Mechanical analysis method for joint for annular assembly pipe jacking working well top force action

Abstract

The application discloses a mechanical analysis method for a joint for a ring-shaped assembly jacking pipe working well top force action, and steps are as follows: 1, input parameters; 2, calculate the height x of the edge of a compression zone to a neutral axis; 3, x<=0, then calculate bolt tension T1 and outer steel plate tension T2 according to a formula for a full section tension, skip 4 and execute 5; x>0, then calculate T1 of a corresponding condition and execute 4; 4, calculate the stress σ0 of the outer edge of a compression zone component, compare σ0 with f c , and perform comparison; σ0 c , a joint structure is adopted in which steel plates are used at the inner and outer edges of a well wall, corresponding T3 and T2 are calculated; σ0<=f c , a joint structure is adopted in which steel plates are used at the outer side of a well wall and bolts are used at the inner side, then corresponding T2 is calculated; 5, calculate the stress σ2 of a tension steel plate and the stress σ3 of a compression steel plate; 6, compare σ2 and σ3 with the tensile, compression and bending strength design values of the steel plate, and then output the calculation process and results, or recalculate after the steel plate specifications or the sectional area size of a prefabricated component is modified. The application can perform fast and accurate mechanical analysis calculation through a computer program.

Description

Technical Field

[0001] This invention relates to the field of computer-aided design technology for pipe jacking shafts, and in particular to a mechanical analysis method for joints used in annular assembled pipe jacking shafts to withstand jacking forces. Background Technology

[0002] Prefabricated working shafts are being used more and more widely in pipe jacking projects. Prefabricated working shaft segments are connected by bolts. Due to the limitation of working space, bolt connections are generally only made on the inner edge of the shaft wall. Under the action of large jacking force, the angle at the joint on the outer edge of the shaft wall of the segment will be too large, and the compressive stress at the joint on the inner edge of the shaft wall will be too large, or even crushed.

[0003] Existing analytical methods mainly rely on manual drawing and calculation, which is very time-consuming and prone to errors.

[0004] Therefore, how to conduct rapid and accurate mechanical analysis on the joints used in annular prefabricated pipe jacking working wells under jacking force based on mechanical balance analysis, deformation coordination analysis, and material physical analysis has become a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of the above-mentioned deficiencies of the prior art, the present invention provides a mechanical analysis method for joints used in annular assembled pipe jacking wells under jacking force. The purpose is to perform rapid and accurate mechanical analysis calculations on joints used in annular assembled pipe jacking wells under jacking force using computer programs, based on mechanical balance analysis, deformation coordination analysis, and material physical analysis.

[0006] To achieve the above objectives, this invention discloses a mechanical analysis method for a joint used in annular assembled pipe jacking wells under jacking force. The method employs a computer to perform the following steps, which are as follows:

[0007] Step 1: Input the joint bending moment M, joint axial force N, bolt preload T0, component cross-sectional width b, component cross-sectional height h, and distance a from the bolt to the edge of the pressure zone, i.e., the inner edge of the well wall. s E, the elastic modulus of concrete c Bolt elastic modulus E s The tensile stiffness k of the bolt t The tensile stiffness k of the steel plate s ;

[0008] Step 2: Using a steel plate joint on the outer side of the well wall and bolts on the inner side, calculate the height x from the edge of the pressure zone to the neutral axis. The specific formula is as follows:

[0009]

[0010]

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017] β=hk s +a s k t ;

[0018]

[0019] Where h0 is the distance from the bolt to the outer edge of the well wall; δ is the ratio of the height x from the inner edge of the well wall to the compression influence depth L0 of the pressure zone edge; k s This refers to the tensile stiffness of the steel plate.

[0020] Step 3: If the height x from the edge of the compression zone to the neutral axis is less than or equal to 0, it indicates that the entire cross-section is under tension. Calculate the bolt tension T1 and the outer steel plate tension T2 according to the formula for tension of the entire cross-section. Skip step 4 and proceed directly to step 5. The specific formula for tension of the entire cross-section is as follows:

[0021]

[0022] If the height x from the edge of the compressed area to the neutral axis is greater than 0, then T1 = -θ(xa) s )k t +T0, and proceed to step 4;

[0023] Step 4: Calculate the stress σ0 at the outer edge of the compression zone of the component. The specific formula is as follows:

[0024]

[0025] And σ0 is compared with the design value of concrete compressive strength f c Compare;

[0026] If σ0>f c If the pressure zone exceeds the limit, a joint structure using steel plates is used on both the inner and outer edges of the well wall.

