Embed Size (px)
Citation preview
Copyright
by
Eric Michael Heumann
2010
The Thesis Committee for Eric Michael Heumann
Certifies that this is the approved version of the following thesis:
Simplified Modeling of Shear Tab Connections in Progressive Collapse
Analysis of Steel Structures
APPROVED BY
SUPERVISING COMMITTEE:
Eric B. Williamson
Michael D. Engelhardt
Co-Supervisor:
Co-Supervisor:
Simplified Modeling of Shear Tab Connections in Progressive Collapse
Analysis of Steel Structures
by
Eric Michael Heumann, B.S.C.E
Thesis
Presented to the Faculty of the Graduate School of
The University of Texas at Austin
in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science in Engineering
The University of Texas at Austin
May 2010
iv
Abstract
Simplified Modeling of Shear Tab Connections in Progressive Collapse
Analysis of Steel Structures
Eric Michael Heumann, M.S.E.
The University of Texas at Austin, 2010
Supervisors: Eric B. Williamson, Michael D. Engelhardt
Recent tragedies involving the collapse of several large and prominent buildings
have brought international attention to the subject of progressive collapse, and the field of
structural engineering is actively investigating ways to better protect structures from such
catastrophic failures. One focus of these investigations is the behavior and performance
of shear tab connections in steel structures during progressive collapse events. The shear
tab, a simple connection, is typically modeled as a perfect pin in standard design, but in
progressive collapse analysis, a much more accurate model of its true behavior and limits
is required. This report documents the development of a simple yet accurate shear tab
model and its use in understanding the behavior and limits of shear tab connections in
column removal scenarios. Particular attention is paid to the connections’ axial force
limit state, an aspect of behavior that is typically unimportant in standard design.
v
Table of Contents
List of Tables ........................................................................................................ vii
List of Figures ...................................................................................................... viii
Chapter 1: Introduction ...........................................................................................1
1.1 The Shear Tab ...........................................................................................1
1.2 Progressive Collapse .................................................................................3
Chapter 2: State of the Field ...................................................................................6
2.1 Strengthening Options ..............................................................................6
2.2 Shear Tab Behavior...................................................................................7
2.3 Shear Tab Performance .............................................................................8
2.4 Shear Tab Modeling ..................................................................................9
2.5 Summary .................................................................................................11
Chapter 3: Purpose ................................................................................................12
3.1 Simple Analysis Model ...........................................................................12
3.2 Shear Tab Resistance to Progressive Collapse .......................................13
3.3 Shear Tab Performance in Column Removal Scenarios .........................14
Chapter 4: Shear Tab Model .................................................................................15
4.1 Use of Design Guidelines .......................................................................15
4.2 Axial Force Modifications ......................................................................24
4.3 Application of Model into SAP 2000 .....................................................25
Chapter 5: Model Verification ..............................................................................30
5.1 Modeling Test Setup ...............................................................................30
5.2 Validation Results ...................................................................................35
Chapter 6: 2D Frame Behavior in Column Removal Scenario .............................39
6.1 Analysis Setup ........................................................................................39
6.2 Results .....................................................................................................43
vi
Chapter 7: 3D Building Performance in Column Removal Scenario ...................56
7.1 Building Choice ......................................................................................56
7.2 Analysis Setup ........................................................................................59
7.3 Results .....................................................................................................61
7.4 Importance of Axial Force Limit State ...................................................69
Chapter 8: Summary and Recommendations ........................................................71
8.1 Shear Tab Modeling ................................................................................71
8.2 Shear Tab Behavior and Performance in Column Removal Scenarios ..72
References ..............................................................................................................74
Vita .......................................................................................................................76
vii
List of Tables
Table 4.1 Shear tab axial force capacites ....................................................19
Table 7.1 Static loads imposed modeled building ......................................58
viii
List of Figures
Figure 1.1 Common uses of shear tab connection..........................................1
Figure 1.2 3D rendering of shear tab connection ...........................................2
Figure 1.3 Collapse of 2 World Trade Center ................................................4
Figure 2.1 Macro-model of a simple shear connection ................................10
Figure 4.1 Input required to determine shear tab capacities.........................16
Figure 4.2 Moment–rotation output of spreadsheet calculator.....................17
Figure 4.3 Shear tab moment–rotation curve proposed by Astaneh ............21
Figure 4.4 SAP 2000 plastic hinge input dialog ...........................................27
Figure 4.5 SAP 2000 plastic hinge output dialog .........................................28
Figure 4.6 Curve points specified by developed spreadsheet calculator ......29
Figure 5.1 Specimen 1 from SAC Report cyclic tests ..................................31
Figure 5.2 Specimen 2 from SAC Report cyclic tests ..................................32
Figure 5.3 Diagram of typical setup of actual tests ......................................33
Figure 5.4 SAP 2000 model of specimen 1. .................................................34
Figure 5.5 SAP 2000 model of specimen 2. .................................................34
Figure 5.6 Behavior comparison of specimen 1 model ................................36
Figure 5.7 Behavior comparison of specimen 2 model ................................37
Figure 6.1 SAP 2000 model with shear tab connections ..............................40
Figure 6.2 SAP 2000 model with fixed connections ....................................42
Figure 6.3 SAP 2000 input for beam axial yielding hinge element. ............43
Figure 6.4 SAP 2000 fixed connection model displaced shape ...................44
Figure 6.5 SAP 2000 pinned connection model displaced shape.................44
ix
Figure 6.6 Shear in fixed connection model at low displacements ..............45
Figure 6.7 Moment in fixed connection model at low displacements ..........45
Figure 6.8 Shear in fixed connection model at high displacements .............46
Figure 6.9 Moment in fixed connection model at high displacements ........46
Figure 6.10 Beam axial force vs. column displacement .................................49
Figure 6.11 Column axial force vs. column displacement. ............................50
Figure 6.12 Beam bending moment vs rotation in best-case shear tab ..........51
Figure 6.13 Beam axial force vs. column displacement with yielding ..........53
Figure 6.14 Column axial force vs. column displacement with yielding .......54
Figure 7.1 Plan view of analyzed health care facility ..................................57
Figure 7.2 Profile view of analyzed health care facility ...............................57
Figure 7.3 Plan view showing removed column ..........................................60
Figure 7.4 Displaced shape of longitudinal cross-section ............................63
Figure 7.5 Displaced shape of transverse cross-section ...............................64
Figure 7.6 Bending moment distribution in longitudinal beams ..................65
Figure 7.7 Bending moment distribution in transverse beams .....................66
Figure 7.8 Axial force distribution in longitudinal beams ...........................67
Figure 7.9 Axial force distribution in transverse beams ..............................68
1
Chapter 1: Introduction
1.1 THE SHEAR TAB
The most common simple shear connection in modern US steel construction is a
single plate connection commonly known as the shear tab (Astaneh-Asl, 2002). In such a
connection, as depicted in Figures 1.1 and 1.2, a single plate is bolted to the web of a
simply supported beam at one end and welded to the web or flange of a supporting
element, which is most commonly a column or girder, at the other end. The number of
bolts used in the connection depends on the depth and weight of the beam, and is
typically in the range of four to eight bolts.
Figure 1.1 Common uses of shear tab connection (Astaneh-Asl, 2002).
The primary purpose of the connection is to transfer shear force from the beam to
the supporting member. This transfer of force is accomplished by transmitting the vertical
force in the beam to the shear tab plate via the bolts, and then from the shear tab plate to
the supporting member via the weld. The plate’s short length and proportionally large
depth give it the required strength to tolerate the shear force transmitted between the bolts
2
and the weld. The allowance for bolt slippage within the bolt holes provides the
connection’s primary rotational capacity, which is further increased by ductility in the
plate. Increasing the number of bolts in the connection will decrease its rotational
capacity (Liu and Astaneh-Asl, 2000).
Figure 1.2 A three dimensional rendering of a shear tab connection between the flange
of a column and the web of a beam (Unified Facilities Criteria, 2010).
In a typical steel frame structure, these simple shear connections are utilized in the
gravity load system, which supports the structure’s dead and live loads acting in the
vertical direction. The stability of the gravity system is dependent upon another part of
the structure, the lateral load system, to resist lateral forces such as wind and seismic
loads and to prevent frame instability. The lateral load systems most commonly used in
steel building systems are braced frames and moment frames. Braced frames resist lateral
load by truss action and are therefore dominated by axial force in their members. .
3
Moment frames, on the other hand, resist lateral load by rigid frame action that produces
bending and shear in the frame members. Moment frames employ moment-resisting
beam-to-column connections to develop rigid frame action. In typical steel building
construction practice, only a small number of frames in a building are lateral load frames.
The majority of the structure is therefore gravity framing, employing simple beam-to-
column connections such as the shear tab.
Shear tab connections, as well as most other simple connections, are commonly
modeled as perfect pins during computational structural analysis. In reality, these
connections do have a certain amount of rotational stiffness, and they do have the ability
to transmit a small bending moment. This stiffness and bending moment capacity,
however, are typically small enough to be considered negligible, and neglecting them is
conservative in standard design. There are situations where this small stiffness and
moment capacity need to be taken into account in order to understand the true behavior
and capabilities of a structural system. One such case is the design of a building to resist
progressive collapse, wherein the typically disregarded rotational stiffness, axial strength,
and bending moment capacity of shear tab connections may be sufficient enough to affect
structural behavior.
1.2 PROGRESSIVE COLLAPSE
Over the past several decades, the complete or partial collapse of several large
buildings, initiated by a malicious attack on the structure, has taken many lives. For this
reason, the issue of collapse has become an important subject in the field of structural
engineering, and many structural engineers have begun working with government
agencies to develop better practices to prevent these disasters. In the United States, the
4
events on September 11th
of 2001, as shown in Figure 1.3, have drawn substantial
attention to a particular type of collapse known as progressive collapse.
Figure 1.3 Collapse of 2 World Trade Center (South Tower), a progressive collapse
occurrence.
Progressive collapse is a self perpetuating phenomenon where a succession of
member failures, initiated by single event, proliferates throughout a structure, eventually
causing its partial or total collapse (Nair, 2004). In such a scenario, the actual destruction
often dwarfs the expected damage of the initial event, and thus this phenomenon is also
referred to as disproportionate collapse. It should be noted that the use and definitions of
these two terms varies among experts.
