37
22.52
4.10
4.05
0.007228
0.009010
0.002950
0.001781
892.81
2608
5773904
1.000
25.55
5.07
0.012563
0.003553
Base Shear
Max Roof Disp
Max Roof Disp/Total H
82
20.71
0.012563
1.40712E-05
1.004
0.996
1.62
1.98
1.96
2.45
0.000533
0.000974
0.002066
0.003490
0.004350
0.006066
0.000533
0.000442
0.001092
0.001424
0.000860
0.001716
1.51
1.49
2.43
2.97
2.93
3.67
0.000799
0.001462
0.003099
0.005235
0.006526
0.009099
0.000799
0.000663
0.001637
0.002136
0.001290
0.002574
2.01
1.99
3.23
3.96
3.91
4.90
15
20
0.006066
0.009099
0.012132
6.79442E-06
1.01916E-05
1.35888E-05
10
2.51
2.49
4.04
4.95
4.89
6.12
25
0.015165
1.6986E-05
0.001331
0.002436
0.005165
0.008726
0.010876
0.015165
0.001331
0.001104
0.002729
0.003561
0.002150
0.004289
9.03
8.96
14.55
17.81
17.60
22.04
0.004793
0.008769
0.018593
0.031412
0.039153
0.054595
0.004793
0.003976
0.009824
0.012819
0.007741
0.015442
10.04
9.96
16.17
19.79
19.55
24.49
90
100
0.0545953
0.0000611
0.0606615
6.79442E-05
83
0.001065
0.001949
0.004132
0.006980
0.008701
0.012132
0.005326
0.009744
0.020659
0.034902
0.043503
0.060661
0.001065
0.000884
0.002183
0.002849
0.001720
0.003432
0.005326
0.004418
0.010915
0.014243
0.008601
0.017158
806Lt7Z*O
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t7s9TST*O
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SSZLSO*O
Lt?9TSO'O
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9T*ot7
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6SEt7ZO*O
STEETTO
EzT9
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Lt7'617
EV017
0617Z
OT*SZ
150.58
149.38
242.55
296.81
293.28
367.40
200.78
199.17
323.40
395.75
391.04
489.86
2000
0.079889
0.066264
0.163731
0.213645
0.129022
0.257370
0.079889
0.146154
0.309885
0.523530
0.652552
0.909922
1500
0.9099218
1.2132290
0.001019163
0.001358883
0.106519
0.194871
0.413180
0.698040
0.870069
1.213229
0.106519
0.088352
0.218308
0.284861
0.172029
0.343160
Pier Wall Section
144
831
187045
0.402
8.31
3.52
0.045057
0.045057
278.00
831
187045
0.558
7.74
4.55
0.092235
0.047178
428.75
831
187045
0.693
8.70
6.35
0.187196
0.094961
591.00
831
187045
0.814
9.37
8.03
0.333327
0.146131
732.25
831
187045
0.906
8.15
7.78
0.425668
0.092341
892.81
831
187045
1.000
9.27
9.77
0.598002
0.172335
Base Shear
Max Roof Disp
Max Roof Disp/Total H
85
40
0.598002
0.000669795
0.88
1.14
1.59
2.01
0.011264
0.023059
0.046799
0.083332
0.011264
0.011794
0.023740
0.036533
1.32
1.71
2.38
3.01
0.016896
0.034588
0.070198
0.124997
0.016896
0.017692
0.035610
0.054799
1.76
2.27
3.18
4.02
0.022528
0.046117
0.093598
0.166663
0.022528
0.023589
0.047480
0.073066
1.95
0.106417
0.023085
2.92
0.159625
0.034628
3.89
0.212834
0.046170
2.44
0.149501
0.043084
3.66
0.224251
0.064625
4.88
0.299001
0.086167
0.112642
10
15
0.149501
0.000167449
0.1911970
0.000214151
20
0.299001
0.000334898 1_1
2.20
0.028161
0.028161
4.40
0.056321
0.056321
8.79
0.112642
2.84
0.057647
0.029486
5.69
0.115294
0.058972
11.37
0.230587
0.117945
3.97
5.02
0.116997
0.208329
0.059350
0.091332
7.94
10.04
0.233994
0.416658
0.118701
0.182664
15.89
20.08
0.467989
0.833317
0.237402
0.365328
4.86
0.266042
0.057713
9.73
0.532084
0.115426
19.45
1.064169
0.230852
6.10
0.373751
0.107709
12.21
0.747503
0.215418
24.42
1.495005
0.430836
25
50
100
0.3737513
0.000418622
0.7475026
0.0008372
0.001674488
1.4950051
86
28.43
0.576468
39.72
50.19
48.63
61.04
1.169972
2.083291
2.660422
3.737513
0.471780 1
400
68.23
95.32
120.45
116.72
146.50
600
0.006697953
0.010046929
45.49
0.294862
0.593505
0.913319
0.577131
1.077091
63.55
80.30
77.81
97.67
250
0.922348 1
1.871955
3.333266
4.256675
5.980020
1.383522 1
2.807933
4.999899
6.385013
8.970031
3.7375128
0.00418622
1.126421
105.54
1.351705
136.46
2.767044
190.65
5.615866
70.36
0.901136
90.97
1.844696
127.10
3.743911
158.87
160.60
6.666532
200.75
