Support structure design method and 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.SOLUTION: A support structure design method is provided to prevent lateral buckling of an H-shaped cross-sectional member in a support structure 47 which has the H-shaped cross-sectional member 25 having a first flange 26, a second flange 27, and a web 28, a plate member 37 supported by the first flange, and a connection member 41 for connecting the first flange and the plate member so that movement and rotation of the first flange are restrained by arbitrary rigidity. When a structure in which movement and rotation of the first flange are completely restrained in the support structure is defined as a completely restrained support structure, elastic lateral buckling resistance is set using reduction ratio of the elastic lateral buckling resistance of the H-shaped cross-sectional member of the support structure which is set based on a horizontal stiffening rigidity coefficient and a rotation stiffening rigidity coefficient, to the elastic lateral buckling resistance of the H-shaped cross-sectional member having the completely restrained support structure.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The present invention relates to a method for designing a support structure and to 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 member 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, 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 (connecting member), 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 2, an elastic lateral buckling resistance formula is derived for a floor structure (support 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.

[0005] These design methods are useful because they enable efficient design. However, these design methods are valid under the assumption that the lateral movement and rotation of the upper flange are completely restrained. On the other hand, the conditions for completely restraining the lateral movement and rotation have not been sufficiently considered. In addition, if the restraint against the lateral movement and rotation of the upper flange is of any rigidity, a certain degree of restraint effect should be expected. However, if the restraint is of any rigidity, the above-mentioned premise is not satisfied, and therefore these evaluation methods cannot be applied.

[0006] In Patent Documents 3 and 4, the lateral movement of the upper flange is assumed to be completely restrained by the floor slab.Then, the ratio of the torsional rigidity between the floor slab and the steel beam required to completely restrain the rotation of the upper flange is analytically obtained, and a design method that specifies the ratio of the torsional rigidity between the floor slab and the steel beam is established. In Patent Documents 3 and 4, the conditions for completely restraining lateral movement are not quantitatively examined, based on the empirical rule based on experimental results that the lateral movement of the upper flange will be restrained if a certain number of headed studs are provided. It is difficult to say that Patent Documents 3 and 4 adequately examine the conditions for completely restraining lateral movement. The conditions for completely restraining rotation are also approximately determined based on limited analytical results, and are not theoretically determined. In addition, Patent Documents 3 and 4 discuss the degree of fixation of the upper flange based on the ratio of the torsional rigidity of the floor slab and the steel beam. However, there is also a problem in that they do not properly consider the effects of local deformation of the joint members that connect the steel beam and the floor slab, such as headed studs. [Prior art documents] [Patent documents]

[0007] [Patent Document 1] Patent No. 6340276 [Patent Document 2] Patent No. 6699639 [Patent Document 3] Patent No. 5885911 [Patent Document 4] Patent No. 6895282 Summary of the Invention [Problem to be solved by the invention]

[0008] As described above, Patent Documents 1 to 4 have examined design methods that take into account the restraining effect of the floor slab on steel beams. However, there is no technology that quantitatively evaluates the fixation degree and elastic lateral buckling strength of the upper flange. Therefore, there is no theoretical evaluation of the rigidity required to completely restrain the lateral movement and rotation of the upper flange. In other words, in order to more reliably restrain the lateral movement and rotation of the upper flange and perform a design that properly evaluates the restraining effect of the floor slab, it is necessary to clarify the rigidity required to completely restrain the lateral movement and rotation of the upper flange.

[0009] In addition, the rigidity required to consider the lateral movement and rotation of the upper flange as completely restrained is thought to differ depending on the cross-sectional dimensions of the H-shaped section member. On the other hand, since the specifications of shear connectors and floor slabs are somewhat standardized, it is possible that, depending on the dimensions of the H-shaped section member, the restraint on the lateral movement and rotation of the upper flange may not be completely restrained. Even in such cases, the lateral movement and rotation of the upper flange will be restrained to a certain extent, and a certain amount of contribution to the elastic lateral buckling strength should be expected. However, in Patent Documents 1 to 4, the lateral movement and rotation of the upper flange are assumed to be completely restrained. Therefore, these design methods cannot be applied, and when the upper flange is restrained with any rigidity, it is not possible to perform a rational design that takes into account the restraining effect.

[0010] The present invention has been made in consideration of these problems, and aims to provide a design method for a support structure in which the elastic lateral buckling strength of an H-shaped cross-section member can be set in a support structure in which the first flange is restrained with any rigidity, a design method for a support structure in which the first flange can be set so as to be considered to be completely restrained, and a support structure in which the first flange is completely restrained. [Means for solving the problem]

[0011] In order to solve the above problems, the present invention proposes the following means. The design method of the present invention is a method for preventing lateral buckling of a support structure comprising a steel H-shaped section member having a first flange, a second flange, and a web joining the first flange and the second flange to each other, a plate member supported by the first flange, and a connection member connecting the first flange and the plate member, in which the movement of the first flange in the thickness direction of the web and the rotation about an axis along the longitudinal direction of the H-shaped section member are each restrained with an arbitrary rigidity, the method comprising the steps of: designing a support structure for preventing lateral buckling of the H-shaped section member, the H-shaped section member having a first flange, a second flange, and a web joining the first flange and the second flange to each other, the plate member supported by the first flange, and a connection member connecting the first flange and the plate member, the movement of the first flange in the thickness direction of the web and the rotation about an axis along the longitudinal direction of the H-shaped section member being each restrained with an arbitrary rigidity; e,fix Horizontal stiffening coefficient k according to Eq. (1) h and the rotation stiffening coefficient k according to equation (2) r The elastic lateral buckling strength M of the H-shaped section member of the support structure set based on e Using the reduction rate β, the elastic lateral buckling strength M e The present invention is characterized by setting the following. However, D w : the plate stiffness of the web, d b : the distance between the thickness centers of the first flange and the second flange, K H : the horizontal stiffening rigidity per unit length of the connecting member and the plate-like member attached to the first flange of the H-shaped cross-section member in the support structure, K R : Rotational stiffening rigidity per unit length of the connecting member and the plate-shaped member attached to the first flange of the H-shaped cross-section member in the support structure.

[0012]

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[0013] In the present invention, in the support structure, the first flange is restrained from moving in the thickness direction of the web with an arbitrary stiffness, and is restrained from rotating about the axis with an arbitrary stiffness. As a result of intensive research, the inventors have found that the elastic lateral buckling strength M of the H-shaped cross-section member in the support structure in this state is e However, we found that it can be set by following the steps below. In other words, a fully restrained support structure is defined in which movement and rotation are completely restrained. The elastic lateral buckling strength M of the H-shaped cross-section member of the fully restrained support structure is e,fix Horizontal stiffening coefficient k in the support structure h and rotational stiffness coefficient k r The elastic lateral buckling strength M of the H-shaped section member of the support structure set based on e Using the reduction factor, the elastic lateral buckling strength M e Set. By the above procedure, the elastic lateral buckling strength M of the H-section member in the support structure where the first flange is restrained with any rigidity is calculated taking into account the reduction rate. e can be set.

