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Progressive Collapse Considerations in the Design of Structures for Vertical Evacuation
from Tsunamis
Luis A. Montejo, PhD Assistant Professor, Engineering Science and Materials, UPRM
Workshop on Vertical Evacuations from Tsunamis Colegio de Ingenieros y Agrimensores de Puerto Rico
18 al 20 de junio de 2012 San Juan, Puerto Rico
1962 Ronan Point Apartment Tower Collapse (London)
Partial collapse of the structure killed 4 people and injured 17
The collapse sheared off the living room portion of the apartments, leaving the bedrooms intact with the exception of floors 17–22, where all the fatalities occurred.
The explosion was not significant in magnitude < 70 kPa (10 psi).
The tower consisted of precast panels joined together without a structural frame.
The connections relied mostly on friction.
The apartment tower lacked alternate load paths to redistribute forces in the event of a partial collapse.
Poor workmanship at the critical connections between the panels.
Progressive and disproportionate collapse definitions
“Progressive collapse is the collapse of all or a large part of a structure precipitated by damage or failure of a relatively small part of it. The phenomenon is of particular concern since progressive collapse is often (though not always) disproportionate, i.e., the collapse is out of proportion to the event that triggers it. Thus, in structures susceptible to progressive collapse, small events can have catastrophic consequences.” Shankar Nair (Progressive Collapse Basics)
Ronan Point Collapse
Progressive
Disproportionate
1995 Murrah Federal Office Building, Oklahoma City
The Murrah Building was a nine-story, conventionally reinforced (nonductile), concrete structure constructed during the mid 1970s
The truck bomb, estimated to be 1,800 kg (4,000 lb) TNT equivalent, was centered approximately 4 m (13 ft) from one of the building columns
Created a paradigm that guided research and development of new structural design guidelines
Murrah Federal Office Building
Progressive
Disproportionate
2001 (9/11) World Trade Center I, 2 and 7
Progressive collapse did NOT occur in the WTC towers, for two reasons. First, the collapse of each tower was not triggered by a local damage or a single initiating event. Second, the structures were able to redistribute loads from the impact and fire-damaged structural components and subsystems to undamaged components and to keep the building standing until a sudden, global collapse occurred.
The failure of WTC 7 was an example of a fire-induced progressive collapse… caused by a single initiating event-the failure of a northeast building column brought on by fire-induced damage to the adjacent flooring system and connections.
According to NIST (National Institute of Standards and Technology):
2001 (9/11) World Trade Center I, 2 and 7
Progressive
Disproportionate WTC
1 a
nd
2
Progressive
Disproportionate
WTC
7
2007 Minnesota I-35 Bridge
Steel deck truss bridge with little or no redundancy
Progressively collapsed over the entire span due to gusset plate connection failure
Progressive Collapse & Tsunami/Hurricane/Flooding
2004 Indian Ocean Tsunami 2005 Hurricane Katrina
2011 Tōhoku earthquake and tsunami (Japan)
1st Ed. - 25 Jan. 2005 2nd Ed. - 14 Jul. 2009 (updated 2010) 3rd Ed. - 2013?
Designing to Resist Progressive Collapse
1st Ed. – June 2003
U.S. General Services Administration
Designing to Resist Progressive Collapse
Direct Design Methods
Alternate Path Method
Specific Load Resistance Method
Indirect Design Methods
Minimum Levels of Strength, Ductility
and Continuity
Tie Force Method (Vertical and
Horizontal Ties)
The Tie Force Method
Illustration from Deneke, 2005
In the Tie Force approach, the building is mechanically tied together, enhancing continuity, ductility, and development of alternate load paths.
Tie forces can be provided by the existing structural elements that have been designed using conventional design methods to carry the standard loads imposed upon the structure.
The Tie Force Method
There are three horizontal ties that must be provided: longitudinal, transverse, and peripheral. Vertical ties are required in columns and load-bearing walls. Unless the structural members and their connections can be shown capable of carrying the required tie forces while undergoing rotations of 0.20-rad (11.3-deg), the longitudinal, transverse, and peripheral tie forces are to be carried by the floor and roof system.