5
To prevent a progressive collapse situation, there are two basic approaches to
strengthening a structure: providing redundancy and providing local resistance (Nair,
2004). Providing redundancy involves giving a structure alternate means for distributing
load if the originally designed load path is disrupted. This method accepts the loss of a
member and ensures that remaining members can pick up the new load. An alternative
path must be available for this new load, and the members along the path must have
reserve strength which can be engaged for this purpose. Preventing progressive collapse
by providing redundancy is the preferred and most commonly accepted way of doing so.
Providing local resistance, alternatively, involves identifying the critical member that will
be subjected to the original attack and designing it to withstand the event, thus avoiding
failure altogether. This method results in a less damaged structure after an event, but it
requires specific information about the nature of an attack. Because these attacks are
often unexpected and unpredictable, this method is rarely feasible.
In this thesis, background information on recent studies concerning steel shear tab
connections and progressive collapse will be used to develop a simplified shear tab model
that can be utilized in the analysis and enhancement of structures subjected to progressive
collapse events. The developed model, as documented in Chapter 4, will be verified in
Chapter 5 and then implemented in two-dimensional and three-dimensional structural
analysis models in Chapters 6 and 7, respectively, to observe the behavior and
performance of steel frame structures with shear tab connections subjected to such
conditions.
6
Chapter 2: Background
Currently, the most effective way to reduce the risk of progressive collapse is to
prevent any possible collapse inducing events from occurring in the first place (Byfield,
2006). However, as noted in Chapter 1, many of these events are unpredictable and often
malicious in nature, and thus achieving this goal is not viewed as a reasonable option.
Strengthening a structure, either locally or by providing redundancy, is considered to be
the most practical alternative.
2.1 STRENGTHENING OPTIONS
Prof. Byfield notes that modern codes tend to produce structures with strong
beams and columns (Byfield, 2006). The connections, conversely, are weak and do not
have sufficient strength to allow the beams and columns to exhibit their full capacity
during extreme loading situations. Such an arrangement can lead to brittle failure of the
connections in cases where an overload occurs, particularly in connections with welds
and bolts in direct tension. In order to design a building that can properly withstand a
catastrophic event and arrest an ensuing progressive collapse, structural engineers must
provide sufficiently strong connections that allow beams and columns to deform
plastically and to fail in a ductile manner.
Much research has been done on moment-resisting steel connections due to their
prominent role in seismic design, and this existing research has led moment-resisting
connections to be a top candidate for strengthening structures to prevent progressive
collapse (Hamburger and Whittaker, 2004). Several studies have also been conducted on
the use of catenary elements such as embedded steel cables in concrete slabs to suspend
floors after a vertical load bearing member has been compromised (Kim and An, 2009;
Astaneh-Asl et al, 2001). These reinforcing techniques, however, are still new concepts
7
with which few engineers have experience, and the use of moment-resisting connections
across an entire structure is prohibitively expensive in most cases.
Despite their prominence in modern steel structures, few studies have been
conducted on the ability of shear tab connections to participate in resisting progressive
collapse (Sadek et al, 2008). Understanding the performance of shear tab connections in
progressive collapse situations is important for existing structures, however, where
strengthening via moment-resisting connections is not an option or would be extremely
costly. The results of recent analyses conducted using shear tab connections in
progressive collapse scenarios (Sadek et al, 2008; Astaneh-Asl et al, 2001; Foley et al,
2006) generally fail to agree on whether progressive collapse can be arrested by such
simple connections, and the results have been shown to depend strongly upon the
structural sections and materials used in the analyses. Furthermore, in order to model
these scenarios, advanced structural software not likely to be found in an average design
office environment, such as the finite element software LS-DYNA (Livermore Software
Technology Corporation, 2010), has been utilized.
If more information were known about a shear tab’s performance and behavior in
such extreme scenarios, and this information could be easily applied by design engineers,
more knowledgeable and practical judgments could be made when strengthening and
renovating structures to be resistant to progressive collapse.
2.2 SHEAR TAB BEHAVIOR
Much of the present understanding of shear tab behavior comes from work done
at U.C. Berkley by Astaneh-Asl and Liu (2000). Their original work focused on the
effects of cyclic loading in an effort to better understand a shear tab’s behavior during
seismic events. Although progressive collapse events are not cyclic, both types of events
8
induce large rotations in connections and expose them to stresses far greater than those
that occur under typical gravity and wind loads. Accordingly, much of the understanding
about the behavior of shear tabs that was gained from Astaneh’s work can be applied in
progressive collapse studies.
Using the knowledge gained from the cyclic tests, a design guide for shear tab
connections was published that provides a means for determining the maximum bending
moment a shear tab connection can carry and the ultimate rotation it can exhibit (Liu and
Astaneh-Asl, 2004). These guidelines, in conjunction with the results of the cyclic tests,
provide a basis for validation of results for analyses that focus closely on the true
behavior of a shear tab connection. Many of the studies that have been done on shear tab
connection performance in blast or column removal events cite Astaneh’s work when
validating or comparing their results (Sadek et al, 2008; Khandelwal et al, 2008).
2.3 SHEAR TAB PERFORMANCE
One of the most recent and pertinent studies done on progressive collapse
involving simple shear connections was supported by the National Institute of Standards
and Technology (NIST). In this study, Fahim Sadek et al. investigated the robustness of a
structural steel system connected by shear tabs (Sadek et al., 2008). Using the LS-DYNA
software, four interior bays of one floor of a ten story steel office building were modeled
and subjected to the loss of a common center column. Lateral load resistance for the
structure was provided by moment-resisting frames around the perimeter of the building,
and therefore the bays analyzed were entirely connected by shear tab connections.
The results of this study showed that the floor beams initially displayed flexural
deformation, but eventually developed catenary behavior under large rotations. The
researchers showed that failure would occur in the connections, mostly due to bolt
9
failure, tear out failure, and weld failure. When the composite floor system, including a
concrete slab and a metal deck, was fully considered in the analysis, significant catenary
and membrane action was demonstrated in the floor response, mostly through the
ductility of the metal deck and steel reinforcement in the slab. The conclusions of this
study indicated that, according to the GSA design guidelines, the building analyzed
would not survive the applied column removal scenario. Other studies have (Sadek et al,
2008; Foley et al, 2006) reported similar behavior for structures with these types of
connections, but the conclusions on collapse resistance have varied due to differences in
the buildings that were modeled.
2.4 SHEAR TAB MODELING
For recent progressive collapse research, a mix of finite element models was
utilized to analyze shear tab connections. While the tests done by Astaneh provide a good
foundation for understanding general shear tab behavior, several aspects of the tests were
unique to seismic conditions and were not directly transferable to progressive collapse
situations; thus, the mix of several models was required to ensure a comprehensive
understanding of connection behavior under column removal scenarios such as the one
examined during the NIST study. One of these models, the Reduced Component
Connection Model, relates closely to a study performed by Kapil Khandelwal et al. that
investigated the use of an array of non-linear springs and short rigid members to represent
a shear tab connection (Khandelwal et al, 2008).
In a set of analyses that used the same prototype structure and column removal
scenario as the aforementioned study by Sadek et al., a study supported by the National
Science Foundation, the University of Michigan, and NIST investigated progressive
collapse performance of steel frames in which connections were model using ―macro-
10
models‖. A macro-model combines the simple individual behavior of multiple line
elements and non-linear springs to define the complex behavior of an entire connection
(Khandelwal et al, 2008). Figure 2.1 shows an example of a simple shear connection
macro-model.
Figure 2.1 Macro-model of a simple shear connection (Khandelwal et al, 2008).
The Khandelwal study provides a similar conclusion to that of the study by Sadek
et al; primarily, shear tab connections have enough ductility to undergo large rotations
under which the beams begin to exhibit catenary action, but they do not have the strength
required to resist the large axial forces encountered under such conditions.
Although Khandelwal’s macro-models are simpler to create than three-
dimensional finite element models, they still require the use of advanced modeling
11
software that is not likely to be found in common design environments. In order for the
proper modeling of shear tab connections in progressive collapse design to be feasible for
the majority of structural design firms, a model is needed that can be quickly and
economically implemented into structural analysis programs that are widely used in
design offices.
2.5 SUMMARY
The field of structural engineering currently needs more experience and
understanding of shear tab connection behavior in progressive collapse conditions than is
currently available in order to more accurately and knowledgably design steel structures
to resist catastrophic events. Furthermore, in order to allow structural engineers to more
easily and comprehensively analyze the performance of shear tab connections in a steel
structure subjected to a progressive collapse condition than current means, a simple yet
versatile shear tab connection model is needed that can be readily introduced into
common structural analysis software and that considers the true behavior and all
applicable limit states of shear tabs under such conditions.
12
Chapter 3: Purpose of Research
The purpose of this study is threefold: (1) to develop a simplified method of
modeling a shear tab connection that can be readily implemented by software used in
typical structural design office environments, (2) to understand the unique contribution of
a shear tab to resisting progressive collapse due to damage inflicted upon its surrounding
members, and (3) to demonstrate whether or not a structural steel frame subsystem
connected entirely by shear tab connections, modeled using the developed modeling
method, has the ability to withstand a column removal scenario.
3.1 SIMPLE ANALYSIS MODEL
For many structural engineering firms, a detailed finite element analysis of a large
structure using shell or solid elements is not economically, or even computationally,
feasible. For this reason, frame analyses using line elements are normally employed.
These methods are significantly faster and less costly than finite element analyses, and
they produce relatively accurate results for typical static and dynamic design cases.
In such models, a shear tab is typically modeled as a perfect pin. For standard
design, neglecting the minimal amount of rotational stiffness a shear tab connection
offers is conservative, and forces and deformations in the connection typically will not
exceed the available capacities. Beams and girders are also typically designed as pure
bending members because the axial forces that arise in standard loading combinations are
rarely significant enough to merit considering the effects of compression or tension in
these members. For design against progressive collapse, however, the capacity of the
shear tab for forces other than shear, including axial force, become a key factor in
whether or not the design is safe or susceptible to collapse, and axial forces in beams can
grow so large that they govern the behavior. A modeling method is needed that
13
incorporates the rotational stiffness, moment strength, axial strength, and deformation
capacities of a shear tab but which is also simple enough to be incorporated into standard
frame analysis software.
