Buckling stress estimation device, buckling stress estimation method, and buckling stress estimation program

Abstract

To provide an estimation device of buckling stress intensity, which estimates buckling stress intensity of an H-shaped section member receiving only a bending moment without convergence calculation.SOLUTION: An estimation device 50 of buckling stress intensity has a pair of flanges and a web, and estimates buckling stress intensity of an H-shaped section member on which only a bending moment acts around a reference axis extending in a plate thickness direction of the web as external force. The estimation device also includes an estimation section 52 for estimating the buckling stress intensity on the basis of a width-thickness ratio of the web in consideration of a buckling restraint effect on the web by the pair of flanges. The buckling restraint effect is represented by a first ratio as a ratio of a plate thickness center distance of the pair of flanges and each width of the pair of flanges and a second ratio as a ratio of each thickness of the pair of flanges and a thickness of the web.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a device for estimating buckling stress, a method for estimating buckling stress, and a program for estimating buckling stress. [Background technology]

[0002] Conventionally, a device for estimating buckling stress is known for estimating buckling stress in H-shaped steel (H-shaped cross section members) subjected to bending moments, taking into account coupled buckling between the web and flange (see, for example, Patent Document 1). In this buckling stress estimation device, the out-of-plane displacement W of the web is used. w The out-of-plane displacement W of the pair of flanges is estimated using equation (1), and the out-of-plane displacement W of the pair of flanges is also estimated. f1 ,W f2 This is estimated using equations (2) and (3).

[0003]

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[0004] However, the axial direction of the H-beam is defined as the x-axis. The web is defined as extending along the x-axis and the y-axis, respectively. The thickness direction of the web is defined as the z-axis. The distance between the centers of a pair of flanges in the direction along the y-axis is defined as b w It is defined as follows: The half-wavelength of the wavy displaced web is defined as a. Then, the buckling stress is calculated using these out-of-plane displacements W. w ,W f1 ,W f2 , and determined in accordance with the Energy Law. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2021-006791 [Overview of the project] [Problems that the invention aims to solve]

[0006] However, in the buckling stress estimation device of Patent Document 1, a convergence (focusing) calculation is required to obtain the buckling stress. In the convergence calculation, if the initial value of an appropriate variable or the setting of the step width is incorrect, it is conceivable that the obtained buckling stress may change or the calculation may take time.

[0007] The present invention has been made in view of such problems, and an object thereof is to provide a buckling stress estimation device, a buckling stress estimation method, and a buckling stress estimation program that estimate the buckling stress of an H-shaped cross-sectional member that receives only a bending moment without performing a convergence calculation.

Means for Solving the Problems

[0008] In order to solve the above problems, the present invention proposes the following means. (1) Aspect 1 of the present invention is a buckling stress estimation device for estimating the buckling stress of an H-shaped cross-sectional member having a pair of flanges and a web, and only a bending moment acts around a reference axis extending in the plate thickness direction of the web as an external force. The device includes an estimation unit that estimates the buckling stress based on the width-thickness ratio of the web in consideration of the buckling restraint effect of the pair of flanges on the web, and the buckling restraint effect is the distance b between the centers of the plate thicknesses of the pair of flanges w and the first ratio that is the ratio of the width B of each of the pair of flanges, and the thickness t of each of the pair of flanges f and the thickness t of the web e w The buckling stress estimation device is represented by using the second ratio that is the ratio of.

[0009] (2) Aspect 2 of the present invention is a buckling stress estimation method for estimating the buckling stress of an H-shaped cross-sectional member having a pair of flanges and a web, and only a bending moment acts around a reference axis extending in the plate thickness direction of the web as an external force. An estimation step of estimating the buckling stress is performed based on the width-thickness ratio of the web in consideration of the buckling restraint effect of the pair of flanges on the web, and the buckling restraint effect is the distance b between the centers of the plate thicknesses of the pair of flanges wThe first ratio is the ratio of the width B of each of the pair of flanges, and the thickness t of each of the pair of flanges. f and the thickness t of the web w This is a method for estimating buckling stress, expressed using the second ratio, which is the ratio of [the two factors].