[0014] Another support structure design method of the present invention is a support structure design method for preventing lateral buckling of a steel H-shaped section member having a first flange, a second flange, and a web joining the first flange and the second flange to each other, a plate-like member supported by the first flange, and a connection member connecting the first flange and the plate-like member, in which the movement of the first flange in the thickness direction of the web and the rotation about an axis along the longitudinal direction of the H-shaped section member are each restrained with an arbitrary rigidity, the support structure comprising: In the support structure, the horizontal stiffening rigidity K per unit length of the connecting member and the plate-like member attached to the first flange of the H-shaped cross-section member H,fix satisfies formula (3), and the rotational stiffening stiffness K per unit length of the connecting member and the plate-like member attached to the first flange of the H-shaped cross-section member is R,fix When a structure that satisfies formula (4) is defined as a fully restrained support structure, the elastic lateral buckling strength M of the H-shaped cross-section member of the fully restrained support structure ise,fix Horizontal stiffening coefficient k according to Eq. (5) h and the rotation stiffening coefficient k according to Eq. (6) r The elastic lateral buckling strength M of the H-shaped section member of the support structure set based on e Using the reduction rate β, the elastic lateral buckling strength M e The present invention is characterized by setting the following. However, D w : the plate stiffness of the web, d b : the distance between the thickness centers of the first flange and the second flange, K H : the horizontal stiffening rigidity per unit length of the connecting member and the plate-like member attached to the first flange of the H-shaped cross-section member in the support structure, K R : Rotational stiffening rigidity per unit length of the connecting member and the plate-shaped member attached to the first flange of the H-shaped cross-section member in the support structure.

[0015]

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[0016] In the present invention, in the support structure, the first flange is restrained from moving in the thickness direction of the web with an arbitrary stiffness, and is restrained from rotating about the axis with an arbitrary stiffness. As a result of intensive research, the inventors have found that the elastic lateral buckling strength M of the H-shaped cross-section member in the support structure in this state is e However, we found that it can be set by following the steps below. That is, in the support structure, the horizontal stiffening stiffness K H,fix satisfies equation (3) and the rotation stiffening stiffness K R,fix The fully restrained support structure satisfies equation (4). The elastic lateral buckling strength M of the H-section member of the fully restrained support structure is e,fix Horizontal stiffening coefficient k in the support structure h and rotational stiffness coefficient k r The elastic lateral buckling strength M of the H-shaped section member of the support structure set based on e Using the reduction factor, the elastic lateral buckling strength M e Set. By the above procedure, the elastic lateral buckling strength M of the H-section member in the support structure where the first flange is restrained with any rigidity is calculated taking into account the reduction rate. e can be set.

[0017] In the support structure design method, the reduction rate β is expressed as follows: (M e / M e,fix ) and may be obtained by equations (7) to (10).

[0018]

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[0019] In the present invention, the reduction rate β can be precisely set using a formula.

[0020] The present invention also provides a design method for a support structure having a steel H-shaped section member including a first flange, a second flange, and a web joining the first flange and the second flange to each other, a plate member supported by the first flange, and a connecting member connecting the first flange and the plate member, in which the movement of the first flange in the thickness direction of the web and the rotation of the first flange about an axis along the longitudinal direction of the H-shaped section member are each restrained with an arbitrary rigidity, the design method being for preventing lateral buckling of the H-shaped section member, the design method comprising the steps of: determining a horizontal stiffening rigidity K per unit length by the connecting member and the plate member attached to the first flange of the H-shaped section member in the support structure; H is set so as to satisfy the formula (12), and the rotational stiffening rigidity K per unit length by the connecting member and the plate-like member attached to the first flange of the H-shaped cross-section member is R is set so as to satisfy the formula (13). However, D w : the plate stiffness of the web, d b : The distance between the thickness centers of the first flange and the second flange.

[0021]

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[0022] In the present invention, in the support structure, the first flange is restrained from moving in the thickness direction of the web with an arbitrary stiffness, and is restrained from rotating about the axis with an arbitrary stiffness. H is set to satisfy equation (12), and the rotational stiffening stiffness per unit length K R so as to satisfy equation (13), the movement of the first flange in the thickness direction is completely restrained and the rotation about the axis is completely restrained. Therefore, in the support structure, it can be set so that it is considered that the first flange is completely restrained by the plate-like member.

[0023] The support structure of the present invention includes a steel H-shaped section member having a first flange, a second flange, and a web that joins the first flange and the second flange to each other, a plate member supported by the first flange, and a connecting member that connects the first flange and the plate member, in which the movement of the first flange in the thickness direction of the web and the rotation of the first flange about an axis along the longitudinal direction of the H-shaped section member are each restrained with an arbitrary rigidity, and the horizontal stiffening rigidity K per unit length by the connecting member and the plate member attached to the first flange of the H-shaped section member is H (15) is satisfied, and the rotational stiffening stiffness K per unit length of the connecting member and the plate-like member attached to the first flange of the H-shaped cross-section member is R However, it is characterized in that it satisfies equation (16). However, D w : the plate stiffness of the web, d b : The distance between the thickness centers of the first flange and the second flange.

[0024]

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[0025] In the present invention, in the support structure, the first flange is restrained from moving in the thickness direction of the web with an arbitrary stiffness, and is restrained from rotating about the axis with an arbitrary stiffness. H satisfies equation (15), and the rotational stiffening stiffness per unit length K R It has been found that if equation (16) is satisfied, the movement of the first flange in the thickness direction of the web is completely restrained and the rotation about the axis is completely restrained. Therefore, in the support structure, the first flange can be completely restrained by the plate-like member. Effect of the Invention

[0026] In the design method of the support structure of the present invention, in a support structure in which the first flange is restrained with an arbitrary rigidity, the elastic lateral buckling strength M of the H-shaped section member is calculated. e can be set. In the design method of the support structure of the present invention, it is possible to set the first flange to be considered as being completely restrained by the plate-like member. And, in the support structure of the present invention, it is possible to bring the first flange into a state in which it is completely restrained by the plate-like member. [Brief description of the drawings]