This study uses the results of experimental cyclic tests performed by Abolhassan
Astaneh-Asl and Judy Liu (Liu and Astaneh-Asl, 2000) on shear tab connections to
develop and verify a simple method of modeling a shear tab in the SAP 2000 analysis
software (Computers and Structures, Inc., 2010). SAP 2000 is considered to be
representative of common analysis packages found in design office environments. The
developed method considers the moment–rotation response, including stiffness and
response limits, of a shear tab as recommended by the conclusions of Astaneh.
3.2 SHEAR TAB RESISTANCE TO PROGRESSIVE COLLAPSE
After developing a suitable modeling strategy for the shear tab connection, the
impact of the connection’s various strengths on a structural system and its ability to resist
collapse can be examined. Current guidelines for design against progressive collapse put
great emphasis on the rotational capacity of simple shear connections (Unified Facilities
Criteria, 2010), but they do not pay significant attention to the axial forces developed in
such cases. As mentioned previously, recent research has indicated that high axial forces,
developed by the catenary action of beams acting as tension members, may be one of the
leading causes for failure in these connections (Sadek et al, 2008). The current study
focuses a large amount of attention on the axial capacity of the connections and the axial
forces that arise in collapse situations, specifically a column removal scenario.
Despite conclusions that a shear tab can carry a non-zero bending moment, and
despite the inclusion of this bending moment capacity in at least two recent studies
(Sadek et al, 2008; Khandelwal et al, 2008), very little has been said about what effect
14
this moment capacity actually has on a shear tab’s behavior as opposed to a perfect pin
connection. The current study performs several comparisons of the developed shear tab
model against perfect pin connections and totally fixed connections in order to gauge
how large a role the moment capacity plays.
3.3 SHEAR TAB PERFORMANCE IN COLUMN REMOVAL SCENARIOS
The conclusions of recent studies involving column removal cases in areas of
structures supported by gravity connections fail to agree on whether a structure can
withstand such an event (Carino and Lew, 2001). Most reports attribute the lack of
agreement to differing members and geometries used. The trend seems to indicate that
steel systems damaged in areas with only simple shear connections must rely heavily on
membrane action in the concrete slab and metal deck. With only the strength of the steel
framing, the system typically does not survive.
Using the developed SAP 2000 model, the failure of such a system with only the
steel frame due to the loss of a column in areas with only shear tab connections is
confirmed using a prototype building documented in the Unified Facilities Criteria
document UFC 4-023-03 (Unified Facilities Criteria, 2010). Comparisons are also made
against the performance of the simple shear connection models used in the original study.
The results from a full building analysis are used to draw conclusions about the
importance of the axial force limit state of shear tab connections that must support beams
experiencing large rotations and catenary behavior.
15
Chapter 4: Shear Tab Model
Due to the well documented observations on the bending moment–rotation
behavior and limit states of several types shear tab connections, the experiments
performed by Astaneh-Asl and Liu involving the cyclic loading of steel frame specimens
connected by shear tabs (Liu and Astaneh-Asl, 2000) were chosen as the basis for the
developed shear tab model in this study.
4.1 USE OF DESIGN GUIDELINES
In SAC Report SAC/BD-00/03 (Liu and Astaneh-Asl, 2000), Astaneh documents
tests performed on eight shear tab specimens and proposes guidelines for the design of
shear tab connections based on his results. The guidelines document the calculated and
observed axial and shear capacities of a shear tab based on the number of bolts used in
the connection. Several equations and methodologies are presented for using these
capacities to determine the maximum bending moment and rotational capacity of a shear
tab based on connection geometry and shear loading. These moment and rotation values
can then be used to determine the rotational stiffness of a connection at various levels of
rotation.
4.1.1 Model Spreadsheet
To aid in the implementation of these guidelines, a simple spreadsheet calculator
was developed for the current study. Connection geometries and material strengths are
input into the spreadsheet, as shown in Figure 4.1, and a moment–rotation behavior curve
is output, as shown in Figure 4.2.
16
Figure 4.1 General input variables required to determine shear tab capacities. Example
values are for a typical four bolt shear tab, and match the properties of the
shear tab used in specimen 1A in Liu and Astaneh-Asl (2000).
17
Figure 4.2 General moment–rotation output of the spreadsheet calculator. Example
values are computed using the input from Figure 4.1.
18
Before a moment–rotation curve can be produced, the input is first used to
determine the axial and shear force capacities of the specified shear tab. An axial force
capacity and a shear force capacity are calculated for each failure mode, of which there
are five that affect a shear tab in a bare steel frame undergoing rotation (Astaneh-Asl,
2002). These failure modes are:
1. Yielding of the gross area of the plate.
2. Bearing yielding of the bolt holes in the plate and beam web.
3. Fracture of edge distance of bolt holes.
4. Fracture of bolts.
5. Fracture of welds.
A sixth failure mode, shear fracture of the net area of the plate, was identified by
Astaneh, but this mode was not considered when developing the model’s moment–
rotation curve due to the low shear forces, relative to the axial forces and bending
moments, present in the connections analyzed by this study.
The capacity results for each limit state are normalized with respect to the number
of bolts in the connection, allowing capacity values of shear tabs constructed of similar
materials but different bolt numbers to be readily compared. Astaneh uses the term ―bolt
element‖ to define a bolt and the tributary plate and web region surrounding it, thus
describing the portion of a shear tab that would individually have the normalized
strength. In the SAC Report guidelines, Astaneh documents these values for the specific
type of shear tab considered in the experiments. As demonstrated in Table 4.1 for the
case of axial force capacities, the developed spreadsheet calculator in the current study
produces comparable values to those reported by Astaneh.
19
Table 4.1 Shear tab axial force capacity per bolt element comparison between
documented values by Astaneh (Liu and Astaneh-Asl, 2000) and developed
spreadsheet calculator.
Failure Mode Documented Axial Capacity
(kips) (per bolt element)
Calculated Axial Capacity
(kips) (per bolt element)
1. Plate Yielding 40.5 40.5
2. Bearing & Edge
Distance Failure
39.1 39.1
3. Net Section
Fracture
43.5 46.4
4. Bolt Fracture 28.9 28.9
5. Weld Fracture 55.7 55.7
The failure mode with the lowest capacity will govern the ultimate strength of a
connection. In the case of the shear tab represented in Figure 4.1 and Table 4.1, for
example, the connection will fail by fracturing of the bolts under a pure axial force
because that mode has the lowest axial capacity.
With the specified input and calculated force capacities, a moment–rotation curve
can be produced. To acquire points for this curve, two additional input values defining
the slip coefficient and minimum tension of the bolts are required, as well as the
magnitude of the static shear force being transferred by the connection. With these
values, rotations and bending moments at three unique points are computed, thus defining
the moment–rotation response of the shear tab. The points are as follows:
1. Rotation at which bolts slip in their bolt holes.
2. Rotation at which the maximum moment is reached and yielding commences in
the plate or beam web.
20
3. Ultimate rotation, at which brittle fracture causes the failure of the connection.
The curve generated by these points is outlined in Figure 4.3, a diagram published
in the guidelines of the SAC Report (Liu and Astaneh-Asl, 2000). The positive rotation
region of the figure is not applicable to this study because no concrete slab and no metal
deck are considered, and therefore the curve defined in the negative rotation region of the
figure is used for both positive and negative rotation in this study.
At the first point, the axial force arising from the bending moment couple exceeds
the static friction force of the tensioned bolts against the plate and beam web, causing the
bolts to slip and readjust in their holes. Per the guidelines, a correction factor must be
applied to the moment value for this point because the original estimate does not match
the observed results. Astaneh notes that the errors in the original values are consistent,
and thus a constant correction factor works well in most cases. The rotation value for this
point is an empirical constant derived by Astaneh, based on observations from test
results.
At the second point, a fully plastic force distribution exists across the bolt group,
and each bolt element is stressed to its capacity, as defined by the least of the computed
limit state strengths defined earlier in this section. Some bolt elements (or fraction of bolt
elements) will be needed to resist the shear load, while the remainder will be available to
resist the bending moment. The bending moment at this point, and therefore the
maximum moment the shear tab can carry, is thus computed by assuming a plastic stress
distribution across the connection and summing the moment capacity provided by all bolt
elements not resisting shear. Through this mechanism, an increased shear load on the
connection will lower the moment capacity. The rotation value for this point is also
entirely empirically based.
21
Figure 4.3 Diagram of the shear tab moment–rotation curve proposed by Astaneh in
SAC Report SAC/BD-00/03 (Liu and Astaneh-Asl, 2000), defined by three
points in the negative rotation region. The positive rotation curve is not
applicable to the current study. Section references pertain to the SAC
Report.
22
The third point maintains the same maximum bending moment as the second
point, but has the ultimate rotation value, which is not empirical. The SAC Report design
guidelines define the ultimate rotation as the rotation at which the beam flange comes
into bearing with the supporting element (e.g., the column flange). The ultimate rotation
is therefore entirely a function of geometry.
The developed spreadsheet calculates the rotations and moments at these points
and outputs them in a table and a graph. An example of this output is documented in
Figure 4.2. Note that because no metal deck or concrete slab is considered in the shear tab
model developed for the current research, the positive and negative rotation behaviors are
symmetric, and therefore the moment–rotation relationship is shown in only one
direction.
4.1.2 Guideline Limitations
The guidelines recommended by Astaneh were originally meant to be
implemented for static design purposes, and thus the results of the spreadsheet calculator
are somewhat simplistic and limited. The simplicity is beneficial for ease of
implementation, but the limitations reduce the fidelity of the model. Four of these
limitations and simplifications are described below:
1. Two of the three calculated rotations are empirical constants. No changes to
loading, geometry, or materials will affect these values. These two rotation values
are in fact the two that pertain to the rotational stiffness of a shear tab. Because
these values are constants, the rotational stiffness of the connection is solely a
function of the bolt slip and maximum bending moments. This limitation causes a
degree of discrepancy between the expected behavior and Astaneh’s observed
23
results. Further experimental testing and finite element modeling are needed to
identify the parameters that produce these rotations.
2. The three points that define the curve do not take into account a reduction in
stiffness due to yielding in the plate and beam after the maximum bending
moment is reached. In the guidelines, the connection upholds its maximum
bending moment capacity until the ultimate rotation is reached. As observed in
the results of the SAC Report, most specimens display a general decay in bending
moment capacity as the rotation increases beyond the point where the maximum
moment is first reached.
