Floor structure and floor structure design method

Abstract

To provide a floor structure in which lateral buckling does not occur in a steel beam.SOLUTION: A floor structure 45 comprises: a floor slab 35; and an H-shaped steel beam 25 both end portions of which are joined to a beam 15, at least one end of which is rigidly joined or semi-rigidly joined to the beam, which supports the floor slab from the below, and an upper flange 26 of which is joined to the floor slab by a shear connector 39. A length of the steel beam is longer than a calculated length L. A calculated elastic lateral buckling moment Me of the steel beam exceeds a yield moment of the steel beam.SELECTED DRAWING: Figure 2

Description

[Technical Field]

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

[0002] In the design of a sub-beam (a beam whose both ends are joined to other beams) in a steel frame, both ends or one end of the sub-beam may be rigidly or semi-rigidly joined to a main girder (a beam whose both ends are joined to columns). In this case, the bending moment acting on the cross section of the sub-beam and the deflection of the sub-beam are reduced compared to the conventional case where both ends of the sub-beam are joined with pins. This makes it possible to reduce the amount of steel used in the sub-beam by making the sub-beam thinner. In conventional cases where both ends of a sub-beam are pin-jointed, only the upper flange of the sub-beam, which is restrained by the floor slab, is compressed. Therefore, lateral buckling of the sub-beam cannot occur. In contrast, when both ends or one end of the sub-beam are rigidly or semi-rigidly joined, a region is created near the end of the sub-beam where the lower flange of the sub-beam is compressed. In this region, lateral buckling of the sub-beam can occur. In known design methods, the need for lateral buckling stiffeners is determined based on the lateral buckling strength of individual steel beams. This design method does not take into account the restraining effect of the sub-beams by the floor slab, and therefore underestimates the lateral buckling strength of the sub-beams. This makes it necessary to provide lateral buckling stiffeners to the sub-beams to prevent lateral buckling. In other words, when sub-beams are rigidly connected, lateral buckling stiffeners are required, which increases costs due to the increased steel weight and processing required for lateral buckling stiffeners.

[0003] For example, as in Patent Documents 1 to 4, design methods have been considered that omit lateral buckling stiffeners by taking into account the lateral movement of the upper flange and rotational restraint (rotational restraint of the web around the joint between the upper flange and the web) as the restraining effect of the floor slab for a large beam rigidly connected to a column. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Patent No. 5885911 [Patent Document 2] Patent No. 6699639 [Patent Document 3] Japanese Patent Application Publication No. 2015-021283 [Patent Document 4] Japanese Patent Application Publication No. 2018-131883 Summary of the Invention [Problem to be solved by the invention]

[0005] Patent documents 1 to 4 are concerned with the antisymmetric moment acting on the main beam when an earthquake force is applied, and assume different loading conditions when a bending moment distribution occurs on the sub-beam due to a vertical load, which is a long-term load.It is known that the deformation behavior due to lateral buckling of a beam is greatly affected by the loading conditions, and these design methods, which have different loading conditions, cannot be applied to the sub-beam.

[0006] Furthermore, these design methods assume that the main beam is connected to a column and that the warping at the end of the main beam is restrained. On the other hand, for sub-beams whose ends are not sufficiently restrained in warping due to their connection to the main beam, if the lateral buckling moment is evaluated assuming that the warping at the end is restrained, it will be overestimated and the design will be on the risky side. Therefore, in order to evaluate the design of sub-beams on the safe side, it is necessary to evaluate the lateral buckling moment when the warping at the end of the sub-beam is not restrained.

[0007] In Patent Documents 3 and 4, only the restraint of lateral movement of the upper flange is considered, so the boundary conditions of the upper flange are evaluated on the conservative side. However, when the sub-beam is connected to the floor slab with a shear connector, the upper flange hardly rotates, and the upper flange is restrained in both lateral movement and rotation. Therefore, to design efficiently in accordance with the actual situation of lateral buckling, it is necessary to evaluate the lateral buckling moment when the upper flange is restrained in lateral movement and rotation.

[0008] The present invention has been made in consideration of these problems, and aims to provide a floor structure in which lateral buckling does not occur in steel beams, and a design method for a floor structure that is designed to prevent lateral buckling from occurring in steel beams. [Means for solving the problem]

[0009] In order to solve the above problems, the present invention proposes the following means. The floor structure of the present invention is a floor structure comprising a floor slab and a steel beam made of H-shaped steel, both ends of which are joined to beams, at least one of which is rigidly or semi-rigidly joined to the beam, which supports the floor slab from below and has its upper flange joined to the floor slab by a shear connector, and in which the length of the steel beam is longer than the length L calculated by formula (1) and the elastic lateral buckling moment M of the steel beam calculated by formula (2) is e is characterized in that the yield moment of the steel beam exceeds the yield moment of the steel beam. where E is the Young's modulus of the steel beam, A f : cross-sectional area of ​​the upper flange and the lower flange of the steel beam, F: steel strength of the steel beam, H: beam depth of the steel beam, G: shear modulus of elasticity of the steel beam, d b : the distance between the center of thickness of the bottom flange and the top flange of the steel beam, J: the Saint-Venant torsion constant of the steel beam, J f : Saint-Venant's torsional constant of each of the upper flange and the lower flange, J w : Saint-Venant torsion constant of the web of the steel beam, I: Moment of inertia around the weak axis of the steel beam of each of the upper flange and the lower flange of the steel beam, D w : The plate stiffness of the web.

[0010]

number

[0011] The length L in formula (1) is the maximum beam length at which the allowable stress for buckling of bending members does not decrease, as determined by the Ministry of Land, Infrastructure, Transport and Tourism Notification No. 1024 of 2001, which defines special allowable stress levels and special material strengths. As a result of extensive research, the inventors have found that when the top flange of a steel beam is connected to a floor slab by a shear connector, the lateral movement of the top flange relative to the floor slab and the rotation of the top flange around the joint relative to the floor slab can be considered to be constrained. In the prior art, when the lateral movement and rotation of the top flange of a steel beam are constrained and the warping of the end of the steel beam is not constrained, the elastic lateral buckling moment M e However, after careful consideration, the inventors have found that the elastic lateral buckling moment M e In this case, the length of the steel beam is longer than the length L, and the elastic lateral buckling moment M e It was found that if the yield moment of the steel beam is greater than the yield moment of the steel beam, lateral buckling will not occur in the steel beam even if lateral buckling stiffeners are not attached to the steel beam. According to this invention, in the floor structure, the length of the steel beam is longer than the length L, and the elastic lateral buckling moment M e By exceeding the yield moment of the steel beam, lateral buckling of the steel beam can be prevented.

