How to design the support structure

Abstract

To provide a support structure design method that enables setting of elastic lateral buckling resistance of an H-shaped cross-sectional member in the case where a first flange of the H-shaped cross-sectional member is fitted to a plate member in consideration of restraint of the plate member fitted to the first flange.SOLUTION: A design method for a support structure which has a steel H-shaped cross-sectional member 25 having a first flange 26, a second flange 27, and a web 28 for connecting the first flange and the second flange to each other and a plate member 37 that is supported by the H-shaped cross-sectional member by being fitted to the first flange, and the method sets elastic lateral buckling resistance Me of the H-shaped cross-sectional member with a mathematical expression.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The present invention relates to a method for designing a support structure. [Background technology]

[0002] H-shaped cross-section steel members (H-shaped cross-section members) are used in many building components, such as the beams that support floor slabs and roofs, the purlins that support roofs, and the furring strips that support wall materials. When bending moments occur in these components due to the weight of the supporting members or external forces, it is rational to use an H-shaped cross section, which has high bending performance around the strong axis relative to the steel weight and good cross-sectional efficiency, so H-shaped cross-section members are commonly used. On the other hand, although H-shaped cross-section members have excellent cross-sectional performance around the strong axis, they have low cross-sectional performance around the weak axis, which makes lateral buckling (deformation in which the member moves out of the plane while twisting) a problem. When lateral buckling occurs, the strength of the member deteriorates rapidly, and the behavior of the H-shaped cross-section member becomes unstable. For this reason, it is necessary to design the H-shaped cross section so that lateral buckling does not occur.

[0003] Specifically, the Ministry of Land, Infrastructure, Transport and Tourism's Notification No. 1024 of 2001, "Determining Special Allowable Stress and Special Material Strength," specifies the allowable stress for buckling of bending members. In this notification, the allowable stress is reduced in cases where the length of a member is long and lateral buckling may occur. When H-section members are long or narrow, and in other conditions where lateral buckling is likely to occur, the allowable stress decreases and the inherent sectional performance of the H-section members is not demonstrated. This requires a larger cross section, which increases the amount of steel, making the H-section members an uneconomical design.

[0004] Another method to prevent the reduction in allowable stress due to lateral buckling is to install stiffeners to prevent lateral buckling. With this method, if a sufficient number of stiffeners are installed, the allowable stress will not decrease. However, the processing and installation of the stiffeners requires time and cost, making this method uneconomical. In response to such a problem, a design method may be adopted in which the restraining effect of the upper flange (first flange) by the floor or roof (plate-like member) is taken into consideration to improve the lateral buckling resistance and stiffening materials for preventing lateral buckling are omitted. In Patent Document 1 and Patent Document 2, an elastic lateral buckling resistance formula is derived for an H-shaped cross-section beam in which the upper flange is fastened to the floor slab by a shear connector, assuming that the lateral movement of the upper flange is completely restrained. This elastic lateral buckling resistance formula is used in the design method and analysis method. In Patent Document 3 and Patent Document 4, an elastic lateral buckling resistance formula is derived for a floor structure having a steel beam and a floor slab joined to the upper surface of the steel beam by a shear connector, assuming that the lateral movement and rotation of the upper flange are completely restrained. This elastic lateral buckling resistance formula is used in the design method. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Patent No. 6340276 [Patent Document 2] Patent No. 6414374 [Patent Document 3] Patent No. 6699639 [Patent Document 4] JP 2020-158953 A Summary of the Invention [Problem to be solved by the invention]

[0006] However, although the design methods disclosed in Patent Documents 1 to 4 are useful in enabling efficient design, their effectiveness can be expected only under the condition that the lateral movement and rotation of the upper flange are completely restrained. For this reason, they can be applied when the surface material (plate-like member) attached to the upper flange has sufficient rigidity, such as a floor slab. However, they cannot be applied when a surface material that is not rigid enough to completely restrain the upper flange, such as a roofing material or exterior wall material, is attached, or when the rigidity of the shear connector that joins the upper flange and the floor slab is not sufficient.

[0007] For this reason, when the upper flange is incompletely restrained by roofing materials, exterior wall materials, etc., designs are generally made to install stiffening materials to prevent lateral buckling without considering these effects, even though they do have a certain degree of effect in improving the strength against lateral buckling. In other words, when the upper flange is incompletely restrained, the processing and installation of the stiffening materials incurs time and costs, making the design uneconomical.

[0008] The present invention has been made in consideration of such problems, and aims to provide a method for designing a support structure that can set the elastic lateral buckling strength of an H-shaped cross-section member when the first flange of the H-shaped cross-section member is attached to a plate-shaped member, taking into account the constraint by the plate-shaped member attached to the first flange. [Means for solving the problem]

[0009] In order to solve the above problems, the present invention proposes the following means. The design method of the support structure of the present invention is a design method of a support structure comprising a steel H-shaped section member having a first flange, a second flange, and a web connecting the first flange and the second flange to each other, and a plate-like member attached to the first flange and supported by the H-shaped section member, e is set by the formula (1). where α is an undetermined coefficient that is any real number between 0 and 1, n is the number of half waves of the buckling wave of the H-shaped section member that is any positive integer, E is the Young's modulus of the H-shaped section member, and I fA : moment of inertia of the second flange, l: length of the H-shaped cross-section member, d b : Distance between the thickness centers of the first flange and the second flange, I fB : moment of inertia of the first flange, G: shear modulus of elasticity of the H-shaped section member, J: Saint-Venant torsional constant of the H-shaped section member, k r : stiffening stiffness coefficient by a rotational movement spring that applies a restraining force to the first flange around an axis along the longitudinal direction of the H-shaped cross-section member, J fA : the Saint-Venant torsional constant of the second flange, J fB : the Saint-Venant torsional constant of the first flange, J w : the Saint-Venant torsional constant of the web, t w : the thickness of the web, k h : stiffening stiffness coefficient by a parallel moving spring that applies a restraining force in the thickness direction of the web to the first flange, D w : The plate stiffness of the web.