3. The curve does not take into account any behavior past the rotation where the
beam comes into bearing with the supporting member. The ultimate rotation value
developed by the guidelines, which represents the point where the connection
ultimately fails, is meant to correspond to the point where the beam comes into
bearing with the column or girder supporting it. Astaneh notes that brittle failure
always occurred in the connection after this event, and thus it was chosen as the
ultimate rotation value for design. Although this decision is conservative and
reasonable for design, it restricts the design curve from capturing the full behavior
of the connection. As shown in the results of the majority of his specimens, the
binding of the beam to the supporting member causes a rapid increase in stiffness,
providing an increased amount of bending strength for a short range of further
rotation before the connection truly fails.
4. No provisions for the presence of an axial force in the connection are explicitly
made in the guidelines. Intuitively, a large axial force in the connection should
affect the bending moment, shear strength, and rotational capacities. This issue
24
was not within the scope of Astaneh’s work, and thus no consideration for axial
load is made in the design guidelines.
Connection behavior in response to high axial forces is an important aspect of the
current study because column removal conditions can cause beams to become catenary
members. Due to resource constraints on this study, no attempts were made to resolve the
first three limitations. However, to address the fourth limitation, several steps were taken
to attempt to modify the design guidelines published by Astaneh to include the effects of
axial force on the developed moment–rotation curve.
4.2 AXIAL FORCE MODIFICATIONS
In the SAC Report guidelines, as mentioned earlier, the maximum bending
moment capacity of a shear tab is computed by summing the moment contribution of
each bolt element. Some fraction of bolt elements, however, must be reserved for
resisting the shear load present in a connection. Using this logic, as exemplified by
Astaneh, a similar reduction in available bolt elements was used for resisting an axial
load present in the connection. Thus, instead of resisting a moment couple with all bolt
elements aside from those resisting the acting shear load, the modified model resisted a
moment couple with all bolt elements aside from those needed to resist shear and those
needed to resist a unidirectional axial load.
The results of this methodology confirmed that an axial load on the connection
model will affect it in a similar way that a shear load on the connection would affect it —
by decreasing its maximum bending moment capacity. However, more work is still
needed. This approach cannot be verified against any real test data because, at this time
and to the knowledge of the author, none has been conducted. Furthermore, the axial
25
forces developed during a column removal scenario are typically coupled to the rotation
and are not just a constant, static value.
It is also logical to assume that a catenary force would affect more than just the
maximum moment capacity of a shear tab connection. The rotations of the three points on
the moment–rotation curve would be affected as well because an axial load would cause
bolt slip to occur earlier and because a brittle failure due to axial loading may occur
before the beam ever comes into bearing with the supporting member. Bolt slip may
occur at different moment values for different bolts because a uniform axial force acting
simultaneously with a bending moment would increase the axial stress in some bolts and
decrease it in other bolts depending on the direction of curvature. At this time, however,
it is unclear how to modify the current model calculations to account for these factors
because most of the rotation values are empirically based and because no experimental
testing has been conducted that considers catenary action in a beam connected by a shear
tab. Although it is important to look more deeply into the matter and better understand
the behavior of a shear tab supporting a hanging beam, these issues will, for the most
part, be neglected throughout the rest of this study for the purpose of maintaining
simplicity in the proposed model.
4.3 APPLICATION OF MODEL INTO SAP 2000
To implement the modeled shear tab behavior, as computed by the developed
spreadsheet calculator based on the design guidelines in SAC Report SAC/BD-00/03, to a
structural analysis program, software must be chosen that has non-linear analysis
capabilities and a means of defining stiffness values at a connection. SAP 2000, a product
of Computers and Structures, Inc., has these capabilities, and it is also a commonly used
program among engineering firms (Computers and Structures, Inc., 2010).
26
4.3.1 SAP 2000 Plastic Hinge Element
SAP 2000 offers a spring element that can be defined at joints, but that element
requires a constant stiffness value. To apply the developed model, multiple stiffnesses at
different intervals of rotation must be defined. Therefore, this study chose to use SAP
2000’s plastic hinge element to define the moment–rotation behavior at the end of a
beam. A ductile plastic hinge, governed by a predefined moment–rotation curve, can be
applied anywhere along a line element; it has a set curve defined by five points. Because
the curve produced by Astaneh’s guidelines contains four points including the origin, the
plastic hinge element is sufficient. By placing the element at the very end of the beam at
the joint connecting the beam to the supporting member, it effectively governs the
moment–rotation behavior of the connection, assuming there are no releases to the
rotational degrees of freedom at the end of the beam. To ensure proper behavior at the
location of the plastic hinge element, SAP 2000 was instructed to subdivide the beam
member into several sub-elements. The input user interface for the plastic hinge element
is shown in Figure 4.4.
The SAP 2000 program offers an interactive output dialog for plastic hinges after
an analysis has run that displays the actual moment versus rotation behavior at the point
of the hinge, as compared to the defined behavior. This tool is useful for verifying that
the model behaved correctly and for graphically studying the condition of the connection
at various analysis states. The user interface for plastic hinge results is shown in Figure
4.5.
27
Figure 4.4 Snapshot of SAP 2000 plastic hinge input dialog showing values for a
model of the shear tab used in the first test specimen by Astaneh in his
cyclic testing of shear tabs. Note that the Acceptance Criteria section is not
used. Section 4.3.2 explains the source of the input values for the plotted
points and scale factors, and it is especially important to note that custom
scale factors are used, not the yield moment and yield rotations. Also, the
load carrying capacity must drop to zero after the final point to indicate
failure.
28
Figure 4.5 Snapshot of SAP 2000 plastic hinge output dialog showing the actual
moment–rotation behavior at the point of the hinge on top of the defined
moment–rotation behavior of the hinge. In this output, the two curves
completely overlap. This output corresponds to the input shown in Figure
4.4.
4.3.2 Computing Input Values
The developed spreadsheet calculator was also designed to take the moment–
rotation curve output and create input values that can be applied to a plastic hinge
element in SAP 2000. The SAP 2000 input requires scale factors (abbreviated in the user
interface as ―SF‖) for rotation and bending moment, and the points on the curve are
29
defined as fractions of these scale factors. For the sake of clarity, the spreadsheet uses the
maximum moment and ultimate rotation as scale factors and provides that fraction for the
five required points on the curve. An example of these values is displayed in Figure 4.6.
Point B ensures that the plastic hinge element is initially rigid for a negligible amount of
bending moment. This behavior is required by the program.
Figure 4.6 Curve points, developed in the shear tab spreadsheet calculator, which are
designed to be input values into a plastic hinge element in SAP 2000. The
values demonstrated in this figure produce plastic hinge element shown in
Figure 4.4.
In order to begin using the developed shear tab model to understand the behavior
of shear tab connections in progressive collapse scenarios, the model first had to be
verified. Its verification was accomplished by introducing the model into SAP 2000
analyses of two of the cyclic test cases performed by Astaneh and then comparing the
SAP 2000 outputs with the documented values in the SAC Report. These results are
presented in Chapter 5.
30
Chapter 5: Model Verification
To verify the shear tab model described in the previous chapter, the first two test
specimens in Astaneh’s cyclic test program were simulated in SAP 2000, and the results
obtained from the SAP 2000 models were compared against the actual results from the
original tests.
5.1 MODELING TEST SETUP
The first two specimens of the cyclic loading tests performed by Abolhassan
Astaneh-Asl and Judy Liu (Liu and Astaneh-Asl, 2000), as documented in SAC Report
SAC/BD-00/03, involved only steel framing with no metal decking or concrete slab.
Because the current study does not investigate the contribution of steel decking or a
concrete slab in the performance of a shear tab connection, these first two specimens
were chosen to validate the developed shear tab model in SAP 2000.
5.1.1 Specimens and Original Setup
The first specimen was a four-bolt shear tab connection between the web of a
W18×35 beam and the web of a W14×90 column, as shown in Figure 5.1. A shear load
of 12 kips was introduced to each beam, along with 0.0041 radians of initial rotation.
These initial conditions were meant to reflect service conditions and were introduced to
ensure that the system had the correct initial stiffness before the cyclic loads were
applied. The actual values applied varied slightly from the aforementioned target values
due to the realities of the test setup. Averages of the actual values are documented in the
SAC Report.
31
Figure 5.1 Specimen 1 from SAC Report cyclic tests. (Liu and Astaneh-Asl, 2000)
The second specimen was a six-bolt shear tab connecting a W24×55 beam to a
W14×90 column. Compared to the first specimen, the shear tab had two additional bolts,
and the beam was significantly deeper and heavier. The initial loading and rotation of the
second specimen also differed from the first specimen. A shear force of 30 kips was
introduced into each beam, and a rotation of 0.0049 radians was maintained. The column
section remained the same between the two tests, although the beam in the second
specimen is connected to the flanges of the column. Also, the same size bolts and plates
were used for both specimens. A detail of the second specimen is shown in Figure 5.2.
32
Figure 5.2 Specimen 2 from SAC Report cyclic tests. (Liu and Astaneh-Asl, 2000)
The test setup of the two specimens can be seen in Figure 5.3. In each test, a
vertical strut supported the beam at the end opposite of the shear tab connection, and a
vertical actuator was positioned approximately at the center of the beam. Through a
combination of tensioning the struts and engaging the vertical actuators, the desired
initial shear force and rotation could be applied to the beams. Once these initial static
conditions were applied to the setup, the cyclic testing could begin. Cyclic lateral loading
was applied through a horizontal actuator attached to the top of the column.
33
Figure 5.3 Diagram of typical setup of actual tests. (Liu and Astaneh-Asl, 2000)
5.1.2 SAP Model
A two-dimensional, static non-linear SAP 2000 model was developed for each of
the two specimens. Screenshots of the models for the two specimens can be seen in
Figure 5.4 for specimen 1 and Figure 5.5 for specimen 2. The simulated gravity load from
the two vertical actuators was modeled as a point load on the beams, and the initial
rotation was modeled via an initial shortening of the HSS members at the far ends of the
beams. Because the SAC Report does not clearly explain which sections were used for
the ―struts‖, HSS3×.125 sections were assumed for the model. The moments were
released at the joints connecting the beams and struts, and the reactions at the base of the
struts and column were all modeled as idealized pins. The developed shear tab model was
included at the connections of the two beams to the column, and thus there were two
shear tab implementations for each test.