[0012] Another floor structure of the present invention is a floor structure comprising a floor slab, and an H-shaped steel beam having both ends joined to a beam, at least one of the ends rigidly or semi-rigidly joined to the beam, supporting the floor slab from below, and having its upper flange joined to the floor slab by a shear connector, characterized in that the length of the steel beam is longer than the length L calculated by equation (3), and the cross-sectional shape index X calculated by equation (4) is equal to or less than the threshold value A calculated by equation (5). where E is the Young's modulus of the steel beam, A f: cross-sectional area of ​​the upper flange and the lower flange of the steel beam, F: strength of the steel beam, H: thickness of the steel beam, t f : The thickness of the bottom flange and the top flange of the steel beam, t w : the thickness of the web of the steel beam, B: the width of the steel beam.

[0013]

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[0014] As a result of extensive research, the inventors have found that when the top flange of a steel beam is connected to a floor slab by a shear connector, the lateral movement of the top flange relative to the floor slab and the rotation of the top flange around the joint relative to the floor slab can be considered to be restrained. In this case, they have found that if the length of the steel beam is longer than length L and the cross-sectional shape index X is equal to or less than threshold value A, lateral buckling will not occur in the steel beam without attaching a lateral buckling stiffener to the steel beam. According to this invention, in the floor structure, the length of the steel beam is longer than the length L and the cross-sectional shape index X is equal to or smaller than the threshold value A, so that lateral buckling can be prevented from occurring in the steel beam.

[0015] Furthermore, in the floor structure, the steel beams do not need to be fitted with lateral buckling stiffeners along their entire length. According to this invention, since no lateral buckling stiffeners are attached to the steel beams, the cost required for the floor structure can be further reduced.

[0016] In addition, in the floor structure, lateral movement of the upper flange relative to the floor slab and rotation of the upper flange about the joint between the upper flange and the web relative to the floor slab may each be restricted.

[0017] The floor structure design method of the present invention is a floor structure design method for designing a floor structure comprising a floor slab and a steel beam made of H-shaped steel, both ends of which are joined to beams, at least one of which is rigidly or semi-rigidly joined to the beam, supporting the floor slab from below and having its upper flange joined to the floor slab by a shear connector, wherein the length of the steel beam is set to be longer than the length L calculated by equation (6), and the elastic lateral buckling moment M of the steel beam calculated by equation (7) is e is set to exceed the yield moment of the steel beam. where E is the Young's modulus of the steel beam, A f : cross-sectional area of ​​the upper flange and the lower flange of the steel beam, F: steel strength of the steel beam, H: beam depth of the steel beam, G: shear modulus of elasticity of the steel beam, d b : the distance between the center of thickness of the bottom flange and the top flange of the steel beam, J: the Saint-Venant torsion constant of the steel beam, J f : Saint-Venant's torsional constant of each of the upper flange and the lower flange, J w : Saint-Venant torsion constant of the web of the steel beam, I: Moment of inertia around the weak axis of the steel beam of each of the upper flange and the lower flange of the steel beam, D w : The plate stiffness of the web.

[0018]

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[0019] According to this invention, the inventors have found, as a result of extensive research, that when the top flange of a steel beam is connected to a floor slab by a shear connector, the lateral movement of the top flange relative to the floor slab and the rotation of the top flange around the joint relative to the floor slab can be considered to be restrained. In this case, the length of the steel beam is set to be longer than the length L, and the elastic lateral buckling moment M e It was found that if the yield moment of the steel beam is set to be greater than the yield moment of the steel beam, lateral buckling will not occur in the steel beam without the need for lateral buckling stiffeners. According to this invention, in the design method of a floor structure, the length of the steel beam is set to be longer than the length L, and the elastic lateral buckling moment M e By setting the value of the yield moment of the steel beam to be greater than the yield moment of the steel beam, lateral buckling can be prevented from occurring in the steel beam.

[0020] Another floor structure design method of the present invention is a floor structure design method for designing a floor structure including a floor slab, and an H-shaped steel beam having both ends joined to beams, at least one of the ends rigidly or semi-rigidly joined to the beam, supporting the floor slab from below, and having its upper flange joined to the floor slab by a shear connector, characterized in that the length of the steel beam is set to be longer than the length L calculated by equation (8), and the cross-sectional shape index X calculated by equation (9) is set to be equal to or less than the threshold value A calculated by equation (10). where E is the Young's modulus of the steel beam, A f : cross-sectional area of ​​the upper flange and the lower flange of the steel beam, F: strength of the steel beam, H: thickness of the steel beam, t f : The thickness of the bottom flange and the top flange of the steel beam, t w : the thickness of the web of the steel beam, B: the width of the steel beam.

[0021]

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[0022] As a result of extensive research, the inventors have found that when the top flange of a steel beam is connected to a floor slab by a shear connector, the lateral movement of the top flange relative to the floor slab and the rotation of the top flange around the joint relative to the floor slab can be considered to be restrained. In this case, they have found that if the length of the steel beam is set to be longer than the length L and the cross-sectional shape index X is set to be equal to or less than the threshold value A, lateral buckling will not occur in the steel beam without the need to attach a lateral buckling stiffener to the steel beam. According to this invention, in the floor structure design method, by setting the length of the steel beam to be longer than the length L and setting the cross-sectional shape index X to be equal to or less than the threshold value A, it is possible to prevent lateral buckling from occurring in the steel beam.

[0023] In the floor structure design method, the steel beams may be configured so that no lateral buckling stiffeners are attached to the entire length. According to this invention, since no lateral buckling stiffeners are attached to the steel beams, the cost required for constructing a floor structure based on a floor structure design method can be further reduced.

