Fatigue safety checking calculation method for welded shear connector steel reinforced concrete composite beam

Abstract

The invention provides a fatigue safety checking calculation method for a welded shear connector steel-reinforced concrete composite beam, and the method comprises the steps: carrying out the normalized fatigue checking calculation of a tensile steel bar, a steel rib, coated concrete and a welded shear connector of the steel-reinforced concrete composite beam, so as to guarantee the safety of the whole composite beam; nr is used as the designed fatigue life of the tensile steel bar; ns is the designed fatigue life of the steel rib; nss is the designed fatigue life of the welding shear connector; fc and f are the compressive fatigue strength of the coated concrete; sigma c, max is the maximum pressure stress for covering the edge of the concrete compression area; wherein Nr / Ns and Ns / Ns are as control indexes as close to 1 as possible for the three assemblies of the steel rib, the tensile steel bar and the welding shear connector; and for coated concrete, fc, f / sigma c, max is as close as 1 and not less than 1 as a control index.

Description

Technical Field

[0001] The invention belongs to the technical field of civil engineering composite structures, and in particular relates to a fatigue safety verification method for a steel-concrete composite beam with a welded shear connector. Background Art

[0002] With the rapid development of my country's high-speed railways, supporting passenger stations, bridges, etc. have been widely built, and steel-reinforced concrete composite beams with excellent performance have been used in such infrastructure structures. Due to the reciprocating action of the super-large loads of high-speed railways, steel-reinforced concrete composite beams face high-cycle fatigue problems. In actual engineering, shear connectors such as studs are generally welded on the surface of the steel frame to give full play to the synergistic effect between the steel frame, steel bars, and covered concrete, improve the stiffness of the components and reduce the width of concrete cracks. However, welding shear connectors will bring about adverse effects such as welding defects, stress concentration effects, and residual tensile stress, making the steel-reinforced concrete composite beam very sensitive to high-cycle fatigue loads, and it is difficult to give full play to the advantages of high stiffness and strong bearing capacity of steel-reinforced concrete composite beams under reciprocating loads.

[0003] However, my country's current composite structure standards, "Composite Structure Design Code (JGJ 138-2016)", "Steel Frame Concrete Structure Design Code (YB 9082-2006)", and foreign current composite structure standards, such as the US "ANSI / AISC 360-22", the European "EN 1994-2:2005", the British "BS5400: Part 10:1980" and other standards, have not made any provisions for the fatigue design or verification of steel-framed concrete composite beams.

[0004] In the prior art, a Chinese patent document with publication number CN114254425A provides a "Fatigue design method for steel-concrete composite beams and its implementation method", which only proposes a fatigue design method and process for steel-concrete composite beams without welded shear connectors. However, welded shear connectors will have serious adverse effects on the fatigue performance of steel-concrete composite beams and significantly increase fatigue sensitivity. At present, there is still a lack of fatigue safety verification methods for steel-concrete composite beams with welded shear connectors. The inability to accurately evaluate the fatigue strength and fatigue life of steel-concrete composite beams with welded shear connectors poses a serious threat to the safe operation and maintenance of high-speed railways. Therefore, it is urgent to propose a fatigue safety verification method for steel-concrete composite beams with welded shear connectors. Summary of the invention

[0005] The technical problem to be solved by the present invention is to overcome the above-mentioned deficiencies of the prior art and provide a fatigue safety calculation method for steel-concrete composite beams with welded shear connectors having strong operability and high reliability.

[0006] The technical problem to be solved can be implemented through the following technical solutions.

[0007] A fatigue safety calculation method for a steel-reinforced concrete composite beam with welded shear connectors, characterized in that normalized fatigue calculations are performed on the tensile reinforcement, steel frame, covering concrete, and welded shear connectors of the steel-reinforced concrete composite beam respectively to ensure the safety of the entire composite beam;

[0008] N r is the design fatigue life of the tensile reinforcement; N s is the design fatigue life of the steel frame; N ss is the design fatigue life of the welded shear connector; c,f is the compressive fatigue strength of the encapsulated concrete; c,max is the maximum compressive stress at the edge of the compression zone of the encapsulated concrete; for the three components of steel frame, tensile reinforcement and welded shear connector, N r / N s and N ss / N s As close to 1 as possible is the control index; for the coating concrete, f c,f / σ c,max The control index should be as close to 1 as possible and not less than 1.

