Abstract: In this study, the effect of three retrofit strategies on enhancing the response of existing steel moment resisting frames designed for gravity loads is investigated using Alternate Path Methods (APM) recommended in the General Services Administration (GSA) and the Department of Defense (DoD) guidelines for resisting progressive collapse. The response is evaluated using 3-D nonlinear dynamic analysis. The studied models represent 6-bay by 3-bay 18-storey steel frames that are damaged by being subjected to six scenarios of sudden removal of one column in the ground floor. Four buildings with bay spans of 5.0 m, 6.0 m, 7.5 m, and 9.0 m were studied. The response of the damaged frames is evaluated when retrofitted using three approaches, namely, increasing the strength of the beams, increasing the stiffness of the beams, and increasing both strength and stiffness of the beams.

The objective of this paper is to assess effectiveness of the studied retrofit strategies by evaluating the enhancement in three performance indicators which are chord rotation, tie forces, and displacement ductility demand for the beams of the studied building after being retrofitted.

Abstract: Numerical analysis of highly dynamic phenomena represents a critical field of study and application for structural engineering as it addresses extreme loading conditions on buildings and the civil infrastructure. In fact, large deformations and material characteristics of elements and structures different from those exhibited under static loading conditions are important phenomena to be accounted for in numerical analysis. The present paper describes the results of detailed numerical analyses simulating blast tests conducted on a porous (i.e. discontinuous) glass fiber reinforced polymer (GFRP) barrier aimed at the conception, validation and deployment of a protection system for airport infrastructures against malicious disruptions. The numerical analyses herein presented were conducted employing the Applied Element Method (AEM). This method adopts a discrete crack approach that allows auto cracking, separation and collision of different elements in a dynamic scheme, where fully nonlinear path-dependant constitutive material models are adopted. A comparison with experimental results is presented and the prediction capabilities of the software are demonstrated.D. Asprone,

A. Nanni, H. Salem, and H. Tagel-Din: Applied Element Method Analysis of Porous GFRP Barrier Subjected to Blast, Advances in Structural Engineering, Volume 13, Number 1, pp 152-170, February 2010.

Abstract: In order to analyze collapse behavior of structure containing irregular and large displacement, many numerical analyses have been conducted. In this study, using a new method, Applied Element Method (AEM) for collapse analysis of structures, collapse behavior of model RC structures is simulated. From these simulations results, displacement of X-direction (or horizontal) and displacement of Y-direction (or vertical) is similar to that of model RC structures. It is confirmed that collapse behavior of structures using AEM is reliable accurately simulated with that of model RC structures.

Hoon Park, Chul-Gi-Suk, Seung-Kon Kim: Collapse Modeling of Model RC Structure using the Applied Element Method, Journal of Korean Society for Rock Mechanics, TUNNEL & UNDERGROUND SPACE, Vol. 19, No. 1, 2009, pp. 43-51.

Abstract: The response of Hotel San Diego, a six-story reinforced concrete infilled-frame structure, is evaluated following the simultaneous removal of two adjacent exterior columns. Analytical models of the structure using the Finite Element Method as well as the Applied Element Method are used to calculate global and local deformations. The analytical results show good agreement with experimental data. The structure resisted progressive collapse with a measured maximum vertical displacement of only one quarter of an inch (6.4 mm). Deformation propagation over the height of the structure and the dynamic load redistribution following the column removal are experimentally and analytically evaluated and described. The difference between axial and flexural wave propagations is discussed. Three-dimensional Vierendeel (frame) action of the transverse and longitudinal frames with the participation of infill walls is identified as the major mechanism for redistribution of loads in the structure. The effects of two potential brittle modes of failure (fracture of beam sections without tensile reinforcement and reinforcing bar pull out) are described. The response of the structure due to additional gravity loads and in the absence of infill walls is analytically evaluated.

 Mehrdad Sasani, Response of a Reinforced Concrete Infilled-Frame Structure to Removal of Two Adjacent Columns, Engineering Structures, Volume 30, Issue 9, September 2008, pp 2478-2491.

Abstract: Within the past 40 years, abnormal loadings resulting from natural hazards, design flaws, construction errors, and man-made threats have induced progressive collapse in structures all over the world. As progressive collapse behavior has become more prominent, it has made the necessity for design and analysis tools evident. In effort to provide one of these tools, Applied Science International, Inc. introduced its Extreme Loading® for Structures (ELS®) software, capable of progressive collapse simulation.