[0024] In addition, in the floor structure design method, the lateral movement of the upper flange relative to the floor slab and the rotation of the upper flange around the joint between the upper flange and the web relative to the floor slab may each be constrained. [Effects of the Invention]

[0025] According to the floor structure of the present invention, it is possible to prevent lateral buckling from occurring in the steel beams. Also, according to the design method of the floor structure of the present invention, it is possible to design the steel beams so that lateral buckling does not occur. [Brief explanation of the drawings]

[0026] [Figure 1] 1 is a perspective view of a building in which a floor structure according to a first embodiment of the present invention is used. [Figure 2] FIG. 2 is a cross-sectional view taken along the line A1-A1 in FIG. [Figure 3] FIG. 10 is a side view of the steel beams of the floor structure. [Figure 4] FIG. [Figure 5] FIG. [Figure 6] FIG. 10 is a cross-sectional view of the floor structure before the web and bottom flange are moved. [Figure 7] FIG. 10 is a cross-sectional view of the floor structure after the web and bottom flange have been moved. [Figure 8]FIG. 10 is a diagram showing an example of the change in the ratio of allowable bending stress to allowable tensile stress with respect to the length of a steel beam. [Figure 9] FIG. 10 is a diagram showing another example of the change in the ratio of allowable bending stress to allowable tensile stress with respect to the length of a steel beam. [Figure 10] FIG. 10 is a diagram showing an example of the change in elastic lateral buckling moment with respect to the length of a steel beam. [Figure 11] FIG. 10 is a diagram showing another example of the change in elastic lateral buckling moment with respect to the length of a steel beam. [Figure 12] FIG. 10 is a diagram showing an example of the change in elastic lateral buckling moment with respect to the length of a steel beam depending on the joining conditions and loading conditions. [Figure 13] FIG. 10 is a diagram showing another example of the change in elastic lateral buckling moment with respect to the length of a steel beam depending on the joining conditions and loading conditions. [Figure 14] FIG. 10 is a diagram showing the change in bending moment with respect to the dimensionless coordinate in the material axis direction depending on the joining conditions and loading conditions. [Figure 15] FIG. 10 is a diagram showing the change in bending moment with respect to the dimensionless coordinate in the material axis direction due to the influence of adjacent steel beams. [Figure 16] This is a diagram showing the change in elastic lateral buckling moment depending on the length of a steel beam. [Figure 17] This figure shows the change in (MFEM / My) or (Mcr,min / My) with respect to the non-dimensional lateral buckling slenderness ratio for steel beams with different cross-sectional shapes. [Figure 18] FIG. 10 is a diagram showing the change in (Mcr, min / My) relative to the cross-sectional shape index X. [Figure 19] FIG. 10 is a diagram showing the change in (MFEM / My) relative to the cross-sectional shape index X. DETAILED DESCRIPTION OF THE INVENTION

[0027] (First embodiment) A first embodiment of a floor structure according to the present invention will be described below with reference to FIGS. 1 to 17. FIG.

[0028] [1. Floor structure] The floor structure of this embodiment is used in a building 1 shown in Fig. 1. The building 1 includes a plurality of columns 10, a plurality of girders (beams) 15, steel beams 25 which are minor beams, and a floor slab 35. 1, the floor slab 35 is indicated by a two-dot chain line. The steel beams 25 and the floor slab 35 constitute a floor structure 45.

[0029] 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), CFT (Concrete Filled Steel Tube), or the like. As shown in Figures 1 and 2, for example, the girder 15 is made of H-shaped steel. The girder 15 is provided with a pair of upper and lower first upper flanges 16 and first lower flanges 17. The first upper flange 16 and the first lower flange 17 are connected to each other by a first web 18. A gusset plate 19 is joined to the first web 18 of the girder 15 by welding or the like. A joint member 20 is fixed to the gusset plate 19 on the first web 18 by welding or the like at a position corresponding to the lower end of the steel beam 25. The girder 15 is placed between adjacent columns 10 and extends in a direction along the horizontal plane. Both ends of the girder 15 are joined to the columns 10 by welding or the like. The girder 15 may be made of reinforced concrete or steel reinforced concrete.

[0030] 3 to 5, the steel beam 25 is made of H-shaped steel. The H-shaped steel is not limited to rolled H-shaped steel, and may be a welded and assembled H-shaped cross-section member. 3 and 5 schematically show a steel beam 25 joined to a main girder 15, and by applying a bending moment to the end, which is modeled as a pin, the bending moment that occurs at the end when the steel beam 25 is rigidly or semi-rigidly joined to the main girder 15 is reproduced. That is, it is assumed that the steel beam 25 is rotatable at a first end in the material axis direction z (details will be described later) but is restricted in movement, and that the steel beam 25 is rotatable at a second end in the material axis direction z but is only allowed to move in the material axis direction z.

[0031] 3 to 5, a steel beam 25 is provided with a pair of upper and lower second upper flanges (upper flange) 26 and second lower flanges (lower flange) 27. In the steel beam 25, the second upper flange 26 and the second lower flange 27 are connected to each other by a second web (web) 28. In the following, the material axis direction of steel beam 25 is defined as z. The height direction of steel beam 25 (the direction in which flanges 26, 27 face each other) is defined as y. The height direction y has joint 25a as its origin, and the downward direction is positive. The width direction of steel beam 25 (the direction perpendicular to material axis direction z and height direction y) is defined as x. The width direction x, height direction y, and material axis direction z form a right-handed Cartesian coordinate system. Here, the origin of the material axis direction z is located on the joint 25a where the second upper flange 26 and the second web 28 are joined. The steel beam 25 and the joint 25a each extend in the material axis direction z. The material axis direction z has its origin at a first end in the material axis direction of the steel beam 25, and the direction from this first end to the second end is positive. The height direction y has its origin at the joint 25a, and the downward direction is positive.

[0032] As shown in Fig. 4, in the steel beam 25, the width direction x is the strong axis (therefore, the direction of rotation about the width direction x is the axis around the strong axis), and in the steel beam 25, the height direction y is the weak axis (therefore, the direction of rotation about the height direction y is the axis around the weak axis).

