1. Analytical Evaluation of Precast Concrete Structures Resistance to Disproportionate Collapse Progressive Collapse:  When a ”disproportionately” large portion of a structure fails successively following the failure of an initial primary structural element Oklahoma City Bombing Before and after: initial structural failure was lower portion of three columns and some connecting slabs (4% of building). Final failure included 42% of structure (Lew, 2002).  Candidate structures analyzed for progressive collapse potential, due to the loss of specified support components: Initial development: Progressive collapse models are extended from previous shake table seismic test models:  Precast components modeled individually throughout structure  Discrete modeling of connections allowing element separation  Elements can be non-ductile  Improvements include vertical connection additions and vertical loading Preliminary results: Dr. Robert B. Fleischman, Dr. Zhang, Kaylene Boroski, Seyedreza Anvar StructureSDCLFRSDiaphragmLost Components Considered for Analysis A: 4-story buildingBCDBCD Ext. precast wallsHollow core- N/S wall panel - E/W wall panel - Corner wall panels B: 12-story buildingCDCD Ext. precast wallsHollow core- E/W wall panel - Corner wall panels C: 4-story parking garage BCDBCD Ext. and Int. precast walls Double Tee- N/S wall panel - E/W wall panel - Exterior column Recently, PCI performed a linear static study on three typical precast structures using the GSA linear procedure, which indicates high possibility of the precast structures to progressive collapse. The objective of this project is to extending this work using a progressive collapse evaluation for precast structures using dynamic analysis following the GSA nonlinear procedures. The project will make use of existing finite element models developed for seismic analyses of precast structures, appropriately modified for progressive collapse. Objectives: →Confirm or provide new information on the performance of the structures relative to the linear analyses →Provide guidelines on the strength and deformation requirements for precast reinforcement for structural integrity →Investigate advanced tools for examining progressive collapse for precast structure OVERVIEWBACKGROUNDCASE STUDY: STRUCTURE A MODEL DEVELOPMENT  Since this occurrence and other famous failures, extensive work on disproportionate collapse has been done; most studies investigate steel and reinforced concrete structures  Precast concrete may be particularly susceptible to progressive collapse due to: →Long spans between vertical support members →Variation on behavior of structure due to connections: concrete components interacting with embedded or attached steel connectors General Security Administration (GSA) Guidelines:  Linear procedure: “sequence-inversion” technique →Begin with unloaded structure, with initial failed elements removed →Design loads applied statically, amplified for dynamic effects, neglects path dependent effects  Nonlinear procedure: “load-history dependent” technique →Begin with static, intact structure →Remove failed elements after applying a gradually decreasing dynamic load CANDIDATE STRUCTURES Structure C Structure BStructure A Re-distribution of forces upon failure: Three spring elements, one in direction of each Cartesian axis:  Z: tensile forces  X and Y: shear forces Example: Horizontal wall joint Representation in model: Analysis Procedure: Three-step process -  Solid structure analyzed to static load distributions  “Collapsed” elements removed  Static load equivalence added to mimic intact structure  Load equivalence removed over 0.02 seconds for re-distribution of loads in structure  Structure allowed 3 seconds of free vibration for continued load distribution and new structural equilibrium Remaining limitations: Realistic progressive collapse behavior not entirely captured. Desired additions:  Vertical unseating of components  3D elements for stress distribution →Prospective aid in readily determining local element failure and approximate locations Structure A description: Four-story residential structure -  Plan 90x64 ft.  Precast wall panels  Exterior shear walls: 10 in. thick  Hollowcore diaphragm: 16 4HC 12+2 panels  Center precast support column: 30x30 in.  Midspan support beam: 28IT48 Emphasis on connection modeling: Add real-life capacity to connections via elements acting as tensile and shear strengths of the connections. Failure Conditions and Distribution: Three failure conditions considered -  N-S panel  E-W panel  Corner panel Connections re-distribute forces in secondary load paths using non-traditional connection behaviors. X-axis stress: Shows shear connector activation in tension Y-axis stress: Shows bending stress distribution across 3D hollowcore panel element Structure oscillation seeking new equilibrium Oklahoma City bombing images: http://911research.wtc7.net/non911/oklahoma/docs/britannica.jpg Ghosh, S. K. (2009). Design and Progressive Collapse Analysis of a Four-Story Residential Building with Exterior Walls. PCI. Lew. (2002). “Blast and Progressive Collapse.” http://www.arquitecturaenacero.org/attachments/article/21/AISC%20-%20FACTS%202%20-%20BLAST%20AND%20PROGRESSIVE%20COLLAPSE.pdf.