finaldraft dissertation

URN: 6247119

Supervisor:

Dr. Boulent Imam

Progressive collapse analysis of steel buildings

Submitted in partial fulfilment of requirement for the Degree of

Bachelor of Engineering in Civil Engineering

Department of Civil and Environmental Engineering

Faculty of Engineering and Physical Sciences

University of Surrey

10th May 2016

Word count: 12084

Mohammed Odeh 2016

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Executive Summary:

Progressive collapse occurs when a key structural component fails and causes the failure of

adjacent structural components. In addition, it is considered as a disproportion in size

between a triggering event and the resulting collapse (Starossek, 2006).

Several guidelines suggest methods to mitigate the possibility of progressive collapse

occurring in structures. General Service Administration, Untied Facilities Criteria and Eurocode

1 provide up to date codes of practice. In this thesis, the alternate path method was

considered as it provides sufficient guidance against progressive collapse. This method

assesses the performance of the structure after a key structural element is removed.

European and British guidelines were not used for the analysis, as they simply provide

mitigation procedures and do not take into account accidental actions that may occur.

In the literature review, current design methods were investigated and different types of

progressive collapses were presented. Furthermore, structures that had experienced

progressive collapse were analysed and collapse-promoting features were discussed.

For the analysis, SAP2000 was used and a ten-storey building was examined by using the

Alternate Load Path method. Furthermore, two analysis methods were performed which were

the linear and non-linear static analysis. Moreover, column removal scenarios were carried

out in each analysis to examine their effect on the structural integrity and robustness of the

building.

The structure used in this report was overdesigned as to determine whether progressive

collapse may occur in overdesigned structures. The linear static analysis results indicated that

although fewer structural members failed, progressive collapse still occurred when a

structural component was removed. In addition, the results obtained were similar to the

results obtained for the original designed members which indicates that it would be

uneconomical to over design the structure. Afterwards, a non-linear analysis was carried out

as the linear-static analysis did not consider geometric and material nonlinearities. For the

non-linear analysis, plastic hinges did not form throughout the structure and with the advice

of the project supervisor section sizes were reduced. After re-running the analysis, plastic

hinges formed throughout the structure and fewer structural members failed when compared

to the linear analysis, which suggests that it is more suitable to use.

Mohammed Odeh

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Acknowledgements:

Firstly, I would like to thank my project supervisor Dr. Boulent Imam as his door was always

open whenever I had a question or a critical decision to make about my analysis and writing.

From the first day he steered me in the right direction and trusted that I would put in sufficient

effort throughout the year. Without his passionate participation and input this project would

have not been completed.

I am grateful to my sisters for the long discussions that helped me figure out the technical

details of my work and they regularly made sure I had used correct grammar and consistent

notations in my writings. Lastly, I would like to thank my mother, Haifa Aldiri, and father,

Osama Odeh, for their love and support, this would have not been possible to complete

without their support.

Mohammed Odeh

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Contents 1 Introduction ........................................................................................................................ 1

General overview ......................................................................................................... 1

Aims of the dissertation: ............................................................................................. 1

Subsequent chapters: .................................................................................................. 2

2 Literature review: ................................................................................................................ 3

Introduction ................................................................................................................. 3

Guidelines available for progressive collapse analysis ................................................ 3

2.2.1 Guidance and formal provisions: ......................................................................... 3

2.2.2 European and UK design codes: ........................................................................... 3

2.2.3 United States of America Codes and design guidelines: ...................................... 5

Types of progressive collapse: ..................................................................................... 6

2.3.1 Pancake type collapse: ......................................................................................... 6

2.3.2 Domino type collapse: .......................................................................................... 8

2.3.3 Mixed-type collapse: ............................................................................................ 9

Collapse-promoting features ....................................................................................... 9

2.4.1 Dynamic action, force concentration, brittle material behaviour and ductile

material behaviour: ............................................................................................................. 9

2.4.2 Structuredness: .................................................................................................. 10

Robustness and integrity of the structure ................................................................. 10

2.5.1 Robustness: ........................................................................................................ 10

2.5.2 Design of a robust structure resistant to different loading events: .................. 10

2.5.3 Redundancy, ductility and continuity: ............................................................... 11

2.5.4 Redundancy: ....................................................................................................... 11

2.5.5 Ductility: ............................................................................................................. 11

Structures that have experienced progressive collapse: .......................................... 12

Mohammed Odeh

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2.6.1 Ronan point: ....................................................................................................... 12

2.6.2 Skyline Plaza: ...................................................................................................... 13

3 Method: ............................................................................................................................ 14

Introduction: .............................................................................................................. 14

Alternate load path method: ..................................................................................... 14

3.2.1 Removal of load bearing components: .............................................................. 14

3.2.2 Primary and secondary components: ................................................................ 15

3.2.3 Force and deformation controlled actions: ....................................................... 16

Linear static procedure: ............................................................................................. 17

3.3.1 Analytical modelling: .......................................................................................... 17

3.3.2 DCR limitation: ................................................................................................... 17

3.3.3 Load cases: ......................................................................................................... 17

3.3.4 P-Δ Effects: ......................................................................................................... 17

3.3.5 Deformation controlled actions QUD: ................................................................. 17

3.3.6 Force controlled actions QUF: ............................................................................. 18

3.3.7 Load increase factor: .......................................................................................... 18

3.3.8 Component and Element acceptance criteria: .................................................. 19

Non-linear static procedure: ..................................................................................... 20

3.4.1 Geometric and material nonlinearity: ................................................................ 20

3.4.2 Analytical modelling: .......................................................................................... 22

3.4.3 Stability/ P-delta effects: .................................................................................... 22

3.4.4 Loads: ................................................................................................................. 23

3.4.5 Loading procedure: ............................................................................................ 23

3.4.6 Dynamic increase factor and yield rotation: ...................................................... 23

3.4.7 Hinge and plastic rotation: ................................................................................. 25

3.4.8 Component and Element acceptance criteria: .................................................. 25

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4 Analysis: ............................................................................................................................ 27

Introduction: .............................................................................................................. 27

Structural specifics of building: ................................................................................. 27

Structure performance levels: ................................................................................... 29

Overdesigned column and beam section sizes: ........................................................ 29

Loading assumptions: ................................................................................................ 29

Column removal positions for LSP and NLSP: ........................................................... 29

4.6.1 1st column removal scenario: ............................................................................. 30

4.6.2 2nd column removal scenario: ............................................................................ 30

4.6.3 3rd column removal scenario: ............................................................................. 31

Linear static procedure: ............................................................................................. 31

4.7.1 DCR and irregularity check: ................................................................................ 31

4.7.2 Primary and secondary component classification: ............................................ 31

4.7.3 Classifying deformation and force controlled actions: ...................................... 31

4.7.4 m-factors for deformation and force controlled actions: .................................. 32

4.7.5 Load increase factors: ........................................................................................ 32

4.7.6 Required load combinations for a LSP: .............................................................. 33

Progressive collapse analysis results: ........................................................................ 34




Acceptance criteria for linear static analysis: ............................................................ 38



4.9.3 3rd column removal scenario .............................................................................. 42

Non-linear static analysis: .......................................................................................... 44

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4.10.1 Primary and secondary component classification: ............................................ 44

4.10.2 Placing plastic hinges on the non-linear model: ................................................ 44

4.10.3 Beam and column hinges: .................................................................................. 45

4.10.4 Connection hinges: ............................................................................................. 45

4.10.5 Dynamic increase factor for non-linear static procedure: ................................. 46

4.10.6 Non-linear Loading applied on frame: ............................................................... 48

Running the nonlinear static analysis: ....................................................................... 49

4.11.1 Progressive collapse analysis results: ................................................................. 49

Acceptance criteria for non-linear static analysis: .................................................... 50

5 Discussion: ........................................................................................................................ 51

Discussion for linear static analysis: .......................................................................... 51




Discussion for non-linear static analysis:................................................................... 52


6 Conclusion and Recommendations: ................................................................................. 54

Conclusion ................................................................................................................. 54

Recommendations for further work: ........................................................................ 55

7 References: ....................................................................................................................... 57

8 Appendices: ....................................................................................................................... 60

Appendix A: ................................................................................................................ 60

8.1.1 X-Z side view frame element number: ............................................................... 60

Appendix B ................................................................................................................. 63

8.2.1 Hinge status of each hinge formed throughout the structure: ......................... 63

Mohammed Odeh

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1 Introduction

General overview

Progressive collapse can be classified as a collapse of a segment of a building generated by

failure of a certain section of the structure as a result of an abnormal event. The degree of

progressivity in a collapse can be determined by measuring the ratio of the collapsed area to

the area destroyed by the triggering event (GSA, 2013). Structures that have failed previously

such as the Ronan point had a ratio of the order of 20 and was clearly disproportionate as a

small explosion in the structure that did not kill someone within a few feet managed to

severely damage the structure.

New and existing structures should be designed to withstand progressive collapse as

catastrophic events are increasing nowadays. Worldwide, several design codes which include

methods of reducing the possibility of progressive collapse are provided by the UFC, GSA and

Eurocode 1. The UK and European codes of practice suggest the tying force method to mitigate

progressive collapse but unfortunately do not taken into consideration explosions and

terrorist attacks when designing a structure.

American design codes recommend two approaches to use, which are the direct and indirect

methods. When considering the direct methods, the Alternate Load Path and the Enhanced

Local Resistance method can be used. In the ALP method, the structure must be able to bridge

over a removed structural component and ensure that the degree of damage is less than the

maximum damage limits. Another method which can be used is the ELR method as it increases

the shear and flexural strength of the structural members by decreasing the possibility and

extent of initial damage. Meanwhile, indirect approaches aim to improve the structural

integrity of the building.

Aims of the dissertation:

The aim of this dissertation is to construct a 10 storey structure using a 3D model on SAP2000,

and examine its structural response after removing a vertical load bearing element under

three different column removal scenarios. The Alternate Load Path method adopted from the

UFC and GSA guidelines shall be used and two approaches will be carried out for the analysis.