[0033] Here, the dimensions of the steel beam 25 are defined. Note that, for units of length etc. described below, SI units such as "m" are preferably used for length. The length of the steel beam 25 in the material axis direction z is l(l b The depth of the steel beam 25 (beam depth) is H. The width of the steel beam 25 (length in the width direction x) is B. The thickness of each of the second upper flange 26 and the second lower flange 27 is t. f The thickness of the second web 28 is t w The distance in the height direction y between the centers of the second lower flange 27 and the second upper flange 26 of the steel beam 25 is defined as the center-to-center distance d b The cross-sectional area of ​​each of the second upper flange 26 and the second lower flange 27 taken along a plane perpendicular to the material axis direction z is defined as A f That is, the cross-sectional area of ​​the second upper flange 26 taken along a plane perpendicular to the material axis direction z is A f The same applies to the second lower flange 27. The Young's modulus of steel beam 25 is E. The steel strength (standard strength) of steel beam 25 is F. Steel strength is specified by "Notice of the Ministry of Construction No. 2464 on the standard strength of allowable stress and material strength of steel materials, etc. and welded joints."

[0034] The shear modulus of elasticity of the steel beam 25 is G. The second moment of area of ​​each of the flanges 26 and 27 about the weak axis of the steel beam 25 is I. That is, the second moment of area of ​​the second upper flange 26 about the weak axis of the steel beam 25 is I. The same applies to the second lower flange 27. The plate stiffness of the second web 28 is D. w The Saint-Venant torsional constant of the steel beam 25 is J. The Saint-Venant torsional constant of each of the second upper flange 26 and the second lower flange 27 is J. f The Saint-Venant torsional constant of the second web 28 is J w Let's say.

[0035] As shown in FIG. 2 , the steel beam 25 is placed between adjacent girders 15 and extends in a direction along the horizontal plane. Both ends of the steel beam 25 are rigidly joined to the girders 15 by welding. Specifically, the second web 28 of the steel beam 25 and the gusset plate 19 are joined to each other by fastening members 29 including high-strength bolts or the like. The second upper flange 26 is joined to the first upper flange 16 of the girder 15 by a welded joint 30 formed by welding, and the second lower flange 27 is joined to the connection member 20 joined to the girder 15 by a welded joint 31 formed by welding.

[0036] Both ends of the steel beam 25 may be semi-rigidly connected to the girder 15. Also, if one end of the steel beam 25 is rigidly or semi-rigidly connected to the girder 15, the other end may be pin-connected to the girder 15. The definitions of pin-connection, semi-rigid connection, and rigid connection are particularly in accordance with European design standards ("Eurocode 3: Design of steel structures - Parts 1-8: Design of joints", 2004, Authority: The European Union Per Regulation 305 / 2011, Directive 98 / 34 / EC, Directive 2004 / 18 / EC).

[0037] In this embodiment, the floor slab 35 is a composite deck floor slab. The floor slab 35 includes a deck plate 36 and concrete 37. The deck plate 36 is formed by bending a steel plate, etc. The deck plate 36 is disposed on the second upper flange 26 of the steel beam 25. The concrete 37 is formed in a flat plate shape with its thickness direction aligned with the vertical direction. The concrete 37 is placed on the deck plate 36. The steel beams 25 support the floor slab 35 from below. The steel beams 25 are joined to the floor slab 35 by a plurality of shear connectors 39 provided on the second upper flanges 26 of the steel beams 25. In this embodiment, headed studs are used as the shear connectors 39. The lower ends of the shear connectors 39 are fixed to the upper surfaces of the second upper flanges 26 of the steel beams 25 at intervals. The shear connectors 39 are embedded in the concrete 37 through the deck plate 36. In other words, the second upper flange 26 is joined (fastened) to the floor slab 35 by the plurality of shear connectors 39.

[0038] The floor slab 35, which is a composite deck floor slab, has high rigidity against horizontal deformation and twisting. Therefore, the upper flanges 26 of the steel beams 25 fastened to the floor slab 35 hardly move horizontally or rotate, and the upper flanges 26 can be considered to be restrained by the floor slab 35. The floor slab may be a reinforced concrete floor slab or a steel floor. In deck composite floor slabs and reinforced concrete floor slabs, reinforcing steel bars may be embedded in the concrete. A perforated steel plate dowel or the like may be used for the shear connector 39. Furthermore, if the floor slab is a composite deck floor slab or a steel floor, the welded joint between the second upper flange 26 and the deck plate 36 or the steel floor may function as the shear connector.

[0039] Next, the elastic lateral buckling moment M of steel beam 25 e and the elastic lateral buckling moment M e Hereinafter, the second upper flange 26, the second lower flange 27, and the second web 28 will also be referred to as the upper flange 26, the lower flange 27, and the web 28, respectively.

[0040] [2. Derivation of the formula for elastic lateral buckling moment] In the following, the following assumptions 1 to 5 are made for the floor structure 45. 1. The upper flange 26 is restricted from moving in the width direction x and from rotating around the material axis direction z. 2. The ends of the steel beam 25 in the direction of the material axis z are not restrained from warping. 3. The load conditions are set to a uniform bending moment that compresses the lower flange 27. 4. The intersections of the flanges 26, 27 and the web 28 remain perpendicular even after buckling. 5. The out-of-plane displacement of the lower flange 27 is given by an arbitrary function. In Assumption 1, the fact that the upper flange 26 is restrained from moving in the width direction x means that the lateral movement (movement in the width direction x) of the upper flange 26 relative to the floor slab 35 is restrained. The fact that the upper flange 26 is restrained from rotating about the material axis direction z means that the rotation of the upper flange 26 about the joint 25a relative to the floor slab 35 is restrained. In other words, even if the web 28 and the lower flange 27 move relative to the floor slab 35 from the state of the steel beam 25 shown in Figure 6 as shown in Figure 7, the upper flange 26 cannot move in the width direction x, and the upper flange 26 cannot rotate about the joint 25a. In Assumption 2, "warping is not restrained" means that flanges 26, 27 and web 28 can rotate around the height direction y at both ends of steel beam 25 in the material axis direction z shown in FIG.

[0041] The displacement function of web 28 in the thickness direction (width direction x) is defined as w. As shown in Fig. 7, the torsion angle of bottom flange 27 is defined as φ, and the out-of-plane displacement of bottom flange 27 (displacement in width direction x) is defined as u. In this case, the torsion angle φ and the displacement function w of web 28 are expressed by equations (21) and (22).

