JP2022144692A - Floor structure, and design method of floor structure - Google Patents

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

The present invention relates to a floor structure and a floor structure design method.

In the design of small steel beams (beams that are joined to other beams at both ends), both ends or one end of the small beams is rigidly connected to a large beam (beam that is joined to columns at both ends). Or it may be semi-rigidly joined. In this case, the bending moment acting on the cross section of the small beam and the deflection of the small beam are reduced compared to the conventional case where both ends of the small beam are joined with pins. Therefore, it is possible to reduce the amount of steel used for the small beams by making the small beams thinner.
When both ends of a small beam are joined with pins as in the conventional method, only the upper flange of the small beam restrained by the floor slab is compressed. Therefore, lateral buckling cannot occur in the small beam. On the other hand, when both ends or one end of the small beam is rigidly joined or semi-rigidly joined, a region in which the lower flange of the small beam is compressed occurs in the vicinity of the end of the small beam. Lateral buckling of the girders can occur in this region.
In a known design method, the necessity of lateral buckling stiffeners is determined based on the lateral buckling strength of a single steel beam. Since this design method does not take into consideration the restraint effect of the small beams by the floor slab, the lateral buckling capacity of the small beams is underestimated. This makes it necessary to provide lateral buckling stiffeners in the small beams in order to prevent lateral buckling. That is, when a small beam is to be rigidly joined, it is necessary to provide a lateral buckling stiffener, which increases the steel weight and processing, resulting in increased costs.

For example, as in Patent Documents 1 to 4, lateral movement of the upper flange and rotational constraint (rotational constraint of the web around the joint between the upper flange and the web) as a constraint effect of the floor slab for a large beam rigidly connected to a column ), a design method that omits lateral buckling stiffeners is being studied.

Japanese Patent No. 5885911 Japanese Patent No. 6699639 JP 2015-021283 A JP 2018-131883 A

Patent Documents 1 to 4 deal with the inversely symmetrical moment that acts on the large beam when seismic force acts on it, and when the bending moment distribution due to the vertical load, which is a long-term load, occurs on the small beam, the assumed load conditions are different. . It is known that deformation behavior due to lateral buckling of beams is greatly affected by loading conditions, and these design methods with different loading conditions cannot be applied to small beams.

Moreover, in these design methods, on the premise that the girders are joined to the columns, it is assumed that the warp at the ends of the girders is restrained. On the other hand, in small beams where the warpage is not sufficiently restrained because the ends are joined to the large beam, if the lateral buckling moment is evaluated assuming that the warpage of the ends is restrained, the estimate will be overestimated and the design will be on the dangerous side. . Therefore, it is necessary to evaluate the lateral buckling moment in the state where the warp at the end of the small beam is not constrained in order to evaluate the design of the small beam on the safe side.

In Patent Documents 3 and 4, only the lateral movement constraint of the upper flange is taken into account, so the boundary conditions of the upper flange are evaluated on the safe side. However, when the girders are joined to the floor slab with shear connectors, the upper flange hardly rotates, and the lateral movement and rotation of the upper flange are restrained. For this reason, it is necessary to evaluate the lateral buckling moment in the state where the lateral movement and rotation of the upper flange are constrained in order to make an efficient design that conforms to the actual situation of lateral buckling.

The present invention has been made in view of such problems, and provides a floor structure in which lateral buckling does not occur in steel beams, and a method of designing a floor structure in which lateral buckling does not occur in steel beams. intended to

In order to solve the above problems, the present invention proposes the following means.
The floor structure of the present invention includes a floor slab, both ends of which are joined to beams, at least one of the ends of which is rigidly or semi-rigidly joined to the beam, and which supports the floor slab from below. and a steel frame beam made of H-shaped steel having an upper flange joined to the floor slab by a shear connector, wherein the length of the steel frame beam is less than the length L calculated by the formula (1) is long, and the elastic lateral buckling moment M _e of the steel beam calculated by the formula (2) exceeds the yield moment of the steel beam.
However, E: Young's modulus of the steel beam, A _f : Cross-sectional area of each of the upper flange and the lower flange of the steel beam, F: Steel material strength of the steel beam, H: Beam thickness of the steel beam, G: The above Shear elastic modulus of the steel beam, d _b : distance between plate thickness centers of the lower flange and the upper flange of the steel beam, J: Saint-Benant torsion constant of the steel beam, J _f : the upper flange and the lower flange Saint-Venin torsion constant of each flange, J _w : Saint-Venin torsion constant of the web of the steel beam, I: cross section around the weak axis of the steel beam of each of the upper flange and the lower flange of the steel beam Second moment, D _w : the plate stiffness of the web.

(1) The length L according to the formula is the reduction of the allowable stress for buckling of the bending material in the matter of determining the special allowable stress and special material strength according to the Ministry of Land, Infrastructure, Transport and Tourism's notification No. 13, National Notification No. 1024. is the maximum beam length that does not occur.
As a result of intensive studies, the inventors found that when the upper flange of the steel frame beam is joined to the floor slab by a shear connector, the lateral movement of the upper flange with respect to the floor slab and the movement of the upper flange around the joint with the floor slab We have found that each rotation can be regarded as constrained. With the conventional technology, it was not possible to evaluate the elastic lateral buckling moment M _e when the lateral movement and rotation of the upper flange of the steel beam were constrained and the warpage at the end of the steel beam was not constrained. rice field. However, as a result of intensive studies, the inventors found that the elastic lateral buckling moment M _e when the lateral movement and rotation of the upper flange of the steel beam are constrained and the warpage of the end of the steel beam is not constrained. It was found that evaluation can be performed with high accuracy. In this case, if the length of the steel beam is longer than the length L, and the elastic lateral buckling moment M _e exceeds the yield moment of the steel beam, then even if the lateral buckling stiffener is not attached to the steel beam, It was found that lateral buckling does not occur in steel beams.
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 exceeds the yield moment of the steel beam so that lateral buckling does not occur in the steel beam. can do.

