Numerical investigations on static and dynamic responses of reinforced concrete sub-assemblages under progressive collapse Anh Tuan Pham a,⇑ , Kang Hai Tan a , Jun Yu b a School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore b College of Civil and Transportation Engineering, Hohai University, 1 Xikang Road, Nanjing, China article info Article history: Available online xxxx Keywords: Reinforced concrete Progressive collapse Catenary action Sub-assemblage Blast load Numerical model abstract To study the effect of blast pressure on structural resistance against progressive collapse under column removal scenario induced by contact detonation, and to investigate the development of catenary action within ultra-fast dynamic regime, a physics-based finite element model is developed in this paper. The model is first validated by a quasi-static test series on reinforced concrete sub-assemblages under middle column loss assumption and a blast test series using the same structural configurations. The sub- assemblage included a two-span beam, a middle column stub and two column stubs at both sides. Besides validations with sub-structure tests, some pull-out tests are also performed to verify the numer- ical models. After the verifications, parametric studies are conducted to investigate the influence of important dynamic and structural factors such as the boundary stiffness, damping ratio, and charge weight attached to the middle column. The study shows that under actual blast conditions, catenary action in sub-assemblages can be mobilised to prevent a structure from collapse even when the bottom longitudinal reinforcement in the bridging beam has already fractured. Moreover, stiffness of horizontal restraints plays an important role to mitigate disproportionate collapse in both static and blast condi- tions. A comparison is also made between nonlinear dynamic procedure and nonlinear static analysis incorporating simplified energy method for dynamic assessment. It is concluded that the simplified static approach in lieu of dynamic analysis can be considered as a conservative method for practical design pur- pose. Nonetheless, this method may over-estimate structural resistance if the localised damage is induced by a contact-detonation event. Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction The risks of progressive collapse on government and civilian buildings have been substantially increased nowadays due to heightened danger for terrorist attacks. Several methods and design guidelines have been released to help engineers to design structures against progressive collapse. Among them, direct method using Alternate Load Path (ALP) approach is an effective means to investigate structural resistance to progressive collapse [1,2]. However, its main assumption consisting of single-column removal scenarios, has often been criticized as un-realistic [3] due to the neglect of initial damages from the blast event. Suffice to say, ALP is a threat-independent approach. Due to the complexity and extensive resources required for nonlinear dynamic analysis, performance-based approach is less preferred for investigating structural response under progressive collapse scenarios. Instead, a nonlinear static procedure incorpo- rating equivalent dynamic factor is usually preferred in practice. Dynamic effects can be considered through load-increase factors [1,2] or by using simplified methods based on energy balance [4]. Although such kind of analysis is computationally efficient, it needs to be verified by actual blast tests. Recently, there have been extensive experimental studies on ALP approach of reinforced concrete (RC) structures [5–8]. Most of them apply quasi-static method to investigate structural responses against progressive collapse situations. The mobilisation and development of both compressive arch action and catenary action, which strongly depend on lateral restraint conditions, were clearly observed. While compressive arch action is an efficient way to enhance the maximum flexural capacity of the beam section, catenary action can be considered as the last safety net to prevent the structure from complete collapse. Nonetheless, the capacity of catenary action under ultra-fast dynamic (blast) regime has not yet been confirmed experimentally. http://dx.doi.org/10.1016/j.engstruct.2016.07.042 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: atpham@ntu.edu.sg (A.T. Pham), ckhtan@ntu.edu.sg (K.H. Tan), yujun@hhu.edu.cn (J. Yu). Engineering Structures xxx (2016) xxx–xxx Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct Please cite this article in press as: Pham AT et al. Numerical investigations on static and dynamic responses of reinforced concrete sub-assemblages under progressive collapse. Eng Struct (2016), http://dx.doi.org/10.1016/j.engstruct.2016.07.042