PSI - Issue 60

Anupoju Rajeev et al. / Procedia Structural Integrity 60 (2024) 222–232 Author name / StructuralIntegrity Procedia 00 (2019) 000–000

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1. Introduction In the realm of structural engineering, the response of buildings and other structures to dynamic loads, such as explosions and impulsive events, has garnered significant attention due to its critical implications for both human safety and property preservation. An explosion, characterized by the sudden release of energy, generates shock waves that exert high pressures on surrounding structures. This phenomenon, while occurring over a brief period, can cause devastating effects on both life and property. The rapid and forceful nature of these events categorizes them as high impulse dynamic loadings, imparting immense momentum to the structures they impact. It is imperative to develop a profound understanding of the dynamic response of structural members to effectively mitigate the potentially catastrophic effects of such loading scenarios. One of the key challenges in dealing with dynamic loads is the prediction of a structure's behavior under the tremendous forces generated by impulsive events. This involves an intricate examination of reinforced concrete (RC) structures under extreme conditions, as well as the establishment of design criteria to ensure structural integrity. Notably, the flexural capacity of structural elements and the overall extent of deformation serve as pivotal performance indicators for quantifying damage during these scenarios. The response of structures subjected to dynamic loads gives rise to two primary failure mechanisms. Firstly, local failure occurs immediately after loading due to high stress concentration at the point of impact, a phenomenon particularly evident during projectile impact. Secondly, global failure encompasses the elastic-plastic deformation of the structure over a more extended period, including the occurrence of free vibrations. Accurate prediction of these mechanisms necessitates an understanding of the magnitude, duration, and loading conditions, with the amount of reinforcement also playing a crucial role in determining the dominant failure mode of RC structures. To analyze the dynamic response of structures under impulsive loads, it is imperative to ascertain the sectional properties of the structural members. This involves the evaluation of stress block parameters to determine the ultimate moment capacity of these elements. Researchers have proposed numerous empirical formulae to calibrate stress-strain curves for concrete in both compression and tension. However, the stress-strain relationship for concrete is influenced by a multitude of factors, contributing to its complexity. Furthermore, the behavior of materials under dynamic loads differs from static conditions, with the material exhibiting a higher stiffness at elevated strain rates. This strain rate effect introduces complexity in quantifying the structural response, compounded by the significant impact of confinement from transverse reinforcement in the case of short-duration loads. Reinforced concrete structures have demonstrated effective performance against extreme loads in the past, with proper steel reinforcement ensuring adequate ductility. Researchers have extensively investigated predicting the behavior of RC structures under extreme conditions such as shock, impact, and blasts [1–5], focusing on failure modes of RC beams subjected to impact loads. While this work doesn't address impact loading directly, studying nonlinear concrete behavior under high strain rate loads offers valuable insights. The dynamic response of structures to explosions and shocks has been extensively studied [6–10]. For studying concrete structures' response to dynamic loads, developing an accurate material model capturing elastic and plastic behavior is crucial. Lubliner et al. [11] proposed a plasticity theory for nonlinear concrete behavior, including yield criteria considering elastic and plastic degradation stiffness. Lee and Fenves [12] developed another plasticity model incorporating fracture-energy based damage and stiffness degradation concepts. Calibration of concrete's stress-strain curve is essential for the CDP model, and equations [13–15]. Mander et al. [16] derive stress-strain curves from fundamental properties like peak compressive strength under static loads. However, accounting for strain rate and confinement effects is necessary for accurate quantification. Dynamic increase factors (DIFs) are used to amplify static properties for higher strain rates [9,17]. Transverse confinement, such as stirrups, enhances concrete resistance. Confinement effects have been thoroughly investigated [16,18], proposing modified stress-strain relations for different confinement shapes. Moment-curvature relationships have been systematically derived [1,19], and maximum deflection serves as a key damage index in dynamic analysis. Analytical techniques, such as continuous beam models and single degree of freedom (SDOF) approximations, are used for estimating deflections and assessing structural response. Due to