[0027] T2 = N + T3;

[0028] If σ0≤f cIf a steel plate is used on the outside of the well wall and a bolted joint is used on the inside, then T2=(hx)θk s ;

[0029] Step 5: Calculate the stress σ2 of the tension steel plate and the stress σ3 of the compression steel plate. The specific formulas are as follows:

[0030] σ2=T2 / As2; σ3=T3 / As3;

[0031] Where As2 is the area of ​​the tension steel plate; As3 is the area of ​​the compression steel plate;

[0032] Step 6: Compare the tensile stress σ2 and compressive stress σ3 of the steel plate with the design values ​​f of the tensile, compressive, and bending strengths of the steel plate. If both σ2 and σ3 are within the range of f, output all calculation processes and results. If σ2 or σ3 exceeds the range of f, recalculate all calculations starting from step 1 after correcting the steel plate specifications or the cross-sectional dimensions of the precast components.

[0033] Preferred, k t =E s A s1 / L s Among them, A s L is the cross-sectional area of ​​the bolt. s This refers to the bolt length.

[0034] The beneficial effects of this invention are:

[0035] This invention uses a computer program to perform rapid and accurate mechanical analysis calculations on the joints used in annular prefabricated pipe jacking working wells under jacking force, based on mechanical balance analysis, deformation coordination analysis, and material physics analysis.

[0036] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0037] Figure 1 The following is a flowchart illustrating the execution of an embodiment of the present invention.

[0038] Figure 2 A schematic diagram of the prefabricated well jacking operation is shown in one embodiment of the present invention.

[0039] Figure 3 This diagram shows a partially enlarged schematic of a joint in a prefabricated manhole according to an embodiment of the present invention.

[0040] Figure 4 This diagram shows a partially enlarged view of the joint of a prefabricated manhole using a double-sided steel plate connection method in one embodiment of the present invention.

[0041] Figure 5 This diagram illustrates a simplified stress model of a joint portion of a prefabricated manhole according to an embodiment of the present invention.

[0042] Figure 6 This diagram illustrates a simplified stress model of another joint portion of a prefabricated manhole according to an embodiment of the present invention.

[0043] Figure 7 This diagram illustrates a stress model of a joint portion of a prefabricated manhole subjected to full-section tension in an embodiment of the present invention.

[0044] Figure 8 This diagram illustrates a stress model of another type of joint portion of a prefabricated manhole subjected to full-section tension in an embodiment of the present invention.

[0045] Figure 9 This diagram illustrates a force model of a prefabricated manhole according to an embodiment of the present invention, showing an increased prefabricated block cross-section in the joint portion, or a connection method using double-sided steel plates, and ignoring the force mode at the joint under bolt action. Detailed Implementation

[0046] Example

[0047] like Figure 1 As shown, the mechanical analysis method for the joint used in the jacking force of the annular assembled pipe jacking well is implemented by computer in the following steps:

[0048] Step 1: Input the joint bending moment M, joint axial force N, bolt preload T0, component cross-sectional width b, component cross-sectional height h, and distance a from the bolt to the edge of the pressure zone, i.e., the inner edge of the well wall. s E, the elastic modulus of concrete c Bolt elastic modulus E s The tensile stiffness k of the bolt t ;

[0049] Step 2: Using a steel plate joint for the outer edge of the well wall and bolts for the inner edge, calculate the height x from the edge of the pressure zone to the neutral axis. The specific formula is as follows:

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] β=hk s +a s k t ;

[0059]

[0060] Where h0 is the distance from the bolt to the outer edge of the well wall; δ is the ratio of the height x from the inner edge of the well wall to the compression influence depth L0 of the pressure zone edge; k s This refers to the tensile stiffness of the steel plate.

[0061] Step 3: If the height x from the edge of the compression zone to the neutral axis is less than or equal to 0, it indicates that the entire cross-section is under tension. Calculate the bolt tension T1 and the outer steel plate tension T2 according to the formula for tension of the entire cross-section. Skip step 4 and proceed directly to step 5. The specific formula for tension of the entire cross-section is as follows:

[0062] T2 = N - T1 + T0;

[0063] If the height x from the edge of the compressed area to the neutral axis is greater than 0, then T1 = -θ(xa) s )k t +T0, and proceed to step 4;

[0064] Step 4: Calculate the stress σ0 at the outer edge of the compression zone of the component. The specific formula is as follows:

[0065]

[0066] And σ0 is compared with the design value of concrete compressive strength f c Compare;

[0067] If σ0>f c If the pressure zone exceeds the limit, a joint structure using steel plates is adopted at both the inner and outer edges of the well wall.

