This study considers a symmetrical finite strip with a length of 2L and a width of 2h containing two collinear edge cracks located at the center of the strip. Each edge crack has a width h&amp / #8211 / a. Two ends of the finite strip are bonded to two rigid plates through which uniformly distributed axial tensile loads of intensity p0 are applied. The finite strip is assumed to be made of a linearly elastic and isotropic material. For the solution of the finite strip problem, an infinite strip of width 2h containing two internal cracks of width b&amp / #8211 / a at y=0 and two rigid inclusions of width 2c at y=&plusmn / L is considered. When the width of rigid inclusions approach the width of the strip, the portion of the infinite strip between the inclusions becomes identical with the finite strip problem. When the outer edges of the internal cracks approach the edge of the strip, they become edge cracks (notches). Governing equations are solved by using Fourier transform technique and these equations are reduced to a system of three singular integral equations. By using Gauss-Lobatto and Gauss-Jacobi integration formulas, these three singular integral equations are converted to a system of linear algebraic equations which is solved numerically.

In many seismic design codes and provisions, such as Uniform Building Code and Turkish Seismic Code, prediction of fundamental period of shear-wall dominant buildings, constructed by tunnel form technique, to compute the anticipated seismic forces is achieved by empirical equations considering the height of the building and ratio of effective shear-wall area to first floor area as the primary predictor parameters. However, experimental and analytical studies have collectively indicated that these empirical formulas are incapable of predicting fundamental period of shear-wall dominant buildings, and consequently result in erroneous computation of design forces. To compensate for this deficiency, an effective yet simple formula has recently been developed by Balkaya and Kalkan (2004), and tested against the data from ambient surveys on existing shear-wall dominant buildings. In this study, previously developed predictive equation is modified to include the effects of soil-structure interaction on the fundamental period. For that purpose, 140 shear-wall dominant buildings having a variety of plans, heights and wall-configurations were re-analyzed for four different soil conditions classified according to NEHRP. The soil effects on the foundation were represented by the translational and rotational springs, and their rigidities were evaluated from foundation size and elastic uniform compressibility of soil. Based on the comprehensive study conducted, improved prediction of fundamental period is achieved. The error in predictions on average is about 15 percent, and lending further credibility to modified formula considering soil-structure interaction to be used in engineering practice.

In this study, a combined genetic algorithm and non-linear optimisation system is designed and used in the identification of structural damage of a cantilever isotropic beam regarding its location and severity. The vibration-based features, both natural frequencies (i.e. eigenvalues) and displacement mode shapes (i.e. eigenvectors) of the structure in the first two out of plane bending modes, are selected as damage features for various types of damage comprising saw-cut and impact. For this purpose, commercial finite element modelling (FEM) and analysis software Msc. Patran/Nastran&reg / is used to obtain the aforementioned features from intact and damaged structures. Various damage scenarios are obtained regarding saw-cut type damage which is modelled as change in the element thicknesses and impact type damage which is modelled as a reduction of the elastic modulus of the elements in the finite element models. These models are generated by using both 1-D bar elements and 2-D shell type elements in Msc. Patran&reg / and then normal mode analyses are performed in order to extract element stiffness and mass matrices by using Msc. Nastran&reg / . Sensitivity matrices are then created by changing the related properties (i.e. reduction in elastic modulus and thickness) of the individual elements via successive normal mode analyses. The obtained sensitivity matrices are used as coefficients of element stiffness and/or mass matrices to construct global stiffness and/or mass matrices respectively. Following this, the residual force vectors obtained for different damage scenarios are minimised via a combined genetic algorithm and non-linear optimisation system to identify damage location and severity. This minimisation procedure is performed in two steps. First, the algorithm tries to minimise residual force vector (RFV) by only changing element stiffness matrices by aiming to detect impact type damage, as elastic modulus change is directly related to stiffness matrix. Secondly, it performs a minimisation over RFV by changing both element stiffness and mass matrices which aims to detect saw-cut type damage where thickness change is a function of both stiffness and mass matrices. The prediction of the damage type is then made by comparing the objective function value of these two steps. The lowest value (i.e. the fittest) indicates the damage type. The results of the minimisation also provide value of intactness where one representing intact and any value lower than one representing damage severity. The element related to that particular intactness value indicates the location of the damage on the structure. In case of having intactness values which are lower than one in value at various locations shows the existence of multi damage cases and provides their corresponding severities. The performance of the proposed combined genetic algorithm and non-linear optimisation system is tested on various damage scenarios created at different locations with different severities for both single and multi damage cases. The results indicate that the method used in this study is an effective one in the determination of type, severity and location of the damage in beam-like structures.