Floor structure, floor structure design method, and floor structure construction method

Abstract

To provide a floor structure having high ratio of a cross section performance to a weight of a beam to secure habitability.SOLUTION: A floor structure 2 comprises: a plurality of column members 10; a plurality of girders 15 stretched on the plurality of column members; a beam 25 surrounded by the plurality of girders and stretched on the plurality of girders; and a floor slab 35 provided above the plurality of girders and the beam. The beam is a weld assembly H-shaped steel. The floor structure satisfies the formula (1) when defining a vibration frequency in a primary vibration mode of the plurality of girders, the beam, and the floor slab as ffloor,1st, defining a vibration frequency in a primary vibration mode of a mode where a lower flange 28 vibrates around an upper end of a web 26 in the beam as fbeam,1st, and defining a rolled H-shaped steel according to JIS G 3192 which corresponds to the beam and has the highest ratio of a response value to an allowance value of 1 or less when receiving a prescribed external force, is a reference beam. The beam has higher ratio of a cross section secondary moment to a weight, compared with the reference beam. ffloor,1st≤fbeam,1st ..(1)SELECTED DRAWING: Figure 1

Description

[Technical field]

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

[0002] Conventionally, minor beams in floor structures are generally not designed as elements that resist horizontal loads that occur in buildings during earthquakes, unlike major beams. For this reason, rolled H-shaped steel with a large width-thickness ratio for the flanges and webs is used for minor beams. In particular, the width-thickness ratio of the web is often set large to make minor beams lightweight and highly rigid. This is because, in general, the cross section of minor beams is regulated by the deflection limit as a design criterion, and it is desirable to reduce the mass while improving the cross-sectional performance such as the second moment of area. In recent years, the span (length) of sub-beams has been increasing. Accordingly, H-shaped steel beams with a large mass-to-weight ratio (thin web) of about 70 are being used for sub-beams, as they have a high mass-to-weight ratio and good cross-sectional efficiency. H-shaped steel beams with a width-to-thickness ratio of about 70 are close to the manufacturing limit of rolled H-shaped steel beams. As a method for further increasing the cross-sectional efficiency, a method of increasing the width-thickness ratio of the web can be considered by using welded assembled H-shaped steel beams, which have fewer manufacturing constraints.

[0003] On the other hand, when H-shaped steel beams are used to construct a floor structure, there is a concern that the lower flange of the beam will rotate and vibrate around the upper end of the web, reducing the livability of the floor structure. This concern becomes more pronounced in beams with a large width-to-thickness ratio (thin web). As a countermeasure to this, Patent Document 1 proposes a method of suppressing the vibration of the lower flange by using anti-vibration materials. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Patent No. 5589565 Summary of the Invention [Problem to be solved by the invention]

[0005] The present invention has been made in consideration of such problems, and aims to provide a floor structure having a high ratio of cross-sectional performance to the mass of the sub-beams and ensuring livability, a method for designing a floor structure, and a method for constructing a floor structure. [Means for solving the problem]

[0006] 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 including a plurality of column members, a plurality of girders erected on the plurality of column members, a sub-girder provided inside the plurality of girders and erected on the plurality of girders, and a floor slab provided above the plurality of girders and the sub-girders. The sub-girders are welded H-shaped steel, and the vibration frequency of the first vibration mode of the plurality of girders, the sub-girders, and the floor slab is f floor,1st , the frequency of the mode in which the lower flange of the sub-beam rotates around the upper end of the web is f beam,1st and when a rolled H-section steel according to JIS G 3192, which corresponds to the sub-beam and has the highest ratio of response value to allowable value (1 or less) when subjected to a specified external force, is defined as a standard beam, the sub-beam satisfies formula (1) and is characterized in that the ratio of area second moment to mass is large compared to the standard beam. f floor,1st ≦f beam,1st (1)

[0007] In addition, the floor structure design method of the present invention is a floor structure design method for designing a floor structure including a plurality of column members, a plurality of girders erected on the plurality of column members, a sub-girder provided inside the plurality of girders and erected on the plurality of girders, and a floor slab provided above the plurality of girders and the sub-girders, the sub-girders being welded H-shaped steel, and the frequency of the first vibration mode of the plurality of girders, the sub-girders, and the floor slab being f floor,1st, the frequency of the first vibration mode in which the lower flange of the sub-beam rotates around the upper end of the web is f beam,1st and when a rolled H-section steel conforming to a certain JIS G 3192 standard that corresponds to the sub-beam and has the highest ratio of response value to allowable value (not exceeding 1) when subjected to a specified external force is defined as a reference beam, the sub-beam is designed to satisfy formula (2) and have a larger ratio of area second moment to mass than the reference beam. f floor,1st ≦f beam,1st (2)

[0008] The floor structure construction method of the present invention is a floor structure construction method for constructing a floor structure including a plurality of column members, a plurality of girders erected on the plurality of column members, a sub-girder provided inside the plurality of girders and erected on the plurality of girders, and a floor slab provided above the plurality of girders and the sub-girders, the sub-girders being welded H-shaped steel, and the frequency of the first vibration mode of the plurality of girders, the sub-girders, and the floor slab being f floor,1st , the frequency of the first vibration mode in which the lower flange of the sub-beam rotates around the upper end of the web is f beam,1st and when a rolled H-section steel according to a certain JIS G 3192 standard, which corresponds to the sub-beam and has the highest ratio of response value to allowable value that is equal to or less than 1 when subjected to a specified external force, is defined as a reference beam, the sub-beam is constructed so that it satisfies formula (3) and has a larger ratio of second moment of area to mass than the reference beam. f floor,1st ≦f beam,1st (3)

[0009] It should be noted that equations (1) to (3) are identical to each other. Generally, the problem from the viewpoint of the habitability of floor structures is the vibrations that occur when people walk on the floor structure. Usually, the vibration frequency when people walk is the source of vibration has a characteristic that a low frequency of about 2 Hz predominates. Usually, the vibration frequency f floor,1st and frequency f beam,1stis greater than the vibration frequency of the person who is the vibration source. By satisfying equation (1), the vibration frequency caused by human walking and the vibration frequency f floor,1st Rather than the difference between the vibration frequency caused by human walking and the vibration frequency f beam,1st The difference between the maximum and minimum values ​​is large. Therefore, even when subjected to vibration caused by people walking, the bottom flange of the sub-beam is less likely to vibrate around the upper end of the web compared to the multiple main girders, sub-beams, and the entire floor slab. If the bottom flange is prone to vibrating, it would be necessary to suppress the vibration of the bottom flange by making the web thicker or using a vibration-proof material, but with the present invention, this is not necessary, so the mass of the sub-beam and the entire floor structure is prevented from becoming too large. By making the bottom flange of the sub-beam less likely to vibrate, the livability of the floor structure can be ensured. In addition, the standard beam is a rolled H-section steel according to JIS G 3192, which has a response value to a specified external force that is equal to or less than the allowable value. Compared to this standard beam, the beam of the present invention has a large ratio of the moment of inertia to the mass, which is one of the indicators of cross-sectional performance. This makes it possible to increase the ratio of the cross-sectional performance to the mass of the beam.

[0010] Further, in the floor structure, the response value includes a bending response value with respect to a bending moment generated by the application of the specified external force to the reference beam, a shear response value with respect to a shear force generated by the application of the specified external force to the reference beam, and a deflection response value generated by the application of the specified external force to the reference beam, and the allowable value includes a bending allowable value with respect to a bending moment acting on the reference beam, a shear allowable value with respect to a shear force acting on the reference beam, and a deflection allowable value allowed for the reference beam, and the ratio of the response value to the allowable value is 1 or less and is the highest when the specified external force is applied may mean that a bending allowable value ratio which is the ratio of the bending response value to the bending allowable value is 1 or less, a shear allowable value ratio which is the ratio of the shear response value to the shear allowable value is 1 or less, a deflection allowable value ratio which is the ratio of the deflection response value to the deflection allowable value is 1 or less, and the maximum values ​​of the bending allowable value ratio, the shear allowable value ratio, and the deflection allowable value ratio are the highest.

