Progressive Collapse

Progressive collapse may be described as a situation originated by the failure of one or more structural members following an abnormal loading event. This local failure leads to a load redistribution in the structure, which results in an overall

damage to an extent disproportionate to the initial triggering event .

The General Services Administration of the United States defines this phenomenon as a situation where local failure of a primary structural component leads to the collapse of adjoining members which, in turn, leads to additional collapse. Hence, the

total damage is disproportionate to the original cause .

A catastrophic partial or total structural failure that ensues from an event that causes local structural damage that cannot be absorbed by the inherent continuity and ductility of the

structural system

The best-known progressive collapse scenarios:

The partial collapse of the 22-storey Ronan Point apartment tower in Newham (east London) in 1968, drew the interest of the research community towards this phenomenon for the first time. A gas explosion in a corner of the 18th floor blew out a load-bearing wall, which in turn caused the collapse of the upper floors due to the loss of support. The impact of the upper floors on the lower ones led to a sequential failure all the way down to

the ground level . As a result, the entire corner of the building collapsed, as can be observed in Figure . This partial collapse was attributed to the inability of the structure to redirect loads after the loss of a load-carrying member.

Another famous example of disproportionate collapse occurred in Oklahoma City in 1995. The Alfred P. Murrah Federal Building collapsed following the explosion of a bomb truck, which initially damaged between one and four ground columns . This partial loss of support resulted in the failure of the transfer girder located right above the failing columns and led to the consequent collapse of the upper floors. The final result was the collapse of about half of the total floor area of the building. Figure shows the building before and after the partial collapse.

the Federal Emergency Management Agency (FEMA) via the Building Performance Investigation Team (BPAT) released the report entitled The Oklahoma City Bombing: Improving Building Performance Through Multi-Hazard Mitigation.The final conclusion was that "Many of the techniques used to upgrade the seismic resistance of buildings also improve a building’s ability to resist the extreme loads of a blast and reduce the

likelihood of progressive collapse following an explosion."

Later works confirmed that the collapse could have been reduced by about 50% if seismic detailing had been provided to this reinforced concrete structure. Fully continuous reinforcement could have reduced both the structural damage and the casualties by 80%.

The large number of casualties and the economic loss that accompanied World Trade Center towers brought arenewed interest in the subject among other federal institutions of the United States, such as the General Services Administration (GSA) and the Department of Defence (DoD), which released their Progressive collapse analysis and design guidelines for new federal office buildings and major modernization projectsand Unified Facilities Criteria (UFC): Design of buildings to resist

progressive collapse .

three basic design methods for progressive collapse prevention:

(1)Event control: protection against incidents that might cause progressivecollapse.Since this approach does not increase the inherent resistance of the structure to progressive collapse and is dependent on factors outside the control of the designer, its application could be very limited.(2) Indirect design: preventing progressive collapse by specifying minimum requirements with respect to strength and continuity(3)Direct design: considering resistance against progressive collapse andthe ability to absorb damage as a part of the design process. The specific local resistance method and the ‘alternate path method’ have been identified as the two basic approaches to

direct design .

For Indirect designthe GSA recommends the following list of general features

- Redundancy

- The use of detailing to provide structural continuity and ductility

- Capacity for resisting load reversals

- Capacity for resisting shear failure

the European standards provides strategies for safeguarding civil engineering works against accidental actions:

-Strategies based on identified accidental actions: – Designing the structure to have sufficient minimum robustness – Preventing or reducing the action (protective measures)-Strategies based on limiting the extent of localized failure – Enhanced redundancy (alternate load paths). – Key element designed to sustain notional accidental action.–integrity and ductility.Analysis of the structural response to a key structural element removal, inorder to simulate a local damage comparable to the one produced in a blastor impact load scenario. If the structure is able to find alternative paths forredistributing the loads, the building is then considered to exhibit a low potentialfor progressive collapse. Although these guidelines provide detailed step-by-step procedures for the ALP analysis in terms of element(s) removal locations, load combinations to be applied and structural acceptance criteria they do not give specific directions in what refers to the computational modelling aspects (i.e. constitutive models, simulation procedures, etc.). Differentstrategies are suggested for linear static, non-linear static and non-linear dynamicanalyses. The vertical load

combinations to be applied to the structure under study are GSA DL + 0.25 LLDoD (0.9 or 1.2) DL + (0.5 LL or 0.2 SL)