[0068]

[0069] If σ0≤f c If a steel plate is used on the outside of the well wall and a bolted joint is used on the inside, then T2=(hx)θk s ;

[0070] Step 5: Calculate the stress σ2 of the tension steel plate and the stress σ3 of the compression steel plate. The specific formulas are as follows:

[0071] σ2=T2 / As2; σ3=T3 / As3;

[0072] Where As2 is the area of ​​the tension steel plate; As3 is the area of ​​the compression steel plate;

[0073] Step 6: Compare the tensile stress σ2 and compressive stress σ3 of the steel plate with the design values ​​f of the tensile, compressive, and bending strengths of the steel plate. If both σ2 and σ3 are within the range of f, output all calculation processes and results. If σ2 or σ3 exceeds the range of f, recalculate all calculations starting from step 1 after correcting the steel plate specifications or the cross-sectional dimensions of the precast components.

[0074] In some embodiments, k t =E s As1 / Ls; where As1 is the cross-sectional area of ​​the bolt; and Ls is the bolt length.

[0075] The principle of this invention is as follows:

[0076] Under the action of top force, the connecting joints of each section of the prefabricated working well, such as Figure 2 The stress pattern shown is axial tension and bending moment causing tension on the outer side. The structure employs an inner bolt and outer steel plate connection method, as shown below. Figure 3 In cases of exceptionally high jacking force, a double-sided steel plate connection method can also be used, such as... Figure 4 .

[0077] Connection method of inner bolts and outer steel plate

[0078] Based on the above joint structure, its simplified analysis model is as follows: Figure 5 , Figure 6 .

[0079] According to the calculation model shown in the diagram, the following can be obtained:

[0080] Based on the mechanical equilibrium condition,

[0081] N+F=T1+T2(2-1)

[0082]

[0083]

[0084] Based on deformation compatibility conditions,

[0085]

[0086] δ=x / l0(2-5)

[0087] Based on material physical conditions,

[0088] -θ(xa S )k t =T1-T0(2-6)

[0089] (hx)θk S =T2(2-7)

[0090] Combining equations (2-1) to (2-7), we get:

[0091]

[0092]

[0093]

[0094] In the formula:

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101] β=hk S +a S k t

[0102]

[0103] Solving the equation from equation (2-9) yields θ, and then x is obtained from equation (2-10); the edge stress σ0 of the joint compression zone is obtained from equation (2-4); finally, the bolt tension T1 and the outer steel plate tension T2 are obtained from equations (2-6) and (2-7) respectively.

[0104] When x ≤ 0 as calculated above, it indicates that the entire cross-section is under tension, and the force pattern at the joint is as follows: Figure 7 , Figure 8 .

[0105] According to the equilibrium condition of forces

[0106] N = T1 - T0 + T2 (2-10)

[0107]

[0108] By combining equations (2-10) and (2-11), the bolt tension T1 and the outer steel plate tension T2 can be obtained.

[0109] Connection method of double-sided steel plates

[0110] When x satisfies x>0 but σ0>fc, the prefabricated block section can be increased, or a double-sided steel plate connection method can be used, such as... Figure 4 Ignoring the effect of bolts, the force pattern at the joint is as follows: Figure 9 As shown.

[0111] N + T3 = T2 (3-1)

[0112]

[0113] Solve equations (3-1) and (3-2) to obtain the tensile forces T3 and T2 on the inner and outer steel plates.

[0114] 4. Steel plate selection and specification modification;

[0115] From the T2 and T3 calculated above, the corresponding tensile and compressive stresses of the steel plate can be further obtained;

[0116] σ2=T2 / As2; σ3=T3 / As3;

[0117] If σ2>f or σ3>f, then increase the steel plate specifications (width, thickness, etc.) and re-analyze and calculate.