[0011] Further, in the design method of a floor structure, the response value includes a bending response value with respect to a bending moment generated by the application of the specified external force to the reference beam, a shear response value with respect to a shear force generated by the application of the specified external force to the reference beam, and a deflection response value generated by the application of the specified external force to the reference beam, and the allowable value includes a bending allowable value with respect to a bending moment acting on the reference beam, a shear allowable value with respect to a shear force acting on the reference beam, and a deflection allowable value allowed for the reference beam, and when the specified external force is applied, the ratio of the response value to the allowable value is 1 or less and is the highest may mean that a bending allowable value ratio which is the ratio of the bending response value to the bending allowable value is 1 or less, a shear allowable value ratio which is the ratio of the shear response value to the shear allowable value is 1 or less, a deflection allowable value ratio which is the ratio of the deflection response value to the deflection allowable value is 1 or less, and the maximum values ​​of the bending allowable value ratio, the shear allowable value ratio, and the deflection allowable value ratio are the highest.

[0012] Generally, when a reference beam corresponding to a sub-beam is used, bending moment and shear force are more likely to act than axial force. According to these inventions, the reference beam can be more accurately selected by using bending moment and shear force that are likely to act on the reference beam, and bending response value, shear response value, deflection response value, bending allowance value, shear allowance value, and deflection allowance value that are indexed by the deflection generated in the reference beam.

[0013] Moreover, in the floor structure, the bending allowable value may be the smaller of the yield strength of the reference beam and the elastic buckling strength taking into account coupled buckling between the web of the reference beam and a pair of flanges when a bending moment acts on the reference beam, divided by a safety factor; the shear allowable value may be the smaller of the yield strength of the reference beam divided by √3 and the elastic buckling strength taking into account coupled buckling between the web of the reference beam and a pair of flanges when a shear force acts on the reference beam, divided by a safety factor; and the deflection allowable value may be the length of the reference beam divided by 300. Further, in the design method of a floor structure, the bending allowable value is the smaller of the yield strength of the reference beam and the elastic buckling strength taking into account coupled buckling between the web of the reference beam and a pair of flanges when a bending moment acts on the reference beam, divided by a safety factor; the shear allowable value is the smaller of the yield strength of the reference beam divided by √3 and the elastic buckling strength taking into account coupled buckling between the web of the reference beam and a pair of flanges when a shear force acts on the reference beam, divided by a safety factor; and the deflection allowable value may be the length of the reference beam divided by 300.

[0014] According to these inventions, the bending allowable value and the shear allowable value can be set to a preferable value in consideration of the yield strength, the elastic buckling strength considering the coupled buckling, and the safety factor. Also, the deflection allowable value can be set to a preferable value.

[0015] In addition, in the floor structure, the sub-beam may have a smaller ratio of mass to length in the material axis direction of the sub-beam than the reference beam. In addition, in the floor structure design method, the sub-beam may have a smaller ratio of mass to length in the material axis direction of the sub-beam than the reference beam. According to these inventions, the ratio of the moment of inertia to the mass of the sub-beam can be increased compared to the reference beam, and the ratio of the mass to the length in the axial direction of the beam can be decreased. Therefore, the sub-beam can be made into a beam with higher cross-sectional performance.

[0016] In addition, in the floor structure, the specified external force may be the sum of the mass of the floor slab corresponding to the burden width of the sub-beam, the live load corresponding to the burden width of the sub-beam, and the weight of the sub-beam. In addition, in the design method of the floor structure, the specified external force may be the sum of the mass of the floor slab corresponding to the burden width of the sub-beam, the live load corresponding to the burden width of the sub-beam, and the weight of the sub-beam. According to these inventions, the predetermined external force can be specifically defined using the burden width, the mass of the floor slab, the live load, and the mass (self-weight) of the sub-beam.

[0017] In addition, in the floor structure design method, the elastic buckling strength may be determined based on an energy method from the out-of-plane displacement of the web and the out-of-plane displacement of the pair of flanges. According to the present invention, the elastic buckling strength can be efficiently calculated from the out-of-plane displacement of the web and the out-of-plane displacement of the pair of flanges based on the energy method. Effect of the Invention

[0018] According to the floor structure, the floor structure design method, and the floor structure construction method of the present invention, the ratio of the cross-sectional performance to the mass of the sub-beam can be increased, thereby ensuring livability. [Brief description of the drawings]

[0019] [Figure 1] 1 is a perspective view of a building equipped with a floor structure according to one embodiment of the present invention. [Diagram 2] 2 is a cross-sectional view taken along line A1-A1 in FIG. [Diagram 3] FIG. 13 is a perspective view showing a schematic state in which the beam is buckled when a shear force is applied to the beam when the beam is sufficiently long in the direction along the x-axis. [Figure 4] FIG. 2 is a cross-sectional view perpendicular to the longitudinal direction of the beam. [Diagram 5] 4 is an enlarged perspective view of the beam of FIG. 3, showing a half-wavelength in the direction along the x-axis. [Figure 6] 6 is a cross-sectional view taken along line A3-A3 in FIG. 5. [Figure 7] 13 is a perspective view showing a schematic state in which a beam is buckled when a bending moment is applied to the beam in the case where the beam is sufficiently long in the direction along the x-axis. FIG. [Figure 8] FIG. 2 is a cross-sectional view perpendicular to the longitudinal direction of the beam. [Figure 9] 8 is an enlarged perspective view of the beam of FIG. 7, showing a half-wavelength in the direction along the x-axis. [Figure 10] 10 is a cross-sectional view taken along line A4-A4 in FIG. 9. [Figure 11]FIG. 1 is a plan view showing an outline of the floor structure used in the study. [Figure 12] FIG. 2 is a cross-sectional view of the floor structure. [Figure 13] FIG. 13 is a diagram showing a cross section of a model of the floor structure. [Figure 14] This is a cross-sectional view of the portion where the main beam and the minor beam of the floor structure are joined. [Figure 15] FIG. 2 is a perspective view of an analytical model of the floor structure. [Figure 16] FIG. 2 is a partially transparent perspective view of the analysis model of the floor structure. [Figure 17] 13 is a perspective view showing an example of an analysis result for the beam case 2. FIG. [Figure 18] 18 is a cross-sectional view taken along line A6-A6 in FIG. 17. [Figure 19] 1 is a perspective view showing an example of an analysis result of vibration of a floor structure in a beam case 4, as viewed obliquely from above. [Figure 20] FIG. 13 is a perspective view showing an example of an analysis result of vibration of a floor structure in a beam case 4, as viewed obliquely from below. [Figure 21] 13 is a perspective view showing an example of an analysis result of vibration of a second lower flange of a beam in a beam case 4, as viewed obliquely from below. FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] Hereinafter, an embodiment of a floor structure, a floor structure design method (hereinafter simply referred to as design method), and a floor structure construction method (hereinafter simply referred to as construction method) according to the present invention will be described with reference to Figs. 1 to 21.

[0021] [1. Floor structure configuration] As shown in Fig. 1, a floor structure 2 is used in a building 1. In Fig. 1, a floor slab 35, which will be described later, is indicated by a two-dot chain line. 1 and 2, the floor structure 2 includes a plurality of column members 10, a plurality of girders 15, a plurality of minor girders 25, and a floor slab 35. The plurality of girders 15, the plurality of minor girders 25, and the floor slab 35 constitute a composite beam structure 3. The number of minor girders 25 included in the floor structure 2 may be one.

[0022] The multiple column members 10 are made of steel, RC (Reinforced Concrete), SRC (Steel Reinforced Concrete), CFT (Concrete Filled Steel Tube), etc. For example, the multiple column members 10 extend in the vertical direction. The multiple column members 10 are arranged on the intersections of multiple straight lines that form a grid in a plan view (in a grid pattern). For example, the main girder 15 and the sub-girders 25 are each made of steel. H-shaped steel is used for the main girder 15 and the sub-girders 25. The main girder 15 and the sub-girders 25 extend in a direction along a horizontal plane, for example. The main girder 15 has a first web 16, a first upper flange 17, and a first lower flange 18. The multiple main girder 15 is installed on the multiple column members 10. The multiple main girder 15 are arranged in a frame shape in a plan view, surrounding a predetermined area. A gusset plate 19 is joined to the first web 16 of the girder 15 by welding or the like (see FIG. 2).