A monotonic displacement-controlled analysis was performed by laterally
displacing the joint at the top of the column. The target displacement was set to match the
34
maximum displacement observed in the final cycle of the original cyclic test. The state of
the structure at the end of the preliminary load case, where the constant shear force and
rotations were applied, was used as the initial condition for the displacement-controlled
analysis.
Figure 5.4 Screenshot of members in SAP 2000 model of specimen 1.
Figure 5.5 Screenshot of members in SAP 2000 model of specimen 2.
35
5.2 VALIDATION RESULTS
The results of the SAP 2000 analysis were tabulated, and the moment–rotation
relationship of the center joint (where the beams connect to the column) was graphed.
Because two shear tab connections existed at the center joint, the moment values in the
moment–rotation curves are twice the value that a single shear tab connection would
produce. These graphs were compared to moment–rotation graphs of the actual tests
provided in the SAC Report.
5.2.1 Moment–Rotation Comparison
A composite of the original results and the SAP 2000 results are shown in Figure
5.6 for specimen 1 and Figure 5.7 for specimen 2. Because the SAP 2000 analyses were
monotonic, the developed moment–rotation curves lack the hysteresis loops present in the
curves from the SAC Report. If the shear tab used in the verification model were assumed
to have no loading history, a perfect match would show the SAP 2000 curves following
the envelopes of the hysteresis curves. Deviations of the SAP 2000 curves from the
envelopes of the SAC Report curves indicate inaccuracy in the model at that location.
Using this basis for comparison, the model of specimen 1 is more accurate than the model
of specimen 2. However, with the simplicity of the models in mind, the resulting
behavior in both models is within acceptable bounds and was adequate for use in this
study.
36
Figure 5.6 Comparison of specimen 1 moment vs. rotation results of actual specimen
behavior in original test (experimental curve) and SAP 2000 model
validation analysis results (SAP 2000 curve).
SAP 2000 Curve
Experimental Curve Region where beam-to-
column binding occurs
37
Figure 5.7 Comparison of specimen 2 moment vs. rotation results of actual specimen
behavior in original test (experimental curve) and SAP 2000 model
validation analysis results (SAP 2000 curve).
5.2.2 Moment–Rotation Observations
In the moment–rotation curve for the specimen 1 model, the moment at which
bolt slip occurs is accurately predicted, as shown by the agreement in the region where
the curve departs from its vertical trend along the y-axis. The model for specimen 2
overestimates this value by several hundred kip-inches. The stiffness of the connection
between when bolt slip occurs and when maximum moment is reached, as shown by the
gentle slope out to 0.05 radians in the curves for both specimens, is also accurate for the
specimen 1 model, and somewhat underestimated for the specimen 2 model. The
maximum moment is overestimated in the curve for specimen 1 by approximately 50 kip-
SAP 2000 Curve
Experimental Curve
38
inches, but is very accurate in the curve for specimen 2. The ultimate rotation of the
specimen 1 model agrees with the rotation at which beam-to-column binding occurs, but
as noted in the previous chapter, this limit fails to capture the true ultimate rotation. The
ultimate rotation predicted by the specimen 2 model overestimates the rotation at which
beam-to-column binding occurs, but it inadvertently comes close to agreeing with the
true ultimate rotation.
As stated previously in Section 4.1.2, the limitations of the design guidelines used
to generate the employed shear tab model inhibit it from fully capturing the details of the
true moment–rotation behavior of the shear tabs. In the results of the specimen 1 model,
the increased stiffness and moment strength after beam-to-column binding occurs is
missing, and the ultimate rotation of the connection is underestimated by almost 0.05
radians. If behavior of the connection after beam-to-column binding could be understood
and calculated, these inaccuracies could be resolved. In the results of the specimen 2
model, the empirical value for the rotation at which the maximum moment capacity is
reached causes the inaccuracy in the post-bolt-slip stiffness. If this empirical value could
be replaced by a function that accurately identifies the rotation at which maximum
moment strength is reached, the true stiffness in the region between bolt slip and
maximum moment strength could be captured. As with the results of the specimen 1
model, capturing the behavior of the connection after beam-to-support binding occurs
would improve the accuracy of the curve in the region preceding ultimate rotation.
Despite the several aforementioned minor inaccuracies, the developed model
performed well in the validation analyses, given its simplicity. This verified model could
now be introduced into studies investigating the behavior of shear tab connections in
progressive collapse conditions such as the removal of a column.
39
Chapter 6: 2D Frame Behavior in Column Removal Scenario
Using the validated shear tab connection model described in Chapter 5,
investigations of a shear tab’s resistance to progressive-collapse-inducing forces were
carried out using a simple two-dimensional frame system. A column removal event was
chosen to be the catalyst for collapse in the model because this type of event is a
commonly cited example of progressive collapse initiation (Hamburger & Whittaker,
2004; Unified Facilities Criteria, 2010).
6.1 ANALYSIS SETUP
As with the shear tab model validation, the SAP 2000 structural analysis software
was utilized to run the column removal analysis. The analysis was a static, non-linear,
displacement-controlled analysis that included large displacements. The governing
displacement was a vertical, downward displacement of a central column into which two
beams framed. Because effects on the column were not considered in this analysis, the
column was not explicitly modeled, and the notional load and monitored displacement on
the column were simply applied to the central joint. A SAP 2000 screenshot of the
primary model is shown in Figure 6.1.
To represent a typical structure, each beam had a length of 30 feet. To capture the
correct force distributions across the beams at large rotations, the members were
subdivided into 50 elements. The far ends of the beams were connected to a fixed
support. At each end of both beams, the shear tab model developed in this study was
implemented to represent the presence of a shear tab connection at those locations. The
same W18×35 beams and 4-bolt shear tab connections used in the first specimen of
Astaneh’s cyclic tests as documented in SAC Report SAC/BD-00/03 (Liu and Astaneh-
Asl, 2000) and as used in the shear tab model validation were also used for this analysis.
40
6.1 Primary Analysis: Best-Case Shear Tab
For the primary analysis, a best-case scenario was considered where no gravity or
lateral loads existed in the frame system. Not even self-weight of the beams was
included. Thus, a notional load at the center joint, which directed the controlled
displacement in the correct downward direction, was the only load specified in the model.
This choice allowed the shear tab models to display the highest bending moment capacity
and rotational stiffness possible.
Figure 6.1 Screenshot of SAP 2000 analysis model for 2D column removal analysis
with shear tab connection models. 3H1 and 3H2 are shear tabs at the left and
right ends of the left beam, respectively. 4H1 (label is obscured) and 4H2
are shear tabs at the left and right ends of the right beam, respectively.
6.1.2 Lower-Bound Comparison: Two-Bar Truss
If gravity or lateral loads had been applied to the analysis model before the
displacement-controlled case, the shear tab connections would have exhibited lower
rotational stiffnesses and lower maximum bending moment capacities than what was
computed. Ignoring the possibility of connection failure, if the axial and shear loads on
the connection were increased substantially, the moment–rotation behavior of the shear
tab model would approach the moment–rotation behavior of a perfect pin. Such a
situation would effectively be a worst-case scenario. For the sake of comparison, a
parametric analysis was performed where all ―best-case‖ shear tab connections were
41
replaced with ―worst-case‖ perfect pins in order to provide a lower bound for evaluating
response.
In the perfect pin case, the model becomes what is commonly known as a ―two-
bar truss‖. The relationship between the displacement of the center joint and the axial
forces in the column and beams can be solved analytically when large displacements are
considered, and therefore a numerical solution from SAP 2000 was not needed for this
case.
6.2 Upper-Bound Comparison: Fixed Connections
The ―best-case‖ shear tab connection model and perfect pin connection model
provide bounds for the possible moment–rotation behavior of a shear tab based on what
percentage of the connection is dedicated to resisting static shear and axial loads as
opposed to resisting bending moment and rotation. It would also be beneficial, however,
to compare these two behaviors to the behavior of the model if all connections were
perfectly fixed. For this reason, a third model was developed in which each end of both
beams was perfectly fixed. The results of this analysis provided insight into how close the
behavior of a ―best-case‖ shear tab is to the behavior of a perfect pin as opposed to the
fixed connection behavior.
Unlike the two-bar truss problem, this model did not have a closed form solution.
Accordingly, an analysis was run in SAP 2000 to determine a solution computationally.
A screenshot of the developed analysis model is shown in Figure 6.2.
42
Figure 6.2 Screenshot of SAP 2000 analysis model for 2D column removal analysis
with fixed connections. The arrow at center shows the notional load applied
at the center joint for the monitored displacement analysis case.
6.3 Beam Yielding
For each of the three cases, (1) the best-case shear tab connection, (2) the worst-
case shear tab connection, which is a perfect pin connection, and (3) the fixed connection,
the analysis was run in two ways. The first setup ignored any yielding of the beams due
to axial stresses reaching the yield stress of the A992 structural steel. The second setup
considered the aforementioned yielding.
To introduce this yielding behavior into the two analysis models that used SAP
2000, a plastic hinge element that couples the axial force in a member to its axial
displacement was applied at the ends of each beam. When the axial force in the beams
reached the material yield stress multiplied by the beam’s cross-sectional area, the
members would begin to exhibit plastic axial deformation in response to any attempt to
further increase the axial load. A screenshot of the SAP 2000 input for the hinge element
is shown in Figure 6.3. This rigid, perfectly plastic yielding behavior was chosen for
simplicity.
43
Figure 6.3 Screenshot of SAP 2000 input for beam axial yielding hinge element.
6.2 RESULTS
6.2.1 Displaced Shape and Force Distribution Comparisons
For the case in which perfect pin connections are assumed, the beams do not
experience any curvature (i.e., the displaced shape is linear) due the absence of any
rotational stiffness in the connections and because only a single point load is assumed to
act at the center joint. The displaced shape of the fixed connection case is a cubic curve
(at least for small displacements) due to the constant presence of rotational stiffness. The
―best-case‖ shear tab results show a displaced shape similar to that of the fixed
44
connection case at low rotation values, but then migrate to a linear displaced shape as the
rotational stiffness in the shear tab decreases and ultimately goes to zero as the rotation
increases. The two displaced shapes associated with fixed supports and with perfect pin
supports are shown, respectively, in Figure 6.4 and 6.5.
