Stress calculation method for steel bar grid panel type reinforced earth retaining wall

Abstract

The invention discloses a method for calculating the stress of a steel bar grid panel type reinforced earth retaining wall, which is simple in concept and practical and easy to operate. The steel bar grid panel type reinforced soil retaining wall is composed of filling soil, horizontally-arranged tie bars and grid panel units, and each grid panel unit comprises an inclined pull rod, a vertical rod and a horizontal rod. The calculation method comprises the following steps: step 100, numbering grid panel units from top to bottom, and calculating lateral soil pressure and tie bar tension acting on any layer of grid panel units according to static balance conditions of local soil wedge bodies; 200, the grid panel unit structure is made into a primary statically indeterminate structure, and the axial force and the normal stress of the cross section of an oblique pull rod of any layer of grid panel unit are calculated; step 300, calculating the axial force, the bending moment, the shearing force and the normal stress of the cross section of the vertical rod of any layer of grid panel unit according to the static balance condition; and step 400, calculating the axial force, the bending moment, the shearing force and the normal stress of the cross section of the horizontal rod of any layer of grid panel unit according to the static balance condition.

Description

Technical Field

[0001] The invention relates to the technical field of force calculation of a steel bar grid panel type reinforced earth retaining wall, and in particular to a force calculation method of a steel bar grid panel type reinforced earth retaining wall. Background Art

[0002] Backfill engineering is a common type of engineering construction in the fields of roads, buildings, municipal engineering, etc. The stability and reinforcement measures of backfill engineering are one of the focal issues of actual engineering. Steel grid panel reinforced earth retaining wall is a new technical means to solve the stability and reinforcement problems of backfill engineering. This type of structure has the advantages of light structure, easy installation, economic savings, strong engineering adaptability, low carbon and environmental protection, and has broad application prospects in practice. For steel grid panel reinforced earth retaining wall, reasonable force calculation and analysis is the prerequisite for its actual engineering design, which is of great significance to the reasonable design of steel grid panel reinforced earth retaining wall engineering.

[0003] Under the action of the fill's own weight and the top surface load of the fill, the steel mesh panels and reinforcement bars in the steel mesh panel reinforced earth retaining wall all show certain stress characteristics, and their stress characteristics vary along the height direction of the wall. Since this type of structure is relatively new, there is no calculation method for the stress of the steel mesh panel reinforced earth retaining wall in the current specifications, which makes the related actual projects lack theoretical reference methods, and are mostly based on experience, which is blind in design. Therefore, for the steel mesh panel reinforced earth retaining wall structure, a more reasonable and simple stress calculation and analysis method is urgently needed in engineering practice.

[0004] At present, there are some calculation and analysis methods for ordinary reinforced earth retaining walls, but they are all aimed at classic integral panel type and solid block type wall panel structures. There is no force calculation and analysis method for reinforced earth retaining walls with steel mesh as the main structure of the wall panel.

[0005] On the other hand, for the force calculation and analysis of reinforced earth retaining walls with steel mesh panels, numerical simulation methods such as finite element and finite difference can be used. However, for numerical simulation methods, it is necessary to establish a numerical model first, and the rationality of the numerical model depends on factors such as model parameters, model mesh accuracy, material constitutive model, boundary conditions, etc. Not only is the modeling process complicated and cumbersome (the modeling difficulty is particularly increased for steel mesh wall panel structures with dense steel bars), there is human subjective operation interference, and it is difficult to have "inheritance" (different people need to start from modeling operations). The study of complex problems can still be used as a reference, but it is not conducive to the rapid analysis and operation of actual engineering and technical personnel.

[0006] Therefore, the current stress calculation and analysis of reinforced earth retaining walls with reinforced mesh panels lacks a simplified theoretical calculation method that is simple in concept and easy to operate in practice, which makes the relevant engineering design lack sufficient and reasonable basis in specific application analysis, or the calculation and analysis operation process is cumbersome. Summary of the invention

[0007] The technical problem to be solved by the present invention is to provide a method for calculating the stress of a reinforced earth retaining wall with a steel grid panel type which is simple in concept and easy to operate in practice.

