Preparing Pressure-Impulse Diagrams for Reinforced Concrete Columns with Constant Axial Load using Single Degree of Freedom Approach

Abstract

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

Numerical and analytical study of seismic response of structural systems with new formulation using energy and impact methods

“…In this system, − � is substituted for the external force F(t), where � denotes the acceleration of the system support and is the relative displacement of mass (or deformation of spring). As proved in technical literature, denoting the displacement of mass by and its velocity and acceleration respectively by and , and assuming linear behavior of spring, i.e., � = , and idealized viscously damping behavior of damper, i.e., � = , we can write the governing equation of motion [2,14].…”

“…SDOF odel is the most known simplification of vibrating systems for seismic analysis of buildings and structures. Solving EOM of SDOF oscillators under base acceleration always have been a place of challenge for earthquake engineering researchers from the very early to the recent efforts [1]. Available methods to the solution of linear differential equations, such as EOM of SDOF systems, are mostly classical approaches like Duhamel's integral and frequency-domain method.…”

“…They are extended for analyzing nonlinear systems. The methods of excitation interpolation, central difference method, and also Newmark's method is the most commonly used numerical procedures in this family [2,3]. Accuracy of some numerical stepwise procedures used to compute the dynamic structural response of the SDOF system to a time-dependent excitation is evaluated in technical report ITL-97-7 published by the U.S. Army Corps of Engineers.…”

Vulnerability assessment of combat aircraft to blast loading

“…13,14 Structures with big aspect ratio, e.g. beams, frames, and trusses, are simplified by one dimension finite elements 15–19 while structures with relatively small thicknesses, e.g. plates, slabs, and shells, are modeled into two-dimension elements.…”