A calculation method for the axial compression bearing capacity of a short concrete-filled steel tube column
By establishing a unified shape factor and constraint effect coefficient MCF expression, the problem of inconsistent axial pressure bearing capacity calculation of round and square steel pipe concrete short columns in the prior art is solved, and a simpler and more accurate bearing capacity calculation is achieved, which is suitable for a variety of material strength and cross-sectional shapes.
Patent Information
- Application Number
- CN202210169496.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-02-24
- Publication Date
- 2025-07-29
- Estimated Expiration
- 2042-02-24
AI Technical Summary
The prior art cannot uniformly calculate the axial pressure bearing capacity of circular and square steel pipe concrete short columns, and the existing specifications cannot calculate the axial pressure bearing capacity of square steel pipe concrete with rounded angles, and the existing formulas fail to reflect the impact of cross-sectional shape factor on the bearing capacity.
A unified axial pressure bearing capacity calculation method for round, square and square concrete short columns with rounded angle steel pipes was established. Through the shape factor and constraint effect coefficient MCF expression, combined with the properties of steel and concrete, a unified bearing capacity expression was established, which was suitable for a variety of material strengths.
The unified calculation of the axial pressure bearing capacity of the concrete short column with rounded angle steel pipes is achieved. The calculation formula is simple and accurate, and has a wide range of application. It is suitable for high-strength materials and conforms to the law of cross-sectional change.
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Figure CN114757010B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a method for calculating bearing capacity in engineering, specifically a method for calculating the axial compression bearing capacity of short concrete-filled steel tubular columns. Background Art
[0002] Currently, there are mainly four codes for calculating the axial compression bearing capacity of short concrete-filled steel tubular columns, namely the Chinese code GB50936-2014, the Japanese AIJ 2001, the European code Eurocode 4, and the American code AISC 360-16. The above four codes can only provide calculation formulas for the bearing capacity of concrete-filled steel tubes with circular and square cross-sections. The relevant formulas are as follows in the table:
[0003]
[0004] As can be seen from the table, the calculation expressions for the bearing capacity of circular and square concrete-filled steel tubes are not unified, and many parameters need to be calculated. In addition, for concrete-filled steel tubes with square cross-sections with rounded corners, the above four codes cannot calculate their axial compression bearing capacity. Moreover, the axial compression bearing capacity calculation formulas provided by the above codes cannot effectively unify circular and square concrete-filled steel tubes, nor can they reflect the inherent continuous evolution law of the two cross-sections (square cross-section and circular cross-section) (that is, reflecting the influence of the shape factor variation law on the cross-section bearing capacity). Summary of the Invention
[0005] The purpose of the present invention is to provide a unified calculation method for the axial compression bearing capacity of short concrete-filled steel tubular columns for people in view of the defects and deficiencies of the above-mentioned existing technologies, which is used for calculating the axial compression bearing capacity of three types of short concrete-filled steel tubular columns: square, circular, and square with rounded corners.
[0006] The technical solution adopted by the present invention to achieve the above purpose is: the calculation method for the axial compression bearing capacity of short concrete-filled steel tubular columns, which includes the following steps:
[0007] The first step: through the outer diameter of the concrete-filled steel tube D the thickness of the steel tube t the inner diameter of the steel tube cross-section B the value of the fillet radius, where = 0 is a short square concrete-filled steel tubular column, = B / 2 is a short circular concrete-filled steel tubular column, 0 < < B / 2 is a short square concrete-filled steel tubular column with rounded corners, reflecting the continuous evolution from the square cross-section to the circular cross-section;
[0008] Establish a shape factor that reflects the influence of the continuous evolution of the above three concrete-filled steel tube cross-sections on the concrete confinement effect Expression
[0009]
[0010] wherein, is the fillet radius and the inner diameter of the steel pipe cross-section B ratio;
[0011] Step 2: Establish the constraint factor MCF Expression
[0012]
[0013] wherein, is the yield strength of the steel, is the standard value of the axial compressive strength of the concrete;
[0014] Step 3: Establish the effective confining pressure Expression
[0015]
[0016] wherein, the parameter is the hoop stress of the steel pipe and the yield strength of the steel pipe ratio;
[0017] Step 4: Establish the axial compressive stress Expression
[0018] ;
[0019] Step 5: Establish the axial compressive stress Expression
[0020] ;
[0021] Step 6, establish the unified axial compressive bearing capacity of circular, square, and square cross-sections with rounded corners
[0022]
[0023] wherein, represents MCF ; represents the cross-sectional area of the concrete in the concrete-filled steel tube cross-section; represents the cross-sectional area of the steel tube in the concrete-filled steel tube cross-section; CF is the constraint effect coefficient.