[0010]

number

[0011] In this invention, it is considered that the first flange is restrained by the plate-shaped member against movement in the thickness direction of the web by a parallel translation spring, and against rotation around an axis along the longitudinal direction of the H-shaped cross-section member by a rotational translation spring. The restraining forces of the parallel translation spring and the rotational translation spring are assumed to have an arbitrary stiffness. After extensive investigation, the inventors derived equation (1) as an equation that can be applied when the cross section perpendicular to the longitudinal direction of the H-shaped cross-section member is symmetrical with respect to the first reference plane along the web, that is, is symmetrical about one axis. For this reason, when the cross section of the H-shaped section member is symmetrical about one axis, the restraint by the plate member attached to the first flange is considered as a spring element, and the elastic lateral buckling strength M of the H-shaped section member is calculated by the formula (1). e can be set.

[0012] In the method for designing a support structure, the undetermined coefficient α may be set by equations (3) to (5).

[0013]

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[0014] In the present invention, the undetermined coefficient α can be precisely set using equations (3) to (5).

[0015] Another support structure design method of the present invention is a support structure design method comprising a steel H-shaped section member having a first flange, a second flange, and a web connecting the first flange and the second flange to each other, and a plate-like member attached to the first flange and supported by the H-shaped section member, the method comprising the steps of: determining the elastic lateral buckling strength M of the H-shaped section member; e is set by equation (8). where α is an undetermined coefficient that is an arbitrary real number between 0 and 1, G is the shear modulus of elasticity of the H-shaped section member, J is the Saint-Venant torsional constant of the H-shaped section member, and d b : the distance between the thickness centers of the first flange and the second flange, k r : stiffening stiffness coefficient by a rotational movement spring that applies a restraining force to the first flange around an axis along the longitudinal direction of the H-shaped cross-section member, J fA : the Saint-Venant torsional constant of the second flange, J fB : the Saint-Venant torsional constant of the first flange, J w : the Saint-Venant torsional constant of the web, t w : the thickness of the web, k h : stiffening stiffness coefficient by a parallel moving spring that applies a restraining force in the thickness direction of the web to the first flange, I fA : Moment of inertia of the second flange, I fB : moment of inertia of the first flange, E: Young's modulus of the H-shaped cross-section member, D w : The plate stiffness of the web.

[0016]

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[0017] In this invention, it is considered that the first flange is restrained by the plate-like member with respect to the movement in the thickness direction of the web by the parallel translation spring, and with respect to the rotation around the axis along the longitudinal direction of the H-shaped cross-section member by the rotational translation spring. It is assumed that the restraining forces of the parallel translation spring and the rotational translation spring have an arbitrary stiffness. After extensive research, the inventors derived equation (8) as an equation that can be applied when the cross section of the H-shaped cross-section member is symmetrical about one axis, regardless of the number of half waves of the buckling wave of the H-shaped cross-section member and the length of the H-shaped cross-section member. Therefore, when the cross section of the H-shaped section member is symmetrical about one axis, the elastic lateral buckling strength M of the H-shaped section member is calculated by the formula (8) considering the restraint by the plate member attached to the first flange as a spring element. e can be easily set.

[0018] In the method for designing a support structure, the undetermined coefficient α may be set by equations (10) to (16).

[0019]

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[0020] In the present invention, the undetermined coefficient α can be precisely set using equations (10) to (16).

[0021] Another support structure design method of the present invention is a support structure design method comprising a steel H-shaped section member having a first flange, a second flange, and a web connecting the first flange and the second flange to each other, and a plate-like member attached to the first flange and supported by the H-shaped section member, the method comprising the steps of: determining the elastic lateral buckling strength M of the H-shaped section member; e is set by equation (21). where α is an undetermined coefficient that is any real number between 0 and 1, n is the number of half waves of the buckling wave of the H-shaped section member that is any positive integer, E is the Young's modulus of the H-shaped section member, I is the second moment of area of ​​each of the first flange and the second flange, l is the length of the H-shaped section member, and d b : the distance between the thickness centers of the first flange and the second flange, G: the shear modulus of the H-shaped section member, J: the Saint-Venant torsional constant of the H-shaped section member, k r : stiffening stiffness coefficient by a rotational movement spring that applies a restraining force to the first flange around an axis along the longitudinal direction of the H-shaped cross-section member, J f : the Saint-Venant torsional constant of each of the first flange and the second flange, J w : the Saint-Venant torsional constant of the web, t w : the thickness of the web, k h : stiffening stiffness coefficient by a parallel moving spring that applies a restraining force in the thickness direction of the web to the first flange, D w : The plate stiffness of the web.

[0022]

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[0023] In this invention, it is considered that the first flange is restrained by the plate-shaped member against the movement in the thickness direction of the web by the parallel translation spring, and against the rotation about the axis along the longitudinal direction of the H-shaped cross-section member by the rotational translation spring. The restraining forces of the parallel translation spring and the rotational translation spring are assumed to have arbitrary stiffness. After extensive investigation, the inventors derived equation (21) as an equation applicable to the case where the cross section of the H-shaped cross-section member is symmetrical with respect to the first reference plane in addition to the second reference plane along each flange, that is, so-called two-axis symmetry. For this reason, when the cross section of the H-shaped section member is biaxially symmetrical, the elastic lateral buckling strength M of the H-shaped section member is calculated by considering the restraint by the plate member attached to the first flange as a spring element using Eq. (21). e can be set.

[0024] In the method for designing a support structure, the undetermined coefficient α may be set by equations (23) to (25).

[0025]

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[0026] In the present invention, the undetermined coefficient α can be precisely set using equations (23) to (25).

[0027] Another support structure design method of the present invention is a support structure design method comprising a steel H-shaped section member having a first flange, a second flange, and a web connecting the first flange and the second flange to each other, and a plate-like member attached to the first flange and supported by the H-shaped section member, the method comprising the steps of: determining the elastic lateral buckling strength M of the H-shaped section member; e is set by equation (28). where α is an undetermined coefficient that is an arbitrary real number between 0 and 1, G is the shear modulus of elasticity of the H-shaped section member, J is the Saint-Venant torsional constant of the H-shaped section member, and d b : the distance between the thickness centers of the first flange and the second flange, k r : stiffening stiffness coefficient by a rotational movement spring that applies a restraining force to the first flange around an axis along the longitudinal direction of the H-shaped cross-section member, J f : the Saint-Venant torsional constant of each of the first flange and the second flange, J w : the Saint-Venant torsional constant of the web, t w : the thickness of the web, k h : stiffening stiffness coefficient by a parallel moving spring that applies a restraining force in the thickness direction of the web to the first flange, E: Young's modulus of the H-shaped cross-section member, I: second moment of area of ​​each of the first flange and the second flange, D w : The plate stiffness of the web.