[0027] [Figure 1] 1 is a perspective view showing a part of a building in which a support structure according to one embodiment of the present invention 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 diagram showing the change in the value of (Mcr,rfix / Mcr,fix) relative to the horizontal stiffening stiffness coefficient kh when the rotation around the axis is fixed and the horizontal stiffening stiffness coefficient kh is a variable. [Figure 8] FIG. 13 is a diagram showing the change in the value of (Mcr,hfix / Mcr,fix) relative to the rotational stiffening stiffness coefficient kr when the lateral movement is fixed and the rotational stiffening stiffness coefficient kr is a variable. [Figure 9] FIG. 13 is a diagram showing the change in the value of (Mcr / Mcr,fix) relative to the horizontal stiffening stiffness coefficient kh when the horizontal stiffening stiffness coefficient kh and the rotational stiffening stiffness coefficient kr are used as variables. [Figure 10] FIG. 13 is a diagram showing the change in the value of (Mcr / Mcr,fix) relative to the horizontal stiffening stiffness coefficient kh when the horizontal stiffening stiffness coefficient kh and the rotational stiffening stiffness coefficient kr are set as arbitrary variables. [Figure 11] FIG. 11 is a diagram illustrating the distribution of bending moment of uniform bending applied to the second H-shaped cross-section member. [Figure 12] FIG. 11 is a diagram illustrating the inversely symmetrical bending moment distribution acting on the second H-shaped cross-section member of the same embodiment. [Figure 13] 11 is a diagram illustrating the bending moment distribution due to a live load acting on the second H-shaped cross-section member of the same embodiment. FIG. [Figure 14] FIG. 13 is a diagram illustrating the bending moment distribution assuming negative pressure due to wind load acting on the second H-shaped cross-section member. [Figure 15] This figure shows the change in elastic lateral buckling strength MFEM versus the value of (l / H) when a uniform bending moment distribution is applied. [Figure 16] This figure shows the change in elastic lateral buckling strength MFEM versus the value of (l / H) when an inversely symmetric bending moment distribution is applied. [Figure 17] This figure shows the change in elastic lateral buckling strength MFEM versus the value of (l / H) when a bending moment distribution due to live load is applied. [Figure 18] This figure shows the change in elastic lateral buckling strength MFEM versus the value of (l / H) when a bending moment distribution assuming negative pressure due to wind load is applied. [Figure 19] This figure shows the change in the non-dimensional elastic lateral buckling strength MFEM versus the value of (l / H) when a uniform bending moment distribution is applied. [Figure 20] This figure shows the change in the non-dimensional elastic lateral buckling strength MFEM versus the value of (l / H) when an inversely symmetric bending moment distribution is applied. [Figure 21] This figure shows the change in the non-dimensional elastic lateral buckling strength MFEM versus the value of (l / H) when a bending moment distribution due to live load is applied. [Figure 22] This figure shows the change in the non-dimensional elastic lateral buckling strength MFEM versus the (l / H) value when a bending moment distribution assuming negative pressure due to wind load is applied. [Diagram 23] 1 is a perspective view showing a cutaway view of a part of a building in which a support structure according to a modified embodiment of the present invention is used. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0028] Hereinafter, a support structure according to one embodiment of the present invention and a support structure to which a design method for a support structure according to one embodiment of the present invention (hereinafter simply referred to as the design method) is applied will be described with reference to Figures 1 to 23.

[0029] [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.

[0030] 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.

[0031] 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.

[0032] 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.

[0033] 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 D w (Nmm). The plate stiffness D w As shown in (36) below, Dw =E t w 3 / (12(1-ν 2 )) where ν represents the Poisson's ratio (-) of the second H-section member 25.

[0034] 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.

[0035] 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).

[0036] 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.

[0037] 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 (connecting member) 41 such as a known metal fitting or fastening member. In other words, the joint member 41 connects the first flange 26 and the bottom plate 37. The plate-like member may be a floor slab, etc. In this case, a shear connector, which is a connecting member, may be fixed to the first flange 26 of the second H-shaped cross-section member 25, and the first flange 26 and the floor slab may be connected by this shear connector.

[0038] In this way, the folded plate roof 35 is attached to the first flange 26 of the second H-shaped section member 25 and is supported by the first flange 26. As shown in Fig. 3, the second H-shaped section member 25, the folded plate roof 35, and the joint member 41 form a support structure 47. Similarly, as shown in Fig. 1, the first H-shaped section member 15, the folded plate roof 35, and the joint member 41 form a support structure 46.

[0039] 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.

[0040] [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.

[0041] 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 (21) and (22).

[0042]

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[0043] Here, α is an undetermined coefficient. As shown in Fig. 4, it is assumed that the first flange 26 is restrained by a parallel movement spring (horizontal spring) 50 and a rotational movement spring (rotational spring) 51. The parallel movement spring 50, as a restraint by the folded plate roof 35 and the joint member 41, restrains the movement of the first flange 26 in the x-axis direction (thickness direction of the web 28) with any rigidity. The rotational movement spring 51, as a restraint by the folded plate roof 35 and the joint member 41, restrains the rotation of the first flange 26 about an axis along the longitudinal direction of the H-shaped cross-section member 25 with any rigidity. 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 b As a function of , it is expressed by equations (23) and (24).

[0044]

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[0045] 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) (-). Horizontal stiffness coefficient k h and rotational stiffness coefficient k r are non-dimensional values ​​based on the bending ease of the web 28. 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 by equations (25) to (27).

[0046]

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[0047] 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 (28).

[0048]

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[0049] where ν is the Poisson's ratio (-) of the H-section member 25. M cr is 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 (21) through (27) into equation (28) and rearranging, the total potential energy Π is expressed by equation (29).

[0050]

number

[0051] By rearranging equation (29) using the relationships in equations (35) to (38) below, the total potential energy Π is expressed by equation (39).

[0052]

number

[0053] Next, the equation is rearranged using equation (40) 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.

[0054]

number

[0055] The first-order or second-order derivative of the displacement distribution u is expressed by equations (41) and (42).

[0056]

number

[0057] Using equations (40) to (42), each definite integral is expressed by equations (43) to (45).

[0058]

number

[0059] Substituting equations (43) through (45) into equation (39) and rearranging, the total potential energy Π is expressed by equation (51).

[0060]

number

[0061] From the principle of minimum potential energy (Π=0), equation (51) is expressed as the elastic lateral buckling strength M cr By rearranging, we obtain equation (52).

[0062]

number

[0063] 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 crIt is preferable to use the value that minimizes the value. Therefore, the equation obtained by partially differentiating equation (52) 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 M cr The undetermined coefficient α that gives the minimum solution is expressed by equation (53). The undetermined coefficient α is calculated by using a convergence calculation or a spreadsheet solver instead of equation (53). cr Alternatively, the value at which is the minimum may be found.

[0064]

number

[0065] Here, X and Y are expressed by equations (54) and (55).

[0066]

number

[0067] Elastic lateral buckling strength M according to Eq. (52) 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 (56).

[0068]

number

[0069] 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,minIt is preferable to use the value that minimizes the elastic lateral buckling strength M obtained by partially differentiating equation (56) with the undetermined coefficient α, and then 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 (56) is cr,min The undetermined coefficient α that gives the minimum solution is expressed by equation (57). Since equation (57) 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 (57) becomes a negative value, and α cannot be calculated. In such cases, α can be calculated by treating the square root of equation (57) as 0, and the minimum elastic lateral buckling strength M cr,min In addition, the undetermined coefficient α can be calculated not by Eq. (57) but by convergence calculation or a solver in a spreadsheet software, etc. cr Alternatively, the value at which is the minimum may be found.

[0070]

number

[0071] Here, U, V, W, X, Y, and Z are expressed by equations (58) to (63).

[0072]

number

[0073] 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, is so-called two-axis symmetrical, the equations can be rearranged using the relationships shown in equations (67) and (68).

