Research on the Ultimate Bearing Capacity of Long Concrete Columns Made of Concrete-filled Steel Tubes with Dumbbell Axial Forces Date:2015-11-13 11:29
Research on ultimate bearing capacity of long concrete column with axially-loaded steel pipe and concrete dumbbells Chen Baochun, Sheng Ye 2 (1. School of Civil Engineering, Fuzhou University, Fuzhou 350002, China; 2. School of Transportation, Fujian Agriculture and Forestry University, Fuzhou, Fujian 350002, China) The failure of the specimen in the axial direction was destroyed by welding the corrugated steel plate in the direction of the weak axis to increase its flexural rigidity. The test results show that this method is feasible. Similar to single-axis axial compression columns, both the ultimate bearing capacity and the tangential stiffness at the elasto-plastic stage of the dumbbell-shaped axially compressed long column specimen decrease with the increase of the length-to-thickness ratio of the specimen. However, under the same slenderness ratio, it is different from the elastic instability failure of a long single-tube column, and the dumbbell-shaped long column is an elastoplastic failure. A non-linear finite element calculation method for a dumbbell-shaped axially long column is proposed. The parameter analysis of the influence of the slenderness ratio on the ultimate bearing capacity is performed. The results show that the stability coefficient of the dumbbell-shaped axial compression column is different from that of the single tube, but the variation of the ultimate bearing capacity along the strong axis and weak axial instability with the change of the slenderness ratio is basically the same. The unified stability factor simplifies the calculation formula. Fund Project: Fujian Province Basic Research Project Major Project (2003F007) Sheng Ye (1978―), female, Qianjiang, Hubei, lecturer, Ph.D., engaged in bridge and structural engineering research (E-mail: shengyefzu.edu.cn). Due to the fact that the dumbbell-shaped section of concrete-filled steel tube has the characteristics of large bending rigidity compared with the single-tube section, it is simpler in structure and simpler in shape than the rib-shaped arch rib, and it is widely used in steel-pipe concrete arch bridges with a span of 100m. application. The experimental study on the concrete-filled-steel concrete dumbbell-shaped axial compression and biased short columns shows that the force performance and the ultimate bearing capacity have their own characteristics compared with the single-tube and jaw-type sections. On the basis of experimental research, a simple iterative method for the ultimate bearing capacity of a concrete-filled steel tubular dumbbell-shaped axially compressed short column, a modified lattice algorithm for the ultimate bearing capacity of a short-biased short column, and an equivalent single-tube method were proposed. In addition, an experimental study was conducted on the dumbbell-shaped beam, and the section stress of the concrete with dumbbell-shaped cross section was analyzed. The slenderness ratio of concrete-filled steel tube dumbbell-shaped members used in arch ribs is large. However, no research has been done on concrete-filled concrete dumbbell-shaped long columns. For this reason, on the basis of the above studies, tests have been carried out to break the concrete-filled steel tubular dumbbell-shaped axially long columns in the weak-axis direction and to break them in the direction of the strong-axis. The finite element analysis with the slenderness ratio as a parameter was performed on a dumbbell-shaped long column. The test results and finite element analysis results show that under the same slenderness ratio change, the stability of dumbbell-shaped axial compression columns is better than that of single-tube axial compression columns, and the calculation formula of the stability coefficient of the dumbbell-shaped axial compression columns is proposed. 1 Introduction to the test 1.1 Specimen design and fabrication Two sets of specimens were used, in which group A was the specimen that was damaged along the weak axis and group C was the specimen that was destroyed along the strong axis. The rigidity of the dumbbell-shaped section in the direction of the strong axis is several times that in the direction of the weak-axis direction. The weak axial direction is basically two single circular tubes subjected to force, and the strong axial bending moment of inertia is relatively large, and the force is also more complicated than the single circular tube. In the absence of external stiffening, the concrete-filled-steel-concrete dumbbell-shaped axially long columns are destabilized and destroyed in the direction of the weak axis. In order to make it break along the strong axis, this paper proposes a test method for stiffening the corrugated steel plate in the direction of the weak axis of the dumbbell-shaped long column. The longitudinal stiffness of the corrugated steel sheet is very small (the axial effective elastic modulus is a few hundredth of the original elastic modulus) and basically does not withstand the axial compressive stress. In the direction of the weak axis of the dumbbell-shaped axially-pressed long column, it is stiffened with a corrugated steel plate. The purpose is to improve the weak axial bending stiffness of the dumbbell-shaped long column without increasing its axial compression bearing capacity. Therefore, in the specimens of this article, the specimens that were damaged in the weak axial direction in the A group were specimens without corrugated steel plates, and the specimens in the C group that were damaged along the strong axis were specimens with corrugated steel plates. The cross-sectional dimensions of the two sets of test pieces are the same as the basic components of the concrete-filled steel tubular dumbbell-shaped short column. See the two small 108mmx4m seamless steel tubes and 4mm thick steel webs welded together. A rectangular steel plate with