Another floor structure of the present invention includes a floor slab, both ends of which are joined to beams, at least one end of which is rigidly or semi-rigidly joined to the beam, and the floor slab is supported from below. and a steel beam made of H-shaped steel whose upper flange is joined to the floor slab by a shear connector, wherein the length of the steel beam is calculated by equation (3) It is longer than the length L, and the cross-sectional shape index X calculated by the formula (4) is equal to or less than the threshold value A calculated by the formula (5).
However, E: Young's modulus of the steel beam, A _f : Cross-sectional area of each of the upper flange and the lower flange of the steel beam, F: Steel material strength of the steel beam, H: Due to the steel beam, t _f : The above Thicknesses of the lower flange of the steel beam and the upper flange, respectively, _tw : thickness of the web of the steel beam, B: width of the steel beam.

As a result of intensive studies, the inventors found that when the upper flange of the steel frame beam is joined to the floor slab by a shear connector, the lateral movement of the upper flange with respect to the floor slab and the movement of the upper flange around the joint with the floor slab We have found that each rotation can be regarded as constrained. In this case, if the length of the steel beam is longer than the length L and the cross-sectional shape index X is equal to or less than the threshold value A, the steel beam is laterally buckled without attaching a lateral buckling stiffener to the steel beam. did not occur.
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 less than the threshold value A, so that lateral buckling of the steel beam can be prevented. .

Further, in the floor structure, the steel beams may not be provided with lateral buckling stiffeners over the entire length.
According to this invention, since no lateral buckling stiffener is attached to the steel frame beam, the cost required for the floor structure can be further reduced.

Further, in the floor structure, lateral movement of the upper flange relative to the floor slab and rotation of the upper flange relative to the floor slab about the junction of the upper flange and the web may be constrained.

The method for designing a floor structure of the present invention includes a floor slab, both ends of which are joined to beams, at least one end of which is rigidly or semi-rigidly joined to the beam, and the floor slab is attached from below. H-section steel steel beams having upper flanges joined to the floor slab by shear connectors, wherein the length of the steel beams is , (6) is set longer than the length L calculated by the formula (7), and the elastic lateral buckling moment M _e of the steel beam calculated by the formula (7) is set to exceed the yield moment of the steel beam. It is characterized by
However, E: Young's modulus of the steel beam, A _f : Cross-sectional area of each of the upper flange and the lower flange of the steel beam, F: Steel material strength of the steel beam, H: Beam thickness of the steel beam, G: The above Shear elastic modulus of the steel beam, d _b : distance between plate thickness centers of the lower flange and the upper flange of the steel beam, J: Saint-Benant torsion constant of the steel beam, J _f : the upper flange and the lower flange Saint-Venin torsion constant of each flange, J _w : Saint-Venin torsion constant of the web of the steel beam, I: cross section around the weak axis of the steel beam of each of the upper flange and the lower flange of the steel beam Second moment, D _w : the plate stiffness of the web.

According to this invention, as a result of extensive studies, the inventors found that when the upper flange of the steel beam is joined to the floor slab by a shear connector, the lateral movement of the upper flange with respect to the floor slab and the joining to the floor slab We have found that the rotation of the upper flange around the joint can be regarded as constrained, respectively. In this case, if the length of the steel frame beam is set longer than the length L and the elastic lateral buckling moment M _e is set to exceed the yield moment of the steel frame beam, the steel frame beam is provided with a lateral buckling stiffener. It was found that lateral buckling does not occur in the steel beam without installing the
According to this invention, in the floor structure design method, the length of the steel frame beam is set longer than the length L, and the elastic lateral _buckling moment Me is set to exceed the yield moment of the steel frame beam. The beam can be prevented from lateral buckling.

Another method of designing a floor structure of the present invention includes a floor slab, both ends of which are joined to beams, at least one end of which is rigidly or semi-rigidly joined to the beam, and the floor slab. H-section steel steel beams supported from below and whose upper flanges are joined to the floor slab by shear connectors, wherein the length of the steel beams is set longer than the length L calculated by the formula (8), and the cross-sectional shape index X calculated by the formula (9) is set to be equal to or less than the threshold value A calculated by the formula (10). Characterized by
However, E: Young's modulus of the steel beam, A _f : Cross-sectional area of each of the upper flange and the lower flange of the steel beam, F: Steel material strength of the steel beam, H: Due to the steel beam, t _f : The above Thicknesses of the lower flange of the steel beam and the upper flange, respectively, _tw : thickness of the web of the steel beam, B: width of the steel beam.

As a result of intensive studies, the inventors found that when the upper flange of the steel frame beam is joined to the floor slab by a shear connector, the lateral movement of the upper flange with respect to the floor slab and the movement of the upper flange around the joint with the floor slab We have found that each rotation can be regarded as constrained. In this case, if the length of the steel frame beam is set 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, the steel frame beam can be obtained without attaching a lateral buckling stiffener to the steel frame beam. It was found that lateral buckling does not occur in
According to the present invention, in the floor structure design method, the length of the steel beam is set 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, so that lateral buckling does not occur in the steel beam. can be made

Further, in the method for designing a floor structure, the steel frame beam may be set so that the lateral buckling stiffener is not attached over the entire length.
According to this invention, since the lateral buckling stiffener is not attached to the steel frame beam, the cost required for the floor structure constructed based on the floor structure design method can be further reduced.

Further, in the floor structure design method, lateral movement of the upper flange with respect to the floor slab and rotation of the upper flange with respect to the floor slab about a joint between the upper flange and the web are constrained. good too.