[0042]

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[0043] At this time, the movement of the upper flange 26 in the width direction x and the rotation around the material axis direction z are restricted. When a bending moment acts on both ends of the steel beam 25 as an external force, compressing the lower flange 27, the total potential energy Π of the floor structure 45 is expressed by equation (23).

[0044]

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[0045] Here, the Poisson's ratio of the steel beam 25 is ν. The elastic lateral buckling moment of the steel beam 25 is M cr The elastic lateral buckling moment M cr is a moment acting on both ends of the steel beam 25 in the material axis direction z, as shown in FIG. Let u' be the function obtained by first differentiating the out-of-plane displacement u with respect to z. Let u'' be the function obtained by second differentiating the out-of-plane displacement u with respect to z. Substituting equations (21) and (22) into equation (23), and rearranging each definite integral with constants A to C calculated from equations (24) to (26), the total potential energy Π of floor structure 45 is expressed by equation (27).

[0046]

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[0047] From the principle of minimum potential energy, equation (28) can be obtained from equation (27). Equation (28) can be transformed into equation (29).

[0048]

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[0049] From equation (29), the elastic lateral buckling moment M cr is expressed by equation (30).

[0050]

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[0051] Next, the out-of-plane displacement u of the lower flange 27 is expressed using a sine wave as in equation (31), and the equation is rearranged. Here, n represents the number of half waves of sine and is given as a positive integer.

[0052]

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[0053] The first-order and second-order differential equations of the out-of-plane displacement u of the lower flange 27 are expressed by equations (32) and (33).

[0054]

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[0055] By rearranging equations (24) to (26) using equations (31) to (33), equations (34) to (36) are obtained.

[0056]

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[0057] Substituting equations (34) to (36) into equation (30) and rearranging, the elastic lateral buckling moment M cr is expressed by equation (37).

[0058]

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[0059] Using the relationships in equations (38) to (41), equation (37) is rearranged to obtain the elastic lateral buckling moment M cr is expressed by equation (42).

[0060]

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[0061] Elastic lateral buckling moment M according to equation (42) cr depends on the number of sine half waves, n. However, the minimum value of the buckling load obtained by substituting any positive integer for n is a constant value regardless of n. The minimum value of the elastic lateral buckling moment M cr,min (Elastic lateral buckling moment M e ) is calculated using equation (43). The length of the steel beam 25 is preferably longer than the length L calculated by equation (44). The length L calculated by equation (44) is the maximum beam length at which the allowable stress for buckling of bending members does not decrease, as defined in the Ministry of Land, Infrastructure, Transport and Tourism Notification No. 1024 of 2001, which defines special allowable stresses and special material strengths. Next, the elastic lateral buckling moment M obtained as above cr We will conduct a study using the following.

[0062]

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[0063] [3. Consideration of elastic lateral buckling moment] As a known design method, the Building Standards Law Notification states that the allowable stress for buckling of bending members taking into account lateral buckling strength (hereinafter referred to as allowable bending stress) is given by equations (51) and (52). In this notification, the design is made using equation (53), which uses the larger of equations (51) and (52).

[0064]

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[0065] Figures 8 and 9 show the change in the ratio of allowable bending stress to allowable tensile stress with respect to the length of a steel beam (beam) when designed in accordance with a known design method. In Figures 8 and 9, the horizontal axis represents the length (m) of the steel beam, and the vertical axis represents the ratio of allowable bending stress to allowable tensile stress. The steel beam is made of H-shaped steel. Here, as an example of a narrow H-shaped steel cross section, the cross section is H-600x200x9x19, and the steel strength F is 235N / mm 2 An example of a medium width H-section steel is shown in Figure 8. The cross section is H-900x300x16x28, and the steel strength F is 325N / mm 2 The case is shown in Figure 9. In both cases, when the length of the steel beam exceeds about 4m, the allowable bending stress is reduced relative to the allowable tensile stress. The reduction in the allowable bending stress means that the steel beam's inherent strength is not exerted, and the cross-sectional efficiency of the steel beam decreases. This also increases the steel weight relative to the cross-sectional performance of the steel beam, leading to an increase in the cost of the steel beam.

[0066] Therefore, in general design, if the length of the steel beam is long enough to reduce the allowable bending stress, it is necessary to provide a lateral buckling stiffener to the steel beam so that the allowable bending stress does not decrease. In other words, the range in which the allowable bending stress according to Equation (52) exceeds the allowable tensile stress is the range in which lateral buckling stiffeners are not required in known design methods. The upper limit of this range, l max is given by equation (54) by transforming equation (52). A lateral buckling stiffener is a structural steel or steel plate that is arranged to connect a steel beam with a beam or other structure that is arranged parallel to the steel beam. It is a component that restrains deformation of the steel beam outside the structural plane by supporting it from outside the structural plane, such as in a perpendicular direction.

[0067]

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[0068] Upper limit value max are shown in Figures 8 and 9, respectively.

[0069] Figures 10 and 11 compare the results of eigenvalue analysis under various boundary conditions using the finite element method (FEM) with the yield moment of a steel beam. In Figures 10 and 11, the horizontal axis represents the length (m) of the steel beam, and the vertical axis represents the elastic lateral buckling moment (kNm). The cross sections of the steel beams in Figures 10 and 11 are the same two sizes as those in Figures 8 and 9. The open circle plots (marks) correspond to cases where the design is based on a known design method. This plot represents the elastic lateral buckling moment of a steel beam with no restraint on the upper flange, when a constant bending moment acts on the lower flange in compression. In Figures 10 and 11, the steel strength F is 235, 325, and 385 N / mm 2 Yield moment M of steel beam in the case y Shows.

[0070] The filled rectangular plot corresponds to the floor structure and the case designed by the floor structure design method (hereinafter simply referred to as the design method). This plot represents the elastic lateral buckling moment of a steel beam when a uniform bending moment acts on the bottom flange in compression and the lateral movement and rotation of the top flange are restrained. From Figures 10 and 11, the open circle plots indicate that the elastic lateral buckling moment is very small, and unless the steel beam is extremely short, the elastic lateral buckling moment will not exceed the yield moment M y It can be seen that it does not exceed On the other hand, the filled square plots have a higher elastic lateral buckling moment than the open circle plots. In the filled square plots, even when the steel beam is long, the elastic lateral buckling moment is higher than the yield moment M y It exceeds.

