Evaluation method for out-of-plane buckling strength of grid walls

Abstract

To establish an evaluating method of a strength of a lattice-like wall with respect to buckling in the out-of-plane direction.SOLUTION: Assuming that a diagonal member 22 between grid intersections of a lattice-like wall 20 is formed by connecting a partition plate 27a of a block 27 and an adhesive layer 28 in series, a Young's modulus Ege and a shearing elastic modulus Gge of the diagonal member 22 are calculated. Assuming that the lattice-like wall 20 is replaced with a brace model 120, the brace model 120 is replaced with a plate-like wall model 220, and rigidities of the lattice-like wall 20, the brace model 120, and the plate-like wall model 220 are equivalent to each other, a thickness Tge of the plate-like wall model 220 is calculated. Using an evaluation formula for an out-of-plane buckling strength of the lattice-like wall 20 obtained from an evaluation formula for an out-of-plane buckling strength of the plate-like wall model 220, a buckling start load Qboe or a maximum withstand load Qboeu of the lattice-like wall 20 is calculated.SELECTED DRAWING: Figure 10

Description

[Technical Field]

[0001] The present invention relates to a method for evaluating the out-of-plane buckling strength of a lattice wall. [Background technology]

[0002] Patent Document 1 discloses a diagonal lattice wall constructed inside the existing column-beam frame of a building. This lattice wall is composed of a plurality of square frame blocks and a plurality of right-angled triangular frame blocks. The right-angled triangular frame blocks are arranged along the inner periphery of the column-beam frame, and the square frame blocks are laid inside the rows of right-angled triangular frame blocks. This type of lattice wall is a seismic reinforcement wall that reinforces the column-beam frame. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 2018-053461 Summary of the Invention [Problem to be solved by the invention]

[0004] When a large earthquake occurs, grid walls may buckle in the out-of-plane direction. Therefore, it is necessary to evaluate the strength of grid walls by determining the load at which the grid wall begins to buckle and the maximum load that the grid wall can withstand. However, because grid walls are arranged in a grid pattern, their mechanical behavior is complex. Therefore, there is no established method for evaluating the strength of grid walls with respect to buckling in the out-of-plane direction. The present invention has been made in view of the above circumstances, and an object of the present invention is to establish a method for evaluating the strength of a lattice wall with respect to buckling in the out-of-plane direction. [Means for solving the problem]

[0005] To solve the above problems, Inside the frame set up along the inner periphery of a rectangular area surrounded by a column-beam framework, multiple blocks are glued together with adhesive and laid in a grid pattern. Evaluating the out-of-plane buckling strength of lattice walls, executed by a computerA method for evaluating the out-of-plane buckling strength of a grid-like wall, comprising: Young's modulus E of left-upward diagonal member and right-upward diagonal member ge and shear modulus G ge Calculate aggregating the left-upward diagonal members into a left-upward diagonal member model and the right-upward diagonal members into a right-upward diagonal member model; The grid wall is replaced with an X-shaped brace model consisting of the left-upward diagonal member model and the right-upward diagonal member model. and The brace model is made of a material with a thickness of t ge Replaced with a plate-like wall model and The shear stress τ when the plate-like wall model begins to buckle cre Calculate a step of forming a thickness t ge , the shear stress τ when the plate-like wall model begins to buckle cre , and the inside width l0 of the rectangular area, The buckling initiation strength Q of the grid wall is the out-of-plane buckling strength of the grid wall. boe The buckling load Q of the equivalent plate-like wall model cre Calculate death, The buckling load Q of the plate-like wall model cre is evaluated as the out-of-plane buckling strength of the grid wall. The method for evaluating the out-of-plane buckling strength of a lattice wall is characterized by comprising the steps of: cre Instead of The maximum load capacity Q of the grid wall is the out-of-plane buckling strength of the grid wall. boeu The maximum load capacity Q of the plate-like wall model is equivalent to u is evaluated as the out-of-plane buckling strength of the lattice wall. There are things that The maximum load capacity Q of the plate-shaped wall model u teeth , the post-buckling strength τ of the plate-like wall model in the elastic region u and the thickness t of the plate-like wall model ge and the inside width l0 of the rectangular area.

[0006] According to the above, An X-shaped brace model with equivalent stiffness to the lattice wall is created, and then a plate wall model with equivalent stiffness to the X-shaped brace model is created. The evaluation formula for the out-of-plane buckling strength of the plate-like wall model is used to evaluate the out-of-plane buckling strength of the grid-like wall. This allows A method for evaluating the out-of-plane buckling strength of lattice walls has been established. Furthermore, because the strength evaluation formula for a plate-like wall model with mechanically simple behavior is used, the out-of-plane buckling strength of lattice walls can be evaluated even if the mechanical behavior of the lattice walls is complex. [Effects of the Invention]