[0023] The sub-beam 25 is a welded H-shaped steel. The sub-beam 25 has a second web 26, a second upper flange 27, and a second lower flange (lower flange) 28. The second web 26 is formed in a flat plate shape that exhibits a rectangular shape when viewed in the thickness direction of the second web 26. The second web 26 is disposed so that the thickness direction of the second web 26 is along a horizontal plane. The flanges 27, 28 are formed in a flat plate shape and are respectively disposed so that the thickness direction of the flanges 27, 28 is along the up-down direction. The second lower flange 28 is disposed below the second upper flange 27. The flanges 27, 28 sandwich the second web 26 in the up-down direction. The second web 26 connects the center of the width direction of the lower surface of the second upper flange 27 and the center of the width direction of the upper surface of the second lower flange 28.

[0024] The small beam 25 is manufactured by welding together the second web 26 and the flanges 27, 28, which have been separately manufactured in advance. The second web 26 and the flanges 27, 28 of the small beam 25 are formed of a steel plate, which is an elastic element. The elastic element is an element that does not take into account material nonlinearity.

[0025] The multiple small beams 25 are provided inside (within the area surrounded by the multiple large beams 15) surrounded by the multiple large beams 15. The multiple small beams 25 are arranged side by side with intervals between each other. The plurality of minor beams 25 are erected on the plurality of major beams 15. The plurality of minor beams 25 are pin-jointed to the plurality of major beams 15. Specifically, as shown in Fig. 2, the second webs 26 of the minor beams 25 and the gusset plates 19 are joined to each other by fastening members 29 including high-strength bolts or the like.

[0026] The floor slab 35 is provided above the multiple girders 15 and the multiple minor joists 25. The floor slab 35 is supported from below by the multiple girders 15 and the multiple minor joists 25. In this embodiment, the floor slab 35 is a composite deck slab. The floor slab 35 includes a deck plate 36, concrete 37, reinforcing steel bars 38, and shear connectors 39. The deck plate 36 is formed by bending a steel plate, etc. The deck plate 36 is disposed on the first upper flange 17 of the main girder 15 and the second upper flange 27 of the secondary girder 25, respectively. The concrete 37 is formed into a flat plate shape with its thickness direction aligned in the vertical direction. The concrete 37 is placed on the deck plate 36.

[0027] The floor slab 35 includes a plurality of reinforcing bars 38. A first reinforcing bar 38a, which is a part of the plurality of reinforcing bars 38, extends along one of the plurality of sub-beams 25. A second reinforcing bar 38b, which is the remaining part of the plurality of reinforcing bars 38, extends in a direction perpendicular to the first reinforcing bar 38a. The first reinforcing bar 38a and the second reinforcing bar 38b are embedded in the concrete 37. For example, the shear connectors 39 are headed studs. The floor slab 35 has a plurality of shear connectors 39. The lower ends of the plurality of shear connectors 39 are fixed to the upper surfaces of the first upper flange 17 of the main girder 15 and the second upper flange 27 of the secondary beam 25 at intervals from each other. The shear connectors 39 are embedded in the concrete 37 through the deck plate 36.

[0028] A calculation method for determining the elastic buckling strength (buckling stress) when a shear force and a bending moment act on the sub-beam 25 will be described below. Hereinafter, the small beam 25 may be referred to as a beam 25. Similarly, the second web 26 may be referred to as a web 26, the second upper flange 27 may be referred to as an upper flange 27, and the second lower flange 28 may be referred to as a lower flange 28.

[0029] [2. Elastic buckling strength when shear force acts on beam] In the calculation method when a shear force acts on the beam 25, the position coordinates of the beam 25 are recognized based on a right-handed Cartesian coordinate system consisting of the x-axis, y-axis, and z-axis, as shown in Fig. 3. Note that Fig. 3 and Fig. 5 described later show the out-of-plane displacement of the web 26, etc., larger than the estimated value. Fig. 3 shows the state in which the beam 25 is buckled. The material axis of beam 25 (axis extending in the direction in which beam 25 extends) is defined as the x-axis. The axis extending in the direction in which flanges 27, 28 sandwich web 26 is defined as the y-axis. The axis extending in the plate thickness direction of web 26 is defined as the z-axis. The x-axis, y-axis, and z-axis are perpendicular to each other. When viewed in a direction along the z-axis (hereinafter referred to as the z-axis direction), web 26 has a side extending in a direction along the x-axis (hereinafter referred to as the x-axis direction) and a side extending in a direction along the y-axis (hereinafter referred to as the y-axis direction). The out-of-plane displacement of web 26 is a displacement of web 26 in the z-axis direction. The out-of-plane displacement of the flanges 27 and 28 is the displacement in the y-axis direction.

[0030] The beam 25 is sufficiently long in the x-axis direction. Here, "beam 25 is sufficiently long in the x-axis direction" means that the beam 25 has a length that allows the effect of the boundary condition of the surfaces 25a (hereinafter referred to as end faces in the x-axis direction) disposed at each end of the beam 25 in the x-axis direction and extending in the y-axis direction on the buckling deformation to be negligible.

[0031] When a shear force F1 acts in the y-axis direction on each of end faces 25a of beam 25 in the x-axis direction, beam 25 may buckle. Note that shear force F1 is transmitted over the entire length of beam 25 in the x-axis direction. The shear forces F1 acting on each end face 25a of the beam 25 in the x-axis direction are external forces of equal magnitude and opposite direction. For example, a shear force F1 acting in a positive direction in the y-axis direction acts on the end face 25a on the negative side in the x-axis direction, and a shear force F1 acting in a negative direction in the y-axis direction acts on the end face 25a on the positive side in the x-axis direction. Note that a shear force F1 acting in a negative direction in the y-axis direction may act on the end face 25a on the negative side in the x-axis direction, and a shear force F1 acting in a positive direction in the y-axis direction may act on the end face 25a on the positive side in the x-axis direction.

[0032] In this case, as the web 26 moves toward the first end in the x-axis direction (one of the end faces 25a in the x-axis direction), the web 26 is displaced alternately in the positive direction of the z-axis and the negative direction of the z-axis, so that the web 26 as a whole is displaced in a wavy shape of a plurality of wavelengths (hereinafter, referred to as wavy in the x-axis direction). Corresponding to the web 26, the flanges 27 and 28 are displaced in a wavy shape. In one wavelength of the web 26 displaced along the x-axis, the second end opposite the first end in the x-axis direction is defined as the origin of the x-axis, and the direction from this second end toward the first end in the x-axis direction is defined as the positive direction of the x-axis.

[0033] 3 and 4, the center position of web 26 in the y-axis direction is defined as the origin of the y-axis. The direction from the origin of the y-axis toward upper flange 27 (one of flanges 27, 28) is defined as the positive direction of the y-axis. The origin of the z-axis is the center in the z-axis direction (center in the thickness direction) of the web 26. The positive direction of the z-axis is a direction that constitutes a right-handed Cartesian coordinate system with the positive directions of the x-axis and y-axis.

[0034] 4, dimensions are defined in a cross section perpendicular to the longitudinal direction of beam 25. Note that for units of length and the like described below, SI units such as "m" are preferably used for length. The thickness of the web 26 (length in the z-axis direction) is t w The distance between the thickness centers of the upper flange 27 and the lower flange 28 in the y-axis direction is defined as b w The height of beam 25 is defined as H. The width (length in the z-axis direction) of the upper flange 27 and the width of the lower flange 28 are equal to each other, and half the width of each of the upper flange 27 and the lower flange 28 is b f The width of each of the upper flange 27 and the lower flange 28 is defined as W. The thickness of the upper flange 27 and the thickness of the lower flange 28 are equal to each other, and the thicknesses of the upper flange 27 and the lower flange 28 are each defined as t f Let us assume that. The Young's modulus of the beam 25 (web 26 and flanges 27, 28) is defined as E, and the Poisson's ratio of the beam 25 is defined as ν.

[0035] In this calculation method, the elastic buckling strength of the beam 25 is estimated when a shear force F1 acts on the beam 25 and causes it to buckle. In the calculation method, the following assumptions 1 to 6 are made when estimating the elastic buckling strength of the beam 25. 1. The thickness of the web 26 is thin, and is shorter than the length of the web 26 in the x-axis direction and the length of the web 26 in the y-axis direction. 2. The deflection of the web 26 (out-of-plane displacement due to buckling) is small and is smaller than the thickness of the web 26. 3. The central plane of the web 26 in the thickness direction does not expand or contract when the web 26 is bent, but remains a neutral plane. 4. In the cross section of beam 25, the assumption of plane retention against bending is valid. 5. The material of the beam 25 is homogeneous and isotropic. 6. When an external force acts on beam 25, its displacement follows Hooke's law.