According to the floor structure of the present invention, lateral buckling can be prevented from occurring in the steel beams. Further, according to the floor structure design method of the present invention, it is possible to design so that lateral buckling does not occur in the steel beams.

1 is a perspective view of a building in which the floor structure of the first embodiment of the invention is used; FIG. 2 is a cross-sectional view taken along a cutting line A1-A1 in FIG. 1; FIG. It is a side view of the steel frame beam of the same floor structure. It is a front view of the same steel beam. It is a top view of the same steel beam. FIG. 4 is a cross-sectional view of the same floor structure before the web and lower flange move; FIG. 4 is a cross-sectional view of the same floor structure after the web and lower flange have been moved; FIG. 4 is a diagram showing an example of change in the ratio of allowable bending stress to allowable tensile stress with respect to the length of a steel frame beam; FIG. 5 is a diagram showing another example of change in the ratio of allowable bending stress and allowable tensile stress with respect to the length of a steel frame beam; FIG. 4 is a diagram showing an example of change in elastic lateral buckling moment with respect to the length of a steel beam; FIG. 5 is a diagram showing another example of change in elastic lateral buckling moment with respect to the length of a steel beam; FIG. 4 is a diagram showing an example of changes in elastic lateral buckling moment with respect to the length of a steel beam due to joining conditions and load conditions; FIG. 5 is a diagram showing another example of changes in elastic lateral buckling moment with respect to the length of steel beams, depending on joint conditions and load conditions; FIG. 4 is a diagram showing changes in bending moment with respect to non-dimensional coordinates in the material axial direction, depending on joining conditions and load conditions. FIG. 4 is a diagram showing changes in bending moment with respect to dimensionless coordinates in the material axis direction due to the influence of adjacent steel beams. FIG. 4 is a diagram showing changes in elastic lateral buckling moment according to the length of a steel frame beam; FIG. 4 is a diagram showing the change of (M _FEM /M _y ) or (M _cr,min /M _y ) with respect to the dimensionless lateral buckling slenderness ratio for steel beams with different cross-sectional shapes. 4 is a diagram showing changes in (M _{cr, min} /M _y ) with respect to cross-sectional shape index X; FIG. 4 is a diagram showing changes in (M _FEM /M _y ) with respect to the cross-sectional shape index X; FIG.

(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.

[1. Configuration of floor structure]
The floor structure of this embodiment is used in a building 1 shown in FIG. The building 1 includes a plurality of columns 10 , a plurality of large beams (beams) 15 , steel beams 25 which are small beams, and a floor slab 35 .
In addition, in FIG. 1, the floor slab 35 is indicated by a two-dot chain line. A floor structure 45 is composed of the steel beams 25 and the floor slab 35 .

The pillar 10 extends along the vertical direction. The multiple pillars 10 are spaced apart from each other. The column 10 is made of steel, RC (Reinforced Concrete), SRC (Steel Reinforced Concrete), CFT (Concrete Filled Steel Tube), or the like.
As shown in FIGS. 1 and 2, for example, the girders 15 are made of H-beam steel. The girders 15 are provided with a pair of first upper flanges 16 and first lower flanges 17 . In the girders 15 , a first upper flange 16 and a 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 and the like of the girders 15 by welding or the like. A connection member 20 is fixed to the gusset plate 19 of the first web 18 by welding or the like at a position corresponding to the lower end of the steel beam 25 .
The girders 15 span between the adjacent pillars 10 and extend in a direction along the horizontal plane. Both ends of the girders 15 are joined to the columns 10 by welding or the like.
The girders 15 may be made of RC or SRC.

As shown in FIGS. 3 to 5, the steel beams 25 are made of H-shaped steel. The H-section steel is not limited to the rolled H-section steel, and may be a welded assembly H-section member.
3 and 5 schematically show the steel beam 25 joined to the girders 15. By applying a bending moment to the ends modeled as pins, the steel beams 25 are attached to the girders 15. It reproduces the bending moment that occurs at the ends when rigid or semi-rigid joints are applied. That is, the steel beam 25 is rotatable at the first end in the material axial direction z (details will be described later), but its movement is constrained, and it is rotatable at the second end in the material axial direction z, but movement is limited in the material axial direction. Assume that only z is possible.

As shown in FIGS. 3 to 5 , the steel beam 25 is provided with a pair of upper and lower second upper flanges (upper flanges) 26 and second lower flanges (lower flanges) 27 . In the steel beam 25 , a second upper flange 26 and a second lower flange 27 are connected to each other by a second web (web) 28 .
Below, the material axis direction of the steel beam 25 is defined as z. The height direction of the steel beam 25 (the direction in which the flanges 26 and 27 face each other) is defined as y. In the height direction y, the downward direction is positive with the joint portion 25a as the origin. The width direction of the steel beam 25 (the direction orthogonal to the material axial direction z and the height direction y) is defined as x. The width direction x, height direction y, and material axial direction z constitute a right-handed orthogonal coordinate system.
Here, the origin of the material axial direction z is located on the joint 25a where the second upper flange 26 and the second web 28 are joined. The steel beams 25 and the joints 25a each extend in the material axial direction z. With respect to the material axial direction z, the direction from the first end of the steel frame beam 25 in the material axial direction to the second end is positive. In the height direction y, the downward direction is positive with the joint portion 25a as the origin.

As shown in FIG. 4, in the steel frame beam 25, the width direction x is the strong axis (therefore, the direction of rotation about the width direction x is around the strong axis). In the steel beam 25, the height direction y is the weak axis (therefore, the direction of rotation about the height direction y is around the weak axis).