[0007] According to the present invention, by creating an X-shaped brace model and a plate-like wall model, the evaluation formula for the out-of-plane buckling strength of the plate-like wall model can be used to evaluate the out-of-plane buckling strength of the lattice wall, even if the mechanical behavior of the lattice wall is complex, thereby establishing a method for evaluating the out-of-plane buckling strength of a lattice wall. This makes it possible to evaluate the load at which the lattice wall buckles, as well as the load against which the lattice wall can resist. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. [Figure 2] This is a front view of a lattice wall constructed inside a column-beam frame. [Figure 3] FIG. 1 is an enlarged view of region III. [Figure 4] FIG. 1 is an enlarged view of region IV. [Figure 5] FIG. 2 is a perspective view schematically illustrating a part of a column-beam frame and a lattice wall. [Figure 6] FIG. 1 is a perspective view of a right-angled triangular block. [Figure 7] FIG. 1 is a perspective view of a square block. [Figure 8] 1 is a graph showing the relationship between horizontal load and horizontal displacement. [Figure 9] FIG. 10 is an explanatory diagram of the calculation step of the Young's modulus of the diagonal member of the unit element. [Figure 10] FIG. 10 is an explanatory diagram of replacing a lattice wall with a brace model. [Figure 11] FIG. 10 is an explanatory diagram of the replacement of a brace model with a wall element. DETAILED DESCRIPTION OF THE INVENTION

[0009] Hereinafter, embodiments of the present invention will be described with reference to the drawings. The embodiments described below are subject to various limitations that are technically preferable for implementing the present invention, but the scope of the present invention is not limited to the following embodiments and illustrated examples.

[0010] 1. Lattice wall and column-beam frame Fig. 1 is a front view of an existing column-beam frame 1 of a building. Fig. 2 is a front view of the column-beam frame 1 that has been seismically reinforced with a lattice wall 20. Fig. 3 is an enlarged view of region III shown in Fig. 2. Fig. 4 is an enlarged view of region IV shown in Fig. 2. Fig. 5 is a perspective view that schematically shows a part of the column-beam frame 1 and the lattice wall 20.

[0011] Below, the configuration of the beam-column frame 1 and the lattice wall 20 inside it will be described, and then a method for evaluating the out-of-plane buckling strength of the lattice wall 20 will be described.

[0012] The column-beam structure 1 consists of adjacent columns 2 and adjacent beams 3 of the existing skeleton of the building. The columns 2 are erected vertically, and the beams 3 are erected horizontally between the columns 2, thereby forming the column-beam structure 1 in the shape of a rectangular frame. The columns 2 and beams 3 are made of reinforced concrete or steel-reinforced concrete.

[0013] A frame body 10 is constructed in the shape of a rectangular frame along the inner periphery of the column-beam frame 1, and a lattice wall 20 is constructed inside the frame body 10. This provides seismic reinforcement to the building and its column-beam frame 1.

[0014] The frame 10 has a pair of column-side guide steels 11 on the left and right and a pair of beam-side guide steels 12 on the top and bottom. The column-side guide steels 11 are installed vertically along the columns 2 inside the column-beam frame 1. The column-side guide steels 11 are adhered to the columns 2 with adhesive and then fixed to the columns 2 with anchors. The beam-side guide steels 12 are installed horizontally along the beams 3 inside the column-beam frame 1. The beam-side guide steel 12 is adhered to the beams 3 with adhesive and then fixed to the beams 3 with anchors. These guide steels 11, 12 are made of, for example, H-shaped steel, T-shaped steel, channel steel, angle steel, or steel plate.

[0015] The lattice wall 20 is arranged in a diagonal lattice pattern. The diagonal lattice pattern means that the sides 22 of the square unit elements 21, which form the units of the lattice, are diagonally angled at 45 degrees to the horizontal, and these unit elements 21 are arranged in a lattice pattern at diagonal angles of 45 degrees to the horizontal. One diagonal of the unit elements 21 arranged in this manner is horizontal, and the other diagonal is vertical. Hereinafter, the sides 22 of the unit elements 21 will also be referred to as diagonal members 22.

[0016] The lattice wall 20 is constructed by laying a plurality of blocks 26 and 27 inside the frame 10.

[0017] Fig. 6 is a perspective view of block 26. As shown in Fig. 6, block 26 is shaped like a right-angled triangle. Block 26 has a partition plate 26a that forms the base of the right-angled triangle and a pair of partition plates 26b that form equal sides of the right-angled triangle. Block 26 is made of cast iron, such as spheroidal graphite cast iron, or cast steel.

[0018] As shown in Figures 2, 4, and 5, the blocks 26 are arranged adjacent to each other along the inner periphery of the frame body 10, with their right-angled vertices 26c facing inward of the frame body 10. The partition plates 26a of each block 26 are adhered to the inner periphery of the frame body 10 with adhesive 28. The partition plates 26a adhered to the column-side guide steels 11 of the frame body 10 are vertical, and the partition plates 26a adhered to the beam-side guide steels 12 of the frame body 10 are horizontal. In addition, the partition plates 26b of adjacent blocks 26 at an inside corner of the frame body 10 are adhered to each other with adhesive 28. The adhesive 28 is a two-part epoxy adhesive that hardens after mixing.