[0036] As shown in FIG. 3, when a shear force F1 acts on a beam 25, the web 26 of the beam 25 may be displaced in a wavy manner in the x-axis direction. When the y-axis coordinate of the web 26 displaced in a wavy manner in the x-axis direction is a certain value, the out-of-plane displacement of the web 26 in the z-axis direction at a certain coordinate on the x-axis is sin(π(x+λsin(πy / b w Assume that the displacement is expressed by the formula: 2a / a. In this case, the wavelength in the x-axis direction of the web 26 displaced in a wavy manner in the x-axis direction of the web 26 is 2a. The half wavelength (half the length of the wavelength) in the x-axis direction of the web 26 is a. FIG. 5 shows the out-of-plane displacement W in the entire region of the beam 25 in the portion where the length of the beam 25 in the x-axis direction is half the wavelength a. w FIG.

[0037] In Fig. 6, the solid line shows the state when shear force F1 acts on beam 25. The dotted line in Fig. 6 shows the state when shear force F1 does not act on beam 25.

[0038] When a shear force F1 acts on the web 26, the out-of-plane displacement of the web 26 has conventionally been estimated using a Fourier series. The inventors have found that, while using trigonometric functions, the number of terms is smaller than that of a Fourier series, when the coordinate of the x-axis is a certain value, the out-of-plane displacement (first out-of-plane displacement) w of the web 26 in the z-axis direction at a certain coordinate of the y-axis is w We considered several functions that can estimate the out-of-plane displacement w w is a function of the y-axis coordinate, not a function of the x-axis coordinate (it is a function of a coordinate on the x-axis). As a result, when a shear force F1 acts on the beam 25, when the coordinate of the x-axis is a certain value, the out-of-plane displacement w of the web 26 in the z-axis direction at a certain coordinate of the y-axis is w It was found that the number of terms can be reduced by using equation (10) compared to the Fourier series. Here, N is a natural number greater than or equal to 2, and a0,a n ,b n is an undetermined coefficient. Equation (10) includes a trigonometric term using the power function of the y-axis coordinate. cosπ(2y / b w ) nand cos(π / 2)(2y / b w ) n Equation (10) can be preferably used to estimate the out-of-plane displacement of a plate element such as the web 26.

[0039]

number

[0040] On the other hand, when the coordinate of the x-axis is an arbitrary value, the out-of-plane displacement (second out-of-plane displacement) W of the web 26 in the z-axis direction at a certain coordinate of the y-axis w is estimated by equation (11). As described above, equation (11) expresses the fact that when the y-axis coordinate of the web 26 is a certain value, the out-of-plane displacement of the web 26 in the z-axis direction at a certain x-axis coordinate is sin(π(x+λsin(πy / b w )) / a), where the undetermined coefficient λ in equation (11) is a real number that represents the phase shift in the y-axis direction. In addition, the out-of-plane displacement W in Fig. 3 w is the out-of-plane displacement W in Figure 5. w The out-of-plane displacement W w is a function of the y-axis coordinate and the x-axis coordinate, respectively, and is used to estimate the elastic buckling strength of the web 26. By substituting equation (10) into equation (11), we obtain equation (12).

[0041]

number

[0042] From the above assumption, the out-of-plane displacement W of the upper flange 27 at a given coordinate of the z axis is f1 is estimated by Eq. (14), and the out-of-plane displacement W f2 is estimated by equation (15). Equations (14) and (15) include terms based on trigonometric functions using power functions of the y-axis coordinate.

[0043]

number

[0044] In the calculation method, when a shear force F1 acts on the beam 25, the out-of-plane displacement W of the web 26 is w is estimated using equation (12), and the out-of-plane displacement W of the upper flange 27 is f1 is estimated using equation (14), and the out-of-plane displacement W of the lower flange 28 is f2 is estimated using equation (15). Here, based on the energy method, the strain energy U generated in the web 26 due to the buckling deformation is w is expressed as equation (17), and the strain energy U f is expressed as equation (18).

[0045]

number

[0046] However, the plate stiffness D of the web 26 w is expressed as equation (19). The plate stiffness D of the flanges 27 and 28 f is expressed as in equation (20). The elastic buckling strength of the beam 25 is τ cr Let us assume that. Function δ w is a function that expresses the deformation of web 26 in the x-axis direction when buckling occurs, and is expressed as shown in equation (21), where δ is the x-axis displacement that occurs at the center of upper flange 27 relative to the center of lower flange 28.

[0047]

number

[0048] In addition, the external force potential energy V of web 26 w is expressed as equation (28), and the external force potential energy V of the flanges 27 and 28 is f is expressed as in equation (29).

[0049]

number

[0050] The total potential energy Π of the beam 25 is expressed as the sum of the strain energy and the external force potential energy, as shown in equation (30).

[0051]

number

[0052] In the calculation method, the elastic buckling strength τ of the beam 25 cr , the out-of-plane displacement W of the web 26 w and out-of-plane displacement W of flanges 27 and 28 f1 , W f2 The calculation method is based on the energy method. In other words, the elastic buckling strength τ cr a is the real number that gives the smallest positive value to n ,b n Based on , λ and half wavelength a, the elastic buckling strength τ cr Request.

[0053]

number

[0054] Specifically, the half wavelength a and the undetermined coefficient λ are treated as constants, and the total potential energy Π is calculated by multiplying the undetermined coefficient a n ,b n By solving a simultaneous equation that shows that the function partially differentiated by is equal to 0, n ,b n Find the solution of the simultaneous equations, a n ,b n If there are multiple pairs of n ,b n Among the multiple sets of elastic buckling strength τ cr gives the smallest positive value to a n ,b n Based on the set of (an ,b n (34) Elastic buckling strength τ cr Next, the half wavelength a and the undetermined coefficient λ are treated as variables, and the a n ,b n The half wavelength a and the undetermined coefficient λ are calculated from the equation that shows that the function obtained by partially differentiating the total potential energy Π with respect to the half wavelength a and the undetermined coefficient λ is equal to 0. n ,b n Elastic buckling strength τ calculated based on the set of half wavelength a and undetermined coefficient λ cr is the desired elastic buckling strength τ cr It becomes. The unknown coefficient a that is the solution of the simultaneous equations n ,b n If there is only one pair of n ,b n The set of elastic buckling strength τ cr If we give the smallest positive value to a n ,b n Based on the set of elastic buckling strength τ cr Next, the half wavelength a and the undetermined coefficient λ are treated as variables, and the elastic buckling strength τ cr Request.

[0055] Elastic buckling strength τ cr is the strength taking into consideration the coupled buckling between the web 26 of the beam 25 and the pair of flanges 27, 28.

[0056] [3. Elastic buckling strength when bending moment acts on a beam] Next, a method for calculating the elastic buckling strength when a bending moment acts on beam 25 will be described, which differs from the method for calculating the elastic buckling strength when a shear force acts on beam 25. In this calculation method, as shown in Fig. 7, the position coordinates of beam 25 are recognized based on a right-handed Cartesian coordinate system consisting of x-axis, y-axis, and z-axis. 7 and 8, the center position of the lower flange 28 (one of the pair of flanges) in the y-axis direction is defined as the origin of the y-axis. The direction from the origin of the y-axis toward the upper flange 27 (the other of the pair of flanges) is defined as the positive direction of the y-axis.

[0057] 7, when bending moment F2 about the z-axis acts on end faces 25a of beam 25 in the x-axis direction, beam 25 may buckle. Note that bending moment F2 is transmitted over the entire length of beam 25 in the x-axis direction. The transmitted bending moment F2 acts about an axis that passes through the neutral axis of beam 25 and is parallel to the z-axis (hereinafter referred to as the rotation axis of bending moment F2). The bending moment F2 acting on each end face 25a of the beam 25 in the x-axis direction is an external force of equal magnitude. In this example, a bending moment F2 acts on the beam 25 such that the lower flange 28 receives a tensile force due to the bending moment F2 and the upper flange 27 receives a compressive force due to the bending moment F2, causing the beam 25 to bend convexly downward.

[0058] In this case, toward the first end of web 26 in the x-axis direction (one of end faces 25a in the x-axis direction), web 26 is alternately displaced in the positive direction of the z-axis and the negative direction of the z-axis, so that web 26 as a whole is displaced in a wavy manner in the x-axis direction. In correspondence with web 26, upper flange 27 receiving a compressive force is displaced in a wavy manner, but lower flange 28 receiving a tensile force is hardly displaced.

