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The Department of Defence introduced the first Unified Facilities Criteria (UFC) (DoD, 2005) for Design of Buildings to Resist Progressive Collapse in 2005. This document is updated in 2010 including significant changes. The document provides the design requirements necessary to reduce the potential of progressive collapse for new and existing buildings that experience localized structural damage as a result of accidental events.

Three design approaches are considered in the document to design new and existing structures to resist progressive collapse; Tie Forces, Alternate Path Method and Enhanced Local Resistance, which depends on the required level of protection for the facility.

1.3.5.1 TIE FORCES APPROACH

As described in the British Standard, the tie forces method prescribes a tensile force capacity of the floor or roof system, to allow the transfer of load from the damaged portion of the structure to the undamaged portion, by providing the continuity and ductility, which play the key roles in the redistribution of the loads over a damaged region. The approach categorizes the ties to be provided in the structure into three categories, Figure 1-8:

1. Longitudinal and Transverse Ties. 2. Peripheral Ties.

3. Vertical Ties.

The following floor load is to be used in the calculation of the required tie strengths:

𝑤_𝑓 = 1.2𝐷𝐿 + 0.5𝐿𝐿 (1-8)

1- Longitudinal and Transverse Ties

The following formula is used to calculate the required tie strength for the longitudinal or transverse ties for framed structures as well as for load bearing wall structures:

𝐹𝑖 = 3 𝑤𝑓 𝐿1 (1-9)

Where

𝐹𝑖 is the required tie strength (lb/ft. or kN/m), 𝑤𝑓 is the floor load and 𝐿1 is the greater of the distances between the centres of the columns, frames, or walls supporting any two adjacent floor spaces in the direction under consideration (ft. or m).

2- Peripheral Ties

The following formula is used to calculate the required peripheral tie strength for framed structures as well as for load bearing wall structures:

𝐹𝑃 = 6 𝑤𝑓 𝐿1𝐿𝑝 (1-10)

Where

𝑤𝑓 is floor load, 𝐿1 is the greater of the distances between the centres of the columns, frames, or walls at the perimeter of the building in the direction under consideration (for exterior peripheral ties) or the length of the bay in which the opening is located, in the direction under consideration (for peripheral ties at openings), and 𝐿𝑝 is 3.3ft (1.0 m).

3- Vertical Ties

The vertical tie must have design strength in tension equal to the largest vertical load received by the column or wall from any one storey. Each column and load-bearing wall shall be tied continuously from the roof level down to the first column- or wall-supported floor above the foundation, i.e., the vertical ties are not required to extend to the foundation.

In the case that the structural elements cannot provide the required tie strength, the elements and connections should be redesigned or retrofitted in order to develop the required tie force. For the vertical ties, however, if any structural element or connection fails to provide vertical required tie strength, redesigning is not required if it can be proven that the structure is capable of bridging over this deficient element using the Alternate Path Method.

Figure 1-8 Locations and Interruptions of ties (UFC 2009)

1.3.5.2 ALTERNATE PATH METHOD (APM)

The second approach is based on the alternate path method, in which the building should bridge across a removed element. UFC allows the structure to be analysed after removing bearing element by using three analysis procedures:

Linear Static (LSP), Nonlinear Static (NSP) and Nonlinear Dynamic (NDP). The load combinations that should be used are as follows:

- For Linear, Non-Linear Static Analysis

𝐺𝑠 = 2.0 [1.2 𝐷𝐿 + (0.5 𝐿𝐿 𝑜𝑟 0.2 𝑆)] (1-11)

To be applied at the bays adjacent to the removed element, and at all floors above the removed element.

𝐺 = 1.2 𝐷𝐿 + (0.5 𝐿𝐿 𝑜𝑟 0.2 𝑆) To those bays not loaded with 𝐺_𝑠 (1-12) Where

𝐺𝑠 , 𝐺 = Increased gravity loads for Linear Static Analysis (lb/ft2 or kN/m2) 𝐷𝐿 = Dead load including façade loads (lb/ft2 _{or kN/m}2₎

𝐿𝐿 = Live load (lb/ft2 _{or kN/m}2₎ 𝑆 = Snow load (lb/ft2 _{or kN/m}2₎

- For Non-Linear dynamic analysis

𝐺_𝐷 = 1.2 𝐷𝐿 + (0.5 𝐿𝐿 𝑜𝑟 0.2 𝑆) To be applied for the entire structure (1-13) Where

𝐺𝐷 = Gravity loads for Nonlinear Dynamic Analysis (lb/ft2 or kN/m2)

It can be seen that the vertical load prescribed for a static analysis is twice the vertical load recommended for a dynamic analysis to allow for dynamic effects.

ACCEPTANCE CRITERIA

The DOD adopted an approach similar to that used by GSA to evaluate the magnitude and distribution of potential progressive collapse for a building. The magnitude and distribution of these demands will be indicated by (DCR), which can be calculated using equation (1-7).

As mentioned before three analysis procedures are suggested in UFC for Design of Buildings to Resist Progressive Collapse; Linear Static Analysis Procedure, Nonlinear Static Analysis Procedure, and Nonlinear Dynamic Analysis Procedure.

If the primary elements and components meet the acceptance criteria for the corresponding procedure, then the building satisfies the progressive collapse requirements, otherwise, it must be redesigned or retrofitted.

1.3.5.3 ENHANCED LOCAL RESISTANCE

In the Enhanced Local Resistance approach, the shear and flexural capacity of the perimeter columns and walls are increased to provide additional protection by reducing the probability and extent of the initial damage. The Enhanced Local Resistance approach is required along with other approaches (e.g. Tie Forces, Alternate Path).