[0019] Fig. 7 is a perspective view of block 27. As shown in Fig. 7, block 27 is shaped like a square frame. Block 27 has four partition plates 27a that form the sides of the square. Block 27 is made of cast iron, such as spheroidal graphite cast iron, or cast steel.

[0020] As shown in Figures 2 to 5, the sides of the blocks 27 are inclined at 45° to the horizontal. The blocks 27 are arranged adjacent to each other in a grid pattern at an angle of 45° to the horizontal, inside the row of blocks 26 arranged along the inner periphery of the frame 10. The partition plates 27a of adjacent blocks 27 are bonded to each other with adhesive 28. The partition plates 27a of adjacent blocks 27 bonded to each other with adhesive 28 form the diagonal member 22 of the unit element 21. The partition plates 26b and 27a of adjacent blocks 26 and 27 are bonded to each other with adhesive 28. The partition plates 26b and 27a of adjacent blocks 26 and 27 bonded to each other with adhesive 28 form the diagonal member 22 of the unit element 21.

[0021] 2. Evaluation method for out-of-plane buckling strength of grid walls Because the grid wall 20 is arranged in a diagonal grid pattern, it exhibits mechanically complex behavior compared to plates and bars, which are fundamental structures in material mechanics and structural mechanics. Therefore, no evaluation formula for calculating the out-of-plane buckling strength of the grid wall 20 has been established. On the other hand, ordinary walls are arranged in a plate-like shape, and their mechanical behavior has been clarified in recent years. The out-of-plane buckling strength of plate-like walls is disclosed in "Guidelines for Buckling Design of Steel Structures," 4th Edition, edited and written by the Architectural Institute of Japan, published by the Architectural Institute of Japan, February 20, 2018, pp. 180-188. Therefore, the grid wall 20 is replaced with a plate-like wall model with equivalent rigidity, and the out-of-plane buckling strength of the grid wall 20 is calculated and evaluated using the evaluation formula for the out-of-plane buckling strength of the plate-like wall model. The following describes in detail the method for evaluating the out-of-plane buckling strength of the grid wall 20.

[0022] (1) Definition The out-of-plane buckling strength of the lattice wall 20 refers to the buckling initiation load or maximum load capacity of the lattice wall 20. The buckling initiation load of the lattice wall 20 refers to the horizontal load at which the lattice wall 20 begins to buckle in the out-of-plane direction when a horizontal load acts on the upper beam 3, causing the upper beam 3 to displace in the horizontal direction. The maximum load capacity of the lattice wall 20 refers to the maximum horizontal load that the lattice wall 20 can resist after a horizontal load acts on the upper beam 3, causing the upper beam 3 to displace in the horizontal direction and causing the lattice wall 20 to buckle in the out-of-plane direction. In other words, the horizontal load Q on the beam 3 and the horizontal displacement δ of the beam 3 are h The relationship between these is shown in Figure 8. Since the grid wall 20 starts to buckle when a horizontal load is applied at point A, the horizontal load at point A corresponds to the buckling initiation load of the grid wall 20. In addition, since the maximum horizontal load that the grid wall 20 can resist is the horizontal load at point B, the horizontal load at point B corresponds to the maximum withstand load of the grid wall 20. Hereinafter, the buckling initiation load of the grid wall 20 will be referred to as Q boe [N], and the maximum load capacity of the grid wall 20 is Q boeu It is represented as [N].

[0023] The symbols used in the following explanation are defined as follows:

[0024] [Table 1]

[0025] The width w of the partition plates 27a and 26b g corresponds to the thickness of the lattice wall 20. When the material of the blocks 26 and 27 is cast iron, E g =170000N / mm 2 and ν g When the adhesive 28 is a two-component mixed curing type epoxy adhesive called Seekadur (registered trademark) WS, E b =5000N / mm 2 (catalog value).

[0026] (2) Calculation step of Young's modulus and shear modulus of elasticity of diagonal members (first step) The method for evaluating the out-of-plane buckling strength of the lattice wall 20 is to calculate the Young's modulus E geand shear modulus G ge The Young's modulus E of the diagonal member 22 is calculated. ge and shear modulus G ge is calculated as follows:

[0027] As shown in Figure 9, when the diagonal members 22 between the intersections of the lattice are removed, the diagonal members 22 can be mechanically regarded as shaft members 22A in which the partition plates 27a and adhesive 28 are connected in series in the length direction of the two overlapping partition plates 27a (or the two overlapping partition plates 26b, 27a). The length of the shaft member 22A is the sum L1 of the length of the partition plates 27a and the thickness L2 of the adhesive 28. 1+2 The cross-sectional area of ​​the shaft 22A is equal to the cross-sectional area A of the diagonal member 22. g The cross-sectional area A of the shaft 22A and the diagonal member 22 is equal to g The figure does not include the adhesive 28 sandwiched between the partition plates 27a.