[0071] Figures 12 and 13 show the results of an eigenvalue analysis using FEM to examine the effects of the connection conditions and loading conditions at the end of the steel beam on the elastic lateral buckling moment when the lateral movement and rotation of the top flange are restrained. In Figures 12 and 13, the horizontal axis represents the length (m) of the steel beam, and the vertical axis represents the elastic lateral buckling moment (kNm). Here, we consider various joint conditions and loading conditions assumed for steel beams, which are sub-beams, as shown in the bending moment distribution in Figure 14. In Figure 14, the horizontal axis represents the non-dimensional coordinate in the material axis direction of the steel beam, and the vertical axis represents the bending moment. The part of the non-dimensional coordinate where 0 is the first end of the steel beam, and the part of the non-dimensional coordinate where 1 is the second end of the steel beam. Among the various connection and loading conditions, when both ends of a steel beam are rigidly connected and an equal bending moment acts on the steel beam, the bending moment is largest in the area where the lower flange is compressed, making lateral buckling more likely to occur.

[0072] As shown in Figures 12 and 13, the elastic lateral buckling moment varies depending on the connection conditions at the ends of the steel beam and the load conditions acting on the steel beam. The elastic lateral buckling moment is smallest and falls under the most severe conditions when both ends of the steel beam are rigidly connected and a uniform bending moment is applied in compression to the bottom flange. Even under other conditions, the elastic lateral buckling moment decreases as the length of the steel beam increases, and gradually approaches the elastic lateral buckling moment when a uniform bending moment is applied. Furthermore, in rigidly or semi-rigidly connected steel beams (sub-beams), the bending moment distribution of the steel beams changes depending on the rigidity and loading conditions of the adjacent steel beams sandwiching the main girder. Figure 15 shows the bending moment distribution of rigidly connected steel beams when the influence of adjacent steel beams is assumed. In Figure 15, the horizontal axis represents the non-dimensional coordinate in the material axis direction of the steel beam, and the vertical axis represents the bending moment. When the frame and loading conditions are uniform (in the case of uniform bending), the maximum bending moment is 2 at the ends and 1 at the center. On the other hand, when the rigidity or loading conditions of adjacent steel beams are different (in the case of non-uniform frame), the bending moment distribution can be close to uniform bending, with the bottom flange being compressed.

[0073] From the above, the elastic lateral buckling moment of a steel beam with rigid or semi-rigid joints at both ends can be evaluated safely regardless of the joint conditions or loading conditions at the ends by assuming a bending moment such as compression of the bottom flange. In this case, there is no need to consider the influence of adjacent steel beams, making the design method simple. In addition, by assuming equal bending as a loading condition, a safe evaluation can be given to steel beams with pin joints at both ends when the bottom flange is compressed.

[0074] Figure 16 shows the results of a comparison between the results of eigenvalue analysis using FEM and the elastic lateral buckling moment calculated in this embodiment. In Figure 16, the horizontal axis represents the length (m) of the steel beam, and the vertical axis represents the elastic lateral buckling moment (kNm). Here, a steel beam with a cross section of H-600x200x9x19 is considered. The elastic lateral buckling moment M cr was calculated from the above formula (42). In formula (42), the elastic lateral buckling moment when the number of half waves n is 1 to 10 is shown by thin dotted lines in Figure 16. The elastic lateral buckling moment M cr is the minimum value of the elastic lateral buckling moment calculated according to the number n of half waves, and is shown by a thick solid line in Figure 16. The minimum value M of the elastic lateral buckling moment calculated by the above equation (43) cr,min is shown by a thick dotted line in Fig. 16. In Fig. 16, the results of eigenvalue analysis by FEM (elastic lateral buckling moment M FEM ) are indicated by open circle plot marks. The elastic lateral buckling moment M according to the above equation (42) cr shows a good correspondence with the eigenvalue analysis results. The minimum elastic lateral buckling moment M cr,min accurately captures the lower limit of the eigenvalue analysis results.

[0075] Figure 17 shows the results of comparing the evaluation method using the minimum value of the elastic lateral buckling moment according to the present invention with the analysis results by FEM. In Figure 17, the horizontal axis is the non-dimensional lateral buckling slenderness ratio (√(M y / M cr,min )) values, and the vertical axis represents (M FEM / M y ) or (M cr,min / M y ) represents the minimum elastic lateral buckling moment M cr,min was calculated using equation (43). The elastic lateral buckling moment M FEM The value is the minimum value for each cross section obtained from the eigenvalue analysis results using FEM. The more the white circle plots overlap with the solid line, the greater the elastic lateral buckling moment M crThis means that the value has high accuracy. The steel beams examined here are approximately 300 sizes, with depths ranging from 400mm to 1000mm. For each size, the value (l / H) obtained by dividing the length l of the steel beam by the beam depth H was varied from 6 to 50. From FIG. 17, it can be seen that the design method of this embodiment can design steel beams of any cross-sectional size with extremely high accuracy.

[0076] From the above, if the upper flange of a steel beam is restrained from lateral movement and rotation by a floor slab, etc., the elastic lateral buckling moment M calculated by Eq. (43) can be applied to steel beams that require lateral buckling stiffeners in conventional designs. e (Minimum value of elastic lateral buckling moment M cr,min ) is the yield moment of the steel beam M y If the strength exceeds this value, lateral buckling will not occur, and it is possible to omit the lateral buckling stiffeners that were previously required. In this case, the steel beams are not fitted with lateral buckling stiffeners along their entire length.

[0077] In the design method of this embodiment, the restraint member is set to the floor slab 35, and the floor structure 45 is designed. In the design method, the length of the steel beam 25 is set to be longer than the length L calculated by the above formula (44). The elastic lateral buckling moment M calculated by the formula (43) e The yield moment M of the steel beam 25 y In this case, the steel beam 25 is set so that no lateral buckling stiffener is attached to the entire length.