[0008] In order to achieve the above object, the present invention provides a force calculation method for a reinforced mesh panel reinforced earth retaining wall, and the technical solution is as follows:

[0009] A force calculation method for a reinforced earth retaining wall with a steel grid panel is provided. The reinforced earth retaining wall with a steel grid panel is composed of backfill, horizontally arranged tension bars, and a steel grid panel structure. The steel grid panel structure is composed of several layers of grid panel units stacked in sequence from top to bottom. Each layer of grid panel unit includes several oblique tension bars, vertical bars, horizontal bars, and connecting bars therebetween. The tension bars and the steel grid panel structure are connected and fixed at each horizontal bar. The calculation method includes the following steps:

[0010] Step 100, numbering the grid panel units from top to bottom, and calculating the lateral earth pressure and the tension of the reinforcement acting on any layer of the grid panel units according to the static equilibrium condition of the local soil wedge;

[0011] Step 200, the grid panel unit structure is a primary hyperstatic structure, and the axial force and cross-sectional normal stress of the oblique tie rod of any layer of grid panel units are calculated;

[0012] Step 300, calculating the axial force, bending moment, shear force and cross-sectional normal stress of the vertical rod of any layer of grid panel units based on static equilibrium conditions;

[0013] Step 400, based on the static equilibrium condition, calculate the axial force, bending moment, shear force and cross-sectional normal stress of the horizontal bars of any layer of grid panel units.

[0014] The force calculation method for the reinforced mesh panel reinforced earth retaining wall of the present invention is based on the static equilibrium conditions of the mesh panel units of the reinforced mesh panel structure and the local soil wedges involved in the units, fully reflects the interaction between the reinforced mesh panel structure and the fill, and can simply and quickly calculate the internal forces of each component (such as oblique tie rods, vertical rods, horizontal rods and horizontal tie rods at corresponding layers) in the reinforced mesh panel reinforced earth retaining wall. The calculation content is comprehensive, the principle is reasonable, the concept is clear, the algorithm is simple, and it is convenient for actual and fast operation. It overcomes the defects of traditional methods and does not require time-consuming, labor-intensive, and costly experiments or numerical simulation calculations. It can greatly improve the design calculation efficiency and provide a fast and effective technical means and algorithm basis for the actual engineering design calculation operation of the reinforced mesh panel reinforced earth retaining wall, which has important technical significance and engineering application value.

[0015] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments. Additional aspects and advantages of the present invention will be partially given in the following description, partially become apparent from the following description, or be learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The drawings constituting a part of the present invention are used to assist in understanding the present invention. The contents provided in the drawings and their related descriptions in the present invention can be used to explain the present invention, but do not constitute improper limitations on the present invention. In the drawings:

[0017] Figure 1 This is a structural schematic diagram of a steel grid panel reinforced earth retaining wall.

[0018] Figure 2 Schematic diagram of the stress analysis model of any layer of mesh panel unit.

[0019] Figure 3 Schematic diagram of the stress analysis model of the local soil wedge associated with any layer of mesh panel elements. DETAILED DESCRIPTION

[0020] The present invention is described clearly and completely below in conjunction with the accompanying drawings. A person skilled in the art will be able to implement the present invention based on these descriptions. Before describing the present invention in conjunction with the accompanying drawings, it should be particularly noted that:

[0021] The technical solutions and technical features provided in each part of the present invention, including the following description, may be combined with each other if there is no conflict.

[0022] In addition, the embodiments of the present invention involved in the following description are generally only a part of the embodiments of the present invention, rather than all the embodiments. Therefore, based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0023] About the terms and units in the present invention: The terms "include", "have" and any variations thereof in the description and claims of the present invention and related parts are intended to cover non-exclusive inclusions.

[0024] The specific implementation method of the force calculation method of the steel grid panel reinforced earth retaining wall of the present invention comprises the following steps:

[0025] Step 100, numbering the grid panel units from top to bottom, and calculating the lateral earth pressure and the tension of the reinforcement acting on any layer of the grid panel units according to the static equilibrium condition of the local soil wedge;

[0026] Step 200, the grid panel unit structure is a primary hyperstatic structure, and the axial force and cross-sectional normal stress of the oblique tie rod of any layer of grid panel units are calculated;

[0027] Step 300, calculating the axial force, bending moment, shear force and cross-sectional normal stress of the vertical rod of any layer of grid panel units based on static equilibrium conditions;

[0028] Step 400, based on the static equilibrium condition, calculate the axial force, bending moment, shear force and cross-sectional normal stress of the horizontal bars of any layer of grid panel units.