Flowcharts are used to determine whether a building is exempt from detailed consideration for progressive collapse. A number of important attributes (including occupancy, type of framing system, number of stories, and standoff distance) are used in the exemption process. If it is determined that further consideration for progressive collapse is required, then either a

linear or nonlinear static/dynamic analysis procedure must be used. A linear analysis approach is limited to low- to mid-rise buildings that are 10 stories or less in height with relatively simple structural layouts. A more sophisticated nonlinear analysis usually is used for taller buildings and/or buildings that have atypical structural configurations.

As a minimum, the building must withstand the loss of one primary vertical load-bearing member without causing progressive collapse. Both exterior and interior scenarios must be examined for typical structural configurations. In the exterior scenario, a framed building is to be analyzed separately for each of the following cases: 1) Instantaneous loss of a column in the first story located near the middle of the short side of the building; 2) Instantaneous loss of a column in the first story located near the middle of the long side of the building; and 3) Instantaneous loss of a column in the first story located at the corner of the building.

Buildings with underground parking areas or uncontrolled ground floor areas must be analyzed for the instantaneous loss of an interior column as well (interior scenario). Similar analyses are required for buildings with exterior and interior walls.

Load = 2(DL + 0.25LL) where DL = dead load, and LL = live load

Since the probability is small that full live load is present during a possible progressive collapse event, 25 percent of the live load is used in the load combination. Also, the factor of 2 is a simplified way to account for dynamic effects that amplify the response when a column or wall is instantaneously removed from a building.

Design material strengths may be increased by a strength-increase factor. Tablesummarizes the strength-increase factors for various construction materials. For structural steel components, the factors for tensile strength and yield strength depend on the grade of the steel and the year it was

fabricated.

After the analysis has been performed, a demand-capacity ratio (DCR) is computed for each of the structural members in the building:where QUD = acting force (demand) determined in a component or connection/joint from the analysis (bending moment, axial force, shear force, and possible combined forces); and QCE = expected ultimate unfactored capacity of the component and/or connection/joint (bending moment, axial

force, shear force, and possible combined forces).

Failure of a structural member depends on the magnitude of the DCR. In typical structural configurations, structural elements and connections in reinforced concrete buildings that have DCR values for bending moment, axial force, shear force, or a combination thereof that exceed 2.0 are considered to be damaged severely or collapsed. In such cases, it is unlikely that members and/or connections will have additional capacity for

redistributing loads. In steel-framed buildings, the maximum DCR values range between 1 and 3, depending on the structural

component .

Once the DCRs have been computed after the required number of analysis runs, it is possible to determine the extent of collapse, if any. The maximum allowable extent of collapse resulting from the instantaneous removal of an exterior column or wall must be confined to the smaller of the following two areas: 1) the structural bays directly associated with the instantaneously removed column or wall; or 2) 1,800 square-feet at the floor level directly above the instantaneously removed column or wall. Similar limits are given for allowable collapse areas based on the removal of interior columns or walls. A high potential for progressive collapse is assumed to exist when collapse areas that are determined from analysis are greater than the appropriate limiting values prescribed in the GSA

Guidelines.

The latest DoD requirements for progressive collapse are in Design of Buildings to Resist Progressive Collapse (UFC 4-023-03), which was published in January 2005. This Unified Facilities Criteria (UFC) applies to new construction, major renovations, and leased buildings and must be used in accordance with Minimum Antiterrorism Standards for Buildings (UFC 4-010-01). According to UFC 4-010-01, all new and existing buildings three stories or more in height must be designed to avoid progressive collapse. Even if a structure has been designed to resist a specific abnormal load or threat, the progressive collapse

requirements of UFC 4-023-03 must still be satisfied.