[0118] σ²≤f

[0119] σ3≤f

[0120] The meanings of the terms and symbols appearing in the above simplified calculation model diagram and formula derivation are as follows:

[0121] M: Joint bending moment;

[0122] N: Axial force at the joint;

[0123] A1, B1, C1, D1, E1, α, β, γ: Process parameters, with no specific meaning;

[0124] T0: Bolt preload;

[0125] T1: Bolt tension;

[0126] T2: Tensile strength of the outer edge steel plate of the well wall;

[0127] T3: Pressure on the inner edge steel plate of the well wall;

[0128] F: The resultant force of pressure in the joint compression zone;

[0129] θ: Joint section rotation angle;

[0130] x: Height from the edge of the pressure zone to the neutral axis;

[0131] b: Width of the component section;

[0132] h: Height of the component section;

[0133] L0: Depth of compression effect in the compressed zone;

[0134] δ: The ratio of the height x from the edge of the compression zone to the neutral axis to the depth L0 of the compression effect of the compression zone;

[0135] σ0, ξ0: Stress and strain at the outer edge of the compression zone of the component;

[0136] σ2, σ3: Tension stress in steel plates under tension and compression;

[0137] h0: Distance from the bolt to the outer edge of the well wall;

[0138] a s The distance from the bolt to the edge of the pressure zone, i.e., the inner edge of the well wall;

[0139] E c : Elastic modulus of concrete;

[0140] k t The tensile stiffness of the bolt, k t =E s As1 / Ls;

[0141] ks: Tensile stiffness of the steel plate, ks=EsAs2 / ls2,

[0142] E s : Modulus of elasticity of bolts (or steel plates);

[0143] As1: Bolt cross-sectional area;

[0144] As2, As3: Area of ​​steel plates subjected to tension and compression;

[0145] Ls: Bolt length;

[0146] ls2: Calculation length in the direction of tensile force on the steel plate.

[0147] fc: Design value of concrete compressive strength;

[0148] Tp: Bolt guarantee load;

[0149] f: Design values ​​for the tensile, compressive, and bending strengths of the steel plate.

[0150] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A mechanical analysis method for the joint used in annular assembled pipe jacking wells under jacking force; characterized in that, The following steps are performed using a computer: Step 1: Input the joint bending moment M, joint axial force N, bolt preload T0, component cross-sectional width b, component cross-sectional height h, and distance a from the bolt to the edge of the pressure zone, i.e., the inner edge of the well wall. s E, the elastic modulus of concrete c Bolt elastic modulus E s The tensile stiffness k of the bolt t ; Step 2: Using a steel plate on the outer side of the well wall and a bolted joint on the inner side, calculate the height x from the edge of the pressure zone to the neutral axis. The specific formula is as follows: β=hk s +a s to t ; Where h0 is the distance from the bolt to the outer edge of the well wall; δ is the ratio of the height x from the inner edge of the well wall to the compression influence depth L0 of the pressure zone edge; k s This refers to the tensile stiffness of the steel plate. Step 3: If the height x from the edge of the compression zone to the neutral axis is less than or equal to 0, it indicates that the entire cross-section is under tension. Calculate the bolt tension T1 and the outer steel plate tension T2 according to the formula for tension of the entire cross-section. Skip step 4 and proceed directly to step 5. The specific formula for tension of the entire cross-section is as follows: T2=N-T1+T0; If the height x from the edge of the compressed area to the neutral axis is greater than 0, then T1 = -θ(xa) s )k t +T0, and proceed to step 4; Step 4: Calculate the stress σ0 at the outer edge of the compression zone of the component. The specific formula is as follows: And σ0 is compared with the design value of concrete compressive strength f c Compare; If σ0>f c If the pressure zone exceeds the limit, a joint structure using steel plates is adopted on both the inner and outer edges of the well wall. T2=N+T3; If σ0≤f c If a steel plate is used on the outside of the well wall and a bolted joint is used on the inside, then T2=(hx)θk s ; Step 5: Calculate the stress σ2 of the tension steel plate and the stress σ3 of the compression steel plate. The specific formulas are as follows: σ2=T2 / As2; σ3=T3 / As3; Where As2 is the area of ​​the tension steel plate; As3 is the area of ​​the compression steel plate; Step 6: Compare the tensile stress σ2 and compressive stress σ3 of the steel plate with the design values ​​f of the tensile, compressive, and bending strengths of the steel plate. If both σ2 and σ3 are within the range of f, output all calculation processes and results. If σ2 or σ3 exceeds the range of f, recalculate all calculations starting from step 1 after correcting the steel plate specifications or the cross-sectional dimensions of the precast components.

2. The mechanical analysis method for the joint used in the jacking force of annular assembled pipe jacking well according to claim 1, characterized in that, k t =E s As / Ls; where As is the cross-sectional area of ​​the bolt; and Ls is the bolt length.

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