8.33316524.0.979
155.63
8.513350
194.54
10.641688
233.44
12.770025
14.950051
293.01
17.940061
195.34
800
0.013395905
11.960041
87.95
0.450113.72
2.305870
244.17
1.1795
4.679889
1ooo
1200
0.016744881
0.020093858
87
0.707670 1
131.92
1.689631
175.90
2.252841
170.58
3.458806
227.43
4.611741
238.31
7.019833
317.74
9.359777
12.499748
15.962532
401.51
16.666330
389.07
21.283375
22.425077
488.35
29.900102
301.13
291.80
366.26
1500
2000
0.025117322
0.033489763
88
Appendix B
SAP2000 Pushover Results
Full Wall Section
PD
PC
PB
PA
Basement
0.01675
0.01675
0.012666
0.012666
0.01466
0.01466
0.016647
0.016647
1
0.026658
0.009908
0.033311
0.020645
0.039981
0.025321
0.046623
0.029976
2
0.050222
0.023564
0.063212
0.029901
0.076241
0.03626
0.089213
0.04259
3
0.078647
0.028425
0.097891
0.034679
0.117195
0.040954
0.136414
0.047201
0.024746
0.103393
4
0.025298
0.128691
Roof
Base Shear
Max Roof Disp
Max Roof Disp/Total H
0.128082
0.160103
0.030191
0.152848
0.035653
0.177505
0.041091
0.032021
0.191612
0.038764
0.222979
0.045474
5
10
15
20
0.128691
0.0001441
0.160103
0.0001793
0.191612
0.0002146
0.222979
0.0002497
P2
P1
PE
P4
P3
0.018634
0.018634
0.028598
0.028598
0.048517
0.048517
0.108276
0.053265
0.034631
0.086572
0.057974
0.153164
0.104647
0.352943
0.687456
0.168035
0.168035
0.244667
0.552718
0.384683
0.334513
1.077612
0.524894
0.108276
0.102185
0.04892
0.167231
0.080659
0.297288
0.144124
0.155632
0.053447
0.252
0.084769
0.444686
0.147398
1.02274
0.335284
1.600774
0.523162
0.12832
1.314626
0.291886
2.056218
0.455444
0.153153
1.669686
0.35506
2.613178
0.55696
0.202161
0.046529
0.325798
0.073798
0.573006
0.25435
0.052189
0.411645
0.085847
0.726159
25
50
100
0.25435
0.0002849
0.4116450
0.0004611
0.7261590
0.0008133
400
250
1.6696860
2.6131780
0.0018701
0.0029269
__160
0.758045 11.351788
3963
2.638186
2.117989
4.033731
___3.912837_
5.022499
_____5.836999_
7.491123
Soo
1000
1500
5.1290750
6.3870350
9.5278230
0.0057448
0.0071538
0.01067171
_
3.142142
0.605984
_____0.605984
0.07590.407059
0.3732 03238
1.085427
PS
P7
P6
Curved Wall Section
PD
PC
PB
PA
1
0.01527
0.047425
0.01527
0.032155
0.026734
0.092255
0.026734
0.065521
0.038239
0.137229
0.038239
0.09899
0.049675
0.181931
0.049675
0.132256
2
0.103799
0.056374
0.206522
0.114267
0.309532
0.172303
0.411931
0.23
3
0.179941
0.076142
0.353033
0.146511
0.526573
0.217041
0.699087
0.287156
4
0.250683
0.070742
0.492841
0.139808
0.73561
0.209037
0.976923
0.277836
Roof
0.332141
0.081458
0.653749
0.160908
0.976145
0.240535
1.296587
0.319664
Basement
Base Shear
Max Roof Disp
Max Roof Disp/Total H
0.653749
15
0.976145
1.296587
0.000732235
0.001093336
0.001452249
5
10
0.332141
0.000372016
91
20
0.8
0.03
1.73147
0.7
0.233166
0.165609
0.450876
0.33241
0.927
6
0.2648
0.5461 .2885 102057
0.7781
2.055343
P4
P3
P2
Pi
PE
0.577228
0.666131
0.577228
0.921249
2_24414_
3.589374
16.086093
250
25.730408
400
__
8.217 995
__5_136839_
0.87066 0.35465 1.73147 0.7909
0.69196
0.796037
.6569713.850877
.46956
4.85042419.375421
6.440763
25
2.429107
3.225144
50
1.617969
3.225144
6.440763
16.086093
25.730408
0.003612339
0.00721401
0.018017311
0.028819475
0.346848
0.399055
1.218914
1.617969
0.001812214
PS
100
P6,
1.397997
1.838651
5.382759
7.175974
12.326418
16.434445
20.772802
27.694071
29.058722
38.741118
38.590123
51.448657
600
800
38.590123
51.448657
0.043223065
0.057625332
92
Flat Wall Section
PD
PC
PB
PA
Basement
1
2
0.019119
0.05905
0.112824
0.019119
0.039931
0.053774
0.032249
0.10879
0.2155
0.032249
0.076541
0.10671
0.045305
0.158241
0.317563
0.045305
0.112936
0.159322
0.058417
0.207914
0.420109
0.058417
0.149497
0.212195
3
0.179134
0.06631
0.348715
0.133215
0.517255
0.199692
0.686644
0.266535
4
0.239854
0.06072
0.471354
0.122639
0.701406
0.184151
0.932662
0.246018
Roof
0.309076
0.211201
1.215027
