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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.

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The calculation of fundamental time period of vibration is a crucial step in seismic design and analysis of the structures to assess global response of the structure. Different international code proposed empirical expressions considering only height for bare frame structures and height and width of the buildings with infill to estimate the fundamental time period. This paper summaries the effect of the following parameters of building height, bay width, number of bays, cracked or un-cracked section of the structural member and support condition at the base on the fundamental time period of reinforced concrete bare frame and buildings with infill. Modal analysis of 360 building models with selected parameters is investigated in this study. A new equation, which is a function of the selected parameters (building height, bay width, number of bays, type of support condition, cracked or un-cracked sections and type of frame chosen for analysis) is also proposed using multiple linear regression analysis for predicting the fundamental period of buildings. The proposed simple model, including the building height, bay width, number of bays, type of support condition, cracked or un-cracked sections and type of frame chosen for analysis, showed better estimate in predicting the fundamental period of buildings compared to the code equations.