Contents lists available at ScienceDirect Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal Energy based load-impulse diagrams with multiple failure modes for blast-loaded reinforced concrete structural elements Ying-kuan Tsai a, ⁎ , Ted Krauthammer b a Department of Environmental Information and Engineering, Chung Cheng Institute of Technology, National Defense University, PO Box 90047-82, Dasi, Taoyuan 335, Taiwan b Center for Infrastructure Protection and Physical Security, University of Florida, PO Box 116580, Gainesville, FL 32611-6580, USA ARTICLE INFO Keywords: Energy based load-impulse diagrams Energy fow Blast Direct shear ABSTRACT An energy based load-impulse diagram is an alternative of damage assessment tool for protective structures. By defning energy fow relationships, the entire domain of structural responses and corresponding damage can be characterized. The damage level or failure type of a reinforced concrete element under a specifc threat or hazard (e.g. impact and blast) can be determined by examining the corresponding combination of energy input and its rate. An energy balance ap- proach for deriving energy based load-impulse diagrams with multiple failure modes for struc- tural elements are presented in this paper. Two diferent structural behaviors of reinforced concrete elements subjected to blast loads were considered (i.e. fexure and direct shear), and the energy fow in a structural system were described by proposing an energy tank analogy. The application of these approaches to the damage assessment of tested structural elements is illu- strated. 1. Introduction The response of reinforced concrete (RC) members when subjected to sever transient loads such as blast and impact is an im- portant consideration for the strength design and damage assessment. A load-impulse diagram is a type of response spectra, generally used to assess the response of a structural member under blast loading, which illustrates the damage level of structures at various loading conditions. However, as noted in other references, the response modes of a RC element subjected to dynamic loads are not necessarily consistent. Knowing the energy fow relationships will characterize the entire domain of structural responses and its corresponding damage, due to the behavior of a structural member is governed by the amount and rate of external energy input and its ability to dissipate energy. An energy based load-impulse diagram is developed to address energy fow as a basis for conventional load-impulse diagrams, which enables designers to investigate the entire load-impulse domain from an energy stand point [1]. However, only fexural response was taken into account in the previous study, which is not sufcient to predict the possible failure types of RC elements subjected to blast loads. This study presents an energy-based approach to investigate the infuence of energy fow (e.g. loading condition) on structural behaviors. An energy tank analogy is proposed to provide a simple and clear description of the energy fow for a structural system under transient loads. The experimental feld test results reported by Slawson [2] and Kiger [3] were used to validate the proposed methodology. It is expected that an energy based load-impulse diagram with multiple failure modes will typify a fundamental improvement in the feld of protective structures. https://doi.org/10.1016/j.engfailanal.2019.06.023 Received 3 November 2018; Received in revised form 18 June 2019 ⁎ Corresponding author. E-mail addresses: ccitb04007@ndu.edu.tw (Y.-k. Tsai), tedk@uf.edu (T. Krauthammer). Engineering Failure Analysis 104 (2019) 830–843 Available online 24 June 2019 1350-6307/ © 2019 Elsevier Ltd. All rights reserved. T