0.282365
Base Shear
Max Roof Disp
Max Roof Disp/Total H
0.069222
0.140448
0.611802
0.912607
5
10
15
0.309076
0.000346182
0.611802
0.00068525
0.912607
0.00102217
0.001360897
P4
P3
P2
P1
PE
20
1.215027
0.66088
1.053772
0.07151
0.07151
0.137024
0.137024
0.267956
0.267956
0.66088
0.257510.522468
0.186
0.264958
0.505684
1.00166
0.733704
2.490084
!3.978386
1.034721
0.36866
0.529037
2.0584411
5.130651
8.202645
0.855675
1.163382
1.516698
0.333207
0.307707
0.353316
1.70666
2.31823
3.026807
0.671939
0.61157
0.708577
3.392334
4.626076
6.044549
8.466097
11.55279
15.101051
13.539552
18.477693
24.150
25
50
1.516698
3.026807
0.001698785
0.003390191
400
100 1250
0.01691401
0.006770228
93
0.02705016
Pier Wall Section
PC
PB
Basement
0.32849
0.32849
0.660809
U.9911bb
1
2
1.122165
0.793675
2.25314
3.377458
7.267349
12.364982
3
4
Roof
Base Shear
Max Roof Disp
Max Roof Disp/Total H
5
7.616062
10
15.278195
17.211867
22.897955
15
22.897955
0.008530409
0.017112421
0.025646972
Pi
PE
1.652722
3.309447
5.629017
11.267506
12.110827
24.24001
20.605025
41.240212
28.681325
57.404229
38.156012
76.367
50
25
38.156012
76.367
0.042736837
0.08553525
94
1.322365
4.504698
9.692261
16.490284
22.953742
30.536252
20
30.536252
0.034202286
Appendix C
In-Plane Failure Results
Full Wall Section-Pier Element Capacities
Pier 1
Pier 2
Pier 3
Pier 4
Pier 5
Rocking
Rocking
Rocking
Rocking
Rocking
0.5
a
hen [in]
26.0
vme
2
27.6
An [in ]
L [in]
36.8
L [in]
57.2
72.5
hen [in]
72.5
hen [in]
72.5
hef [in]
80.1
heff [in]
Bed Joint Sliding
27.0
vte [psi]
1.2
2547.1
Vr [lb]
Bed Joint Sliding
27.0
vte [psi]
26.0
vme
2
27.6
An [in ]
0.7
L/he
1017.2
Vr [lb]
Bed Joint Sliding
27.0
vte [psi]
26.0
vme
2
27.6
An [in ]
PCE [psi]
2
Vbjsi
718.7
Vbjsl
Vbjs2
1656.1
Diagonal Tension
Vbjs2
2436.2
VbIs2
1539.5
Diagonal Tension
Vbjs2
Vdt
f'dt
315.9
Vdt
13.0
1.0
Beta
417.8
f'me [Psi]
Weight above [lbs]
0.7
Beta
291.6
Vdt
3.1
780.0
3312.3
4.6
fae [Psi]
780.0
N'e [Psi]
Weight above [lbs]
4872.4
2.9
fae [PSI]
780.0
f'me [Psi]
26.0
2
1063.3
VbJs2
718.7
6082.7
Diagonal Tension
13.0
0.7
258.6
Vdt
27.6
An [in ]
13.0
f'dt
0.7
Beta
351.9
Vdt
Toe Crushing
2.0
fae [Psi]
780.0
f'me [Psi]
fae [Psi]
11.4
f'me [psi]
780.0
12165.4
Weight above [lbs]
3079.1
Weight above [lbs]
2126.6
Weight above [lbs]
Area [in 2]
1065.6
Area [in 2]
1065.6
Vtc
Min
Vtc
Min
4255.3
351.9
Area [in 2]
1065.6
Area [in 2]
1065.6
Area [in 2]
VC
Min
1300.5
315.9
Vc
Min
2806.4
417.8
Vtc
Min
1124.2
291.6
Diagonal Tension
27.0
vme
Toe Crushing
1065.6
Diagonal Tension
Bed Joint Sliding
vte [psi]
Vbjsl
Beta
3911.6
Vr [Ib]
718.7
f'dt
0.7
L/heff
Diagonal Tension
Toe Crushing
Toe Crushing
Toe Crushing
fae [Psi]
13.0
f'dt
27.6
An [in ]
718.7
13.0
0.8
26.0
vme
Vbjsl
Beta
485.2
Bed Joint Sliding
27.0
vte [psi]
718.7
Diagonal Tension
0.5
L/heff
Vr [lb]
Vbjsl
f'dt
12165.4
PCE [psi]
53.2
72.5
1177.1
V, [lb]
2126.6
0.5
a
84.2
57.2
L/heff
0.5
a
3079.1
4872.4
0.8
L/heff
0.5
a
PCE [psi]
L [in]
PCE [psi]
L [in]
3312.3
PCE [psi]
L [in]
0.5
a
Diagonal Tension
537.2
258.6
Diagonal Tension
Diagonal Tension
0.5
a
PCE [psi]
L [in]
17895.3
84.2
1w, [i]
80.1
1.1
L/heff
8464.0
Vr [Ib]
-Rocking
0.5
a
PCE
11308.9
53.2
[PSI]
L [in]
80.1
hff [in]
0.7
L/heff
3380.2
Vr [Ib]
vte [psi]
vine
27.0
26.0
vte [psi]
vme
An [in2 ]
27.6
An [in 2 ]
27.6
718.7
-T8947.7
1.0
Beta
544.0
Vdt
PS]780.0
Weight above
[lbs]
17895.3
2
]
Area [in1
_____
m
_
twf [in]
0.5
L/heff
1612.4
Vr [Ib]
L [in]
91.8
0.6
L/heff
6000.3
Vr [lb]
PCE
31457.1
84.2
[psi]
L [in]
91.8
heff [in]
0.9
L/heff
12983.8
Vr [lb]
Bed Joint Sliding
Bed Joint Sliding
vte [psi]
vme
27.0
26.0
vte [psi]
vme
27.0
26.0
vte [psi]
vine
27.0
26.0
An [in2]
27.6
An [in 2]
27.6
An [in 2]
27.6
Vbjsl
718.7
Vbjsl
718.7
Vbjsl
718.7
Vbjsz
5654.4
Vbjs2
3905.3
Vbjsz
10692.4
Vbjs2
15728.6
13.0
f'dt
0.7
Beta
324.5
Vdt