[0009] Furthermore, for the tensile reinforcement, the reference SN curve of the tensile longitudinal reinforcement is corrected by the steel frame fatigue crack growth reduction factor γ and the tensile reinforcement diameter correction factor ρ, thereby realizing the fatigue verification of the tensile longitudinal reinforcement.

[0010] Going further,

[0011] The reduction factor γ is calculated as follows:

[0012]

[0013] In the formula, is the fatigue crack growth rate of the steel frame;

[0014] N r0 To provide a preliminary prediction of fatigue life for tensile reinforcement;

[0015] Δσ r0 is the nominal stress amplitude of the tensile reinforcement calculated when the steel frame has no initial fatigue damage;

[0016] Δσ r1 is the fatigue crack extension of steel frame N r0 The nominal stress amplitude of the tensile reinforcement calculated after the second time;

[0017] f() is the conversion function between the steel frame fatigue crack size and the nominal stress amplitude of the tensile reinforcement;

[0018] The tension steel bar diameter correction factor ρ is a correction factor caused by the change in the tension steel bar diameter, and is calculated by the ratio of the fatigue strength of the tension steel bar with a diameter of Φ to the fatigue strength of the tension steel bar with a diameter of 12 mm, wherein the fatigue strength of the tension steel bar is determined according to the SN curve recommended by the Japanese JSCE standard "Standard Specifications for Concrete Structures";

[0019] The tensile reinforcement diameter correction factor ρ is calculated using the following formula:

[0020]

[0021] Where, Φ is the diameter of the tensile steel bar, in mm;

[0022] is the fatigue strength of the tensile reinforcement with a diameter equal to Φ;

[0023] S r 12 is the fatigue strength of the tensile steel bar with a diameter of 12 mm;

[0024] in, Calculated using the following formula:

[0025]

[0026] Where N r is the design fatigue life of the tensile reinforcement;

[0027] σ sp is the stress value caused by permanent load;

[0028] f ud It is the design value of tensile strength of tensile reinforcement.

[0029] Furthermore, the reference SN curve of the tension longitudinal reinforcement is lgN r =16.658-5·lgΔσ r0 , where N r is the design fatigue life of the tensile reinforcement; Δσ r0 It is the nominal stress amplitude of the tensile reinforcement calculated when the steel frame has no initial fatigue damage.

[0030] Further, the following correction is used:

[0031]

[0032] in, is the fatigue crack growth rate of the steel frame;

[0033] Nr0 To provide a preliminary prediction of fatigue life for tensile reinforcement;

[0034] Φ is the diameter of the tensile steel bar, in mm.

[0035] Furthermore, for steel skeleton,

[0036] (1) According to Miner's linear cumulative damage criterion and combined with the following formula, the remaining fatigue cycle number N of the steel frame after the tensile reinforcement breaks is determined: rem :

[0037] N r / N s0 +N rem / N s1 =1

[0038] Where N s0 、N s1 are respectively the fatigue life of steel frame calculated according to the notch stress SN curve when none of the tensile reinforcements are broken and when all of the tensile reinforcements are broken; N rem is the number of remaining fatigue cycles of the steel frame after the tensile reinforcement breaks;

[0039] (2) Calculate the design fatigue life of the steel frame N by the following formula s , thereby verifying whether the design requirements are met:

[0040] N s =N r +N rem =N r +N s1 ·(1-N r / N s0 ).

[0041] Furthermore, the notch stress SN curve is lgN s '=C s -3·lg(K t ·Δσ s ), where N s ' is the initial predicted fatigue life of the steel frame; C s K is the fatigue structural constant of the steel frame; t is the fatigue notch stress concentration factor of the steel frame caused by the welded shear connector; Δσ s is the nominal stress amplitude of the steel frame fatigue verification point.

