Geopolymer-based cold-formed thin-walled steel composite column and load-bearing capacity calculation method thereof

Abstract

The application discloses a geopolymer-based cold-bending thin-walled steel composite column and a bearing capacity calculation method thereof, the composite column comprising two cold-bending thin-walled C-shaped steels and geopolymer foam concrete filled in a closed cavity surrounded by the two cold-bending thin-walled C-shaped steels. The bearing capacity calculation method of the composite column comprises the following steps: S1, finite element analysis; S2, stiffening rib influence analysis; S3, axial compression strength enhancement coefficient analysis; and S4, comprehensive calculation. The ultimate bearing capacity of the composite column is improved by 1.4 times compared with a hollow split component, and the section shape influence coefficient gamma of the composite column and the axial compression strength enhancement coefficient omega c of the geopolymer foam concrete are introduced into a conventional bearing capacity calculation formula, the bearing capacity calculation formula is modified, and the expected calculation result of the bearing capacity of the composite column is more accurate.

Description

Technical Field

[0001] This invention relates to the field of building structural materials technology, specifically to a geopolymer-based cold-formed thin-walled steel composite column and its load-bearing capacity calculation method. Background Technology

[0002] With the continuous development of green building, the concept of sustainable development is receiving increasing attention, and green environmental protection has become an issue that cannot be ignored in the development of the construction industry today. Cold-formed steel (CFS) structure low-rise residential systems have advantages such as low carbon footprint, low energy consumption, lightweight and high strength, environmental friendliness and economy, and short construction period, which aligns with my country's direction of strengthening the prefabrication and industrialization of residential components. However, due to the relatively thin thickness and large width-to-thickness ratio of CFS sections, it is prone to buckling failure, seriously affecting the safety and comfort of the building structure. Therefore, further optimization of its structural system is necessary.

[0003] Geopolymers are inorganic cementitious materials primarily made from solid wastes such as fly ash, slag, and tailings. They are produced through a chemical reaction in an alkaline environment using appropriate processes, and are a new type of green building material. Slag is a solid waste generated after ore smelting, and fly ash is the fine ash from the flue gas produced after coal combustion. Compared to ordinary silicate cement, slag and fly ash, as raw materials for geopolymers, can reduce carbon emissions by 26% to 45% during the preparation process. By rationally utilizing these solid wastes to replace silicate cement and combining them with an alkali activator, geopolymer foamed concrete (GFC) possesses advantages such as early strength and rapid hardening, corrosion resistance, high temperature resistance, sound insulation and noise reduction, and thermal insulation. Casting it into CFS columns can also eliminate the hollow sound present in existing light steel structure systems. It exhibits excellent performance in waste utilization, energy conservation and environmental protection, lateral stiffness, and seismic performance. Compared to earlier reinforced concrete columns and steel-concrete composite columns, cold-formed steel-polymer foamed concrete columns (CFS-GFC columns) have better seismic performance due to their high ductility and energy absorption. Furthermore, they are more economical than traditional construction methods, reducing labor requirements and allowing for rapid construction. This not only aligns with the development direction of my country's construction industrialization but also conforms to the development trend of energy conservation and emission reduction in the construction industry.

[0004] To promote the widespread use of this type of component, many scholars have conducted related research. However, there is limited research on CFS composite columns filled with polymer foamed concrete. The impact of the polymer foamed concrete filling on the buckling capacity and buckling mode of the CFS tube is not discussed in detail, and the influence of the density of the polymer foamed concrete filling on the buckling capacity and buckling mode of the CFS tube remains unclear. More importantly, no current code specifically proposes a method for calculating the bearing capacity of CFS-GFC columns. Therefore, it is necessary to analyze the stress characteristics and failure modes of CFS-GFC columns under axial compression, discuss their performance under axial compression and their mutual constraint relationship, and thus explore the calculation formula for CFS-GFC columns. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a geopolymer-based cold-formed thin-walled steel composite column and a method for calculating its bearing capacity.

[0006] The technical solution of this invention is:

[0007] A geopolymer-based cold-formed thin-walled steel composite column includes two cold-formed thin-walled C-shaped steels and geopolymer foam concrete filled in a closed cavity enclosed by the two cold-formed thin-walled C-shaped steels. The two ends of the two cold-formed thin-walled C-shaped steels are sealed by welding steel plates.

[0008] The inner rolled edges of the two cold-formed thin-walled C-shaped steels are butted together and welded together. Four welding points are evenly spaced along the length of the inner rolled edges. A stiffening rib is provided at the center of the outer wall of each of the two cold-formed thin-walled C-shaped steels to form a symmetrical single rib. The width of the stiffening rib is 0.5-1mm and the length of the stiffening rib is 10-15mm.

[0009] The geopolymer foamed concrete is obtained by pouring geopolymer foamed concrete slurry into the sealed cavity and curing it. The geopolymer foamed concrete slurry is made by mixing slag and fly ash raw materials, alkali activator, water reducing agent and plant-based foaming agent. The density grade of the geopolymer foamed concrete slurry is A07, A10 or A12.

[0010] Furthermore, the length of the two cold-formed thin-walled C-shaped steel sections is 400-1000 mm, the outer wall height of the cold-formed thin-walled C-shaped steel section is 100-400 mm, the width of the upper and lower sides of the cold-formed thin-walled C-shaped steel section is 20-140 mm, the length of the inner rolled edge of the cold-formed thin-walled C-shaped steel section is 15-30 mm, the thickness of the cold-formed thin-walled C-shaped steel section is 0.5-3.5 mm, and the ratio of the width of the upper and lower sides of the cold-formed thin-walled C-shaped steel section to its thickness is 40-100.