13.0
f'dt
0.7
Beta
301.1
Vdt
13.0
f'dt
0.7
Beta
384.0
Vdt
f'e[S]780.0
f'me [PSI]
Weight above
[lbs]
Weight above
[lbs]
11308.9
1.0
649.9
Vdt
Toe Crushing
20.1
7.3 -fae [PSI]
fae [PSI]
13.0
f'dt
Beta
Toe Crushing
Toe Crushing
fe[S]10.6
Diagonal Tension
Diagonal Tension
Diagonal Tension
Toe Crushing
16.8
80.1
21384.9
57.2
0.5
a
718.7
Toe Crushing
fae [PSI]
PCE [PSI]
hegt[n]
Diagonal Tension
13.0
f'dt
7810.6
36.8
780.0
7810.6
f'e[S]780.0
f'e[S]780.0
Weight above
[lbs]
2
29.5
fae [PSI]
21384.9
Weight above
[lbs]
Area [in 2]
1065.6
Area [in ]
1065.6
Area [in ]
1065.6
Area [in ]
9115.2
Vtc
3682.8
Vt
Mi
1767.5
Vtc
6422.0
Vtc
Diagonal Tension
544.0
324.5
Min
Diagonal Tension
2
301.1
Diagonal Tension
97
384.0
Min
Diagonal Tension
31457.1
2
1065.6
T
____
VbJsl
Diagonal Tension
f'e
L [in]
0.5
a
Bed Joint Sliding
27.0
26.0
Vbjs2
[psi]
Bed Joint Sliding
Bed Joint Sliding
Vbjsl
0.5
a
PCE
Pier 10
Rocking
Pier 9
Rocking
Pier 8
Pier 7
Rocking
Pier 6
Rocking
13646.4
649.9
Min
Bed Joint Sliding
0.5
a
L [in]
Rocking
Rocking
Rocking
PCE [psi]
Pier 13
Pier 12
Pier 11
0.5
a
19879.3
53.2
PCE [psij
91.8
he [in]
heo [in)
0.6
L/heff
5185.2
Vr [lb]
Bed Joint Sliding
27.0
vte [psi]
26.0
vme
2
27.6
An [in ]
20478.3
36.8
L [in]
87.5
0.4
L/heff
3872.6
V, [Ib]
Bed Joint Sliding
27.0
vte [psi]
26.0
vine
2
An [in ]
27.6
0.5
a
PCE [psi]
L [in]
Pier 14
Pier 15
Rocking
Rocking
0.5
a
31896.0 PCE [psi]
57.2 1L [in]
46919.0
84.2
hf [in]
87.5
87.5
htf [in]
0.7
L/heff
9394.8
Vr [Ib]
Bed Joint Sliding
27.0
vte [psi]
26.0
vme
2
An [in ]
27.6
1.0
L/heff
20328.9
V, [Ib]
Bed Joint Sliding
27.0
vte [psi]
vine
2
An [in ]
0.5
29650.4
53.2
a
PCE [psi]
L [in]
87.5
heff [in]
0.6
L/heff
8118.5
Vr [Ib]
Bed Joint Sliding
27.0
vte [psi]
26.0
vine
26.0
27.6
An [in 2]
27.6
Vblsl
718.7
Vbjsl
718.7
Vbjsl
718.7
Vbjsl
718.7
Vbjsi
718.7
Vbjs2
9939.6
Diagonal Tension
Vbjs2
10239.2
Diagonal Tension
Vbjs2
15948.0
Diagonal Tension
Vbjs2
23459.5
Diagonal Tension
VbJs2
14825.2
Diagonal Tension
13.0
f'dt
0.7
Beta
375.7
Vdt
13.0
f't
0.7
Beta
379.0
Vdt
0.7
Beta
437.5
Vt
18.7
fae [PSI]
780.0
f' me [PSI]
19879.3
fae [PSI]
19.2
f'me [PSI]
780.0
Weight above
[lbs]
13.0
f'_t
1.0
Beta
752.6
Vdt
20478.3
29.9
fae [PSI]
f'm
31896.0
Weight above
[lbs]
Area [in 2]
1065.6
Area [in 2]
1065.6
Area [in 2]
1065.6
Area [in2]
Vtc
Min
5564.5
375.7
Vtc
Min
4151.5
379.0
Vtc
Min
9866.4
437.5
Vtc
Min
Diagonal Tension
Diagonal Tension
Diagonal Tension
98
0.7
Beta
V
_
426.6
_
Toe Crushing
44.0
fa. [psi]
_f'me [PSI]_
PI78.
Weight above
[lbs]
13.0
f'_t
Toe Crushing
Toe Crushing
Toe Crushing
Toe Crushing
weight above
[lbs]
13.0
f'_t
780__ _f'me[PSI]_
_ _
46919.0
1065.6
20766.2
718.7
Bed Joint Sliding
27.8
fae [PSI]
Weight above
[lbs]
__
_
780.0
29650.4
Area [in2]
1065.6
Vtc
Min
8560.9
426.6
Diagonal Tension
0.5
a
PCE [PSi]
L [in]
heff [in]
L/heff
Vr [lb]
13729.8
36.8
91.8
0.4
2473.4
Bed Joint Sliding
27.0
vte [psi]
26.0
vine
An [in 2]
27.6
0.5
a
PCE [psi]
L [in]
heff [in]
L/heff
Bed Joint Sliding
27.0
vte [psi]
An [in
0.7
Beta
339.7
Toe Crushing
Vdt
fae [PSI]
f'me [PSI]
12.9
780.0
27.6
13.0
0.7
Beta
478.0
Toe Crushing
Vdt
fae [PSI]
f'me [psi]
38.2
780.0
13729.8
above [Ibs]
40754.9
5381.2
Vr [lb]
Bed Joint Sliding
27.0
vte [psi]
26.0
vme
2
27.6
An [in ]
0.5
a
L [in]
Bed Joint Sliding
27.0
vte [psi]
0.7
407.4
Toe Crushing
Vdt
24.2
fae [PSI]
780.0
f'me [PSI]
26.0
vme
2
27.6
An [in ]
13.0
0.7
Beta
564.1
Vdt
56.3
f'me [PSI]
above [Ibs]
2
1065.6
Area [in2]
1065.6
Area [in ]
1065.6
Area [in ]
Vtc
Min
2683.4
339.7
Vtc
Min
6975.5
478.0
Vtc
Min
5713.9
407.4
Vtc
Min
Diagonal Tension
Bed Joint Sliding
27.0
vte [psi]
59950.4
1065.6
18285.2
564.1
Diagonal Tension
Diagonal Tension
99
26.0
vine
2
27.6
An [in ]
0.5
a
L [in]
Bed Joint Sliding
27.0
vte [psi]
2
472.3
Toe Crushing
Vdt
27.6
An [in ]
Vbjs2
0.7