A linear static approach will be used followed by a non-linear static approach.

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Subsequent chapters:

The following report is split into 6 chapters:

Chapter 1 introduces the term progressive collapse and states which guidelines are used to

mitigate progressive collapse in structures.

Chapter 2, presents the background and history of progressive collapse. In addition, collapse

promoting features and different types of progressive collapse were discussed. Progressive

collapse guidelines used in the United States and Europe were presented. Lastly, previous

structures that have failed were listed such as Ronan Point and Skyline Plaza.

Chapter 3 gives a detailed description of which analysis procedure shall be used for this report.

The method chosen was the Alternate Load path method and was obtained from the UFC and

GSA progressive collapse guidelines.

Chapter 4 provides calculations for the analysis chosen and the structure used will be tested

using the linear and non-linear static approach.

Chapter 5 analyses the results obtained in chapter 4 and gives a detailed discussion for both

the linear and non-linear static analysis.

Chapter 6 summarises the work carried out throughout the report and suggests further work

that can be done to improve the issues in the field of progressive collapse.

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2 Literature review:

Introduction

Following the collapse of World Trade Centre, structural safety has become a key concern

when designing complex buildings. One of the mechanisms of structural failure that has

received considerable attention following the collapse of the Ronan point structure is

progressive collapse. Progressive collapse occurs when several structural members fail either

by accidents, earthquakes or attacks. Moreover, during a progressive collapse, every load

acting on the structure would redistribute unevenly causing the failure of other structural

elements until catastrophic failure occurs. The field of structural response to abnormal events

whether accidental or intentional has gathered and detailed research has been undertaken to

make new and existing structures safer following the unfortunate events of September 11,

2001.

Guidelines available for progressive collapse analysis

2.2.1 Guidance and formal provisions:

The first formal guidance published which included the terms disproportionate and robust

was the CP 110 code of practice for concrete (BSI, 1972) in 1972 which stated that there should

be a high chance that the structure will not collapse catastrophically after an incident has

occurred. After Ronan Point collapsed, the Institution of Structural Engineers published a

paper before the CP 110 code of practice, which recommended that a continuous framed

structure should resist irregular loads as long as it was designed to accord to the codes of

practice available.

2.2.2 European and UK design codes:

2.2.2.1 Eurocode 1: Actions on structures – Part 1-7: General actions – Accidental actions:

Eurocodes are a broad set of standards intended to cover all parts of structural design using

conventional construction materials (Vidalis, 2014). It must be noted that when choosing

certain factors for design, they can differ from one country to another and can be located in

the National Annex. In terms of robustness, clauses relating to it can be found in Part 1-7 of

the BS EN 1991 (BSI, 2006). In addition, the UK implementation of Eurocode BS EN 1090 states

that a building has to be designed in a certain manner that it does not fail to a degree

disproportionate to the cause if an event such as an explosion occurs.

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Unfortunately, the Eurocode does not taken into account accidental actions that are caused

by an external source so when designing a structure against a terrorist attack the guidelines

used are the ones for an unspecified accidental action.

Figure 2.1: Strategies for accidental design situations (BS EN 1991-1-7:2006)

2.2.2.2 Approved document A of the Building Regulations:

In England, the approved document A offers guidance on applying the robustness requirement

A3 of the Building regulations, and states that the building shall be built in a way that if an

incident occurs it will not collapse to a level disproportionate to the cause (Building

Regulations, 2010).

Buildings are split into several classes and are categorized depending on the type of occupancy

and number of storeys (Vidalis, 2014). A summarized table is provided below:

Figure 2.2: Summary of requirements of each building class (Vidalis, 2014)

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For class 1 buildings, steel beams and connections are required to withstand a tension capacity

force of 75 kN (Vidalis, 2014). For class 2A buildings, horizontal ties with a minimum capacity

of 75 kN are introduced in order to increase the structural stability (Vidalis 2014). Class 2B

buildings requires the floor area at any floor at risk of collapse should not be greater than 15%

of the floor area of that floor (Vidalis, 2014). Class 3 buildings need to evaluate risk in order to

foresee all normal and abnormal hazards during the life span of the building.

2.2.3 United States of America Codes and design guidelines:

The United States of America have published two guidelines that address progressive collapse

in structural systems. The two documents are the Unified Facilities Criteria (UFC, 2013) and

the General Services Administration progressive collapse guidelines (GSA, 2013). These

guidelines follow 3 approaches which are the tie force, ALP and ELR method.

2.2.3.1 General Services Administration 2013:

The GSA guidelines aim to decrease the possibility of progressive collapse in recently built and

existing buildings, and encourage possible improvements to facilities if needed. GSA focus on

providing ways to protect the public and federal buildings by minimising the possibility of

progressive collapse. Two approaches could be used to minimize progressive collapse, the first

approach limits the initial damage through hardening of structural components (Marchand,

2015), while the second approach limits the propagation of the initial damage without

consideration for the cause of the event (GSA, 2013). Before designing the structure against

progressive collapse, it is essential to examine certain building attributes. Figure 2.3 below

lists the most important attributes:

Figure 2.3: GSA criteria for detailed building progressive collapse design (GSA, 2013)

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The details above indicate that a linear analysis is required, either a static or dynamic analysis

for structures less than 10 storeys. For structures constructed which rise higher than 10

storeys a non-linear dynamic analysis would be preferred.

2.2.3.2 United Facilities Criteria of the Department of Defence:

UFC provide design requirements needed to reduce progressive collapse in structures that

have experienced severe structural damage through abnormal events. Similar to the Approval

Document A, depending on size and importance of structure, three basic approaches can be

used, which are the tying force, ALP and ELR method. UFC split their buildings into 4 categories

which is based on occupancy of the building (UFC, 2013). Occupancy category I does not need

any progressive collapse design. For Occupancy category ii, there are two routes to use, the

first route requires the tie forces for the whole structure and ELR for the corner columns, while

the other route determines several alternate paths for specific column removal locations. For

Occupancy category iii, the ALP and ELR method could be used while the OC iv can use ALP,

ELR and tie forces (UFC, 2013).

Types of progressive collapse:

Progressive collapse of structures is essentially considered as a disproportion in size between

a triggering incident and the resulting collapse (Starossek, 2006).

Listed below are several forms of progressive collapse:

1. The pancake type collapse

2. The domino type collapse

3. The mixed typed collapse

2.3.1 Pancake type collapse:

Generally this type of collapse offers the least chance of survival for victims as progressive

collapse occurs in a vertical motion. During a pancake collapse, a large pile of debris forms and

floors collapse on each other. The collapse of the World Trade centre towers illustrates this

collapse as the building failed due to the failure of the vertical load bearing elements.

Originally, collapse occurred only in a few floors but it gradually extended to the entire cross

section of the structure and led to the segregation of key structural elements.

The following features are associated with a pancake type collapse (Starossek, 2009):

- Initially vertical load bearing components fail

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- Fractional or total segregation and components fall in a vertical direction

- GPE is converted into KE

- Falling components impact on the remaining part of structure

Figure 2. 4: Pancake type collapse of the World Trade Centre towers in 2001 (Sharp printing, n.d.)

The pancake type collapses has several key features which include the segregation of

mechanical components, the rate of impact forces and the release of potential energy.

Potential energy released during collapse is governed by the weight and magnitude of the

falling components and at what height they fell from. During collapse, the potential energy

exceeds the strain energy present throughout the structure. Furthermore, energy would be

reinstated into the building and large internal forces will form. Other features of interest are

the propagating action, principal forces of the failing elements and the direction of the failure

propagation (parallel) (Starossek, 2009).

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2.3.2 Domino type collapse:

A domino type collapse can be characterized as a row of domino collapses in a chain reaction

which occurs when one elements fails at the push of the finger (Starossek, 2009).

Figure 2. 5: Domino type collapse (Vasilieva, 2013)

Mechanisms behind this type of collapse is (Starossek, 2009):

- Overturning of a structural component;

- GPE turns into KE;

- Overturning of the adjacent structural elements as a result of the horizontal pushing

force from the falling elements.

Domino and pancake type collapses are somewhat similar in regards to the occurrence of

impact forces. However, the forces present in the failing elements act in an orthogonal

direction and act as a parallel load transfer system until collapse occurs. Domino type collapses

have other features that distinguish it from pancake type and zipper collapses such as the

overturning of individual elements and the forces that cause the components to fail do not

act in direction of the principal forces transmitted (Starossek, 2009).

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2.3.3 Mixed-type collapse:

2.3.3.1 Murrah Federal building (Oklahoma city, 1995):

The 9-storey structure experienced two types of progressive collapse following the terrorist

attack in 1995, which were the pancake and domino type collapses. After the initial blast, the

concrete columns failed which resulted in the brittle failure of another two columns. In

addition, Suspended transfer girders placed on the exterior columns failed as there was no

support which resulted in the collapse of the upper floors. The horizontal tensile forces led to

overturning of other structural elements and could have been induced by the falling

components (Starossek, 2009).

Figure 2. 6: Mixed type collapse (Jenkins, 2012)

In some specific structures, several features of the different collapses combine and form

progressive collapse. For example, the zipper type collapse could involve the buckling of

columns, which could lead to overloading, and buckling of adjacent columns while stiffness

could be reduced as the propagating action can consist of destabilization, which is a feature

associated with an instability type collapse (Starossek, 2006).

Collapse-promoting features

2.4.1 Dynamic action, force concentration, brittle material behaviour and ductile material

behaviour:

There are several collapse features that have not been mentioned such as the dynamic action,

force concentration and brittle material behaviour (Starossek, 2006). Dynamic action was

initially associated with a pancake collapse but it may affect other discussed type of collapses.

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Failure in one element will induce a concentration force to another element which is likely to

fail. With time the material of the element is likely to fail as it becomes brittle as a result of

the dynamic action and force concentration (Starossek, 2006). Ductile materials are able to

absorb kinetic energy and redistribute forces which reduces the concentration force.