Here, the dimensions and the like of the steel beams 25 are defined. It should be noted that SI units such as "m" are preferably used for the units of length and the like to be described below.
The length of the steel frame beam 25 in the axial direction z is defined as l (also referred to as l _b ). Let H be the thickness of the steel beam 25 (beam thickness). Let B be the width (the length in the width direction x) of the steel beam 25 . _{Let tf} be the thickness of each of the second upper flange 26 and the second lower flange 27 . Let the thickness of the second web 28 be _tw . The distance in the height direction y between the plate thickness centers of the second lower flange 27 and the second upper flange 26 of the steel beam 25 is defined as a plate thickness center distance db (see _FIG . 3). _{Let Af} be 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 axial direction z. That is, the cross-sectional area of the second upper flange 26 perpendicular to the axial direction z is _Af . The same applies to the second lower flange 27 as well.
Let E be the Young's modulus of the steel beam 25 . Let F be the steel material strength (reference strength) of the steel beam 25 . The strength of steel materials is stipulated by the "Matters Determining Allowable Stress of Steel Materials, etc. and Welds, and Standard Strength of Material Strength (Ministry of Construction Public Notice No. 2464)."

Let G be the shear elastic modulus of the steel beam 25 . Let I be the area moment of inertia of each of the flanges 26 and 27 about the weak axis of the steel beam 25 . That is, I is the moment of inertia of area about the weak axis of the steel beam 25 of the second upper flange 26 . The same applies to the second lower flange 27 as well. Let _Dw be the plate stiffness of the second web 28 . Let J be the Saint-Venant torsion constant of the steel beam 25 . _Let Jf be the Saint-Venin torsion constant of each of the second upper flange 26 and the second lower flange 27 . Let Jw be the Saint- _Venin torsion constant of the second web 28 .

As shown in FIG. 2, the steel beams 25 span between the adjacent girders 15 and extend in a direction along the horizontal plane. Both ends of the steel beams 25 are rigidly joined to the large beams 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 and the like. The second upper flange 26 is joined to the first upper flange 16 of the girder 15 by a welded portion 30 formed by welding, and the second lower flange 27 is formed by welding to the joint member 20 joined to the girder 15. They are joined together by welds 31 .

Both ends of the steel frame girders 25 may be semi-rigidly joined to the girders 15 respectively. Also, if one end of the steel beam 25 is rigidly or semi-rigidly connected to the girders 15 , the other end may be pinned to the girders 15 . Definitions of pin joints, semi-rigid joints and rigid joints are found in particular in the European Design Code ("Eurocode 3: Design of steel structures - Part 1-8: Design of joints", 2004, Authority: The European Union Per Regulation 305/ 2011, Directive 98/34/EC, Directive 2004/18/EC).

In this embodiment, floor slab 35 is a deck composite floor slab. Floor slab 35 has deck plate 36 and concrete 37 .
The deck plate 36 is formed by bending a steel plate or the like. The deck plate 36 is arranged on the second upper flange 26 of the steel beam 25 .
The concrete 37 is formed in a flat plate shape whose thickness direction extends in the vertical direction. Concrete 37 is placed on deck plate 36 .
The steel beams 25 support the floor slab 35 from below. The steel beam 25 is joined to the floor slab 35 by a plurality of shear connectors 39 provided on the second upper flange 26 of the steel beam 25 . In this embodiment, a headed stud is used as the shear connector 39 . The lower ends of the shear connectors 39 are fixed to the upper surface of the second upper flange 26 of the steel beam 25 with a space therebetween. Shear connector 39 is embedded in concrete 37 through deck plate 36 . That is, the second upper flange 26 is joined (fastened) to the floor slab 35 by a plurality of shear connectors 39 .

Floor slab 35, which is a deck composite floor slab, has high stiffness against horizontal deformation and torsion. Therefore, horizontal movement and rotation of the upper flange 26 of the steel beam 25 tightly connected to the floor slab 35 hardly occur, and it can be considered that the upper flange 26 is 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 bars may be embedded in the concrete.
A perforated steel plate dowel or the like may be used for the shear connector 39 . If the floor slab is a composite deck 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 a shear connector.

Next, the derivation process of the elastic lateral buckling moment M _e of the steel beam 25 and the results of examination of the elastic lateral buckling moment M _e will be described. Below, the second upper flange 26, the second lower flange 27 and the second web 28 are also referred to as the upper flange 26, the lower flange 27 and the web 28, respectively.

[2. Derivation of the formula for obtaining the elastic lateral buckling moment]
Below, assumptions 1 to 5 below are made for the floor structure 45 .
1. The upper flange 26 is restrained from moving in the width direction x and rotating around the material axial direction z.
2. Warp is not restrained at the ends of the steel beams 25 in the material axial direction z.
3. The load condition is for an equal bending moment in which the lower flange 27 is compressed.
4. The intersections of the flanges 26, 27 and the web 28 maintain their respective right angles 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 with respect to the floor slab 35 is restrained. The restraint of rotation of the upper flange 26 about the material axial direction z means that the rotation of the upper flange 26 about the joint 25a with respect to the floor slab 35 is restrained. That is, even if the web 28 and the lower flange 27 move with respect to the floor slab 35 as shown in FIG. 7, the upper flange 26 cannot move in the width direction x from the state of the steel beam 25 as shown in FIG. , the upper flange 26 cannot rotate around the joint 25a.
In Assumption 2, warpage is not restrained means that the flanges 26 and 27 and the web 28 can rotate about the height direction y at both ends of the steel beam 25 shown in FIG.

Let w be the displacement function in the thickness direction (width direction x) of the web 28 . As shown in FIG. 7, let φ be the torsion angle of the lower flange 27, and let u be the out-of-plane displacement of the lower flange 27 (displacement in the width direction x). At this time, the torsion angle φ and the displacement function w of the web 28 are expressed by equations (21) and (22).