26.0
vme
18942.8
Diagonal Tension
13.0
5530.7
Vr [lb]
Vbjsl
Beta
78.2
0.5
he [in]
L/heff
718.7
f'dt
26166.0
36.8
PCE [psi]
718.7
13083.0
Diagonal Tension
13.0
f'dt
0.7
Beta
409.2
Crushing
Toe
Vdt
fae [PSI]
35.6
fae [PSI]
24.6
f'me [PSI]
780.0
f'me [PSI]
780.0
Weight
above [lbs]
Area [in 2]
Diagonal Tension
780.0
11594.5
Vr [lb]
Toe Crushing
fae [PSI]
78.2
0.7
hef [in]
L/heff
Vbjs2
Weight
25810.0
1 [in]
29975.2
Diagonal Tension
f'dt
37885.5
53.2
PCE [psi]
Vbjsl
Weight
2
0.5
a
718.7
VbJs2
Beta
18347.2
Vr [Ib]
12905.0
Tension
Diagonal
13.0
78.2
0.7
heff [in]
L/heff
Vbjsl
f'dt
59950.4
53.2
PCE [psi]
718.7
Vbjs2
f'dt
78.2
0.5
heff [in]
L/heff
20377.4
Diagonal Tension
Weight
Weight
above [lbs]
]
L [in]
Vbjsl
Vbjs2
13.0
2
25810.0
36.3
PCE [psi]
718.7
6864.9
Diagonal Tension
f'dt
26.0
vine
Vbjsi
Vbjs2
78.2
0.4
6750.8
Vr [lb]
718.7
Vbjsl
40754.9
28.8
0.5
a
Pier 21
Rocking
Pier 20
Rocking
Pier 19
Rocking
Pier 18
Rocking
Pier 17
Rocking
Pier 16
Rocking
above [lbs]
2
Area [in ]
Vtc
Min
37885.5
1065.6
12043.9
472.3
Diagonal Tension
above [bs]
2
26166.0
Area [in ]
1065.6
Vtc
Min
5868.8
409.2
Diagonal Tension
Curved Wall Section-Pier Element Capacities
1018.5
17.6
PCE [psi]
L [in]
3079.1
53.2
PCE [psi]
L [in]
0.5
0.5 a
0.5
0.5 a
a
PCE [psi]
L [in]
Pier 7
Rocking
Pier 6
Rocking
Pier 4
Rocking
Pier 3
Rocking
Pier 2
Rocking
0.5
a
2126.6
36.8
PCE [psi]
L [in]
3740.6
17.6
PCE [psi]
L [in]
11308.9
53.2
80.1
h.n [in]
72.5
heff [inff
[in]he
72.5
he [in]
80.1
he [in]
L/heff
0.24
L/heff
0.7
0.51
L/heff
0.22
L/heff
111.3
Vr [lb]
Bed Joint Sliding
27
vte [psi]
26
vme
Vr [lb]
1017.2
Bed Joint Sliding
27
vte [psi]
26
vme
485.2
Vr [Ib]
Bed Joint Sliding
27
vte [psi]
26
vme
369.8
V, [Ib]
Bed Joint Sliding
27
vte [psi]
26
vme
0.66
3380.2
Vr [Ib]
Bed Joint Sliding
27
vte [psi]
26
vme
An [in 2]
An [in 2 ]
An [in 2 ]
An [in2 ]
An [in 2 ]
27.6
27.6
L/heff
27.6
27.6
27.6
Vbjsl
718.7
Vbjsl
718.7
Vbjsl
718.7
Vbjsl
718.7
Vbjsl
718.7
Vbjs2
509.2
Diagonal Tension
Vbjs2
1539.5
Diagonal Tension
Vbjs2
1063.3
Diagonal Tension
Vbjs2
1870.3
Diagonal Tension
Vbjs2
5654.4
Diagonal Tension
f'dt
Beta
Vdt
13
0.67
f'dt
249.4
Vdt
Beta
13
0.73
f'dt
291.6
Vdt
Beta
Toe Crushing
Toe Crushing
13
0.67
f'dt
258.6
Vdt
Beta
Toe Crushing
13
1
fdt
404.9
Vdt
13
0.67
Beta
324.5
Toe Crushing
Toe Crushing
fae [Psi]
1.0
fae [Psi]
2.9
fae [Psi]
2.0
fae [Psi]
3.5
fae [Psi]
10.6
f'me [Psi]
780
f'me [Psi]
780
f'me [PSI]
780
f'me [PSI]
780
f'me [Psi]
780
Weight above
[lbs]
Area [in 2]
1018.5
1065.6
123.4
Vtc
111.3
Min
Rocking
2126.6
Weight above
[lbs]
3740.6
Weight above
[lbs]
1065.6
Area [in2]
1065.6
Area [in 2]
1065.6
408.3
Vtc
3682.8
369.8
Min
Weight above [lbs]
Area [in 2]
3079.1
1065.6
Weight above
[lbs]
Area [in 2]
Vtc
1124.2
Vtc
537.2
Vtc
Min
291.6
Min
258.6
Min
Diagonal Tension
Diagonal Tension
100
Rocking
11308.9
324.5
Diagonal Tension
0.5
a
0.5
a
6575.4
0.5
a
7810.6
36.8
[PSI]
L [in]
lwf [in]
80.1
hff9
L/heff
0.46
L/heff
0.19
L/heff
Vr [Ib]
567.3
Vr [lb]
Vr
1612.4
[lb]
PCE
17.6
L [in]
i
0.5
a
PCE [Psi]
20478.3
L [in]
17.6
91.8
he [in]
87.5
hf[in]
87.5
L/heff
0.20
Vr [lb]
888.2
0.6
5185.2
0.4
1/heff
3872.6
Vr [lb]
Bed Joint Sliding
Bed Joint Sliding
27
vte [psi]
27
vte [psi]
27
vte [psi]
vne
26
vme
26
vme
26
vie
26
27.6
An [in 2 ]
27.6
An [in 2 ]
9807.3
36.8
vte [psi]
27.6
PCE [Psi]
L [in]
27
An [in 2 ]
0.5
a
53.2
Bed Joint Sliding
Bed Joint Sliding
Bed Joint Slidin
19879.3
PCE [PsI]
[PSI]
L [in]
PCE
Pier 14
Rocking
Pier 12
Rocking
Pier 11
Rocking
Pier 10
Rocking
Pier 8
Rocking
2
27.6
An [in ]
vte [psi]
27
vie
26
2
An [in ]
27.6
Vbjsl
718.7
Vbjsl
718.7
Vbjsl
718.7
Vbjsi
718.7
Vbjsl
718.7
Vbjs2
3905.3
VbJs2
3287.7
Vbjs2
9939.6
VbJs2
10239.2
Vbjs2
4903.7
13
f'dt
0.67
Beta
301.1
Vdt
Toe Crushing
dt
1
Diagonal Tension
13ft
f't Diagonal Tension
13
f'dt
1
Beta