[0059] In this calculation method, the above assumptions 1 to 6 are made when estimating the elastic buckling strength when a bending moment acts on the beam 25.

[0060] As shown in Figure 7, when bending moment F2 acts on beam 25, web 26 of beam 25 may be displaced in a wavy manner in the x-axis direction. When the y-axis coordinate of web 26 displaced in a wavy manner in the x-axis direction is a certain value, it is assumed that the out-of-plane displacement of web 26 in the z-axis direction at a certain x-axis coordinate is expressed by the formula sin(πx / a). In this case, the wavelength in the x-axis direction of web 26 displaced in a wavy manner in the x-axis direction of web 26 is 2a. The half wavelength (half the length of the wavelength) of web 26 in the x-axis direction is a. FIG. 9 shows the out-of-plane displacement W in the entire region of the beam 25 in the portion where the length of the beam 25 in the x-axis direction is half the wavelength a. w FIG.

[0061] In Fig. 10, the solid line shows the state when bending moment F2 acts on beam 25. The dotted line in Fig. 10 shows the state when bending moment F2 does not act on beam 25.

[0062] When a bending moment F2 acts on the web 26, the out-of-plane displacement of the web 26 has conventionally been estimated using a Fourier series. The inventors have found that, while using trigonometric functions, the number of terms is smaller than that of a Fourier series, when the coordinate of the x-axis is a certain value, the out-of-plane displacement (first out-of-plane displacement) w of the web 26 in the z-axis direction at a certain coordinate of the y-axis is w We considered several functions that can estimate As a result, when a bending moment F2 acts on the beam 25, when the coordinate of the x-axis is a certain value, the out-of-plane displacement w of the web 26 in the z-axis direction at a certain coordinate of the y-axis is w It was found that the number of terms can be reduced by using equation (40) compared to the Fourier series. Here, N is a natural number of 2 or more, and a0,a n ,b n is an undetermined coefficient. Equation (40) includes a trigonometric term using the power function of the y-axis coordinate. cos(2πy n / b w n ) and sin(πy n / b w n) is the basis. Equation (40) can be preferably used to estimate the out-of-plane displacement of a plate element such as the web 26.

[0063]

number

[0064] On the other hand, when the coordinate of the x-axis is an arbitrary value, the out-of-plane displacement (second out-of-plane displacement) W of the web 26 in the z-axis direction at a certain coordinate of the y-axis w is estimated by equation (41). As described above, equation (41) is based on the assumption that when the y-axis coordinate of the web 26 is a certain value, the out-of-plane displacement of the web 26 in the z-axis direction at a certain x-axis coordinate is expressed by the equation sin(πx / a). In addition, the out-of-plane displacement W w is the out-of-plane displacement W in Figure 9. w The out-of-plane displacement W w is a function of the y-axis coordinate and the x-axis coordinate, respectively, and is used to estimate the elastic buckling strength of the web 26. By substituting equation (40) into equation (41), we obtain equation (42).

[0065]

number

[0066] From the above assumption, the out-of-plane displacement W of the upper flange 27 at a given coordinate of the z axis is f1 is estimated by Eq. (44), and the out-of-plane displacement W f2 is estimated by equation (45). Equations (44) and (45) include terms based on trigonometric functions using power functions of the y-axis coordinate.

[0067]

number

[0068] In the calculation method, when a bending moment acts on the beam 25, the out-of-plane displacement W of the web 26 is w is estimated using equation (42), and the out-of-plane displacement W of the upper flange 27 is f1 is estimated using Eq. (44), and the out-of-plane displacement W f2 is estimated using equation (45). Here, based on the energy method, the strain energy U generated in the web 26 due to the buckling deformation is w is expressed as equation (47), and the strain energy U f is expressed as in equation (48).

[0069]

number

[0070] However, the plate stiffness D of the web 26 w is expressed as equation (49). The plate stiffness D of the flanges 27 and 28 f is expressed as in Equation (50). The stress function σ of the web 26 to which the bending moment F2 acts is w is the elastic buckling strength of beam 25, σ cr It is expressed as equation (51), where the stress function σ w considers compression to be positive. Function δ w is the displacement in the x-axis direction at a certain coordinate on the y-axis of the web 26 when buckling occurs, and is expressed as in equation (52), where δ is the displacement in the x-axis direction occurring at the center of the lower flange 28.

[0071]

number

[0072] Stress function σ f1 ,σ f2 is the stress function of each of the flanges 27 and 28 on which the bending moment F2 acts. f1 is -σ cr and the stress function σ f2 is σ cr where the stress function σf1 ,σ f2 considers compression to be positive. Function δ f1 , δ f2 is a function that expresses the displacement of the flanges 27 and 28 in the x-axis direction when buckling occurs. f1 is equal to -δ, and the function δ f2 is equal to δ.

[0073] In addition, the external force potential energy V of web 26 w is expressed as equation (58), and the external force potential energy V of the flanges 27 and 28 is f is expressed as in equation (59).

[0074]

number

[0075] The total potential energy Π of the beam 25 is expressed as the sum of the strain energy and the external force potential energy, as shown in equation (60).

[0076]

number

[0077] In the calculation method, the elastic buckling strength σ of beam 25 cr , the out-of-plane displacement W of the web 26 w and out-of-plane displacement W of flanges 27 and 28 f1 , W f2 The calculation method is based on the energy method, using equations (61) to (64), and the elastic buckling strength σ cr a is the real number that gives the smallest positive value to n ,b n Based on the half wavelength a, the elastic buckling strength σ cr Request.

[0078]

number

[0079] Specifically, with the half wavelength a treated as a constant, the total potential energy Π is multiplied by the undetermined coefficient a n ,b n By solving a simultaneous equation that shows that the function partially differentiated by is equal to 0, n ,b n Find the solution of the simultaneous equations, a n ,b n If there are multiple pairs of n ,b n Among the multiple sets of elastic buckling strength σ cr gives the smallest positive value to a n ,b n Based on the set of (a n ,b n (65) Elastic buckling strength σ cr Next, treat the half wavelength a as a variable and calculate the a n ,b n The half wavelength a is calculated from the equation that shows that the function obtained by partially differentiating the total potential energy Π with respect to the half wavelength a is equal to 0. n ,b n The elastic buckling strength σ calculated based on the set of cr is the desired elastic buckling strength σ cr It becomes. The unknown coefficient a that is the solution of the simultaneous equations n ,b n If there is only one pair of n ,b n The set of elastic buckling strength σ cr If we give the smallest positive value to a n ,b n Based on the set of elastic buckling strength σ cr Next, the half wavelength a is treated as a variable, and the elastic buckling strength σ cr Request.

[0080] Elastic buckling strength σ cr is the strength taking into consideration the coupled buckling between the web 26 of the beam 25 and the pair of flanges 27, 28.

[0081] [4. Consideration of floor structure cross-sectional performance and livability] Next, the results of a study on improving the cross-sectional performance and livability of the floor structure will be explained.

[0082] [4.1.Analysis conditions] A study was conducted using the floor structure 2 shown in Fig. 11. An axis along a part of the multiple girders 15 (hereinafter also referred to as girder 15A) provided in the floor structure 2 is defined as the X-axis. An axis along the remaining parts of the multiple girders 15 (hereinafter also referred to as girder 15B) and multiple minor girders 25 provided in the floor structure 2 is defined as the Y-axis. An axis perpendicular to the X-axis and Y-axis is defined as the Z-axis. The configuration and boundary conditions of the floor structure 2 were set as follows:

[0083] (composition) The column member 10 is made of CFT (800×800×28). The column member 10 is modeled as a rigid rod within a range of ±500 mm above and below the upper and lower ends of the girder 15. The pitch L1 of the column members 10 in the X-axis direction is 19,200 mm. The pitch of the column members 10 in the Y-axis direction is L2 (variable). For the 15A girder, welded H-shaped steel beams with cross-sectional dimensions of 900 x 400 x 19 x 32 were used. - For the main girder 15B, welded assembled H-shaped steel beams with cross-sectional dimensions of 900 x 350 x 22 x 40 were used. The girder 15 is rigidly connected to the column member 10. The multiple small beams 25 are arranged at a pitch L3.

