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An effective form-finding method for form-fixed spatial network structures is presented in this paper. The adaptive formfinding method is introduced along with the example of designing an ellipsoidal network dome with bar length variations being as small as possible. A typical spherical geodesic network is selected as an initial state, having bar lengths in a limit group number. Next, this network is transformed into the ellipsoidal shape as desired by applying compressions on bars according to the bar length variations caused by transformation. Afterwards, the dynamic relaxation method is employed to explicitly integrate the node positions by applying residual forces. During the form-finding process, the boundary condition of constraining nodes on the ellipsoid surface is innovatively considered as reactions on the normal direction of the surface at node positions, which are balanced with the components of the nodal forces in a reverse direction induced by compressions on bars. The node positions are also corrected according to the fixed-form condition in each explicit iteration step. In the serial results of time history, the optimal solution is found from a time history of states by properly choosing convergence criteria, and the presented form-finding procedure is proved to be applicable for form-fixed problems.

This paper investigates the application and reliability of using high-order mode shape derivatives especially, the fourth derivative in damage detection of plate-like structures. Numerical analyses have been carried out for low-and high-order mode shapes of simply supported and cantilever steel plate models. Six scenarios of damages are studied for plate models to represent different damage characteristics. The influence of artificial noise on the damage identification using changes in fourth derivative of mode shapes has been investigated. Based on the numerical studies, it is shown that the fourth derivative of mode shape is promising in detecting and locating structural damage in plate-like structures since it is localized at the damage locations even for a small amount of damage using only one of the mode shapes. Both low-and high-order mode shapes give successful results. Also, damage indices of the fourth derivatives give smoother localization and consequently better damage identification than those of curvature of mode shapes. Furthermore, using high-order modes (which can be measured by advanced sensors) does not improve the results of damage identification using the fourth derivative. Unfortunately, damage detection using changes in fourth derivative of mode shapes is sensitive to measurement noise.

Pushover analysis has been recommended as a reliable tool to estimate the seismic capacity of the structures. Vertical irregular structures are highly vulnerable during earthquakes due to stiffness irregularity in their elevations. Hence, seismic capacities of these types of structures need to be re-estimated during structural design stage. So, in this paper, an attempt has been made to assess the actual seismic performance of buildings with two common types of vertical irregularities such as; soft story and setback in comparison with regular (reference) building. These types of vertical irregularities are studied in individual cases, combined in one story, and combined in two different stories of the building models, while most previous studies satisfy with individual type of vertical irregularity case in the studied model. In addition, combined vertical irregularity generates extra weak points, which alter the seismic capacities, failure mode mechanism, and performance point location. Three-dimensional numerical models are created to find out significant response demand such as; the variation in periods of vibration, lateral displacement, inter-story drift, pushover curve, and plastic hinges formation. The results showed that vertical irregular buildings are subjected to early damages and have less seismic capacity than regular one. The fundamental time period becomes misleading term in seismic force calculation for vertical geometric irregular buildings and needs to be re-considered. In addition, extra lateral displacement and inter-story drift are passively generated in the vertical irregular buildings due to sudden change in stiffness. Significant negative variation in the pushover curves, ductility ratios, and plastic hinges' formation is observed when combinations of pre-mentioned vertical irregularity cases occur. Buildings with open soft ground story with asymmetric setback should have additional precautions from international codes during structural design stage according to their irregularity ratio. Therefore, response modification/reduction factor (R) may be scaled-down to adapt these negative variation in seismic capacities.

Most design codes assume the nonlinear seismic performance of structures using response reduction/modification factor (R). The R factor is sensitive to a variety of factors in terms of overall ductility and over-strength. This research assesses the actual R factor for vertical irregularity cases for RC bare buildings with moment-resisting frames (MRF) systems. Also, this research derives a significant relationship between R values and identified vertical irregularity index calculated from relative stiffness between adjacent stories. Three-dimensional numerical models are carried out for the soft story and setback irregularity scenarios using ETABS. Modal pushover analysis (MPA) is selected to obtain the inelastic seismic capacity. The obtained results demonstrate that vertical irregular buildings have weak inelastic seismic capacities compared to regular one. So, the response modification factor (R) should be scaled down before the design stage by 15% to 40% for single and combined vertical irregularity scenarios. Structures with a combined asymmetric setback with a soft ground story experience the worst R factor. Also, R factors are sensitive to the identified vertical irregularity index (Vtm) that has 80% regression percent. So, it may be used to specify the allowable vertical irregularity ratio, location, and combination for each seismic zone.

Structural damage identification has recently become one of the most important topics for engineering structures due to its benefits in enhancing safety, reducing life-cycle cost, and providing guidance for system construction and maintenance. This research studies the accuracy of using displacement influence lines (DIL) and their derivatives (first and second derivative) for detecting structural damage characteristics (location and severity). The study includes analytical and numerical studies to investigate the sensitivity of displacement influence lines and their derivatives (first and second derivative) as a main parameter for damage identification. The results illustrate that the method can locate and quantify damage in both simply supported and continuous beams without the need for an optimization algorithm. Although, for simply supported beam, the optimal location of the displacement measurement point is at the middle of span. While, for continuous beam, one displacement sensor at the middle of each span enables locating the damages reliably. The advantages and disadvantages of using this index are also discussed.