436.4
Vdt
Crushing
____Toe
Diagonal Tension
1
13
f'dt
0.67
Beta
375.7
Vdt
'tDiagonal Tension
f'dt
0.67
Beta
379.0
Vdt
Weight above
Weight above
f m [PI]780
f'e[S]780
f'me [psi]
780
19.2
20478.3
[lbs]
Weight above [lbs]
7810.6
Weight above [Ibs]
6575.4
Weight above [lbs]
Area [in 2]
1065.6
Area [in 2 ]
1065.6
Area [in 2]
1065.6
Area [in2 ]
Vtc
Min
1767.5
301.1
Vtc
Min
Vtc
Min
5564.5
375.7
Vtc
Mi
101
Toe Crushing
780
fae [PSI]
Diagonal Tension
469.6
Vdt
f'me [PSI]
18.7
Diagonal Tension
1
Beta
f'e[S]780
fae [PSI]
Diagonal Tension
13
9.2
fe[S]6.2
19879.3
1
fae [PSI]
fae PSI]7.3
623.2
436.4
dtDiagonal Tension
f'dt
Toe Crushing
Crushing
____Toe
1
13
1065.6
4151.5
379.0
Diagonal Tension
[lbs]
9807.3
Area [in 2]
1065.6
Vtc
Min
970.3
469.6
Diagonal Tension
Rocking
0.5
a
0.5
0.5
a
13729.8
53.2
PCE [psi]
L [in]
36.8
PCE [psi]
L [in]
he [in]
87.5
he [in]
91.8
hI[in]
L/heff
0.61
L/heff
0.40
L/heff
PCE [psi]
L [in]
Vr [lb]
29650.4
8118.5
Vr [Ib]
Bed Joint Sliding
vte [psi]
vme
An [in 2]
Rocking
Rocking
Rocking
a
2473.4
Vr [lb]
Bed Joint Sliding
25810.0
0.5
36.3
78.2
hef [in)
0.5
5381.2
59950.4
Vr [lb]
0.5
a
17.6
PCE [psi]
L [in]
78.2
he[in]
L/heff
Bed Joint Sliding
Rocking
Rocking
a
PCE [psi]
L [in]
Pier 21
Pier 20
Pier 19
Pier 18
Pier 16
Pier 15
0.2
6068.6
53.2
PCE [psi]
L [in]
78.24
he [in]
78.2
L/heff
0.5
37885.5
0.7
L/heff
Vr [lb]
Bed Joint Sliding
0.5
a
11594.5
Vr [lb]
Bed Joint Sliding
26166.0
36.8
5530.7
Bed Joint Sliding
27
26
vte [psi]
vme
27
26
vte [psi]
vine
27
26
vte [psi)
vme
27
26
vte [psi]
vine
27
26
27.6
An [in 2 ]
27.6
An [in 2]
27.6
An [in 2]
27.6
An [in2]
27.6
vte [psi]
vme
27
26
An [in 2]
27.6
Vbjsl
718.7
Vbjsi
718.7
Vbjsl
718.7
Vbjsi
718.7
Vbjsl
718.7
Vbjsl
718.7
Vbjs2
14825.2
Vbjs2
6864.9
VbJs2
12905
Vbjs2
29975.2
Vbjs2
18942.8
Vbjs2
13083
Diagonal Tension
Diagonal Tension
13
f'dt
0.67
Beta
426.6
Vdt
Diagonal Tension
13_____
Beta
f'dt
339.7
Vdt
Toe Crushing
13
0.67
Beta
Diagonal Tension
0.67
407.4
Vt
Toe Crushing
Diagonal Tension
13
f't
0.22
Beta
186.6
Vt
Toe Crushing
Diagonal Tension
13
f'dt
0.68
Beta
472.3
Vm
Toe Crushing
13
f'dt
0.67
Beta
409.2
Vdt
Toe Crushing
Toe Crushing
fae [PSI]
27.8
fae [PSI]
12.9
fae [PSI]
24.2
fae [PSI]
56.3
fae [PSI]
35.6
fae [PSI]
24.6
f'me [PSI]
780
f'me [PSI]
780
f' me [PSI]
780
f'me [PSI]
780
f'me [PSI]
780
f'me [PSI]
780
Weight
above [lbs]
29650.4
Weight
above [lbs]
13729.8
Weight
above [lbs]
25810
Weight
above [lbs]
59950.4
Weight
above [lbs]
Area [in 2]
1065.6
Area [in 2]
1065.6
Area [in 2]
1065.6
Area [in 2]
1065.6
Area [in 2]
Vtc
Min
8560.9
426.6
Vtc
Min
2683.4
339.7
Vtc
Min
5713.9
407.4
Vtc
Min
6048.1
186.6
Vtc
Min
Diagonal Tension
Diagonal Tension
Diagonal Tension
Diagonal Tension
102
37885.5
1065.6
12043.9
472.3
Diagonal Tension
Weight
above [lbs]
26166
Area [in 2]
1065.6
Vtc
5868.8
Min
409.2
Diagonal Tension
Pier 1
Pier 2
Rocking
Rocking
0.5
a
PCE [psi]
L [in]
he [in]
3312.3
57.2
72.5
0.8
L/heff
V, [lb]
Bed Joint Sliding
1177.1
27.0
vte [psi]
26.0
vme
2
27.6
An [in ]
718.7
Vbjsl
1656.1
Vbjs2
a
PCE [psi]
L [in]
hew [in]
Vr [Ib]
Bed Joint Sliding
0.8
315.9
Vdt
26.0
vme
2
718.7
VbJsl
1927.0
Vbjs2
Beta
406.2
Vdt
0.7
Vr [lb]
Bed Joint Sliding
3.1
780.0
f'.. [psi]
27.0
vte [psi]
26.0
vme
2
27.6
An [in ]
L [in]
heff [in]
1.9
L/heff
Vr [Ib]
Bed Joint Sliding
3.6
780.0
PCE [psi]
L [in]
hew [in]
Vr [Ib]
Bed Joint Sliding
27.0
vte [psi]
27.0
vme
26.0
vme
26.0
2
27.6
An [in ]
2
718.7
Vbjsl
Vbjs2
6082.7
13238.7
Diagonal Tension
Vbjs2
t
351.9
Vdt
Beta
Vdt
11.4
780.0
f'me [P-si]
3312.3
1065.6
3853.9
1065.6
1300.5
315.9
Vtc
Min
1758.9
406.2
Vtc
Min
12165.4
1065.6
4255.3
351.9
Diagonal Tension
103
718.7
10692.4
Diagonal Tension
13.0
1.0
f'dt
613.1
Vdt
13.0
0.7
384.0
Beta
Toe Crushin g
Toe Crushing
fae [Psi]
27.6
An [in ]
Vbjs2
0.7
6000.3
vte [psi]
Vbjsl
0 f'.