[0011] Note: By optimizing and adjusting the length of the cold-formed thin-walled C-shaped steel, the overall length of the composite column is kept at a suitable value, which is more in line with the commonly used dimensions in production.

[0012] Further, by weight, the components of the slag and fly ash raw materials include: 330-340 parts of slag, 80-85 parts of fly ash, the alkali activator is made by mixing 12-15 parts of NaOH solid powder and 85-90 parts of water glass and dissolving them in 100-110 parts of deionized water, stirring until the NaOH solid powder is completely dissolved, the water-reducing agent is 0.3-0.5 parts, the foam after foaming by the plant-based foaming agent is 30-35 parts, and the curing method is to cover the surface of the combined column with a layer of plastic wrap and cure it at room temperature for 2 days before demolding.

[0013] Note: The preferred raw materials for slag and fly ash are widely available and have low costs.

[0014] Furthermore, two stiffening ribs are provided at equal intervals on the outer side walls of the two cold-formed thin-walled C-shaped steels to form symmetrical double ribs.

[0015] Note: By setting symmetrical double ribs, the appropriate option can be selected based on the usage environment of the composite column.

[0016] Furthermore, a corner stiffening rib is provided at the upper and lower ends of the outer side wall of each of the two cold-formed thin-walled C-shaped steel sections. The width of the corner stiffening rib is 0.5 to 1 mm, the extension direction of the corner stiffening rib is at 45° with the upper and lower sides of the cold-formed thin-walled C-shaped steel section, and the length of the corner stiffening rib is 10 to 15 mm.

[0017] Note: By setting symmetrical double ribs, the appropriate option can be selected based on the usage environment of the composite column.

[0018] A method for calculating the bearing capacity of a geopolymer-based cold-formed thin-walled steel composite column, as described in any of the above, includes the following steps:

[0019] S1. Finite element analysis: Four types of composite columns were established using ABAQUS software: composite column without stiffeners, symmetrical single-rib composite column, symmetrical double-rib composite column, and corner stiffener composite column. The ABAQUS concrete plastic damage model was used for modeling. The actual size of the composite column was used in the finite element model, and the mesh size was set to 5mm×5mm.

[0020] S2. Stiffening Rib Influence Analysis: The ultimate bearing capacity at the axial center of the composite column is calculated using the finite element model. The ultimate bearing capacity P1 of the composite column without stiffening ribs, the ultimate bearing capacity P2 of the symmetrical single-rib composite column, the ultimate bearing capacity P3 of the symmetrical double-rib composite column, and the ultimate bearing capacity P4 of the corner stiffening rib composite column are calculated respectively. The ultimate bearing capacity improvement coefficients γ1 = P2 / P1, γ2 = P3 / P2, and γ3 = P4 / P3 of the symmetrical single-rib composite column, the symmetrical double-rib composite column, and the corner stiffening rib composite column are calculated.

[0021] This leads to the coefficient of influence of the cross-sectional shape of the composite column, γ = (γ 1+ γ2+γ3) / 3;

[0022] S3. Analysis of Axial Compressive Strength Enhancement Coefficient: The stress zone is divided according to its area, specifically: A1: Central geopolymer foam concrete stress-enhancing zone area; A2: Corner geopolymer foam concrete stress-enhancing zone area; A3: Edge geopolymer foam concrete stress-enhancing zone area. A2 is the sum of the areas of the three grids at each corner; A3 is the sum of the grid areas corresponding to the cold-formed thin-walled C-shaped steel; A1 is the sum of the remaining grid areas, with a total grid area of ​​Ac. Then, based on the experimentally measured compressive strength f of the geopolymer foam concrete... c Furthermore, the average stress distribution af of the central geopolymer foam concrete was calculated using a finite element model. c The average stress distribution of corner geopolymer foam concrete, bf c The average stress distribution of edge-grown polymer foam concrete (cf) c Therefore, the area equivalent formula for the axial compressive strength enhancement factor ωc of geopolymer foam concrete can be derived as follows:

[0023] ω c f c A c =af c A1+bf c A2+cf c A3

[0024] Since A1+A2+A3=A c Therefore, ω can be derived. c The value;

[0025] S4. Comprehensive Calculation: The cross-sectional shape influence coefficient γ of the composite column obtained in step S2 and the axial compressive strength enhancement coefficient ωc of the geopolymer foam concrete obtained in step S3 are introduced into the modified bearing capacity calculation formula, which is shown in the following formula:

[0026] N≤0.9ψγ(α1ωc f c b c h c +2f a bt+2f a h c t)

[0027] Where: N is the design value of the axial compressive bearing capacity of the composite column; φ is the axial compressive stability coefficient of the composite column; fa is the design value of the compressive and tensile strength of the rectangular steel tube; bc is the cross-sectional width of the polymer foam concrete filling in the composite column; hc is the cross-sectional height of the polymer foam concrete filling in the composite column; b is the cross-sectional width of the composite column; and t is the thickness of the cold-formed thin-walled C-shaped steel.