[0084] ·Floor slab 35 is a deck composite slab. The deck plate used is EZ75 (manufactured by Nippon Steel Construction Materials Co., Ltd.), which has multiple ridges. The deck plate has a thickness of 1.2 mm and a height of 75 mm (see Figure 12). The load per unit area of ​​the deck plate is 142.1 N / m 2 It is. Six deck plates (not shown), each with a width of 3,200 mm in the X-axis direction, were lined up in the X-axis direction. -Concrete is lightweight concrete. The design strength of concrete is 18N / mm 2 , specific gravity is 2.0, and the load per unit area of ​​concrete is 2,420N / m 2 The Young's modulus of concrete E c is the Young's modulus of steel, E s 1 / 15 of the force, 205,000 / 15 = 13,667N / mm 2 It is. The thickness of the concrete on the top of the hill is 85 mm (see Figure 12).

[0085] The floor slab 35 shown in Figure 12 was modeled with reference to the following references, for example. As shown in Figure 13, the deck plate 36A was simplified to an equivalent floor slab 35A with a flat shape without ridges and the thickness of the concrete 37A being 122.5 mm. References: Aida et al., "Eigenvibration Analysis of Deck Plate Slabs and Study on Conversion to Flat Plates," Architectural Institute of Japan Technical Report, Vol. 21, No. 47, pp. 171-176, February 2015 As shown in FIG. 14, the secondary beam 25 is joined to the primary beam 15 via a gusset plate 19. The area where the second web 26 of the beam 25 and the gusset plate 19 overlap is modeled so that the displacement of both is shared.

[0086] (Boundary conditions) A symmetric boundary condition was applied on the central axis (center line) of girder 15. The girder 15B was restrained from displacement in the X-axis direction, but was free to displace in the Y-axis and Z-axis directions. The girder 15B was free to rotate about the Y-axis, but was restrained from rotation about the X-axis and Z-axis. The girder 15A was restrained from displacement in the Y-axis direction, but was free to displace in the X-axis and Z-axis directions. The girder 15A was free to rotate about the Y-axis, but was restrained from rotation about the X-axis and Z-axis. -Long-term P as load long to 4,900N / m 2 The floor vibration evaluation P vib (P long / 3).

[0087] A perspective view of an analytical model of the floor structure 2 is shown in Fig. 15. Fig. 16 shows a perspective view of the floor slab 35A. Vibration analysis of floor structure 2 was performed using FEM analysis. The vibration frequency (natural frequency) f floor,1st Furthermore, the frequency f of the first vibration mode in which the second lower flange 28 of the sub-beam 25 rotates around the upper end of the second web 26 was calculated. beam,1st asked for. For the sub-beam 25, analysis was performed using the specifications of beam case 1 to beam case 10 shown in Table 1.

[0088] [Table 1]

[0089] For example, the beam case 1 is a sub-beam 25 which is a welded H-shaped steel. The cross-sectional dimensions of the sub-beam 25 are 400×150×4.5×4.5. The span (length) l of the sub-beam 25 is 4.8 m. The span of the sub-beam 25 corresponds to the pitch L2. That is, the span l of the sub-beam 25 was changed to 4.8 m, 6.4 m, 7.2 m, 9.6 m, and 10.8 m.

[0090] [4.2. How to select the reference beam corresponding to the sub-beam] When selecting the standard beam, the mass W per unit area of ​​the floor slab 35 is taken into consideration as shown in Table 2. d 2,562N / m 2 The load weight W l is rated at 4,900N / m2 based on the Building Standards Act for a building equipped with floor structure 2 to be used as an office. 2 The load weight W l 2,900N / m 2 In addition, if the building is used as a residence, a garage, etc., the live load W l may be set.

[0091] The rolled H-shaped steel beam according to JIS G 3192:2014 "Shape, dimensions, mass and tolerances thereof for hot-rolled steel sections" (hereinafter simply referred to as the JIS standard) that corresponds to the small beam 25 and has the highest ratio of response value to the allowable value of 1 or less when subjected to a specified external force is defined as the standard beam. The specified external force is the mass of the floor slab 35 corresponding to the bearing width b of the sub-beam 25 and the live load W corresponding to the bearing width b of the sub-beam 25. l and the weight (mass) of the minor beam 25. When the floor structure 2 has multiple minor beams 25 in an area surrounded by multiple major beams 15, the burden width b is the pitch L3 of the minor beams 25. When the floor structure 2 has one minor beam 25 in an area surrounded by multiple major beams 15, the burden width b is L1 / 2. In this study, the burden width b was set to 3.2 m. In this case, the uniformly distributed load w acting on the floor structure 2 is obtained by equation (70). (W d +W l )×b ··(70) The bending moment M acting on the sub-beam 25 is given by equation (71). (w / 1000)×l 2 / 8 ··(71) The shear force Q acting on the sub-beam 25 is obtained by equation (72). (w / 1000)×l / 2 (72)

[0092] Table 2 shows the results of determining the cross-sectional performance, etc. for beam cases 1 to 10.

[0093] [Table 2]

[0094] As shown in Table 2, for example, the cross-sectional area A of the beam case 1 is 3,110 mm 2 The cross-sectional area A of the web 26 is calculated as follows: s is 1,760mm 2 The second moment of area I of the beam 25 is 7.52×10 7 mm 4For example, 7.52E+7 is calculated as 7.52×10 7 The section modulus Z of the beam 25 is 3.76×10 5 mm 3 It is required. The mass per unit length of the beam 25 is calculated to be 24.4 kg / m.

[0095] The response value is the bending response value σ b1 (N / mm 2 ) and the shear response value τ s1 (N / mm 2 ) and a deflection response value δ1 (mm).

[0096] [Table 3]

[0097] Bending response value σ b1 is a response value (to a bending moment) caused by a bending moment generated by a predetermined external force acting on the sub-beam 25 and the reference beam. Bending response value σ b1 is obtained by equation (74). σ b1 =M / Z×10 6 (74) Shear response value τ s1 is the response value (to shear force) caused by a shear force acting on the sub-beam 25 and the reference beam when a predetermined external force is applied. s1 is obtained by equation (75). τ s1 = Q × 10 3 / A s (75) The deflection response value δ1 is a response value due to the deflection (maximum deflection) caused by a predetermined external force acting on the sub-beam 25 and the reference beam. The deflection response value δ1 is obtained by equation (76). δ1=5w(l×10 3 ) 4 / (384×205000×I×10 3 ) ··(76)

[0098] The tolerance is a bending tolerance σ b2 (N / mm 2 ) and shear allowance τ s2 (N / mm 2 ) and a deflection allowance δ2 (mm). Bend tolerance σ b2 is the long-term allowable stress for the bending moment acting on the sub-beam 25 and the reference beam (the allowable value for the bending moment acting on the reference beam). In other words, the bending allowable value σ b2 is the yield strength of the sub-beam 25 and the standard beam σ by , and the elastic buckling strength σ when a bending moment acts on the sub-beam 25 and the reference beam cr The smaller value of the two is divided by the safety factor. by is equal to the design standard strength F of the sub-beam 25 and the standard beam. The sub-beam 25 in the present invention is formed of a hot-rolled steel strip. As with conventional steel materials for construction formed of hot-rolled steel strips, the sub-beam 25 in the present invention is wound into a coil and then unwound into a flat plate during the manufacturing process. by is 295N / mm 2 On the other hand, the yield strength of the standard beam σ by Considering that the standard beam is a conventional hot-rolled steel section and no winding or unwinding process is performed during the manufacturing process, for example, 235N / mm 2 It is. Elastic buckling strength of small beam 25 and standard beam σ cr is calculated using the method described in [3.]. For example, the safety factor is 1.5.

