Method for calculating axial compression bearing capacity of concrete filled steel tube with void defect by considering Poisson's ratio

Abstract

The invention provides a void defect steel tube concrete axial compression bearing capacity calculation method considering the Poisson's ratio. The void defect steel tube concrete axial compression bearing capacity calculation method comprises the following steps that S1, the strain, the Poisson's ratio, the steel tube inner diameter, the steel tube outer diameter, the steel tube wall thickness t and the void chord length of a steel tube concrete member are determined; step S2, calculating a constraint strength reduction coefficient of the void defect based on the parameters obtained in the step S1; s3, calculating the strength of the concrete filled steel tube with the void defect according to the constraint strength reduction coefficient obtained in the step S2; and S4, calculating the bearing capacity of the concrete-filled steel tube with the void defect by combining the Poisson's ratio change of the concrete and the influence of the void defect. By the adoption of the technical scheme, the influence of concrete Poisson ratio changes and void defects on the structure is considered, the calculation precision of the axial pressure bearing capacity is remarkably improved, the result is closer to the actual situation, the structure failure risk is reduced, and the method is particularly suitable for key projects such as bridges and high-rise buildings.

Description

Technical Field

[0001] The invention relates to the technical field of structural engineering, and in particular to a method for calculating the axial compressive bearing capacity of a hollow defective concrete-filled steel tube considering Poisson's ratio. Background Art

[0002] The existing calculation methods for the axial compressive bearing capacity of steel tube concrete columns take into account the strength and area of ​​the steel tube and concrete materials, and the hooping effect of the external steel tube on the expansion of the internal concrete when under pressure. Another method considers the effect of concrete crushing and filling the internal voids in the case of void defects, and all of them have given calculation formulas that are relatively close to the actual axial compressive bearing capacity. However, they basically ignore the increase in the Poisson's ratio of concrete caused by the expansion of concrete in the steel tube when under pressure. The change in Poisson's ratio will affect the overall axial compressive bearing capacity of the steel tube concrete, resulting in a certain error between the existing theoretical calculation method and the actual bearing capacity. Summary of the invention

[0003] In response to the above technical problems, the present invention discloses a method for calculating the axial compressive bearing capacity of steel tube concrete with void defects taking into account the Poisson's ratio. By taking into account the Poisson's ratio of concrete and the void defects, the accuracy of the axial compressive bearing capacity calculation is improved. The method is suitable for structural design and optimization, and effectively reduces the risk of structural failure caused by defects.

[0004] To this end, the technical solution adopted by the present invention is:

[0005] A method for calculating the axial compressive bearing capacity of concrete-filled steel tubes with void defects considering Poisson's ratio comprises the following steps:

[0006] Step S1, determining the strain, Poisson's ratio, inner diameter of the steel tube, outer diameter of the steel tube, wall thickness t of the steel tube and the hollow chord length of the steel tube concrete component;

[0007] Step S2, calculating the restraint strength reduction coefficient of the void defect based on the parameters obtained in step S1;

[0008] Step S3, calculating the strength of the steel tube concrete with void defects according to the restraint strength reduction factor obtained in step S2;

[0009] Step S4, calculating the bearing capacity of the steel tube concrete with void defects by combining the change of the Poisson's ratio of concrete and the influence of void defects.

[0010] This technical solution takes into account the Poisson's ratio and void defects of concrete, improves the accuracy of bearing capacity calculation, ensures that the calculation results are more in line with reality, reduces the risk of structural failure, and thus improves the safety and economy of engineering design.

[0011] As a further improvement of the present invention, in step S1, the Poisson's ratio v of the steel tube concrete member is calculated using the following formula:

[0012]

[0013] Among them, v0 is the initial value of the Poisson's ratio of concrete, ε1 is the actual strain of concrete under compression, and ε cu is the critical strain of concrete;

[0014] As a further improvement of the present invention, v0=2.

[0015] As a further improvement of the present invention, the wall thickness t of the steel pipe and the hollow chord length l are measured from actual conditions. In the inner diameter and outer diameter of the steel pipe, for a round steel pipe, r1 is the inner radius of the round steel pipe, r2 is the outer radius of the round steel pipe, and for a square steel pipe, b1 is half of the inner side length of the square steel pipe, and b2 is half of the outer side length of the square steel pipe.