[0028] Furthermore, in step S1, the steel plates at both ends of the composite column are simulated using rigid elements R3D4, the two cold-formed thin-walled C-shaped steels are simulated using 4-node reduced integral S4R shell elements, and the geopolymer foam concrete is simulated using 8-node reduced integral C3D8R solid elements. A binding method is used to simulate the weld points. The cold-formed thin-walled C-shaped steels and the geopolymer foam concrete are in surface-to-surface contact, with a "penalty" contact in the tangential direction, a friction coefficient of 0.25, and a "hard" contact in the normal direction. The two cold-formed thin-walled C-shaped steels are connected by a binding method to simulate the weld points. The yield strength of the cold-formed thin-walled C-shaped steels is 267.5 MPa, and the elastic modulus is 1.74 × 10⁻⁶. 5 MPa, Poisson's ratio is 0.3.

[0029] Note: The finite element model is made more accurate by optimizing and adjusting the parameters in the finite element analysis.

[0030] Furthermore, in step S2, the cold-formed thin-walled C-shaped steel and the stiffening ribs are connected by a binding connection.

[0031] Note: The finite element model is made more accurate by optimizing and adjusting the parameters in the finite element analysis.

[0032] The beneficial effects of this invention are:

[0033] (1) The present invention provides a composite column of polymer-based cold-formed thin-walled steel by pouring polymer foam concrete into two welded cold-formed thin-walled C-shaped steels. This not only retains the advantages of high industrialization and fast construction of cold-formed steel structure housing system, but also overcomes the shortcomings of cold-formed steel structure in terms of overall safety and comfort. The ultimate bearing capacity of the composite column is 1.4 times higher than that of hollow spliced ​​components, which enriches the structural system of low-rise housing and is of great significance for further research on light steel and light concrete structure system.

[0034] (2) The ultimate load of a geopolymer-based cold-formed thin-walled steel composite column of the present invention decreases as the width-to-thickness ratio increases. When the width-to-thickness ratio of the plate is in the range of 60-100, the utilization rate of geopolymer foam concrete is relatively high. The geopolymer foam concrete filling inside delays the occurrence of local buckling of CFS plate and the effect is more obvious when the width-to-thickness ratio is larger.

[0035] (3) The bearing capacity calculation method of the composite column based on polymer cold-formed thin-walled steel in this invention takes into account that since the internal core strength of the composite column is strengthened, the stress of the polymer foam concrete is smaller near the center and larger near the edge. At the same time, the stress reaches the maximum at the corner of the polymer foam concrete. Therefore, the stress area is divided according to the stress area. The cross-sectional shape influence coefficient γ of the composite column and the axial compressive strength enhancement coefficient ωc of the polymer foam concrete are introduced into the bearing capacity calculation formula in the "Technical Specification for Composite Structures". The bearing capacity calculation formula is modified to make the expected calculation result of the bearing capacity of the composite column more accurate. Attached Figure Description

[0036] Figure 1 These are the axial load-displacement relationship curves of the three combined columns in Experiment Example 1 of this invention;

[0037] Figure 2 These are the load-width-to-thickness ratio curves of different column combinations in Experimental Example 2 of this invention;

[0038] Figure 3 These are the load-axial displacement curves under different density levels in Experiment Example 3 of this invention;

[0039] Figure 4 This is the triaxial stress diagram of the composite column in Experimental Example 4 of this invention;

[0040] Figure 5 This is the stress cloud diagram of the composite column foam concrete in Experiment Example 4 of this invention;

[0041] Figure 6 This is a stress zone division diagram of the geopolymer foam concrete in Experiment Example 4 of this invention;

[0042] Figure 7 This refers to the error between the theoretical calculation value and the experimental and finite element values ​​in Experiment Example 4 of this invention;

[0043] Figure 8 This is a flowchart of a method for calculating the bearing capacity of a geopolymer-based cold-formed thin-walled steel composite column according to the present invention. Detailed Implementation

[0044] Example 1

[0045] A geopolymer-based cold-formed thin-walled steel composite column includes two cold-formed thin-walled C-shaped steels and geopolymer foam concrete filled in the closed cavity enclosed by the two cold-formed thin-walled C-shaped steels. The two ends of the two cold-formed thin-walled C-shaped steels are sealed by welding steel plates.

[0046] Two cold-formed thin-walled C-shaped steel sections have their inner rolled edges butt-jointed and welded together. Four weld points are evenly spaced along the length of the inner rolled edges. A stiffening rib is provided at the center of the outer wall of each of the two cold-formed thin-walled C-shaped steel sections, forming a symmetrical single rib. The width of the stiffening rib is 0.5 mm, and the length of the stiffening rib is 10 mm. The length of the two cold-formed thin-walled C-shaped steel sections is 900 mm. The height of the outer wall of the cold-formed thin-walled C-shaped steel section is 200 mm. The width of the upper and lower sides of the cold-formed thin-walled C-shaped steel section is 108 mm. The length of the inner rolled edge of the cold-formed thin-walled C-shaped steel section is 20 mm. The thickness of the cold-formed thin-walled C-shaped steel section is 1.8 mm. The ratio of the width of the upper and lower sides of the cold-formed thin-walled C-shaped steel section to its thickness is 60.