[0074]

number

[0075] where I is the second moment 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 (69) to (72).

[0076]

number

[0077] Minimum elastic lateral buckling strength M cr,min is expressed by equations (73) to (77).

[0078]

number

[0079] [3. Study on elastic lateral buckling strength of H-shaped members with support structure restrained by arbitrary stiffness] Here, the horizontal stiffening stiffness K is defined as follows: H and rotational stiffness K R We will consider the following: Horizontal stiffening stiffness K H : The stiffening rigidity per unit length in the longitudinal direction of the H-shaped section member 25 against horizontal movement in the thickness direction of the web 28 by the joint member 41 attached to the first flange 26 of the H-shaped section member 25 and the folded plate roof 35 in the supporting structure 47. Rotational stiffness K R : The stiffening rigidity per unit length in the longitudinal direction of the H-shaped section member 25, against rotation around an axis along the longitudinal direction of the H-shaped section member 25, by the joint member 41 attached to the first flange 26 of the H-shaped section member 25 and the folded plate roof 35 in the supporting structure 47. The horizontal stiffening stiffness coefficient kh and rotational stiffness coefficient k r are expressed by equations (81) and (82) by modifying equations (23) and (24).

[0080]

number

[0081] By using equation (73), any horizontal stiffening stiffness K H and rotational stiffness K R The minimum elastic lateral buckling strength M cr,min In addition, in equation (73), the horizontal stiffening coefficient k h or rotation stiffening coefficient k r By rearranging equation (73) assuming that is infinity, equation (85) can be obtained from equation (83).

[0082]

number

[0083] Equation (83) is the horizontal stiffening coefficient k h That is, in the case where the lateral movement (translation in the x-axis direction) of the first flange 26 is fixed (the lateral movement is completely restrained) by using the formula (83), an arbitrary rotation stiffening stiffness K R Elastic lateral buckling strength M cr,hfix can be sought.

[0084] Equation (84) is the rotational stiffening coefficient k r That is, in the case where the rotation of the first flange 26 around the axis is fixed (completely restrained), any horizontal stiffening stiffness K H Elastic lateral buckling strength M cr,rfix It is possible to ask for: Equation (85) is the horizontal stiffening coefficient k h and rotational stiffness coefficient k rIn other words, when the lateral movement and rotation of the first flange 26 are completely restrained, the elastic lateral buckling strength M cr,fix It is possible to ask for:

[0085] Using these formulas, the horizontal stiffening stiffness K for three types of H-shaped cross-section members 25 with different cross-sectional dimensions, namely narrow, medium, and wide, is calculated. H and rotational stiffness K R The effect of on the elastic lateral buckling strength is verified. The cross-sectional dimensions of the narrow H-shaped section member 25 are H-600x200x11x17. The cross-sectional dimensions of the medium-width H-shaped section member 25 are H-900x300x16x28. The cross-sectional dimensions of the wide H-shaped section member 25 are H-400x400x13x21. These three types of cross-sectional dimensions were selected to cover (represent) all cross-sectional dimensions of H-shaped steel by selecting three types with different cross-sectional dimension characteristics. First, the horizontal stiffening stiffness K H and rotational stiffness K R The effects of each are analyzed separately. FIG. 7 shows the horizontal stiffening coefficient k h The results of the study are shown below when the variable is used. In Fig. 7, the vertical axis is the elastic lateral buckling strength M cr,rfix is the elastic lateral buckling strength M cr,fix Divided by and made non-dimensional, (M cr,rfix / M cr,fix The horizontal axis represents the value of the horizontal stiffening coefficient k h is expressed on a logarithmic axis.

[0086] In Fig. 7, the horizontal stiffening coefficient k h As increases, (M cr,rfix / M cr,fix ) approaches 1. In other words, the elastic lateral buckling strength M cr,rfix However, the elastic lateral buckling strength M when the lateral movement and rotation of the first flange 26 are completely restrained cr,fix The horizontal stiffening coefficient k h Unless becomes infinite, the elastic lateral buckling strength M cr,rfix is the elastic lateral buckling strength M according to Eq. (85)cr,fix However, from Fig. 7, the horizontal stiffening coefficient k h When exceeds 100, the elastic lateral buckling strength M cr,rfix The elastic lateral buckling strength M when the lateral movement and rotation of the first flange 26 are restrained cr,fix It can be seen that it is almost equivalent to In addition, the horizontal stiffening coefficient k h Elastic lateral buckling strength M with change in cr,rfix It can be seen that there is almost no difference in the rate of change of the elastic lateral buckling strength M for the three types of cross-sectional dimensions. cr,rfix is the elastic lateral buckling strength M cr,fix The value obtained by dividing by and making it non-dimensional and the horizontal stiffening coefficient k h It can be said that the relationship between these two can be clarified.

[0087] Figure 8 shows the stiffness coefficient k r The results of the study are shown below when the variable is used. In Fig. 8, the vertical axis is the elastic lateral buckling strength M cr,hfix is the elastic lateral buckling strength M cr,fix Divided by and made non-dimensional, (M cr,hfix / M cr,fix ) value. The horizontal axis represents the rotation stiffening coefficient k r is expressed on a logarithmic axis. Figure 8 shows the rotation stiffening coefficient k r As increases, (M cr,hfix / M cr,fix ) approaches 1. In other words, the elastic lateral buckling strength M cr,hfix The elastic lateral buckling strength M when the lateral movement and rotation of the first flange 26 are restrained cr,fix The rotation stiffening coefficient k r Unless becomes infinite, the elastic lateral buckling strength M cr,hfix is the elastic lateral buckling strength M according to Eq. (85) cr,fix However, from Fig. 8, the rotation stiffening coefficient k r When exceeds 100, the elastic lateral buckling strength M cr,hfix The elastic lateral buckling strength M when the lateral movement and rotation of the first flange 26 are restrained cr,fixIt can be seen that it is almost equivalent to

[0088] In addition, the rotation stiffening coefficient k r Elastic lateral buckling strength M with change in cr,hfix It can be seen that there is almost no difference in the rate of change of the elastic lateral buckling strength M for the three types of cross-sectional dimensions. cr,hfix is the elastic lateral buckling strength M cr,fix The value obtained by dividing by and making it non-dimensional and the rotation stiffening coefficient k r It can be said that the relationship between these two can be clarified.