[0028]

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[0029] In this invention, it is considered that the first flange is restrained by the plate-like member against the movement in the thickness direction of the web by the parallel translation spring, and against the rotation around the axis along the longitudinal direction of the H-shaped cross-section member by the rotational translation spring. The restraining forces of the parallel translation spring and the rotational translation spring are assumed to have arbitrary stiffness. After extensive research, the inventors derived equation (28) as an equation that can be applied when the cross section of the H-shaped cross-section member is symmetrical about two axes, regardless of the number of half waves of the buckling wave of the H-shaped cross-section member and the length of the H-shaped cross-section member. Therefore, when the cross section of the H-shaped section member is biaxially symmetrical, the elastic lateral buckling strength M of the H-shaped section member is calculated by the formula (28) considering the restraint by the plate member attached to the first flange as a spring element. e can be easily set.

[0030] In the method for designing a support structure, the undetermined coefficient α may be set by equations (30) to (33).

[0031]

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[0032] In the present invention, the undetermined coefficient α can be precisely set using equations (30) to (33). Effect of the Invention

[0033] In the design method of a support structure of the present invention, the elastic lateral buckling strength of the H-shaped cross-section member when the first flange of the H-shaped cross-section member is attached to the plate-shaped member can be set taking into account the restraint by the plate-shaped member attached to the first flange. [Brief description of the drawings]

[0034] [Figure 1] 1 is a perspective view showing a cutaway view of a portion of a building in which a support structure to which a support structure design method according to one embodiment of the present invention is applied is used. [Diagram 2] FIG. 2 is a perspective view of a second H-shaped section member. [Diagram 3] 2 is a cross-sectional view taken along line A1-A1 in FIG. [Figure 4] FIG. 4 is a cross-sectional view of the second H-shaped section member before it is displaced. [Diagram 5] FIG. 4 is a side view illustrating a bending moment acting on the second H-shaped cross-section member. [Figure 6] FIG. 4 is a cross-sectional view of the second H-shaped section member after it has been displaced. [Figure 7] This is a graph showing the change in elastic lateral buckling strength versus l / H for a given cross-sectional shape of an H-shaped section member. [Figure 8] This is a graph showing the change in elastic lateral buckling strength versus l / H for a given cross-sectional shape of an H-shaped section member. [Figure 9] This is a graph showing the change in elastic lateral buckling strength versus l / H for a given cross-sectional shape of an H-shaped section member. [Figure 10] This is a graph showing the change in elastic lateral buckling strength versus l / H for a given cross-sectional shape of an H-shaped section member. [Figure 11] This is an oblique cutaway view of a part of a building in which another support structure is used, to which the support structure design method of one embodiment of the present invention is applied. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0035] Hereinafter, a support structure to which a support structure design method according to one embodiment of the present invention (hereinafter also simply referred to as a design method) is applied will be described with reference to FIGS. 1 to 11. FIG.

[0036] [1. Structure of buildings using supporting structures] The support structures 46, 47 are used in the building 1 shown in Fig. 1. The building 1 includes a plurality of columns 10, a plurality of first H-shaped cross-section members (H-shaped cross-section members) 15 which are main beams, a plurality of second H-shaped cross-section members (H-shaped cross-section members) 25 which are minor beams, and a folded plate roof 35. The number of columns 10, first H-shaped section members 15, and second H-shaped section members 25 provided in the building 1 may be one each. The pillars 10 extend in the vertical direction. The pillars 10 are arranged at intervals from one another. The pillars 10 are made of steel, RC (Reinforced Concrete), SRC (Steel Reinforced Concrete), or the like.

[0037] The first H-shaped section member 15 and the second H-shaped section member 25 are each made of steel. The first H-shaped section member 15 includes a first flange 16, a second flange 17, and a web 18. The first flange 16, the second flange 17, and the web 18 are each formed of a steel plate. The first flange 16 and the second flange 17 are each disposed along a horizontal plane and face each other in the up-down direction. The first flange 16 is disposed above the second flange 17. The web 18 is disposed between the first flange 16 and the second flange 17. The web 18 joins the center of the first flange 16 in the width direction and the center of the second flange 17 in the width direction to each other.

[0038] A gusset plate (not shown) is joined by welding or the like to the web 18 of the first H-shaped section member 15, which serves as a main girder. The first H-shaped section member 15 is placed between the adjacent columns 10 and extends in a direction along the horizontal plane. Both ends of the first H-shaped section member 15 are joined to the columns 10 by welding or the like.

[0039] As shown in Figures 1 to 3, the second H-shaped section member 25 includes a first flange 26, a second flange 27, and a web 28. The first flange 26, the second flange 27, and the web 28 are each formed of a steel plate. The first flange 26 and the second flange 27 are each disposed along a horizontal plane and face each other in the up-down direction. The first flange 26 is disposed above the second flange 27. The web 28 is disposed between the first flange 26 and the second flange 27. The web 28 joins the center of the first flange 26 in the width direction and the center of the second flange 27 in the width direction to each other. The H-shaped cross-section members 15 and 25 each have an H-shape in cross section perpendicular to the longitudinal direction (material axis direction). The orientation in which the H-shaped section members 15, 25 are arranged is not limited to this. The second H-shaped section member 25 and the first H-shaped section member 15 may be H-shaped steel. More specifically, the second H-shaped section member 25 and the first H-shaped section member 15 may be rolled H-shaped steel or welded H-shaped steel.