[0047] Geopolymer foamed concrete is obtained by pouring geopolymer foamed concrete slurry into a closed cavity and curing it. The geopolymer foamed concrete slurry is made by mixing slag and fly ash raw materials, alkali activator, water-reducing agent and plant-based foaming agent. The density grade of the geopolymer foamed concrete slurry is A07. The components of the slag and fly ash raw materials include: 335 parts slag, 83 parts fly ash, the alkali activator is made by mixing 13 parts NaOH solid powder and 87 parts water glass and dissolving them in 105 parts deionized water, stirring until the NaOH solid powder is completely dissolved, the water-reducing agent is 0.4 parts, and the foam after foaming by the plant-based foaming agent is 32 parts. The curing method is to cover the surface of the composite column with a layer of plastic wrap and cure it at room temperature for 2 days before demolding.

[0048] Example 2

[0049] The difference between this embodiment and Embodiment 1 is that the specific parameters are selected differently.

[0050] Two cold-formed thin-walled C-shaped steel sections have their inner rolled edges butted together and welded together. Four weld points are evenly spaced along the length of the inner rolled edges. Two stiffening ribs are evenly spaced on the outer walls of the two cold-formed thin-walled C-shaped steel sections, forming symmetrical double ribs. The width of the stiffening ribs is 1 mm, and the length of the stiffening ribs is 15 mm. The length of the two cold-formed thin-walled C-shaped steel sections is 1000 mm. The height of the outer wall of the cold-formed thin-walled C-shaped steel section is 400 mm. The width of the upper and lower sides of the cold-formed thin-walled C-shaped steel section is 140 mm. The length of the inner rolled edge of the cold-formed thin-walled C-shaped steel section is 30 mm. The thickness of the cold-formed thin-walled C-shaped steel section is 3.5 mm. The ratio of the width of the upper and lower sides of the cold-formed thin-walled C-shaped steel section to its thickness is 40.

[0051] Geopolymer foamed concrete is obtained by pouring geopolymer foamed concrete slurry into a closed cavity and curing it. The geopolymer foamed concrete slurry is made by mixing slag and fly ash raw materials, alkali activator, water-reducing agent and plant-based foaming agent. The density grade of the geopolymer foamed concrete slurry is A10. The components of the slag and fly ash raw materials include: 330 parts slag, 80 parts fly ash, the alkali activator is made by mixing 12 parts NaOH solid powder and 85 parts water glass and dissolving them in 100 parts deionized water, stirring until the NaOH solid powder is completely dissolved, the water-reducing agent is 0.3 parts, and the foam after foaming by the plant-based foaming agent is 30 parts. The curing method is to cover the surface of the composite column with a layer of plastic wrap and cure it at room temperature for 2 days before demolding.

[0052] Example 3

[0053] The difference between this embodiment and Embodiment 1 is that the specific parameters are selected differently.

[0054] Two cold-formed thin-walled C-shaped steel sections have their inner rolled edges butt-jointed and welded together. Four weld points are evenly spaced along the length of the inner rolled edges. A corner stiffening rib is provided at the upper and lower ends of the outer side walls of the two cold-formed thin-walled C-shaped steel sections. The corner stiffening rib is 0.6 mm wide and extends at a 45° angle to the upper and lower sides of the cold-formed thin-walled C-shaped steel section. The length of the corner stiffening rib is 12 mm. The length of the two cold-formed thin-walled C-shaped steel sections is 400 mm. The height of the outer side wall of the cold-formed thin-walled C-shaped steel section is 100 mm. The width of the upper and lower sides of the cold-formed thin-walled C-shaped steel section is 50 mm. The length of the inner rolled edge of the cold-formed thin-walled C-shaped steel section is 15 mm. The thickness of the cold-formed thin-walled C-shaped steel section is 0.5 mm. The ratio of the width to the thickness of the upper and lower sides of the cold-formed thin-walled C-shaped steel section is 100.

[0055] Geopolymer foamed concrete is obtained by pouring geopolymer foamed concrete slurry into a closed cavity and curing it. The geopolymer foamed concrete slurry is made by mixing slag and fly ash raw materials, alkali activator, water-reducing agent and plant-based foaming agent. The density grade of the geopolymer foamed concrete slurry is A12. The components of the slag and fly ash raw materials include: 340 parts slag, 85 parts fly ash, the alkali activator is made by mixing 15 parts NaOH solid powder and 90 parts water glass and dissolving them in 110 parts deionized water, stirring until the NaOH solid powder is completely dissolved, the water-reducing agent is 0.5 parts, and the foam after foaming by the plant-based foaming agent is 35 parts. The curing method is to cover the surface of the composite column with a layer of plastic wrap and cure it at room temperature for 2 days before demolding.

[0056] Example 4

[0057] The difference between this embodiment and Embodiment 3 is that the specific parameters are selected differently.

[0058] The corner stiffener is 1mm wide, and its extension direction is at 45° to the upper and lower sides of the cold-formed thin-walled C-shaped steel. The length of the corner stiffener is 15mm.