[0024] Restraint effect coefficient CF For concrete-filled circular, square, and square with rounded corners steel tubes:
[0025] 。
[0026] Parameter For concrete-filled circular steel tube:
[0027]
[0028] Among them, when the concrete cylinder strength MPa, ; when the concrete cylinder strength MPa, ; when the concrete cylinder strength is 60 MPa < < 70 MPa, Obtained by linear interpolation;
[0029] For concrete-filled square steel tube:
[0030]
[0031] For concrete-filled square steel tube with rounded corners:
[0032] 。
[0033] The range of the shape factor in the first step is 。
[0034] The present invention is used for calculating the axial compressive bearing capacity of three types of concrete-filled steel tube short columns, namely square, circular, and square with rounded corners. The calculation expression realizes the unification. The bearing capacity expression established based on the mature and general yield criterion has a clear concept, conforms to the cross-section change law, and the bearing capacity calculation formula is not limited by the material strength, and is applicable to calculating the axial compressive bearing capacity of various concrete-filled steel tube short columns. Compared with the existing code calculation formula, it has the characteristics of being simpler, more accurate, and more stable, and realizes the unification of the bearing capacity calculation formulas for circular and square concrete-filled steel tubes, and the physical meaning is clearer and more definite. Brief Description of the Drawings
[0035] Figure 1 Are the cross-sections of square, circular, and square with rounded corners concrete-filled steel tube short columns.
[0036] Figure 2 Is a schematic diagram of the evolution law of the axial compressive bearing capacity of concrete-filled steel tube.
[0037] Figure 3 Is the comparison of the experimental data of circular concrete-filled steel tube with the bearing capacity calculation formula of this article and the calculation formula of the existing code.
[0038] Figure 4 The comparison of the experimental data of concrete-filled square steel tubes with the bearing capacity calculation formula in this paper and the calculation formula in the existing code. Specific implementation mode
[0039] As Figure 1 shown, we can obtain the outer diameter of the concrete-filled steel tube by measurement D , the thickness of the steel tube t , the inner diameter of the steel tube cross-section B , and the value of the fillet radius . Among them = 0 is a short column of concrete-filled square steel tube, = B / 2 is a short column of concrete-filled circular steel tube, 0 < < B / 2 is a short column of concrete-filled square steel tube with fillets, reflects the continuous evolution from a square cross-section to a circular cross-section.
[0040] Calculation method for the axial compressive bearing capacity of short columns of concrete-filled steel tubes, which includes the following steps:
[0041] The first step: Through the outer diameter of the concrete-filled steel tube D , the thickness of the steel tube t , the inner diameter of the steel tube cross-section B , and the value of the fillet radius , establish the shape factor expression
[0042]
[0043] wherein, is the ratio of the fillet radius to the inner diameter of the steel tube cross-section B .
[0044] The range of the shape factor is: .
[0045] The second step: Establish the confinement factor MCF expression
[0046]
[0047] wherein, is the yield strength of the steel, is the standard value of the axial compressive strength of the concrete.
[0048] The third step: Establish the effective confining pressure expression
[0049]
[0050] Among them, the parameter is the circumferential stress of the steel pipe and the yield strength of the steel pipe ratio.
[0051] Step 4: Establish the axial compressive stress of the steel pipe expression
[0052] .
[0053] Step 5: Establish the axial compressive stress of the concrete under the constraint of the steel pipe expression
[0054] .
[0055] Step 6: Establish the unified axial compressive bearing capacity of circular, square, and square with rounded corners cross-sections expression
[0056]
[0057] Among them, represents MCF ; represents the cross-sectional area of the concrete in the concrete-filled steel tube cross-section; represents the cross-sectional area of the steel pipe in the concrete-filled steel tube cross-section; CF is the confinement effect coefficient.
[0058] Confinement effect coefficient CF calculation, for circular, square, and square with rounded corners concrete-filled steel tubes:
[0059] .