[0029] The following is a detailed description of each step.

[0030] Step 100

[0031] Figure 1 The structural diagram of the reinforced earth retaining wall with steel mesh panels is shown in Figure 1. Figure 1 The steel mesh panel reinforced earth retaining wall shown is composed of fill 10, horizontally arranged tension bars 60, and a steel mesh panel structure, wherein the steel mesh panel structure is composed of a plurality of layers of mesh panel units 20 stacked in sequence from top to bottom, each layer of mesh panel units 20 includes a plurality of oblique tension rods 30, vertical rods 40 and horizontal rods 50 and connecting rods therebetween, and the tension bars 60 are connected and fixed to the steel mesh panel structure at each horizontal rod 50; each vertical rod 40 and horizontal rod 50 is the same steel bar, and the bending angle of the steel bar is 90° or close to 90°; the tension bars 60 are generally made of geosynthetics.

[0032] Figure 2 is a schematic diagram of the force analysis model of any layer of grid panel unit. Figure 2 As shown, for Figure 2 The rod system OAB (AB represents the diagonal tie rod, AO represents the vertical rod and BO represents the horizontal rod) of the i-th layer grid panel unit structure from top to bottom is subjected to the following forces: i , lateral earth pressure E acting on the vertical rod i , the upper vertical pressure P acting on the top of the horizontal rod i and the lower vertical reaction force N acting on the bottom of the horizontal rod i .

[0033] According to the static equilibrium condition, we can get:

[0034] T i +R L i -R U i =E i cosδ (1)

[0035] P i +E i sinδ=N i (2)

[0036]

[0037] Where i is the unit layer number of the mesh panel from top to bottom, i = 1, 2, 3…n, and n is the total number of unit layers in the reinforced mesh panel structure; are the horizontal frictions of the upper and lower surfaces of the horizontal bars in the i-th grid panel unit; δ is the external friction angle between the vertical bars and the fill; a and b are the lengths of the vertical bars and horizontal bars in the i-th grid panel unit structure, respectively; x i N i The horizontal distance between the action point and the bottom end of the vertical rod; ξ i For E i The ratio of the height of the point of action from the bottom of the vertical rod to a.

[0038] ξ i The calculation expression is:

[0039]

[0040] Figure 3 Schematic diagram of the load analysis model of the local soil wedge associated with any layer of mesh panel elements. Figure 3 The local soil wedge (expressed as OADB) associated with the i-th layer of grid panel units from top to bottom shown in the figure can be obtained from the vertical and horizontal static equilibrium conditions:

[0041]

[0042]

[0043] Where W i is the soil weight within the height range of the i-th grid panel unit, W i =γab, γ is the fill weight; is the internal friction angle of fill; for N i , N 0 =q w b, q w is the static area distributed load acting on the top surface of the wall, which is generally taken as zero; It is the lateral earth pressure acting on the rear side BD of the local soil wedge.

[0044] According to the classical earth pressure theory, The calculation expression is:

[0045]

[0046] Where k is the lateral earth pressure coefficient, which is between the static earth pressure coefficient and active earth pressure coefficient k a =tan 2 In between, generally can be taken as π is the ratio of a circle to its circumference; h is the ratio of a circle to its circumference. i is the depth of the bottom of the horizontal bar of the i-th grid panel unit from the top surface of the fill, h i =ai+h 0 ,h 0 is the equivalent soil column height of the top surface load of the backfill behind the wall, h 0 =q / γ, q is the static area distributed load acting on the top surface of the fill.

[0047] According to Coulomb's friction theorem, we can get The calculation expression is:

[0048]

[0049] Where f is the friction coefficient between the horizontal rod and the fill soil. According to the Technical Specification for Application of Geosynthetics (GBT50290-2014), its value can be approximately taken as Generally acceptable

[0050] Combining equations (6) and (8), we can get:

[0051]

[0052] Combining equations (1) to (9), we can obtain:

[0053] T i =Ei (cosδ-f sinδ) (10)

[0054]

[0055] P i =N i -E i sinδ (12)

[0056]

[0057] Therefore, substituting equation (7) into equation (9) can calculate the lateral earth pressure E acting on the vertical rod in the i-th layer grid panel unit: i , and then the lateral earth pressure E i Substituting into equation (10) the corresponding upper vertical pressure P can be calculated: i , lower vertical reaction force N i and the tensile force T i .