[0040] Here, the dimensions of the second H-shaped section member 25 are defined as shown in FIG. The height of the second H-shaped section member 25 is H (mm). The distance between the center of the plate thickness of the first flange 26 and the center of the second flange 27 (the distance between the center of the first flange 26 in the thickness direction and the center of the second flange 27 in the thickness direction) is d b The thickness of each of the first flange 26 and the second flange 27 is t f The thickness of the web 28 is t w The length of the second H-shaped section member 25 is l (mm) (see FIG. 2). Furthermore, the specifications of the second H-shaped section member 25 are defined as follows. The Young's modulus of the second H-shaped section member 25 is E (N / mm 2 The second moment of area of ​​the first flange 26 is I fB (mm 4 The second moment of area of ​​the second flange 27 is I fA (mm 4 The shear modulus of the second H-shaped section member 25 is G (N / mm 2 The Saint-Venant torsional constant of the second H-shaped section member 25 is J (mm 4 The Saint-Venant torsional constant of the first flange 26 is J fB (mm 4 The Saint-Venant torsional constant of the second flange 27 is J fA (mm 4 ) The Saint-Venant torsional constant of the web 28 is J w (mm 4 ) The stiffness of the web 28 is Dw (Nmm). The plate stiffness D w As shown in (56) below, D w =E t w 3 / (12(1-ν 2 )) where ν represents the Poisson's ratio (-) of the second H-shaped section member 25.

[0041] 1, the second H-shaped section member 25 is placed between the opposing first H-shaped section members 15 and extends in a direction along the horizontal plane. Both longitudinal ends of the second H-shaped section member 25 are connected to the gusset plates of the first H-shaped section member 15 by high-strength bolts (not shown) or the like.

[0042] The folded plate roof 35 is a roofing material. For example, the folded plate roof 35 is formed by folding a metal plate. The folded plate roof 35 is formed by arranging a plurality of corrugated members 36 extending in a first horizontal direction D1 along a horizontal surface in a second horizontal direction D2 along the horizontal surface and perpendicular to the first horizontal direction D1. The corrugated member 36 has a bottom plate 37, a first inclined plate 38, a top plate 39, and a second inclined plate 40. The bottom plate 37, the first inclined plate 38, the top plate 39, and the second inclined plate 40 are each a plate-shaped member (surface material).

[0043] The bottom plate 37 and the top plate 39 are disposed along a horizontal plane. The top plate 39 is disposed higher than the bottom plate 37. The first inclined plate 38 is inclined gradually upward from the end of the bottom plate 37 on the first side D21 in the second horizontal direction D2 toward the first side D21. The top plate 39 extends from an end of the first side D21 of the first inclined plate 38 toward the first side D21. The second inclined plate 40 is inclined gradually downward from the end of the first side D21 of the top plate 39 toward the first side D21. The second inclined plate 40 is connected to an end of a second side D22, which is opposite to the first side D21 in the second horizontal direction D2, of the bottom plate 37 of the corrugated member 36 adjacent to the first side D21.

[0044] 3, the bottom plate 37 of the folded plate roof 35 is disposed on the opposite side (above) of the web 28 of the second H-shaped section member 25, with the first flange 26 sandwiched therebetween. The bottom plates 37 are aligned in the second horizontal direction D2, which is the longitudinal direction of the second H-shaped section member 25. As shown in Fig. 1, the folded plate roof 35 is supported by the first flange 16 of the first H-shaped section member 15 and the first flange 16 of the second H-shaped section member 25 from below the folded plate roof 35. As shown in Fig. 3, in this example, the folded plate roof 35 is attached to the first flange 26 of the second H-shaped section member 25 via a joint member 41 such as a known metal fitting or fastening member.

[0045] In this way, the folded plate roof 35 is supported by the second H-shaped section member 25 by being attached to the first flange 26. 1, the second H-shaped section member 25 and the folded plate roof 35 form a support structure 47. Similarly, the first H-shaped section member 15 and the folded plate roof 35 form a support structure 46. The bottom plate 37, the first inclined plate 38, the top plate 39, and the second inclined plate 40 of the folded plate roof 35 may be directly attached to the first flanges 16, 26 of the H-shaped cross-section members 15, 25, respectively.

[0046] In the following, the results of examining the elastic lateral buckling strength of the second H-shaped section member 25 out of the H-shaped section members 15, 25 will be described as an example.

[0047] [2. Study on the elastic lateral buckling strength formula for H-shaped cross-section members] 2, the z-axis was defined as the longitudinal direction of the second H-shaped section member 25 (hereinafter also simply referred to as the H-shaped section member 25). The y-axis was defined as the direction in which the flanges 26, 27 face each other, and the x-axis was defined as the thickness direction of the web 28. The following assumptions (1) to (6) are made for the H-shaped cross-section member 25. (1) The flange attached to the folded plate roof 35 is referred to as the first flange 26. The second flange 27 is not directly restrained by the folded plate roof 35. (2) The first flange 26 is elastically restrained by the folded plate roof 35 from moving in the x-axis direction and from rotating about the z-axis (the axis along the longitudinal direction of the H-shaped cross-section member 25). (3) The H-shaped section member 25 is not restrained from warping. (4) The load condition is a uniform bending moment that compresses the second flange 27. That is, as shown in FIG. 5, the load is a bending moment M cr was applied. (5) The intersections of the flanges 26, 27 and the web 28 maintain a right angle even after the H-section member 25 buckles laterally. (6) The out-of-plane displacement of flanges 26, 27 is given by an arbitrary function.

[0048] As shown in FIG. 6, the out-of-plane displacement (displacement in the x-axis direction) u A (mm) and the out-of-plane displacement u of the first flange 26 B (mm) are expressed as functions of an arbitrary displacement distribution u (mm) by equations (41) and (42).

[0049]

number

[0050] Here, α is an undetermined coefficient. 4, it was assumed that the first flange 26 was restrained by a parallel movement spring (horizontal spring) 50 and a rotation movement spring (rotation spring) 51. The parallel movement spring 50 is a spring that simulates the restraint by the folded-plate roof 35 to which the first flange 26 is attached, and applies a restraining force to the first flange 26 in the x-axis direction (thickness direction of the web 28). The rotational movement spring 51 is a spring that simulates the constraint by the folded-plate roof 35 to which the first flange 26 is attached, and applies a constraint force to the first flange 26 about an axis along the longitudinal direction of the H-shaped cross-section member 25. The stiffness of the elastic spring that is attached to the first flange 26 and restricts the horizontal movement and rotation is defined as the plate stiffness D of the web 28. w and the distance between the plate thickness centers d bAs a function of , it is expressed by equations (43) and (44).