[0016] As a further improvement of the present invention, in step S2, the constraint strength reduction factor k of the void defect d It is calculated using the following formula:

[0017] For the crown to be empty:

[0018]

[0019] The sector angle corresponding to the hollow spherical crown of the cylinder r1 is the inner radius of the round steel pipe, the hollow area Ball crown free string length The cross-sectional area of ​​concrete in the steel tube concrete after hollowing out A c =A Q -A e , A Q is the inner cross-sectional area of ​​the steel pipe, A Q =πr1 2 , A c is the equivalent cross-sectional area of ​​concrete, A c =πr3 2 For round steel tubes, r3 is the equivalent radius of the core concrete area equivalent to the annular hollow component; for square steel tubes, r3 is the equivalent inner side length of the core concrete area equivalent to the annular hollow component; δ is the cross-sectional expansion coefficient, δ=2εν+ε 2 ν 2 , where ε is the axial strain of the CFST member and v is the Poisson’s ratio of the CFST member;

[0020] For annular degassing:

[0021]

[0022] Concrete area after annular voiding A c =π(r1-t) 2, r1 is the inner radius of the round steel pipe, t is the wall thickness of the steel pipe, and the hollow area A e =A Q -A c , A Q is the inner area of ​​the steel pipe, A c is the equivalent area of ​​concrete, and the expansion of concrete is A' c =A c ·δ, δ is the cross-sectional expansion coefficient, δ=2εν+ε 2 ν 2 , where ε is the axial strain of the CFST member and v is the Poisson’s ratio of the CFST member.

[0023] As a further improvement of the present invention, in step S3, the strength f of the steel tube concrete with void defects is z It is calculated using the following formula:

[0024] f sc =(1+k d k e η c )[(1-β)f ck +βf y ],

[0025] in, ξ sc is the hoop coefficient, f ck 、f y are the standard strength values ​​of concrete and steel, A s is the cross-sectional area of ​​the steel tube in the steel tube concrete, A c is the cross-sectional area of ​​concrete in the steel tube concrete after hollowing;

[0026] β is the steel content ratio, through the steel area A s Area A of concrete-filled steel tube sc The ratio of is calculated;

[0027] k d k is the reduction factor of the restraint strength of the void defect, e is the cross-section correction factor, The physical meaning is the degree to which the cross-sectional shape weakens the constraint enhancement effect. n is the cross-sectional shape parameter. For a circular cross-section, f(n) = 1; for a quadrilateral cross-section, f(n) = 0.4.

[0028] As a further improvement of the present invention, in step S4, the bearing capacity N of the steel tube concrete with void defects is calculated using the following formula:

[0029] N = f sc (A s +A c ),

[0030] Among them, f sc A is the axial compression combined strength of concrete-filled steel tube with void defects; s A is the cross-sectional area of ​​the steel tube in the steel tube concrete; c It is the cross-sectional area of ​​concrete in the steel tube concrete after hollowing out.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] By adopting the technical solution of the present invention, the influence of the change of concrete Poisson's ratio and void defects on the structure is taken into account, which significantly improves the calculation accuracy of the axial compressive bearing capacity, makes the result closer to the actual situation, reduces the risk of structural failure, and is particularly suitable for key projects such as bridges and high-rise buildings. In addition, the more accurate bearing capacity assessment of the technical solution of the present invention can optimize the use of materials, avoid over-design, reduce engineering costs, and ensure safety and economy. This method has a wide range of applications, especially in high-stress environments. It is a powerful supplement to the existing steel tube concrete bearing capacity assessment method and has important engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of a method for calculating the axial compressive bearing capacity of concrete-filled steel tubes with void defects considering Poisson's ratio according to an embodiment of the present invention.

[0034] Figure 2 The diagram is a schematic diagram of spherical crown hollowing and annular hollowing of a circular steel tube concrete according to an embodiment of the present invention; wherein a) is spherical crown hollowing, and b) is annular hollowing.

[0035] Figure 3 It is a schematic diagram of the equivalent area of ​​the core concrete of the spherical crown-shaped hollow circular cross-section of the circular steel tube concrete according to an embodiment of the present invention.

[0036] Figure 4 The present invention is a schematic diagram of a spherical crown hollowing and annular hollowing of a square steel tube concrete according to an embodiment of the present invention; wherein a) is a spherical crown hollowing, and b) is annular hollowing.

