The Unified Solution of Dumbbell Type Steel Pipe Concrete Arch Rib Considering Initial Stress Date:2015-10-28 09:07

The large number of applications of concrete-filled steel tubular arch bridges in various countries has attracted extensive attention from engineering and academia, and its theoretical research on ultimate bearing capacity has also been continuously improved. However, the existing research generally only considers geometric nonlinearity and material nonlinearity problems, but considers less impact on the initial stress of the steel pipe (abbreviated as â€œinitial stressâ€, the same below). The existence of the initial stress occupies part of the bearing capacity of the steel tube, resulting in the reduction of the ultimate bearing capacity of the concrete filled steel tube and the advancement of the yielding stage of the steel tube. It affects the elasto-plastic stage of the overall work of the member and increases the structural deformation. Therefore, research on the influence of initial stress on the ultimate bearing capacity of CFST arch bridge is of great significance to the design and construction of CFST arch bridge, and it can provide a reliable basis for improving the design theory of CFST arch bridge. The theoretical research on the initial stress of concrete-filled steel tubular arch ribs is mainly reflected in some early monographs and norms. In contrast, China has made more researches in recent years. The main ones are: Zhou Shuixing et al. The solid-space beam element and space beam element are used to calculate the bearing capacity of dumbbell-shaped concrete-filled steel tubular arch bridges. The initial stress limit of the dumbbell-type concrete-filled steel tubular arch ribs and the calculation formula of the initial stress influence coefficient are given. Yang Menggang et al. applied the finite element analysis method. The ultimate bearing capacity stability factor of steel-concrete-filled concrete arch bridges with or without initial stress was obtained. Wei Jiangang et al., through experimental research and finite element analysis, proposed the calculation formula for the ultimate bearing capacity of single-tube concrete-filled steel tubular arch ribs under initial stress. Although there have been many studies on the initial stress of concrete-filled steel tubular arch ribs in China, there are still some deficiencies in various calculation theories. The main expressions are as follows: 1 The calculation formula of the initial stress influence coefficient is mostly fitted by the test curve or numerical simulation curve. Too, there is a lack of theoretical basis; 2 The computational process or computational expressions are tedious and inconvenient for practical application of engineering. Therefore, other simplified methods for calculating the ultimate bearing capacity of steel-concrete arch ribs are of great significance to the engineering practice. In this paper, based on the unified strength theory, a new simplified method for calculating the bearing capacity of dumbbell-shaped concrete-filled steel tubular arch ribs is proposed. The formula for calculating the initial stress-influencing coefficient is deduced and a unified solution for the ultimate bearing capacity of arch ribs is established to provide a practical application for the project. 1 Unified strength theory The unified strength theory takes into account the influence of the intermediate principal stress and the ratio of material tension and pressure, and can be applied to various stress states and various types of materials. It includes infinite strength theory and yield criterion such as Tresca yield criterion and Mises yield criterion, and proposes a series of new strength theory. The formula derived from its ultimate bearing capacity is called unified solution of ultimate bearing capacity. The principal stress expression of the unified strength theory is 1, 2nd and 3rd principal stress; a is the ratio of material tension and compression; (s, (c, Ts) are the material's tensile yield stress, compressive yield stress and shear yield respectively. Stress; b is the coefficient that reflects the degree of influence of the intermediate principal shear stress and the normal stress of the corresponding surface on the material damage, and is also the parameter of choosing different strength theory. When b=Â°, it is the Mohr-Coulomb strength criterion, when b=1 For double shear strength theory, when a = 1, b = Â°, and Â° 5,1, then the linear approximation of the resca's yield criterion, Mises yield criterion and double shear yield criterion B are the shear stress coefficients. The ultimate bearing capacity of concrete arch ribs is shown in the dumbbell section of steel-concrete concrete, where D is the outer diameter of a single-limb concrete-filled steel tube in which the diameter of the core concrete in the core of the single-limb tube is the thickness of the steel tube and the web, and a is the spacing between the webs. 4 is the web height A is the distance between the two limbs of the steel tube heart;H is the total height of the dumbbell-shaped section.Steel-filled concrete dumbbell section 2.1 Equivalent bias column equivalent beam column method Equivalent beam column method Borrow the elastic buckling calculation of the equivalent column Concept, will Arch ribs are equivalent to simply supported straight columns of concrete-filled steel tubes. Eccentric axial forces (axial forces and bending moments of the corresponding arch sections) are applied at both ends of the columns. Equivalents are obtained by using the method for calculating the ultimate bearing capacity of concrete-filled steel columns. The ultimate axial force of the column is the ultimate axial force of the corresponding arch section, and then the ultimate bearing capacity of the arch rib is calculated using the relationship between the internal force of the arch rib and the external load. When the influence of the vector span ratio is not considered, it is called simple. The equivalent beam-column method, when considering the influence of the span-span ratio, is called the