[0058] For the case where the vertical rod in the grid panel unit is inclined, that is, the angle between it and the horizontal rod is less than 90°, the angle between the vertical rod and the vertical is β. The actual β value is generally small. It can still be derived according to the above basic method. Just replace δ in the above expression with δ-β to obtain the approximate calculation result in this case.

[0059] Step 200

[0060] Depend on Figure 2 It can be seen from the force analysis model shown that the grid panel unit is a primary hyperstatic structure. Therefore, the force method in structural mechanics can be used to analyze its internal force in detail, and the axial force F of the oblique tie rod in the i-th grid panel unit can be obtained: i The calculation expression is:

[0061]

[0062]

[0063] Δ 1P =Y 1 +Y 2 +Y 3 (16)

[0064]

[0065]

[0066]

[0067] Where E is the elastic modulus of the steel bar in the mesh panel unit; EA is the axial compressive or tensile stiffness of the diagonal tie rod in the i-th layer of mesh panel unit; I is the cross-sectional inertia moment of the vertical and horizontal rods in the i-th layer of mesh panel unit, and EI is its corresponding bending stiffness; δ 11 Yes F i is the relative displacement between the two ends of the oblique tie rod in the grid panel unit (i.e., between points A and B on the rod system OAB) caused by unit force; Δ 1P is the relative displacement between the two ends of the diagonal tie rod (i.e., between points A and B in the rod system OAB) caused by the external load on the grid panel unit, Y 1 , Y 2 , Y 3 To calculate the intermediate variable, the axial force is the positive force that causes the diagonal tie rod to produce axial tension.

[0068] Therefore, according to the material mechanics stress analysis method, the cross-sectional normal stress of the oblique tie rod in the i-th layer grid panel unit can be obtained: The calculation expression is:

[0069]

[0070] In the formula, S 2 is the arrangement spacing of the oblique tie rods AB in the i-th layer of grid panel units; d 2 is the diameter of the diagonal tie rod AB in the i-th grid panel unit.

[0071] Steps 300-400

[0072] For the vertical bar in the i-th layer grid panel unit, the shear force Q of the vertical bar can be obtained from the static equilibrium condition: OA , axial force N OA and bending moment M OA The calculation expressions are:

[0073]

[0074]

[0075]

[0076] In the formula, the axial force is the tensile force that causes the vertical rod to produce axial stretching, the shear force is the clockwise rotation around the vertical rod isolator, and the bending moment is the clockwise rotation; y is the height from the bottom end of the vertical rod, point O.

[0077] For the horizontal bar in the i-th layer of mesh panel unit, the shear force Q of the horizontal bar can be obtained from the static equilibrium condition: OB , axial force N OB , bending moment M OB The expressions are:

[0078]

[0079]

[0080]

[0081] Where x is the horizontal distance from the bottom end of the vertical rod, point O; the axial force is the tensile force that causes the horizontal rod to produce axial tension, the shear force is the clockwise rotation around the horizontal rod isolator, and the bending moment is the clockwise rotation.

[0082] For the case where the vertical rod in the grid panel unit is inclined, that is, the angle between it and the horizontal rod is less than 90°, the internal force of each rod in the grid panel unit can still be derived and calculated according to the above basic method. The result can be expressed by multiplying the relevant result when the vertical rod is completely along the vertical direction by an increase coefficient greater than 1. This increase coefficient is related to the angle β of the vertical rod to the vertical direction. When β = 5°, 10°, and 15°, the increase coefficients of the internal force of the vertical rod are 1.043, 1.083, and 1.122, respectively.

[0083] Therefore, according to the material mechanics stress analysis method, the cross-sectional normal stress of the vertical rod in the i-th layer grid panel unit can be obtained: and the cross-sectional normal stress of the horizontal bar The calculation expressions are:

[0084]

[0085]

[0086] In the formula, S 1 is the arrangement spacing of the vertical bars in the i-th grid panel unit; d 1 is the diameter of the vertical rod in the i-th grid panel unit.