2.4.2 Structuredness:

Another essential feature that is important when considering types of collapses is

structuredness as it is the degree to which a system holds a certain pattern of organization of

its independent units (Starossek, 2009). For example, a building with a pattern of beams

(horizontal) and columns (vertical) is highly structured whereas a reinforced concrete

industrial tube is not. Structuredness is associated with pancake and domino collapses but not

an essential condition when considered for a zipper, section and instability type collapse.

Robustness and integrity of the structure

2.5.1 Robustness:

The awareness towards robustness of structures has significantly increased over time due to

the collapse of several high profile structures. Robustness can be considered as a characteristic

of a structural network that relates to its capability to achieve its purpose when adverse events

occur (Holický, 2012). Robustness is a desirable property of structural systems as it mitigates

its susceptibility to progressive collapse and is insensitive to local failure, which indicates that

it is purely a structural property (CPNI, 2011).

Terrorist attacks have increased the need for development of rational approaches and it is

essential to ensure that risks to people, assets and environment are acceptable to society. A

large amount of research has been undertaken with regards to the several features of

robustness, which resulted in numerous useful recommendations amongst experts in the field

of civil engineering. However, with all the theoretical and technological advances, structural

robustness is a cause of concern and poses many difficulties with regards to its interpretation.

2.5.2 Design of a robust structure resistant to different loading events:

The first step required to design a robust structure resistant to different loading throughout

its life span is the knowledge of previous failure mechanisms of existing constructions.

Generally experience and judgment receive less attention in literature than for example the

description of recently constructed and efficient structural designs (Bangash, 2006). A full

analysis of failure cases can be as useful as presentations of great engineering landmarks as

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the information gives a detailed overview of the safety and reliability of structures and

provides several ways of improving the design codes, hazard scenarios and possible risk

situations.

2.5.3 Redundancy, ductility and continuity:

Several factors have been associated with structural robustness such as redundancy and

ductility. In relation to buildings subject to sudden column removal, it can be seen that each

of these factors can have a significant effect on limit state and may sometimes not be

appropriate as measures of robustness.

2.5.4 Redundancy:

The ability of a structural system to carry a load after a member reaches its maximum capacity

can be defined as structural redundancy (Gurley, 2008). Redundancy allows the system to

carry additional load after the component reaches its strength limit by redistributing the

additional load across other members that have not reached their maximum capacities. A

system can be classified as nonredundant when one element fails and results in the failure of

another element, which in turn leads to failure throughout the structure. Increasing structural

robustness through redundancy maybe be carried out if there are more alternate load paths

available.

2.5.5 Ductility:

The role ductility plays cannot be understated in absorbing the energy and altering the

structural behaviour under the effect of an earthquake loading or explosion (Smilowitz, 2012).

Smilowitz believed that the ductility of the steel tube system was one of the key reasons in

decreasing the effects of the explosion that occurred in the World Trade Centre (Smilowitz,

2009). Ductility is defined as the ability of material to endure large deformations without

rupture before failure. It is beneficial to the occupants of structures, as if overloading occurs

and the structure is about to collapse it provides warning to the occupants, which ultimately

reduces loss of life. Ductility can be increased in steel structures by an increase in compression

steel content and decreased by an increase in tension steel content.

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Structures that have experienced progressive collapse:

2.6.1 Ronan point:

Figure 2. 7: Ronan point collapse which killed 4 people and injured 17 (http://www.debunking911.com/WTC7.htm)

The 22-story building was built in London and was composed of precast concrete structural

elements. Partial collapsed occurred in 1968 as a result of a gas explosion on the 18th floor

(Pearson, 2006). The resulting pressure of the explosion passed through the walls of the room

and destroyed a vertical load-bearing wall, which led to the partial collapse of a corner of the

structure (Pearson, 2006). Progressive collapse ensued when the walls of the southeast corner

on floors 19 through 22 completely collapsed (Pearson, 2006). Afterwards, progressive

collapse increased as floor 18 was overloaded by the impact of the collapsed floors above

(Pearson, 2006). No alternate load paths existed that allowed for redistribution of loads which

led to the immediate re-evaluation of the codes governing construction and design methods

(Pearson, 2006). There were major changes in building codes following the collapse of the

structure as it became a requirement to consider external actions when designing a structure.

Years after the collapse the building was dismantled and the results indicated that the

structure lacked structural robustness.

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2.6.2 Skyline Plaza:

Skyline Plaza was a large complex located in Bailey’s crossroads, which was under construction

when progressive collapse occurred in 1973. Construction workers were pouring concrete

into the buildings in the complex when progressive collapse took place in the centre of the

building. Collapse occurred due to the increased shear forces around the columns as a result

of the premature removal of forms supporting the 23rd floor (Schellhammer, 2013). The freshly

poured concrete did not reach its full strength capacity when collapse occurred and was

unable to resist the increased forces. The trigger mechanism of the resulting collapse was

shear failure surrounding several columns on the 23rd floor. As these columns were unable to

support the structure, as a result several other columns were overstressed which led to the

complete collapse of the 23rd concrete floor slab onto the 22nd floor (Schellhammer, 2013).

Hence, increased loads were now present on the 22nd floor from the floors above and led to a

progressive collapse to the bottom floors.

Figure 2. 8: Skyline plaza collapse which killed 14 construction workers (http://www3.gendisasters.com/virginia/18405/bailey-039s-crossroads-va-high-rise-apartment-collapses-mar-1973)

Several important lessons were learned following the collapse of Skyline Plaza:

1. Construction loads have to be considered during design

2. Formwork and shoring plans need to be detailed

3. Concrete testing must be performed before the removal of shoring

4. In order to prevent progressive collapse redundancy within structural design is

essential

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3 Method:

Introduction:

The purpose of this phase is to advance progressive collapse methods and to establish the

required analysis procedures. Firstly, it is essential to determine which guidelines are suitable

to use for the analysis. European and British guidelines were not used in the analysis as they

do not take into consideration explosions and terrorist attacks when designing a structure.

Alternate load path method:

This approach uses three types of analysis which are the linear static, non-linear static and

the non-linear dynamic procedure (GSA, 2013). The alternate load path method is used when

a vertical structural component cannot offer the necessary tie strength or when a specific

vertical load bearing component is removed (GSA, 2013)

3.2.1 Removal of load bearing components:

The ALP method shall be used and it is essential to determine at which locations columns

should be removed. Columns are not removed randomly as UFC provides guidance to which

external or internal columns are removed (UFC, 2013).

UFC recommended column removal positions (UFC, 2013):

For external columns:

1. Corner of the structure

2. Middle of the long or short side of the structure

3. Adjacent to the corner of the building

For internal columns:

1. Columns close to the middle of the short side of the structure

2. At the Corner of the uncontrolled space

3. Columns near the long side of the structure

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Figure 3. 1: Recommended external column removal positions (GSA, 2013)

Figure 3. 2: Recommended internal column removal position (GSA, 2013)

3.2.2 Primary and secondary components:

Structural elements are termed as primary or secondary. Primary components enable the

building to resist collapse after a vertical load bearing component is removed (GSA, 2013).

While all other components can be defined as secondary components. Primary members

include connections which are partially restrained, while secondary components may be for

example, a steel gravity beam which is pinned at both ends of the girders and ignores any

flexural strength present at the connection (GSA, 2013).

16

3.2.3 Force and deformation controlled actions:

Actions are termed as deformation-controlled or force-controlled by using the component

force versus deformation curve.

Figure 3. 3: Deformation and Force-controlled actions (UFC, 2013)

A primary component may be classified as a deformation controlled action if it uses a type 1

curve and e is greater than or equal to 2g (UFC, 2013). Furthermore, a primary component

action may be force controlled if it uses a type 1 or 2 curve and e is less than 2g, or, in some

cases if it has a type 3 curve (UFC, 2013). Meanwhile, a secondary component action is

classified as a deformation action if it uses a type 1 curve for any given e/g ration or if it has a

type 2 curve and e is less than 2g (UFC, 2013). Moreover, a secondary component action can

be termed as a force controlled action only if it has a type 2 curve with e being less than 2g or

if it uses a type 3 curve (UFC, 2013).

Figure 3.4: Examples of Deformation and Force-controlled action from ASCE 41 (UFC, 2013)

17

Linear static procedure:

The linear static procedure determines the potential for collapse by finding the demand

capacity ratios of the structural members (UFC, 2013). If no structural irregularities exist within

the structure then the analysis may be carried out and it would not be essential to calculate

the DCRs. If structural irregularities exist then the analysis can only be carried out if all of the

member DCRs are less than or equal to two.

3.3.1 Analytical modelling:

The linear 3D model includes all primary and secondary components except the removed

column.

3.3.2 DCR limitation:

The deformation controlled load case is used which includes the gravity and live loads and are

increased by the load increase factor ΩLD. The resulting actions are defined as QUDLim:

DCR = QUDLim /QCE (3.1), where QCE = Expected strength of the element.

3.3.3 Load cases:

Two different load cases are used which are the deformation and force-controlled actions.

3.3.4 P-Δ Effects:

A P-Δ analysis is not carried out for a linear analysis due to the small deformations present.

3.3.5 Deformation controlled actions QUD:

The following load combinations are applied when determining the deformation controlled

actions (UFC, 2013):

1) Gravity loads are placed on the adjacent bays to the detached component and at all

areas above the removed component.

GLD = ΩLD [1.2 D + (0.5L or 0.2S)] (3.2)

Where GLD = Increased gravity loads

D = Dead load (kN/m2)

S = Snow load (kN/m2)

L = Live load (kN/m2)

ΩLD = Load increase factor

18

2) Gravity loads for floor areas away from removed column:

G (Gravity load) = 1.2 D + (0.5L or 0.2S) (3.3)

3.3.6 Force controlled actions QUF:

The following load combinations are applied when determining the force controlled actions

(UFC 2013):

1) Gravity load combinations are placed on the adjacent bays to the detached component

and at all areas above the removed component.