[0028] Length L 1+2 And cross-sectional area A g The axial stiffness K2 [N / mm] of the shaft member 22A is expressed as in formula (1). 1+2 And cross-sectional area A g If the entire shaft member 22B is made of the same material as the partition plate 27, the shaft stiffness K1 [N / mm] of the shaft member 22B is expressed as in equation (2). Then, as in equation (3), the ratio of the shaft stiffness K2 to the shaft stiffness K1 is calculated, and this is used as the correction coefficient β g Let's say.

[0029]

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[0030] As shown in equation (4), the Young's modulus E of the partition plate 27a is g Correction coefficient β g The product obtained by multiplying by is the Young's modulus E of diagonal member 22. ge Similarly, as shown in equation (5), the shear modulus G of the partition plate 27a is g Correction coefficient β g The product obtained by multiplying by is the shear modulus G of the diagonal member 22. geLet's say.

[0031]

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[0032] As is clear from equation (4), the Young's modulus E of the diagonal member 22 ge is the Young's modulus E of the partition plate 27a g and length L1 and Young's modulus E of adhesive 28 g and the layer thickness L2. As is clear from equation (5), the shear modulus G of the diagonal member 22 is ge is the Young's modulus E of the partition plate 27a g , Poisson's ratio ν g and length L1 and Young's modulus E of adhesive 28 g and the layer thickness L2.

[0033] Young's modulus E in equations (4) and (5) g , Poisson's ratio ν g , length L1, Young's modulus E b and the layer thickness L2 are known. Therefore, using equation (4), the Young's modulus E g , length L1, Young's modulus E b From the layer thickness L2, the Young's modulus E of diagonal member 22 is ge Also, using equation (5), the Young's modulus E g , Poisson's ratio ν g , length L1, Young's modulus E b From the value of the layer thickness L2, the shear modulus G of the diagonal member 22 ge Calculate.

[0034] The Poisson's ratio of the diagonal member 22 is ν g is assumed to be equivalent to

[0035] (3) Calculation step of thickness of plate-like wall model (2nd step) The method for evaluating the out-of-plane buckling strength of the lattice wall 20 includes the steps of creating an X-shaped brace model with equivalent rigidity to the lattice wall 20 and a plate-like wall model with equivalent rigidity to the brace model, and calculating the thickness of the plate-like wall model. Hereinafter, the thickness of the plate-like wall model is calculated as follows.

[0036] (3-1) Replacement with brace model The lattice wall 20 can be considered a collection of multiple diagonal members 22. Therefore, as shown in Figure 10, the left-upward diagonal members 22 are aggregated into a left-upward diagonal member model 122L, and the right-upward diagonal members 22 are aggregated into a right-upward diagonal member model 122R, thereby replacing the lattice wall 20 with an X-shaped brace model 120 consisting of diagonal member models 122L and 122R. Both ends of the diagonal member models 122L and 122R are rotatably connected to the upper and lower beam models 103 by pins perpendicular to the in-plane direction. The diagonal member models 122L and 122R are inclined at 45° to the horizontal and perpendicular to each other. The beam model 103 is a rigid body modeled after the combination of the beam 3 and the beam-side guide steel 12. Both ends of the column models 102 on both sides of the brace model 120 are rotatably connected to the upper and lower beam models 103 by pins perpendicular to the in-plane direction.

[0037] The diagonal member models 122L and 122R are aggregates of the diagonal members 22. Therefore, the Young's modulus, Poisson's ratio, and shear elasticity of the diagonal member models 122L and 122R are calculated by the Young's modulus E ge , Poisson's ratio ν g and shear modulus G ge The cross-sectional area A of the diagonal member models 122L and 122R is gb [mm 2 ] can be expressed by equation (6). The length L of the diagonal member models 122L and 122R g [mm] can be expressed by equation (7).

[0038]

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[0039] As shown in equation (6), the cross-sectional area A of the diagonal member models 122L and 122R gb The cross-sectional area A of diagonal member 22 g When expressed as h The ratio of the horizontal load Q to the horizontal displacement δ of the beam model 103 h It was confirmed through experiments that this is equivalent to the ratio of the horizontal load Q to the horizontal load Q.

[0040] Here, the work done by the horizontal load Q is balanced with the work done by the stresses of the two diagonal member models 122L and 122R, so the relationship between these works can be expressed as in equation (8). The left side of equation (8) represents the work done by the horizontal load Q, and the right side represents the work done by the axial force and axial deformation of the two diagonal member models 122L and 122R. The first term on the right side is the work done by the axial force and axial deformation of the diagonal member model compressed by the horizontal load Q, and the second term on the right side is the work done by the axial force and axial deformation of the diagonal member model pulled by the horizontal load Q. δ g [mm] is the amount of deformation in the axial direction of the diagonal member models 122L and 122R.

[0041]

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[0042] The stress σ [N / mm] of the diagonal member models 122L and 122R can be expressed by Hooke's law as shown in equation (9). g can be expressed as equation (10).

[0043]

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[0044] The right side of equation (10) is δ of equation (8) g Substituting into, equation (8) becomes equation (11). Transforming equation (11) gives δ h can be expressed as equation (12).