[0037] Figure 5 It is a schematic diagram of the equivalent area of ​​the core concrete of the square steel tube concrete spherical crown hollow square cross-section according to an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The preferred embodiments of the present invention are described in further detail below.

[0039] A method for calculating the axial compressive bearing capacity of steel tube concrete considering the concrete Poisson's ratio and void defects is designed to improve the safety and economy of structural design through more accurate bearing capacity assessment. It is particularly suitable for engineering fields with high bearing capacity requirements such as bridges and high-rise buildings. Figure 1As shown, the method comprises the following steps:

[0040] Step S1, determine the basic parameters of the steel tube concrete component: first, determine the strain ε of the steel tube concrete component, the Poisson's ratio ν of the concrete, the inner and outer diameters r1 and r2 or b1 and b2 of the steel tube, the wall thickness t of the steel tube, and the hollow chord length l. The acquisition of these key parameters is the basis for calculating the bearing capacity of the steel tube concrete. The Poisson's ratio of concrete changes with strain, which determines the lateral expansion behavior of concrete under pressure and affects the relationship between the steel tube and concrete;

[0041] Step S2, calculate the constraint strength reduction factor k of the void defect d :For the existence of void defects, calculate the reduction coefficient of the restraint effect of the steel pipe on the concrete. This is because the existence of void defects will reduce the hoop effect of the steel pipe on the core concrete and affect the stress of the concrete. In this step, it is necessary to introduce the cross-sectional expansion coefficient in combination with the change of Poisson's ratio to make it more in line with the actual situation;

[0042] Step S3, calculating the strength f of the steel tube concrete with void defects sc :Based on the reduction factor calculated in the previous step, further calculate the overall strength of the steel tube concrete with void defects. This step fully considers the expansion behavior of concrete and the bearing capacity of the defective part;

[0043] Step S4, calculating the bearing capacity N of the steel tube concrete with void defects: Finally, the axial compressive bearing capacity of the steel tube concrete is calculated based on the change of the Poisson's ratio of concrete and the influence of the void defects.

[0044] Wherein, step S1 is specifically as follows:

[0045] The strain ε of the concrete member is the axial strain of the steel tube concrete when it is subjected to axial load; the Poisson's ratio v of the concrete is determined according to the following formula

[0046]

[0047] Where v0 is the initial value of the concrete Poisson's ratio, which is generally taken as v0 = 2, ε1 is the actual strain of the concrete under compression, and ε cu is the critical strain of concrete.

[0048] like Figure 2 and Figure 3 As shown, in the inner and outer diameters of the steel pipe, for a round steel pipe, r1 is the inner radius of the round steel pipe, and r2 is the outer radius of the round steel pipe; Figure 4 and Figure 5 As shown, for the square steel tube, b1 is half of the inner side length of the square steel tube, and b2 is half of the outer side length of the square steel tube; the steel tube wall thickness t and the hollow chord length l are measured according to actual conditions.

[0049] Step S2 is specifically as follows:

[0050] like Figure 2 and Figure 3 As shown, in the cylinder, for the annular void r3 is the core concrete radius, and for the spherical cap void, r3 is the core concrete area equivalent to the equivalent radius of the annular void component; Figure 4 and Figure 5 As shown, in the square column, for the annular void b3 is half of the inner side length of the core concrete, and for the spherical cap void b3 is the core concrete area equivalent to half of the equivalent inner side length of the annular void component.

[0051] For a circular column, the full-section concrete expansion is A′ Q The calculation formula of the concrete expansion after degassing is A′ c The calculation formula is as follows:

[0052] A' Q =π(r1+ενr1) 2 -πr1 2 =πr1 2 (2εν+ε 2 ν 2 )

[0053] A' c =π(r3+ενr3) 2 -πr3 2 =πr3 2 (2εν+ε 2 ν 2 )

[0054] For square columns, the full-section concrete expansion is A′ Q The calculation formula of the concrete expansion after degassing is A′ C The calculation formula is as follows:

[0055]

[0056]

[0057] At this time, the cross-sectional expansion coefficient δ is introduced, δ = 2εν + ε 2 ν 2

[0058] Since the inner area of ​​the steel pipe is A Q and concrete equivalent area A C The calculation formula is:

[0059] A Q =πr1 2

[0060] A c =πr3 2

[0061] Therefore, the above expansion area can be equivalent to:

[0062] A' Q =A Q ·δ

[0063] A' c =A c ·δ

[0064] Therefore, if the core concrete is in the ultimate compressive stress state, the concrete expansion A′ C Greater than or equal to the empty area A of the concrete in the steel tube e , then the voids produced during the production of the steel tube concrete can be filled by the expansion of concrete. If the concrete expansion amount A′ C Smaller than the hollow area A of concrete in the steel tube e , the void defects produced in the steel tube concrete during the production process cannot be filled by concrete expansion.