GLF = ΩLF [1.2 D + (0.5L or 0.2S)] (3.4)

Where GLF = Increased gravity loads

D = Dead load (kN/m2)

S = Snow load (kN/m2)

L = Live load (kN/m2)

ΩLD = Load increase factor

2) Gravity loads for floor areas away from removed column:

G (Gravity load) = 1.2 D + (0.5L or 0.2S) (3.5)

3.3.7 Load increase factor:

Values of load increase factors for deformation and force controlled actions for columns are

listed below:

Figure 3.5: Dynamic load increase factors for Linear Static Analysis (UFC, 2013)

The values of ΩLD and ΩLF depend on the material used for the frame. mLIF is the lowest m value

of any primary beam linked to the columns or directly over the column removal position (UFC,

2013)

19

Figure 3.6: Loads and Load positions for external and internal columns (UFC, 2013)

3.3.8 Component and Element acceptance criteria:

3.3.8.1 Deformation controlled actions:

All primary and secondary components must satisfy the following equation (UFC, 2013):

Φ m QCE ≥ QUD (3.6)

Where,

20

QUD = Deformation-controlled action

m = Element demand modifier (m-factor)

Φ = Strength reduction factor

QCE = Expected strength of the component

Note, QCE is calculated by considering all existing actions on the element

3.3.8.2 Force controlled actions:

All primary and secondary components must satisfy the following equation (UFC, 2013):

Φ QCL≥ QUF (3.7)

Where,

QUF = Force-controlled action

QCL = Lower-bound strength

Φ = Strength reduction factor

Note, QCL is calculated by considering all existing actions on the element

Non-linear static procedure:

The LSP does not predict in detail how a structure responds to the loss of a primary member.

Therefore, to further our understanding on the performance of a building undergoing

progressive collapse, a nonlinear procedure is required even though it is more sophisticated.

In a NLS analysis, it is essential to consider material and geometric nonlinear behaviours.

3.4.1 Geometric and material nonlinearity:

When structural members experience large deformations due to localised damage, geometric

nonlinearities develop and have an effect on the internal forces throughout the structure.

Generally, the geometric nonlinearity associated with progressive collapse is the P-Delta

effect. For this analysis, the P-Delta effect causes several changes in shear, overturning

moments and axial force spreading at the base when a building is subjected to a large lateral

displacement. The magnitude of these effects is related to the slenderness of elements,

stiffness of the building and the magnitude of the axial load applied P. The non-linear static

21

analysis allows several nonlinear conditions to be considered, which include both P-delta

effects and stress stiffening.

Carrying out a P-delta analysis only is not sufficient in progressive collapse as material yielding

occurs along with large deformations. During progressive collapse, several structural elements

shall exceed their elastic load limit and undergo plastic yielding. When flexural components

deform elastically their extreme fibers reach their ultimate yield capacity and become

nonlinear. After yielding, the material becomes strained to a degree that the stress-strain

behaviour becomes nonlinear and results in a change of stiffness.

Implementing a nonlinear analysis accurately captures the behaviour of the structure and it is

essential to define and assign plastic hinges to beams and columns.

Figure 3.7: Force displacement curve (FEMA356, 2000)

Hinge properties are assigned to every structural frame element and for each degree of

freedom there is a corresponding force-displacement curve that displays every yield value and

plastic deformation after yielding.

Point What it represents

A The origin

B Yielding and no deformation occurs up until point B

C Ultimate limit capacity

D Residual strength

E Total failure

Table 3.1: Summarizing definitions of points A, B, C, D and E (FEMA356, 2000)

22

Each building performance level includes a structural performance level which describes the

damage state of the structure. For example, when a structural component moves into

plasticity, the extent of its damage can be termed as either operational, immediate occupancy,

life safety or collapse prevention.

Figure 3.8: Target Building Performance Levels and Ranges (FEMA356, 2000)

3.4.2 Analytical modelling:

A 3D model is used and whether to include secondary components or not is up to the author.

If secondary components are not used in the analysis, they need to be compared against the

allowable deformation criteria as to check for the connections of gravity beams and the chord

rotation versus the allowable plastic rotation angle (GSA, 2013).

3.4.3 Stability/ P-delta effects:

Overall lateral torsional buckling must be considered when running the analysis.

23

3.4.4 Loads:

A gravity load combination must be applied to calculate the force and deformation controlled

actions. Firstly, increased gravity loads are applied to floor areas above the removed column

and to bays immediately adjacent to the removed structural component by applying the

following equation (UFC, 2013):

GN = ΩN [1.2 D + (0.5 L or 0.2 S)] (3.8) , Where,

GN Increased gravity loads

L Live load (kN/m2)

S Snow load (kN/m2)

D Dead load (kN/m2)

ΩN Dynamic increase factor

Table 3.2: Defining each component used (UFC, 2013)

Another gravity load combination can be used for floor areas away from the removed column

and is applied to bays not loaded with GN (UFC, 2013):

G = 1.2 D + (0.5 L or 0.2 S) (3.9)

3.4.5 Loading procedure:

A load history must be used which begins with zero and is gradually increased to the required

final results. A minimum of 10 load steps are needed to reach the complete load and SAP2000

must incrementally increase the load and iteratively reach convergence before proceeding to

the following load increment (UFC, 2013).

3.4.6 Dynamic increase factor and yield rotation:

The lowest fraction of θpra/θy for any primary component or connection must be used to

determine the dynamic increase factor.

24

Figure 3.9: Dynamic increase factors for nonlinear static analysis (UFC, 2013)

Where, θpra is the plastic rotation angle given in the acceptance criteria tables in ASCE 41. For

steel, θy is the yield rotation and is given in Equation 5-1 in ASCE 41.

For steel beams and columns, ASCE41 calculates θ using the equations below and assumes

that the point of contraflexure occurs at the middle of the column or beam.

Beams: θ𝑌 = 𝑍∗ 𝐹𝑦𝑒∗𝐿𝑏

6∗𝐸∗𝐼𝐵 (3.10) Columns: θ𝑌 = (

𝑍∗𝐹𝑦𝑒∗𝐿𝑐

6∗𝐸∗𝐼𝐶)(

1−𝑃

𝑃𝑦𝑒) (3.11)

Where,

Z Plastic section

modulus

Fye Expected yield

capacity

E Young’s modulus

L Length

I Second moment

of area

Table 3.3: Defining each component (UFC, 2013)

For steel structures, multiples of yield rotation are used to classify the acceptance criteria in

terms of plastic rotation for several structural components

25

3.4.7 Hinge and plastic rotation:

Plastic rotation may be considered as a inelastic rotation which occurs when the yield rotation

is achieved and the entire area has yielded. Figures 3.10 and 3.11 define total, yield and plastic

rotation:

Figure 3.10: Plastic hinge and rotation (UFC, 2013)

Figure 3.11: Defines yield, total and plastic rotation (UFC, 2013)

3.4.8 Component and Element acceptance criteria:

3.4.8.1 Deformation-Controlled Actions:

The deformation capacities of the structural components should be greater than the

maximum calculated deformation demands. All coexisting forces and deformations should be

considered when determining the expected deformation capacities.

26

3.4.8.2 Force controlled actions:

The following equation applies for all structural components:

Φ QCL ≥ QUF, where

QUF Force controlled action

QCL Lower bound strength

Φ Strength reduction factor

Table 3.4: Defining each value (UFC, 2013)

Note, QCL is calculated by considering all existing actions on the element.

27

4 Analysis:

Introduction:

This part of the project requires an analysis of a multi-store building under different damage

scenarios using a computer software called SAP2000. These scenarios involve the removal of

different structural components, which represent local damage and examines how they affect

the robustness of the structure. A linear and non-linear analysis will be used but before

carrying out the analysis the geometric parameters of the building must be defined.

Structural specifics of building:

The structure used in this analysis was obtained from Stefan Szyniszewski’s article for energy

flow in progressive collapse of steel framed buildings (Szyniszewski, 2012). A former student

at the University of Surrey, Alexandra Koufoudakis, used the same structure for her

dissertation but she transformed the member and section sizes from American sections to

Eurocode sections. For this analysis, member and section sizes were increased throughout the

structure to determine whether progressive collapse may occur in overdesigned structures.

Figure 4.1: 3D view of structure (SAP2000)

28

Figure 4.2: Side view of structure (SAP2000)

Computer software used: SAP2000 (3D model used)

Structure has 10 floors

Height of each floor is 3 m

Elevations in the X-Z and Y-Z directions have the same number of bays (5)

Length of each bay: 9.2 m

Beams and columns are made out of steel while the material used for the slab is concrete

Structure is analysed as a moment resistance steel frame building

Columns are pinned at the base to resist moments created during column removal

scenarios

Table 4.1: Structural details of structure (SAP2000)

29

Structure performance levels:

Welded unreinforced flange fully restrained moment connections are used to resist the

moment resistance throughout the structure. These connections are fully penetrated welds

between beams and columns and transfer forces throughout the structural components but

increase the connection’s moment resistance.

Overdesigned column and beam section sizes:

Floor

Internal beams

External beams

Internal

columns

Peripheral

columns

Corner

columns

1,2,3 838x292x226 838x292x176 356x406x551 356x406x393 356x406x235

4,5,6 838x292x226 762x267x147 356x406x340 356x406x235 356x368x202

7,8,9 838x292x226 686x254x140 356x406x235 356x368x153 356x368x153

10 (roof) 762x267x147 686x254x170 356x368x177 356x368x129 305x305x283

Table 4.2: Overdesigned section members (Author of the report)

Loading assumptions:

The dead and live loads acting on the structure are summarized in the table below:

Dead load 6.25 kN/m2

Live load 4 kN/m2

Table 4.3: Assumed loads (Szyniszewski, 2012)

Column removal positions for LSP and NLSP:

Three column removal scenarios will be analysed. Firstly, a corner column on the ground floor

will be removed, secondly, the external column close to the middle of the long side of the

ground level will be removed. For the third column removal scenario, an internal column on

the 6th floor will be removed.