[0042] Furthermore, for the sake of simplicity, the following formula is used to verify whether fatigue failure occurs at the outermost edge of the compression zone, thereby determining the fatigue safety of the encapsulated concrete:

[0043] σ c,max ≤f c,f =γρ ·f ck

[0044] In the formula, σ c,max is the maximum compressive stress at the edge of the compression zone of the encapsulated concrete;

[0045] f c,f is the compressive fatigue strength of the covering concrete;

[0046] γ ρ is the stress ratio correction factor for compressive concrete, which is determined according to the 2015 edition of the Chinese standard GB 50010-2010 Code for Design of Concrete Structures, taking into account the stress ratio R c The impact of

[0047] f ck It is the standard value of axial compressive strength of covering concrete.

[0048] Furthermore, for welded shear connectors, the fatigue SN curve of the following formula is used to check whether the welded shear connectors meet the shear design requirements:

[0049] lgN ss =C ss -m ss lgΔτ ss

[0050] Where N ss Design fatigue life for welded shear connectors;

[0051] C ss 、m ss is the fatigue construction constant of the welded shear connector;

[0052] Δτ ss is the nominal shear stress amplitude of the welded shear connector.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] (1) The verification method proposed in the present invention takes into account the mutual coupling effect of fatigue damage among multiple components and is scientific and reasonable.

[0055] (2) The verification method proposed in the present invention decouples the coupled fatigue problem into fatigue verification of several key components, and has clear logic, simplicity, practicality and operability.

[0056] (3) The calculation method proposed in the present invention adopts the notch stress method to perform fatigue calculation on the steel frame, which effectively reduces the influence of fatigue discreteness and improves the reliability of fatigue calculation.

[0057] (4) The verification method proposed in the present invention adopts a fatigue life / fatigue strength normalization verification method, which can optimize the test piece during design to maximize the use of all materials.

[0058] (5) In summary, the calculation method proposed in the present invention is scientific and reasonable, with clear logic, simple and practical, and operable. It has important guiding and reference value for the fatigue calculation of steel-reinforced concrete composite beams with welded shear connectors. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a fatigue safety calculation flow chart of the steel-concrete composite beam with welded shear connector provided by the present invention;

[0060] Figure 2 It is a fatigue SN curve diagram of the tensile steel bars in the steel-concrete composite beam of the welded shear connector provided by the present invention.

[0061] Among them, the above-mentioned drawings are only provided for the embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work. DETAILED DESCRIPTION

[0062] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. According to the following description, the purpose, technical solutions and advantages of the present invention will become clearer. It should be noted that the described embodiments are preferred embodiments of the present invention, but not all embodiments.

[0063] The present invention provides a fatigue safety calculation method for a steel-reinforced concrete composite beam with welded shear connectors, and performs normalized fatigue calculations on the tensile steel bars, steel frames, covering concrete, and welded shear connectors of the steel-reinforced concrete composite beam, thereby ensuring the safety of the entire composite beam (such as Figure 1 shown).

[0064] Furthermore, for the tensile reinforcement, since the fatigue failure of the tensile reinforcement and the steel frame is mutually coupled, the reduction effect of the steel frame fatigue crack extension on the fatigue strength of the tensile reinforcement needs to be considered, and the correction effect caused by the change in the diameter of the tensile reinforcement also needs to be considered.

[0065] The reduction effect of steel fatigue crack extension on the fatigue strength of tensile reinforcement is considered by the reduction factor γ, which is determined according to the equivalent damage caused by steel fatigue crack extension and can be calculated according to formula (1):

[0066]

[0067] In the formula, is the fatigue crack growth rate of the steel frame; N r0is the preliminary predicted fatigue life of the tensile reinforcement; Δσ r0 Δσ is the nominal stress amplitude of the tensile reinforcement calculated when the steel frame has no initial fatigue damage; r1 is the fatigue crack extension of steel frame N r0 The nominal stress amplitude of the tensile reinforcement calculated after the second calculation; f() is the conversion function between the steel frame fatigue crack size and the nominal stress amplitude of the tensile reinforcement.