[0099] Shear tolerance τ s2 is the long-term allowable stress for the shear force acting on the sub-beam 25 and the reference beam (allowable value for the shear force acting on the sub-beam 25 and the reference beam). In other words, the shear allowable value τ s2 is the yield strength of the sub-beam 25 and the standard beam σ by The value obtained by dividing by √3, and the elastic buckling strength τ of the sub-beam 25 and the standard beam when a shear force acts on the sub-beam 25 and the standard beam crThe smaller value of these is divided by the safety factor. cr can be calculated using the method described in [2.]. The deflection allowable value δ2 is the deflection allowable for the sub-beam 25 and the reference beam (the allowable value allowable for the sub-beam 25 and the reference beam). For example, the deflection allowable value δ2 is the value obtained by dividing the length of the sub-beam 25 and the reference beam by 300. The ratio of the response value to the allowable value when a predetermined external force is applied (hereinafter, referred to as the response value ratio) means the following three ratios. The first ratio is the bending allowance σ b2 Bending response value σ b1 The bending allowance ratio C is the ratio of b (σ b1 / σ b2 ) The second ratio is the shear allowance τ s2 Shear response value τ for s1 The shear allowance ratio C is the ratio of s (τ s1 / τ s2 The third ratio is the deflection tolerance ratio C, which is the ratio of the deflection response value δ1 to the deflection tolerance value δ2. d (δ1 / δ2).

[0100] The rolled H-section steel according to the JIS standard with the highest response value ratio of 1 or less is selected as the reference beam. Beam case 2 is a candidate for the reference beam for beam case 1, which is a sub-beam 25. Similarly, beam case 4 is a candidate for the reference beam for beam case 3, beam case 6 is a candidate for the reference beam for beam case 5, beam case 8 is a candidate for the reference beam for beam case 7, and beam case 10 is a candidate for the reference beam for beam case 9. Table 4 shows the allowable ratios C for beam cases 2, 4, 6, 8, and 10. b ,C s ,C d etc.

[0101] [Table 4]

[0102] In addition, the tolerance ratio C b ,C s ,C d The maximum value of is defined as the tolerance C.

[0103] The allowable value C of beam case 2 is 0.91. When there are multiple reference beams that can be selected as the reference beam for beam case 1, beam case 2 has the highest allowable value C among the multiple reference beams. When there is only one reference beam that can be selected as the reference beam for beam case 1, beam case 2 is that one reference beam. From these, it can be seen that beam case 2 is the reference beam for beam case 1, which is sub-beam 25. Similarly, it can be seen that beam cases 4, 6, 8, and 10 are the reference beams for beam cases 3, 5, 7, and 9.

[0104] [4.3. Comparison of vibration frequencies in the first vibration mode] Table 4 shows the frequency f of the first vibration mode of the composite beam structure 3 for beam cases 1, 3, 5, 7, and 9, which are the sub-beams 25. floor,1st and the frequency f of the first vibration mode of the lower flange 28 of the beam 25 beam,1st The results are shown below. In this case, beam cases 1, 3, 5, 7, and 9 satisfy equation (80). f floor,1st ≦f beam,1st (80) For example, in beam case 1, the frequency f of composite beam structure 3 floor,1st The frequency f of the lower flange 28 of the beam 25 is 8.7 Hz. beam,1st is 18.0 Hz or less, which satisfies equation (80).

[0105] [4.4. Comparison of the ratio of moment of inertia to mass] Hereinafter, the ratio of the second moment of area to the mass will be referred to as the second moment of area ratio. Note that the second moment of area ratio may be the ratio of the second moment of area to the mass per unit length in the material axis direction of the sub-beam 25. As shown in Table 4, the area moment ratio of beam case 1, which is a sub-beam 25, is 6.42 × 10 5 mm 4 / kg, and the second moment ratio of the reference beam, beam case 2, is 4.09×10 5 mm 4 / kg. Therefore, the area second moment ratio of beam case 1, which is the minor beam 25, is larger than the area second moment ratio of beam case 2, which is the reference beam. The ratio of the area second moment ratio of beam case 1 to the area second moment ratio of beam case 2 is 157%. The relationship of the area moment of inertia ratio of beam case 3 to beam case 4, the relationship of the area moment of inertia ratio of beam case 5 to beam case 6, the relationship of the area moment of inertia ratio of beam case 7 to beam case 8, and the relationship of the area moment of inertia ratio of beam case 9 to beam case 10 are also similar.

[0106] In the design method for designing the floor structure 2 of this embodiment, the formula (80) is satisfied and the area second moment ratio of the sub-beam 25 is designed to be larger than the area second moment ratio of the reference beam. In addition, in the construction method for constructing the floor structure 2 of this embodiment, construction is performed so that formula (80) is satisfied and the area second moment ratio of the sub-beam 25 is larger than the area second moment ratio of the reference beam.

[0107] 17 and 18 show an example of an analysis result for the beam case 2. In Fig. 18, it can be seen that the second lower flange 28 of the beam 25 is vibrating. An example of the analysis results for the beam case 4 is shown in Figures 19 to 21. As shown in Figures 19 and 20, in the vibration mode of the entire floor structure 2, it can be seen that the displacement of the center of the floor slab 35A is large. As shown in Figure 21, in the vibration mode of the second lower flange 28 of the beam 25, it can be seen that the vibration displacement of the second lower flange 28 of the beam 25 is large.

[0108] As explained above, generally, the problem from the viewpoint of the habitability of floor structures is the vibrations that occur when people walk on the floor structure. Usually, the vibration frequency when people walk is the source of vibration has a characteristic that a low frequency of about 2 Hz predominates. Usually, the vibration frequency f floor,1st and frequency f beam,1stis greater than the vibration frequency of the human being that is the source of vibration. In the floor structure 2, the design method, and the construction method of this embodiment, by satisfying the formula (80), the vibration frequency due to human walking and the vibration frequency f floor,1st Rather than the difference between the vibration frequency caused by human walking and the vibration frequency f beam,1st The difference between the second lower flange 28 and the second lower flange 26 is large. Therefore, even when subjected to vibration caused by a person walking, the second lower flange 28 of the second lower flange 25 is less likely to vibrate around the upper end of the second web 26 compared to the plurality of girders 15, the plurality of sub-girders 25, and the entire floor slab 35. If the lower flange 28 is prone to vibrate, it becomes necessary to suppress the vibration of the lower flange 28 by thickening the second web 26 or using a vibration-proof material, but this is not necessary in the present invention, and therefore the mass of the sub-girders 25 and the entire floor structure 2 is suppressed from becoming too large. Since the second lower flange 28 of the sub-girders 25 is less likely to vibrate, the livability of the floor structure 2 can be ensured. In addition, a rolled H-shaped steel according to the JIS standard, which has a response value to a predetermined external force equal to or less than a permissible value, is defined as a standard beam corresponding to the sub-beam 25. Compared to this standard beam, the sub-beam 25 of this embodiment has a large area second moment ratio, which is one of the indices representing the cross-sectional performance. This allows the ratio of the cross-sectional performance to the mass of the sub-beam 25 to be increased.

[0109] The response value to a given external force is equal to or less than the allowable value if the bending response value σ b1 is the bending allowance σ b2 and the shear response value τ s1 is the shear tolerance τ s2 This means that the deflection response value δ1 is equal to or less than the deflection allowable value δ2. Generally, when using a reference beam corresponding to the sub-beam 25, bending moment and shear force are more likely to act than axial force. Therefore, the bending moment and shear force that are likely to act on the reference beam, and the bending response value σ b1 , shear response value τ s1 , deflection response value δ1, bending tolerance value σ b2 , shear tolerance τ s2 , and the deflection allowance δ2 can be used to select the reference beam more accurately.

[0110] Bend tolerance σ b2 is the yield strength of the reference beam σ by and elastic buckling strength σ cr The smaller value of the two is divided by the safety factor, and the shear allowable value τ s2 is the yield strength of the reference beam σ by Divided by √3 and elastic buckling strength τ cr The deflection allowable value δ2 is the value obtained by dividing the length of the reference beam by 300. This gives the elastic buckling strength τ cr ,σ cr , and the bending allowance σ b2 and shear allowance τ s2 can be set to a preferred value. Also, the deflection allowable value δ2 can be set to a preferred value.

[0111] The specified external force is the mass of the floor slab 35 corresponding to the bearing width b of the sub-beam 25 and the live load W corresponding to the bearing width b of the sub-beam 25. l and the weight of the minor beam 25. Therefore, the specified external force can be specifically defined using the burden width b, the mass of the floor slab 35, the live load, and the weight of the minor beam 25. Elastic buckling strength τ cr ,σ cr is the out-of-plane displacement W of the web 26 w and out-of-plane displacement W at flanges 27 and 28 f1 , W f2 Based on the energy method, the out-of-plane displacement W of the web 26 is calculated. w and out-of-plane displacement W at flanges 27 and 28 f1 , W f2 Elastic buckling strength τ cr ,σ cr can be efficiently calculated.