[0045]

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[0046] (3-2) Replacement with a plate-like wall model As shown in FIG. 11, the brace model 120 consisting of diagonal member models 122L and 122R is ge Here, the width of the plate-like wall model 220 is equal to the inside width l0 of the rectangular area surrounded by the column-beam frame 1, the height of the plate-like wall model 220 is equal to the inside height h0 of the rectangular area surrounded by the column-beam frame 1, and the Young's modulus of the plate-like wall model 220 is equal to the Young's modulus E of the diagonal member 22. ge The shear modulus of the plate-like wall model 220 is equal to the shear modulus of the diagonal member 22, G ge The Poisson's ratio of the plate-like wall model 220 is equal to the Poisson's ratio ν g The beam model 203 is a rigid body that models the beam 3.

[0047] When the upper beam model 203 is displaced by a horizontal load Q, the shear stress τ [N / mm 2 ] can be expressed by equation (13). In equation (13), κ is the shape factor of the rectangular cross section, and κ = 1.2. On the other hand, the shear stress τ and shear strain δ of the plate-like wall model 220 are h Since Hooke's law holds true for the relationship between / h0, equation (14) holds true. Transforming equation (14) gives δ h can be expressed as equation (15).

[0048]

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[0049] Here, if the stiffness of the brace model 120 and the stiffness of the plate-like wall model 220 are equivalent, δ in Eq. (12) h and δ in Eq. (15) h are equal to each other, we obtain the following equation (16). By transforming equation (16), we obtain the thickness t gecan be expressed as equation (17). Since equation (7) is satisfied, equation (17) can be expressed as equation (18).

[0050]

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[0051] In equation (18), the inner height h0, inner width l0, and cross-sectional area A g , number n g , number n gv , length L1 and clearance height h1 are known. Young's modulus E in Eq. (18) ge and shear modulus G ge is calculated as above. Therefore, using equation (18), the inside height h0, the inside width l0, and the cross-sectional area A g , number n g , number n gv , length L1, Young's modulus E ge and shear modulus G ge From the numerical values ​​of the thickness t of the plate wall model 220 ge Alternatively, use equation (18) to calculate the inner height h0, inner width l0, and cross-sectional area A g , number n g , inner height h1, Young's modulus E ge and shear modulus G ge From the numerical values ​​of the thickness t of the plate wall model 220 ge Calculate.

[0052] (4) Buckling load evaluation step (third step) According to the document "Guideline for Buckling Design of Steel Structures," the shear stress τ when the plate-like wall model 220 begins to buckle is cre [N / mm 2 ] can be expressed as in equation (19). In addition, since the shear force is the product of the shear stress and the area, the buckling load Q of the plate-like wall model 220 is cre [N] can be expressed as equation (20).

[0053]

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[0054] Here, k is the plate buckling coefficient. In the case of a loading condition such as horizontal load Q, and a simply supported flat plate such as the plate-like wall model 220, k can be expressed as in equation (21).

[0055]

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[0056] In the formulas (19) to (21), the width of the plate-like wall model 220 is equal to the inside width l0 of the rectangular area surrounded by the column-beam frame 1, the height of the plate-like wall model 220 is equal to the inside height h0 of the rectangular area surrounded by the column-beam frame 1, and the Young's modulus of the plate-like wall model 220 is equal to the Young's modulus E of the diagonal member 22. ge The shear modulus of the plate-like wall model 220 is equal to the shear modulus of the diagonal member 22, G ge The Poisson's ratio of the plate-like wall model 220 is equal to the Poisson's ratio ν g shall be equal to

[0057] Since the rigidity of the plate-like wall model 220 and the rigidity of the lattice wall 20 are equivalent, the buckling start load Q cre is the buckling load Q of the grid wall 20 boe Therefore, the buckling load Q of the grid wall 20 is boe can be expressed as equation (22).

[0058]

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[0059] Equation (22) expresses the Young's modulus, Poisson's ratio, and shear modulus of the plate-like wall model 220 as the Young's modulus E ge , Poisson's ratio ν g and shear modulus G ge The buckling load Q of the plate-like wall model 220 is creThe evaluation formula for the out-of-plane buckling strength of the lattice wall 20 is based on the evaluation formulas (19) to (21) for determining the inner height h0, inner width l0, and Poisson's ratio ν g is known. Young's modulus E in Eq. (22) ge and thickness t ge is calculated as above. Therefore, using equation (22), the inner height h0, inner width l0, and Poisson's ratio ν g , Young's modulus E ge and thickness t ge From the numerical value, the buckling start load Q of the grid wall 20 boe Calculate the buckling load Q of the grid wall 20. boe is an index for evaluating the horizontal load at which the grid wall 20 buckles in the out-of-plane direction.

[0060] Since equation (18) is satisfied, equation (22) can be transformed into equation (23).

[0061]

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[0062] Furthermore, since equations (4) and (5) are satisfied, equation (23) can be transformed into equation (24).