The level of progressive collapse design for a structure is correlated to the Level of Protection (LOP) assigned to the building as determined by the Security Engineering Facility

Planning Manual

A design requirement not in Table 2 that must be satisfied for all LOPs is that the floor system at all levels, including the roof, must be able to withstand a net upward load equal to 1.0D + 0.5L, where D is the dead load based on self-weight only, and L is the live load. This uplift load, which accounts for the effects that may be caused when a building is subject to abnormal loading, is applied to each bay in the structure, one bay at a time. The members and connections are designed for this load using the appropriate criteria in Chapters 4 through 8 in UFC 4-

023-03.

Tie force method—In the Tie Force method, a building is mechanically tied together. Minimum tie forces, which vary with construction type and location in the structure, typically are resisted by the structural members and connections that are designed for gravity and lateral loads. The purpose of the horizontal and vertical ties is to enhance continuity and ductility, and to develop alternate load paths in the structure. Internal and peripheral horizontal ties must be provided, along with ties to external columns and walls. Required tie strengths are given in Chapters 4, 5, 6, 7, and 8 of UFC 4-023-03 for reinforced concrete, structural steel, masonry, wood, and cold-formed steel construction, respectively. In all cases, the paths of ties must be

straight and continuous; no changes in direction are permitted.

In a reinforced concrete structure, the flexural reinforcement in slabs, beams, and girders can be used to satisfy the horizontal tie force requirements. Similarly, longitudinal steel in concrete

columns can be used to satisfy vertical tie force requirements.

Structural members that do not provide the required horizontal tie force capacity must be redesigned or retrofitted in new and existing construction, respectively. The Alternate Path (AP) method, which is described below, is not to be used in these types of situations. However, if a vertical structural member cannot provide the required vertical tie force capacity, either the member must be redesigned or the AP method must be used,

where that particular member is removed from the structure.

Alternate path method—The AP method, which is applicable to buildings assigned to medium and high LOPs, is similar to the method in the GSA Guidelines in that vertical load-bearing elements are removed at various locations in the building. However, unlike the GSA Guidelines where the members are removed at only the first floor level, in the DoD AP method the vertical elements are removed at each floor level, one at a time. For example, if there are three exterior columns that must be investigated and there are five stories in the building, 15 AP

analyses must be performed .

In a linear or nonlinear static analysis, apply the following amplified factored load to those bays immediately adjacent to

the removed element and at all floors

above the removed element

Load = 2[(0.9 or 1.2)D + (0.5L or 0.2S)] + 0.2W

where D = dead load, L = live load, S = snow load, and W = wind load

For the rest of the structure, the following load is applied

Load = (0.9 or 1.2)D + (0.5L or 0.2S) + 0.2W

When an external column or load-bearing wall is removed, the collapsed area of the floor directly above the removed element

must be less than the smaller of 750 square feet or 15 percent of the total area of that floor. Also, the floor directly beneath the removed element should not fail, The damage limits for interior columns and walls is two times that of exterior ones. Any collapse must not extend into the bays immediately adjacent to

the removed element .

Additional ductility requirements, The main goal of the additional ductility requirements, which are applicable to all types of construction in structures assigned to Medium and High Levels of Protection, is to ensure that the failure mode for all external columns and walls in the ground floor is flexural

(ductile) rather

than shear brittle.

Analysis Procedures for Progressive Collapse

When analyzing a structure, four different analytical procedures may be used toinvestigate the structures behavior; Linear Static (LS), Nonlinear Static (NLS),LinearDynamic (LD), and Nonlinear Dynamic (NLD), in order of increasingcomplexity.A complex analysis is desired to obtain better and more realistic results representing the actual nonlinear and dynamic response of the structure during the progressive collapse. However, both GSA and DoD guide lines prefer the simplest method, linear static, for the progressive collapse analysis since this method is cost-

effective and easy to perform .