[0078] As explained above, according to the floor structure 45 of this embodiment, the inventors have found, as a result of careful consideration, that when the second upper flange 26 of the steel beam 25 is joined to the floor slab 35 by the shear connector 39, it can be considered that the lateral movement of the second upper flange 26 relative to the floor slab 35 and the rotation of the second upper flange 26 around the joint 25a relative to the floor slab 35 are both constrained. In this case, if the length of the steel beam 25 is longer than the length L calculated by equation (44), and the elastic lateral buckling moment M e is the yield moment M of the steel beam 25 y It was found that if the load exceeds this value, lateral buckling will not occur in the steel beam 25 without attaching a lateral buckling stiffener to the steel beam 25. According to this invention, in the floor structure 45, the length of the steel beam 25 is longer than the length L, and the elastic lateral buckling moment M e is the yield moment M of the steel beam 25 y By exceeding this value, lateral buckling of the steel beam 25 can be prevented.

[0079] Furthermore, according to the design method of this embodiment, the inventors have found, as a result of careful consideration, that when the second upper flange 26 of the steel beam 25 is joined to the floor slab 35 by the shear connector 39, it can be considered that the lateral movement of the second upper flange 26 relative to the floor slab 35 and the rotation of the second upper flange 26 around the joint 25a relative to the floor slab 35 are both constrained. In this case, the length of the steel beam 25 is set to be longer than the length L calculated by equation (44), and the elastic lateral buckling moment M e is the yield moment M of the steel beam 25 y It has been found that if the bending moment is set to be greater than 100%, lateral buckling will not occur in the steel beam 25 without the need to attach a lateral buckling stiffener to the steel beam 25. According to this invention, in the design method, the length of the steel beam 25 is set to be longer than the length L, and the elastic lateral buckling moment M e is the yield moment M of the steel beam 25 y By setting the value to be greater than , lateral buckling of the steel beam 25 can be prevented.

[0080] No lateral buckling stiffeners are attached to the entire length of the steel beams 25. Since no lateral buckling stiffeners are attached to the steel beams 25, the cost required for the floor structure 45 can be further reduced. Generally, floor slabs have sufficiently higher rigidity against horizontal displacement and torsion than steel beams. By joining the steel beam 25 to the floor slab 35, the lateral movement of the second upper flange 26 relative to the floor slab 35 and the rotation of the second web 28 around the joint 25a relative to the floor slab 35 can be more reliably restrained.

[0081] In the design method, the steel beams 25 are set so that no lateral buckling stiffeners are attached along their entire length. Because no lateral buckling stiffeners are attached to the steel beams 25, the cost required for constructing the floor structure 45 based on the design method can be further reduced.

[0082] (Second embodiment) Next, a second embodiment of the present invention will be described with reference to FIGS. The basic configuration of the floor structure 45 of this embodiment is the same as that of the first embodiment. The length of the steel beam 25 is preferably longer than the length L calculated by the above formula (44).

[0083] [4. Consideration of cross-sectional shape index] In this embodiment, the floor structure 45 is subjected to an elastic lateral buckling moment M e and the yield moment M of steel beam 25 y Instead of the relationship, the cross-sectional shape index X calculated by the formula (61) and the threshold value A calculated by the formula (62) were examined.

[0084]

number

[0085] Figure 18 shows the minimum elastic lateral buckling moment M cr,min and the yield moment M y18 shows the relationship between the ratio of the cross-sectional shape index X and the cross-sectional shape index X. In FIG. 18, the horizontal axis represents the cross-sectional shape index X, and the vertical axis represents the cross-sectional shape index X (M cr,min / M y The steel beams considered here are approximately size 600, with depths ranging from 400mm to 1000mm. Figure 19 shows the minimum value M for each cross section of the eigenvalue analysis results by FEM. FEM and the yield moment M y 19 shows the relationship between the ratio of the cross-sectional shape index X and the cross-sectional shape index X. In FIG. 19, the horizontal axis represents the cross-sectional shape index X, and the vertical axis represents the cross-sectional shape index X (M FEM / M y The steel beams considered here are approximately 270 sizes, with depths ranging from 400mm to 1000mm. The solid lines in each figure are lines that envelop the lower limits for each strength of the steel beam. These lines are expressed by equation (63), and in both figures, it can be seen that the elastic lateral buckling moment is accurately approximated to the safe side.

[0086]

number

[0087] If the left side of equation (63) is changed to 1, the minimum value of the elastic lateral buckling moment M cr,min is the yield moment M y The threshold value of the cross-sectional shape index X that exceeds this is given by equation (62). From Figures 18 and 19, the strength of the steel is 235N / mm 2 In the case of a steel beam, if the cross-sectional shape index X is approximately 164 or less, the elastic lateral buckling moment will be greater than the yield moment, and lateral buckling will not occur under any load conditions. 2 In the case of a steel beam with a cross-sectional shape index X of approximately 124 or less, the steel strength is 385N / mm 2 The same applies to steel beams with a cross-sectional shape index X of approximately 107 or less. These cross-sectional shape indices X are expressed for any steel strength in the form of equation (62). In the floor structure 45, the cross-sectional shape index X is equal to or smaller than the threshold value A. In the design method of this embodiment, the cross-sectional shape index X is set to a value equal to or smaller than the threshold value A.

[0088] By using this cross-sectional shape index X, it is possible to evaluate very simply and with sufficient accuracy the elastic lateral buckling moment when the upper flange of a steel beam is continuously restrained from lateral movement and rotation by a floor slab, etc. It is possible to easily evaluate the occurrence of lateral buckling for each steel strength and the need for lateral buckling stiffeners for any steel beam cross-sectional dimensions.

[0089] As described above, the floor structure 45 of this embodiment can prevent lateral buckling from occurring in the steel beams 25. Furthermore, the design method of this embodiment can design the steel beams 25 so that lateral buckling does not occur. Furthermore, as a result of extensive research, the inventors have found that when the second upper flange 26 of the steel beam 25 is joined to the floor slab 35 by the shear connector 39, it can be considered that the lateral movement of the second upper flange 26 relative to the floor slab 35 and the rotation of the second upper flange 26 around the joint 25a relative to the floor slab 35 are both constrained. In this case, they have found that if the length of the steel beam 25 is longer than the length L calculated by equation (44) and the cross-sectional shape index X is equal to or less than the threshold value A, lateral buckling will not occur in the steel beam 25 without attaching a lateral buckling stiffener to the steel beam 25. According to this invention, in the floor structure 45, the length of the steel beams 25 is longer than the length L, and the cross-sectional shape index X is equal to or smaller than the threshold value A, so that lateral buckling of the steel beams 25 can be prevented.