[0089] Comparing Figures 7 and 8, the rotational stiffening coefficient k r The horizontal stiffening coefficient k h It can be seen that the effect on elastic lateral buckling strength is greater than when is used as a variable. There is also a slight difference in the value of the stiffening coefficient, which can be considered to be fixed for lateral movement and rotation. From the examination of Figure 7, the horizontal stiffening coefficient k h When is used as a variable, the horizontal stiffening coefficient k h By setting the value to 200 or more, the elastic lateral buckling strength M cr,rfix The elastic lateral buckling strength is 99% of that when the lateral movement and rotation of the first flange 26 are fixed, and the decrease in the elastic lateral buckling strength is limited to about 1%. Similarly, from the examination of Figure 8, the rotational stiffening stiffness coefficient k r When the variable is used, the rotation stiffening coefficient k r By setting the value to 150 or more, the elastic lateral buckling strength M cr,hfix The stiffness coefficient k of the first flange 26 is 99% of that of the first flange 26 when the lateral movement and rotation of the first flange 26 are fixed, and the decrease in the buckling strength is limited to about 1%. r The horizontal stiffening coefficient k h The required value for it to be considered fixed is slightly smaller than that of

[0090] Figure 9 shows the horizontal stiffening coefficient k h and rotational stiffness coefficient k r The results of the study are shown in Fig. 9. In Fig. 9, the vertical axis is the elastic lateral buckling strength M cr is the elastic lateral buckling strength M cr,fix Divided by and made non-dimensional, (M cr / Mcr,fix The horizontal axis represents the value of the horizontal stiffening coefficient k h is expressed on a logarithmic axis. Note that the relationship between the values ​​required to consider the value as fixed (k h ≧200,k r ≧150), the rotation stiffening coefficient k r is the horizontal stiffness coefficient k h The ratio is set to 0.75 (150 / 200). Figure 9 shows the horizontal stiffening coefficient k h and the rotation stiffening coefficient k r The overall tendency is the same as in Figures 7 and 8. Here, the horizontal stiffening coefficient k h is 200, and the rotation stiffening coefficient k r When is 150, the elastic lateral buckling strength M cr The strength of the first flange 26 is 98% of that when the lateral movement and rotation of the first flange 26 are fixed, and the decrease in the elastic lateral buckling strength is limited to about 2%.

[0091] Theoretically, the horizontal stiffness stiffness coefficient k h and rotational stiffness coefficient k r Unless it becomes infinite, the elastic lateral buckling strength M cr The elastic lateral buckling strength M of the first flange 26 is fixed against lateral movement and rotation. cr,fix Therefore, in a realistic joint detail, the elastic lateral buckling strength M cr,fix Elastic lateral buckling strength M equal to cr It is difficult to achieve this. On the other hand, a strength reduction of about 2% can be said to be a small effect that falls within the range of variation in elastic lateral buckling strength that can occur due to variations in the dimensions and strength of the H-shaped cross-section member 25, variations in construction accuracy, etc. For this reason, the horizontal stiffening coefficient k h is 200 or more, and the rotation stiffening coefficient k r If the axial length of the first flange 26 is 150 or more, the lateral movement and rotation of the first flange 26 can be considered to be completely restricted. Horizontal stiffness coefficient k h When is 200 or more, the horizontal stiffening stiffness K His expressed as in Eq. (88). Rotational stiffening coefficient k r When is 150 or more, from equation (82), the rotation stiffening stiffness K R is expressed as in equation (89).

[0092]

number

[0093] According to Figures 7 to 9, the horizontal stiffening coefficient k h and rotational stiffness coefficient k r When the horizontal stiffening coefficient k is less than the condition that can be considered to be completely restrained, the elastic lateral buckling strength is lower than when the lateral movement and rotation of the first flange 26 are completely restrained. h and rotational stiffness coefficient k r Depending on the value of , the elastic lateral buckling strength can be significantly greater than when lateral movement and rotation are not restrained at all. Therefore, the elastic lateral buckling strength M when the lateral movement and rotation of the first flange 26 are restrained with an arbitrary rigidity (incompletely restrained) is e Let us consider a simple method for estimating this.

[0094] As a result of careful consideration, the inventors have determined that the horizontal stiffening coefficient k h and any rotational stiffening coefficient k r The reduction rate of the elastic lateral buckling strength in the case where the lateral movement and rotation of the first flange 26 are completely restrained is defined as the horizontal stiffening stiffness coefficient k h and rotational stiffness coefficient k r It was found that the horizontal stiffening coefficient k h Reduction rate of elastic lateral buckling strength due to h is expressed by Eq. (92). Rotational stiffening coefficient k r Reduction rate of elastic lateral buckling strength due to r is expressed by equation (93).

[0095]

number

[0096] Figure 7 shows the reduction rate β calculated using Eq. (92). h The elastic lateral buckling strength estimated using the reduction rate β calculated using Eq. (93) is shown in Fig. 8. r The elastic lateral buckling strength estimated using is shown by a solid line. In Figures 7 and 8, the solid lines show good correspondence with the markers, and it is clear that the elastic lateral buckling strength can be estimated with high accuracy.

[0097] Equations (92) and (93) give the reduction rate when one of the stiffening coefficients is set to infinity in the form corresponding to Figs. 7 and 8. As a result of intensive study, the inventors have determined that the horizontal stiffening coefficient k h and rotational stiffness coefficient k r When both are variables, the horizontal stiffening coefficient k h and rotational stiffness coefficient k r Correction value β taking into account the interaction of hr It was found that it was necessary to take into account

[0098]

number

[0099] In Fig. 9, h , β r , β hr The elastic lateral buckling strength estimated using the reduction rate β is shown by the solid line. In Fig. 9, the reduction rate β value shown by the solid line shows a good correspondence with the marker, and it is clear that the elastic lateral buckling strength can be estimated with high accuracy. The reduction rate β is shown in equation (95) and can be obtained from equations (92) to (95).

[0100]

number

[0101] In Fig. 9, the horizontal stiffening coefficient k h and rotational stiffness coefficient k rHowever, the rotation stiffening coefficient k r is the horizontal stiffness coefficient k h Because of the limited condition of 0.75 times the horizontal stiffening coefficient k h and the rotational stiffening coefficient k r The validity of the estimation formula for elastic lateral buckling strength is confirmed for the combination of the above. Figure 10 shows the horizontal stiffening coefficient k for the cross-sectional dimensions of H-900x300x16x28. h and rotational stiffness coefficient k r In Fig. 10, the vertical axis represents the elastic lateral buckling strength M cr is the elastic lateral buckling strength M cr,fix Divided by and made non-dimensional, (M cr / M cr,fix The horizontal axis represents the value of the horizontal stiffening coefficient k h is expressed on a logarithmic axis.

[0102] Rotational stiffness stiffness coefficient k r is the horizontal stiffness coefficient k h The five magnifications are different: 0.1, 0.4, 1, 2.5, and 10 times. h , β r , β hr The solid line shows the elastic lateral buckling strength estimated using the rotational stiffening coefficient k r All of the markers in five different conditions show good correspondence. From the above, the elastic lateral buckling strength M when the lateral movement and rotation of the first flange 26 expressed by equation (96) are restrained by an arbitrary stiffness is e The estimation formula is given by the horizontal stiffening coefficient k h and rotational stiffness coefficient k r For the combination of e It can be said that we can estimate

[0103]

number

[0104] Here, in the support structure 47, a structure in which the movement of the first flange 26 in the thickness direction of the web 28 is completely restrained and the rotation about the axis is completely restrained is defined as a completely restrained support structure. Elastic lateral buckling strength M e,fix is the elastic lateral buckling strength of the H-shaped section member 25 of the fully restrained support structure, and the elastic lateral buckling strength M of the H-shaped section member 25 shown in Eq. (85) cr,fix The reduction rate β is set as follows: (M e / M e,fix ) value. From the above considerations, in the completely restrained support structure, the horizontal stiffening stiffness K H,fix can be considered to satisfy equation (99). In a fully restrained support structure, the rotation stiffening stiffness K R,fix can be considered to satisfy equation (100). In addition, the horizontal stiffening stiffness K H,fix (200D w / d b 3 ) is preferable. R,fix (150D w / d b ) is preferred because it allows the system to be considered fully constrained even if the constraint is not perfect.

