In this paper, moment-curvature behavior of reinforced concrete column with constant axial load is determined using finite element method and then it is introduced to a single degree of freedom (SDOF) model based on EulerBernoulli theory. Using this SDOF model, dynamic response of the RC column under the blast loading is estimated. The introduced SDOF includes secondary moments (P-δ) effects, nonlinear behavior of the material and effects of strain rate on concrete and steel materials through the time calculation of the model. Results obtained from SDOF model for transverse displacement of RC column under blast loading is compared to analysis by finite element software OPENSEES. Then, introduced SDOF method is used for drawing Pressure-Impulse (P-I) diagram of the column with considering the presence of axial compressive load. According to the results, introduced SDOF model has simple and quick computations and accuracy of predictions is acceptable.P-δ effects and overall and local damages and their impact on the P-I diagram can be evaluated. However, this method due to the high complexity, high time of calculations and the need to have enough skills and experience of using software, for extensive parametric studies isn't very appropriate.In this paper, the flexural behavior (moment-curvature) of a reinforced concrete column section using finite element software of open system for earthquake engineering simulation (OpenSees) has been determined and introduced to the calculation of SDOF analytical model in order to estimate transverse displacement response of column under simultaneous compressive axial force and lateral loading of blast. The SDOF introduced model includes the effects of secondary moments (P-δ) and also the effects of high strain rates on the behavior specifications of concrete and steel rebar. In this method, to consider the effects of the existence of column axial loading (P-δ) the concept of reduced resistance function is used. Using the introduced process, P-I dimensionless curves have been plotted for reinforced concrete column. Figure 2 shows the distribution of stress and strain in the rectangular RC section at the ultimate state. Strain distribution in the height of the section has been assumed to be linear and curvature of section (θ) is equal to the slope of this line. Also, the tensile strength of concrete has been ignored. In the figure above, f yk is the yield stress of reinforcement steel, f cu is the ultimate strength of concrete, ε cu is the ultimate strain of concrete, xu is the depth of neutral axis in the ultimate state, b is the width, h is Equivalent Single Degree of Freedom Model

Columns are the most important load bearing structural elements in buildings. Under the effect of external explosions near the building, columns in the ground and first floors may have severe damage that can cause progressive collapse of the whole building frames. Residual axial load bearing capacity of the reinforced concrete column after the effect of lateral blast loading could be a practical criterion to damage assessment of the column. This is essential to determine whether the column has to be replaced or repaired for future use. In this paper, residual axial capacity of the square RC columns under the effect of initial axial force and lateral blast loading is investigated. Explicit finite element package LS-DYNA is used for analysis of the considered models and determining their residual capacity. There are some empirical formulas for estimating of the residual axial capacity of the blast damaged RC columns including Bao and Li (2010), Wu et al (2010) and Arlery et al (2013). Here, FEM results are compared to the estimations of these formulas. Different levels of initial axial force in the columns and different scale distances of blast loading are considered.

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Different factors can affect blast response of structural components. Hence, experimental tests could be the best method for evaluating structures under blast loading. Therefore, an experimental explosion loading has been done on RC members by the authors. Four RC components, with identical geometry and material, with and without axial load were imposed to air blast. Observed data of the members' response under blast loading was used for validation of finite element modeling process using ABAQUS software. With respect to complexity, limitations, and high costs of experimental tests, analytical studies and software modeling can be good alternatives. Accordingly, in this paper, the behavior of 6 different models of normal and strengthened RC columns under blast loading was evaluated using ABAQUS. Strengthening configurations considered here were designed for enhancing axial capacity of RC columns. Therefore, we can investigate the effectiveness of axial strengthening of column on its blast resistance capacity and residual axial strength. The considered strengthening methods were different steel jacket configurations including steel angle, channel, and plate sections. The results showed that retrofitting significantly improves blast performance of the columns. Moreover, residual strength capacity of the columns strengthened with steel channel is higher than the other models.

Seismic fragility curves are used to assess the probability of vulnerability of structures at various damage states. This research deals with the effects of different isolation systems on the seismic safety of a two-dimensional reinforced concrete moment-resisting frame. The reference structure was a hotel building in California. A comparative probability-based seismic safety of building components was investigated on the superstructure hypothetically fitted with various isolation systems. In this regard, two categories of isolation systems including, rubber-based and friction‐based were selected here. The High Damping Rubber Bearings and Friction Pendulum Systems were considered here. Incremental Dynamic Analyses were carried out for a suite of earthquake records to develop the fragility curves considering modeling, demand, and capacity uncertainties. Based on the main results, the influence of seismic isolation systems on the reduction of failure probability of building rather than fixed base (un-retrofitted) model was observed. Moreover, the High Damping Rubber Bearings were more reliable than Friction Pendulum Systems in the limit states studied. No significant discrepancy was, however, seen in the performance of building fitted with isolation systems at higher damage states.