---

By identifying the damage index of a structure, in addition to a correct understanding from real behavior of the structure, the required criterion for strengthening would be given. Researchers have given many relations for determination of damage index but such relations have been based upon laboratory methods which challenge their usage in a broad term. In this paper two new methods are given for calculation of damage index. Surveying the first crack limit and total structure failure is based upon the formation of plastic joints in the first column and basic floor columns. To give a qualitative simple and functional damage index, the functional method was given in the form of a qualitative method with statistical analysis and collection of different views. Using this method is very simple and meantime offers suitable accuracy. With a numerical study on three models it was made clear that the difference of new method with amended method of Papadopolos in approximate 3%. This shows that given qualitative method is suitable to be used in a broad terms.

---

In recent years, different damage indexes have been introduced in engineering literature. The most prominent one among other

counterparts is the 1985 Park and Ang's damage index (DIPA), which demonstrates well calibration against experimental

results. Hence, it has traditionally had broad application in the field of structural engineering. Commonly, in DIPA relevant

parameters are assessed based on plastic-hinge approach, which is not well suited to consider the coupled response between

stress resultants (axial force and flexural moment) especially in grossly nonlinear domain. The reason is that named approach

is utilized constant shape plastic moment-curvature curve, which is not capable of varying the shape throughout loading history.

Another drawback of plastic-hinge method is the difficulty of representing precisely partial yielding of the cross-section. To

remedy the situation, the fiber discretization technique is used in this paper. Based on the fiber discretization strategy, not only

have the stiffness and strength degradation been characterized more accurately, but also the distribution of plasticity along the

plastic zone has been considered. Besides, the multi-directional effect of axial force and flexural moment is considered to assess

DI parameters. Additionally, this strategy directly incorporates the effect of transverse confinement into cross sectional

constitutive behaviour.

---

An energy based damage index based on a new nonlinear Finite element (FE) approach applicable to RC structures subjected to cyclic, earthquake or monotonic loading is proposed. The proposed method is based on the evaluation of nonlinear local degradation of materials and taking into account of the pseudo-plastic hinge produced in the critical sections of the structure. A computer program is developed, considering local behavior of confined and unconfined concretes and steel elements and also global behavior and damage of reinforced concrete structures under cyclic loading. The segments located between the pseudoplastic hinges at critical sections and the inflection points are selected as base-models through simulation by the proposed FE method. The proposed damage index is based on an energy analysis method considering the primary half-cycles energy absorbed by the structure during loading. The total primary half-cycles absorbed energy to failure is used as normalizing factor. By using the proposed nonlinear analytical approach, the structure's force-displacement data are determined. The damage index is then calculated and is compared with the allowable value. This damage index is an efficient means for deciding whether to repair or demolish structures after an earthquake. It is also useful in the design of new structures as a design parameter for an acceptable limit of damage defined by building codes.  The proposed approach and damage index are validated by results of tests carried out on reinforced concrete columns subjected to cyclic biaxial bending with axial force.

---

An analytical nonlinear stress-strain model and a microscopic damage index for confined and unconfined concretes together with a macroscopic damage index for reinforced concrete (RC) structures under cyclic loading are proposed. In order to eliminate the problem of scale effect, an adjustable finite element computer program was generated to simulate RC structures subjected to cyclic loading. By comparing the simulated and experimental results of tests on the full-scale structural members and concrete cylindrical samples, the proposed stress-strain model for confined and unconfined concretes under cyclic loading was accordingly modified and then validated. The proposed model has a strong mathematical structure and can readily be adapted to achieve a higher degree of precision by modifying the relevant coefficients based on more precise tests. To apply the proposed damage indices at the microscopic and macroscopic levels, respectively, stress-strain data of finite elements (confined and unconfined concrete elements) and moment-curvature data of critical section are employed. The proposed microscopic damage index can easily be calculated by using the proposed simple analytic nonlinear stress-strain model for confined and unconfined concretes. The proposed macroscopic damage index is based on the evaluation of nonlinear local degradation of materials and taking into account the pseudo-plastic hinge produced in the critical section of the structural element. One of the advantages of the macroscopic damage index is that the moment-curvature data of the critical section is sufficient in itself and there is no need to obtain the force-displacement data of the structural member.

---

This paper describes both global and local versions of an energetic analytical model to quantify the damage caused to reinforced concrete (RC) structures under monotonic, cyclic or fatigue loading. The proposed model closely represents the damage to structures and yields a damage index (DI) for the RC members. The model is cumulative and is based on the energy absorbed. The energy under the monotonic envelope curve at the failure of the member is taken as a reference capacity. The data required to apply the model in any given situation or member can be obtained either by numerical simulation or from experimental tests. An analytical computer program was developed to simulate numerically the response of RC members taking into account the nonlinear behavior of the materials and structures involved. The proposed model was verified by comparison with practical tests undertaken by other researchers on over 20 RC columns. The comparison demonstrates that the model provides a realistic estimation of the damage of the RC structural members. The comparison between values of the proposed DI calculated based on experimental test data and numerical simulation results for a cyclic loading case shows that to calculate DI, it is not necessary to perform expensive experimental tests and that using a nonlinear structural analytical simulation is sufficient. The results are also compared to a damage model proposed by Meyer (1988).