[0105]

number

[0106] From these considerations, regardless of the cross-sectional dimensions of the H-shaped section member 25, the elastic lateral buckling strength M when the lateral movement and rotation of the first flange 26 are restrained with an arbitrary rigidity is e The reduction rate β can be used to easily estimate the horizontal stiffening stiffness K H and rotational stiffness K R , the plate stiffness D w and the distance between the plate thickness centers d bThe horizontal stiffening stiffness coefficient k, which is non-dimensionalized by the bending ease of the web 28, is h and rotational stiffness coefficient k r This is the effect of discovering how to treat it as

[0107] Next, the effect of different bending moment distributions will be examined. The above study was about the conditions under which the lateral movement and rotation of the first flange 26 can be considered to be restrained when the second flange 27 is subjected to a bending moment such as compression. In the following, we will use elastic buckling analysis using FEM (Finite Element Method) to confirm whether it is possible to make a similar evaluation when the bending moment distribution is different.

[0108] In the analysis model shown in FIG. 2, the H-shaped cross-section member 25 is constructed using four-node shell elements. 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, the movement in the x-axis direction was restrained by the translation spring 50, and the rotation around the z-axis was restrained by the rotational movement spring 51.

[0109] 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.

[0110] The load acting on the H-shaped section member 25 was set so that the bending moment distribution would be one of the four types of bending moment distributions shown in Figures 11 to 14. In Figures 11 to 14, the horizontal axis represents the dimensionless coordinate in the longitudinal direction of the H-shaped section member 25, and the vertical axis represents the dimensionless bending moment obtained by non-dimensionalizing the bending moment acting on each dimensionless coordinate in the longitudinal direction of the H-shaped section member 25 with the maximum bending moment acting on the H-shaped section member 25. Fig. 11 shows the bending moment distribution of uniform bending where the second flange 27 is compressed, which is the premise of the above-mentioned study. Fig. 12 shows the inversely symmetrical bending moment distribution assuming an earthquake. Fig. 13 shows the bending moment distribution due to live load assuming normal use. Fig. 14 shows the bending moment distribution assuming negative pressure due to wind load.

[0111] 14 only assumes that the longitudinal ends of the H-shaped section member 25 are pin-jointed. The moment at each longitudinal end of the H-shaped section member 25 is zero. 11 to 14, in the non-dimensional coordinates where the non-dimensional bending moment is positive, the second flange 27 of the H-shaped section member 25 is in compression.

[0112] In this analysis model, the cross-sectional dimensions of the H-shaped section member 25 are H-900x300x16x28. Horizontal stiffening coefficient k h and rotational stiffness coefficient k r was set as a variable. Horizontal stiffening coefficient k h and rotational stiffness coefficient k r is the stiffening coefficient k shown in Table 1. h ,k r The five conditions were set, ranging from a range in which the resistance was very small to a state in which the lateral movement and rotation of the first flange 26 were completely restricted (Conditions Nos. 1 to 5).

[0113] [Table 1]

[0114] Four types of bending moment distribution and five levels of stiffening coefficient kh ,k r The analysis was performed for a total of 20 cases of combinations of the above, with 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 being changed in the range of 6 to 50.

[0115] The analysis results for each bending moment distribution are shown in Fig. 15 to Fig. 18. In Fig. 15 to Fig. 18, the vertical axis is the elastic lateral buckling strength M obtained by the elastic buckling analysis. FEM The horizontal axis represents the value of (l / H). In any case of bending moment distribution, the horizontal stiffening coefficient k h and rotational stiffness coefficient k r As the elastic lateral buckling strength M FEM The horizontal stiffening coefficient k h is 200 and the rotation stiffening coefficient k r Elastic lateral buckling strength M when is 150 FEM is the horizontal stiffness coefficient k h is ∞(+∞) and the rotational stiffening coefficient k r Elastic lateral buckling strength M with ∞ FEM is roughly equal to In other words, the horizontal stiffening stiffness coefficient k , which is derived on the assumption that the second flange 27 is compressed and the bending moment distribution of the equal bending is uniform, is used to completely restrain the lateral movement and rotation of the first flange 26. h and rotational stiffness coefficient k r It can be said that the above condition can be applied regardless of the bending moment distribution.

[0116] Figures 19 to 22 show the elastic lateral buckling strength M FEM The elastic lateral buckling strength M FEM In Fig. 19 to Fig. 22, the vertical axis is the non-dimensional elastic lateral buckling strength M FEM The horizontal axis represents the value of (l / H). The vertical axis in FIG. 19 to FIG. 22 is the elastic lateral buckling strength M when the lateral movement and rotation of the first flange 26 are completely restrained. FEMAny horizontal stiffening coefficient k h and any rotational stiffening coefficient k r Elastic lateral buckling strength M FEM In each figure, the reduction rate β of the elastic lateral buckling strength is shown by a solid line or a dashed line.

[0117] In the case of the uniform bending moment distribution shown in Fig. 19, the reduction rate β and the markers, which are the results of the elastic buckling analysis, show a good correspondence. Also, in the cases of bending moment distributions other than the uniform bending moment distribution shown in Fig. 20 to Fig. 22, the reduction rate β captures the distribution trend of the markers, which are the results of the elastic buckling analysis. In other words, the horizontal stiffening coefficient k h and rotational stiffness coefficient k r The reduction rate β of the elastic lateral buckling strength due to the above was derived based on the minimum value of the elastic lateral buckling strength in a uniform bending moment distribution in which the second flange 27 is compressed. However, this reduction rate β can be applied as a method for estimating the elastic lateral buckling strength for various bending moment distributions, not limited to a uniform bending moment distribution. That is, the elastic lateral buckling strength M when the lateral movement and rotation of the first flange 26 expressed by equation (96) are restrained by an arbitrary stiffness e The estimation formula of (96) can be applied as a method for estimating the elastic lateral buckling strength for various bending moment distributions. In that case, the elastic lateral buckling strength M of the H-shaped cross-section member 25 of the fully restrained support structure used in formula (96) is e,fix is the elastic lateral buckling strength M of the H-shaped section member 25 of the fully restrained support structure shown in Eq. (85). cr,fix Alternatively, it may be set based on a value calculated using an elastic lateral buckling strength evaluation formula for other fully restrained support structures, or based on the elastic lateral buckling strength calculated using FEM.