Figure 6.4 SAP 2000 analysis results screenshot showing the displaced shape exhibited
by the fixed connection case. The primary shear tab connection case also
exhibited this shape at low rotations.
Figure 6.5 SAP 2000 analysis results screenshot showing the displaced shape exhibited
by the perfect pin connection case. The primary shear tab connection case
also exhibited this shape at higher rotations.
For the best-case shear tab analysis and the fixed connection analysis, the shear
and moment distributions, at small rotations, matched the common distribution shape for
a beam undergoing a bending moment and exhibiting small displacements. The shear
45
distribution is shown in Figure 6.6 and the moment is shown in Figure 6.7. Because the
perfect pin case is a truss, no shear or moment forces existed in the beams.
Figure 6.6 Screenshot of SAP 2000 analysis results shear diagram of fixed connection
and best case shear tab cases at low column displacements.
Figure 6.7 Screenshot of SAP 2000 analysis results moment diagram of fixed
connection and best case shear tab cases at low column displacements.
As the column displacements increased in magnitude beyond what may be
considered small displacements, nonlinear geometry effects began to affect the shear and
moment distributions. Figure 6.8 shows a higher-order curve forming in the shear
distribution, as does Figure 6.9 for the moment distribution. As the rotation increases,
these higher-order curves become more and more pronounced and deviate further and
further from the constant and linear trends shown at small rotations. The fixed case
46
continued to do so indefinitely, whereas the best-case shear tab case arrived at a final
shape when its ultimate rotation was reached. At rotations beyond a shear tab’s ultimate
rotation, the shear and moment distributions of that connection remain constant at the
values present at maximum rotation.
Figure 6.8 SAP 2000 screenshot of shear diagram for fixed connection and best-case
shear tab cases at high rotations.
Figure 6.9 SAP 2000 screenshot of moment diagram for fixed connection and best-case
shear tab cases at high rotations.
For all cases, the axial force is constant across the beams, and the magnitude of
the axial force is dependent upon the displacement of the column. The relationship
between the axial force magnitude and the column displacement varies among the three
cases due to the different rotational stiffnesses of the three types of connections. This
topic will be discussed further in the next two sections.
47
6.2.2 Rotational Stiffness Comparisons
The aforementioned relationship between the magnitude of the axial force in the
beams and the displacement of the center column is dependent upon the rotational
stiffness of the connections. A stiffer connection, such as the fixed connections, will
produce higher axial forces in the beams than would a perfect pin connection
experiencing the same column displacement.
As shown in Figure 6.10, the two shear tab cases exhibit very similar rotational
stiffness compared to the fixed connection case. Essentially, regardless of whether the 4-
bolt shear tab connection in this study has its maximum bending moment capacity of 528
kip-inches or whether it has no bending moment capacity at all, a 21-inch drop of the
center column will induce approximately 500 kips of axial force in each of the W18×35
beams. Alternatively, a column drop of this magnitude would induce almost 600 kips of
axial force in each of the beams if they were connected by a fixed connection. These
observations neglect any yield or failure limits of the members and connections.
Another way to compare the rotational stiffness behaviors is to consider the force
pushing down on the center column as a function of the column displacement. As shown
in Figure 6.11, the two shear tab cases behave similarly and are in great contrast to the
fixed connection case. However, unlike when examining the axial force in the beams,
when examining the axial force in the column, the two shear tab cases exhibit a
noticeable difference in behavior. To displace the center column 10 inches downward
when the beams are connected by best-case shear tabs, 10 kips of force must be applied
to the column. In contrast, to displace the column the same amount when the beams are
connected by worst-case shear tabs, 6 kips of force must be applied to the column. This
difference in force demonstrates that the rotational stiffness of the best-case shear tab
connection does provide some resistance to the downward motion of a column line
48
suffering the removal of one of its columns. Although the effect is small, this simple 2D
frame analysis only includes two connections. The cumulative resistance of an array of
shear tab connections in a 3D building may be significant. This topic is discussed in
Chapter 7.
49
Figure 6.10 Comparison of the axial force developed in the beams vs. the downward
vertical displacement of the center column for the ―best-case‖ shear tab
connection analysis, the ―worst-case‖ shear tab connection analysis (or
perfect pin, two bar truss analysis), and the fixed connection analysis. The
two shear tab cases are indistinguishable in this graph. This figure
demonstrates how similarly a shear tab connection with maximum rotational
stiffness and a shear tab connection with no rotational stiffness behave in
relation to a fixed, rigid connection.
50
Figure 6.11 Comparison of the axial force exerted on the center column vs. the resulting
downward vertical displacement of the column for the ―best-case‖ shear tab
connection analysis, the ―worst-case‖ shear tab connection analysis (or
perfect pin, two bar truss analysis), and the fixed connection analysis.
Unlike Figure 6.10, this graph shows a noticeable difference between the
two shear tab cases, but this difference is most likely the result of the even
greater difference between the shear tab cases and fixed connection case in
this graph.
As seen by the upward curving trends in Figure 6.10 and Figure 6.11, the
difference between the shear tab connection results and the fixed connection results
increases as the column displacement increases. The difference between the two shear tab
cases initially increases at small column displacements, but it then remains constant
beyond the displacement at which the rotational stiffness of the shear tab becomes zero.
Figure 6.12 displays the relationship between the bending moment in the best-case shear
51
tab as a function of the vertical column displacement. As seen in the figure, the
connections reach their maximum moment capacity, and thus lose all rotational stiffness,
at a vertical column drop of approximately 19 inches, which is therefore the column
displacement beyond which the displaced shape of the beams in the ―best-case‖ shear tab
connection results changes from matching the fixed connection results to matching the
perfect pin connection results.
Figure 6.12 Bending moment in the ―best-case‖ shear tab connections vs. the vertical
downward displacement of the center column. This figure shows that the
vertical column displacement at which the best-case shear tab connections
lose all rotational stiffness is approximately 19 inches. Not shown on this
figure, the ultimate rotational capacity, at which the moment capacity drops
to zero, occurs at a vertical column displacement of 41 inches.
(2 inches, 235 kips)
(19 inches, 528 kips)
52
When yielding in the beams is considered, the behavior of the systems changes
slightly. Beyond the yield point, the axial force in the beams remains constant. Compared
to the case where yielding of the beams is not considered, the reduction in beam axial
stiffness due to yielding allows smaller loads on the column to produce the same
displacements. Figures 6.13 and 6.14 show how Figures 6.10 and 6.11, respectively,
would change due to the consideration of axial yielding of the beams.
As shown in Figure 6.13, the axial yield force of a W18×35 made of A992
structural steel is 566 kips. The beams yield at a lower column displacement in the fixed
connection case than in the shear tab connection cases due to the fact that beams with
fixed connections must carry higher axial forces, as explained previously. In the fixed
connection case, the beams yield at a column displacement of approximately 21 inches,
whereas in the shear tab cases, the beams yield at a column displacement of
approximately 22 inches. This small difference indicates that axial forces in the beams,
and thus beam yielding, is strongly dependent upon the degree of column displacement
and is largely independent of the type of connection used.
Without considering beam yielding, a 100-kip force is required to displace the
column 25 inches downward when the beams are connected by perfect pins, for example.
As shown in Figure 6.14, when beam yielding is considered, this required force changes
to 78 kips. This trend is common to the best-case shear tab connection and the fixed
connection case as well.
53
Figure 6.13 Comparison of the axial force developed in the beams vs. the downward
vertical displacement of the center column for the ―best-case‖ shear tab
connection analysis, the ―worst-case‖ shear tab connection analysis (or
perfect pin, two-bar truss analysis), and the fixed connection analysis with
yielding of the beams considered. The beams yield at an axial force of 566
kips.
54
Figure 6.14 Comparison of the axial force exerted on the center column vs. the resulting
downward vertical displacement of the column for the ―best-case‖ shear tab
connection analysis, the ―worst-case‖ shear tab connection analysis (or
perfect pin, two-bar truss analysis), and the fixed connection analysis with
yielding of the beams considered.
6.2.3 Axial Force Capacity
The rotational stiffness comparisons made in the previous section did not take into
account the axial force capacity of any connections. Using the output of the spreadsheet
used to develop the shear tab model described in Chapter 4, the 4-bolt shear tab used in
the comparisons was found to have an axial force capacity of 115 kips. Any axial force
greater than this value, when applied to this 4-bolt shear tab connection, will cause bolt
fracture, and the connection will therefore fail.
55
Inspecting Figure 6.10 or Figure 6.12 reveals that the shear tab connections, for
both the best and worst cases, would fail at approximately 10 inches of vertical column
displacement. Figure 6.11 and Figure 6.13 show that this column displacement correlates
to an axial load on the column of 10 kips for the best-case shear tab connections and 6
kips for the worst-case shear tab connections, both of which are small compared to the
column axial capacity. Furthermore, Figure 6.12 shows that when the center column
displaces downward by 10 inches, the best-case shear tab connections will not have
reached their maximum moment strength yet, and they will be at only one-quarter of their
rotational capacity. The SAP 2000 output for the best-case shear tab analysis shows that
the shear force in the connections at a column displacement of 10 inches is approximately
5 kips. This shear load is well below a 4-bolt shear tab’s shear capacity of 97 kips.
The axial force capacity is clearly the limiting factor for the shear tab connections
in these analyses. Overwhelming catenary forces develop in the beams long before the
shear tab connections have a chance to display their rotational ductility. These results
indicate that checking axial forces in connections during progressive collapse analyses
should be a priority.
To further support this argument and to exemplify the use of the developed model
in a full, 3-D building analysis, the next chapter uses SAP 2000 to compare the developed
model to a current standard in progressive collapse design and draws conclusions about
the failure criteria of both models.
56
Chapter 7: 3D Building Performance in Column Removal Scenario
After studying the behavior of a column removal in a simply connected two-
dimensional (2D) frame, the developed shear tab model was introduced into a three-
dimensional (3D) analysis of a full building in which the effects of redundancy and
alternate load paths could be considered. Because the results of this analysis are
dependent upon the building chosen, the number of general conclusions gathered from
observations in this chapter is limited. This part of the study mostly 1) exemplifies use of
the developed shear tab model in a full building analysis and 2) demonstrates the
significance of considering the axial force limit state of a shear tab connection in
progressive collapse analyses.