30

4.6.1 1st column removal scenario:

Figure 4.3: Corner column removal scenario (SAP2000)

4.6.2 2nd column removal scenario:

Figure 4.4: External column removal scenario (SAP2000)

31

4.6.3 3rd column removal scenario:

Figure 4.5: Internal column removal scenario (SAP2000)

Linear static procedure:

4.7.1 DCR and irregularity check:

There are no vertical discontinuities and the stiffness does not vary at corner columns,

therefore, the linear static procedure may be used.

4.7.2 Primary and secondary component classification:

All structural components are classified as primary. In addition, they provide capacity to

withstand collapse after a column is removed.

4.7.3 Classifying deformation and force controlled actions:

Two analyses will be run, the deformation controlled analysis will present moments, while the

force controlled analysis presents shear force values.

32

4.7.4 m-factors for deformation and force controlled actions:

The m-factor differs for force and deformation controlled actions. For force controlled action,

the m-factor is 2.0, while the m-factor for the deformation controlled action depends on the

depth of the beam (UFC, 2013). The following equation used to calculate the m-factor can be

found in table 5-1 of the UFC progressive collapse manual.

For primary components and fully restrained WUF moment connections:

m-factor = 4.3 – 0.083d (4.1), where d = depth of beam section (inches)

Beam location

Beam size

Beam component

m-factors

WUF connection

m-factors

1,2,3 838x292 x176 5.85 1.572

4,5,6 762x267x147 6.4 1.836

7,8,9 686x254x140 6.97 2.067

10 (roof) 686x254x170 6.65 2.036

Internal beams(roof) 762x267x147 6.4 1.836

Internal beams(1-9) 838x292x226 5.93 1.520

Table 4.4: m-factor values (UFC, 2013)

4.7.5 Load increase factors:

Load increase factor for force-controlled actions:

For steel frame structures, the load increase factor ΩLF, will always be equal to 2.

Load increase factor for deformation-controlled actions:

ΩLD = 0.9 mLIF +1.1 (4.2), where mLIF is the smallest m-factor of any primary component.

ΩLD = 0.9(1.520) + 1.1= 2.468

33

4.7.6 Required load combinations for a LSP:

4.7.6.1 Bays directly above and adjacent to removed column

For deformation-controlled actions:

GLD = ΩLD [1.2 D + (0.5L or 0.2S)]

Floors 1-9 (3.2):

GLD = 2.468[1.2(6.25) + (0.5(4))] = 23.45kN/m2

Roof (3.2):

GLD = 2.468[1.2(6.25) + (0.5(0))] = 18.51 kN/m2

For force-controlled actions:

Floors 1-9 (3.4):

GLF = 2[1.2(6.25) + (0.5(4))] = 19.00 kN/m2

Roof (3.4):

GLF = 2[1.2(6.25) + (0.5(0))] = 15.00 kN/m2

4.7.6.2 Floor areas away from removed column:

For deformation and force controlled actions:

G (Gravity load) = 1.2 D + (0.5L or 0.2S)

Floors 1-9 (3.3, 3.5):

G =1.2(6.25) + 0.5(4) = 9.50 kN/m2

Roof (3.3, 3.5):

G =1.2(6.25) + 0.5(0) = 7.5 kN/m2

34

Progressive collapse analysis results:


4.8.1.1 X-Z deformed shape of model:

Figure 4.6: X-Z façade deformed shape (SAP2000)

4.8.1.2 Deformation-controlled action results from SAP2000:

Figure 4.7: Deformation-controlled values (SAP2000)

35

4.8.1.3 Force-controlled action results from SAP2000:

Figure 4.8: Force-controlled values (SAP2000)



Figure 4.9: X-Z façade deformed shape (SAP2000)

36




Figure 4.11: Force controlled values (SAP2000)

37



Figure 4. 12: X-Z second section deformed shape (SAP2000)



38


Figure 4.14: Force-controlled values (SAP2000)

Acceptance criteria for linear static analysis:

After running the analysis using SAP2000, the demand capacity ratio of each structural

component must be compared to the acceptance criteria. For deformation-controlled actions,

m-factors of the structural components and connections are compared to the demand

capacity ratios to check whether structural members have failed (UFC, 2013). For force-

controlled actions, the DCR value must be less than 1. In addition, the acceptability of the

columns for the deformation-controlled model must be reviewed. The axial load ratio of any

column with a value greater than 0.5 must be redefined as a force-controlled action (UFC,

2013).


4.9.1.1 Beams and connections for both controlled actions:

Deformation Controlled values:

Floor

Frame (beam)

Section Size

Moment values

Φ mQCE ≥ QUD

m-factor

1 651 838x292x176 1.554 1.572

2 652 838x292x176 1.72 1.572

39

3 653 838x292x176 1.617 1.572

4 654 767x267x147 1.808 1.836

5 655 767x267x147 1.751 1.836

6 656 767x267x147 1.658 1.836

7 657 686x254x140 1.482 2.067

8 658 686x254x140 1.444 2.067

9 659 686x254x140 1.478 2.067

10 660 686x254x170 1.001 2.036

Table 4.5: Acceptance criteria for beams and connections (UFC, 2013)

Force controlled values:

Floor

Frame (beam)

Section Size

Shear values

Φ mQUD ≥ QCE

Compared

to

1 651 838x292x176 0.341 1

2 652 838x292x176 0.370 1

3 653 838x292x176 0.347 1

4 654 767x267x147 0.339 1

5 655 767x267x147 0.331 1

6 656 767x267x147 0.316 1

7 657 686x254x140 0.316 1

8 658 686x254x140 0.310 1

9 659 686x254x140 0.314 1

10 660 686x254x170 0.245 1

Table 4 6: Acceptance criteria for beams and connections (UFC, 2013)

4.9.1.2 Columns for both controlled actions:

Floor

Frame

(column)

Section size

P/Pcl

Classification

Interaction

values from

F-C case

1 351 356x406x393 Deleted Deleted Deleted

40

2 352 356x406x393 0.0147 D-C 2.012

3 353 356x406x393 0.0393 D-C 1.504

4 354 356x406x235 0.0671 D-C 1.377

5 355 356x406x235 0.0687 D-C 1.013

6 356 356x406x235 0.0669 D-C 1.019

7 357 356x368x153 0.0810 D-C 0.958

8 358 356x368x153 0.0607 D-C 0.777

9 359 356x368x153 0.0381 D-C 0.685

10 360 356x368x177 0.0086 D-C 0.776

1 291 356x406x393 1.252 F-C 1.553

2 292 356x406x393 1.109 F-C 1.709

3 293 356x406x393 0.959 F-C 1.600

4 294 356x406x235 1.374 F-C 2.041

5 295 356x406x235 1.160 F-C 1.870

6 296 356x406x235 0.947 F-C 1.731

7 297 356x368x153 1.157 F-C 1.973

8 298 356x368x153 0.857 F-C 1.726

9 299 356x368x153 0.561 F-C 1.443

10 300 356x368x177 0.224 D-C 1.350

Table 4.7: Acceptance criteria for columns (UFC, 2013)


4.9.2.1 Beams and connections for controlled actions:

Deformation Controlled actions:

Floor

Frame (beam)

Section size

(UB)

Moment values Φ m QCE ≥ QUD

m-factor

1 641 838x292x176 2.099 1.572

2 642 838x292x176 2.048 1.572

3 643 838x292x176 1.974 1.572

4 644 767x267x147 2.061 1.836

5 645 767x267x147 1.99 1.836

6 646 767x267x147 1.923 1.836

41

7 647 686x254x140 1.672 2.067

8 648 686x254x140 1.634 2.067

9 649 686x254x140 1.624 2.067

10 650 686x254x170 1.281 2.036

1 631 838x292x176 2.143 1.572

2 632 838x292x176 2.1 1.572

3 633 838x292x176 2.02 1.572

4 634 767x267x147 2.114 1.836

5 635 767x267x147 2.046 1.836

6 636 767x267x147 1.975 1.836

7 637 686x254x140 1.72 2.067

8 638 686x254x140 1.682 2.067

9 639 686x254x140 1.678 2.067

10 640 686x254x170 1.31 2.036 Table 4.8: Acceptance criteria for beams and connections (UFC, 2013)

Force controlled actions:

Floor

Frame

(beam)

Section size

Shear values

Φ m QCE ≥ QUD Compared to

1 651 838x292x176 0.341 1

2 652 838x292x176 0.37 1

3 653 838x292x176 0.347 1

4 654 767x267x147 0.339 1

5 655 767x267x147 0.331 1

6 656 767x267x147 0.316 1

7 657 686x254x140 0.316 1

8 658 686x254x140 0.31 1

9 659 686x254x140 0.314 1

10 660 686x254x170 0.245 1

Table 4. 9: Acceptance criteria for beams and connections (UFC, 2013)

4.9.2.2 Columns for controlled actions:

Floor Frame Section size Axial demand/capacity

Classification Interaction values from F-C case

(column) P/Pcl

1 231 356x406x393 Deleted Deleted Deleted 2 232 356x406x393 0.0257 D-C 0.945 3 233 356x406x393 0.0532 D-C 0.736 4 234 356x406x235 0.248 D-C 0.831

42

5 235 356x406x235 0.249 D-C 0.801 6 236 356x406x235 0.241 D-C 0.741 7 237 356x368x153 0.338 D-C 0.783 8 238 356x368x153 0.255 D-C 0.676 9 239 356x368x153 0.081 D-C 0.532