[0118] [4. Consideration of the contribution of plate-like members to stiffening rigidity] Next, when plate-like members such as floor slabs and roofing materials are attached to the H-shaped cross-section member, how much horizontal stiffening rigidity K these plate-like members have against the first flange 26? H and rotational stiffness K RHere, calculations are performed based on the calculation method described in the Architectural Institute of Japan's "Problems Regarding Buckling of Steel Structures 2013" and other publications. Horizontal stiffness per unit length when floor slab is attached K u is the shear stiffness of the headed stud, K u1 , in-plane bending stiffness of floor slab K u2 This can be evaluated as a series system using equations (105) to (107).

[0119]

number

[0120] Here, the number of headed studs in the gauge direction is n s The ultimate shear strength of the headed stud is Q s Let us assume that. Q s The deformation of the headed stud at the ultimate shear strength is expressed as δ s The pitch of the headed stud is l p The Young's modulus of concrete is E c The moment of inertia of the slab for the effective width is I c Let the span of the beam be l b Let us assume that.

[0121] Rotational stiffness K per unit length when floor slab is attached θ is the stiffness K due to the slip-out of the headed stud s , stiffness K due to out-of-plane deformation of flange f , stiffness K due to out-of-plane deformation of floor slab c As a series system, it can be evaluated using equations (110) to (114).

[0122]

number

[0123] Here, the cross-sectional area of ​​the headed stud shaft is A s The Young's modulus of the headed stud is E sThe distance from the center of rotation to the stud is b s The neck length of the headed stud is l s The Young's modulus of the flange is E f The moment of inertia of the flange per unit length against out-of-plane bending is l f The gauge distance of the headed stud is b g The width of the beam flange is B. The moment of inertia of the slab against out-of-plane bending per unit length is I cy The span of the slab is l c Let us assume that. For the member dimensions and material constants shown in Table 2, the horizontal stiffness per unit length K u and rotational stiffness K θ Request.

[0124] [Table 2]

[0125] The symbols in Table 2 are defined as above. c represents the thickness of the floor slab. d s represents the shaft diameter of the headed stud. By using the values ​​shown in Table 2, the cross-sectional properties used in equations (105) to (114) can be calculated. Table 3 shows the stiffness of each part and the horizontal stiffness per unit length K u and rotational stiffness K θ Shows.

[0126] [Table 3]

[0127] In addition, the horizontal stiffness K u The horizontal stiffness stiffness K H and the rotational stiffness K θ Rotating stiffness K R The horizontal stiffening coefficient k calculated using equations (81) and (82) ish and rotational stiffness coefficient k r The details are also shown in Table 3. Horizontal stiffness coefficient k h is less than 200 and the rotation stiffening coefficient k r In sample No. 1, where the rigidity is less than 150, the lateral movement and rotation of the first flange 26 are not completely restrained, and it is determined that they are restrained with an arbitrary rigidity. On the other hand, the horizontal stiffness stiffness coefficient k h is 200 or more and the rotation stiffening coefficient k r In sample No. 2, where the value is 150 or more, it is determined that the lateral movement and rotation of the first flange 26 are completely restricted. In this way, the horizontal stiffening coefficient k h is 200 or more and the rotation stiffening coefficient k r If the restraint is not 150 or more, it is determined that the lateral movement and rotation of the first flange 26 are not completely restrained.

[0128] In this way, the horizontal stiffening rigidity K of the first flange 26 when the floor slab is attached to the H-shaped section member 25 is H and rotational stiffness K R can be calculated based on the specifications of the headed studs, which are shear connectors, and the floor slab. Then, the horizontal stiffening coefficient k h and rotational stiffness coefficient k r varies greatly depending on the conditions of the H-shaped section member 25, floor slab, and headed studs. In addition, these studies are based on the assumption that a floor slab is attached to the H-shaped cross-section member 25, but the rigidity can also be calculated by considering the deformation of the surface material and joint material when a roofing material or exterior wall material is attached. In that case, the rigidity of the surface material of the roofing material or exterior wall material is smaller than that of the floor slab, so the horizontal stiffening rigidity coefficient k h and rotational stiffness coefficient k r It is easy to imagine that the values ​​shown in Table 3 will be smaller than those shown.

[0129] 5. Support structure design method and support structure The design method of this embodiment is a method for preventing lateral buckling of the H-shaped section member 25 in the support structure 47. In this design method, the elastic lateral buckling strength M e,fix In the support structure 47, the horizontal stiffening stiffness coefficient k h and rotational stiffness coefficient k r The elastic lateral buckling strength M of the H-shaped section member 25 of the support structure 47 set based on e Using the reduction rate β, the elastic lateral buckling strength M e Set. In addition, in another design method of this embodiment, in the support structure 47, the horizontal stiffening rigidity K H is set so as to satisfy the formula (88). The rotation stiffening stiffness K R is set so as to satisfy equation (89). In addition, in the support structure 47 of this embodiment, the horizontal stiffening rigidity K H The rotation stiffening stiffness K by the joint member 41 attached to the first flange 26 of the H-shaped section member 25 and the folded plate roof 35 is R satisfies equation (89).

[0130] 6. Effects of this embodiment As described above, in the design method of this embodiment, in the support structure 47, the movement of the first flange 26 in the thickness direction of the web 28 is restrained with an arbitrary rigidity, and the rotation about the axis is restrained with an arbitrary rigidity. As a result of intensive research, the inventors have found that the elastic lateral buckling strength M e However, we found that it can be set by following the steps below. That is, the support structure 47 defines a completely restrained support structure in which movement and rotation are completely restrained. The elastic lateral buckling strength M of the H-shaped section member 25 of the completely restrained support structure is e,fix Horizontal stiffening coefficient k in the support structure 47 h and rotational stiffness coefficient k rThe elastic lateral buckling strength M of the H-shaped section member 25 of the support structure 47 set based on e Using the reduction rate β, the elastic lateral buckling strength M e Set. By the above-mentioned procedure, taking into account the reduction rate β, the elastic lateral buckling strength M of the H-shaped section member 25 in the support structure 47 in which the first flange 26 is restrained with an arbitrary rigidity is calculated. e can be set.

[0131] In this embodiment, the elastic lateral buckling strength M of the H-shaped section member 25 in the support structure 47 e However, it has been found that the above-mentioned procedure can be different from the above procedure and can be set by the following procedure. That is, in the support structure 47, the horizontal stiffening stiffness K H,fix satisfies equation (99), and the rotation stiffening stiffness K R,fix The fully restrained support structure satisfies the formula (100). The elastic lateral buckling strength M of the H-shaped section member 25 of the fully restrained support structure is e,fix Horizontal stiffening coefficient k in the support structure 47 h and rotational stiffness coefficient k r The elastic lateral buckling strength M of the H-shaped section member 25 of the support structure 47 set based on e Using the reduction rate β, the elastic lateral buckling strength M e Set. By the above-mentioned procedure, taking into account the reduction rate β, the elastic lateral buckling strength M of the H-shaped section member 25 in the support structure 47 in which the first flange 26 is restrained with an arbitrary rigidity is calculated. e can be set.