[0068] The correction factor ρ caused by the change in the diameter of the tensile steel bar is calculated by the ratio of the fatigue strength of the tensile steel bar with a diameter of Φ to the fatigue strength of the tensile steel bar with a diameter of 12 mm, where the fatigue strength of the tensile steel bar is determined according to the SN curve recommended by the Japanese JSCE "Standard Specifications for Concrete Structures" (i.e., formula (2)). The calculation formula of the correction factor ρ obtained in this way is shown in formula (3).

[0069]

[0070] Where Φ is the diameter of the tensile reinforcement (in mm); is the fatigue strength of the tensile steel bar with a diameter equal to Φ; N r is the design fatigue life of the tensile reinforcement; sp is the stress value caused by permanent load; f ud It is the design value of tensile strength of tensile reinforcement.

[0071]

[0072] The reference SN curve of the tensile longitudinal reinforcement (i.e., formula (4)) is calculated by using the steel frame fatigue crack growth reduction factor γ and the tensile reinforcement diameter correction factor ρ. Figure 2 (as shown in formula (5)) is used to perform fatigue calculation on the tensile longitudinal reinforcement.

[0073] lgN r =16.658-5·lgΔσ r0 (4)

[0074]

[0075] Furthermore, for steel skeleton, the adverse effect of tensile reinforcement fracture on the fatigue life of steel skeleton needs to be considered. First, according to Miner linear cumulative damage criterion, the remaining fatigue cycle number N of steel skeleton after tensile reinforcement fracture is determined. rem (i.e., formula (6)).

[0076] N r / N s0 +N rem / N s1 =1 (6)

[0077] Where N s0 、N s1 are respectively the fatigue life of the steel frame calculated according to the notch stress SN curve (i.e., formula (7)) when none of the tensile reinforcements are broken and when all of the tensile reinforcements are broken; N rem It is the remaining number of fatigue cycles of the steel frame after the tensile reinforcement breaks.

[0078] lgN s '=C s -3·lg(K t ·Δσ s ) (7)

[0079] Where N s ' is the initial predicted fatigue life of the steel frame; C s K is the fatigue structural constant of the steel frame; t is the fatigue notch stress concentration factor of the steel frame caused by the welded shear connector; Δσ s is the nominal stress amplitude of the steel frame fatigue verification point.

[0080] Then, the design fatigue life N of the steel frame can be calculated by formula (8): s , so as to verify whether it meets the design requirements.

[0081] N s =N r +N rem =N r +N s1 ·(1-N r / N s0 ) (8)

[0082] Furthermore, for the sake of simplicity, for the coated concrete, whether fatigue failure occurs at the outermost edge of the compression zone can be verified according to formula (9), thereby determining the fatigue safety of the coated concrete.

[0083] σ c,max ≤f c,f =γ ρ ·f ck (9)

[0084] In the formula, σ c,max is the maximum compressive stress at the edge of the compression zone of the encapsulated concrete; f c,f is the compressive fatigue strength of the covering concrete; ρ is the stress ratio correction factor of compressive concrete, which can be determined according to the Chinese standard "Code for Design of Concrete Structures" (GB50010-2010) (2015 edition), taking into account the stress ratio of compressive concrete R c The impact of ck It is the standard value of axial compressive strength of covering concrete.

[0085] Furthermore, for welded shear connectors, the fatigue SN curve shown in formula (10) can be used to verify whether the welded shear connectors meet the shear design requirements.

[0086] lgN ss =C ss -m ss lgΔτ ss (10)

[0087] Where N ss is the design fatigue life of the welded shear connector; C ss 、m ss is the fatigue structural constant of the welded shear connector; Δτ ss is the nominal shear stress amplitude of the welded shear connector.