[0065] Calculate the restraint strength reduction factor k of the void defect d :

[0066] For the crown to be empty:

[0067]

[0068] The sector angle corresponding to the hollow spherical crown of the cylinder Empty area Ball crown free string length Concrete area after voiding A c =A Q -A e .

[0069] For annular degassing:

[0070]

[0071] Concrete area after annular voiding A c =π(r1-t) 2 , empty area A e =A Q -A c , concrete expansion A' c =A c ·δ.

[0072] For square columns, i.e. square steel tubes, r1 in the above formula can be replaced by b1, that is, the value of r1 is half of the inner side length of the square steel tube, and the value of r3 is half of the equivalent inner side length of the annular hollow component when the core concrete area is equivalent.

[0073] Step S3 is specifically as follows:

[0074] According to existing research results, the combined strength of solid circular steel tube concrete can be expressed by a formula:

[0075] f sc =(1+η c )[(1-β)f ck +βf y ]

[0076]

[0077] Where β is the steel content ratio, through the steel area A s Area A of concrete-filled steel tube sc The relationship between it and the steel content α is: β=α / (1+α); f ck ,f y are the standard strength values ​​of concrete and steel respectively;

[0078] ξ sc Hoop coefficient, by Calculated.

[0079] Introducing the non-uniform void constraint reduction factor k d The strength formula of the square column can be combined with the strength calculation formula of the square column component without voids. The strength calculation formula of the square column component without voids is:

[0080] f sc =(1+k e η c )[(1-β)f ck +βf y ]

[0081]

[0082] k e is the cross-section correction factor, which means the degree to which the cross-section shape weakens the constraint enhancement effect. For a circular cross-section column, f(n) = 1, and for a quadrilateral cross-section column, f(n) = 0.4. Introducing the non-uniform void constraint reduction factor k d The strength calculation formula of the steel tube concrete column with void defects is expanded to a quadrilateral:

[0083] f sc =(1+k d k e η c )[(1-β)f ck +βf y ]

[0084] Step S4 is specifically as follows:

[0085] Strength bearing capacity formula of concrete-filled steel tube columns with void defects:

[0086] N = f sc A sc =f sc (A s +A c )

[0087] Among them, f sc A is the axial compression combined strength of concrete-filled steel tube with void defects; sc A is the full cross-sectional area of ​​the concrete-filled steel tube after being hollowed out; s A is the cross-sectional area of ​​the steel pipe in the concrete tube; c It is the cross-sectional area of ​​concrete in the steel tube concrete after hollowing out.

[0088] The above method is used to calculate the axial compressive bearing capacity of the actual circular steel tube concrete with void defects. The relevant parameters and calculation results of the steel tube concrete are shown in Table 1 below:

[0089] Table 1

[0090]

[0091] f y : Standard value of steel strength; can be measured experimentally or directly used as theoretical strength.

[0092] f cu : Standard value of concrete strength; can be measured experimentally or directly used as theoretical strength.

[0093] N t : The theoretical value of the axial compressive bearing capacity of steel tube concrete is calculated by the method of the present invention.

[0094] N e : Experimental value of axial compressive bearing capacity of concrete-filled steel tube, measured experimentally.

[0095] N s : The finite element simulation value of the axial compressive bearing capacity of steel tube concrete. Finite element simulation is obtained. Abaqus software is used here for simulation, and other finite element software can also be used.

[0096] For actual steel tube concrete with void defects, the theoretical value of the axial compressive bearing capacity of the steel tube concrete calculated by the method of the present invention is 14822.49508KN. The peak load obtained by actual detection is 15057.09KN, and the peak load obtained by finite element calculation is 15220KN. It can be seen that the calculation method of the technical solution of the present invention is very close to the experimental value.