At this time, the movement of the upper flange 26 in the width direction x and the rotation around the member axial direction z are restrained. The total potential energy Π of the floor structure 45 when an equal bending moment that compresses the lower flange 27 acts on both ends of the steel beam 25 as an external force is expressed by equation (23).

However, the Poisson's ratio of the steel beam 25 is ν. Let _Mcr be the elastic lateral buckling moment of the steel beam 25 . The elastic lateral buckling moment _Mcr is a moment acting on both ends of the steel beam 25 in the axial direction z, as shown in FIG.
Let u′ be a function obtained by first differentiating the out-of-plane displacement u with respect to z. Let u'' be a function obtained by second-order differentiating the out-of-plane displacement u with respect to z.
Substitute the equations (21) and (22) into the equation (23), and organize the definite integrals with the constants A to C calculated from the equations (24) to (26). Then, the total potential energy Π of the floor structure 45 is expressed by Equation (27).

Equation (28) is obtained from equation (27) according to the principle of minimum potential energy. Equation (28) can be transformed into Equation (29).

From the equation (29), the elastic lateral buckling moment _Mcr is expressed by the equation (30).

Next, the out-of-plane displacement u of the lower flange 27 is expressed using a sine wave as shown in Equation (31), and the equations are organized. Here, n represents the number of half-waves of sin and is given as a positive integer.

Equations (32) and (33) represent equations obtained by differentiating the first-order and second-order differentials of the out-of-plane displacement u of the lower flange 27 .

By arranging the equations (24) to (26) using the equations (31) to (33), the equations (34) to (36) are obtained.

Equations (34) to (36) are substituted into equation (30) and rearranged. Then, the elastic lateral buckling moment _Mcr is represented by the formula (37).

Equation (37) is rearranged using the relationships of equations (38) to (41). The elastic lateral buckling moment _Mcr is represented by the formula (42).

The elastic lateral buckling moment M _cr according to equation (42) depends on the number of sine half-waves n. However, the minimum buckling load obtained by substituting any positive integer for n is a constant value regardless of n. The minimum value M _cr,min (elastic lateral buckling moment M _e ) of the elastic lateral buckling moment at this time is calculated by the equation (43).
In addition, the length of the steel beam 25 is preferably longer than the length L calculated by the formula (44). (44) The length L according to the formula is the reduction of the allowable stress for buckling of the bending material in the matter of determining the special allowable stress and special material strength according to the Ministry of Land, Infrastructure, Transport and Tourism's notification No. 13, National Notification No. 1024. is the maximum beam length that does not occur.
Next, a study using the elastic lateral buckling moment _Mcr obtained as described above will be conducted.

[3. Study on Elastic Lateral Buckling Moment]
As a known design method, in the notification of the Building Standards Act, the allowable stress for buckling of a bending member in consideration of the lateral buckling strength (hereinafter referred to as the allowable bending stress) is described in Equations (51) and (52). It is In this notification, design is made by formula (53) using the larger of formulas (51) and (52).

8 and 9 show changes in the ratio of allowable bending stress to allowable tensile stress with respect to the length of a steel frame beam (beam) designed according to a known design method. 8 and 9, the horizontal axis represents the length (m) of the steel frame beam, and the vertical axis represents the ratio between the allowable bending stress level and the allowable tensile stress level. The steel beams are made of H-beam steel.
Here, FIG. 8 shows a case where the cross section is H-600×200×9×19 and the steel material strength F is 235 N/mm ² as an example of the narrow width of the cross section of the H-shaped steel. FIG. 9 shows an example of an H-shaped steel having a medium cross-sectional width, where the cross-section is H-900x300x16x28 and the steel material strength F is 325 N/mm ² .
In both cases, when the length of the steel frame beam exceeds about 4 m, the allowable bending stress is reduced with respect to the allowable tensile stress. A reduction in the allowable bending stress means that the steel beam's original yield strength is not exerted, and the cross-sectional efficiency of the steel beam is reduced. In addition, the steel weight relative to the cross-sectional performance of the steel beam increases, leading to an increase in the cost of the steel beam.

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 the steel beam with lateral buckling stiffeners so that the allowable bending stress does not decrease. That is, the range in which the allowable bending stress degree according to the equation (52) exceeds the allowable tensile stress degree is the range in which the lateral buckling stiffener in the known design method is unnecessary. The upper limit _lmax of the range is given by equation (54) by modifying equation (52).
Lateral buckling stiffeners are shaped steels and steel plates that are arranged to connect steel beams and beams that are arranged parallel to the steel beams. It is a member that restrains by supporting it from outside the structural plane such as direction.

The upper limit l _max is shown in FIGS. 8 and 9, respectively.

10 and 11 are diagrams comparing eigenvalue analysis results under various boundary conditions by FEM (Finite Element Method) and yield moments of steel beams. 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).
10 and 11, the cross-sections of the target steel beams are of two sizes, which are the same as in FIGS. The white round plots (marks) correspond to the case of design according to a known design method. This plot represents the elastic lateral buckling moment of a steel beam with an equal bending moment acting in compression on the lower flange and no constraint on the upper flange. 10 and 11 show the yield _moments My of the steel beams when the strength F of the steel material is 235, 325 and 385 N/mm ² .

Plotted squares correspond to floor structures and floor structure design methods (hereinafter simply referred to as design methods). This plot represents the elastic lateral buckling moment of a steel beam subjected to an equal bending moment with the lower flange in compression and constrained from lateral movement and rotation of the upper flange.
From FIGS. 10 and 11, it can be seen that the elastic lateral buckling moment is very small in the open round plots, and that the elastic lateral _buckling moment does not exceed the yield moment My unless the steel beam is extremely short.
On the other hand, the filled square plots have higher elastic lateral buckling moments than the open circle plots. In the solid square plot, the elastic lateral buckling _moment exceeds the yield moment My even when the length of the steel beam is long.