[0010] (3) A third aspect of the present invention is a buckling stress estimation program for an estimation device that estimates the buckling stress of an H-shaped cross section member having a pair of flanges and a web, wherein the only external force acting is a bending moment around a reference axis extending in the thickness direction of the web, wherein the estimation device functions as an estimation unit that estimates the buckling stress based on the width-to-thickness ratio of the web, taking into account the buckling constraint effect of the pair of flanges on the web, and the buckling constraint effect is the distance between the thickness centers of the pair of flanges b w The first ratio is the ratio of the width B of each of the pair of flanges, and the thickness t of each of the pair of flanges. f and the thickness t of the web w This is a program for estimating buckling stress, expressed using the second ratio, which is the ratio of [the two factors].

[0011] In these inventions, the inventors, after careful consideration, have taken into account the buckling restraint effect of a pair of flanges on the web, expressed using the first ratio and the second ratio. And the web width-to-thickness ratio (b w / t w Based on this, we found that the buckling stress can be estimated for H-shaped cross-section members subjected only to bending moments without performing convergence calculations. Therefore, for H-shaped cross-section members subjected only to bending moments, the buckling stress can be estimated without performing convergence calculations.

[0012] (4) Aspect 4 of the present invention is that the estimation unit calculates the variable X using the first ratio and the second ratio when the H-shaped cross section member satisfies equation (11), using equation (12), the variable X and the width-to-thickness ratio (b w / t w The buckling stress σ is obtained by equation (13) using ). crThe buckling stress estimation device described in (1) may be used to estimate the buckling stress. Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, a1 is a constant between 0.620 and 0.685, a2 is a constant between 77.747 and 88.247, b1 is a constant between 1.445 and 1.550, and b2 is a constant between 5.950 and 6.055.

[0013]

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[0014] (5) Embodiment 5 of the present invention is an estimation step in which, when the H-shaped cross section member satisfies equation (14), the variable X is calculated using the first ratio and the second ratio, and the variable X and the width-to-thickness ratio (b w / t w The buckling stress σ is obtained by equation (16) using ). cr The method for estimating buckling stress described in (2) may also be used. Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, a1 is a constant between 0.620 and 0.685, a2 is a constant between 77.747 and 88.247, b1 is a constant between 1.445 and 1.550, and b2 is a constant between 5.950 and 6.055.

[0015]

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[0016] (6) Aspect 6 of the present invention is that the estimation unit calculates the variable X using the first ratio and the second ratio when the H-shaped cross section member satisfies equation (17), using equation (18), the variable X and the width-to-thickness ratio (b w / t w The buckling stress σ is obtained by equation (19) using ). cr The program used to estimate the buckling stress may be the program described in (3). Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, a1 is a constant between 0.620 and 0.685, a2 is a constant between 77.747 and 88.247, b1 is a constant between 1.445 and 1.550, and b2 is a constant between 5.950 and 6.055.

[0017]

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[0018] Here, equation (11) is identical to equations (14) and (17). Equation (12) is identical to equations (15) and (18), and equation (13) is identical to equations (16) and (19). In these inventions, when the H-shaped cross-sectional member satisfies equation (11), the variable X calculated by equation (12) using the first ratio and the second ratio, this variable X and the width-to-thickness ratio (b w / t w Equation (13) using ) gives the buckling stress σ cr This is estimated. In this way, when the H-shaped cross section member satisfies equation (11), the buckling stress can be accurately estimated for the H-shaped cross section member subjected only to bending moment without performing convergence calculations, using equations (12) and (13).

[0019] (7) Aspect 7 of the present invention is that the estimation unit calculates the variable X using the first ratio and the second ratio when the H-shaped cross section member satisfies equation (21), using equation (22), the variable X and the width-to-thickness ratio (b w / t w The buckling stress σ is obtained by equation (23) using ). cr The buckling stress estimation device described in (1) may be used to estimate the buckling stress. Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, a1 is a constant between 0.726 and 0.796, and a2 is 4.71 × 10 6 The above 5.50 x 10 6 The following are constants, where b1 is a constant between 9.087 and 9.197, and b2 is a constant between 11.976 and 12.086.

[0020]

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[0021] (8) Embodiment 8 of the present invention is an estimation step in which, when the H-shaped cross section member satisfies equation (24), the variable X is calculated using the first ratio and the second ratio, and the variable X and the width-to-thickness ratio (b w / t w The buckling stress σ is obtained by equation (26) using ). cr The method for estimating buckling stress described in (2) may also be used. Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, a1 is a constant between 0.726 and 0.796, and a2 is 4.71 × 10 6 The above 5.50 x 10 6 The following are constants, where b1 is a constant between 9.087 and 9.197, and b2 is a constant between 11.976 and 12.086.