a)Linear Static Procedure

The primary method of analysis presented in the GSA guidelines is the linear static (LS) approach. In general, the LS procedure is the most simplified of the four procedures, and thus the analysis can be completed quickly and easy to evaluate the results. However, it is difficult to predict accurate behavior in a structure, due to the lack of the dynamic effect and material nonlinearity by sudden loss of one or more members The analysis is run under the assumptions that the structure only undergoes small deformations and that the materials respond in a linear elastic fashion. The LS procedure, therefore, is limited to simple and low- to medium rise structures (i.e., less than ten

stories) with predictable behavior (GSA, 2003).

b)Nonlinear Static Procedure

In a nonlinear static (NLS) procedure, geometric and material nonlinear behaviors are considered during the analysis. The NLS procedure is widely performed for a lateral load called pushover analysis. For progressive collapse analysis, a stepwise increase of vertical loads is applied until the maximum loads are reached or until the structure collapses, which is known as vertical pushover analysis. This procedure is a step above the linear static procedure because structural members are allowed to undergo nonlinear behavior during the NLS analysis. However,

vertical push over analysis for the progressive collapse potential might lead to overly conservative results.

c)Linear Dynamic Procedure

Dynamic analysis accounts for dynamic amplification factors, inertia, and damping forces, which are calculated during analysis. Considering these dynamic parameters, dynamic analysis is much more complex and time-consuming than static analysis, whether it is linear or nonlinear. However, the linear dynamic (LD)procedure provides more accurate results, compared with static analysis. The LD procedure still needs to consider nonlinear behaviors for better results. For the structure with large plastic deformations, it should be careful to use this

analysis because of in correctly calculated dynamic parameters.

d)Nonlinear Dynamic Procedure

The nonlinear dynamic (NLD) procedure is the most detailed and thoroughmethod of progressive collapse analysis. This method includes both dynamic nature andnonlinear behavior of the progressive collapse phenomenon. More accurate andrealisticresults can be obtained from the NLD method while it is very time-consuming toevaluateand validate analysis resultsNLD analysis isperformed by instantaneously removing a load-bearing member from the alreadyloaded structure and analyzing time history of the structure response caused by the lossof thatmember. Both dynamic effects and geometric and

material nonlinearity were considered in the NLD analysis.

D.1)Dynamic Effect

Progressive collapse is an inherently dynamic event. Dynamic effects may comefrom many sources during the collapse. After a structural member is failed, thestructure transfers the load of that member and comes to rest in a newequilibrium position.During this dynamic load redistribution, internal dynamic forces affected byinertia anddamping are produced and vibrations of building elements are involved. Asuddenrelease in

forces from any failed member can be another source of dynamiceffectsMoreover, progressive collapse is generally initiated by dynamic event such asexplosion, impact, and instantaneous failure of a structural member such as a connection.Therefore dynamic effects for frame structures should be taken into consideration in progressive collapse analysis .

D.2)Nonlinear Effect

Geometrical and Material Nonlinearity

The performance of any structure under abnormal loadings depends not only onits geometrical properties, but also on the properties of the materials used to construct thestructure. Member stiffness ratio is derived to account for geometrical nonlinearity andmember shear deformation. The effect of shear deformation is generallyinsignificant forthe conventional framed structure, but it can be considerably important for heavytransverse loading. Geometric nonlinearity is commonly described in terms of "P-DeltaEffect" in the model. Member axial compressive forces act through the displacement ofone end of a member relative to the other amplify the lateral bending response of a beamcolumnTherefore, the P-Delta effect influences the transverse bending stiffness of anelement.

Most failure or collapse causing in typical structures are mainly due to the adventof nonlinear material behavior, referred to as post-elastic or plastic behavior. Therefore material properties such as yield strength, ultimate strength, and ductility are important parameters to design buildings with safety.

Catenary Action

Failure of a column creates a double span condition in the adjoining beams abovethe failed column. If the beams have large moment capacity and the connections havesufficient ductility and substantial inelastic rotational capacity, excessivedeformationoccurs in the double span, resulting in the sagging floor. The beams act as cablesbetween columns, developing significant tensile forces that the connection must be ableto withstand. The double span across the failed column can be supported by catenaryaction. Alternately, the vertical loads start to be transferred upward throughtension incolumns above the failed column and theremaining structure transfers the loads to adjacent and unfailed spans.