Abstract
Objective: To present a methodology for implementing in MathCAD, a based on force densities for analytical form finding to three-dimensional cable net structures subjected to static loading. It is desired that the routines present a stability of the solution algorithm and fast convergence. Methodology: Theoretical background of the cable net structures behavior and FDM are first introduced. Then, a series of MathCAD routines are created to perform the nonlinear analysis of cable net structures. Finally, a well-documented cable net structure example found in the literature, and the results from a cable net software are used as a way to validate the output results provided by the created MathCAD routines. Results: The simulation results show that the proposed methodology implemented in MathCAD can accurately estimate the free nodes displacements and cable forces of 3D cable net structures subjected to vertical and horizontal static loading. Conclusions: This paper has demostrated that the propossed methodology is consistent when comparing with the results given in the reference paper and the used software. Stability of the algorithms is controlled and no numerical issues was presented during the analyzed examples thus, divergence complications were not found. The routines provided a clear way to visualize the assumptions, methods, and critical data obtained in the geometric analysis of cable net structures helping to overcome the inherit limitations of commercial packages.
Highlights
Cable net structures are commonly encountered in facade systems, buildings lobbies, stadiums, and other structures
The nonlinear analysis of cable structures is decomposed into smaller well-defined Mathcad programming functions, and in a second step, the combination of these programing functions comprises the way to perform the structural analysis of cable structures
A methodology for implementing in Mathcad an approach based on force densities for analytical form finding of three-dimensional cable net structures subjected to static loading is presented
Summary
Cable net structures are commonly encountered in facade systems, buildings lobbies, stadiums, and other structures. These type of structures are comprised by tension only hinge-connected members. The analysis of cable structures represents a significant challenge because of factors such as: (i) the definition of the analytical model to find the initial shape of the cable net structure and the cable forces associated to that state, (ii) in cable net analysis is rather common to find divergence in the calculations as a result of the selected iterative scheme, (iii) cable net structures are generally more flexible than conventional structural systems, but the system can exhibit a significant increase of rigidity when cable pretension is applied, (iv) the relation between a change in the loading and the corresponding displacement is nonlinear, (v) cable structures cannot transfer external loads through shear, axial compression or bending moment, and (vi) the possibility of wind-induced oscillations to affect cable net structures. The displacement is decomposed into a rigid body motion in the global coordinate system and a pure small deformation in the local coordinate system [2]
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