[0090] Furthermore, according to the design method of this embodiment, the inventors have found, as a result of careful consideration, that when the second upper flange 26 of the steel beam 25 is joined to the floor slab 35 by the shear connector 39, it can be considered that the lateral movement of the second upper flange 26 relative to the floor slab 35 and the rotation of the second upper flange 26 around the joint 25a relative to the floor slab 35 are both constrained. In this case, it has been found that lateral buckling does not occur in the steel beam 25 without attaching a lateral buckling stiffener to the steel beam 25 if the length of the steel beam 25 is set to be longer than the length L calculated by equation (44) and the cross-sectional shape index X is set to be equal to or less than the threshold value A. According to this invention, in the design method, by setting the length of the steel beam 25 to be longer than the length L and setting the cross-sectional shape index X to be equal to or less than the threshold value A, it is possible to prevent lateral buckling from occurring in the steel beam 25.

[0091] Although the first and second embodiments of the present invention have been described above in detail with reference to the drawings, the specific configurations are not limited to these embodiments, and the present invention also includes modifications, combinations, deletions, etc. of the configurations within the scope of the gist of the present invention. Furthermore, it goes without saying that the configurations shown in each embodiment can be used in appropriate combinations. [Explanation of symbols]

[0092] 15 Large beam (beam) 25 Steel beams 25a joint 26 Second upper flange (upper flange) 27 Second lower flange (lower flange) 28 Second Web (Web) 35 Floor slab 39 Shear Connector 45 Floor structure

Claims

1. Floor slab and An H-shaped steel beam whose both ends are joined to the beam, at least one of the ends is rigidly joined to the beam, supports the floor slab from below, and has its upper flange joined to the floor slab by a shear connector; A floor structure comprising: The length of the steel beam is longer than the length L calculated by equation (1), (2) The elastic lateral buckling moment M of the steel beam calculated by the formula ｅ However, the floor structure exceeds the yield moment of the steel beam. where E is the Young's modulus of the steel beam, A ｆ : cross-sectional area of ​​the upper flange and the lower flange of the steel beam, F: steel strength of the steel beam, H: thickness of the steel beam, G: shear modulus of elasticity of the steel beam, d ｂ : the distance between the thickness centers of the lower flange and the upper flange of the steel beam, J: the Saint-Venant torsion constant of the steel beam, J ｆ : Saint-Venant's torsional constant of each of the upper flange and the lower flange, J ｗ : Saint-Venant torsion constant of the web of the steel beam, I: moment of inertia of the area around the weak axis of the steel beam of each of the upper flange and the lower flange of the steel beam, D ｗ : The plate stiffness of the web. [Equation 1]

2. Floor slab and An H-shaped steel beam whose both ends are joined to the beam, at least one of the ends is rigidly joined to the beam, supports the floor slab from below, and has its upper flange joined to the floor slab by a shear connector; A floor structure comprising: The length of the steel beam is longer than the length L calculated by equation (3), A floor structure in which the cross-sectional shape index X calculated by equation (4) is equal to or less than the threshold value A calculated by equation (5). where E is the Young's modulus of the steel beam, A ｆ : cross-sectional area of ​​the upper flange and the lower flange of the steel beam, F: steel strength of the steel beam, H: thickness of the steel beam, t ｆ : the thickness of the lower flange and the upper flange of the steel beam, t ｗ : the thickness of the web of the steel beam, B: the width of the steel beam. [Equation 2]

3. 3. The floor structure according to claim 1, wherein no lateral buckling stiffeners are attached to the steel beams over their entire length.

4. 4. The floor structure according to claim 1, wherein the lateral movement of the upper flange relative to the floor slab and the rotation of the upper flange about the joint between the upper flange and the web relative to the floor slab are each restricted.

5. Floor slab and An H-shaped steel beam whose both ends are joined to the beam, at least one of the ends is rigidly or semi-rigidly joined to the beam, supports the floor slab from below, and has its upper flange joined to the floor slab by a shear connector; A floor structure design method for designing a floor structure comprising: The length of the steel beam is set to be longer than the length L calculated by equation (6), The elastic lateral buckling moment M of the steel beam calculated by the formula (7) ｅ is set to exceed the yield moment of the steel beam. where E is the Young's modulus of the steel beam, A ｆ : cross-sectional area of ​​the upper flange and the lower flange of the steel beam, F: steel strength of the steel beam, H: thickness of the steel beam, G: shear modulus of elasticity of the steel beam, d ｂ : the distance between the thickness centers of the lower flange and the upper flange of the steel beam, J: the Saint-Venant torsion constant of the steel beam, J ｆ : Saint-Venant's torsional constant of each of the upper flange and the lower flange, J ｗ : Saint-Venant torsion constant of the web of the steel beam, I: moment of inertia of the area around the weak axis of the steel beam of each of the upper flange and the lower flange of the steel beam, D ｗ : The plate stiffness of the web. [Equation 3]

6. Floor slab and An H-shaped steel beam whose both ends are joined to the beam, at least one of the ends is rigidly or semi-rigidly joined to the beam, supports the floor slab from below, and has its upper flange joined to the floor slab by a shear connector; A floor structure design method for designing a floor structure comprising: The length of the steel beam is set to be longer than the length L calculated by equation (8), A method for designing a floor structure, in which a cross-sectional shape index X calculated by equation (9) is set to be equal to or less than a threshold value A calculated by equation (10). where E is the Young's modulus of the steel beam, A ｆ : cross-sectional area of ​​the upper flange and the lower flange of the steel beam, F: steel strength of the steel beam, H: thickness of the steel beam, t ｆ : the thickness of the lower flange and the upper flange of the steel beam, t ｗ : the thickness of the web of the steel beam, B: the width of the steel beam. [Equation 4]

7. 7. The floor structure design method according to claim 5, wherein the steel beams are set so that no lateral buckling stiffeners are attached to the entire length of the beams.

8. A floor structure design method according to any one of claims 5 to 7, wherein the lateral movement of the upper flange relative to the floor slab and the rotation of the upper flange about the joint between the upper flange and the web relative to the floor slab are each restricted.

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