10 240 356x368x177 0.0286 D-C 0.418 1 291 356x406x393 1.319 F-C 1.686 2 292 356x406x393 1.159 F-C 1.863 3 293 356x406x393 0.998 F-C 1.716 4 294 356x406x235 1.422 F-C 2.163 5 295 356x406x235 1.199 F-C 1.978 6 296 356x406x235 0.978 F-C 1.848 7 297 356x368x153 1.191 F-C 2.102 8 298 356x368x153 0.833 F-C 1.848 9 299 356x368x153 0.578 F-C 1.561

10 300 356x368x177 0.236 D-C 1.497 1 171 356x406x393 1.307 F-C 1.68 2 172 356x406x393 1.15 F-C 1.867 3 173 356x406x393 0.991 F-C 1.72 4 174 356x406x235 1.412 F-C 2.16 5 175 356x406x235 1.191 F-C 1.978 6 176 356x406x235 0.973 F-C 1.845 7 177 356x368x153 1.186 F-C 2.095 8 178 356x368x153 0.88 F-C 1.843 9 179 356x368x153 0.577 F-C 1.552

10 180 356x368x177 0.235 D-C 1.487 Table 4.10: Acceptance criteria for columns (UFC, 2013)

4.9.3 3rd column removal scenario

4.9.3.1 Beams and connections for controlled actions:

Deformation controlled actions:

Floor Frame Section size Deformation controlled m-factor

Moment values

(beam) Φ m QCE ≥ QUD

1 461 838x292x176 0.322 1.572

2 462 838x292x176 0.353 1.572

3 463 838x292x176 0.392 1.572

4 464 838x292x176 0.46 1.836

5 465 838x292x176 0.769 1.836

6 466 838x292x176 1.346 1.836

7 467 838x292x176 1.247 2.067

8 468 838x292x176 1.205 2.067

9 469 838x292x176 1.175 2.067

43

10 470 767X267X147 1.653 2.036

1 471 838x292x176 0.303 1.572

2 472 838x292x176 0.347 1.572

3 473 838x292x176 0.398 1.572

4 474 838x292x176 0.478 1.836

5 475 838x292x176 0.787 1.836

6 476 838x292x176 1.513 1.836

7 477 838x292x176 1.413 2.067

8 478 838x292x176 1.355 2.067

9 479 838x292x176 1.287 2.067

10 480 767X267X147 1.619 2.036 Table 4. 11: Acceptance criteria for beams and connections (UFC, 2013)

Force controlled actions:

Floor Frame (beam)

Section size Shear values Φ m QCE ≥ QUD

Compared to

1 461 838x292x176 0.168 1

2 462 838x292x176 0.173 1

3 463 838x292x176 0.182 1

4 464 838x292x176 0.196 1

5 465 838x292x176 0.298 1

6 466 838x292x176 0.497 1

7 467 838x292x176 0.469 1

8 468 838x292x176 0.46 1

9 469 838x292x176 0.444 1

10 470 767X267X147 0.363 1

1 471 838x292x176 0.154 1

2 472 838x292x176 0.165 1

3 473 838x292x176 0.176 1

4 474 838x292x176 0.195 1

5 475 838x292x176 0.3 1

6 476 838x292x176 0.48 1

7 477 838x292x176 0.46 1

8 478 838x292x176 0.448 1

9 479 838x292x176 0.432 1

10 480 767X267X147 0.371 1

Table 4.12: Acceptance criteria for beams and connections (UFC, 2013)

4.9.3.2 Columns for controlled actions:

Floor Frame (column)

Section size Axial demand/capacity

P/Pcl

Classification

Interaction values from F-C case

1 141 356x406x551 1.31 F-C 1.22

44

2 142 356x406x551 1.223 F-C 1.137

3 143 356x406x551 1.138 F-C 1.059

4 144 356x406x340 1.728 F-C 1.6

5 145 356x406x340 1.61 F-C 1.5

6 146 356x406x340 1.435 F-C 1.806

7 147 356x368x235 1.624 F-C 2.172

8 148 356x368x235 1.182 F-C 1.768

9 149 356x368x235 0.753 F-C 1.396

10 150 356x368x177 0.447 D-C 1.18

1 81 356x406x551 0.687 F-C 0.653

2 82 356x406x551 0.585 F-C 0.555

3 83 356x406x551 0.475 D-C 0.437

4 84 356x406x340 0.583 F-C 0.53

5 85 356x406x340 0.369 D-C 0.345

6 86 356x406x340 Deleted Deleted Deleted

7 87 356x368x235 0.0385 D-C 0.143

8 88 356x368x235 0.0551 D-C 0.135

9 89 356x368x235 0.0582 D-C 0.133

10 90 356x368x177 0.0647 D-C 0.161

1 21 356x406x393 1.125 F-C 1.077

2 22 356x406x393 1.067 F-C 1.055

3 23 356x406x393 1.011 F-C 0.976

4 24 356x406x235 1.613 F-C 1.486

5 25 356x406x235 1.534 F-C 1.384

6 26 356x406x235 1.362 F-C 2.213

7 27 356x368x153 1.651 F-C 2.844

8 28 356x368x153 1.198 F-C 2.434

9 29 356x368x153 0.754 F-C 2.034

10 30 356x368x129 0.383 F-C 1.954 Table 4.13: Acceptance criteria for columns (UFC, 2013)

Non-linear static analysis:

4.10.1 Primary and secondary component classification:

All structural components are classified as primary. In addition, they provide capacity to

withstand collapse after a column is removed.

4.10.2 Placing plastic hinges on the non-linear model:

In numerical models such as SAP2000, connections are designed with plastic hinges. Plastic

hinges may form along the members and are based on maximum moment values obtained by

using over strength and phi factors. The FEMA 356 manual recommends that three plastic

hinges that should be assigned in the beams which are at the end points and centre of the

45

beam (FEMA356, 2000). In addition, it states that columns should be assigned hinges at both

ends of the columns only (FEMA356, 2000).

4.10.3 Beam and column hinges:

The beams and columns are automatically set default hinges through SAP2000. Beam hinges

must be assigned under deformation-controlled actions and the moments located are located

in the major axis M3. For columns, axial forces are present and transverse moments (M2 and

M3).

4.10.4 Connection hinges:

Connection hinges depend on the type of connection used and must be calculated manually.

Table 5-6 from the FEMA356 manual is used to determine the hinge parameters for the

connections. After calculating the required values, the hinge properties are assigned in

SAP2000. Table 4.13 and figure 4.15 show how the calculations are obtained and how

connection hinges are defined in SAP2000 for a 838x292x176 beam section.

Acceptance criteria

Modelling parameters Plastic rotation angle (rad)

Plastic rotation angle (rad)

Residual strength

ratio

Primary

Beam section a b c IO LS CP

Floor WUF connection

Depth of

section (in)

0.051-0.0013

d

0.043-0.0006d

0.2

0.0128-0.0003d

0.0337- 0.0009d

0.0284- 0.0004d

1,2,3 838x292x176 32.87 0.00827

0.0233 0.2 0.00294 0.00412 0.0153

4,5 762x267x147 29.685 0.0124 0.0252 0.2 0.00389 0.00698 0.0165

6,7 686x254x140 26.909 0.016 0.0269 0.2 0.00472 0.00948 0.0176

8 (roof) 686x254x170 27.28 0.0155 0.0266 0.2 0.00462 0.00915 0.0175

Internal beams

roof

762x267x147 29.685 0.0124 0.0252 0.2 0.00389 0.00698 0.0165

Internal beams

1-7

838x292x226 33.5 0.00745

0.0229 0.2 0.00275 0.00355 0.015

Table 4.14: Modelling parameters and acceptance criteria (FEMA356, 2000)

46

Figure 4.15: Moment rotation data for 838x292x176 WUF connection (SAP2000)

4.10.5 Dynamic increase factor for non-linear static procedure:

The nonlinear static dynamic increase factors are obtained from table 3-5 in the UFC

progressive collapse guidelines. θpra values are obtained from the acceptance criteria tables in

the ASCE 41 manual.

47

Floor

Structural

members

Depth of

section

(in)

Ib

(cm4)

θpra

(radians)

Z

(cm3)

θy

(rad)

Θpra/θY

1,2,3 838x292x176 32.87 246021 0.00412 6808 0.00702 0.5869

4,5,6 762x267x147 29.685 168502 0.00698 5156 0.00776 0.8995

7,8,9 686x254x140 26.909 136267 0.00948 4558 0.00848 1.1179

10 (roof) 686x254x170 27.28 170326 0.00915 5631 0.00838 1.0918

Internal

beams

(roof)

762x267x147

29.685

168502

0.00355

5156

0.00767

0.457474

Internal

beams 1-9

838x292x226

33.5

339704

0.0006

9155

0.00683

1.0220

Table 4.15: Values of θpra/θy (ASCE41, 2007)

Young’s Modulus of

steel

210,000 N/mm2

Yield strength of steel 355 N/mm2

Length of beams 9 m

Table 4.16: Given values (Author)

θpra/θy is the small ratio in any primary structural component in the model. Moreover the value

of θy was found by using the equation below:

θy = Z ∗ Fye ∗ 𝐿𝑏

6 ∗ 𝐸 ∗ 𝐼𝑏

The dynamic increase factor is calculated by using the equation from table 3.5 in the UFC

guidelines:

Ω𝑁 = 1.08 + 0.76

[(𝜃𝑝𝑟𝑎

𝜃𝑦+ 0.83)}

Ω𝑁 = 1.08 + 0.76

[(0.457 + 0.83)}= 1.591

48

4.10.6 Non-linear Loading applied on frame:

Equations 3.8 is applied to bays directly above and adjacent to the removed column:

GN = ΩN [1.2 D + (0.5 L or 0.2 S)

Floors 1-9:

GN = 1.591[1.2(6.25) + (0.5(4))] = 15.115 kN/m2

Roof:

GN = 1.591[1.2(6.25) + (0.5(0))] = 13.115 kN/m2

For gravity loads for floor areas away from removed column (3.9):

G (Gravity load) = 1.2 D + (0.5L or 0.2S)

Floors 1-9:

G = 1.2(6.25) + 0.5(4) = 9.5 kN/m2

Roof:

G = 1.2(6.25) + 0.5(0) = 7.5 kN/m2

49

Running the nonlinear static analysis:

4.11.1 Progressive collapse analysis results:

When running the overdesigned structure on SAP2000, plastic hinges did not form across the

beams and columns. As shown below:

Figure 4.16: Original overdesigned structure X-Z façade deformed shape (SAP2000)

Therefore, with the advice of the project supervisor, several section members were reduced

in order to form plastic hinges throughout the structure. Due to the scope of the project, only

the 1st column removal scenario was analysed for the non-linear static analysis.