a thickness of 10mm and a length and width of 320mmx180mm. The cross section of the test piece section/mm wave plate is 180mm, and the vertical distance from the wave crest to the wave trough is 40mm and the thickness is 4mm. The schematic diagram is as shown in the figure, in order to make the wave plate and the press bottom plate not contact when the component is compressed in the longitudinal direction. Its longitudinal length is slightly shorter than the length of the test piece, and 4mm thick stiffener plates are installed at both ends of the wave plate to prevent premature buckling. The corrugated steel plate/mm steel pipe and abdominal cavity were filled with C50 concrete. The steel pipe was made of Q345 steel. The steel material yield strength was determined to be 321.6MPa, tensile strength/=469MPa, steel elastic modulus K=2.01x105MPa, and concrete cubic resistance. Compression strength/ca=49.9MPa, axial standard compressive strength/t=33.4MPa, concrete elastic modulus £c=3.45x104MPa. For group A specimens, the flexural rigidity in the direction of the strong axis and weak axis of the section =9.93: The flexural stiffness in the x-axis (strong axis) direction is greater than the flexural stiffness in the minor axis (weak axis) direction. Axially loaded long column specimens will lose stability in the direction of the weak axis (y-axis). For group C specimens, the bending stiffness/f and flexural stiffness in the x-axis and j-axis directions are set to be 1.41x (the strong axis direction of the front section of the corrugated steel plate is not set) instead of the bending stiffness of the corrugated steel plate. Less than j-axis bending stiffness. This makes the failure of long column specimens destabilize along the strong axis (x axis). =Z// is the parameter change, in which i is the test piece design length, which is 400mm, 800mm, 1600mm, 2400mm, 3200mm, respectively, / is the radius of gyration of the cross section. The group A specimen is weak along the weak axis, weak axial equivalent Radius of gyration /=/y/A= 26mm. The corrugated steel plate is set in the direction of the weak axis of the test piece of Group C. The axial force is destabilized along the strong axis, and the strong equivalent gyration radius of the axial direction is yj/x/A. = 74.3mm. The details of each test piece are shown in Table 1, in which A0-0, C0-0, and C1-0 are short columns. There are two functions: one is to compare the stability coefficient of the long column; the other is to compare the effect of the corrugated steel plate on the axial compressive strength of the component (because there is no problem of destruction of the strong axis direction or failure of the weak axis direction) . Table 1 Specimen data list Table Specimen number Corrugated steel web has 1.2 test erection test carried out on a 500t press at the structural engineering test center of Fuzhou University. The test piece is equipped with longitudinal and circumferential strain gages at the middle section and the four point cross section, and a dial indicator is set at the upper and lower end plates to test the vertical displacement. Weak Axis Instability Test Sets a displacement meter at each quartile of the weak axis to measure the horizontal deflection at i/4, i/2, and 3i/4. The middle section is unable to set the percent due to the stiffening of the corrugated steel plate. In the table, a dial gauge with a range of 30 was set on the outside of two dumbbell-shaped tubes to test the weak axial deflection of the long column. Strong axial destabilization test Set a dial gauge with a range of 50 in the axial section of the middle section to test the axial deflection. The test device is shown. The test adopts graded loading, and the load holding time of each stage is about 2 The effect of the corrugated steel plate on the strength of the dumbbell-shaped axial compression The purpose of the corrugated steel plate welding on the C-type test piece is to increase the weak axial bending stiffness, so that the specimen It can be destroyed along strong axial directions, but it should not affect the strength of axially compressed short columns. For this purpose, the results of the axial compression short column test for corrugated plateless A0-0 and corrugated steel plate C0-0 and C1-0 are compared (A0-0, C0-0 specimen length to thin ratio 1 is 5.4, C1 The -0 slenderness ratio 1 is 10.8, both less than 16, within the short column range). From the load-vertical deformation curves of the three specimens, it can be seen that the ultimate bearing capacity of A0-0 and C0-0, C1-0 is basically the same, and the load-vertical deformation curve is also very similar. The setting of the waveform steel plate is similar to the dumbbell. The ultimate bearing capacity of axially compressed short columns does not substantially affect the strength of specimens (see). 3 axial compression column test results and analysis 3.1 test specimen failure morphology Axial compression column tests show that the specimen is very good elastoplasticity and ductility, in the case of large deformation can still withstand a certain amount of load. The long column specimens of group A suffered weak axial bending and the weak axial deflection of the specimens. The long column specimens of group C showed strong axial compression and bending, and the setting of corrugated steel plates effectively inhibited the instability of the dumbbell-shaped long columns from weak axial failure. The folding effect of the corrugated steel plate makes it entirely free to deform with the overall deformation of the test piece, and only part of the test piece will undergo local buckling due to local deformation (mainly near the end) in the middle of the corrugated steel plate. 