[0022]

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[0023] (9) Aspect 9 of the present invention is that the estimation unit calculates the variable X using the first ratio and the second ratio when the H-shaped cross section member satisfies equation (27), using equation (28), the variable X and the width-to-thickness ratio (b w / t w The buckling stress σ is obtained by equation (29) using ). cr The program used to estimate the buckling stress may be the program described in (3). Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, a1 is a constant between 0.726 and 0.796, and a2 is 4.71 × 10 6 The above 5.50 x 10 6 The following are constants, where b1 is a constant between 9.087 and 9.197, and b2 is a constant between 11.976 and 12.086.

[0024]

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[0025] Here, equation (21) is identical to equations (24) and (27). Equation (22) is identical to equations (25) and (28), and equation (23) is identical to equations (26) and (29). In these inventions, when the H-shaped cross-sectional member satisfies equation (21), the variable X calculated by equation (22) using the first ratio and the second ratio, this variable X and the width-to-thickness ratio (b w / t w Using equation (23), the buckling stress σ cr This is estimated. In this way, when the H-shaped cross section member satisfies equation (21), the buckling stress can be accurately estimated for the H-shaped cross section member subjected only to bending moment without performing convergence calculations, using equations (22) and (23).

[0026] (10) Embodiment 10 of the present invention is that the estimation unit calculates the variable X using the first ratio and the second ratio when the H-shaped cross section member satisfies equation (31), using equation (32), the variable X and the width-to-thickness ratio (b w / t w The buckling stress σ is obtained by equation (33) using ). cr The buckling stress estimation device described in (1) may be used to estimate the buckling stress. Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a1 has an absolute value of 8.10 × 10 6 The above 9.10 × 10 6 The following constants apply, where a2 has an absolute value of 5.306 × 10⁻⁶. 3 The above is 6.206 × 10 3 The following are constants, where b1 is a constant between -8.087 and -7.887, and b2 is a constant between -6.553 and -6.353.

[0027]

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[0028] (11) In embodiment 11 of the present invention, in the estimation step, when the H-shaped cross section member satisfies equation (34), the variable X is calculated using the first ratio and the second ratio, and the variable X and the width-to-thickness ratio (b w / t w The buckling stress σ is obtained by equation (36) using ). cr The method for estimating buckling stress described in (2) may also be used. Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a1 has an absolute value of 8.10 × 10 6 The above 9.10 × 10 6 The following constants apply, where a2 has an absolute value of 5.306 × 10⁻⁶. 3 The above is 6.206 × 10 3 The following are constants, where b1 is a constant between -8.087 and -7.887, and b2 is a constant between -6.553 and -6.353.

[0029]

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[0030] (12) Aspect 12 of the present invention is that the estimation unit calculates the variable X using the first ratio and the second ratio when the H-shaped cross section member satisfies equation (37), using equation (38), the variable X and the width-to-thickness ratio (b w / t w The buckling stress σ is obtained by equation (39) using ). cr The program used to estimate the buckling stress may be the program described in (3). Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a1 has an absolute value of 8.10 × 10 6 The above 9.10 × 10 6 The following constants apply, where a2 has an absolute value of 5.306 × 10⁻⁶. 3 The above is 6.206 × 10 3 The following are constants, where b1 is a constant between -8.087 and -7.887, and b2 is a constant between -6.553 and -6.353.

[0031]

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[0032] Here, equation (31) is identical to equations (34) and (37). Equation (32) is identical to equations (35) and (38), and equation (33) is identical to equations (36) and (39). In these inventions, when the H-shaped cross-sectional member satisfies equation (31), the variable X calculated by equation (32) using the first ratio and the second ratio, this variable X and the width-to-thickness ratio (b w / t w Equation (33) using ) gives the buckling stress σ cr This is estimated. In this way, when the H-shaped cross section member satisfies equation (31), equations (32) and (33) can be used to accurately estimate the buckling stress for the H-shaped cross section member subjected only to bending moment without performing convergence calculations.