[0060] Parameter calculation, for circular concrete-filled steel tubes:
[0061]
[0062] Among them, when the concrete cylinder strength MPa, ; when the concrete cylinder strength MPa, ; when the concrete cylinder strength 60 MPa < < 70 MPa, obtained by linear interpolation;
[0063] For square concrete-filled steel tubes:
[0064]
[0065] For concrete-filled square steel tubes with rounded corners:
[0066] 。
[0067] As Figure 2 shown, under the condition of the same cross-section parameters (for example: the same inner diameter of the cross-section B , the same wall thickness of the steel tube t , the same yield strength of the steel and the standard value of the same axial compressive strength of the concrete , the same hoop stress of the steel tube and the ratio to the yield strength of the steel tube ), the schematic diagram of the evolution law of the axial compressive bearing capacity of concrete-filled steel tubes with circular, square and continuously transitional cross-sections between square and circular (i.e., square with rounded corners).
[0068] Figure 4 It reflects that under the same conditions, as the square concrete-filled steel tube short column gradually evolves into a circular concrete-filled steel tube short column, its axial compressive bearing capacity gradually increases, and the increase in the axial compressive bearing capacity is continuously changing. The gradual increase in the bearing capacity also indirectly indicates that the restraint effect of the steel tube on the concrete gradually increases. This also reasonably explains the bearing capacity calculation formulas recommended by the above four codes. For circular cross-sections, the restraint effect of the steel tube on the concrete is considered, and for square cross-sections, the four codes all weaken the restraint effect of the steel tube on the concrete, or even do not consider the restraint effect of concrete-filled steel tubes (such as the American code AISC 360-16).
[0069] Compared with the calculation formulas of the four codes, the calculation formula of this invention patent has the following advantages:
[0070] 1. The bearing capacity calculation formula is simple and requires fewer parameters to calculate (only the parameters ) need to be calculated. The Chinese code needs to calculate three parameters, and the European code needs to calculate three parameters.
[0071] 2. It realizes the unification of the bearing capacity calculation expressions for circular and square concrete-filled steel tubes. In essence, the cross-section shape change between square and circular cross-sections should be continuous. Therefore, the bearing capacity calculation expressions should also be unified. However, the above codes give different bearing capacity calculation formulas for the two cross-section shapes, and the physical concept is not clear. The calculation expression of this invention patent realizes the unification of the two. The bearing capacity expression established based on the mature and general yield criterion has a clear concept and also conforms to the cross-section change law.
[0072] 3. The present invention provides a bearing capacity calculation formula for short concrete-filled steel tubular columns with a square cross-section with rounded corners, while the existing codes have not yet provided a bearing capacity calculation formula for this new type of concrete-filled steel tubular cross-section.
[0073] 4. The bearing capacity calculation formula in the existing codes is only applicable to concrete-filled steel tubular cross-sections composed of concrete with a strength grade below C80 and steel with strengths such as Q235, Q345, and Q390. However, the bearing capacity calculation formula proposed in this invention patent is not restricted by the material strength. By comparing the experimental values of the axial compression bearing capacity of existing short concrete-filled steel tubular columns and the calculated values based on the bearing capacity formula of this patent, it can be seen that the applicable range of the bearing capacity calculation formula in this paper is as follows: the cylinder strength of concrete can reach 164 MPa, and the strength of steel can reach 835 MPa. The bearing capacity calculation formula given in the existing codes is more or less affected by the material strength parameters.
[0074] As Figure 3 shown, in the figure represents the experimental value, represents the calculated value of the formula of this invention patent, represents the calculated value of the formula in the Chinese code, represents the calculated value of the formula in the European code, represents the calculated value of the formula in the Japanese code,
[0075] represents the calculated value of the formula in the American code, H represents the height of the specimen, D represents the outer diameter of the circular concrete-filled steel tubular cross-section, collectively represents the experimental value respectively with 、 ratio.
[0076] NN-C-CFST represents the cylinder strength of concrete f c ⩽60 MPa, the yield strength of steel f y ⩽450 MPa circular concrete-filled steel tubular short columns.
[0077] HN-C-CFST represents the cylinder strength of concrete f c >60 MPa, the yield strength of steel f y ⩽450 MPa circular concrete-filled steel tubular short columns.
[0078] HH-C-CFST represents the cylinder strength of concrete f c >60 MPa, the yield strength of steelf y Circular concrete-filled steel tube short columns with a strength > 450 MPa.
[0079] NH-C-CFST represents the strength of the concrete cylinder f c ⩽ 60 MPa, the yield strength of the steel f y Circular concrete-filled steel tube short columns with a strength > 450 MPa.