modified equivalent beam-column method.In this paper, the modified equivalent beam-column method is used, the equivalent length is the reference, and the equivalent length and equivalent force are selected as the table. Table 1. Table 1 Parameters for selection of equivalent beam-column method parameters Asymmetric load action Symmetrical load action Equivalent force Cross-section position Arch foot arch 2.1.2 Equivalent eccentric column Ultimate load capacity According to the equivalent beam column method, the initial stress will be considered. The dumbbell-shaped concrete-filled steel tube arch rib is equivalent to a biased column. Its ultimate bearing capacity is expressed as Nu-KeNf, (3) the ultimate bearing capacity of the compressed column, and Np is the dumbbell-type concrete-filled steel tube axial compression column considering initial stress. Limit bearing Force;% is the stability factor that considers factors such as slenderness ratio, span-to-span ratio, and initial defects, and the value of the calculation method is the reduction factor considering the eccentricity.The eccentricity r is the dumbbell-shaped concrete-filled steel tube section etc. The radius of the dumbbell-shaped concrete-filled steel tube column defines the initial stress and the index of the axial stress of the 24-tube axial compression coefficient is determined according to â€œSpecifications for Design of Steel Structuresâ€ (GB5...17-20.3). The equivalent single-tube method can obtain the cross-sectional area of â€‹â€‹As soil; AS1, Ad are the cross-sectional area of â€‹â€‹the single-limb steel pipe and the single-limb steel concrete respectively. A1 - is also widely Kdt, A11 - n4. A2, Ac2 is the web and The cross-sectional area of â€‹â€‹the intra-abdominal concrete, the As2 equivalent single-tube cross-section and the force conditions are shown as follows: The equivalent single-tube cross-section has an outer diameter of dia., the core concrete diameter is d, and the steel tube thickness is /, in the axial direction. Under the action of load ore, the lateral restraining force provided for the core equivalent single-pipe cross-section and the stressed concrete is that the steel pipe is subjected to a circumferential tensile stress of %, and the axial compressive stress is the initial stress. When you do two. At that time, the concrete-filled steel tube members were degraded into concrete-filled steel tube members that did not consider initial stress. 2.2.1 Stress analysis of steel tubes When steel tubes are yielded under triaxial stress with axial compression, ring pull, and radial compression, the hoop stress increases, the longitudinal load capacity decreases, and the steel yield strength/s and the strength of the concrete are reduced. And other factors such as the impact. 1p and fc external impact analysis According to statistics, the commonly used value of the span ratio w = / / L of the dumbbell-shaped concrete-filled steel pipe arch ribs is 0. 10.5 (/ is the height of the arch ribs, L is the arch rib span), n The value range is 4% to 10%, and the value of A is 60.

The large number of applications of concrete-filled steel tubular arch bridges in various countries has attracted extensive attention from engineering and academia, and its theoretical research on ultimate bearing capacity has also been continuously improved. However, the existing research generally only considers geometric nonlinearity and material nonlinearity problems, but considers less impact on the initial stress of the steel pipe (abbreviated as â€œinitial stressâ€, the same below). The existence of the initial stress occupies part of the bearing capacity of the steel tube, resulting in the reduction of the ultimate bearing capacity of the concrete filled steel tube and the advancement of the yielding stage of the steel tube. It affects the elasto-plastic stage of the overall work of the member and increases the structural deformation. Therefore, research on the influence of initial stress on the ultimate bearing capacity of CFST arch bridge is of great significance to the design and construction of CFST arch bridge, and it can provide a reliable basis for improving the design theory of CFST arch bridge. The theoretical research on the initial stress of concrete-filled steel tubular arch ribs is mainly reflected in some early monographs and norms. In contrast, China has made more researches in recent years. The main ones are: Zhou Shuixing et al. The solid-space beam element and space beam element are used to calculate the bearing capacity of dumbbell-shaped concrete-filled steel tubular arch bridges. The initial stress limit of the dumbbell-type concrete-filled steel tubular arch ribs and the calculation formula of the initial stress influence coefficient are given. Yang Menggang et al. applied the finite element analysis method. The ultimate bearing capacity stability factor of steel-concrete-filled concrete arch bridges with or without initial stress was obtained. Wei Jiangang et al., through experimental research and finite element analysis, proposed the calculation formula for the ultimate bearing capacity of single-tube concrete-filled steel tubular arch ribs under initial stress. Although there have been many studies on the initial stress of concrete-filled steel tubular arch ribs in China, there are still some deficiencies in various calculation theories. The main expressions are as follows: 1 The calculation formula of the initial stress influence coefficient is mostly fitted by the test curve or numerical simulation curve. Too, there is a lack of theoretical basis; 2 The computational process or computational expressions are tedious and inconvenient for practical application of engineering. Therefore, other simplified methods for calculating the ultimate bearing capacity of steel-concrete arch ribs are of great significance to the engineering practice. In this paper, based on the unified strength theory, a new simplified method for calculating the bearing capacity of dumbbell-shaped concrete-filled steel tubular arch ribs is proposed. The formula for calculating the initial stress-influencing coefficient is deduced and a unified solution for the ultimate bearing capacity of arch ribs is established to provide a practical application for the project. 