Beta
0.6
L/heff
718.7
Weight above
[lbs]
Area [in 2]
Diagonal Tension
22287.5
0.5
21384.9
57.2
91.8
a
Vbjsi
Weight above
[Ibs]
Area [in 2]
Diagonal Tension
PCE [psi]
Toe Crushing
fae [Psi]
f'me [Psi]
3911.6
0.5
26477.4
124.6
66.6
a
Diagonal Tension
13.
1.0
f'dt
57.2
80.1
L/heff
Toe Crushingi
_fae [PSI]
Vtc
Min
27.6
An [in ]
Toe Crushing
Weight above
[Ibs]
Area [in2]
27.0
12165.4
L [in]
hew [in]
Diagonal Tension
13.0
Beta
1593.6
vte [psi]
Diagonal Tension
f'dt
0.9
L/heff
0.5
a
PCE [psi]
Rocking
Rocking
Rocking
0.5
3853.9
66.6
72.5
Pier 9
Pier 6
Pier 5
24.8
fae [Psi]
780.0
f'me [Psi]
780.0
f'me [Psi]
Weight above
[lbs]
Area [in2]
26477.4
1065.6
Weight above [lbs]
Area [in 2]
Vtc
Min
23637.0
613.1
Vtc
Min
Diagonal Tension
20.1
fae [Psi]
21384.9
1065.6
6422.0
384.0
Diagonal Tension
a
PCE [psi]
L [in]
heff [n]
0.5
24881.8
66.6
91.8
0.7
L/heff
Vr [Ib]
Bed Joint
8123.2
Sliding
a
PCE [psi]
L [in]
he" [inl
0.5
31896.0
57.2
87.5
0.7
L/heff
V, [lb]
Bed Joint
Sliding
9394.8
vte [psi]
27.0
vte [psi]
27.0
vme
An [in 2 ]
26.0
27.6
718.7
12440.9
vme
An [in2]
26.0
27.6
718.7
15948.0
Vbjsl
Vbjs2
Vbjsl
Vbjs2
Beta
13.0
1.0
13.0
f'dt
0.7
Beta
437.5 Vm 689.2 Vm 478.0 Vm 407.4 Vdt
Toe Crushing
Toe Crushing
29.9
23.4 fae [PSI]
fae [PSI]
600._ 9 Vdt
V_
f'me [PSI]
Weight
above [lbs]
780.0
24881.8
PCE [psi]
L [in]
heff iat]
f'me [PSI]
Weight
above [lbs]
780.0
31896.0
Vr [Ib]
Bed Joint
Sliding
12718.6
PCE [psi]
L [in]
hei [in]
0.5
40754.9
28.8
78.2
0.4
L/heff
Vr [lb]
Bed Joint
6750.8
Sliding
27.0
vte [psi]
27.0
vme
An [in 2 ]
26.0
27.6
718.7
18555.9
vme
An [in 2]
26.0
27.6
718.7
20377.4
Vbjsl
Vbjs2
Vbjsl
Vbjs2
f'dt
Beta
13.0
1.0
a
PCE [psi]
L [in]
heff [n]
0.7
Beta
0.5
Vr [lb]
Bed Joint
Sliding
vte [psi]
vme
An [in 2 ]
Vbjsl
Vbjs2
5381.2
a
PCE [psi]
L [in]
heff [in]
0.3
Vr [Ib]
Bed Joint
9361.5
Sliding
27.0
26.0
27.6
718.7
12905.0
13.0
f'dt
0.5
59950.4
27.2
78.2
L/heff
vte [psi]
vme
An [in 2 ]
Vbjsl
Vbjs2
0.7
Beta
27.0
26.0
27.6
718.7
29975.2
Diagonal Tension
Diagonal Tension
13.0
f'dt
0.5
25810.0
36.3
78.2
L/heff
Diagonal Tension
Diagonal Tension
13.0
f'dt
0.3
Beta
287.8
Toe Crushing
34.8
fae [PSI]
f'me [PSI]
Weight
above [lbs]
1065.6
Area [in 2]
1065.6
Area [in2]
Vtc
Min
8639.7
600.9
Vtc
Min
9866.4
437.5
Vtc
Min
Diagonal Tension
0.8
a
vte [psi]
Area [in 2]
Diagonal Tension
0.5
37111.7
66.6
87.5
L/heff
Diagonal Tension
Diagonal Tension
f'dt
a
Pier 19
Rocking
Pier 18
Rocking
Pier 17
Rocking
Pier 14
Rocking
Pier 13
Rocking
Pier 10
Rocking
780.0
37111.7
1065.6
13230.3
689.2
Toe Crus ing
38.2
fae [PSI]
f'me [PSI]
Weight
above [lbs]
780.0
40754.9
Toe Crushing
24.2
fae [PSI]
f'me [PSI]
Weight
above [lbs]
780.0
25810.0
Toe Crushing
56.3
fae [PSI]
f'e [PSI]
Weight
above [lbs]
780.0
59950.4
Area [in 2]
1065.6
Area [in 2]
1065.6
Area [in 2]
1065.6
Vtc
Min
6975.5
478.0
Vtc
Min
5713.9
407.4
Vtc
Min
9329.9
287.8
Diagonal Tension
Bed Joint Sliding
104
Diagonal Tension
Diagonal Tension
Von Mises Shear Stresses from SAP2000
Full Wall
Max Von Mises Shear Stress [psil at various base shears
-t
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
4
DQT7
agona
enson
)6'77 '1 95 A4 A
28
Diagonal Tension
Diagonal Tension
Diagonal Tension
Diagonal Tension
Diagonal Tension
Bed Joint Sliding
Diagonal Tension
Diagonal Tension
Diagonal Tension
Bed Joint Sliding
Diagonal Tension
Diagonal Tension