[0097] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A method for calculating the axial compressive bearing capacity of concrete-filled steel tubes with void defects considering Poisson's ratio, characterized in that: The steps include: Step S1, determining the strain, Poisson's ratio, inner diameter of the steel tube, outer diameter of the steel tube, wall thickness t of the steel tube and the hollow chord length of the steel tube concrete component; Step S2, calculating the restraint strength reduction coefficient of the void defect based on the parameters obtained in step S1; Step S3, calculating the strength of the steel tube concrete with void defects according to the restraint strength reduction factor obtained in step S2; Step S4, calculating the bearing capacity of the steel tube concrete with void defects by combining the change of the Poisson's ratio of concrete and the influence of void defects.

2. The method for calculating the axial compressive bearing capacity of concrete-filled steel tubes with void defects considering Poisson's ratio according to claim 1 is characterized in that: In step S1, the Poisson's ratio v of the steel tube concrete member is calculated using the following formula: Among them, v0 is the initial value of the Poisson's ratio of concrete, ε1 is the actual strain of concrete under compression, and ε cu is the critical strain of concrete.

3. The method for calculating the axial compressive bearing capacity of concrete-filled steel tubes with void defects considering Poisson's ratio according to claim 2 is characterized in that: v0=2, the wall thickness t of the steel pipe and the hollow chord length l are measured according to the actual situation.

4. The method for calculating the axial compressive bearing capacity of concrete-filled steel tubes with void defects considering Poisson's ratio according to claim 3 is characterized in that: In step S2, the constraint strength reduction factor k of the void defect is d The following formula is used to calculate: For the spherical cap to be empty: The sector angle corresponding to the hollow spherical crown of the cylinder r1 is the inner radius of the round steel tube or half of the inner side length of the square steel tube, and the hollow area Ball crown free string length The cross-sectional area of ​​concrete in the steel tube concrete after hollowing out A c =A Q -A e , A Q is the inner cross-sectional area of ​​the steel pipe, A Q =πr1 2 , A c is the equivalent cross-sectional area of ​​concrete, A c =πr3 2 , r3 is the equivalent radius of the circular steel tube core concrete area equivalent to the annular hollow component or the equivalent inner side length of the square steel tube core concrete area equivalent to the annular hollow component; δ is the cross-sectional expansion coefficient, δ=2εν+ε 2 ν 2 , where ε is the axial strain of the CFST member and v is the Poisson’s ratio of the CFST member; For annular degassing: Concrete area after annular voiding A c =π(r1-t) 2 , r1 is the inner radius of the round steel tube or half of the inner side length of the square steel tube, t is the wall thickness of the steel tube, and the void area A e =A Q -A c , A Q is the inner area of ​​the steel pipe, A C is the equivalent area of ​​concrete, δ is the cross-sectional expansion coefficient, δ=2εν+ε 2 ν 2 , where ε is the axial strain of the CFST member and v is the Poisson’s ratio of the CFST member.

5. The method for calculating the axial compressive bearing capacity of concrete-filled steel tubes with void defects considering Poisson's ratio according to claim 4 is characterized in that: In step S3, the strength of the steel tube concrete with void defects is sc The following formula is used to calculate: sc =(1+k d k e η c )[(1-β)f ck +βf y ], in, ξ sc is the hoop coefficient, f ck 、f y are the standard strength values ​​of concrete and steel, A s is the cross-sectional area of ​​the steel tube in the steel tube concrete, A C is the cross-sectional area of ​​concrete in the steel tube concrete after hollowing; β is the steel content ratio, through the steel area A s Area A of concrete-filled steel tube sc The ratio of is calculated; k d k is the reduction factor of the restraint strength of the void defect, e is the cross-section correction factor, n is the cross-sectional shape parameter. For a circular cross-section, f(n)=1; for a quadrilateral cross-section, f(n)=0.

4.

6. The method for calculating the axial compressive bearing capacity of concrete-filled steel tubes with void defects considering Poisson's ratio according to claim 5 is characterized in that: In step S4, the bearing capacity N of the steel tube concrete with void defects is calculated using the following formula: N = f sc (A s +A c ), Among them, f sc A is the axial compression combined strength of concrete-filled steel tube with void defects; s A is the cross-sectional area of ​​the steel tube in the steel tube concrete; c It is the cross-sectional area of ​​concrete in the steel tube concrete after hollowing out.

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