Figures 12 and 13 show the results of FEM-based eigenvalue analysis of the effects of joint conditions and load conditions at the ends of steel beams on the elastic lateral buckling moment when lateral movement and rotation of the upper flange are constrained. indicates 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, various joint conditions and load conditions assumed for steel beams, which are small beams, shown in the bending moment distribution in FIG. 14 are examined. In FIG. 14, the horizontal axis represents non-dimensional coordinates in the material axis direction of the steel frame beam, and the vertical axis represents the bending moment. The portion with dimensionless coordinates of 0 represents the first end of the steel beam, and the portion with dimensionless coordinates of 1 represents the second end of the steel beam.
Among various joint conditions and load conditions, when both ends of the steel frame beam are rigidly joined and an equal bending moment acts on the steel frame beam, the bending moment is the largest in the area where the lower flange is compressed and lateral buckling occurs. easier.

As shown in FIGS. 12 and 13, the elastic lateral buckling moment varies depending on the joining conditions of the ends of the steel beams and the load conditions acting on the steel beams. The elastic lateral buckling moment is the smallest and the most severe condition when both ends of the steel frame beam are rigidly joined and the lower flange is compressed and an equal bending moment acts. Under other conditions, the elastic lateral buckling moment decreases as the length of the steel beam increases, and approaches the elastic lateral buckling moment when an equal bending moment acts.
In addition, in rigidly or semi-rigidly joined steel beams (small beams), the bending moment distribution of the steel beams changes depending on the rigidity and load conditions of the steel beams adjacent to each other across the large beam. FIG. 15 shows the bending moment distribution of rigidly joined steel beams assuming the influence of adjacent steel beams. In FIG. 15, the horizontal axis represents non-dimensional coordinates in the material axis direction of the steel frame beam, and the vertical axis represents the bending moment.
If the framework and load conditions are uniform (equal bending), the maximum bending moment is 2 at the ends and 1 at the center. On the other hand, when the rigidity and load conditions of the adjacent steel beams are different (in the case of an uneven frame), the bending moment distribution can become a distribution close to equibending where the lower flange is compressed.

From the above, the elastic lateral buckling moment of a steel frame beam with rigid or semi-rigid joints at both ends can be calculated by assuming that the lower flange is compressed and an equal bending moment acts. However, it can be evaluated on the safe side. In this case, there is no need to consider the influence of the adjacent steel frame beams, etc., so the design method can be performed simply.
In addition, by assuming equal bending as a load condition, it is possible to give an evaluation on the safe side even to a steel frame beam whose both ends are pin-joined when the lower flange is in compression.

FIG. 16 shows the result of comparison between the eigenvalue analysis result by FEM and the elastic lateral buckling moment obtained in this embodiment. In FIG. 16, the horizontal axis represents the length (m) of the steel frame beam, and the vertical axis represents the elastic lateral buckling moment (kNm). Here, we are considering a steel beam with a cross section of H-600x200x9x19. The elastic lateral buckling moment _Mcr was obtained from the above equation (42). In the equation (42), elastic lateral buckling moments when the number of half waves n is 1 to 10 are indicated by thin dotted lines in FIG. The elastic lateral buckling moment _Mcr is the minimum value among the elastic lateral buckling moments obtained according to the number n of half waves, and is indicated by the thick solid line in FIG. The minimum value M _cr,min of the elastic lateral buckling moment according to the equation (43) is indicated by a thick dotted line in FIG. In FIG. 16, the eigenvalue analysis results (elastic lateral buckling moment M _FEM ) by FEM are indicated by white circular plot marks.
The elastic lateral buckling moment _Mcr obtained from the above equation (42) shows good correspondence with the result of eigenvalue analysis. The minimum value M _cr,min of the elastic lateral buckling moment obtained by the equation (43) accurately captures the lower limit of the eigenvalue analysis result.

FIG. 17 shows the result of comparing the evaluation method using the minimum value of the elastic lateral buckling moment according to the present invention with the analysis result by FEM. In FIG. 17, the horizontal axis represents the dimensionless lateral buckling slenderness ratio (√(M _y /M _{cr, min} )), and the vertical axis represents (M _FEM /M _y ) or (M _{cr, min} /M _y ). The minimum value M _cr,min of the elastic lateral buckling moment was obtained by the equation (43). The value of the elastic lateral buckling moment M _FEM is the minimum value for each section of the eigenvalue analysis results by FEM.
It means that the more the outline circle plot overlaps with the solid line, the higher the accuracy of the value of the elastic lateral buckling moment _Mcr of this embodiment. The steel beams considered here are about 300 sizes of 400 mm to 1000 mm. For each size, the value (l/H) obtained by dividing the length l of the steel frame beam by the beam height H is varied from 6 to 50.
From FIG. 17, it can be seen that the design method of this embodiment can design steel beams of all cross-sectional dimensions with extremely high accuracy.

From the above, if the lateral movement and rotation of the upper flange of the steel beam is constrained by a floor slab, etc., the steel beam, which required lateral buckling stiffeners in the conventional design, can be calculated using equation (43). If the elastic lateral buckling moment M _e (minimum value M _cr,min of the elastic lateral buckling moment) exceeds the yield moment M _y of the steel frame beam, lateral buckling will not occur, and the lateral buckling that has been required in the past will not occur. It is possible to omit stiffeners.
In this case, no lateral buckling stiffeners are attached to the steel beam over the entire length of the steel beam.

In the design method of this embodiment, the floor structure 45 is designed by setting the restraining member to the floor slab 35 . In the design method, the length of the steel frame beam 25 is set longer than the length L calculated by the formula (44). The elastic lateral buckling moment M _e calculated by the equation (43) is set to exceed the yield moment M _y of the steel frame beam 25 . In this case, the steel frame beam 25 is set so that the lateral buckling stiffener is not attached over the entire length.