3.2 Load-Vertical Deformation Curves (a), (b) are load-vertical deformation curves for two sets of specimens at different slenderness ratios. It can be seen that with the increase of the slenderness ratio, the tangential stiffness of the elastoplastic stage of the specimen decreases, the elastic segment shortens, and the ultimate bearing capacity decreases significantly. The finite element analysis in Section 4.2 further validates this rule. The relationship between the ultimate load and the slenderness ratio of the two sets of test pieces can be seen. It can be seen that when the lengths and deniers of the two sets of specimens are the same, the ultimate load is basically the same, and the variation law with the slenderness ratio is basically the same. It should be pointed out that strong axial destabilization occurs in the specimens of group C, and the strong axial stiffness is 2.82 times the weak axial stiffness. In the same length (high) degree, the slenderness ratio is much smaller than that of the group A specimens. , The ultimate bearing capacity is much larger than the A group specimen. Slenderness ratio L// Limit load and slenderness ratio curve 3.3 Load-horizontal deflection curve The load-middle cross-sectional horizontal deflection curve of the two sets of specimens is given. It can be seen from the above that the horizontal deflection curve of the dumbbell-shaped long column specimen and the single-column-long column specimen is basically consistent with the change rule of the slenderness ratio. With the increase of the slenderness ratio, the corresponding load of the component entering the elastic-plastic segment decreases. small. The increase in the horizontal deflection of the specimen of Group A was faster than that of the Group C specimens, and the falling segment was also more pronounced than that of the Group C specimens. This is because group A specimens are destabilized along the weak axis. When horizontal deflection occurs, their ability to resist deformation is similar to that of a single tube. The bending moment of inertia in the strong axis direction of the dumbbell section is much larger than that of a single tube. The ability to resist deformation is stronger than that of a single tube, and there is no single tube that is prone to destabilization. m/horizontal deflection/mm load - mid-span horizontal deflection test curve 3.4 Load-midsection longitudinal edge strain curve is the load-middle section edge longitudinal strain curve of the test piece, where the left side is the maximum longitudinal compression strain, and the right side is the maximum longitudinal Pull strain. It can be seen from the above that, under the effect of additional bending moments, the specimens of group A are deformed by the compression and bending of the whole section, and the strain distribution of the middle section shows a large biasing force when the specimens are near failure. The specimens of group C have a slenderness ratio of 5.4-43.1, which is equivalent to a medium-long column. Under close to failure, the entire section is compressed. The mid-section strain distribution shows a small bias dumbbell-length column specimen and a single tube length. The change rule of the load-strain curve with the slenderness ratio of the column specimens is basically the same, and the ultimate bearing capacity and the maximum longitudinal compressive strain decrease with the increase of the slenderness ratio. However, in the case of the slenderness ratio Z//e(80,120), the maximum longitudinal strain at the edges of the dumbbell-shaped long columns exceeds 30008 at the time of failure. This is much larger than the yield strain of the steel measured in this paper's material test of 1600 呷, which is elastic-plastic. Instability. When the length of the long single-tube tube is Z//e(80,120), the longitudinal strain corresponding to the maximum edge is about 1000 mesh to 1500 mesh, which is elastic instability failure. 4 Finite Element Analysis 4.1 Finite Element Analysis According to the statistical data of the actual arch bridge, the slenderness ratio Z// of the dumbbell-shaped concrete-filled steel tubular arch varies from 40 to 120 (where the calculated length Z takes the arc length of the half-span arch With an effective length factor of 0.72). Due to the limitation of experimental conditions, the number of specimens in Group A and the length-to-fineness ratio of Group C specimens are restricted in this paper. The scope of parameter analysis needs to be expanded by finite element calculation. This article uses a large-scale general-purpose software ANSYS for finite element analysis. The dumbbell-shaped concrete-filled steel tubular column was modeled by the elastic-plastic beam element BEAM188, and the corrugated steel plate was modeled by the SHELL181 element. The finite element model of the test piece was 0. Due to the fact that the actual structure had initial defects, the calculation was made to allow the group A (group C) specimen along In the direction of the weak axis (strong axis), instability is lost, and the initial bending of i/1000 (i is the length of the member) is given in the weak axis (strong axis) direction of the specimen. Steel-tube concrete composite materials are modeled using a two-unit approach, in which the external unit is assigned the properties of the steel material and the internal unit is assigned the properties of the concrete material. It is known that the load-deformation curve and the Poisson's ratio curve of the two circular tubes in the dumbbell-shaped section are basically the same as those of the single-tube concrete-filled steel tube, which can be considered as a single-tube. Intra-abdominal concrete has minimal cuffs and can be considered as ordinary concrete. Therefore, in this article, the core concrete in the round pipe adopts the hoop concrete constitutive relationship expressed in one-dimensional manner. The specific formulas are described in detail. The Hognested ordinary concrete constitutive model was used for the intra-abdominal concrete, and the stress-strain relationship of the steel was a tetra-line constitutive model. The input of the material constitutive relation model adopts the multi-linear isotropic reinforcement model (MISO) provided by ANSYS based on the Von Mises yield criterion. Newton-Raph on method for solving nonlinear finite element method. 