[0051]

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[0052] Where k h is the stiffness coefficient of the parallel translation spring 50 (horizontal stiffness coefficient) (-). k r is the stiffness coefficient of the rotational movement spring 51 (rotational stiffness coefficient) (-). K H is the stiffening stiffness (N / mm / mm) per unit length in the longitudinal direction of the H-shaped section member 25 by the translation spring 50. R is the stiffening rigidity (Nmm / mm) per unit length in the longitudinal direction of the H-shaped section member 25 due to the rotational movement spring 51. Twist angle φ of second flange 27 A (rad), the twist angle φ of the first flange 26 B (rad), and the displacement function w (mm) of the web 28 is expressed as a function of an arbitrary displacement distribution u (mm) by equations (45) to (47).

[0053]

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[0054] However, the intersection point between the first flange 26 and the web 28 is defined as the origin of the y axis. At this time, the translation of the first flange 26 in the x-axis direction and the rotation around the z-axis are restrained by the elastic spring, and a uniform external bending force that compresses the second flange 27 acts on both longitudinal ends of the H-shaped cross-section member 25. The total potential energy Π (Nmm) in this case is expressed by equation (48).

[0055]

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[0056] where ν is the Poisson's ratio (-) of the H-section member 25. M cris the elastic lateral buckling strength (elastic lateral buckling moment) (Nmm) of the H-shaped section member 25. A ’ ,u B ’ u A ,u B is the first derivative of with respect to z. A ’’ ,u B ’’ u A ,u B is the second derivative of with respect to z. A ’ ,φ B ’ is φ A ,φ B is the first derivative of with respect to z. By substituting equations (41) through (47) into equation (48) and rearranging, the total potential energy Π is expressed by equation (49).

[0057]

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[0058] By rearranging equation (49) using the relationships in equations (55) to (58) below, the total potential energy Π is expressed by equation (59).

[0059]

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[0060] However, J w is the Saint-Venant torsional constant of the web 28 (mm 4 ). Next, the equation is rearranged using equation (60) where the displacement distribution u is a sine wave, where n represents the number of half waves of the sine wave (the buckling wave of the H-shaped cross-section member 25) and can be any positive integer.

[0061]

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[0062] The first-order or second-order derivative of the displacement distribution u is expressed by equations (61) and (62).

[0063]

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[0064] Using equations (60) to (62), each definite integral is expressed by equations (63) to (65).

[0065]

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[0066] By substituting equations (63) through (65) into equation (59) and rearranging, the total potential energy Π is expressed by equation (71).

[0067]

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[0068] From the principle of minimum potential energy (Π=0), equation (71) is expressed as the elastic lateral buckling strength M cr By rearranging, we obtain equation (72).

[0069]

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[0070] Here, α is an undetermined coefficient related to the displacement of the first flange 26. The elastic lateral buckling strength M cr The undetermined coefficient α is the elastic lateral buckling strength M cr It is preferable to use the value that minimizes the value. Therefore, the equation obtained by partially differentiating equation (72) with the undetermined coefficient α is expanded. The undetermined coefficient α is an arbitrary real number between 0 and 1. Taking this into consideration, the elastic lateral buckling strength Mcr The undetermined coefficient α that gives the minimum solution is expressed by equation (73). The undetermined coefficient α is calculated by convergence calculation or spreadsheet solver, not by Eq. (73), to determine the elastic lateral buckling strength M cr Alternatively, the value at which is the minimum may be found.

[0071]

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[0072] Here, X and Y are expressed by equations (74) and (75).

[0073]

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[0074] Elastic lateral buckling strength M according to Eq. (72) cr depends on the number of half waves of the sine wave, n. However, the elastic lateral buckling strength M cr The minimum buckling load obtained by substituting any positive integer for n is a constant value regardless of n. The minimum elastic lateral buckling strength M cr,min is given by equation (76).

[0075]

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[0076] Elastic lateral buckling strength M cr As in the case of , α is an undetermined coefficient related to the displacement of the first flange 26, and the minimum elastic lateral buckling strength M can be determined by taking any real number in the range of 0 or more and less than 1 according to the assumed displacement distribution of the first flange 26. cr,min The undetermined coefficient α is the minimum elastic lateral buckling strength M cr,min It is preferable to use the value that minimizes the elastic lateral buckling strength M obtained by partially differentiating equation (76) with the undetermined coefficient α, and then expanding the equation, ignoring higher-order terms as being infinitesimal. Considering that the undetermined coefficient α is a value between 0 and 1, the minimum elastic lateral buckling strength M obtained by equation (76) is cr,minThe undetermined coefficient α that gives the minimum solution is expressed by equation (77). Since equation (77) is an approximate solution, the horizontal stiffening coefficient k h and the rotational stiffening coefficient k r Under special conditions, such as when is extremely small, the square root of equation (77) becomes a negative value, and α cannot be calculated. In such cases, α can be calculated by treating the square root of equation (77) as 0, and the minimum elastic lateral buckling strength M cr,min In addition, the undetermined coefficient α can be calculated not by Eq. (77) but by convergence calculation or a solver in a spreadsheet software, etc. cr Alternatively, the value at which is the minimum may be found.

[0077]

number

[0078] Here, U, V, W, X, Y, and Z are expressed by equations (78) to (83).

[0079]

number

[0080] The above formulas have been derived for a uniaxially symmetrical cross section in which the cross-sectional dimensions of the flanges 26, 27 are different from each other. As shown in Fig. 3, in a uniaxially symmetrical cross section, the cross section perpendicular to the longitudinal direction of the H-shaped section member 25 is symmetrical with respect to the first reference plane S1 along the web 28. On the other hand, in the case where the cross section of the H-shaped cross-section member 25 is symmetrical with respect to the first reference plane S1 in addition to the second reference plane S2 along each flange 26, 27, that is, in the case where the cross section is so-called two-axis symmetrical, the equations can be rearranged using the relationships shown in equations (87) and (88).

[0081]

number

[0082] where I is the moment of inertia of area of ​​each flange 26, 27 (mm 4 ) f is the Saint-Venant torsional constant (mm 4 ). At this time, the elastic lateral buckling strength M cr is expressed by equations (89) to (92).

[0083]

number

[0084] Minimum elastic lateral buckling strength M cr,min is expressed by equations (93) to (97).