[0059] Example 5

[0060] This embodiment is a method for calculating the bearing capacity of a geopolymer-based cold-formed thin-walled steel composite column, as described in Embodiment 1. Figure 8 As shown, it includes the following steps:

[0061] S1. Finite Element Analysis: Four types of composite columns were modeled using ABAQUS software: a composite column without stiffeners, a symmetrical single-rib composite column, a symmetrical double-rib composite column, and a corner-stiffened composite column. The ABAQUS concrete plastic damage model was used for modeling. The finite element models used the actual dimensions of the composite columns, with a mesh size of 5mm × 5mm. The steel plates at both ends of the composite columns were simulated using rigid R3D4 elements. The two cold-formed thin-walled C-shaped steel sections used 4-node reduced integral S4R shell elements, and the geopolymer foam concrete used 8-node reduced integral C3D8R solid elements. Weld joints were simulated using a binding method. The cold-formed thin-walled C-shaped steel sections and the geopolymer foam concrete were in surface-to-surface contact, with a penalty contact in the tangential direction, a friction coefficient of 0.25, and a hard contact in the normal direction. The two cold-formed thin-walled C-shaped steel sections were connected using a binding method to simulate weld joints. The yield strength of the cold-formed thin-walled C-shaped steel sections was 267.5 MPa, and the elastic modulus was 1.74 × 10⁻⁶. 5 MPa, Poisson's ratio of 0.3, and taking into account the beneficial effect of stiffening ribs on the confinement effect of geopolymer foam concrete, a cross-sectional shape influence coefficient γ was introduced. i The concrete plastic damage model built into ABAQUS is used for modeling, as shown in the following formula:

[0062]

[0063] in,

[0064]

[0065]

[0066] In the above formula, EIsi is the flexural section modulus of the i-th stiffener from the center line of the outer wall of the cold-formed thin-walled C-section steel, and Is = 1 / 3tsbs 3 ts is the thickness of the stiffening rib, bs is the width of the stiffening rib; EIc is the section modulus of the core concrete about the neutral axis perpendicular to the i-th stiffening rib, fy is the yield strength of the cold-formed thin-walled C-shaped steel, and fck is the compressive strength of the geopolymer foam concrete. The sum of the constraint effect coefficients for all stiffeners;

[0067] S2. Stiffening Rib Influence Analysis: The cold-formed thin-walled C-shaped steel and stiffening ribs are connected by binding. The ultimate bearing capacity at the axial position of the composite column is calculated using the finite element model. The ultimate bearing capacity P1 of the composite column without stiffening ribs, the ultimate bearing capacity P2 of the symmetrical single-rib composite column, the ultimate bearing capacity P3 of the symmetrical double-rib composite column, and the ultimate bearing capacity P4 of the corner stiffening rib composite column are calculated respectively. The ultimate bearing capacity improvement coefficients γ1 = P2 / P1, γ2 = P3 / P2, and γ3 = P4 / P3 of the symmetrical single-rib composite column, the symmetrical double-rib composite column, and the corner stiffening rib composite column are calculated.

[0068] This leads to the coefficient of influence of the cross-sectional shape of the composite column, γ = (γ 1+ γ2+γ3) / 3;

[0069] S3. Analysis of Axial Compressive Strength Enhancement Coefficient: Due to the enhanced core strength of the composite column, the stress of the polymer foam concrete is lower near the center and higher near the edges, reaching its maximum at the corners. Therefore, the stress areas are divided according to their areas: A1: Stress-enhanced area of ​​the central polymer foam concrete, A2: Stress-enhanced area of ​​the corner polymer foam concrete, A3: Stress-enhanced area of ​​the edge polymer foam concrete. A2 is the sum of the areas of the three grids at each corner, A3 is the sum of the grid areas corresponding to the cold-formed thin-walled C-shaped steel, and A1 is the sum of the remaining grid areas, with a total grid area of ​​Ac. The compressive strength f of the polymer foam concrete is then measured experimentally. c Furthermore, the average stress distribution af of the central geopolymer foam concrete was calculated using a finite element model. c The average stress distribution of corner geopolymer foam concrete, bf c The average stress distribution of edge-grown polymer foam concrete (cf) c Therefore, the area equivalent formula for the axial compressive strength enhancement factor ωc of geopolymer foam concrete can be derived as follows:

[0070] ω c f c A c =af c A1+bf c A2+cf c A3

[0071] Since A1+A2+A3=A c Therefore, ω can be derived. c The value;

[0072] S4. Comprehensive Calculation: The cross-sectional shape influence coefficient γ of the composite column obtained in step S2 and the axial compressive strength enhancement coefficient ωc of the geopolymer foam concrete obtained in step S3 are introduced into the modified bearing capacity calculation formula. The modified bearing capacity calculation formula is shown in the following formula:

[0073] N≤0.9ψγ(α1ω c f c b c h c +2f a bt+2f a h c t)

[0074] Where: N is the design value of the axial compressive bearing capacity of the composite column; φ is the axial compressive stability coefficient of the composite column; fa is the design value of the compressive and tensile strength of the rectangular steel tube; bc is the cross-sectional width of the polymer foam concrete filling in the composite column; hc is the cross-sectional height of the polymer foam concrete filling in the composite column; b is the cross-sectional width of the composite column; and t is the thickness of the cold-formed thin-walled C-shaped steel.