[0063]

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[0064] In equation (24), the inner height h0, inner width l0, and Young's modulus E g , Poisson's ratio ν g , length L1, Young's modulus E b , layer thickness L2, cross-sectional area A g , number n g and number n gv Since the values ​​of are known, the buckling load Q of the grid wall 20 can be calculated from these values. boe Alternatively, the inner height h0, inner width l0, and Young's modulus E g , Poisson's ratio ν g , length L1, Young's modulus E b, layer thickness L2, cross-sectional area A g , number n g Since the values ​​of the inner height h1 and the inner height h2 are known, the buckling start load Q of the grid wall 20 can be calculated from these values. boe It is also possible to calculate

[0065] (5) Maximum load-bearing capacity evaluation step (3rd step) According to the document "Guidelines for Buckling Design of Steel Structures," the post-buckling strength τ of the plate-like wall model 220 in the elastic region is u [N / mm 2 ] can be expressed as equation (25a), and the post-buckling strength τ of the plate-like wall model 220 in the inelastic region is u [N / mm 2 ] can be expressed as in equation (25b). In addition, considering the range of application to the lattice wall 20, λ * >λ p * Since the above condition applies, equation (25a) is used.

[0066]

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[0067] τ y is the shear yield strength [N / mm 2 ], where τ is the reference strength of the material of blocks 26 and 27 divided by the square root of 3. y α is the ratio of proportional limit stress to shear yield stress, and here α = 0.5. Substituting this value of α into equations (27) and (28), λ p * =0.67.

[0068] Since shear force is the product of shear stress and area, the maximum load capacity Q of the plate wall model 220 is u [N] can be expressed as equation (29).

[0069]

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[0070] In the formulas (25a), (25b), and (26) to (29), the width of the plate-like wall model 220 is equal to the inside width l0 of the rectangular area surrounded by the column-beam frame 1, the height of the plate-like wall model 220 is equal to the inside height h0 of the rectangular area surrounded by the column-beam frame 1, and the Young's modulus of the plate-like wall model 220 is equal to the Young's modulus E ge The shear modulus of the plate-like wall model 220 is equal to the shear modulus of the diagonal member 22, G ge The Poisson's ratio of the plate-like wall model 220 is equal to the Poisson's ratio ν g shall be equal to

[0071] Since the rigidity of the plate-shaped wall model 220 and the rigidity of the lattice wall 20 are equivalent, the maximum load capacity Q u The maximum load capacity Q of the grid wall 20 is boeu Therefore, the maximum load capacity Q of the grid wall 20 is boeu can be expressed as equation (30) from equations (29), (25a), and (26) to (28).

[0072]

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[0073] Equation (30) expresses the Young's modulus, Poisson's ratio, and shear modulus of the plate-like wall model 220 as the Young's modulus E ge , Poisson's ratio ν g and shear modulus G ge The maximum load capacity Q of the plate wall model 220 is u This is an evaluation formula for the out-of-plane buckling strength of the grid wall 20 using the evaluation formulas (25a), (25b), and (28) to (29) to obtain the inner height h0, inner width l0, and shear yield strength τ y is known. Young's modulus E in Eq. (30) ge and thickness t ge is calculated as above. Therefore, using equation (30), the inside height h0, the inside width l0, and the shear yield strength τ y , Young's modulus Ege and thickness t ge From the values, the maximum load capacity Q of the grid wall 20 boeu Calculate the maximum load capacity Q of the grid wall 20. boeu is an index for evaluating the load that the buckled grid wall 20 can withstand.

[0074] Since equation (18) is satisfied, equation (30) can be transformed into equation (31).

[0075]

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[0076] Furthermore, since equations (4) and (5) are satisfied, equation (31) can be transformed into equation (32).

[0077]

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[0078] In equation (32), the inner height h0, inner width l0, and Young's modulus E g , Poisson's ratio ν g , length L1, Young's modulus E b , layer thickness L2, cross-sectional area A g , number n g , number n gv and shear yield strength τ y Since the values ​​of are known, the maximum load capacity Q of the grid wall 20 can be calculated from these values. boeu Alternatively, the inner height h0, inner width l0, and Young's modulus E g , Poisson's ratio ν g , length L1, Young's modulus E b , layer thickness L2, cross-sectional area A g , number n g , inner height h1 and shear yield strength τ y Since the values ​​of are known, the maximum load capacity Q of the grid wall 20 can be calculated from these values. boeu It is also possible to calculate

[0079] 3. Application Examples Buckling load Q of grid wall 20 boe and maximum load capacity Q boeu may be calculated by a computer according to a program. In this case, the program incorporates equations (4), (5), (18), (22), and (30), and the program is stored in a storage medium such as a semiconductor memory or a hard disk. When the computer reads the program from the storage medium and executes it, the computer first displays an input screen on the LCD display. The user operates an input device such as a mouse, keyboard, or touch panel to enter the inside width l0, Young's modulus E, etc. on the input screen. g , Poisson's ratio ν g , length L1, Young's modulus E b , layer thickness L2, cross-sectional area A g , number n g and number n gv (number n gv Instead of the height h1, you can input the values ​​of the clearance height h1. Then the computer will obtain those values. Then the computer will calculate the Young's modulus E according to equation (4). ge Calculate the shear modulus G according to equation (5). ge Then, the computer calculates the thickness t ge Next, the computer calculates the buckling load Q according to equation (22). boe Calculate the maximum load capacity Q according to equation (30). boeu The computer then calculates the buckling load Q boe and maximum load capacity Q boeu The computer displays the value of the buckling load Q on the display device. boe and maximum load capacity Q boeu The numerical value is recorded in a storage medium.