4.2 Load-Vertical Deformation Curve Calculation Results The load-vertical deformation curve of group A specimens and group C specimens is consistent with the variation of slenderness ratio. In the load-vertical deformation curve of group 1, two sets of tests are given. The finite element calculation curve (dotted line) of the test curve (solid line) and part of the slenderness ratio change. The calculation curve and the test curve fit better. 4.3 Calculation results of ultimate bearing capacity The test values ​​and calculated values ​​of the ultimate bearing capacity are defined in the same way. When the load-vertical displacement curve has no descending section, the load corresponding to a longitudinal strain of 10000 为 is the ultimate bearing capacity with a descending section. The load corresponding to the highest point of the load-displacement curve is the ultimate bearing capacity. Table 2 shows the comparison between the calculated values ​​of the finite element and the experimental values, in which the stability factor test value ==/W0e, the calculation value of the stability factor ==%/%, and the meaning =16 is used as the long and thin score of the short column and the long column. The boundary points, W0e, and % meters respectively correspond to the experimental values ​​of the ultimate bearing capacity of the axially compressed short columns with slenderness ratio of 1 to 16 and the calculated average values. Table 2 Comparison between calculated value and test value Loss of direction Slenderness ratio 1 Ultimate load capacity/kN Stability factor Ni meter N, calculated by gage meter Weak axial strength Axial ratio Mean value ratio variance From Table 2 can be seen: ultimate bearing capacity The ratios of the calculated values ​​of the stability coefficient and the experimental values ​​are 0.970 and 1.017, respectively, and the ratio variances are 0.014 and 0.015, respectively, which indicates that the finite element method proposed in this paper can calculate the stable ultimate bearing capacity of the axially-stressed concrete-filled steel tubular columns with high axial compression. . 5 Simplified algorithm for ultimate bearing capacity Following the equivalent single-tube method in a short column, the dumbbell-shaped axially-elongated column is equivalent to a single-column tube with an outer diameter = 4/(/for a dumbbell-shaped radius of gyration). The formula for calculating the ultimate bearing capacity of a long column is as follows: For details, see the following discussion of the method for calculating the coefficient of stability milk. The test values ​​for the coefficient of stability of the members of Group A and Group C (see the penultimate column in Table 2) are marked in 2 in the form of small dots and small triangles. Calculate the value of the calculated value of the stability factor of the A group member and the C group member (see the penultimate column in Table 2) in the form of hollow dots and hollow triangles. The relationship between the slenderness ratio L//2 stability factor and slenderness ratio curve 2 is also given in the domestic CECS, JCJ and DL/T three steel tube concrete structure specifications provided by the single-tube long column stability coefficient milk curve. It can be seen from Fig. 2 that the stability coefficients provided by the domestic CECS, JCJ, and DL/T three regulations for single-column long columns cannot be directly applied to long-duty dumbbell-shaped columns. The calculated value of the stability coefficient of the long shaft compression column (weak axial instability) for the calculated value of the milk pressure meter and the experimental value of the component A of the group A component is as follows: The calculated value of the calculated value of the group C component is the following: The slenderness ratio i/z is a variable regression fitting (the regression coefficient quadratic value is 0.9806), and the calculation formula for the stability factor of the long shaft compression column (strong axial instability) is as follows: Due to the strong (weak) dumbbell-shaped long columns The ultimate bearing capacity of the shaft destabilization decreases exponentially with the increase of the slenderness ratio, and the regular curves are basically the same. Consider the formula (4) (Regression coefficient A square is visible by 2 and the formula (4) energy It is a good reflection of the regularity of the ultimate bearing capacity of concrete-filled steel tubular dumbbell-shaped axially-pressed columns (disrupted along strong and weak shafts), which can be used for engineering purposes. For strong axial damage, this paper proposes a method for welding the corrugated steel plate to the direction of the weak axis of the test piece. The test results show that it does not affect the strength of the axially compressed short column and can increase the weak axial stiffness to damage along the strong axis. The test results show that this method is feasible. Whether the failure is along the strong axis or the weak axis, the outer wall of the long column specimen has no local convexity or cracking, and the failure mode is the overall instability failure; with the increase of the slenderness ratio, the elasticity of the specimen The tangential stiffness of the stage is reduced, the elastic segment is shortened, and the ultimate bearing capacity is significantly reduced.Using the large-scale general program ANSYS, a finite element analysis of a dumbbell-shaped axially compressed long column is performed. The calculated results are in good agreement with the experimental results. The law of the change of the ultimate bearing capacity with the slenderness ratio of the column (strong axis, weak axial instability) is basically the same, and the ultimate bearing capacity of the two can be calculated using a unified formula. A simplified simplified formula for engineering applications is proposed in this paper.