[0075] Experimental Example 1

[0076] The following verifies the geopolymer-based cold-formed thin-walled steel composite column and its bearing capacity calculation method of the present invention. Specifically, in step S2, when calculating P1, P2, P3, and P4, the dimensions of the cold-formed thin-walled C-shaped steel and ribs in Example 1 are uniformly adopted. The dimensions of the corner stiffening ribs are the same as those of the symmetrical double ribs and symmetrical single ribs. A WA-1000CI electro-hydraulic servo universal testing machine loading system is used. Before loading, the composite column is geometrically aligned. Before the test, the centroid of the specimen is marked on the end plates welded to both ends of the specimen. During loading, the centroid of the composite column is aligned with the center of the loading device to ensure axial compression. The loading process is divided into two stages. The first stage is the application of preload. The lower crossbeam is adjusted to fix the composite column, and an initial load of 1kN is applied. The strain gauges and displacement gauges are observed to ensure normal operation, and the gap between the composite column and the loading device is eliminated. Then, displacement loading begins at a loading rate of 0.2mm / min. While the loading device is started to apply the load, data from the strain gauges and displacement gauges are collected to ensure data accuracy. When the composite column fails, loading is stopped when the load drops to 70% of the ultimate load, the data is saved, and the test ends. Figure 1 The diagram shows the axial load-displacement curves for three composite columns (symmetrical single-rib, symmetrical double-rib, and corner stiffener). In the early stages of loading, the curves are approximately linear, indicating good stress distribution between the concrete and steel tubing. The internal foamed concrete filling restricts the buckling of the outer steel tubing, thus increasing the ultimate load of the member. After reaching the ultimate load, the internal foamed concrete fails and can no longer provide restraint, causing the load to decrease rapidly.

[0077] Experimental Example 2

[0078] To expand the range of experimental parameters and comprehensively analyze the axial compression performance of CFS composite columns and CFS-GSC combined structures, this paper selected 24 components with web section width-to-thickness ratios of 40, 58, 78, and 100, corresponding to thicknesses of 3.5 mm, 2.4 mm, 1.8 mm, and 1.4 mm, respectively. The parameter analysis results are as follows: Figure 2 As shown, the decrease in the ultimate load of the member gradually decreases with the increase of the width-to-thickness ratio. When the width-to-thickness ratio is in the range of 40-60, the downward curve is steeper, while when the width-to-thickness ratio is in the range of 60-100, the downward curve is relatively gentle. This indicates that the influence of the width-to-thickness ratio on the ultimate load is more significant in the range of 40-60. Furthermore, when the width-to-thickness ratio is 40, the ultimate loads of the CFS composite column and the CFS combined column are relatively close. However, as the width-to-thickness ratio gradually increases, the ultimate load of the combined column begins to be significantly greater than that of the composite column. This phenomenon is particularly evident when the width-to-thickness ratio exceeds 60. This indicates that as the width-to-thickness ratio increases, the thickness of the member gradually decreases, and the plate is prone to local buckling. The internally filled polymer foam concrete has a significant restraining effect on the thinner plate, thus leveraging the internal infill material to increase the ultimate load of the steel column. Conversely, as the width-to-thickness ratio decreases, the member thickness increases, and the utilization rate of the internal infill material is lower.

[0079] Experimental Example 3

[0080] Figure 3 The figure shows the load-axial displacement curves of CFS-GFC composite columns with different foamed concrete density grades. It reveals that the ultimate load of the composite column increases with increasing foamed concrete density. In the elastic stage, the elastic modulus of foamed concrete increases with its density, leading to a greater stiffness of the CFS-GFC composite column. For each increase in foamed concrete density grade, the ultimate load of the CFS-GFC composite column increases by approximately 1.5%. Therefore, increasing the density grade of foamed concrete can increase both the stiffness and axial bearing capacity of the composite column.

[0081] Experiment Example 4

[0082] This experimental example further explores the method for calculating the bearing capacity of composite columns based on Experiment 1. Because the inner wall of the CFS is relatively smooth, the synergistic effect of the two is not ideal, such as... Figure 4The stress cloud diagram of the internal concrete shows that the stress decreases closer to the center and increases closer to the edge, with the stress reaching its maximum at the corners. This indicates that the CFS (Coil-Fiber Stiffening System) has a significant restraining effect on the corner concrete, while the restraining effect at the edges is weaker. To investigate the effect of web stiffening on the ultimate load improvement of CFS-GFC composite column members and its restraining effect on concrete, this invention considers adding stiffening ribs to the inner wall of the CFS. The finite element model data is shown in Table 1. The ultimate load improvement factor of the ribbed section is between 1.12 and 1.22, indicating that the stiffening ribs significantly improve the ultimate load of the CFS-GFC composite column members. The improvement factor is the largest at the corner stiffening rib section. From the perspective of material consumption, setting symmetrical single ribs can achieve a higher ultimate load improvement effect with less material consumption.

[0083] Table 1 Comparison of ultimate loads of components with different stiffening rib types

[0084] stiffening form Ultimate load Increase coefficient 1 Increase coefficient 2 No ribs 210.78 - - Symmetrical single rib 236.92 1.124 - Symmetrical double ribs 256.52 1.217 1.083 Corner Ribs 257.78 1.223 1.088

[0085] Therefore, the influence coefficient of the cross-sectional shape of the composite column γ can be calculated as γ = (γ 1+ γ2+γ3) / 3=(1.124+1.083+1.088) / 3=1.09833.

[0086] Then, based on the stress distribution diagram of foamed concrete, as shown below... Figure 6 As shown, the area of ​​each small square in the figure is 58.6 mm². 2 The area of ​​each small rectangle is 28.29 mm². 2 The total area Ac is 13053.92 mm². 2 Therefore, we can deduce that A1 = 7840.28 mm. 2 A2 = 703.2 mm 2 A3 = 4510.18mm 2 Therefore, the relationship between the area of ​​each part and the total area Ac is A1 = 0.6Ac, A2 = 0.05Ac, and A3 = 0.35Ac. From... Figure 6 The stress distribution (from inside to outside) of the central foamed concrete is: 1.09fc, 1.14fc, 1.19fc, with an average of 1.14fc. The stress distribution (from inside to outside) of the corner foamed concrete is: 1.38fc, 1.43fc, 1.48fc, 1.52fc, with an average of 1.45fc. The stress distribution (from inside to outside) of the edge foamed concrete is: 1.24fc, 1.28fc, 1.33fc, with an average of 1.28fc. Therefore, we can conclude that:

[0087] ω c f c A c=1.14f c A1+1.45f c A2+1.28f c A3

[0088] Substituting the converted area, we get:

[0089] ω c f c A c =1.2045f c A c

[0090] That is, the axial compressive strength enhancement factor ω of foamed concrete in this article. c The value is 1.2045.