[0085]

number

[0086] 3. Support structure design method As explained above, when the cross section of the H-shaped section member 25 is symmetrical with respect to one axis, the elastic lateral buckling strength M e In order to precisely set, in the design method of the support structure of this embodiment, the elastic lateral buckling strength M of the H-shaped cross-section member 25 shown in Equation (72) is cr In this case, it is preferable to set the undetermined coefficient α according to equations (73) to (75). When the cross section of the H-shaped section member 25 is symmetrical along one axis, the elastic lateral buckling strength M e In order to set the elastic lateral buckling strength M of the H-shaped cross-section member 25 shown in Equation (76) in the design method of the support structure of this embodiment, cr,min Formula (76) is an equation that does not depend on the number n of half waves of the buckling wave of the H-shaped section member 25 and the length l of the H-shaped section member 25. At this time, it is preferable to set the undetermined coefficient α according to equations (77) to (83).

[0087] When the cross section of the H-shaped section member 25 is symmetrical on two axes, the elastic lateral buckling strength M eTo set it precisely, in the design method of the support structure of this embodiment, the elastic lateral buckling strength M of the H-shaped section member 25 shown in formula (89) is cr In this case, it is preferable to set the undetermined coefficient α according to equations (90) to (92). When the cross section of the H-shaped section member 25 is symmetrical on two axes, the elastic lateral buckling strength M e In order to set the elastic lateral buckling strength M of the H-shaped cross-section member 25 shown in Equation (93) in the design method of the support structure of this embodiment, cr,min Formula (93) is an equation that does not depend on the number n of half waves of the buckling wave of the H-shaped section member 25 and the length l of the H-shaped section member 25. At this time, it is preferable to set the undetermined coefficient α according to equations (94) to (97).

[0088] [4. Study on elastic lateral buckling strength of H-shaped cross-section members] To confirm the accuracy of the evaluation formula for the elastic lateral buckling strength of the H-shaped section member 25, a comparison was made with the results of an elastic buckling analysis using FEM (Finite Element Method). In the analysis model shown in Figure 2, the H-shaped section member 25 is constructed using four-node shell elements.

[0089] As a restraining effect of the folded plate roof 35 attached to the first flange 26, the node at the center of the cross section of the first flange 26 in Fig. 4 was restrained as follows. That is, for this node, movement in the x-axis direction was restrained by a horizontal spring 50, and rotation around the z-axis was restrained by a rotational spring 51.

[0090] In addition, both ends of the H-shaped section member 25 in the longitudinal direction are fixed ends with respect to torsion of the H-shaped section member 25 and free ends with respect to warping of the flanges 26, 27. That is, as shown in Fig. 2, at a first end 25a in the longitudinal direction of the H-shaped section member 25, dx = 0, dy = 0, dz = 0, and rotz (rotation around the z-axis) = 0. At a second end 25b opposite to the first end 25a in the longitudinal direction of the H-shaped section member 25, dy = 0, dx = 0, and rotz = 0.

[0091] For this analysis model, the dimensions of the H-shaped section member 25 and the horizontal stiffening coefficient k h , and the rotation stiffening stiffness coefficient k r was set as a variable. Specifically, four types of H-shaped cross-section members 25 with different cross-sectional dimensions in the longitudinal direction were used. Two of the four types had cross sections symmetrical about one axis, with the two flanges 26, 27 having different widths. In the cross sections symmetrical about one axis, the cross section perpendicular to the longitudinal direction of the H-shaped cross-section member 25 is symmetrical with respect to the first reference plane S1. In addition, the stiffening stiffness of the spring is calculated by the stiffening stiffness coefficient k h ,k r was set in five stages, ranging from 0 (equivalent to no horizontal spring 50 and no rotation spring 51) to a sufficiently large range. For a total of 20 samples shown in Table 1, which are combinations of these, analysis was performed by changing the length of the H-shaped cross-section member 25 so that the ratio (l / H) of the length l of the H-shaped cross-section member 25 to the height H of the H-shaped cross-section member 25 was in the range of 6 to 50.

[0092] [Table 1]

[0093] For example, in sample No. 1-1, the height H of the H-section member 25 is 400 mm. The width B1 of the first flange 26 is 100 mm, and the width B2 of the second flange 27 is 150 mm. The thickness t w is 6 mm, and the thickness of each of the flanges 26 and 27 is t f is 9mm. (Horizontal stiffness coefficient k h , rotational stiffness coefficient k r ) The pairs used were (0,0), (1,1), (6,2), (10,20), and (1000,1000).

[0094] 7 to 10 show the results of elastic buckling analysis for each cross-sectional shape of the H-shaped section member 25, and the elastic lateral buckling strength M e , and elastic lateral buckling strength M eThe cross section of the H-shaped section member 25 corresponding to Figures 7 and 9 is a cross section symmetrical with one axis, in which the widths of the two flanges 26, 27 are different from each other. The curve in the figure shows the elastic lateral buckling strength M e The straight line in the figure represents the elastic lateral buckling strength M calculated using Eq. (76). e Represents. The cross section of the H-shaped section member 25 corresponding to Figures 8 and 10 is a biaxially symmetrical cross section in which the cross-sectional dimensions of the two flanges 26, 27 are equal to each other. The curves in the figures represent the elastic lateral buckling strength M e The straight line in the figure represents the elastic lateral buckling strength M calculated using Eq. (93). e Represents. In addition, in Figs. 7 to 10, the horizontal stiffening coefficient k h and rotational stiffness stiffness coefficient k r For the cases where each is 0, the minimum elastic lateral buckling strength according to equation (76) or equation (93) is 0, so the description is omitted. Figures 7 to 10 show the elastic lateral buckling strength M FEM also showed.

[0095] Dimensions of H-shaped section member 25 and stiffening coefficient k due to spring h ,k r Regardless of this, the elastic lateral buckling strength M according to equations (72) and (89) e is the elastic lateral buckling strength M FEM In addition, the elastic lateral buckling strength M e The minimum value of is determined by the dimensions of the H-shaped section member 25 and the stiffening coefficient k h ,k r Regardless of the elastic lateral buckling strength M FEM It accurately captures the lower limit of

[0096] 5. Effects of this embodiment As described above, in the design method of this embodiment, when the cross section of the H-shaped section member 25 is symmetrical with respect to one axis, the elastic lateral buckling strength M eIt may be necessary to set precisely. In this design method, it is considered that the first flange 26 is restrained by the folded plate roof 35, and since the restraining force depends on the rigidity of the folded plate roof, it is assumed that it is restrained by the translation spring 50 and the rotation spring 51 having arbitrary rigidity. The translation spring 50 is a spring element that applies a restraining force in the thickness direction of the web 28. The rotation spring 51 is a spring element that applies a restraining force around an axis along the longitudinal direction of the H-shaped cross-section member 25. After extensive investigation, the inventors derived equation (72) as an equation that can be applied when the cross section perpendicular to the longitudinal direction of the H-shaped cross-section member 25 is symmetric about one axis. For this reason, when the cross section of the H-shaped section member 25 is symmetrical with respect to one axis, the elastic lateral buckling strength M of the H-shaped section member 25 is calculated by the formula (72) considering the restraint of the folded plate roof 35 attached to the first flange 26 as a spring element. e can be set.