[0087] It can be seen from equations (16) to (23) that the maximum values ​​of the shear force, axial force, bending moment and cross-sectional normal stress of the vertical and horizontal bars in each layer of the grid panel unit are all located at the intersection point O of the vertical and horizontal bars, that is, y = 0 and x = 0. Therefore, the shear force, axial force, bending moment and cross-sectional normal stress values ​​of the vertical and horizontal bars at point O can be used as the representative values ​​of their shear force, axial force, bending moment and cross-sectional normal stress.

[0088] The beneficial effects of the present invention are described below through specific embodiments.

[0089] The calculation object of this embodiment is the earthwork project supported by reinforced earth retaining wall with reinforced mesh panels. The steel bars of the mesh panels are of the same type. The friction coefficient between the horizontal bars of the mesh panel units and the earthwork is taken as Take the lateral earth pressure coefficient The other relevant calculation parameters are shown in Table 1.

[0090] Table 1

[0091]

[0092] Substituting the relevant parameters into equations (7) and (9), we can obtain:

[0093]

[0094] Then E i Substituting into formula (10), we can get:

[0095]

[0096] At the same time, according to formulas (11) to (13), N can be calculated i , P i and x i .

[0097] Specifically, the lateral earth pressure E on the i-th layer of reinforced mesh panel element can be obtained as i , tensile force T i , lower vertical reaction force N i , upper vertical pressure P i and the lower vertical reaction force N i The horizontal distance x from the point of action to the bottom of the vertical rod i The results are shown in Table 2. Then, the cross-sectional normal stress of the diagonal tie rod can be calculated by equations (14) and (20): See Table 2 for specific results.

[0098] Table 2

[0099]

[0100] Substituting the relevant parameters into equations (21), (22), (23), (27) and (24), (25), (26), (28), we can obtain the shear force, axial force, bending moment and cross-sectional normal stress of the vertical and horizontal bars in the i-th layer of grid panel units. The maximum values ​​of these internal forces of the vertical and horizontal bars of each layer of grid panel units are all located at the intersection point O of the vertical and horizontal bars, that is, y = 0 and x = 0. Therefore, the shear force, axial force, bending moment and maximum cross-sectional normal stress of the vertical and horizontal bars at point O are taken as the representative values ​​of their internal forces. The specific calculation results are shown in Table 3.

[0101] Table 3

[0102]

[0103] For the embodiment, the comparison of the maximum normal stress values ​​of the cross sections of the vertical bars and horizontal bars at point O in each layer of the grid panel unit obtained by the FLAC3D numerical simulation method and the results of the present invention is shown in Table 4.

[0104] Table 4

[0105]

[0106] It can be seen that the calculation results of the method of the present invention are relatively consistent with those of the numerical simulation method, and the maximum absolute value of the relative deviation between the two (the results of the present invention relative to the numerical simulation results) is only 13.92%, which is acceptable in actual engineering, indicating that the method of the present invention has certain rationality.

[0107] The above is a description of the relevant contents of the present invention. A person skilled in the art will be able to implement the present invention based on these descriptions. Based on the above contents of the present invention, all other embodiments obtained by a person skilled in the art without creative work shall fall within the scope of protection of the present invention.

Claims

1. Force calculation method of reinforced earth retaining wall with steel grid panel. The reinforced earth retaining wall with steel grid panel consists of backfill, horizontally arranged reinforcement and steel grid panel structure. The steel mesh panel structure is composed of several layers of mesh panel units stacked from top to bottom, each layer of mesh panel unit includes several oblique tie rods, vertical rods and horizontal rods and connecting rods therebetween, and the tie rods and the steel mesh panel structure are connected and fixed at each horizontal rod, which is characterized in that the calculation method includes the following steps: Step 100, numbering the grid panel units from top to bottom, and calculating the lateral earth pressure and the tension of the reinforcement acting on any layer of the grid panel units according to the static equilibrium condition of the local soil wedge; Step 200, the grid panel unit structure is a primary hyperstatic structure, and the axial force and cross-sectional normal stress of the oblique tie rod of any layer of grid panel units are calculated; Step 300, calculating the axial force, bending moment, shear force and cross-sectional normal stress of the vertical rod of any layer of grid panel units based on static equilibrium conditions; Step 400, based on the static equilibrium condition, calculate the axial force, bending moment, shear force and cross-sectional normal stress of the horizontal bars of any layer of grid panel units.