This research evaluates the effectiveness of Extreme Loading® for Structures as an emerging, nonlinear dynamic analysis software package in modeling progressive collapse scenarios. The ELS® software utilizes the Applied Element Method (AEM) of numerical analysis, separating it from other available software packages. The software and analysis methodology’s accuracy are investigated through simulation of two structural implosions. Comparing the predicted response to the documented response, each scenario is evaluated by analyzing the material models, failure criteria, local structural behavior, and global collapse behavior.

Griffin J. W. (2008) “Experimental and analytical investigation of progressive collapse through demolition scenarios and computer modeling”, M. Sc., Civil engineering, North Carolina.

Abstract: A new extension of the Applied Element Method (AEM) for structural analysis is introduced. A brief overview of the method’s formulation is presented. Then, modifications needed to analyze the behavior of structures subjected to large displacements under static loading are introduced. As no geometric stiffness matrix is needed, the formulation is simple, general and applicable to any type of structural configuration or material. A series of examples that verify the applicability of the proposed technique are presented. The AEM is shown to be an efficient tool for structural analysis in both the small and large displacement ranges.

Abstract: A new extension for the applied-element method for structural analysis is introduced. In this method, the structure is modeled as an assembly of elements made by dividing the structure virtually. This paper first introduces the element formulation of the applied-element method. Next, the effects of the element size and arrangement are discussed, and finally, the accuracy of the proposed method in a nonlinear material case is verified by studying the behavior of RC structures under cyclic loading. For effects caused by the size and arrangement of the elements, it is shown that accurate results of stresses and strains can be obtained if elements of small size are used. As for failure behavior simulation of RC structures, the complicated behavior of cracks in structures subjected to cyclic loading, such as crack initiation and propagation, and opening and closure of cracks during the unloading process, can be simulated automatically and without any use of complicated techniques. No special knowledge about the crack location or direction of propagation is needed before the analysis. The calculated load-displacement relation and the failure load show reliable accuracy.

Kimiro Meguro and Hatem Tagel-Din: Applied Element Simulation of RC Structures under Cyclic Loading, ASCE, Vol. 127, Issue 11, pp. 1295-1305, November 2001

Abstract:  A new extension of the Applied Element Method (AEM) for structural analysis is introduced. This paper deals with the large deformation of structures under dynamic loading condition. As no geometric stiffness matrix is adopted, the formulation used for large deformation is simple and it can be applied for any structural configuration or material type. A new technique based on determining the residual forces due to geometrical changes is proposed. The accuracy of this technique is verified in small deformation range by eigen value analysis. In large deformation range, the collapse behavior of structures and the rigid body motion of the failed structural elements can be followed accurately.

Hatem Tagel-Din and Kimiro Meguro: Applied Element Method for Dynamic Large Deformation Analysis of Structures, Structural Eng./Earthquake Eng., International Journal of the Japan Society of Civil Engineers (JSCE), Vol. 17, No. 2, pp. 215s-224s, October 2000.

Abstract: A new extension for the Applied Element Method (AEM) is introduced. Using this method, the structure is modeled as an assembly of distinct elements made by dividing the structural elements virtually. These elements are connected by distributed springs in both normal and tangential directions. This paper describes the applicability of the AEM for different fields of analysis and structure types and it deals with the formulations used for RC structures under monotonic loading. It is proved in this paper that the structural failure behavior including crack initiation and propagation can be simulated accurately with reasonable CPU time and without any use of complicated material models.

Abstract: A new method, Applied Element Method (AEM) for analysis of structures is introduced. The structure is modeled as an assembly of distinct elements made by dividing the structural elements virtually. These elements are connected by distributed springs in both normal and tangential directions. We introduce a new method by which the total behavior of structures can be accurately simulated with reasonable CPU time. This paper deals with the formulations used for linear elastic structures in small deformation range and for consideration of the effects of oisson's ratio. Comparing with theoretical results, it is proved that the new method is an efficient tool to follow mechanical behavior of structures in elastic conditions.

Kimiro Meguro and Hatem Tagel-Din: Applied Element Method for Structural Analysis: Theory and Application for Linear Materials, Structural Eng./Earthquake Eng., International Journal of the Japan Society of Civil Engineers (JSCE) , Vol. 17, No. 1, 21s-35s, April 2000.