[0080] As Figure 4 shown, in the figure represents the experimental value, represents the calculated value from the formula of this invention patent, represents the calculated value from the Chinese code formula, represents the calculated value from the European code formula, represents the calculated value from the American code formula, Collectively represents the experimental value Respectively with 、 The ratio of.
[0081] NN-S-CFST represents the strength of the concrete cylinder f c ⩽ 60 MPa, the yield strength of the steel f y Square concrete-filled steel tube short columns with a strength ⩽ 450 MPa.
[0082] HN-S-CFST represents the strength of the concrete cylinder f c > 60 MPa, the yield strength of the steel f y Square concrete-filled steel tube short columns with a strength ⩽ 450 MPa.
[0083] HH-S-CFST represents the strength of the concrete cylinder f c > 60 MPa, the yield strength of the steel f y Square concrete-filled steel tube short columns with a strength > 450 MPa.
[0084] NH-S-CFST represents the strength of the concrete cylinder f c ⩽ 60 MPa, the yield strength of the steel f y Square concrete-filled steel tube short columns with a strength > 450 MPa.
[0085] From Figure 3 And Figure 4It can be seen from [reference] that there will be obvious errors in the predicted values of the bearing capacity of square or circular concrete-filled steel tube short columns made of some high-strength steels or high-strength concretes according to the Chinese code. For circular concrete-filled steel tube short columns with H / D ≤ 2.5 and high-strength concrete and ordinary steel, the European code will give calculation results with overestimated bearing capacity. The Japanese code and the American code both give relatively conservative predicted values of bearing capacity. The predicted values of bearing capacity given by the formula in this paper are in good agreement with the experimental values.
[0086] Therefore, compared with the existing code calculation formulas, the unified bearing capacity calculation formula for circular and square concrete-filled steel tubes and square concrete-filled steel tubes with rounded corners proposed in this paper is simpler, more accurate, and more stable. Moreover, it unifies the bearing capacity calculation formulas for circular and square concrete-filled steel tubes, and the physical meaning is clearer and more definite.
Claims
1. A calculation method for the axial compression bearing capacity of a short concrete-filled steel tubular column, characterized in that It includes the following steps: Step 1: Through the outer diameter of the concrete-filled steel tube D , the thickness of the steel tube t , the inner diameter of the steel tube cross-section B , and the value of the fillet radius, where = 0 is a square concrete-filled steel tube short column, = B / 2 is a circular concrete-filled steel tube short column, 0 < < B / 2 is a square concrete-filled steel tube short column with fillets, reflects the continuous evolution from a square cross-section to a circular cross-section; Establish the shape factor reflecting the influence of the continuous evolution of the cross-section response of the above three concrete-filled steel tube cross-sections on the concrete confinement effect Expression Among them, is the fillet radius and the inner diameter of the steel pipe cross-section B ratio; Step 2: Establish the confinement factor reflecting the confinement effect of the reactive steel tubes on the concrete for the above three concrete-filled steel tube sections MCF Expression Among them, is the yield strength of steel,[ is the standard value of the axial compressive strength of concrete.[ Step 3: Establish the effective confining pressure of the concrete inside the steel pipe Expression Among them, the parameter is the circumferential stress of the steel pipe and the yield strength of the steel pipe ratio; Step 4: Establish the axial compressive stress of the steel pipe Expression ； Step 5: Establish the axial compressive stress of concrete under the confinement of steel pipes Expression ； Step 6: Establish the unified axial compression bearing capacity expressions for circular, square, and square with rounded corners cross-sections of the expressions Among them, represents MCF ; represents the cross-sectional area of concrete in the concrete-filled steel tube section; represents the cross-sectional area of the steel tube in the concrete-filled steel tube section; CF is the confinement effect coefficient.
2. The calculation method for the axial compression bearing capacity of a concrete-filled steel tubular short column according to claim 1, characterized in that Restraint effect coefficient CF For the calculation of circular, square, and square concrete-filled steel tubes with rounded corners: 。 3. A calculation method for the axial compressive bearing capacity of a concrete-filled steel tubular short column according to claim 1 or 2, characterized in that Parameter For concrete-filled circular steel tubes: Among them, when the concrete cylinder strength MPa, ; when the concrete cylinder strength MPa, ; when the concrete cylinder strength is 60 MPa < < 70 MPa, Obtained by linear interpolation; For concrete-filled square steel tubes: For concrete-filled square steel tubes with rounded corners: 。 4. The calculation method for the axial compressive bearing capacity of a short concrete-filled steel tubular column according to claim 1 or 2, characterized in that The range of the shape factor in the first step is .