Research on ultimate bearing capacity of long concrete column with axially-loaded steel pipe and concrete dumbbells Chen Baochun, Sheng Ye 2 (1. School of Civil Engineering, Fuzhou University, Fuzhou 350002, China; 2. School of Transportation, Fujian Agriculture and Forestry University, Fuzhou, Fujian 350002, China) The failure of the specimen in the axial direction was destroyed by welding the corrugated steel plate in the direction of the weak axis to increase its flexural rigidity. The test results show that this method is feasible. Similar to single-axis axial compression columns, both the ultimate bearing capacity and the tangential stiffness at the elasto-plastic stage of the dumbbell-shaped axially compressed long column specimen decrease with the increase of the length-to-thickness ratio of the specimen. However, under the same slenderness ratio, it is different from the elastic instability failure of a long single-tube column, and the dumbbell-shaped long column is an elastoplastic failure. A non-linear finite element calculation method for a dumbbell-shaped axially long column is proposed. The parameter analysis of the influence of the slenderness ratio on the ultimate bearing capacity is performed. The results show that the stability coefficient of the dumbbell-shaped axial compression column is different from that of the single tube, but the variation of the ultimate bearing capacity along the strong axis and weak axial instability with the change of the slenderness ratio is basically the same. The unified stability factor simplifies the calculation formula. Fund Project: Fujian Province Basic Research Project Major Project (2003F007) Sheng Ye (1978―), female, Qianjiang, Hubei, lecturer, Ph.D., engaged in bridge and structural engineering research (E-mail: shengyefzu.edu.cn). Due to the fact that the dumbbell-shaped section of concrete-filled steel tube has the characteristics of large bending rigidity compared with the single-tube section, it is simpler in structure and simpler in shape than the rib-shaped arch rib, and it is widely used in steel-pipe concrete arch bridges with a span of 100m. application. The experimental study on the concrete-filled-steel concrete dumbbell-shaped axial compression and biased short columns shows that the force performance and the ultimate bearing capacity have their own characteristics compared with the single-tube and jaw-type sections. On the basis of experimental research, a simple iterative method for the ultimate bearing capacity of a concrete-filled steel tubular dumbbell-shaped axially compressed short column, a modified lattice algorithm for the ultimate bearing capacity of a short-biased short column, and an equivalent single-tube method were proposed. In addition, an experimental study was conducted on the dumbbell-shaped beam, and the section stress of the concrete with dumbbell-shaped cross section was analyzed. The slenderness ratio of concrete-filled steel tube dumbbell-shaped members used in arch ribs is large. However, no research has been done on concrete-filled concrete dumbbell-shaped long columns. For this reason, on the basis of the above studies, tests have been carried out to break the concrete-filled steel tubular dumbbell-shaped axially long columns in the weak-axis direction and to break them in the direction of the strong-axis. The finite element analysis with the slenderness ratio as a parameter was performed on a dumbbell-shaped long column. The test results and finite element analysis results show that under the same slenderness ratio change, the stability of dumbbell-shaped axial compression columns is better than that of single-tube axial compression columns, and the calculation formula of the stability coefficient of the dumbbell-shaped axial compression columns is proposed. 1 Introduction to the test 1.1 Specimen design and fabrication Two sets of specimens were used, in which group A was the specimen that was damaged along the weak axis and group C was the specimen that was destroyed along the strong axis. The rigidity of the dumbbell-shaped section in the direction of the strong axis is several times that in the direction of the weak-axis direction. The weak axial direction is basically two single circular tubes subjected to force, and the strong axial bending moment of inertia is relatively large, and the force is also more complicated than the single circular tube. In the absence of external stiffening, the concrete-filled-steel-concrete dumbbell-shaped axially long columns are destabilized and destroyed in the direction of the weak axis. In order to make it break along the strong axis, this paper proposes a test method for stiffening the corrugated steel plate in the direction of the weak axis of the dumbbell-shaped long column. The longitudinal stiffness of the corrugated steel sheet is very small (the axial effective elastic modulus is a few hundredth of the original elastic modulus) and basically does not withstand the axial compressive stress. In the direction of the weak axis of the dumbbell-shaped axially-pressed long column, it is stiffened with a corrugated steel plate. The purpose is to improve the weak axial bending stiffness of the dumbbell-shaped long column without increasing its axial compression bearing capacity. Therefore, in the specimens of this article, the specimens that were damaged in the weak axial direction in the A group were specimens without corrugated steel plates, and the specimens in the C group that were damaged along the strong axis were specimens with corrugated steel plates. The cross-sectional dimensions of the two sets of test pieces are the same as the basic components of the concrete-filled steel tubular dumbbell-shaped short column. See the two small 108mmx4m seamless steel tubes and 4mm thick steel webs welded together. A rectangular steel plate with a thickness of 10mm and a length and width of 320mmx180mm. The cross section of the test piece section/mm