1 Unified strength theory The unified strength theory takes into account the influence of the intermediate principal stress and the ratio of material tension and pressure, and can be applied to various stress states and various types of materials. It includes infinite strength theory and yield criterion such as Tresca yield criterion and Mises yield criterion, and proposes a series of new strength theory. The formula derived from its ultimate bearing capacity is called unified solution of ultimate bearing capacity. The principal stress expression of the unified strength theory is 1, 2nd and 3rd principal stress; a is the ratio of material tension and compression; (s, (c, Ts) are the material's tensile yield stress, compressive yield stress and shear yield respectively. Stress; b is the coefficient that reflects the degree of influence of the intermediate principal shear stress and the normal stress of the corresponding surface on the material damage, and is also the parameter of choosing different strength theory. When b=Â°, it is the Mohr-Coulomb strength criterion, when b=1 For double shear strength theory, when a = 1, b = Â°, and Â° 5,1, then the linear approximation of the resca's yield criterion, Mises yield criterion and double shear yield criterion B are the shear stress coefficients. The ultimate bearing capacity of concrete arch ribs is shown in the dumbbell section of steel-concrete concrete, where D is the outer diameter of a single-limb concrete-filled steel tube in which the diameter of the core concrete in the core of the single-limb tube is the thickness of the steel tube and the web, and a is the spacing between the webs. 4 is the web height A is the distance between the two limbs of the steel tube heart;H is the total height of the dumbbell-shaped section.Steel-filled concrete dumbbell section 2.1 Equivalent bias column equivalent beam column method Equivalent beam column method Borrow the elastic buckling calculation of the equivalent column Concept, will Arch ribs are equivalent to simply supported straight columns of concrete-filled steel tubes. Eccentric axial forces (axial forces and bending moments of the corresponding arch sections) are applied at both ends of the columns. Equivalents are obtained by using the method for calculating the ultimate bearing capacity of concrete-filled steel columns. The ultimate axial force of the column is the ultimate axial force of the corresponding arch section, and then the ultimate bearing capacity of the arch rib is calculated using the relationship between the internal force of the arch rib and the external load. When the influence of the vector span ratio is not considered, it is called simple. The equivalent beam-column method, when considering the influence of the span-span ratio, is called the modified equivalent beam-column method.In this paper, the modified equivalent beam-column method is used, the equivalent length is the reference, and the equivalent length and equivalent force are selected as the table. Table 1. Table 1 Parameters for selection of equivalent beam-column method parameters Asymmetric load action Symmetrical load action Equivalent force Cross-section position Arch foot arch 2.1.2 Equivalent eccentric column Ultimate load capacity According to the equivalent beam column method, the initial stress will be considered. The dumbbell-shaped concrete-filled steel tube arch rib is equivalent to a biased column. Its ultimate bearing capacity is expressed as Nu-KeNf, (3) the ultimate bearing capacity of the compressed column, and Np is the dumbbell-type concrete-filled steel tube axial compression column considering initial stress. Limit bearing Force;% is the stability factor that considers factors such as slenderness ratio, span-to-span ratio, and initial defects, and the value of the calculation method is the reduction factor considering the eccentricity.The eccentricity r is the dumbbell-shaped concrete-filled steel tube section etc. The radius of the dumbbell-shaped concrete-filled steel tube column defines the initial stress and the index of the axial stress of the 24-tube axial compression coefficient is determined according to â€œSpecifications for Design of Steel Structuresâ€ (GB5...17-20.3). The equivalent single-tube method can obtain the cross-sectional area of â€‹â€‹As soil; AS1, Ad are the cross-sectional area of â€‹â€‹the single-limb steel pipe and the single-limb steel concrete respectively. A1 - is also widely Kdt, A11 - n4. A2, Ac2 is the web and The cross-sectional area of â€‹â€‹the intra-abdominal concrete, the As2 equivalent single-tube cross-section and the force conditions are shown as follows: The equivalent single-tube cross-section has an outer diameter of dia., the core concrete diameter is d, and the steel tube thickness is /, in the axial direction. Under the action of load ore, the lateral restraining force provided for the core equivalent single-pipe cross-section and the stressed concrete is that the steel pipe is subjected to a circumferential tensile stress of %, and the axial compressive stress is the initial stress. When you do two. At that time, the concrete-filled steel tube members were degraded into concrete-filled steel tube members that did not consider initial stress. 2.2.1 Stress analysis of steel tubes When steel tubes are yielded under triaxial stress with axial compression, ring pull, and radial compression, the hoop stress increases, the longitudinal load capacity decreases, and the steel yield strength/s and the strength of the concrete are reduced. And other factors such as the impact. 1p and fc external impact analysis According to statistics, the commonly used value of the span ratio w = / / L of the dumbbell-shaped concrete-filled steel pipe arch ribs is 0. 10.5 (/ is the height of the arch ribs, L is the arch rib span), n The value range is 4% to 10%, and the value of A is 60.

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