Research On Optimum Design Of The Arch-cable-supported Roof Stadium's Configuration

In the existing arch-cable-supported roof stadiums,the main arches of vertical,outward and intersecting slopes have been all adopted,but the research and application of inclining main arches are rare.In this paper,the inclining arch-cable-supported roof structure adopted in the bidding scheme of a stadium in Weifang City is used as the background project,and the research on the canopy's static performance and shape parameters is carried out.Based on the optimization of cable tensions and optimization of arch section,the influence of roof shape and cable-arch shape parameters on the static characteristics of cable-arch system is studied.The main conclusions of this paper as follows:1.The arch-cable-supported roof structures are high-order statically indeterminate,and the cable forces influence each other to make the optimal cable force difficult to solve.The arch bending strain energy is used as the optimization goal,and the impact matrix method is used to consider the mutual influence of cable forces.The method of iteratively solving the optimal cable force has higher accuracy and stability,and provides a reliable basis for the parametric analysis of the body shape.2.Research on the shape of the roof revealed that:For roofs at both ends of the stands,if the cable hanging points are directly placed on the inner ring beams,the inner cables will have a low internal force and thus generate a large bending moment in the main arch.The terminal hanging point is set on the extension line of the inner ring of the main stand,which can greatly improve the hanging effect of the roofs at both ends and significantly reduce the internal force of the end cable and the bending moment of the main arch.It is a more reasonable and effective cable arrangement.3.The arch-cable-supported roof structure has many parameters,and it is difficult to express the relationship between each parameter and the overall performance index with explicit functional relationships.The automatic analysis and processing method for multi-parameter models based on the MATLAB platform can realize the automation of modeling,analysis,optimization,and results display of thousands models.It has greatly improved the efficiency of the analysis and facilitated the identification of the interaction between various parameters.4.Comparing the two arrangement methods of equal distance or vertical plane of the cable on the main arch,it is found that the cable along the vertical plane is better arranged.Due to the height of the arches,the end cables require multiple cables to share the same arch.When using equally spaced ropes,the distance between the hanging points has a significant influence on the bending moments of the arches,which needs to be optimized.5.The study of arch heights found that:When the arch height changes from 60m to 95m,the arch height ratio is between 1/3.8 and 1/2.4.With the increase of arch height,the arch bending strain energy decreases first and then increases.When the arch height is 80m,the bending strain energy is minimum.With the increase of the arch height,the amount of steel used for cable arches increases,the cable force distribution becomes more uniform,and the efficiency of hanging cables is significantly improved.However,after the arch height exceeds 85 meters,the cable force no longer significantly changes.Therefore,the arch height ranged from 65m to 85m,the corresponding arch span ratio range was 1/3.5 to1/2.68,and the minimum arch height was 80m,corresponding to a span height ratio of1/2.85.6.Through the study of the arch axis,we found:The bending energy of the main arch is closely related to the arch axis.When the arch axis uses a catenary or a parabola similar to the shape of a catenary,the bending energy of the main arch and the amount of steel volume are the smallest,and the range of reasonable inclination of the main arch is also relatively large.7.The distance between the main arches and the optimal inclination angle are the main factors that affect the bending strain energy of the arch and the amount of steel volume for the arching.The optimal position of the arch connecting line on the same side is within the1/2 span from the inner edge of the main stand roof.When the distance between the main arches is constant,if the arch angle is too large or too small,the bending strain energy and the amount of steel volume for the cable arch will increase.Each main arch spacing corresponds to an optimal inclination angle.When the distance between the main arches increases,the corresponding optimal inclination angle also gradually increases,reaching a maximum of 16~0.8.According to the corresponding relationship between the distance between the main arch and the optimal inclination angle,a series of main arch side facades with different spacing and inclination angles are drawn on the same figure.These projection lines are approximately equal to one point,and the intersection height is approximately 4/5.High,horizontal projection is about 1/10 of the inner edge of the main grandstand roof.Using this feature,the approximate optimal position of the main arch can be obtained by crossing the intersection with a slash.9.After optimization of the distance and inclination of the main arch,it is economically reasonable to use the inclining arch in the stadium's canopy.