[0097] When the design method according to the present embodiment is used, the elastic lateral buckling strength M of the H-shaped cross-section member 25 having the horizontal stiffening stiffness by the arbitrary parallel translation spring 50 and the rotation stiffening stiffness by the rotation translation spring 51 in the restraint part of the first flange 26 is calculated by taking into account the restraint effect. e This allows for a higher elastic lateral buckling strength than when the restraint effect is not taken into account, which results in the omission of stiffening materials and reduced processing and construction costs, enabling economical design.

[0098] The undetermined coefficient α is set by equations (73) to (75). Therefore, the undetermined coefficient α can be precisely set by using equations (73) to (75).

[0099] In addition, in the design method of this embodiment, when the cross section of the H-shaped section member 25 is symmetrical with respect to one axis, the elastic lateral buckling strength M eIn the design method for this case, it is considered that the first flange 26 is restrained by the folded plate roof 35, and since the restraining force depends on the rigidity of the folded plate roof, it is assumed that the first flange 26 is restrained by the parallel movement spring 50 and the rotational movement spring 51 having arbitrary rigidity. After extensive investigation, the inventors derived equation (76) as an equation that can be applied regardless of the number n of half waves of the buckling wave of the H-shaped cross-section member 25 and the length l of the H-shaped cross-section member 25 when the cross section of the H-shaped cross-section member 25 is symmetrical about one axis. Therefore, when the cross section of the H-shaped section member 25 is symmetrical with respect to one axis, the elastic lateral buckling strength M of the H-shaped section member 25 is calculated by the formula (76) considering the restraint of the folded plate roof 35 attached to the first flange 26 as a spring element. e can be easily set.

[0100] The undetermined coefficient α is set by equations (77) to (83). This allows the undetermined coefficient α to be precisely set using equations (77) to (83).

[0101] In addition, in the design method of this embodiment, when the cross section of the H-shaped section member 25 is biaxially symmetric, the elastic lateral buckling strength M e In the design method for this case, it is considered that the first flange 26 is restrained by the folded plate roof 35, and since the restraining force depends on the rigidity of the folded plate roof 35, it is assumed that the first flange 26 is restrained by the parallel movement spring 50 and the rotation movement spring 51 having arbitrary rigidity. After extensive investigation, the inventors derived the formula (89) as a formula applicable when the cross section of the H-shaped cross section member 25 is symmetric about two axes. For this reason, when the cross section of the H-shaped section member 25 is biaxially symmetrical, the elastic lateral buckling strength M of the H-shaped section member 25 is calculated by considering the restraint of the folded plate roof 35 attached to the first flange 26 as a spring element according to the formula (89). e can be set.

[0102] The undetermined coefficient α is set by equations (90) to (92). Therefore, the undetermined coefficient α can be precisely set by using equations (90) to (92).

[0103] In addition, in the design method of this embodiment, when the cross section of the H-shaped section member 25 is biaxially symmetric, the elastic lateral buckling strength M e In the design method for this case, it is considered that the first flange 26 is restrained by the folded plate roof 35, and since the restraining force depends on the rigidity of the folded plate roof 35, it is assumed that the first flange 26 is restrained by the parallel movement spring 50 and the rotation movement spring 51 having arbitrary rigidity. After extensive investigation, the inventors derived equation (93) as an equation that can be applied regardless of the number n of half waves of the buckling wave of the H-shaped cross-section member 25 and the length l of the H-shaped cross-section member 25 when the cross section of the H-shaped cross-section member 25 is symmetrical about two axes. Therefore, when the cross section of the H-shaped section member 25 is biaxially symmetrical, the elastic lateral buckling strength M of the H-shaped section member 25 is calculated by the formula (93) considering the restraint of the folded plate roof 35 attached to the first flange 26 as a spring element. e can be easily set.

[0104] The undetermined coefficient α is set by equations (94) to (97). This allows the undetermined coefficient α to be precisely set by using equations (94) to (97).

[0105] Although one embodiment of the present invention has been described in detail above with reference to the drawings, the specific configuration is not limited to this embodiment, and changes, combinations, deletions, etc. of the configuration are also included within the scope that does not deviate from the gist of the present invention. For example, as shown in FIG. 11, in a building 1A, a folded plate roof 35 is attached to a first H-shaped section member 15, which is a main girder, via a second H-shaped section member 25, which is a purlin. Furthermore, a second H-shaped section member 25, which is a furring strip, is fixed to the column 10, and an exterior wall material 55 is attached to this second H-shaped section member 25 via a joint member (not shown). The second H-shaped section member 25 and the exterior wall material 55 form a support structure 57. For example, the exterior wall material 55 has a plurality of siding boards (plate-shaped members) 56. Each siding board 56 is made of steel, cement, or the like, and extends in the vertical direction. The plurality of siding boards 56 are arranged in the longitudinal direction of the second H-shaped cross-section member 25. The plurality of siding boards 56 are disposed on opposite sides of the web 28 with the first flange 26 sandwiched therebetween, and are each attached to the first flange 26 via a joint member (not shown).