[0033] (13) Aspect 13 of the present invention is that the estimation unit calculates the variable X using the first ratio and the second ratio when the H-shaped cross section member satisfies equation (41), using equation (42), the variable X and the width-to-thickness ratio (b w / t w The buckling stress σ is obtained by equation (43) using ). cr The buckling stress estimation device described in (1) may be used to estimate the buckling stress. Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a1 has an absolute value of 4.05 × 10 3 The above 4.30 × 10 3 The following are constants, where a2 is a constant with an absolute value between 430 and 460, b1 is a constant between -3.21 and -3.17, and b2 is a constant between -4.15 and -3.95.

[0034]

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[0035] (14) Aspect 14 of the present invention is that in the estimation step, when the H-shaped cross section member satisfies equation (44), the variable X is calculated using the first ratio and the second ratio, and the variable X and the width-to-thickness ratio (b w / t w The buckling stress σ is obtained by equation (46) using ). cr The method for estimating buckling stress described in (2) may also be used. Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a1 has an absolute value of 4.05 × 10 3 The above 4.30 × 10 3 The following are constants, where a2 is a constant with an absolute value between 430 and 460, b1 is a constant between -3.21 and -3.17, and b2 is a constant between -4.15 and -3.95.

[0036]

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[0037] (15) Aspect 15 of the present invention is that the estimation unit calculates the variable X using the first ratio and the second ratio when the H-shaped cross section member satisfies equation (47), using equation (48), the variable X and the width-to-thickness ratio (b w / t w The buckling stress σ is obtained by equation (49) using ). cr The program used to estimate the buckling stress may be the program described in (3). Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a1 has an absolute value of 4.05 × 10 3 The above 4.30 × 10 3 The following are constants, where a2 is a constant with an absolute value between 430 and 460, b1 is a constant between -3.21 and -3.17, and b2 is a constant between -4.15 and -3.95.

[0038]

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[0039] Here, equation (41) is the same as equations (44) and (47). Equation (42) is the same as equations (45) and (48), and equation (43) is the same as equations (46) and (49). In these inventions, when the H-shaped cross-sectional member satisfies equation (41), the variable X calculated by equation (42) using the first ratio and the second ratio, this variable X, and the width-to-thickness ratio (b w / t w ) are used in equation (43) to estimate the buckling stress σ cr . Thus, when the H-shaped cross-sectional member satisfies equation (41), using equations (42) and (43), for an H-shaped cross-sectional member subjected only to a bending moment, the buckling stress can be accurately estimated without performing a convergence calculation.

Advantages of the Invention

[0040] In the buckling stress estimation device, buckling stress estimation method, and buckling stress estimation program of the present invention, for an H-shaped cross-sectional member subjected only to a bending moment, the buckling stress can be estimated without performing a convergence calculation.

Brief Description of the Drawings

[0041] [Figure 1] It is a perspective view of a building including an H-shaped steel to which the buckling stress estimation device according to an embodiment of the present invention is applied. [Figure 2] It is a diagram showing an overview of the buckling stress estimation device. [Figure 3] It is a perspective view schematically showing a state where an H-shaped steel subjected to a bending moment is buckled. [Figure 4] It is a side view of a main part showing the first buckling mode of the H-shaped steel. [Figure 5] It is a side view of a main part showing the second buckling mode of the H-shaped steel. [Figure 6] It is a cross-sectional view perpendicular to the material axis direction of the H-shaped steel. [Figure 7] It is a flowchart showing the buckling stress estimation method according to an embodiment of the present invention. [Figure 8]This figure shows the relationship between buckling stress σcr,cal and buckling stress σcr,FEM when the H-shaped steel satisfies equation (61). [Figure 9] This figure shows the relationship between buckling stress σcr,cal and buckling stress σcr,FEM when the H-shaped steel satisfies equation (62). [Figure 10] This figure shows the relationship between buckling stress σcr,cal and buckling stress σcr,FEM when the H-shaped steel satisfies equation (63). [Figure 11] This figure shows the relationship between buckling stress σcr,cal and buckling stress σcr,FEM when the H-shaped steel satisfies equation (64). [Modes for carrying out the invention]

[0042] Hereinafter, an embodiment of the buckling stress estimation device, buckling stress estimation method, and buckling stress estimation program according to the present invention will be described with reference to Figures 1 to 11.