[0112] The ratio of mass to length in the axial direction of the sub-beam 25 may be smaller than that of the reference beam. By configuring the sub-beam 25 in this way, the ratio of mass to length in the axial direction of the sub-beam 25 can be made smaller in addition to the ratio of moment of inertia of area being larger than that of the reference beam. Therefore, the sub-beam 25 can be made into a beam with higher cross-sectional performance. It is preferable that the ratio of the mass to the length in the material axis direction of the sub-beam 25 is smaller than that of the reference beam by 30% or more.

[0113] Although one embodiment of the present invention has been described in detail above with reference to the drawings, the specific configuration is not limited to this embodiment, and changes, combinations, deletions, etc. of the configuration are also included within the scope that does not deviate from the gist of the present invention. [Explanation of symbols]

[0114] 2 floor structure 10 Column members 15 Large beam 25 Small beam 26 Second Web (Web) 28 Second lower flange (lower flange) 35 Floor slab

Claims

1. A plurality of column members; A plurality of girders installed on the plurality of column members; A small beam is provided inside the plurality of girders and is supported by the plurality of girders; A floor slab provided above the plurality of girders and the minor girders; In a floor structure comprising: The small beam is a welded H-shaped steel, The vibration frequency of the first vibration mode of the plurality of girders, the sub-girders, and the floor slab is f ｆｌｏｏｒ，１ｓｔ The frequency of the first vibration mode in which the lower flange of the small beam rotates around the upper end of the web is f ｂｅａｍ，１ｓｔ It stipulates that: When a rolled H-shaped steel according to JIS G 3192, which has the same length as the sub-beam and has the highest ratio of response value to the allowable value when subjected to a specified external force and is equal to or less than 1, is defined as a reference beam corresponding to the sub-beam, (1) formula is satisfied, The ratio of the moment of inertia to the mass of the small beam is large compared to the reference beam, A floor structure in which the specified external force is the sum of the mass of the floor slab corresponding to the burden width of the sub-beam, the live load corresponding to the burden width of the sub-beam, and the weight of the sub-beam. f ｆｌｏｏｒ，１ｓｔ ≦f ｂｅａｍ，１ｓｔ ・・(1)

2. The response value is A bending response value to a bending moment generated by the application of the predetermined external force to the reference beam; and a shear response value to a shear force generated by the application of the predetermined external force to the reference beam; and A deflection response value generated by the application of the predetermined external force to the reference beam; and having The tolerance is: A bending allowance for a bending moment acting on the reference beam; A shear allowance for a shear force acting on the reference beam; and A deflection allowable value allowed for the reference beam; having The ratio of the response value to the tolerance when the predetermined external force is applied is equal to or less than 1 and is the highest. a bending tolerance ratio, which is a ratio of the bending response value to the bending tolerance, is 1 or less; a shear tolerance ratio, which is a ratio of the shear response value to the shear tolerance, is 1 or less; The floor structure according to claim 1, wherein a deflection tolerance ratio, which is a ratio of the deflection response value to the deflection tolerance, is equal to or less than 1, meaning that the maximum values ​​of the bending tolerance ratio, the shear tolerance ratio, and the deflection tolerance ratio are the highest.

3. The bending allowable value is a value obtained by dividing the smaller of the yield strength of the reference beam and the elastic buckling strength taking into consideration the coupled buckling between the web of the reference beam and a pair of flanges when a bending moment acts on the reference beam by a safety factor, The shear allowable value is a value obtained by dividing the smaller of the yield strength of the reference beam by √3 and the elastic buckling strength considering the coupled buckling between the web of the reference beam and a pair of flanges when a shear force acts on the reference beam, by a safety factor; The floor structure according to claim 2 , wherein the deflection allowable value is a value obtained by dividing the length of the reference beam by 300.

4. The floor structure according to claim 1 , wherein the sub-beam has a ratio of mass to length in the material axis direction of the sub-beam smaller than that of the reference beam.

5. A plurality of column members; A plurality of girders installed on the plurality of column members; A small beam is provided inside the plurality of girders and is supported by the plurality of girders; A floor slab provided above the plurality of girders and the minor girders; A method for designing a floor structure comprising: The small beam is a welded H-shaped steel, The vibration frequency of the first vibration mode of the plurality of girders, the sub-girders, and the floor slab is f ｆｌｏｏｒ，１ｓｔ The frequency of the first vibration mode in which the lower flange of the small beam rotates around the upper end of the web is f ｂｅａｍ，１ｓｔ It stipulates that: When a rolled H-shaped steel according to JIS G 3192, which has the same length as the sub-beam and has the highest ratio of response value to the allowable value when subjected to a specified external force and is equal to or less than 1, is defined as a reference beam corresponding to the sub-beam, Designed to satisfy formula (2), The sub-beam is designed to have a larger ratio of moment of inertia to mass relative to the reference beam; A method for designing a floor structure, wherein the specified external force is the sum of the mass of the floor slab corresponding to the burden width of the sub-beam, the live load corresponding to the burden width of the sub-beam, and the weight of the sub-beam. f ｆｌｏｏｒ，１ｓｔ ≦f ｂｅａｍ，１ｓｔ ・・(2)

6. The response value is A bending response value to a bending moment generated by the application of the predetermined external force to the reference beam; and a shear response value to a shear force generated by the application of the predetermined external force to the reference beam; and A deflection response value generated by the application of the predetermined external force to the reference beam; and having The tolerance is: A bending allowance for a bending moment acting on the reference beam; A shear allowance for a shear force acting on the reference beam; and A deflection allowable value allowed for the reference beam; having The design method for a floor structure according to claim 5, wherein the ratio of the response value to the allowable value is 1 or less and is the highest when the specified external force is applied means that a bending allowable value ratio which is the ratio of the bending response value to the bending allowable value is 1 or less, a shear allowable value ratio which is the ratio of the shear response value to the shear allowable value is 1 or less, a deflection allowable value ratio which is the ratio of the deflection response value to the deflection allowable value is 1 or less, and the maximum values ​​of the bending allowable value ratio, the shear allowable value ratio, and the deflection allowable value ratio are the highest.

7. The bending allowable value is a value obtained by dividing the smaller of the yield strength of the reference beam and the elastic buckling strength taking into consideration the coupled buckling between the web of the reference beam and a pair of flanges when a bending moment acts on the reference beam by a safety factor, The shear allowable value is a value obtained by dividing the smaller of the yield strength of the reference beam by √3 and the elastic buckling strength considering the coupled buckling between the web of the reference beam and a pair of flanges when a shear force acts on the reference beam, by a safety factor; The method for designing a floor structure according to claim 6 , wherein the deflection allowable value is a value obtained by dividing the length of the reference beam by 300.

8. The floor structure design method according to claim 5 , wherein the sub-beam has a ratio of mass to length in the material axis direction of the sub-beam smaller than that of the reference beam.

9. The method for designing a floor structure according to claim 7, wherein the elastic buckling strength is determined based on an energy method from the out-of-plane displacement of the web and the out-of-plane displacement of the pair of flanges.

10. A plurality of column members; A plurality of girders installed on the plurality of column members; A small beam is provided inside the plurality of girders and is supported by the plurality of girders; A floor slab provided above the plurality of girders and the minor girders; A method for constructing a floor structure comprising: The small beam is a welded H-shaped steel, The vibration frequency of the first vibration mode of the plurality of girders, the sub-girders, and the floor slab is f ｆｌｏｏｒ，１ｓｔ The frequency of the first vibration mode in which the lower flange of the small beam rotates around the upper end of the web is f ｂｅａｍ，１ｓｔ It stipulates that: When a rolled H-shaped steel according to JIS G 3192, which has the same length as the sub-beam and has the highest ratio of response value to the allowable value when subjected to a specified external force and is equal to or less than 1, is defined as a reference beam corresponding to the sub-beam, (3) The construction is carried out so as to satisfy the formula, The sub-beam is constructed so that the ratio of the moment of inertia to the mass is large relative to the reference beam, A construction method for a floor structure, wherein the specified external force is the sum of the mass of the floor slab corresponding to the burden width of the sub-beam, the live load corresponding to the burden width of the sub-beam, and the weight of the sub-beam. f ｆｌｏｏｒ，１ｓｔ ≦f ｂｅａｍ，１ｓｔ ・・(3)

Images