[0091] Therefore, the final formula for calculating the bearing capacity of the polymer-based cold-formed thin-walled steel composite column applicable to this invention, obtained in step S4, is as follows:

[0092]

[0093] The calculated values ​​of this formula are compared and analyzed with experimental and finite element results to verify the applicability of the formula proposed in this paper for calculating polymer-based cold-formed thin-walled steel composite columns. Figure 7 As shown in the figure, the theoretical calculation values ​​agree well with the experimental and finite element values ​​overall, with an average value of 0.95 and a standard deviation of 0.07. Furthermore, the errors between the theoretical calculation values ​​and the experimental and finite element values ​​are concentrated around 5%, indicating that the calculation formula for the axial compression bearing capacity of the CFS-GFC column proposed in this paper is accurate.

[0094] Table 2 compares existing bearing capacity calculation formulas with experimental results. The bearing capacity of the CFS-GFC composite column calculated by the Japanese AIJ standard and the American LRFD standard is too high, and the average ratios of Nu,A / Pt and Nu,L / Pt of the composite column bearing capacity measured by experiments are 1.26 and 1.21, respectively. This indicates that the bearing capacity calculation of the component in this paper based on the Japanese AIJ standard and the American LRFD standard is unsafe. Therefore, the calculation formulas given by the superposition of the bearing capacity of the two materials and the pseudo-steel theory are not applicable to the component in this paper. One possible reason is that the strength of the steel is not fully utilized in the actual stress process, and the strength formulas do not make corresponding reductions for the strength of the steel, thus making the calculated theoretical results higher than the experimental values. The bearing capacity of the composite column calculated by the "Technical Specification for Composite Structures" is lower than the experimental value, and the average value of its ratio Nu,j / Pt is 0.87, indicating that the theoretical value calculated by the "Technical Specification for Composite Structures" is conservative. Therefore, the bearing capacity calculation method of the geopolymer-based cold-formed thin-walled steel composite column of this invention can be designed based on the pseudo-concrete theory. However, since the test members were all short columns, the stability coefficient of this standard is 1 when the slenderness ratio is less than 28 (i.e., the length of the composite column in this invention is <1616.72 mm). Therefore, when the column length is less than 1616.72 mm, the members all experience strength failure. The bearing capacity of the composite column calculated by the "Technical Specification for Concrete-Concrete Composite Structures" is slightly higher than the experimental value. The average ratio of Nu,G / Pt between the composite column and the experimental result is 1.12, indicating that the formula for calculating the bearing capacity of the composite column based on the unified theory can be used as a formula for predicting the axial compressive bearing capacity of the members in this paper, but it is somewhat unsafe.

[0095] Table 2 Comparison of calculated values ​​from the standard formula with experimental values ​​from this invention.

[0096]

[0097]