[0043] [1. Structure of buildings equipped with H-shaped steel] This buckling stress estimation device (hereinafter simply referred to as the estimation device) is used, for example, to estimate the buckling stress of an H-shaped steel beam (H-shaped cross section member) 10 used as a steel beam in building 1 shown in Figure 1. The H-shaped steel beam 10 comprises a first flange 11, a second flange 12, and a web 13. In Figure 1, the floor slab 20, which will be described later, is shown by a dashed line. The first flange 11, the second flange 12, and the web 13 are each formed from steel plates.

[0044] The H-shaped steel beam 10 extends, for example, in a direction along a horizontal plane. The first flange 11 is formed in a flat plate shape and is positioned such that the thickness direction of the first flange 11 is aligned with the vertical direction. The second flange 12 is formed in a flat plate shape and is positioned above the first flange 11. The thickness direction of the second flange 12 is aligned with the vertical direction. The web 13 is formed in a flat plate shape that exhibits a rectangular shape when viewed in the thickness direction of the web 13. The web 13 is positioned so that its thickness direction aligns with the horizontal plane. The web 13 is joined to the center in the width direction on the upper surface of the first flange 11 and to the center in the width direction on the lower surface of the second flange 12, respectively.

[0045] The ends of the H-shaped steel beam 10 in the direction of the material axis are fixed to columns 15, etc. The H-shaped steel beam 10 supports the floor slab 20 from below. Shear connectors 21, such as headed studs, are provided on the second flange 12 of the H-shaped steel beam 10. The shear connectors 21 are embedded in the floor slab 20. Building 1 is used by installing equipment (not shown) on the floor slab 20, etc.

[0046] [2. Configuration of the estimation device] Figure 2 shows the estimation device 50 of this embodiment. The estimation device 50 is a computer and includes a CPU (Central Processing Unit) 51, a main memory 55, an auxiliary storage device 60, an input / output interface (IO / I / F) 65, and a recording / playback device 70. The CPU 51, main memory 55, auxiliary storage device 60, input / output interface 65, and recording / playback device 70 are connected to each other by a bus 75. The main memory 55 is RAM (Random Access Memory) or the like, which serves as the work area for the CPU 51. The input / output interface 65 is connected to an input device 66 such as a keyboard or mouse, and a display device 67. The recording and playback device 70 records and plays back data to and from a recording medium 71 such as a USB (Universal Serial Bus) memory.

[0047] The auxiliary storage device 60 is a hard disk drive or the like that stores various data and programs. The auxiliary storage device 60 stores a buckling stress estimation program (hereinafter simply referred to as the estimation program) 61 for making the computer function as an estimation device 50, as well as various other programs such as the OS program. The estimation program 61 and other programs are imported from the recording medium 71 to the auxiliary storage device 60 via the recording and playback device 70. The estimation program 61 and the like are stored on the recording medium 71. These programs may also be imported into the auxiliary storage device 60 from an external device via a disc-type recording medium such as a CD or DVD, or via a communication device (not shown).

[0048] The CPU 51 performs various calculations. Functionally, the CPU 51 includes an estimation unit 52. The processing performed by the estimation unit 52 will be described in detail later. The estimation unit 52, a functional component of the CPU 51, functions when the CPU 51 executes an estimation program 61, etc., stored in the auxiliary storage device 60. The estimation program 61, etc., is a program for the estimation device 50. The estimation program 61 causes the estimation device 50 to function as the estimation unit 52.

[0049] [3. Processing details of the estimation device and estimation unit] As shown in Figure 3, the estimation device 50 estimates the buckling stress of the H-shaped steel beam 10, where only a bending moment F1 (pure bending moment) acts as an external force around a reference axis L5 extending in the thickness direction of the web 13. Figure 3 shows the H-shaped steel beam 10 in a buckled state. The bending moment F1 acts on each end face 10a of the H-shaped steel beam 10 in the material axis direction. The H-shaped steel beam 10 is subjected to uniform bending.