2. The force calculation method for the steel grid panel reinforced earth retaining wall according to claim 1 is characterized in that: In step 100, the calculation expressions of the earth pressure and the reinforcement tension acting on any layer of mesh panel units are: P i =N i -E i sinδ; T i =E i (cosδ-fsinδ); Where i is the layer number of the mesh panel unit from top to bottom, i = 1, 2, 3…n, and n is the total number of layers of mesh panel units in the reinforced mesh panel structure; E i is the lateral earth pressure acting on the vertical rod in the i-th layer grid panel unit; N i is the lower vertical reaction force at the bottom of the horizontal bar of the i-th layer grid panel unit; P i is the upper vertical pressure acting on the top of the horizontal rod of the i-th grid panel unit; T i is the tension of the reinforcement of the i-th layer of mesh panel unit; E i s is the lateral earth pressure acting on the rear side of the local soil wedge associated with the i-th grid panel element; is the internal friction angle of fill; W i is the deadweight of the soil within the height range of the i-th grid panel unit; f is the friction coefficient between the horizontal rod and the fill; δ is the external friction angle between the vertical rod and the fill.

3. The force calculation method for the steel grid panel reinforced earth retaining wall according to claim 2 is characterized in that: E i s The calculation expression is: h i The calculation expression is: i =ai+h0; Where k is the lateral earth pressure coefficient; γ is the fill weight; h i is the depth from the bottom of the horizontal bar of the i-th grid panel unit to the top surface of the fill; a is the length of the vertical bar in the i-th grid panel unit; h0 is the equivalent soil column height of the top surface load of the fill behind the wall, h0 = q / γ, q is the static area distributed load acting on the top surface of the fill.

4. The method for calculating the force of a reinforced grid panel reinforced earth retaining wall according to claim 3, characterized in that: The calculation expressions of the axial force and cross-sectional normal stress of the oblique tie rod of any layer of grid panel unit in step 200 are: Δ 1P =Y1+Y2+Y3; In the formula, F i is the axial force of the diagonal tie rod; i AB is the cross-sectional normal stress of the oblique tie rod; b is the length of the horizontal rod in the i-th layer of mesh panel unit; E is the elastic modulus of the steel bar in the mesh panel unit; I is the cross-sectional inertia moment of the vertical and horizontal rods in the i-th layer of mesh panel unit, and EI is its corresponding bending stiffness; EA is the axial compressive stiffness or tensile stiffness of the oblique tie rod in the i-th layer of mesh panel unit; x i N i The horizontal distance between the action point and the bottom end of the vertical rod; ξ i For E i The ratio of the height of the action point to the bottom of the vertical rod to a; S2 is the arrangement spacing of the oblique tie rods in the i-th layer of grid panel units; d2 is the diameter of the oblique tie rods in the i-th layer of grid panel units; π is the circumference of a circle; δ 11 Yes F i The relative displacement between the two ends of the diagonal tie rod in the grid panel unit caused by unit force; Δ 1P It is the relative displacement between the two ends of the oblique tie rod caused by the external load on the grid panel unit. Y1, Y2, and Y3 are intermediate variables for calculation.

5. The force calculation method for the steel grid panel reinforced earth retaining wall according to claim 4 is characterized in that: ξ i The calculation expression is: x i The calculation expression is:

6. The force calculation method for the steel grid panel reinforced earth retaining wall according to claim 4 is characterized in that: The calculation expressions of the axial force, bending moment, shear force and cross-sectional normal stress of the vertical bar of any layer of grid panel unit are: In the formula, Q OA is the shear force of the vertical rod; N OA is the axial force of the vertical rod; M OA is the bending moment of the vertical rod; σ i OA is the cross-sectional normal stress of the vertical rod; y is the height from the bottom end of the vertical rod; S1 is the arrangement spacing of the vertical rods in the i-th layer grid panel unit.

7. The force calculation method for the steel grid panel reinforced earth retaining wall according to claim 4 is characterized in that: The calculation expressions of the axial force, bending moment, shear force and cross-sectional normal stress of the horizontal bar of any layer of mesh panel unit are: In the formula, R i U , R i L are the horizontal frictions on the upper and lower surfaces of the horizontal bars in the i-th grid panel unit; Q OB is the shear force of the horizontal bar; N OB is the axial force of the horizontal rod; M OB is the bending moment of the horizontal bar; σ i OB is the cross-sectional normal stress of the horizontal rod; x is the horizontal distance from the bottom end of the vertical rod.

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