Claims

1. A method for calculating the bearing capacity of a geopolymer-based cold-formed thin-walled steel composite column, characterized in that, The geopolymer-based cold-formed thin-walled steel composite column includes two cold-formed thin-walled C-shaped steels and geopolymer foam concrete filled in the closed cavity enclosed by the two cold-formed thin-walled C-shaped steels. The two ends of the two cold-formed thin-walled C-shaped steels are sealed by welding steel plates. The inner rolled edges of the two cold-formed thin-walled C-shaped steels are butted together and welded together. Four welding points are evenly spaced along the length of the inner rolled edges. A stiffening rib is provided at the center of the outer wall of each of the two cold-formed thin-walled C-shaped steels to form a symmetrical single rib. The width of the stiffening rib is 0.5~1mm and the length of the stiffening rib is 10~15mm. Two stiffening ribs are provided at equal intervals on the outer side walls of the two cold-formed thin-walled C-shaped steels to form symmetrical double ribs; A corner stiffening rib is provided at the upper and lower ends of the outer side wall of each of the two cold-formed thin-walled C-shaped steel sections. The geopolymer foamed concrete is obtained by pouring geopolymer foamed concrete slurry into the sealed cavity and curing it. The geopolymer foamed concrete slurry is made by mixing slag and fly ash raw materials, alkali activator, water reducing agent and plant-based foaming agent. The density grade of the geopolymer foamed concrete slurry is A07, A10 or A12. The method for calculating bearing capacity includes the following steps: S1. Finite element analysis: Four types of composite columns were established using ABAQUS software: composite column without stiffeners, symmetrical single-rib composite column, symmetrical double-rib composite column, and corner stiffener composite column. The ABAQUS concrete plastic damage model was used for modeling. The actual size of the composite column was used in the finite element model, and the mesh size was set to 5mm×5mm. S2. Stiffening Rib Influence Analysis: The ultimate bearing capacity at the axial center of the composite column is calculated using the finite element model. The ultimate bearing capacity P1 of the composite column without stiffening ribs, the ultimate bearing capacity P2 of the symmetrical single-rib composite column, the ultimate bearing capacity P3 of the symmetrical double-rib composite column, and the ultimate bearing capacity P4 of the corner stiffening rib composite column are calculated respectively. The ultimate bearing capacity improvement coefficients γ1=P2 / P1, γ2=P3 / P2, and γ3=P4 / P3 of the symmetrical single-rib composite column, the symmetrical double-rib composite column, and the corner stiffening rib composite column are also calculated. Therefore, the influence coefficient of the cross-sectional shape of the composite column is obtained as γ = (γ 1+ γ2+γ3) / 3; S3. Analysis of Axial Compressive Strength Enhancement Coefficient: The stress zone is divided according to its area, specifically: A1: Central geopolymer foam concrete stress-enhancing zone area; A2: Corner geopolymer foam concrete stress-enhancing zone area; A3: Edge geopolymer foam concrete stress-enhancing zone area. A2 is the sum of the areas of the three grids at each corner; A3 is the sum of the grid areas corresponding to the cold-formed thin-walled C-shaped steel; A1 is the sum of the remaining grid areas, with a total grid area of ​​Ac. Then, based on the experimentally measured compressive strength f of the geopolymer foam concrete... c Furthermore, the average stress distribution af of the central geopolymer foam concrete was calculated using a finite element model. c The average stress distribution of corner geopolymer foam concrete, bf c The average stress distribution of edge-grown polymer foam concrete (cf) c Therefore, the area equivalent formula for the axial compressive strength enhancement factor ωc of geopolymer foam concrete can be derived as follows: ω c f c A c =af c A1+bf c A2+cf c A3 Since A1+A2+A3=A c Therefore, ω can be derived. c The value; S4. Comprehensive Calculation: The cross-sectional shape influence coefficient γ of the composite column obtained in step S2 and the axial compressive strength enhancement coefficient ωc of the geopolymer foam concrete obtained in step S3 are introduced into the modified bearing capacity calculation formula, which is shown in the following formula: Where: N is the design value of the axial compressive bearing capacity of the composite column; denoted as axial compressive stability coefficient of the composite column; fa is the design value of compressive and tensile strength of the rectangular steel tube; bc is the cross-sectional width of the polymer foam concrete filling inside the composite column; hc is the cross-sectional height of the polymer foam concrete filling inside the composite column; b is the cross-sectional width of the composite column; and t is the thickness of the cold-formed thin-walled C-shaped steel.

2. The method for calculating the bearing capacity of a geopolymer-based cold-formed thin-walled steel composite column according to claim 1, characterized in that, The length of the two cold-formed thin-walled C-shaped steel sections is 400~1000mm, the outer wall height of the cold-formed thin-walled C-shaped steel section is 100~400mm, the width of the upper and lower sides of the cold-formed thin-walled C-shaped steel section is 20~140mm, the length of the inner rolled edge of the cold-formed thin-walled C-shaped steel section is 15~30mm, the thickness of the cold-formed thin-walled C-shaped steel section is 0.5~3.5mm, and the ratio of the width of the upper and lower sides of the cold-formed thin-walled C-shaped steel section to its thickness is 40~100.

3. The method for calculating the bearing capacity of a geopolymer-based cold-formed thin-walled steel composite column according to claim 1, characterized in that, The raw materials of slag and fly ash, by weight, include: 330-340 parts of slag, 80-85 parts of fly ash, the alkali activator is made by mixing 12-15 parts of NaOH solid powder and 85-90 parts of water glass and dissolving them in 100-110 parts of deionized water, stirring until the NaOH solid powder is completely dissolved, the water-reducing agent is 0.3-0.5 parts, the foam produced by the plant-based foaming agent is 30-35 parts, and the curing method is to cover the surface of the composite column with a layer of plastic wrap and cure it at room temperature for 2 days before demolding.

4. The method for calculating the bearing capacity of a geopolymer-based cold-formed thin-walled steel composite column according to claim 1, characterized in that, The corner stiffener has a width of 0.5~1mm, the extension direction of the corner stiffener is at 45° with the upper and lower sides of the cold-formed thin-walled C-shaped steel, and the length of the corner stiffener is 10~15mm.

5. The method for calculating the bearing capacity of a geopolymer-based cold-formed thin-walled steel composite column according to claim 1, characterized in that, In step S1, the steel plates at both ends of the composite column are simulated using rigid elements R3D4. The two cold-formed thin-walled C-shaped steel sections are simulated using 4-node reduced integral S4R shell elements, and the geopolymer foam concrete is simulated using 8-node reduced integral C3D8R solid elements. A binding method is used to simulate the weld points. The cold-formed thin-walled C-shaped steel sections and the geopolymer foam concrete are in surface-to-surface contact, with a "penalty" contact in the tangential direction, a friction coefficient of 0.25, and a "hard" contact in the normal direction. The two cold-formed thin-walled C-shaped steel sections are connected by a binding method to simulate the weld points. The yield strength of the cold-formed thin-walled C-shaped steel section is 267.5 MPa, and the elastic modulus is 1.74 × 10⁻⁶. 5 MPa, Poisson's ratio is 0.

3.

6. The method for calculating the bearing capacity of a geopolymer-based cold-formed thin-walled steel composite column according to claim 1, characterized in that, In step S2, the cold-formed thin-walled C-shaped steel and the stiffening ribs are connected by binding.

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