[0050] Here, we will explain the buckling behavior of the H-shaped steel beam 10. As shown in Figure 3, the outer edge of the first flange 11 on the side of arrow A1 is called the first outer edge 11a. The outer edge of the first flange 11 on the opposite side of arrow A1 is called the second outer edge 11b. Fig. 4 shows the first buckling mode of the H-shaped steel 10, and Fig. 5 shows the second buckling mode of the H-shaped steel 10. Figs. 4 and 5 are views of the buckled H-shaped steel 10 seen in the direction of arrow A1 in Fig. 3. In Figs. 4 and 5, the portions on the web 13 where there is no displacement in the thickness direction of the web 13 are shown in white, and the portions with more displacement in the thickness direction of the web 13 are shown in a color closer to black. The web 13 is displaced in a wavy pattern alternately on one side and the other side in the thickness direction of the web 13 in the material axis direction. Note that in Figs. 4 and 5, the displacement is exaggerated.

[0051] As shown in Fig. 4, in the H-shaped steel 10 in the first buckling mode, the length of the buckling wavelength in the material axis direction is relatively short. The displacement in the thickness direction of the first flange 11 is relatively small. The first buckling mode is a buckling that is likely to occur when the H-shaped steel 10 has a cross-sectional shape other than the case where the second buckling mode described below is likely to occur. On the other hand, as shown in Fig. 5, in the H-shaped steel 10 in the second buckling mode, the length of the buckling wavelength in the material axis direction is relatively long. The displacement in the thickness direction of the first flange 11 is relatively large. The second buckling mode is a buckling that is likely to occur when the aspect ratio of the cross-section of the H-shaped steel 10 (the slenderness ratio (H / B) of the H-shaped steel 10 with respect to the width B of the flanges 11, 12) is small and the thickness ratio (the ratio of the thickness t w of the web 13 to the thickness t f of the flanges 11, 12 f t w / t

[0052] Here, as shown in Fig. 6, the dimensions in the cross-section perpendicular to the material axis direction of the H-shaped steel 10 are defined. The thickness of each of the flanges 11, 12 is defined as t f (mm). The width of each of the flanges 11, 12 is defined as B (mm). The value of half of the width of each of the flanges 11, 12 is defined as b f (mm). The thickness of the web 13 is defined as t w (mm). The width of the web 13 is defined as d (mm). The slenderness of the H-shaped steel 10 is defined as H (mm). The distance between the centers of the thicknesses of the flanges 11, 12 is b w(mm) is specified. Distance between the centers of the plate thickness b w This refers to the distance between the center of the first flange 11 in the thickness direction and the center of the second flange 12 in the thickness direction, in the direction in which flanges 11 and 12 face each other. In this case, the distance between the centers of the plate thickness is b. w (Ht f ) is equal to . The value of H is (d+2t f It is equal to ). The Young's modulus of the H-shaped steel beam 10 is defined as E (N / mm). The Poisson's ratio of the H-shaped steel beam 10 is defined as ν (-). The width-to-thickness ratio of web 13 is (b w / t w ) is defined as follows: The first ratio is defined as the distance between the centers of the plate thickness b w The ratio of width B (b w The second ratio is defined as the thickness t. f and thickness t w The ratio (t f / t w ) is stipulated.

[0053] In the H-shaped steel beam 10, the preferred range of dimensions is as follows: • Width-to-thickness ratio of flanges 11 and 12 (b f / t f ): 20 or less • Web width-to-thickness ratio of web 13 (b w / t w ): 300 or less • Aspect ratio (dB): 1.0 or higher, 10 or lower ·Plate thickness ratio (t f / t w ):1.0 or more and 5.0 or less

[0054] In the estimation device described in Patent Document 1, convergence calculations are required to determine the buckling stress. As a result of diligent research, the inventors have investigated a method to explicitly determine the buckling stress without using convergence calculations. Then, the estimation unit 52 considers the buckling restraint effect of the flanges 11 and 12 on the web 13 and calculates the width-to-thickness ratio of the web 13 (b w / t w We proposed a method to estimate buckling stress based on the first ratio (b). Specifically, the estimation unit 52 uses the first ratio (b w / B) and the second ratio (tf / t w Equation (56) calculates the variable X using the variable X and the width-to-thickness ratio (b w / t w The buckling stress σ is obtained by equation (57) or (58) using ). cr (N / mm 2 We estimate ). Here, a1, a2, b1, and b2 are real constants.

[0055]

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[0056] Note that the first term on the right-hand side of equation (57), "23.9," is the buckling coefficient of a flat plate where two sides are simply supported and only a bending moment acts on it. In the second term on the right-hand side of equation (57), (a1X / (X+a2)) is added to 1. Since the value of (a1X / (X+a2)) is positive, the buckling coefficient corresponding to the H-shaped steel 10, (23.9+(a1X / (X+a2)) is greater than 23.9. This (a1X / (X+a2)) is the term in equation (57) that takes into account the buckling restraint effect of flanges 11 and 12 on the webs.