[0132] The reduction rate β is (M e / M e,fix ) and is obtained by equations (92) to (95). Therefore, the reduction rate β can be precisely set by using the equations.

[0133] In addition, in another design method of the support structure of this embodiment, in the support structure 47, the horizontal stiffening rigidity K His set so as to satisfy the formula (88). The rotation stiffening stiffness K R is set so as to satisfy equation (89). In the support structure 47, the first flange 26 is restrained from moving in the thickness direction of the web 28 with an arbitrary stiffness, and is restrained from rotating about the axis with an arbitrary stiffness. H is set to satisfy equation (88), and the rotation stiffening stiffness K R so as to satisfy the formula (89), the movement of the first flange 26 in the thickness direction is completely restrained, and the rotation about the axis is also completely restrained. Therefore, in the support structure 47, it can be set so that the first flange 26 is considered to be completely restrained by the joint member 41 and the folded plate roof 35.

[0134] In addition, in the support structure 47 of this embodiment, the movement of the first flange 26 in the thickness direction of the web 28 is restricted by an arbitrary stiffness, and the rotation around the axis is restricted by an arbitrary stiffness. H satisfies equation (88), and the rotation stiffening stiffness K R It has been found that if equation (89) is satisfied, the movement of the first flange 26 in the thickness direction is completely restrained, and the rotation about the axis is completely restrained. Therefore, in the support structure 47, the first flange 26 can be completely restrained by the joint member 41 and the folded plate roof 35.

[0135] 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. 23, in a building 1A, a folded plate roof 35 is attached to a first H-shaped section member 15, which is a main beam, 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, the exterior wall material 55, and the joint member 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).

[0136] In the above embodiment, the reduction rate β may be obtained from an equation other than equations (92) to (95). [Explanation of symbols]

[0137] 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) 41 Joint members (connecting members) 46,47,57 Support structure

Claims

1. a steel H-shaped cross-section member having a first flange, a second flange, and a web that joins the first flange and the second flange to each other; a plate-like member supported by the first flange; and a connecting member that connects the first flange and the plate-like member; A method for designing a support structure for preventing lateral buckling of an H-shaped section member, in which the movement of the first flange in the thickness direction of the web and the rotation of the first flange about an axis along the longitudinal direction of the H-shaped section member are each restrained with an arbitrary rigidity, comprising: In the support structure, when a structure in which the movement of the first flange in the thickness direction and the rotation about the axis are completely restrained is defined as a completely restrained support structure, The elastic lateral buckling strength M of the H-shaped cross-section member of the fully restrained support structure ｅ，ｆｉｘ Horizontal stiffening coefficient k according to equation (1) ｈ and the rotation stiffening coefficient k according to equation (2) ｒ The elastic lateral buckling strength M of the H-shaped section member of the support structure set based on ｅ Using the reduction rate β, the elastic lateral buckling strength M ｅ How to design support structures. However, D ｗ : Plate stiffness of the web, d ｂ : Distance between the thickness centers of the first flange and the second flange, K Ｈ : Horizontal stiffening rigidity per unit length of the connecting member and the plate-like member attached to the first flange of the H-shaped cross-section member in the support structure, K Ｒ : Rotational stiffening rigidity per unit length of the connecting member and the plate-shaped member attached to the first flange of the H-shaped cross-section member in the support structure. [0010]

2. a steel H-shaped cross-section member having a first flange, a second flange, and a web that joins the first flange and the second flange to each other; a plate-like member supported by the first flange; and a connecting member that connects the first flange and the plate-like member; A method for designing a support structure for preventing lateral buckling of an H-shaped section member, in which the movement of the first flange in the thickness direction of the web and the rotation of the first flange about an axis along the longitudinal direction of the H-shaped section member are each restrained with an arbitrary rigidity, comprising: In the support structure, the horizontal stiffening rigidity K per unit length by the connecting member and the plate-like member attached to the first flange of the H-shaped cross-section member Ｈ，ｆｉｘ satisfies formula (3), and the rotational stiffening rigidity K per unit length of the connecting member and the plate-like member attached to the first flange of the H-shaped cross-section member is Ｒ，ｆｉｘ When a structure that satisfies equation (4) is defined as a fully restrained support structure, The elastic lateral buckling strength M of the H-shaped cross-section member of the fully restrained support structure ｅ，ｆｉｘ Horizontal stiffening coefficient k according to equation (5) ｈ and the rotational stiffening coefficient k according to equation (6) ｒ The elastic lateral buckling strength M of the H-shaped section member of the support structure set based on ｅ Using the reduction rate β, the elastic lateral buckling strength M ｅ How to design support structures. However, D ｗ : Plate stiffness of the web, d ｂ : Distance between the thickness centers of the first flange and the second flange, K Ｈ : Horizontal stiffening rigidity per unit length of the connecting member and the plate-like member attached to the first flange of the H-shaped cross-section member in the support structure, K Ｒ : Rotational stiffening rigidity per unit length of the connecting member and the plate-shaped member attached to the first flange of the H-shaped cross-section member in the support structure. [0025]

3. The reduction rate β is (M ｅ / M ｅ，ｆｉｘ ) value, The method for designing a support structure according to claim 1 or 2, which is obtained by equations (7) to (10). [0030]

4. a steel H-shaped cross-section member having a first flange, a second flange, and a web that joins the first flange and the second flange to each other; a plate-like member supported by the first flange; and a connecting member that connects the first flange and the plate-like member; A method for designing a support structure for preventing lateral buckling of an H-shaped section member, in which the movement of the first flange in the thickness direction of the web and the rotation of the first flange about an axis along the longitudinal direction of the H-shaped section member are each restrained with an arbitrary rigidity, comprising: In the support structure, Horizontal stiffening rigidity K per unit length by the connecting member and the plate-like member attached to the first flange of the H-shaped cross-section member Ｈ is set so as to satisfy the formula (12), Rotational stiffening rigidity K per unit length by the connecting member and the plate-like member attached to the first flange of the H-shaped cross-section member Ｒ A method for designing a support structure, in which: However, D ｗ : Plate stiffness of the web, d ｂ : The distance between the thickness centers of the first flange and the second flange. [0045]

5. a steel H-shaped cross-section member having a first flange, a second flange, and a web that joins the first flange and the second flange to each other; a plate-like member supported by the first flange; and a connecting member that connects the first flange and the plate-like member; A support structure in which the movement of the first flange in the thickness direction of the web and the rotation of the first flange about an axis along the longitudinal direction of the H-shaped section member are each restricted by a given rigidity, Horizontal stiffening rigidity K per unit length by the connecting member and the plate-like member attached to the first flange of the H-shaped cross-section member Ｈ satisfies equation (15), Rotational stiffening rigidity K per unit length by the connecting member and the plate-like member attached to the first flange of the H-shaped cross-section member Ｒ A support structure that satisfies equation (16). However, D ｗ : Plate stiffness of the web, d ｂ : The distance between the thickness centers of the first flange and the second flange. [0050]

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