wave plate is 180mm, and the vertical distance from the wave crest to the wave trough is 40mm and the thickness is 4mm. The schematic diagram is as shown in the figure, in order to make the wave plate and the press bottom plate not contact when the component is compressed in the longitudinal direction. Its longitudinal length is slightly shorter than the length of the test piece, and 4mm thick stiffener plates are installed at both ends of the wave plate to prevent premature buckling. The corrugated steel plate/mm steel pipe and abdominal cavity were filled with C50 concrete. The steel pipe was made of Q345 steel. The steel material yield strength was determined to be 321.6MPa, tensile strength/=469MPa, steel elastic modulus K=2.01x105MPa, and concrete cubic resistance. Compression strength/ca=49.9MPa, axial standard compressive strength/t=33.4MPa, concrete elastic modulus £c=3.45x104MPa. For group A specimens, the flexural rigidity in the direction of the strong axis and weak axis of the section =9.93: The flexural stiffness in the x-axis (strong axis) direction is greater than the flexural stiffness in the minor axis (weak axis) direction. Axially loaded long column specimens will lose stability in the direction of the weak axis (y-axis). For group C specimens, the bending stiffness/f and flexural stiffness in the x-axis and j-axis directions are set to be 1.41x (the strong axis direction of the front section of the corrugated steel plate is not set) instead of the bending stiffness of the corrugated steel plate. Less than j-axis bending stiffness. This makes the failure of long column specimens destabilize along the strong axis (x axis). =Z// is the parameter change, in which i is the test piece design length, which is 400mm, 800mm, 1600mm, 2400mm, 3200mm, respectively, / is the radius of gyration of the cross section. The group A specimen is weak along the weak axis, weak axial equivalent Radius of gyration /=/y/A= 26mm. The corrugated steel plate is set in the direction of the weak axis of the test piece of Group C. The axial force is destabilized along the strong axis, and the strong equivalent gyration radius of the axial direction is yj/x/A. = 74.3mm. The details of each test piece are shown in Table 1, in which A0-0, C0-0, and C1-0 are short columns. There are two functions: one is to compare the stability coefficient of the long column; the other is to compare the effect of the corrugated steel plate on the axial compressive strength of the component (because there is no problem of destruction of the strong axis direction or failure of the weak axis direction) . Table 1 Specimen data list Table Specimen number Corrugated steel web has 1.2 test erection test carried out on a 500t press at the structural engineering test center of Fuzhou University. The test piece is equipped with longitudinal and circumferential strain gages at the middle section and the four point cross section, and a dial indicator is set at the upper and lower end plates to test the vertical displacement. Weak Axis Instability Test Sets a displacement meter at each quartile of the weak axis to measure the horizontal deflection at i/4, i/2, and 3i/4. The middle section is unable to set the percent due to the stiffening of the corrugated steel plate. In the table, a dial gauge with a range of 30 was set on the outside of two dumbbell-shaped tubes to test the weak axial deflection of the long column. Strong axial destabilization test Set a dial gauge with a range of 50 in the axial section of the middle section to test the axial deflection. The test device is shown. The test adopts graded loading, and the load holding time of each stage is about 2 The effect of the corrugated steel plate on the strength of the dumbbell-shaped axial compression The purpose of the corrugated steel plate welding on the C-type test piece is to increase the weak axial bending stiffness, so that the specimen It can be destroyed along strong axial directions, but it should not affect the strength of axially compressed short columns. For this purpose, the results of the axial compression short column test for corrugated plateless A0-0 and corrugated steel plate C0-0 and C1-0 are compared (A0-0, C0-0 specimen length to thin ratio 1 is 5.4, C1 The -0 slenderness ratio 1 is 10.8, both less than 16, within the short column range). From the load-vertical deformation curves of the three specimens, it can be seen that the ultimate bearing capacity of A0-0 and C0-0, C1-0 is basically the same, and the load-vertical deformation curve is also very similar. The setting of the waveform steel plate is similar to the dumbbell. The ultimate bearing capacity of axially compressed short columns does not substantially affect the strength of specimens (see). 3 axial compression column test results and analysis 3.1 test specimen failure morphology Axial compression column tests show that the specimen is very good elastoplasticity and ductility, in the case of large deformation can still withstand a certain amount of load. The long column specimens of group A suffered weak axial bending and the weak axial deflection of the specimens. The long column specimens of group C showed strong axial compression and bending, and the setting of corrugated steel plates effectively inhibited the instability of the dumbbell-shaped long columns from weak axial failure. The folding effect of the corrugated steel plate makes it entirely free to deform with the overall deformation of the test piece, and only part of the test piece will undergo local buckling due to local deformation (mainly near the end) in the middle of the corrugated steel plate. 