As described above, according to the floor structure 45 of the present embodiment, as a result of extensive studies, the inventors found that the second upper flange 26 of the steel beam 25 is joined to the floor slab 35 by the shear connector 39. found that the lateral movement of the second upper flange 26 with respect to the floor slab 35 and the rotation of the second upper flange 26 with respect to the floor slab 35 about the joint 25a can each be considered constrained. In this case, if the length of the steel beam 25 is longer than the length L calculated by the equation (44) and the elastic lateral _buckling moment _Me exceeds the yield moment My of the steel beam 25, the steel beam It was found that the steel frame beam 25 does not undergo lateral buckling 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 elastic lateral _buckling moment _Me exceeds the yield moment My of the steel beams 25, thereby It can prevent bending.

Further, according to the design method of the present embodiment, the inventors, as a result of extensive studies, found that when the second upper flange 26 of the steel frame beam 25 is joined to the floor slab 35 by the shear connector 39, the floor slab We have found that the lateral movement of the second upper flange 26 with respect to 35 and the rotation of the second upper flange 26 about the joint 25a with respect to the floor slab 35 can each be considered constrained. In this case, the length of the steel beam 25 is set longer than the length L calculated by the equation (44) so that the elastic lateral _buckling moment _Me exceeds the yield moment My of the steel beam 25. It has been found that, if set, no lateral buckling occurs in the steel beam 25 without attaching 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 longer than the length L, and the elastic lateral _buckling moment Me is set to _exceed the yield moment My of the steel beam 25, Horizontal buckling can be prevented from occurring in the steel beam 25 .

No lateral buckling stiffener is attached to the steel beam 25 over its entire length. Since no lateral buckling stiffeners are attached to the steel beams 25, the cost required for the floor structure 45 can be further reduced.
In general, floor slabs have significantly higher horizontal displacement stiffness and torsional stiffness than steel beams. By joining the steel beam 25 to the floor slab 35, the lateral movement of the second upper flange 26 with respect to the floor slab 35 and the rotation of the second web 28 about the joint 25a with respect to the floor slab 35 are constrained more reliably. be able to.

In the design method, the steel frame beam 25 is set so that no lateral buckling stiffener is attached over the entire length. Since no lateral buckling stiffeners are attached to the steel beams 25, the cost required for the floor structure 45 constructed based on the design method can be further reduced.

(Second embodiment)
Next, a second embodiment of the invention will be described with reference to FIGS. 18 and 19. FIG.
The basic configuration of the floor structure 45 of this embodiment is the same as that of the first embodiment. It is preferable that the length of the steel beam 25 is longer than the length L calculated by the formula (44).

[4. Examination of cross-sectional shape index]
In this embodiment, for the floor structure 45, instead of the relationship between the elastic lateral buckling moment M _e and the yield moment M _y of the steel frame beam 25, the cross-sectional shape index X calculated by the equation (61) and (62 ), the threshold value A calculated by the formula was examined.

FIG. 18 shows the relationship between the cross-sectional shape index X and the ratio of the minimum elastic lateral buckling moment _{Mcr ,min} to the yield moment My according to the equation (43). In FIG. 18, the horizontal axis represents the cross-sectional shape index X, and the vertical axis represents the value of (M _{cr, min} /M _y ). The steel beams considered here are about 600 sizes with a depth of 400 mm to 1000 mm.
FIG. 19 shows the relationship between the cross-sectional shape index X and the ratio of the minimum value M _FEM to the yield moment M _y for each section in the eigenvalue analysis results by FEM. In FIG. 19, the horizontal axis represents the cross-sectional shape index X, and the vertical axis represents the value of (M _FEM /M _y ). The steel beams considered here are about 270 sizes with a depth of 400 mm to 1000 mm.
The solid line in each figure is a line that envelops the lower limit for each strength of the steel frame beam. These lines are represented by equation (63), and it can be seen that the elastic lateral buckling moment can be accurately approximated to the safe side in both figures.

If the left side of the equation (63) is changed to 1, the equation (62) is obtained as the threshold value of the cross-sectional shape index X at which the minimum elastic lateral buckling moment _{Mcr ,min} exceeds the yield moment My.
18 and 19, the elastic lateral buckling moment of the steel beam with a steel material strength of 235 N/mm ² becomes larger than the yield moment when the cross-sectional shape index X is approximately 164 or less, and it is It can be said that no lateral buckling occurs. In the case of a steel beam with a steel material strength of 325 N/mm ² and a cross-sectional shape index X of approximately 124 or less, the same applies to the case of a steel beam with a steel material strength of 385 N/mm ² and a cross-sectional shape index X of approximately 107 or less. is.
These cross-sectional shape indices X are expressed in the form of equation (62) with respect to any steel material strength.
In the floor structure 45, the cross-sectional shape index X is equal to or less than the threshold value A.
Further, in the design method of this embodiment, the cross-sectional shape index X is set to be equal to or less than the threshold value A. FIG.

By using this cross-sectional shape index X, the elastic lateral buckling moment when the lateral movement and rotation of the upper flange of the steel beam are continuously constrained by a floor slab or the like can be evaluated very simply and with sufficient accuracy. . It is possible to easily evaluate the presence or absence of lateral buckling and the necessity of lateral buckling stiffeners for each steel material strength in an arbitrary cross-sectional dimension of a steel frame beam.