Diagonal Tension
Diagonal Tension
Diagonal Tension
Diagonal Tension
Diagonal Tension 1
154
13Q4A O
50kips
22.93
19.43
21.99
100
kips
28.2
26.23
28.3
250
kips
67.72
53.23
50.14
500
kips
145.23
102.24
97.52
34.82
45.69
55.4
70.57
52.82
74.03
94.98
120.43
67.37
102.83
139.33
180.23
80.14
107.33
161.02
175.63
226.39
29.49
53.81
70.32
88.38
38.8
86.31
122.19
157.38
39.49
119.35
179.16
241.65
74.23
85.96
176.42
233.25
321.67
61.55
115.84
118.38
144.12
99.35
138.79
206.84
269.11
174.57
201.49
239.27
242.42
242.18
350.66
1000
kips
300.28
202.15
185.37
1l44
.
Pier
1
2
3
40.74
kips
22.08
18.5
20.9
Failure
Shear
315.88
417.77
291.64
Failure
Mechanism
Diagonal Tension
Diagonal Tension
Diagonal Tension
.
Characterization
351.86
543.98
324.46
301.07
383.97
649.86
375.68
379.00
437.51
718.66
426.64
339.72
478.00
407.37
564.06
472.27
409.19
36.91
44.57
52.77
67.36
56.86
72.29
90.07
114.25
74.44
100.64
132.05
168.98
95.13
113.77
157.27
168.08
215.48
239.04
232.74
415.1
327.84
1500
ki s
297.68
Characterization
Fail
Failure
.
Pier Mechanism Shear
Diagonal
315.9
1
5
6
Diagonal
Tension
Diagonal
Tension
Diagonal
Tension
10
Diagonal
Tension
Diagonal
13
Tension
Diagonal
60
kips
31.07
80
kips
38.41
90
kips
100
kips
175
kips
250
kips
42.31
46.29
79.38
117.88
20.0
22.81
32.85
36.71
44.74
48.87
53.05
85.25
118.08
I
351.9
42.5
39.69
43.11
47.46
59.09
69.75
80.61
162.25
243.96
613.1
47.3
51.05
80.64
90.96
111.61
121.96
123.81
209.93
287.56
384.0
68.3
61.92
64.08
86.25
130.67
152.93
175.17
342.14
600.9
78.5
89.21
155.15
176.68
219.72
241.29
262.83
424.49
437.5
92.7
79.17
118.99
156.36
231.24
268.77
306.28
292.5
400.84
404.48
441.82
273.8
383.02
464.42
___________
I
689.2
113.0
146.05
255.21
478.0
110.1
61.48
210.29
407.4
176.0
202.5
278.84
Tension
565.15
___
___
___
Tension
Diagonal
19
406.3
Tension
Diagonal
18
50
kips
28.12
Tension
Diagonal
17
20.71
kips
21.13
Tension
9
14
10
kips
19.6
Tension
Diagonal
2
Flat Wall Section
Max Von Mises Shear Stress [psi] at various base shears
302.78
359.69
386.99
287.8
Curved Wall Section
Characterization
ailure F17.6
Failure Shear
Mechanism
.
Pier
Rocking
2
111.29
Max Von Mises Shea Stress [psi] at various base shears
175
100
90
80
60
50
23.07
26.19
33.13
47.69
55.15
62.67
109.67
61.24
66.39
105.4
Diagonal Tension
291.64
25.87
41.05
46.02
4
Diagonal Tension
258.57
45.56
75.25
84.82
104.13
113.89
123.68
197.58
6
Rocking
369.81
114.76
141.89
100-02
198.01
226.55
127.29
255.33
136.63
208.34
1178.31
7
Di
onal Tension
.
3
56.12
32446
49.13
65 34
8
Diagonal Tension
301.07
98.72
10
Diagonal Tension
436.35
31.47
11
12
Diagonal Tension
Diagona1 Tension
375.68
242.59
379.00
109.93
14
jDiagonal Tension
469.60
27.19
15
Diagonal Tension
426.64
157.28
16
Diagonal Tension
339.72
245.3
19
Diagonal Tension
186.57
35.36
20
Diagonal Tension
472.27
199.59
21
Diagonal Tension
409.19
327.24
91.28
229.41
106
118.06
1 206.65 1 259.61
300.92
444.07
j 286.27
Long Pier Section
Max Von Mises Shear Stress [psi] at various base shears
g
.~_
7 1 Diagonal Tension_ ,
11 1 Diagonal Tension ,
15
20
Diagonal Tension
Diagonal Tension
Failure Shear
7.5 kips
29Q14
327
__
_
324.46
375.68
426.64
472.27
98.39
197.2
330.5
457.64
10 kips
+
3966
.
,
31
Failure
Mechanism
IaTe-nsion%
Dia
,
Pier
107
t
15 kips
20 kips
40 kips
50 kips
5346
67.34
100.32
150.77
.
Characterization