[0088] Among them, the welded shear connector steel-concrete composite beam contains multiple components, each of which has the risk of fatigue failure. The fatigue life / fatigue strength normalization calculation method can be used to achieve the purpose of optimized design. For the three key components of steel frame, tensile steel bar and welded shear connector, N r / N s 、N ss / N s As the control index; for the coating concrete, f c,f / σ c,max These three indicators should be as close to 1 as possible, and f c,f / σ c,max It should not be less than 1, so that the fatigue failure life of each component is close and the utilization of all materials is maximized.

[0089] The fatigue safety verification method of the steel-concrete composite beam with welded shear connector provided by the present invention performs normalized fatigue verification on the tensile steel bars, steel frame, coated concrete, and welded shear connector of the steel-concrete composite beam, respectively, so as to ensure the safety of the entire composite beam. The mutual coupling effect of fatigue damage of the steel frame and the tensile steel bars is taken into account, and not only the reduction and correction of the fatigue life of the tensile steel bars by the expansion of fatigue cracks in the steel frame and the change of the steel bar diameter are considered, but also the adverse effect of the tensile steel bar fracture on the fatigue life of the steel frame is considered. For the coated concrete and welded shear connectors, for the sake of simplicity, the fatigue safety is verified by the maximum compressive stress and shear stress amplitude at the edge of the compression zone respectively. Finally, by means of fatigue life / fatigue strength normalization verification, the fatigue failure life of multiple components is made close, all materials are utilized to the maximum extent, and the purpose of optimized design is achieved. The verification method proposed by the present invention is scientific and reasonable, with clear logic, simple and practical, and operable, and has important guiding and reference value for the fatigue verification of steel-concrete composite beams with welded shear connectors.

[0090] The above is only a description of the preferred embodiment of the present invention, and is not intended to limit the scope of protection of the present invention. Obviously, any technician familiar with the field can easily think of replacements or changes to obtain other embodiments based on the above embodiments, which should all be included in the scope of protection of the present invention.

Claims

1. A fatigue safety calculation method for steel-concrete composite beams with welded shear connectors, characterized in that: This includes normalized fatigue calculations of the tensile reinforcement, steel frame, covered concrete, and welded shear connectors of the steel-reinforced concrete composite beam to ensure the safety of the entire composite beam; N r is the design fatigue life of the tensile reinforcement; N s is the design fatigue life of the steel frame; N ss is the design fatigue life of the welded shear connector; c,f is the compressive fatigue strength of the encapsulated concrete; c,max is the maximum compressive stress at the edge of the compression zone of the encapsulated concrete; for the three components of steel frame, tensile reinforcement and welded shear connector, N r / N s and N ss / N s As close to 1 as possible is the control index; for the coating concrete, f c,f / σ c,max The control index should be as close to 1 as possible and not less than 1.

2. The fatigue safety calculation method for a steel-concrete composite beam with welded shear connector according to claim 1 is characterized in that: For the tensile reinforcement, the reference SN curve of the tensile longitudinal reinforcement is corrected by the steel frame fatigue crack growth reduction factor γ and the tensile reinforcement diameter correction factor ρ, thereby realizing the fatigue verification of the tensile longitudinal reinforcement.

3. A fatigue safety calculation method for steel-concrete composite beams with welded shear connectors according to claim 2, characterized in that: The reduction factor γ is calculated as follows: In the formula, is the fatigue crack growth rate of the steel frame; N r0 To provide a preliminary prediction of fatigue life for tensile reinforcement; Δσ r0 is the nominal stress amplitude of the tensile reinforcement calculated when the steel frame has no initial fatigue damage; Δσ r1 is the fatigue crack extension of steel frame N r0 The nominal stress amplitude of the tensile reinforcement calculated after the second time; f() is the conversion function between the steel frame fatigue crack size and the nominal stress amplitude of the tensile reinforcement; The tension steel bar diameter correction factor ρ is a correction factor caused by the change in the tension steel bar diameter, and is calculated by the ratio of the fatigue strength of the tension steel bar with a diameter of Φ to the fatigue strength of the tension steel bar with a diameter of 12 mm, wherein the fatigue strength of the tension steel bar is determined according to the SN curve recommended by the Japanese JSCE standard "Standard Specifications for Concrete Structures"; The tensile reinforcement diameter correction factor ρ is calculated using the following formula: Where, Φ is the diameter of the tensile steel bar, in mm; is the fatigue strength of the tensile reinforcement with a diameter equal to Φ; is the fatigue strength of the tensile steel bar with a diameter of 12 mm; in, Calculated using the following formula: Where N r is the design fatigue life of the tensile reinforcement; σ sp is the stress value caused by permanent load; f ud It is the design value of tensile strength of tensile reinforcement.

