Advances in Materials Science and Engineering

Volume 2018, Article ID 2364297, 9 pages

https://doi.org/10.1155/2018/2364297

## Multilevel Seismic Damage Behavior Correlation Analysis for RC Framed Structures

College of Civil Engineering, Nanjing Tech University, Nanjing 211800, China

Correspondence should be addressed to Jianguang Yue; nc.ude.hcetjn@euygj

Received 9 January 2018; Revised 17 March 2018; Accepted 1 April 2018; Published 10 May 2018

Academic Editor: João M. P. Q. Delgado

Copyright © 2018 Jianguang Yue. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Five structural levels, that is, material level, section level, member level, storey level, and structure level, were proposed to analyze the multilevel nonlinear mechanism of the reinforced concrete (RC) framed structures. Based on the presented deformation equivalent principle, a generalized stiffness damage model was developed for each structural level. At each structural level, the stiffness damage value can be calculated by the integration of the material stiffness damage. Furthermore, an impact factor was proposed to reflect the damage correlations between different structural levels. In order to verify this method, the proposed method was used to study the damage evolutions at various structural levels of a 12-storey frame structure. The numerical model utilizing the proposed analysis method produces results in good agreement with the test results of the 12-storey frame structure. It shows that the proposed method is useful to assess the structure multilevel damage performance and to design a new structure.

#### 1. Introduction

In damage mechanics of concrete structures, a damage model can directly calculate the inherent damage states of structures, members, or sections. For this reason, in the performance-based design method (PBDM), the damage degree is often evaluated in an explicit way by introducing the damage performance levels, which corresponds to the seismic intensity levels. The performance levels describe damage with the aid of damage models. However, in actual design works by now, the damage model is usually used to assess the nonlinear behavior for structure level or member level and very limitedly used in designing. The most important reason is that there is no any perfect damage model to describe the damage states for every structural level, and the damage correlations between the different levels are unknown. That is to say, it is not like the force-based design method which can clearly calculate the force relations between the structure level, storey level, member level, section level, and material level. Therefore, it is necessary to propose a new damage model which can calculate damage for every structural level and find a way to reflect the damage correlations between different structural levels.

For different analytical purposes, the damage model can be defined by different mechanical indicators, such as stiffness, deformation, energy, and vibration characteristics. For example, the hysteretic energy-based damage model is often used to evaluate the damage for structure level or member level [1, 2]. In some researches, the deformation has been verified as a good damage indicator not only for the bending-failure-type members (RC columns, beams, and walls) but also for the shear-failure-type members [3]. The deformation-characterized interstorey drift ratio or plastic rotation was used to define the damage model by the study of Banon and Veneziano [4] and Wang et al. [5]. The widely-known Park and Ang damage model [6] was defined by both maximum displacement and plastic energy of dissipation. The strains of concrete and rebar were used to establish a procedure of damage determination for member level by Sharifi et al. [7]. Moreover, the bearing capacity of the M-N relationship can be used to evaluate the damage of section level [8], and the variations of the stiffness or intrinsic period can be used to evaluate the damage of structure level [9].

In the theory of engineering mechanics, the stiffness means the deformation-resistant capacity, that is, the ratio of force to deformation, for any structural level. Thus, the stiffness could be an ideal damage indicator for the multilevel damage assessment. In fact, the stiffness-based damage index in a well-known concrete plastic-damage model [10] has been widely used for the nonlinear numerical analysis [11, 12]. It was proposed from the strain equivalent principle [13] that the strain of damage material caused by nominal stress is equal to the strain of undamaged material caused by the effective stress. Furthermore, this stiffness-based damage index using the integrating method with the weight coefficient (such as the lengths or important factors of the damage zones) can be used to predict the damage performance of the structure level [14–16].

In this paper, a deformation equivalent principle was firstly proposed based on the strain equivalent principle. Secondly, a generalized stiffness-based damage model was presented for every structural level. Its arithmetic expression in an integrating form and the correlation impact factor were used to analyze the multilevel damage mechanism. As an example, a shaking table seismic test of a single-span 12-storey RC framed structure was analyzed by the proposed method.

#### 2. Multilevels for RC Framed Structure

Under earthquake seismic motion, the mechanical behavior-like deformation capacity, bearing capacity of material, member, or structure can be characterized at material level, section level, member level, storey level, and structure level. As shown in Figure 1, each structural level can be expressed as the analysis object , in which the letter means the structural level. The values of are 1, 2, 3, 4, and 5 for the structure level, storey level, member level, section level, and material level, respectively. An example for the multilevel definition is shown in Figure 1. In Figure 1, the subscript of denotes the structural level and the subscript is the object number; that is, means the object at level , and means the object at structure level (the global structure). The superscript “” of means it is a part of ; that is, means the object at level as a part of . As shown in Figure 1, the global structure is denoted as and storey 2 is denoted as . In storey 2 (), the columns 1, 2, 3, and 4 are denoted as , , , and , respectively, and the beams 1, 2, and 3 are denoted as , , and , respectively. In column 1 (), section 1 can be written as . The material point of section 1 is denoted as .