7.1 BUILDING CHOICE
The US Department of Defense oversees an initiative to unify and standardize the
technical criteria pertaining to the full lifecycle of all facilities that it governs (WBDG,
2010). This initiative, known as the Unified Facilities Criteria program, publishes
documents and releases them to the public on the Whole Building Design Guide website.
One of these documents, Design of Buildings to Resist Progressive Collapse, UFC 4-023-
03 (Unified Facilities Criteria, 2010), standardizes the design of facilities to withstand
destructive events that could result in the progressive collapse of a structure. To
demonstrate and to illustrate the design process specified in the document, UFC 4-023-03
provides several design examples in the appendices. For the benefit of having a basis of
comparison, the four-story steel frame health care facility used in Appendix E of the UFC
progressive collapse document was used for the 3D analysis of this study.
57
7.1.1 Building Layout
As shown in Figures 7.1 and 7.2, the structure considered for this example is a
four-story building with nine bays in the north-south (transverse) direction and two bays
in the east-west (longitudinal) direction, thus giving it a high aspect ratio. All four stories
are equal in height, and all transverse bays are equal in width. The building resists lateral
forces via moment connections in the perimeter frames and via a set of braces in the
center. All interior connections are shear tab connections.
Figure 7.1 Plan view of the health care facility analyzed. (Unified Facilities Criteria,
2010)
Figure 7.2 Profile view of the health care facility analyzed. (Unified Facilities Criteria,
2010)
58
7.1.2 Loading
The loading shown in Table 7.1 was imposed on the building prior to the column
removal event.
Table 7.1 Static loads imposed on the building.
Load Per Floor (psf) Roof (psf)
Self Weight Self Weight Self Weight
Slab & Deck 75 + 3 5
Ceiling & Mechanical 15 15
Cladding 15 (15 psf x 14′-8″ = 220 plf) 15
Partition 20
Live Load 80 20
7.1.3 Model Assumptions
As documented in Appendix E of UFC 4-023-03, the UFC example model was
created with the following ten assumptions (Unified Facilities Criteria, 2010).
1. Members are modeled using centerline dimensions.
2. All moment connections are improved Welded Unreinforced Flange (WUF).
3. Gravity framing connections are assumed to be pinned except for secondary
member checks when they are considered partially restrained.
4. Column-to-foundation connections are considered pinned.
5. Each floor is modeled as a rigid diaphragm.
6. Gravity framing is designed assuming composite section behavior.
7. All steel shapes are ASTM A992.
8. Concrete has a nominal specified compressive strength of 4000 psi.
9. Floor system consists of a 3-inch composite steel deck + 4.5-inch topping.
59
10. Roof system is comprised of a metal deck only (i.e., no concrete fill).
7.2 ANALYSIS SETUP
Two models were created for this study. Both models demonstrate the behavior of
a full building subjected to a column removal event in a region of the structure that is
connected by shear tabs. The first model utilizes the shear tab connection model
developed in this study. The second uses the shear tab connection model specified by the
UFC guidelines and serves as a basis for comparison.
Much like the analyses presented in Chapter 6, the two building models were
analyzed using static non-linear load cases in SAP 2000. The moment–rotation behavior
of shear tabs in both models was implemented using non-linear plastic hinge elements
placed at the ends of beam members. For both buildings, as shown in Figure 7.3, a first
floor interior column of the structure was removed to simulate the mechanism for a
progressive collapse event. For both models, the original static loads on the structure
were incrementally applied onto the damaged building until either the full load was
applied or until a shear tab connection failed by exceeding one of the limit states of the
guidelines used to model it. Due to the assumption that modern design standards produce
strong members and weak connections, and because the focus of these analyses was on
connection performance, limit states and capacities of beam elements and column
elements were not included in the failure criteria for the analyses as it was assumed that
these members were sized adequately when developing the example structure that
appears in the UFC document.
60
Figure 7.3 SAP 2000 screenshot showing a plan view of the first story of the analyzed
building. The bold circle highlights the location of the column removal.
7.2.1 Model Comparison
The building model using the developed shear tab model inherits all of the
assumptions of the UFC building model. The two models are identical in all ways except
the simple connection design. The UFC guidelines consider shear tabs to be ―partially
restrained‖ connections that have a predefined moment–rotation behavior, much as the
model developed in this study assumes. For a static non-linear analysis, the UFC shear
tab connections use a moment–rotation behavior curve that is dependent upon the
maximum moment capacity of the connection and the depth of the bolt group. The UFC
guidelines refer to ASCE 41 (American Society of Civil Engineers, 2007) for the method
of calculating the maximum moment capacity. This approach has several similarities to
the guidelines presented by Astaneh-Asl in SAC Report SAC/BD-00/03 but lacks many
of the details regarding bolt slip and ultimate rotation. Furthermore, the ASCE 41
guidelines apply to structures subjected to seismic loads that cause cyclic response of
structural connections, and it is not clear how suitable these guidelines are for evaluating
progressive collapse. The shear tab elements produced using the UFC model, when
compared to the shear tab elements produced using the model developed in this study for
61
the same shear tabs, typically have slightly lower maximum moment capacities, slightly
greater initial stiffnesses, and lower ultimate rotations. These differences, while
noticeable, did not result in significantly different assessments of performance for the
building considered in this example.
The significant difference between the two approaches involves consideration for
an axial limit state of the connection. The connection failure criteria in the UFC
guidelines are only dependent upon rotational deformation limit states. Unlike the model
developed in this study, which takes rotation capacity, shear force capacity, and axial
force capacity into account, the UFC guidelines do not include design criteria for
resisting axial forces in simple shear connections.
7.3 RESULTS
The results of the building model using the shear tab model from this study and
the results of the building model using the shear connection model from the UFC
guidelines agree that the modeled medical facility could not withstand the loss of the
specified first-floor interior column.
7.3.1 Deformation
Both models show similar displaced shapes at the time of failure. As shown in
Figure 7.4, large vertical displacements occur in the columns and beams above the
removed column, and the beam members framing into those columns exhibit large
rotations at their ends.
The displaced shapes of the beams, particularly those shown in Figure 7.5, are not
linear due the minor initial rotational stiffness of the shear tab connections. This
observation corresponds to the initial displaced shape of the beams in the best-case shear
tab model analysis presented in Chapter 6. If the analyses had continued further, the
62
beams’ displaced shapes would have become more linear as the connections’ stiffnesses
reduced.
The analysis using the developed shear tab model failed at a much smaller vertical
column drop than the analysis using the UFC shear tab model. At the point of failure, the
maximum vertical drop of the columns above the removed column in the analysis using
the developed shear tab model was approximately 4.4 inches. In the analysis using the
UFC shear tab model, the vertical drop was nearly 17.5 inches. The large difference in
displacements indicates that, although the two models ultimately support the same
conclusion, the developed shear tab model analysis fails much sooner and fails under a
much smaller load due to the fact that the developed shear tab model accounts for a
failure limit state based on axial capacity whereas the UFC shear tab model does not.
The largest rotations exhibited by shear tab connections at the point of failure in
the building model using the developed shear tab model were nearing 0.025 radians. For
the UFC model, several shear tabs exhibited rotations in excess of 0.05 radians.
According to the UFC guidelines, the rotations in these shear tabs exceeded their
rotational capacity, indicating connection failure. It was therefore the rotational
deformation capacity limit state that was exceeded and constituted failure in the UFC
connection model analysis. By arriving at this limit state before the design load was fully
present in the structure, the analysis indicates, according to the UFC guidelines, that the
shear tab connections in the modeled medical facility are not adequate to resist
progressive collapse.
No shear tab’s rotation exceeded its rotational capacity in the analysis using the
connection model developed in Chapter 4. This limit state, therefore, was not the cause of
failure in that model. Rather, axial force is what controls the connection behavior, and
this point is discussed further in Section 7.3.3.
63
Figure 7.4 SAP 2000 screenshot showing the displaced shape of a longitudinal cross-
section of the interior column line in the region of the removed column. This
is the displaced shape for both building models at the point of failure (they
have negligible differences in shape). The differences in magnitude for the
two models are, alternatively, very different. For the developed shear tab
model analysis, the damaged column dropped approximately 4.4 inches and
therefore this figure has a scale factor of 20. For the UFC shear tab model
analysis, the damaged column dropped approximately 17.5 inches and
therefore this figure has a scale factor of 7.
64
Figure 7.5 SAP 2000 screenshot showing the displaced shape of a transverse cross-
section of the column line with the removed column. Similarly to Figure 7.4,
the displaced shape is nearly identical for the two analyses at the point of
failure. For the developed shear tab model analysis, this figure has a scale
factor of 18, and for the UFC shear tab model analysis, this figure has a
scale factor of 5.
65
7.3.2 Bending Moments
The magnitudes of the bending moments in the beams framing into the columns
above the removed column were generally less than the magnitudes of the bending
moments in beams located elsewhere in the structure. Also, unlike the rest of the
structure, no negative curvature was observed at the ends of beams framing into the
damaged column set. This difference is expected because, in the damaged region,
columns impose a downward force on the beams, whereas in undamaged regions, the
beams impose a downward force on the columns.
Figure 7.5 shows the bending moment diagrams across the region on the structure
where the column removal was assumed to occur. Aside from the aforementioned
anomalies due to the column removal, the structure exhibits a bending moment
distribution very similar to that expected of a simply supported steel frame system.
Figure 7.6 SAP 2000 screenshot of bending moment distribution in longitudinal beams.
This cross-section is the same as the cross-section in Figure 7.4.
66
Figure 7.7 SAP 2000 screenshot of bending moment distribution in transverse beams.
The cross-section shown in this figure is the same as the cross-section in
Figure 7.5.
7.3.3 Axial Forces
Figure 7.6 shows the axial force distribution at the end of the analyses in the
region of the structure where the column has been removed. Similarly to the displaced
shape and moment distribution, the axial distribution is nearly identical in shape for both
connection model cases. All beams in the structure have negligible axial forces except for
those framing into the damaged column set, which have very large internal axial forces.
The greatest axial forces exist in the first floor longitudinal beams, in the ends
farthest from the removed column. Due to several factors, including the high aspect ratio
of the structure, the axis orientation of the columns, and the member sizes specified, the
axial forces of beams in the longitudinal direction are much greater than the axial forces
of beams in the transverse direction. The stepped shape of the axial distribution along the
67
longitudinal beams is caused by the two minor transverse beams framing into them along
their lengths.