The Tie Force Method (required tie strength)
The vertical tie must have a design strength in tension equal to the largest vertical load received by the column or wall from any one story, using the tributary area and the floor load wF
Internal ties:
Peripheral ties:
Floor load:
Alternate Path Method
Illustration from Deneke, 2005
In the Alternate Path method, the designer must show that the structure is capable of bridging over a removed column or section of wall and that the resulting deformations and internal actions do not exceed the acceptance criteria.
1. What elements to remove? 2. How to remove them (type of analysis)? 3. Acceptance criteria?
Alternate Path Method (Removal of elements)
Beam-to-beam continuity is assumed to be maintained across a removed column, i.e. remove the clear height between lateral restraints. For walls, remove a length that is twice the clear story height H. For external corners with intersecting walls remove a length of wall equal to the clear story height H in each direction.
Alternate Path Method (Removal of elements - location)
Exterior Columns Interior Columns
Remove one element at a time. For each plan location defined for element removal, perform analyses for: 1. First story above grade 2. Story directly below roof 3. Story at mid-height 4. Story above the location of a column splice or change in column size
Alternate Path Method (Types of Analyses)
1. Linear Static / 2. Non-Linear Static / 3. Non-Linear Dynamic
Linear Static
Limited to non-irregular structures or demand to capacity ratios (DCR) ≤ 2 Construct a linear 3D model with all primary components with the exception of the removed wall or column (no 2D model allowed). Load cases:
Adjacent and above elem. removed (displacement controlled)
Adjacent and above elem. removed (force controlled)
Gravitational elsewhere
Lateral
Alternate Path Method (Linear Static)
Load increase factors for linear static analysis
mLIF is the smallest m of any member connected to the one removed, m is an indirect measure of the nonlinear deformation capacity of the component
Alternate Path Method (Linear Static)
Acceptance Criteria
Deformation controlled actions
Force controlled actions
Alternate Path Method (Non-Linear Static)
Create a non-linear 3D model without the removed element. The force-displacement behavior of all components shall be explicitly modeled, including strength degradation and residual strength, if any.
Strength reduction factors are applied to the nonlinear strength models of the deformation controlled components.
Apply the loads using a load history that starts at zero and is increased to the final values. Apply at least 10 load steps to reach the total load.
Alternate Path Method (Non-Linear Static)
Load increase factors for non-linear static analysis
θpra is the plastic rotation angle given in the acceptance criteria tables in ASCE 41 for the particular element, component or connection; θy is the yield rotation.
Alternate Path Method (Non-Linear Static)
Acceptance Criteria
Deformation controlled actions
Force controlled actions
Primary and secondary elements and components shall have expected deformation capacities greater than the maximum calculated deformation demands.
Alternate Path Method (Non-Linear Dynamic)
Same modeling requirements than for the non-linear static but this time include the element that will be removed.
Same load combinations but NO dynamic amplification factors.
Apply the gravity loads and lateral loads in steps to the entire model.
After equilibrium is reached, remove the column or wall section.
The duration for removal must be less than one tenth of the period associated with the structural response mode for the vertical motion of the bays above the removed column.
The analysis shall continue until the maximum displacement is reached or one cycle of vertical motion occurs at the column or wall section removal location.
Acceptance criteria is the same than for the non-linear static analyses.
Recent and Current Research Efforts
Force redistribution, slab contribution and catenary effects during progressive structural collapse
Alternate Path Method (Linear Static)
Acceptance Criteria – Secondary elements
“All secondary components and elements must be checked to ensure that they meet the acceptance criteria. This can either be done directly for each component or element where displacements are known, or alternately, a second mathematical model can be constructed that includes the secondary components. If the model is re-analyzed with the secondary components included, their stiffness and resistance must be set to zero, i.e., the advantage of including the secondary components is that the analyst may more easily check the secondary elements deformations rather than perform hand calculations of the original model.”
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