Figure 4.17: X-Z façade deformed shape of the new designed structure with lower section sizes (SAP2000)

50

Figure 4.18: X-Z first section deformed shape (SAP2000)

Acceptance criteria for non-linear static analysis:

After running the analysis on SAP2000, the deformation controlled actions will be linked with

the acceptance criteria of the plastic hinge deformation with the aid of table 3.1 and figure

3.7. Moreover, the immediate occupancy, life safety and collapse prevention of the plastic

hinges will determine the degree of damage of the structure after a column is suddenly

removed (FEMA356, 2000). For the force-controlled actions, the assessment criteria follows

the same method used in the linear static analysis. In addition, Appendix B provides the hinge

status of each hinge formed throughout the structure.

51

5 Discussion:

Discussion for linear static analysis:

The m-factor approach for the linear static analysis is used as it is recommended by the UFC

and GSA guidelines. This approaches aims to approximate the dynamic nature of the load

redistribution by increasing the gravity loads and determine the ductile non-linear behaviour

of the building by increasing the capacity of the structural components (UFC, 2013). Gravity

loads are applied to the floor areas before running the linear static analysis and the gravity

loads floor areas directly above or adjacent to the removed columns were increased by

introducing a dynamic increase factor as they consider inertial effects and geometric non-

linearities (GSA, 2013). For force controlled actions, the dynamic increase factor has a fixed

value of 2.0 whereas for deformation-controlled actions the dynamic increase factor depends

on the depth of the beam and is manually calculated by using the UFC progressive collapse

guidelines (UFC, 2013).

A Linear static analysis is easy to perform, as the steps required to carry out the analysis are

straightforward. However, the linear static analysis has several limitations, firstly, it does not

consider dynamic effects. Secondly, it cannot provide accurate results when analysing

complex structures, as it is limited to simple structures with predictable behaviour. Lastly, the

linear static analysis does not take into account material nonlinear behaviour. Therefore, to

provide more accurate results, a non-linear analysis shall be carried out after completing this

analysis as it considers material and geometric nonlinearities


The analysis showed that the removal of the corner column triggered the failure of key

structural components throughout the structure. The members highlighted in red indicate

the members that did not meet the acceptance criteria while the orange and yellow members

indicated that the members were extremely close to failure. After removing the corner

column, the beams directly above the removed columns failed while the columns directly

above and adjacent to the removed column failed or were about to fail.

Failure in beams occurred due to the connections failure even though the member sections

passed the acceptance criteria with m factor values ranging from 5.85 to 7. Stronger

connections are required to avoid beam failure and progressive collapse in the structure.

52

Normally, failed columns must be redesigned and larger sections are needed but it may be

uneconomical to increase member sections as proved by this analysis. The section members

throughout this structure were increased but yielded the same results as the original designed

members which proves that it would be a waste of money to overdesign a structure, therefore

structural engineers should try to increase the structural robustness and integrity of the

structure rather than overdesign the structure.


For the inner column removal scenario, the analysis showed that several structural members

failed throughout the structure. The beams directly adjacent to the column failed which can

be seen on figure 4.10, whereas the columns above the removed inner column did not fail

and passed the acceptance criteria. Meanwhile, adjacent columns to the left and the right of

the removed external column failed for all floors.


For the internal column removal scenario, the internal column from the 6th floor was

removed. The analysis results showed that structure experienced a domino type collapse but

caused less damage than the other two column removal scenarios as fewer members failed.

Adjacent columns to the left and right of the internal removed column failed for all floors,

however, all columns directly above and below the internal column did not fail. All adjacent

beams directly above the column removed failed whereas the adjacent beams below the

removed column did not fail.

Discussion for non-linear static analysis:

For this analysis, geometric and material non-linearity was considered by introducing plastic

hinges in the structural components. The beam and column hinges were assigned through

SAP2000, whereas connection hinges were calculated manually with the guidance of the

FEMA 356 manual. Similar to the linear static analysis, gravity loads were placed over and

adjacent to the column removed after calculating the dynamic increase factor. After running

the analysis, the results are compared to the acceptance criteria with the guidance of the GSA

and UFC progressive collapse guidelines. For the acceptance criteria, three terms were used

to describe the hinge status which are the Immediate Occupancy, Life Safety and Collapse

Prevention. At the Immediate Occupancy stage, elastic behaviour is displayed and immediate

53

evacuation is required as several serious incidents might occur which includes yielding of steel

and cracking of concrete. During the Life Safety stage, it is essential to limit the damage

caused to the structure and its components as to lower the risk of injury or causalities. At the

Collapse prevention stage, a portion or the whole building collapses and measures have to be

taken to prevent further collapse.


Initially, plastic hinges did not form throughout the overdesigned structure, as stated in the

previous chapter, the author of this report with the advice of his project supervisor reduced

section sizes of the beams and columns to determine whether hinges may form when smaller

sections are used. After re-running the analysis and viewing the X-Z facade, plastic hinges

formed in columns adjacent to the removed column from floors 3 to 7. Hinges were in the

segment BC which indicates that the structural elements undergo strain hardening and

immediate evacuation is required as to lower the risk of injury. None of the columns were in

the final stage of the acceptance criteria (Collapse Prevention stage) which means that

extreme measures should not be carried out when re-designing the structure. In addition,

several plastic hinges formed in the columns throughout the structure and were in the BC

segment. For beams and connections, few plastic hinges formed throughout the structure

and were in segment AB. To conclude, very few section members failed throughout the

structure and indicates even with the reduced section sizes the building is slightly

overdesigned, therefore the non-linear static analysis can be used as a sanity check.

54

6 Conclusion and Recommendations:

Conclusion

Over the past three decades, extreme consideration has been given of how to prevent

progressive collapse in structures and with all the extensive research carried out, structural

engineers still seem confused with the term “progressive collapse”. Several codes of practice

such as the GSA, Eurocode 1 and UFC provide methods on how to mitigate the possibility of

progressive collapse as to help structural engineers when designing structures.

For the analysis undertaken in this report, the Alternate Load Path was used as it takes into

account geometric and material nonlinearities throughout the structure. In addition, the

method adopted for the analysis follows the UFC and GSA guidelines. The structure used for

this report was attained from Stefan Szyniszewski article for energy flow in progressive

collapse of steel framed buildings (Szyniszewski, 2012). However, the author of this report

decided to overdesign the multi-story steel frame structure as to check whether progressive

collapse could still occur in overdesigned structures. The linear and non-linear static analysis

were used when checking the structure’s resistance to progressive collapse after a critical

structural component was removed. Moreover, three column removal scenarios were

performed for the linear analysis whereas only one column removal scenario was done for

the nonlinear analysis, in addition, their removal locations were chosen with the guidance of

the UFC guidelines. After running the linear static analysis using SAP2000, the overdesigned

structure experienced collapse which suggests that overdesigning a structure is uneconomical

as it would be very costly and still fail. Moreover, using the original sections of the structure

yielded similar results to the overdesigned structure.

It was determined that the linear static analysis does not provide accurate results and does

not consider geometric and material non-linearity. Furthermore, it does not determine the

actual damage caused to the structure after a column is removed. Therefore, a non-linear

static analysis is required as it provides better results and considers geometric and material

non-linearity. However, when running the non-linear analysis, the structure was

overdesigned to an extent that the plastic hinges could not form. Therefore, with the advice

of the project supervisor, lower section sizes were used and the analysis was re-run, which

led to plastic hinges forming throughout the structure.

55

In conclusion, this report suggests that overdesigning structures does not always necessarily

change the behaviour of structures when incidents such as progressive collapse occurs.

Recommendations for further work:

Unfortunately, with all the previous progressive collapse incidents that have occurred,

terminology is still inconsistent in the field of robustness and amongst design guidelines used

worldwide such as the national codes of practice. For example, confusion still exists between

the meaning of progressive and disproportionate. A collapse can be defined as progressive in

nature but not disproportionate in its own extents and vice versa. In the United States, these

two terms are unfortunately used interchangeably as the term progressive is used in many

cases where in fact the true meaning is disproportionate. A certain collapse scenario is termed

as disproportionate when evaluated against UK guidance but when assessed against the UFC

criteria it might not be the same. Clear terminology is essential when it is related to hazards,

consequences and risks but unfortunately it currently remains as an issue across several

industries.

The minimum design requirements for robustness in the building regulations and approved

document A must be revised. Firstly, building risk classes must be reviewed to keep up date

with modern building design as there have been advances in construction technologies. The

review should assess whether further consideration should be given to risk factors such as

building occupancy and evacuation time. The tolerable area at risk of collapse should be

increased from 70 m2 to 100 m2 as structural spans have increased since the Fifth Amendment

was first published and this change must be in accordance with BS EN 1991-1-1-7.

European codes of practice such as Eurocode 1 only follow the design methods of an

unspecified accidental action and do not take into consideration explosions and terrorist

attacks when designing a structure. Extensive research should be carried out to provide

guidance on how to design against progressive collapse in the UK when it is caused by an

explosion or terrorist attack.

When using the GSA and UFC guidelines for the analysis, only one column removal scenario

can be carried at a time which is not sufficient to represent the damage of the building. A

progressive collapse analysis where several key structural members are removed at the same

time should be considered as it will accurately represent the damage of the structure as the

56

removal of several members can damage other key structural members throughout the

structure.