[0080] The formula (24) or formula (32) may be incorporated into the program. In this case, the user inputs the inner width l0 and Young's modulus E g , Poisson's ratio ν g , length L1, Young's modulus E b , layer thickness L2, cross-sectional area A g, number n g and number n gv (number n gv Instead of the height h1, the computer calculates the buckling load Q according to equation (24). boe Calculate the maximum load capacity Q according to equation (32). boeu Calculate.

[0081] 4. Beneficial Effects Even if the mechanical behavior of the lattice wall 20 is complex, by replacing the lattice wall 20 with a brace model 120 having equivalent rigidity, and by replacing the brace model 120 with a plate wall model 220 having equivalent rigidity, the evaluation formula for the out-of-plane buckling strength of the plate wall model 220, which has a mechanically simple behavior, can be used to evaluate the out-of-plane buckling strength of the lattice wall 20. Therefore, a method for evaluating the out-of-plane buckling strength of the lattice wall 20 has been established, and the buckling initiation load Q of the lattice wall 20 can be calculated using the evaluation formula for the buckling strength of the surface material. boe or maximum load capacity Q boeu Therefore, the strength and safety of the lattice wall 20 with respect to out-of-plane buckling can be evaluated.

[0082] 5. Additional Notes The above description discloses the following method for evaluating the out-of-plane buckling strength of a lattice wall.

[0083] a calculation step of replacing the lattice wall with an X-shaped brace model by aggregating diagonal members between intersections of the diagonal lattice wall with those diagonal in the same direction, and replacing the brace model with a plate-like wall model, and calculating the thickness of the plate-like wall model on the assumption that the rigidities of the lattice wall, the brace model, and the plate-like wall model are equivalent to each other; and an evaluation step of evaluating the strength of the lattice wall against out-of-plane buckling based on the Young's modulus of the diagonal members and the thickness of the plate-like wall model, using an evaluation formula for the strength of the plate-like wall model against out-of-plane buckling, assuming that the Young's modulus of the diagonal members is equivalent to the Young's modulus of the plate-like wall model.

[0084] A method for evaluating the strength of a lattice wall formed by stacking a plurality of square frame-shaped blocks consisting of four partition plates in a lattice pattern inside a beam-column framework, with the partition plates of the blocks being inclined relative to the horizontal direction and bonded together with an adhesive, comprising: a first step of calculating the Young's modulus and shear modulus of the diagonal member based on the length of the partition member, the thickness of the adhesive layer, the Young's modulus of the partition member, the Poisson's ratio of the partition member, and the Young's modulus of the adhesive layer, assuming that the diagonal member between the intersections of the lattice of the lattice wall is formed by connecting the partition member and the adhesive layer of the adjacent block in series in the longitudinal direction of the diagonal member; a second step of replacing the lattice wall with a brace model on the inside of the beam-column frame consisting of two orthogonal diagonal member models in which diagonal members diagonally in the same direction are aggregated, and replacing the brace model with a plate-like wall model on the inside of the beam-column frame, and assuming that the rigidities of the lattice wall, the brace model, and the plate-like wall model are equivalent to each other, calculating a thickness of the plate-like wall model based on the Young's modulus, shear modulus, and cross-sectional area of ​​the diagonal member and the inside width and height of the beam-column frame; and a third step of calculating a buckling initiation load or maximum load-bearing load of the lattice wall based on the Young's modulus and Poisson's ratio of the diagonal member, the thickness of the plate-like wall model, and the inside width and height of the beam-column frame, using a strength evaluation formula for calculating the buckling initiation load or maximum load-bearing load of the lattice wall, assuming that the Young's modulus and Poisson's ratio of the diagonal member are equal to the Young's modulus and Poisson's ratio of the plate-like wall model, respectively.

[0085] Preferably, in the first step, the shear modulus of elasticity of the diagonal member is calculated by the following formula: where L1 [mm] is the length of the partition member, L2 [mm] is the thickness of the adhesive layer, and E is the Young's modulus of the partition plate. g [N / mm 2 ], the Poisson's ratio of the partition plate is , and the Young's modulus of the adhesive layer is E b [N / mm 2 ] and the shear modulus of the diagonal member is E ge [N / mm 2] and the shear modulus of the diagonal member is G ge [N / mm 2 ].