3.2 Load-Vertical Deformation Curves (a), (b) are load-vertical deformation curves for two sets of specimens at different slenderness ratios. It can be seen that with the increase of the slenderness ratio, the tangential stiffness of the elastoplastic stage of the specimen decreases, the elastic segment shortens, and the ultimate bearing capacity decreases significantly. The finite element analysis in Section 4.2 further validates this rule. The relationship between the ultimate load and the slenderness ratio of the two sets of test pieces can be seen. It can be seen that when the lengths and deniers of the two sets of specimens are the same, the ultimate load is basically the same, and the variation law with the slenderness ratio is basically the same. It should be pointed out that strong axial destabilization occurs in the specimens of group C, and the strong axial stiffness is 2.82 times the weak axial stiffness. In the same length (high) degree, the slenderness ratio is much smaller than that of the group A specimens. , The ultimate bearing capacity is much larger than the A group specimen. Slenderness ratio L// Limit load and slenderness ratio curve 3.3 Load-horizontal deflection curve The load-middle cross-sectional horizontal deflection curve of the two sets of specimens is given. It can be seen from the above that the horizontal deflection curve of the dumbbell-shaped long column specimen and the single-column-long column specimen is basically consistent with the change rule of the slenderness ratio. With the increase of the slenderness ratio, the corresponding load of the component entering the elastic-plastic segment decreases. small. The increase in the horizontal deflection of the specimen of Group A was faster than that of the Group C specimens, and the falling segment was also more pronounced than that of the Group C specimens. This is because group A specimens are destabilized along the weak axis. When horizontal deflection occurs, their ability to resist deformation is similar to that of a single tube. The bending moment of inertia in the strong axis direction of the dumbbell section is much larger than that of a single tube. The ability to resist deformation is stronger than that of a single tube, and there is no single tube that is prone to destabilization. m/horizontal deflection/mm load - mid-span horizontal deflection test curve 3.4 Load-midsection longitudinal edge strain curve is the load-middle section edge longitudinal strain curve of the test piece, where the left side is the maximum longitudinal compression strain, and the right side is the maximum longitudinal Pull strain. It can be seen from the above that, under the effect of additional bending moments, the specimens of group A are deformed by the compression and bending of the whole section, and the strain distribution of the middle section shows a large biasing force when the specimens are near failure. The specimens of group C have a slenderness ratio of 5.4-43.1, which is equivalent to a medium-long column. Under close to failure, the entire section is compressed. The mid-section strain distribution shows a small bias dumbbell-length column specimen and a single tube length. The change rule of the load-strain curve with the slenderness ratio of the column specimens is basically the same, and the ultimate bearing capacity and the maximum longitudinal compressive strain decrease with the increase of the slenderness ratio. However, in the case of the slenderness ratio Z//e(80,120), the maximum longitudinal strain at the edges of the dumbbell-shaped long columns exceeds 30008 at the time of failure. This is much larger than the yield strain of the steel measured in this paper's material test of 1600 呷, which is elastic-plastic. Instability. When the length of the long single-tube tube is Z//e(80,120), the longitudinal strain corresponding to the maximum edge is about 1000 mesh to 1500 mesh, which is elastic instability failure. 4 Finite Element Analysis 4.1 Finite Element Analysis According to the statistical data of the actual arch bridge, the slenderness ratio Z// of the dumbbell-shaped concrete-filled steel tubular arch varies from 40 to 120 (where the calculated length Z takes the arc length of the half-span arch With an effective length factor of 0.72). Due to the limitation of experimental conditions, the number of specimens in Group A and the length-to-fineness ratio of Group C specimens are restricted in this paper. The scope of parameter analysis needs to be expanded by finite element calculation. This article uses a large-scale general-purpose software ANSYS for finite element analysis. The dumbbell-shaped concrete-filled steel tubular column was modeled by the elastic-plastic beam element BEAM188, and the corrugated steel plate was modeled by the SHELL181 element. The finite element model of the test piece was 0. Due to the fact that the actual structure had initial defects, the calculation was made to allow the group A (group C) specimen along In the direction of the weak axis (strong axis), instability is lost, and the initial bending of i/1000 (i is the length of the member) is given in the weak axis (strong axis) direction of the specimen. Steel-tube concrete composite materials are modeled using a two-unit approach, in which the external unit is assigned the properties of the steel material and the internal unit is assigned the properties of the concrete material. It is known that the load-deformation curve and the Poisson's ratio curve of the two circular tubes in the dumbbell-shaped section are basically the same as those of the single-tube concrete-filled steel tube, which can be considered as a single-tube. Intra-abdominal concrete has minimal cuffs and can be considered as ordinary concrete. Therefore, in this article, the core concrete in the round pipe adopts the hoop concrete constitutive relationship expressed in one-dimensional manner. The specific formulas are described in detail. The Hognested ordinary concrete constitutive model was used for the intra-abdominal concrete, and the stress-strain relationship of the steel was a tetra-line constitutive model. The input of the material constitutive relation model adopts the multi-linear isotropic reinforcement model (MISO) provided by ANSYS based on the Von Mises yield criterion. Newton-Raph on method for solving nonlinear finite element method. 