As there was a 12000 word limit for this report and a lack of time, several sections throughout

the report could not be discussed thoroughly and a non-linear dynamic analysis could not be

performed.

57

7 References:

ASCE (2007) ASCE41-06: Seismic rehabilitation of existing buildings. USA: American Society of

Civil Engineers.

Bangash, T. (2006) Explosion-Resistant Buildings, Berlin: Springer-Verlag Berlin Heidelberg,

p.234-247.

BSI (2006) Eurocode 1: Actions on structures – Part 1 – 7: General actions – Accidental actions,

BS EN 1991-1-7: 2006

Computers and Structures, Inc. (2016) SAP2000, Watch and Learn, [online] Available at:

https://www.csiamerica.com/products/sap2000/watch-and-learn [Accessed 15th Feb 2016].

CPNI (2011) Review of international research on structural robustness and disproportionate

collapse. UK: Department for Communities and Local Government, Centre for the Protection

of National Infrastructure.

Debunking (n.d.) World Trade Center 7 South Side Hole, [online] Available at: http://www.debunking911.com/WTC7.htm [Accessed 23rd Dec 2016]

Ellingwood, B. and Dusenberry, D. (2005) Building Design for Abnormal Loads and Progressive

Collapse, Computer‐Aided Civil and Infrastructure Engineering, 20(3), p.194-205.

Farrag, T. (2011) Progressive collapse analysis of multi-storey steel frame. MSc Thesis,

Department of Civil and Environmental Engineering, University of Surrey, UK

FEMA 356 (2000) Prestandard and commentary for the seismic rehabilitation of buildings.

USA: Federal Emergency Management Agency

Foley, C. M., Schneeman, C., Barnes, K. (2008) Quantifying and enhancing the robustness in

steel structures: Part-1 Moment resisting frames [Online] Available at:

https://www.researchgate.net/publication/275337604QuantifyingandEnhancingtheRobustn

essinSteelStructuresPart1-Moment-ResistingFrames [Accessed 3rd Feb 2016]

General Services Administration (2013) Alternate path analysis & design guidelines for

progressive collapse resistance. USA: General services Administration

Gurley, C. (2008). Progressive collapse and earthquake resistance. Practice Periodical on

Structural Design and Construction, 13, p.19-23.

https://www.csiamerica.com/products/sap2000/watch-and-learn

https://www.researchgate.net/publication/275337604QuantifyingandEnhancingtheRobustnessinSteelStructuresPart1-Moment-Resisting_Frames

https://www.researchgate.net/publication/275337604QuantifyingandEnhancingtheRobustnessinSteelStructuresPart1-Moment-Resisting_Frames

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Izzuddin, B. A. (1991). Nonlinear dynamic analysis of framed structures. PhD Thesis,

Department of Civil Engineering, Imperial College London, UK

Jenkins, J. (2012) Oklahoma City bombing [Online] Available at:

http://www.britannica.com/event/Oklahoma-City-bombing [Accessed 5th Mar 2016]

Kato, B. (2003). Seismic Design of Moment Resisting Connection - Welded Flange, Bolted Web

Type-. Steel Structures, 3, p.155-162.

Khandelwal, K. (2008) Multi-scale computational simulation of progressive collapse of steel

frames. PhD Thesis, Department of Civil Engineering, University of Michigan, USA.

Koufoudakis, A. (2013) Steel building design: Progressive collapse analysis. Msc Thesis,

Department of Civil and Environmental Engineering, University of Surrey, UK

Marchand, K. and Stevens, D. (2015) Progressive collapse criteria and design approaches

improvement, Journal of Performance of Constructed Facilities, 29(5), p.13.

McConnell, J. and Houston, B. (2011) Evaluation of progressive collapse alternate load path

analyses in designing for blast resistance of steel columns, Engineering structures, 33(10),

p.2899-2929

McKay, A. and Diaz, M. (2012) Alternate Path Method in progressive collapse analysis:

Variation of dynamic and non-linear load increase factors, Practice Periodical on Structural

Design and Construction, 17(4), p.152-160.

Nair, S. (2004) Progressive Collapse Basics, The steel conference, 3(3), p.1-3.

Pearson, C., and Delatte, N. (2005). Ronan Point Apartment Tower Collapse and its Effect on

Building Codes. Journal of Performance of Constructed Facilities., 19(2), 172-177.

SAP2000. Version 11, analysis reference manual, Computers and Structures, Inc., Berkeley.

Schellhammer, J., Delatte, N., and Bosela, P. (2013). Another Look at the Collapse of Skyline

Plaza at Bailey’s Crossroads, Virginia. Journal of Performance of Constructed Facilities, 27(3),

p.354-361.

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Sharp Printing (n.d.) Testing the thesis for validity, [online] Available at:

http://www.sharpprintinginc.com/911/index.php?module=pagemaster&PAGE_user_op=vie

w_page&PAGE_id=288&MMN_position=573:573 [Accessed 1st Mar 2016]

Smilowitz, Robert (2012) Analytical tools for progressive collapse analysis. USA: Applied

Sciences Division of Weidlinger Associates.

Starossek, U. (2006) Typology of progressive collapse. Engineering structures. 29(1), pp.

2302-2307 [Online] Available at:

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Starossek, U. (2009) Progressive collapse of structures, London: Thomas Telford Ltd, p.15-27

Szyniszewski, S. and Krauthammer, T. (2012) Energy flow in progressive collapse of steel

framed buildings, Engineering Structures, 42 (n.d), p.142-153.

The Building Regulations (2010) Approved Document A. UK: HM Government

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Unified Facilities Criteria

Vasilieva, A. (2013) Progressive collapse, Methods of prevention. Bachelor’s thesis. Civil and

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60

8 Appendices:

Appendix A:

8.1.1 X-Z side view frame element number:

Figure 8.1: Side view X-z façade

Figure 8.2: Side view first section

61

Figure 8.3: Side view section section

Figure 8.4: Side view third section

62

Figure 8.5: Side view fourth section

Figure 8.6: Side view fifth section

63

Appendix B

8.2.1 Hinge status of each hinge formed throughout the structure:

Frame text RelDist Unitless Absolute distance Hinge state Hinge status

341 0 0 A to B A to IO




342 0 0 B to C A to IO








344 0 0 B to C IO to LS











64



















601 1 9.2 A to B A to IO

601 0.5 4.6 A to B A to IO


601 1 9.2 A to B A to IO

601 0.5 4.6 A to B A to IO


602 1 9.2 A to B A to IO

602 0.5 4.6 A to B A to IO

65


602 1 9.2 A to B A to IO

602 0.5 4.6 A to B A to IO


603 1 9.2 A to B A to IO

603 0.5 4.6 A to B A to IO


603 1 9.2 A to B A to IO

603 0.5 4.6 A to B A to IO


604 1 9.2 A to B A to IO

604 0.5 4.6 A to B A to IO


604 1 9.2 A to B A to IO

604 0.5 4.6 A to B A to IO


605 1 9.2 A to B A to IO

605 0.5 4.6 A to B A to IO


605 1 9.2 A to B A to IO

605 0.5 4.6 A to B A to IO


606 1 9.2 A to B A to IO

606 0.5 4.6 A to B A to IO


606 1 9.2 A to B A to IO

66

606 0.5 4.6 A to B A to IO


607 1 9.2 A to B A to IO

607 0.5 4.6 A to B A to IO


607 1 9.2 A to B A to IO

607 0.5 4.6 A to B A to IO


608 1 9.2 A to B A to IO

608 0.5 4.6 A to B A to IO


608 1 9.2 A to B A to IO

608 0.5 4.6 A to B A to IO


609 1 9.2 A to B A to IO

609 0.5 4.6 A to B A to IO


609 1 9.2 A to B A to IO

609 0.5 4.6 A to B A to IO


610 1 9.2 A to B A to IO

610 0.5 4.6 A to B A to IO


610 1 9.2 A to B A to IO

610 0.5 4.6 A to B A to IO

Table 8.1: Acceptance criteria for columns

67

Frame text RelDist Unitless Absolute distance Hinge state Hinge status


























68



























69



























70

651 1 9.2 A to B A to IO

651 0.5 4.6 A to B A to IO


651 1 9.2 A to B A to IO

651 0.5 4.6 A to B A to IO


652 1 9.2 A to B A to IO

652 0.5 4.6 A to B A to IO


652 1 9.2 A to B A to IO

652 0.5 4.6 A to B A to IO


653 1 9.2 A to B A to IO

653 0.5 4.6 A to B A to IO


653 1 9.2 A to B A to IO

653 0.5 4.6 A to B A to IO


654 1 9.2 A to B A to IO

654 0.5 4.6 A to B A to IO


654 1 9.2 A to B A to IO

654 0.5 4.6 A to B A to IO


655 1 9.2 A to B A to IO

655 0.5 4.6 A to B A to IO

71


655 1 9.2 A to B A to IO

655 0.5 4.6 A to B A to IO


656 1 9.2 A to B A to IO

656 0.5 4.6 A to B A to IO


656 1 9.2 A to B A to IO

656 0.5 4.6 A to B A to IO


657 1 9.2 A to B A to IO

657 0.5 4.6 A to B A to IO


657 1 9.2 A to B A to IO

657 0.5 4.6 A to B A to IO


658 1 9.2 A to B A to IO

658 0.5 4.6 A to B A to IO


658 1 9.2 A to B A to IO

658 0.5 4.6 A to B A to IO


659 1 9.2 A to B A to IO

659 0.5 4.6 A to B A to IO


659 1 9.2 A to B A to IO

72

659 0.5 4.6 A to B A to IO


660 1 9.2 A to B A to IO

660 0.5 4.6 A to B A to IO


660 1 9.2 A to B A to IO

660 0.5 4.6 A to B A to IO

Table 8.2: Acceptance criteria for columns

finaldraft dissertation

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