[0057] The first term on the right-hand side of equation (58), "0.425," is the buckling coefficient of a flat plate that is simply supported on three sides and subjected only to compressive forces. In the second term on the right-hand side of equation (58), (a1X / (X+a2)) is added to 1. Since the value of (a1X / (X+a2)) is positive, the buckling coefficient corresponding to the H-shaped steel 10, (0.425+(a1X / (X+a2)) is greater than 0.425.

[0058] The buckling constraint effect is given by the first ratio (b) as shown in equation (56). w / B) and the second ratio (t f / t w It is expressed using ).

[0059] Furthermore, the inventors determined that in each case where the cross-sectional dimensions of the H-shaped steel 10 satisfy equations (61) to (64), the buckling stress σ crWe found that the range of the constants a1, a2, b1, and b2 appropriate for finding the value changes.

[0060]

number

[0061] For example, equation (61) corresponds to the case where the buckling of the web 13 is dominant in the first buckling mode, and the buckling strength of the H-shaped steel (H-section member) 10 is determined by the buckling of the web 13. Equation (62) corresponds to the case where the buckling of the web 13 in the first buckling mode is the main factor determining the buckling strength of the H-shaped steel 10, but the buckling of the flanges 11 and 12 also affects the buckling strength of the H-shaped steel 10. Equation (63) corresponds to the case where the buckling of flanges 11 and 12 in the second buckling mode is the main factor determining the buckling strength of the H-shaped steel 10, but the buckling of the web 13 also affects the buckling strength of the H-shaped steel 10. Equation (64) corresponds to the case where the buckling of flanges 11 and 12 is dominant in the second buckling mode, and the buckling strength of the H-shaped steel 10 is determined by the buckling of flanges 11 and 12.

[0062] Buckling stress σ estimated by FEM (Finite Element Method) cr,FEM Assuming this is the true value, this buckling stress σ cr,FEM The buckling stress σ was determined to be... cr,FEM The maximum error in the buckling stress estimated by the estimation device described in Patent Document 1 is approximately 5%. Buckling stress degree σ cr,FEM The buckling stress σ estimated by the estimation device 50 for cr The constants a1, a2, b1, and b2 were determined so that the maximum error would be approximately 7%. The constants a1, a2, b1, and b2 in this case are preferably within the following ranges, depending on equations (61) to (64) that the H-shaped steel 10 satisfies.

[0063] If the H-shaped steel 10 satisfies equation (61), the constant a1 is between 0.620 and 0.685. The constant a2 is between 77.747 and 88.247, the constant b1 is between 1.445 and 1.550, and the constant b2 is between 5.950 and 6.055. Then, according to equations (56) and (57), the buckling stress σ cr We estimate this. Furthermore, it is most preferable that the constants a1, a2, b1, and b2 have the following values: Constant a1 is 0.645, Constant a2 is 83.247, Constant b1 is 1.495, and Constant b2 is 6.000 (hereinafter referred to as the optimal values ​​of constants a1, a2, b1, and b2 when the H-shaped steel 10 satisfies equation (61)).

[0064] If the H-beam 10 satisfies equation (62), the constant a1 is between 0.726 and 0.796. The constant a2 is 4.71 × 10 6 The above 5.50 x 10 6 The constant b1 is between 9.087 and 9.197, and the constant b2 is between 11.976 and 12.086. Then, according to equations (56) and (57), the buckling stress σ cr We estimate this. Furthermore, it is most preferable that the constants a1, a2, b1, and b2 have the following values: Constant a1 is 0.756, Constant a2 is 5004649, Constant b1 is 9.142, and Constant b2 is 12.031 (hereinafter referred to as the optimal values ​​of constants a1, a2, b1, and b2 when the H-shaped steel 10 satisfies equation (62)).