4.2 Load-Vertical Deformation Curve Calculation Results The load-vertical deformation curve of group A specimens and group C specimens is consistent with the variation of slenderness ratio. In the load-vertical deformation curve of group 1, two sets of tests are given. The finite element calculation curve (dotted line) of the test curve (solid line) and part of the slenderness ratio change. The calculation curve and the test curve fit better. 4.3 Calculation results of ultimate bearing capacity The test values ​​and calculated values ​​of the ultimate bearing capacity are defined in the same way. When the load-vertical displacement curve has no descending section, the load corresponding to a longitudinal strain of 10000 为 is the ultimate bearing capacity with a descending section. The load corresponding to the highest point of the load-displacement curve is the ultimate bearing capacity. Table 2 shows the comparison between the calculated values ​​of the finite element and the experimental values, in which the stability factor test value ==/W0e, the calculation value of the stability factor ==%/%, and the meaning =16 is used as the long and thin score of the short column and the long column. The boundary points, W0e, and % meters respectively correspond to the experimental values ​​of the ultimate bearing capacity of the axially compressed short columns with slenderness ratio of 1 to 16 and the calculated average values. Table 2 Comparison between calculated value and test value Loss of direction Slenderness ratio 1 Ultimate load capacity/kN Stability factor Ni meter N, calculated by gage meter Weak axial strength Axial ratio Mean value ratio variance From Table 2 can be seen: ultimate bearing capacity The ratios of the calculated values ​​of the stability coefficient and the experimental values ​​are 0.970 and 1.017, respectively, and the ratio variances are 0.014 and 0.015, respectively, which indicates that the finite element method proposed in this paper can calculate the stable ultimate bearing capacity of the axially-stressed concrete-filled steel tubular columns with high axial compression. . 5 Simplified algorithm for ultimate bearing capacity Following the equivalent single-tube method in a short column, the dumbbell-shaped axially-elongated column is equivalent to a single-column tube with an outer diameter = 4/(/for a dumbbell-shaped radius of gyration). The formula for calculating the ultimate bearing capacity of a long column is as follows: For details, see the following discussion of the method for calculating the coefficient of stability milk. The test values ​​for the coefficient of stability of the members of Group A and Group C (see the penultimate column in Table 2) are marked in 2 in the form of small dots and small triangles. Calculate the value of the calculated value of the stability factor of the A group member and the C group member (see the penultimate column in Table 2) in the form of hollow dots and hollow triangles. The relationship between the slenderness ratio L//2 stability factor and slenderness ratio curve 2 is also given in the domestic CECS, JCJ and DL/T three steel tube concrete structure specifications provided by the single-tube long column stability coefficient milk curve. It can be seen from Fig. 2 that the stability coefficients provided by the domestic CECS, JCJ, and DL/T three regulations for single-column long columns cannot be directly applied to long-duty dumbbell-shaped columns. The calculated value of the stability coefficient of the long shaft compression column (weak axial instability) for the calculated value of the milk pressure meter and the experimental value of the component A of the group A component is as follows: The calculated value of the calculated value of the group C component is the following: The slenderness ratio i/z is a variable regression fitting (the regression coefficient quadratic value is 0.9806), and the calculation formula for the stability factor of the long shaft compression column (strong axial instability) is as follows: Due to the strong (weak) dumbbell-shaped long columns The ultimate bearing capacity of the shaft destabilization decreases exponentially with the increase of the slenderness ratio, and the regular curves are basically the same. Consider the formula (4) (Regression coefficient A square is visible by 2 and the formula (4) energy It is a good reflection of the regularity of the ultimate bearing capacity of concrete-filled steel tubular dumbbell-shaped axially-pressed columns (disrupted along strong and weak shafts), which can be used for engineering purposes. For strong axial damage, this paper proposes a method for welding the corrugated steel plate to the direction of the weak axis of the test piece. The test results show that it does not affect the strength of the axially compressed short column and can increase the weak axial stiffness to damage along the strong axis. The test results show that this method is feasible. Whether the failure is along the strong axis or the weak axis, the outer wall of the long column specimen has no local convexity or cracking, and the failure mode is the overall instability failure; with the increase of the slenderness ratio, the elasticity of the specimen The tangential stiffness of the stage is reduced, the elastic segment is shortened, and the ultimate bearing capacity is significantly reduced.Using the large-scale general program ANSYS, a finite element analysis of a dumbbell-shaped axially compressed long column is performed. The calculated results are in good agreement with the experimental results. The law of the change of the ultimate bearing capacity with the slenderness ratio of the column (strong axis, weak axial instability) is basically the same, and the ultimate bearing capacity of the two can be calculated using a unified formula. A simplified simplified formula for engineering applications is proposed in this paper.
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