4. A fatigue safety calculation method for steel-concrete composite beams with welded shear connectors according to claim 2 or 3, characterized in that: The reference SN curve of the tension longitudinal reinforcement is lgN r =16.658-5·lgΔσ r0 , where N r is the design fatigue life of the tensile reinforcement; Δσ r0 It is the nominal stress amplitude of the tensile reinforcement calculated when the steel frame has no initial fatigue damage.

5. A fatigue safety calculation method for steel-concrete composite beams with welded shear connectors according to claim 4, characterized in that: Use the following formula for correction: in, is the fatigue crack growth rate of the steel frame; N r0 To provide a preliminary prediction of fatigue life for tensile reinforcement; Φ is the diameter of the tensile steel bar, in mm.

6. The fatigue safety calculation method for steel-concrete composite beams with welded shear connectors according to claim 1 is characterized in that: For steel bones, (1) According to Miner's linear cumulative damage criterion and combined with the following formula, the remaining fatigue cycle number N of the steel frame after the tensile reinforcement breaks is determined: rem : N r / N s0 +N rem / N s1 =1 Where N s0 、N s1 are respectively the fatigue life of steel frame calculated according to the notch stress SN curve when none of the tensile reinforcements are broken and when all of the tensile reinforcements are broken; N rem is the number of remaining fatigue cycles of the steel frame after the tensile reinforcement breaks; (2) Calculate the design fatigue life of the steel frame N by the following formula s , thereby verifying whether the design requirements are met: N s =N r +N rem =N r +N s1 ·(1-N r / N s0 )。 7. A fatigue safety calculation method for steel-concrete composite beams with welded shear connectors according to claim 6, characterized in that: The notch stress SN curve is lgN s '=C s -3·lg(K t ·Δσ s ), where N s ' is the initial predicted fatigue life of the steel frame; C s K is the fatigue structural constant of the steel frame; t is the fatigue notch stress concentration factor of the steel frame caused by the welded shear connector; Δσ s is the nominal stress amplitude of the steel frame fatigue verification point.

8. The fatigue safety calculation method for steel-concrete composite beams with welded shear connectors according to claim 1 is characterized in that: For the purpose of simplification, the following formula is used to verify whether fatigue failure occurs at the outermost edge of the compression zone, thereby determining the fatigue safety of the encapsulated concrete: s c,max ≤f c,f =c ρ ·f ck In the formula, σ c,max is the maximum compressive stress at the edge of the compression zone of the encapsulated concrete; f c,f is the compressive fatigue strength of the covering concrete; γ ρ is the stress ratio correction factor for compressive concrete, which is determined according to the 2015 edition of the Chinese standard GB 50010-2010 Code for Design of Concrete Structures, taking into account the stress ratio R c The impact of f ck It is the standard value of axial compressive strength of covering concrete.

9. The fatigue safety calculation method for steel-concrete composite beams with welded shear connectors according to claim 1 is characterized in that: For welded shear connectors, the fatigue SN curve according to the following formula is used to check whether the welded shear connectors meet the shear design requirements: lgN ss =C ss -m ss ·lgΔτ ss Where N ss Design fatigue life for welded shear connectors; C ss 、m ss is the fatigue construction constant of the welded shear connector; Δτ ss is the nominal shear stress amplitude of the welded shear connector.

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