[0106] In this design method, when the cross section of the H-shaped section member 25 is biaxially symmetrical, the elastic lateral buckling strength M of the H-shaped section member 25 is calculated by Eq. (72). e Alternatively, the elastic lateral buckling strength M of the H-section member 25 may be set according to equation (76). e may be set. The first flange 26 of the H-shaped section member 25 may be attached directly to the bottom plate 37 of the folded plate roof 35, or may be attached via a joint member. [Explanation of symbols]

[0107] 15 1st H-shaped cross-section member (H-shaped cross-section member) 16,26 First flange 17,27 Second flange 18,28 Web 25 2nd H-shaped cross-section member (H-shaped cross-section member) 35 Folded plate roof (plate-shaped member) 37 Bottom plate (plate-shaped member) 38 First inclined plate (plate-shaped member) 39 Top plate (plate-shaped member) 40 Second inclined plate (plate-shaped member) 46,47,57 Support structure 50 Parallel translation spring 51 Rotational movement spring 56 Siding board (plate-shaped component)

Claims

1. A method for designing a support structure comprising a steel H-shaped section member having a first flange, a second flange, and a web connecting the first flange and the second flange to each other, and a plate-like member attached to the first flange and supported by the H-shaped section member, comprising: determining an elastic lateral buckling strength M of the H-shaped section member; ｅ A method for designing a support structure, in which: Here, α is an undetermined coefficient that is an arbitrary real number between 0 and 1, n is the number of half waves of the buckling wave of the H-shaped section member that is an arbitrary positive integer, E is the Young's modulus of the H-shaped section member, and I ｆＡ : moment of inertia of the second flange, l: length of the H-shaped cross-section member, d ｂ : Distance between the thickness centers of the first flange and the second flange, I ｆＢ : moment of inertia of the first flange, G: shear modulus of elasticity of the H-shaped section member, J: Saint-Venant torsional constant of the H-shaped section member, k ｒ : stiffening stiffness coefficient by a rotational movement spring that applies a restraining force to the first flange about an axis along the longitudinal direction of the H-shaped cross-section member, J ｆＡ : Saint-Venant torsional constant of the second flange, J ｆＢ : Saint-Venant torsional constant of the first flange, J w t : Saint-Venant torsional constant of the web ｗ : the thickness of the web, k ｈ : stiffening stiffness coefficient by a parallel moving spring that applies a restraining force in the thickness direction of the web to the first flange, D ｗ : Plate stiffness of the web. [0010]

2. 2. The method for designing a support structure according to claim 1, wherein the undetermined coefficient α is set by any one of equations (3) to (5). [0025]

3. A method for designing a support structure comprising a steel H-shaped section member having a first flange, a second flange, and a web connecting the first flange and the second flange to each other, and a plate-like member attached to the first flange and supported by the H-shaped section member, comprising: determining an elastic lateral buckling strength M of the H-shaped section member; ｅ A method for designing a support structure, in which: Here, α is an undetermined coefficient that is an arbitrary real number between 0 and 1, G is the shear modulus of elasticity of the H-shaped section member, J is the Saint-Venant torsional constant of the H-shaped section member, and d ｂ : Distance between the thickness centers of the first flange and the second flange, k ｒ : stiffening stiffness coefficient by a rotational movement spring that applies a restraining force to the first flange about an axis along the longitudinal direction of the H-shaped cross-section member, J ｆＡ : Saint-Venant torsional constant of the second flange, J ｆＢ : Saint-Venant torsional constant of the first flange, J w t : Saint-Venant torsional constant of the web ｗ : the thickness of the web, k ｈ : stiffening stiffness coefficient by a parallel moving spring that applies a restraining force in the thickness direction of the web to the first flange, I ｆＡ :Area second moment of area of ​​the second flange, I ｆＢ : moment of inertia of the first flange, E: Young's modulus of the H-shaped cross-section member, D ｗ : Plate stiffness of the web. [0030]

4. 4. The method for designing a support structure according to claim 3, wherein the undetermined coefficient α is set by any one of equations (10) to (16). [0045]

5. A method for designing a support structure comprising a steel H-shaped section member having a first flange, a second flange, and a web connecting the first flange and the second flange to each other, and a plate-like member attached to the first flange and supported by the H-shaped section member, comprising: determining an elastic lateral buckling strength M of the H-shaped section member; ｅ A method for designing a support structure, in which: Here, α is an undetermined coefficient that is an arbitrary real number between 0 and 1, n is the number of half waves of the buckling wave of the H-shaped section member that is an arbitrary positive integer, E is the Young's modulus of the H-shaped section member, I is the second moment of area of ​​each of the first flange and the second flange, l is the length of the H-shaped section member, d ｂ : Distance between the thickness centers of the first flange and the second flange, G: Shear modulus of elasticity of the H-shaped section member, J: Saint-Venant torsional constant of the H-shaped section member, k ｒ : stiffening stiffness coefficient by a rotational movement spring that applies a restraining force to the first flange about an axis along the longitudinal direction of the H-shaped cross-section member, J ｆ : Saint-Venant torsional constant of each of the first flange and the second flange, J w t : Saint-Venant torsional constant of the web ｗ : the thickness of the web, k ｈ : stiffening stiffness coefficient by a parallel moving spring that applies a restraining force in the thickness direction of the web to the first flange, D ｗ : Plate stiffness of the web. [0050]

6. 6. The method for designing a support structure according to claim 5, wherein the undetermined coefficient α is set by any one of equations (23) to (25). [006]

7. A method for designing a support structure comprising a steel H-shaped section member having a first flange, a second flange, and a web connecting the first flange and the second flange to each other, and a plate-like member attached to the first flange and supported by the H-shaped section member, comprising: determining an elastic lateral buckling strength M of the H-shaped section member; ｅ A method for designing a support structure, in which: Here, α is an undetermined coefficient that is an arbitrary real number between 0 and 1, G is the shear modulus of elasticity of the H-shaped section member, J is the Saint-Venant torsional constant of the H-shaped section member, and d ｂ : Distance between the thickness centers of the first flange and the second flange, k ｒ : stiffening stiffness coefficient by a rotational movement spring that applies a restraining force to the first flange about an axis along the longitudinal direction of the H-shaped cross-section member, J ｆ : Saint-Venant torsional constant of each of the first flange and the second flange, J w t : Saint-Venant torsional constant of the web ｗ : the thickness of the web, k ｈ : stiffening stiffness coefficient by a parallel moving spring that applies a restraining force in the thickness direction of the web to the first flange, E: Young's modulus of the H-shaped cross-section member, I: second moment of area of ​​each of the first flange and the second flange, D ｗ : Plate stiffness of the web. [0070]

8. 8. The method for designing a support structure according to claim 7, wherein the undetermined coefficient α is set by equations (30) to (33). [0080]

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