As described above, according to the floor structure 45 of the present embodiment, it is possible to prevent lateral buckling from occurring in the steel beams 25 . Further, according to the design method of the present embodiment, the steel frame beam 25 can be designed so as not to cause lateral buckling.
Furthermore, as a result of extensive studies, 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, the lateral movement of the second upper flange 26 with respect to the floor slab 35 , and rotation of the second upper flange 26 about the joint 25a with respect to the floor slab 35 can be considered respectively constrained. In this case, if the length of the steel beam 25 is longer than the length L calculated by the equation (44) and the cross-sectional shape index X is equal to or less than the threshold value A, the steel beam 25 is provided with a lateral buckling stiffener. It was found that lateral buckling does not occur in the steel beam 25 without attaching the
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 less than the threshold value A, so that lateral buckling of the steel beams 25 is prevented. be able to.

Further, according to the design method of the present embodiment, the inventors, as a result of extensive studies, found that when the second upper flange 26 of the steel frame beam 25 is joined to the floor slab 35 by the shear connector 39, the floor slab We have found that the lateral movement of the second upper flange 26 with respect to 35 and the rotation of the second upper flange 26 about the joint 25a with respect to the floor slab 35 can each be considered constrained. In this case, if the length of the steel beam 25 is set longer than the length L calculated by the equation (44) and the cross-sectional shape index X is set to be equal to or less than the threshold value A, the steel beam 25 is laterally buckled. It was found that horizontal buckling does not occur in the steel beam 25 without attaching stiffeners.
According to this invention, in the design method, the length of the steel beam 25 is set 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, thereby preventing lateral buckling of the steel beam 25. be able to.

As described above, the first embodiment and the second embodiment of the present invention have been described in detail with reference to the drawings. change, combination, deletion, etc. of Furthermore, it goes without saying that the configurations shown in the respective embodiments can be used in combination as appropriate.

15 girders (beams)
25 Steel beam 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 (8)

a floor slab;
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 its upper flange is joined to the floor slab by a shear connector. A steel beam made of H-beam steel,
A floor structure comprising
The length of the steel beam is longer than the length L calculated by the formula (1),
(2) The floor structure, wherein the elastic lateral buckling moment M _e of the steel beam calculated by the formula exceeds the yield moment of the steel beam.
However, E: Young's modulus of the steel beam, A _f : Cross-sectional area of each of the upper flange and the lower flange of the steel beam, F: Steel material strength of the steel beam, H: Due to the steel beam, G: The steel frame Shear elastic modulus of the beam, d _b : distance between plate thickness centers of the lower flange and the upper flange of the steel beam, J: Saint-Benant torsion constant of the steel beam, J _f : the upper flange and the lower flange Each Saint-Venin torsion constant, J _w : Saint-Venin torsion constant of the web of the steel beam, I: the cross-section of each of the upper flange and the lower flange of the steel beam around the weak axis of the steel beam Next moment, D _w : the plate stiffness of the web.

a floor slab;
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 its upper flange is joined to the floor slab by a shear connector. A steel beam made of H-beam steel,
A floor structure comprising
The length of the steel beam is longer than the length L calculated by the formula (3),
(4) A floor structure in which the cross-sectional shape index X calculated by the formula is equal to or less than the threshold value A calculated by the formula (5).
However, E: Young's modulus of the steel beam, A _f : Cross-sectional area of each of the upper flange and the lower flange of the steel beam, F: Steel material strength of the steel beam, H: Due to the steel beam, t _f : The above Thicknesses of the lower flange of the steel beam and the upper flange, respectively, _tw : thickness of the web of the steel beam, B: width of the steel beam.

3. The floor structure according to claim 1 or 2, wherein said steel beams are not provided with lateral buckling stiffeners over their entire length. 4. Any one of claims 1 to 3, wherein lateral movement of the upper flange with respect to the floor slab and rotation of the upper flange with respect to the floor slab about the joint of the upper flange and the web are each constrained. Floor structure as described in paragraph. a floor slab;
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 its upper flange is joined to the floor slab by a shear connector. A steel beam made of H-beam steel,
A floor structure design method for designing a floor structure comprising
The length of the steel beam is set longer than the length L calculated by the formula (6),
(7) A method of designing a floor structure, wherein the elastic lateral buckling moment M _e of the steel beam calculated by the formula is set to exceed the yield moment of the steel beam.
However, E: Young's modulus of the steel beam, A _f : Cross-sectional area of each of the upper flange and the lower flange of the steel beam, F: Steel material strength of the steel beam, H: Due to the steel beam, G: The steel frame Shear elastic modulus of the beam, d _b : distance between plate thickness centers of the lower flange and the upper flange of the steel beam, J: Saint-Benant torsion constant of the steel beam, J _f : the upper flange and the lower flange Each Saint-Venin torsion constant, J _w : Saint-Venin torsion constant of the web of the steel beam, I: the cross-section of each of the upper flange and the lower flange of the steel beam around the weak axis of the steel beam Next moment, D _w : the plate stiffness of the web.

a floor slab;
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 its upper flange is joined to the floor slab by a shear connector. A steel beam made of H-beam steel,
A floor structure design method for designing a floor structure comprising
The length of the steel beam is set longer than the length L calculated by the formula (8),
(9) A method of designing a floor structure, wherein the cross-sectional shape index X calculated by the formula (9) is set to be equal to or less than the threshold value A calculated by the formula (10).
However, E: Young's modulus of the steel beam, A _f : Cross-sectional area of each of the upper flange and the lower flange of the steel beam, F: Steel material strength of the steel beam, H: Due to the steel beam, t _f : The above Thicknesses of the lower flange of the steel beam and the upper flange, respectively, _tw : thickness of the web of the steel beam, B: width of the steel beam.

7. The method of designing a floor structure according to claim 5 or 6, wherein the steel frame beam is set so that the lateral buckling stiffener is not attached over the entire length. 8. Any one of claims 5 to 7, wherein lateral movement of the upper flange with respect to the floor slab and rotation of the upper flange with respect to the floor slab about the joint of the upper flange and the web are each constrained. The design method of the floor structure described in the paragraph.

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