[0086]

number

[0087] Preferably, in the first step, the shear modulus of elasticity of the diagonal member is calculated by the following formula:

[0088]

number

[0089] Preferably, in the second step or the calculation step, the thickness of the plate-like wall model is calculated by the following formula: g [mm 2 ], the inner height of the column-beam frame is h0 [mm], the inner width of the column-beam frame is l0 [mm], and the number of diagonal members that are diagonal in the same direction and intersect a common horizontal plane is n g The number of diagonal members that are diagonal in the same direction and intersect a common vertical plane is n gv The shape coefficient of the rectangular cross section is κ, and the thickness of the plate-like wall model is t ge [mm].

[0090]

number

[0091] Preferably, in the third step or the evaluation step, the buckling initiation load of the grid wall is calculated by the following formula: where Q boe Let's say [N].

[0092]

number

[0093] Preferably, in the third step or the evaluation step, the maximum load capacity of the grid wall is calculated by the following formula: where τ is the shear yield strength of the partition plate. y [N / mm 2 ] and the maximum load capacity of the grid wall is Q boeu Let's say [N].

[0094]

number

[0095] 1…Column beam frame 2...Pillar 3…Beam 20…Lattice wall 21...Unit element 22...Diagonal member 27...Block 27a...Partition board 28...Adhesive 120...Brace model 122L, 122R...Diagonal model 220...Slab wall model

Claims

1. A computer-implemented method for evaluating the out-of-plane buckling strength of a grid wall, which is formed by bonding a plurality of blocks with an adhesive and laying them in a grid pattern inside a frame provided along the inner periphery of a rectangular area surrounded by a column-beam framework, comprising: The Young's modulus E of the left-upward diagonal member and the right-upward diagonal member that are orthogonal to each other provided in the lattice wall ｇｅ and shear modulus G ｇｅ and calculating a process of aggregating the left-upward diagonal members into a left-upward diagonal member model, aggregating the right-upward diagonal members into a right-upward diagonal member model, and replacing the lattice wall with an X-shaped brace model consisting of the left-upward diagonal member model and the right-upward diagonal member model; The brace model is defined by the shape factor κ of the rectangular cross section and the inner height h between the pair of upper and lower beam side guide steels that constitute the frame body. １ The thickness t is calculated using the following formula: ｇｅ a step of replacing the wall model with a plate-like wall model; The shear stress τ when the plate-like wall model begins to buckle ｃｒｅ a step of calculating the plate buckling coefficient k using the following formula: The thickness t of the plate-like wall model ｇｅ , the shear stress τ when the plate-like wall model begins to buckle ｃｒｅ , and the inner width l of the rectangular area ０ , and the buckling initiation strength Q of the lattice wall, which is the out-of-plane buckling strength of the lattice wall, is calculated by the following formula: ｂｏｅ The buckling load Q of the plate-like wall model equivalent to ｃｒｅ is calculated, and the buckling start load Q of the plate-like wall model is calculated. ｃｒｅ as the out-of-plane buckling strength of the lattice wall; Including, The Young's modulus E of the diagonal member ｇｅ is the Young's modulus E of the material of the block ｇ Correction coefficient β ｇ The shear modulus of elasticity G of the diagonal member is calculated by multiplying ｇｅ is the shear modulus G of the material of the block ｇ Correction coefficient β ｇ Calculate by multiplying The brace model is The Young's modulus, Poisson's ratio, and shear elasticity of the left-upward diagonal member model and the right-upward diagonal member model are respectively ｇｅ , Poisson's ratio ν ｇ and shear modulus G ｇｅ and the cross-sectional area A ｇｂ Each of the cross-sectional areas A of the diagonal members ｇ The number of diagonal members inclined in the same direction that intersect a common horizontal plane is n ｇ and the length L ｇ are calculated by the following formula using the length L 1 of the side of the square formed by the block and the number of diagonal members n gv that are inclined in the same direction and intersect a common vertical plane, or the internal height h 1 between a pair of upper and lower beam-side guide steels that make up the frame body: The plate-like wall model is The width is the inside width 1 of the rectangular area. ０ The height is the inner height h of the rectangular area. ０ , the Young's modulus of the diagonal member E ｇｅ The shear modulus of elasticity is the shear modulus of elasticity G of the diagonal member. ｇｅ The Poisson's ratio is the Poisson's ratio ν ｇ A method for evaluating the out-of-plane buckling strength of lattice walls, characterized in that the

2. The method for evaluating the out-of-plane buckling strength of a lattice wall according to claim 1, The buckling initiation load Q of the plate-like wall model ｃｒｅ Instead, the maximum load capacity Q of the grid wall, which is the out-of-plane buckling strength of the grid wall ｂｏｅｕ The maximum load capacity Q of the plate-like wall model is equivalent to ｕ is evaluated as the out-of-plane buckling strength of the lattice wall, The maximum load capacity Q of the plate-shaped wall model ｕ teeth, Post-buckling strength τ of the plate-like wall model in the elastic region ｕ and the thickness t of the plate-like wall model ｇｅ and the inside width l of the rectangular area ０ A method for evaluating the out-of-plane buckling strength of a lattice wall, characterized by calculating the out-of-plane buckling strength based on the following formula:

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