Structure Acceptance Criteria

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. For each

procedure, UFC defines acceptance criteria for primary and secondary elements, components, or connections. 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 re-designed or retrofitted.

2.3.2.6 Linear Static Analysis Procedure

The Linear Static Procedure can be employed only if the structure meets certain conditions about irregularity and Demand-Capacity Ratios (DCR). If there are no irregularities in the structure, then UFC allows using the Linear Static Procedure. If there are irregularities in the structure, then the use of Linear Static Procedure depends on the level of the Demand-Capacity Ratios of the structural elements under a given loading. A linear model of the structure with the specified column or load bearing wall removed is analyzed under gravity dead and live loads increased by the load increase factor ΩLD.

Calculation of load factor ΩLD is explained in the following sections. Then the DCRs are

calculated with the following formula:

DCR = QUDLim/QCE

where QUDLim is the resulting actions (internal forces and moments) in the element and

QCE is expected strength of the component or element.

If all of the component DCRs calculated are less than or equal to 2.0, then the linear static procedure can be used. If one or more of the DCRs exceed 2.0, then a linear static procedure cannot be used.

2.3.2.6.1 Analytical Modeling

In Linear Static Procedure, only three-dimensional models are allowed to be employed to model, analyze, and evaluate a building. Two-dimensional models are not permitted.

In the analytical model of the structure, only the primary elements and components are expected to be included. If the model includes also the secondary elements and components, their stiffness and resistance should be set to zero.

2.3.2.6.2 Loading

The structure is required to be analyzed separately for the deformation-controlled actions and the force-controlled actions. UFC defines different load combinations to calculate the deformation-controlled actions and the force-controlled actions.

2.3.2.6.2.a Load Case for Deformation-Controlled Actions (QUD)

In the calculation of deformation-controlled actions, the structure is required to be analyzed under gravity and lateral loads simultaneously. Four different analyses are required to be performed. In each analysis, the lateral loads are to be applied in one of each principal direction of the building while the gravity loads are the same. Gravity loads on the plan are not applied uniformly. Two different gravity load combinations are defined:

1. Increased Gravity Loads for Floor Areas Above Removed Column or Wall For the bays immediately adjacent to the removed element and at all floors above the removed element, the following load combination is required to be applied:

GLD = ΩLD [(0.9 or 1.2) D + (0.5 L or 0.2 S)]

where

GLD = Increased gravity loads for deformation-controlled actions for Linear Static

Analysis

D = Dead load including façade loads

L = Live load including live load reduction per ASCE/SEI 7-10 S = Snow load

ΩLD= Load increase factor for calculating deformation-controlled actions for Linear

Static analysis.

2. Gravity Loads for Floor Areas Away From Removed Column or Wall

For all other areas over the plan, the following load combination is required to be applied:

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

where G = Gravity loads 3. Lateral Loads

The following lateral load is required to be applied to each side of the building in combination with the gravity loads.

LLAT = 0.002ΣP

where

LLAT = Lateral load

0.002ΣP = Notional lateral load applied at each floor; this load is applied to every floor

on each face of the building, one face at a time

ΣP = Sum of the gravity loads (Dead and Live) acting on only that floor; load increase

factors are not employed.

2.3.2.6.2.b Load Case for Force-Controlled Actions QUF

Similar to the calculation of deformation-controlled actions, in the calculation of force-controlled actions, the structure is required to be analyzed under gravity and lateral loads simultaneously. Again a separate analysis is required to be performed for each principal direction of the building for the lateral loads to apply (four analyses in total) and two different gravity load combinations are defined for the floor areas above removed element and for the floor areas away from removed element.

1. Increased Gravity Loads for Floor Areas above Removed Column or Wall For the bays immediately adjacent to the removed element and at all floors above the removed element, the following load combination is required to be applied:

GLF = ΩLF [(0.9 or 1.2) D + (0.5 L or 0.2 S)]

where

D = Dead load including façade loads

L = Live load including live load reduction per ASCE/SEI 7-10 S = Snow load

ΩLF = Load increase factor for calculating force-controlled actions for Linear Static

analysis

2. Gravity Loads for Floor Areas Away From Removed Column or Wall

For all other areas over the plan, the following load combination is required to be applied:

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

where G = Gravity loads 3. Lateral Loads

The following lateral load is required to be applied to each side of the building in combination with the gravity loads.

LLAT = 0.002ΣP

where

LLAT = Lateral load

0.002ΣP = Notional lateral load applied at each floor; this load is applied to every floor

on each face of the building, one face at a time

ΣP = Sum of the gravity loads (Dead and Live) acting on only that floor; load increase

factors are not employed.

2.3.2.6.3 Load Increase Factor

As stated above, UFC requires applying increased gravity loads to the floor areas above the removed column or wall. Amplification of the gravity loads is achieved by means of load increase factors. UFC provides load increase factors for the analyses to

calculate deformation-controlled and force-controlled actions separately. Table 2.2 shows the load increase factors to be used for reinforced concrete structures.

In Table 2.2, mLIF is the smallest m of any primary beam, girder, spandrel or wall

element that is directly connected to the columns or walls directly above the column or wall removal location. For each primary beam, girder, spandrel or wall element, m is the

m-factor defined in Chapter 4 of UFC for RC. Columns are omitted from the

determination of mLIF.

2.3.2.6.4 Component and Element Acceptance Criteria

The component and element acceptance criteria are given below for deformation- controlled or force-controlled actions:

Deformation-Controlled Actions

All primary and secondary components and elements shall satisfy the requirement below for deformation-controlled actions

Φ m QCE = QUD

where

QUD = Deformation-controlled action, from Linear Static model

m = Component or element demand modifier (m-factor) Φ = Strength reduction factor.

QCE = Expected strength of the component or element for deformation-controlled actions.

Force-Controlled Actions

All primary and secondary components and elements shall satisfy the requirement below for force-controlled actions

Φ QCL = QUF

where

QCL = Lower-bound strength of a component or element for force-controlled actions

Φ = Strength reduction factor.