As shown in Figure 7.9, the columns above the removed column experience
tensile forces, with the columns on the upper floor experiencing the greatest magnitudes.
These tensile forces are caused by the roof beams resisting the downward movement of
the column line where the first-floor column has failed. It should also be noted that,
unlike in the longitudinal beams, the axial forces in the transverse beams do not vary
from floor to floor. Much like the discrepancy in magnitudes between the two directions,
this phenomenon is most likely a consequence of the building design.
Figure 7.8 SAP 2000 screenshot of the axial force distribution in longitudinal beams.
The cross-section shown in this figure is the same as the cross-section in
Figure 7.4. Axial forces in the beams of the left-most and right-most bays
shown in the figure were not proportionally large enough to appear in the
display. The compressive axial loads in the columns are not shown.
68
Figure 7.9 SAP 2000 screenshot of the axial force distribution in transverse beams. The
cross-section shown in this figure is the same as the cross-section in Figure
7.5. The compressive axial loads in the perimeter columns are not shown.
Much like the magnitudes of displacements, the magnitudes of the axial forces in
the afflicted region of the structure at the point of failure differ greatly between the two
analyses. For the building model using the developed shear tab model, the largest axial
load present in the entire structure at the time of failure was 80 kips. For the building
model using the UFC connection guidelines, the largest axial load was approximately 800
kips. Both of these forces occurred in first-floor longitudinal beams framing into the
damaged column set. In the transverse direction, the largest axial loads were 27 kips for
the developed shear tab model analysis and 220 kips for the UFC shear tab model
analysis. The UFC guidelines do not specify an axial force limit state, and thus the large
axial forces in that model do not directly affect the collapse criteria. However, in the
shear tab model developed in Chapter 4, a shear tab has a specified axial force capacity.
69
Exceeding this capacity indicates connection failure. The maximum axial force of 80 kips
in the developed shear tab model analysis corresponds to the axial force capacity of the
shear tabs connecting the W24×62 longitudinal beams above the first story to the column
adjacent to the removed column. Failure of the building model using the developed shear
tab model was therefore caused by the failure of the aforementioned shear tab
connections due to excessive axial force.
7.4 IMPORTANCE OF AXIAL FORCE LIMIT STATE
The results of both models indicate that the loss of the first floor column
identified in Figure 7.3 would cause the shear tab connections in the region of the
structure surrounding that column to fail. The failure of these connections would most
likely cause the progressive collapse of that portion of the structure. Although the results
of the two models support the same conclusion, they arrive at it in different manners. The
UFC shear tab model indicates that connection failure would occur at a column drop of
17.5 inches due to excessive rotation. The developed shear tab model indicates that
connection failure would occur much earlier at a column drop of four inches due to
excessive axial force.
This chapter, through the use of the simple shear tab model documented in
Chapter 4, has demonstrated that the axial force limit state of shear tab connections can
be the controlling limit state in progressive collapse design of steel structures when only
the steel frame is considered. Further research on other structures needs to be done to
support these results, and several improvements need to be made to the shear tab model
to increase its accuracy and further validate its use in progressive collapse analyses.
Nevertheless, the results of this chapter suggest that modern progressive collapse design
70
standards include criteria for considering the axial force limit state of simple connections
when evaluating performance.
71
Chapter 8: Summary and Recommendations
8.1 SHEAR TAB MODELING
8.1.1 Summary
The shear tab model documented in Chapter 4 and verified in Chapter 5 considers
the shear force, axial force, bending moment, and rotational capacities of a shear tab.
Given these limits, the model produces a moment-rotation diagram for the connection
that was proven to be reasonably accurate for the two test cases from SAC Report
SAC/BD-00/03 against which they were verified. The model was easily implemented into
the SAP 2000 structural analysis software using a ductile plastic hinge element that
considered moment and rotation interaction. By applying such a plastic hinge element at
the end of a beam member where it framed into a column or girder, the behavior of the
modeled shear tab connection was effectively applied to that joint.
8.1.2 Limitations and Future Work
The current model only considers moment-rotation interaction. Applying a static
shear load or axial load to the connection will adjust the moment-rotation behavior
appropriately, but the model does not account for shear forces or axial forces developed
due to rotation. Increasing shear forces and increasing axial forces in the connection both
reduce its bending moment capacity. Developed axial force may also decrease the
rotational capacity. The guidelines on which the current model is based do not provide a
means for calculating shear force and axial force interaction, and many of the values on
which the rotation behavior is defined are empirical. Further research needs to be done to
investigate the interaction among the rotation, axial force, shear force, and bending
moment of a shear tab connection, and developed guidelines need to base calculations off
of physical parameters of the shear tab and its loading conditions.
72
8.2 SHEAR TAB BEHAVIOR AND PERFORMANCE IN COLUMN REMOVAL SCENARIOS
8.2.1 Summary
In the column pull-down analyses of Chapter 6, the developed shear tab model
showed that a shear tab’s small bending stiffness results in slightly different behavior
from that of a perfect pin connection, but this difference is small when compared to the
difference between a shear tab and a moment-resisting connection or fixed connection.
The analyses also showed that under such conditions, the axial force capacity of the
connection is exceeded before the rotational capacity is exceeded. The results
documented in Chapter 7 supported the importance of this observation because the
building model that considered a shear tab’s axial limit state suggested that the building
would fail under far less load than the building model that only considered the rotational
capacity of a shear tab.
8.2.2 Recommendations
This study focused completely on bare steel frame models. Without contributions
from a concrete slab or metal deck, the catenary forces developed in beams during
progressive collapse scenarios appear to be too great for shear tab connections to
withstand. When the strengths and stiffnesses of a concrete slab or metal deck are
considered, different behavior may occur and different conclusions may be drawn, as
shown in a recent report from NIST (Sadek et al, 2008). Further research needs to be
done that considers the contribution of floor slabs and metal decks when analyzing, using
simplified methods, the performance of structures during a progressive collapse event
involving steel frames connected by shear tabs.
The results of Chapter 7 promote the importance of considering the axial force
limit state of shear tabs when carrying out progressive collapse analyses on steel
73
structures. Current design standards, such as the Department of Defense’s Unified
Facilities Criteria, do not mandate that this limit state be considered. Further
investigations need to be done to confirm the importance of this limit state and promote
its inclusion in modern progressive collapse design standards.
74
References
American Society of Civil Engineers (ASCE). (2007). Seismic Rehabilitation of Existing
Buildings, (ASCE/SEI 41-06). Reston, Virginia.
Astaneh-Asl, A., Madsen, E., McCallen, D., & Noble, C. (2001). Study of catenary
mechanism of cables and floor to prevent progressive collapse of buildings
subjected to blast loads. Rep. to Sponsor: General Services Administration, Dept.
of Civil and Environmental Engineering, University of California, Berkley,
California.
Astaneh-Asl, A., Liu, J., & McMullin, K. M. (2002). Behavior and design of single plate
shear connections. Journal of Constructional Steel Research, 58, 1121–1141.
Byfield, M. P. (2006). Behavior and design of commercial multistory buildings subjected
to blast. Journal of Performance of Constructed Facilities, 20(4), 324–329.
Carino, N., & Lew, H. S. Structures Devision, Building and Fire Research Laboratory.
(2001). Summary of NIST/GSA workshop on application of seismic rehabilitation
technologies to mitigate blast-induced progressive collapse, (NISTIR 6831).
Department of Commerce.
Computers and Structures. (2010). SAP 2000. Retrieved April 1st, 2010, from
http://www.csiberkeley.com/products_SAP.html
Foley, C. M., Martin, K., & Schneeman, C. (2006). Robustness in structural steel framing
systems. Rep. No. MU-CEEN-SE-06-01, Marquette University, Milwaukee,
Wisconsin.
Hamburger, R. O., & Whittaker, A. S. (March, 2004). Design of steel structures for blast-
related progresseive collapse resistance. Modern Steel Construction.
Kim, J., & An, D. (2009). Evaluation of progressive collapse potential of steel moment
frames considering catenary action. Structural Design of Tall and Special
Buildings, 18, 455–465.
Khandelwal, K., El-Tawil, S., Kunnath, S. K., & Lew, H. S. (2008). Macromodel-based
simulation of progressive collapse: steel frame structures. Journal of Structural
Engineering, 134(7), 1070–1078.
Liu, J., & Astaneh-Asl, A. (2004). Moment–rotation parameters for composite shear tab
connections. Journal of Structural Engineering, 130(9), 1371–1380.
Liu, J., & Astaneh-Asl, A. (2000). Cyclic tests on simple connections, including effects
of the slab. SAC Steel Project, SAC/BD-00/03.
75
Livermore Software Technology Corporation. (2010). LS-DYNA. Retrieved April 1st,
2010, from http://www.lstc.com/lsdyna.htm
Nair, R. (March, 2004). Progressive Collapse Basics. Modern Steel Construction.
Sadek, F., El-Tawil, S., & Lew, H. S. (2008). Robustness of Composite Floor Systems
with Shear Connections: Modeling, Simulation, and Evaluation. Journal of
Structural Engineering, 134(11), 1717–1725.
Unified Facilities Criteria (UFC). (2010). Design of Buildings to Resist Progressive
Collapse, (UFC4-023-03). Department of Defense.
Whole Building Design Guide (WBDG). (2010). Unified Facilities Criteria. Retrieved
April 1st, 2010, from http://www.wbdg.org/ccb/browse_cat.php?o=29&c=4
76
Vita
Eric Michael Heumann was born in Houston, Texas in 1985. As a child, he had an
appreciation for creative endeavors, Scouting, and the outdoors. He earned his Eagle
Scout award in the spring of 2002 and went on to graduate from James E. Taylor High
School with high honors in May of 2004. Inspired by his father, a chemical engineer and
graduate of Cornell University, Eric chose to carry on that legacy and enrolled in
Cornell’s civil engineering program. While in Ithaca, he continued his passion for music
in several of the university’s bands, and he also carried on his commitment to community
service and environmental awareness by joining the Alpha Phi Omega service fraternity
and Engineers for a Sustainable World. In 2008, Eric graduated cum laude from Cornell
and chose to further his education in engineering by attending the structural engineering
masters program at the University of Texas at Austin. He plans on starting his career as a
structural designer after earning his degree on May 22nd
of 2010.
Permanent email: [email protected]
This thesis was typed by the author.
