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This article develops a vector-based 3D graphic statics framework that uses synthetic and intuitive graphical means for the analysis and design of spatial structures such as networks of bar elements in static equilibrium. It is intended to support the collaborative work of structural engineers and architects from the conceptual phase of the design process. Several procedures for the construction of a vector-based 3D force diagram for any given 3D form diagram with an underlying planar or non-planar graph are identified and described. In the non-planar case, the proposed procedures rely on the preliminary topological planarization of the graph by cutting the crossing edges and reconnecting them to one or more newly inserted auxiliary vertices. The resulting planar graph can be then used as a base for the assembly of the 3D force diagram, without altering the static equilibrium of the structure. An implementation of the proposed framework to real design scenarios is presented through two case studies. These examples show how to take advantage of the bi-directional manipulation of the diagrams in the structural design process.

Rehabilitation of weak and damaged structures has been considered widely during recent years. A relatively modern way of strengthening concrete components is to confine parts under tension and shear by means of carbon fiber reinforce polymer (CFRP). This way of strengthening due to the conditions of composite materials such as light weight, linear elastic behavior until failure point, high tensile strength, high elastic modulus, resistance against corrosion, and high fatigue resistance has become so common. During structural strengthening by means of not pre-stressed FRP materials, usually, it is not possible to benefit from the maximum capacity of FRP materials. In addition, sometimes, the expensive cost of such materials will not make a suitable balance between rates of strengthening and consuming spending. Thus, pre-stressing CFRP materials has an undeniable role in the effective use of materials. In the current research, general procedure of simulation using finiteelement method (FEM) by means of the numerical package ABAQUS has been presented. In this article, 12 reinforced concrete (RC) models in two states (strengthened with simple and pre-stressed CFRP) under cycling loading have been considered. A parametric study has been carried out in this research on the effects of parameters such as CFRP surface area, percentage of tensile steel rebar and pre-stressing stress on ultimate load carrying capacity (ULCC), stiffness, and the ability of depreciation energy for the samples. In the current article also, for design parameters, percentages of tensile steel rebars, surface area of CFPR sheets, and the effective pre-stressing stress in RC beams retrofitted with pre-stressed CFPR sheets have investigated. In this paper, it was investigated that using different amount of parameters such as steel rebar percentage, CFRP surface area percentage, and CFRP pre-stressing, the resulted ULCC and energy depreciation of the specimens was observed to be increasing and decreasing. Results from examined specimens with optimum steel rebar percentage, CFRP surface area percentage, and CFRP pre-stressing which had the most enhancement on ULCC and energy depreciation are reported in the current article.

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