[0065] If the H-beam 10 satisfies equation (63), then the absolute value of the constant a1 is 8.10 × 10 6 The above 9.10 × 10 6 The absolute value of the constant a2 is 5.306 × 10⁻⁶. 3 The above is 6.206 × 10 3 The constant b1 is between -8.087 and -7.887, and the constant b2 is between -6.553 and -6.353. Then, according to equations (56) and (58), the buckling stress σ cr We estimate this. The constants a1, a2, b1, and b2 are most preferably the following values: Constant a1 is 8622949, Constant a2 is 5506.458, Constant b1 is -7.987, and Constant b2 is -6.453 (hereinafter referred to as the optimal values ​​of constants a1, a2, b1, and b2 when the H-shaped steel 10 satisfies equation (63)).

[0066] If the H-beam 10 satisfies equation (64), then the absolute value of the constant a1 is 4.05 × 10 3 The above 4.30 × 10 3 The following applies: The absolute value of constant a2 is between 430 and 460, constant b1 is between -3.21 and -3.17, and constant b2 is between -4.15 and -3.95. Then, according to equations (56) and (58), the buckling stress σ cr We estimate this. Furthermore, the constants a1, a2, b1, and b2 are most preferably the following values: Constant a1 is 4176.84, Constant a2 is 444.227, Constant b1 is -3.188, and Constant b2 is -4.022 (hereinafter referred to as the optimal values ​​of constants a1, a2, b1, and b2 when the H-shaped steel 10 satisfies equation (64)).

[0067] Taking a safety factor into account, the first term on the right-hand side of equation (57) may be set to 23.9 or less. That is, equation (57) may be modified to look like equation (67) using a coefficient α greater than 0 and less than or equal to 1.0 (0 < α ≤ 1.0). Similarly, equation (58) may be modified to look like equation (68).

[0068]

number

[0069] However, σ cr ’ The buckling stress σ is determined by considering the safety factor. cr This is the buckling stress of the H-shaped steel beam 10, calculated as a smaller value than the given value. In equations (56) to (58), the distance between the centers of the plate thickness is b. w Instead, the internal dimensions of web 13 bw '(=b w -t f ), you may also use H.

[0070] [4. Method for estimating buckling stress] Next, the method for estimating buckling stress in this embodiment (hereinafter simply referred to as the estimation method) will be described. Figure 7 is a flowchart of the estimation method S1. In estimation method S1, the buckling stress of an H-shaped steel beam 10 is estimated when only a bending moment F1 acts as an external force around the reference axis L5. In estimation method S1, estimation step S5 is performed. In estimation step S5, the buckling restraint effect of flanges 11 and 12 on the web is considered, and the width-to-thickness ratio of the web 13 (b w / t w Based on ), buckling stress σ cr We estimate this. In estimation step S5, based on equations (61) to (64), the buckling stress σ is calculated using equations (56) to (58) as described above. cr We estimate this. Once estimation process S5 is completed, all steps of estimation method S1 are finished, and the buckling stress σ of the H-shaped steel 10 is determined. cr It is estimated that...

[0071] [5. Estimation results using the estimation device] Figures 8 to 11 show the estimation results obtained by the estimation device 50. In Figures 8 to 11, the horizontal axis represents the buckling stress σ estimated by the estimation device 50. cr (σ cr,cal )(N / mm 2 The graph shows the buckling stress σ estimated by the buckling eigenvalue analysis of FEM, with the vertical axis representing the buckling stress σ. cr,FEM (N / mm 2 ) represents the buckling stress σ cr,cal σ is the buckling stress cr,FEM The closer the value is to the given value, the higher the accuracy of the buckling stress estimation is considered to be. The circles (〇) in Figures 8 to 11 represent the relationship between the vertical axis and the horizontal axis in each analysis case for the H-shaped steel beam 10 in which the buckling eigenvalue analysis was performed. Also, line L1 in Figures 8 to 11 represents the buckling stress σ cr,cal σ is the buckling stresscr,FEM This represents a state that is equal to [a certain value]. Figure 8 shows the relationship when the H-shaped steel beam 10 satisfies equation (61). Similarly, Figure 9 shows the relationship when the H-shaped steel beam 10 satisfies equation (62), Figure 10 shows the relationship when the H-shaped steel beam 10 satisfies equation (63), and Figure 11 shows the relationship when the H-shaped steel beam 10 satisfies equation (64).

[0072] For the buckling eigenvalue analysis using FEM, an analysis model was used for a shell model of an H-shaped steel beam 10 with a material axial length 50 times its depth, and meshed to approximately 20 mm squares. Here, the material axial direction of the analysis model is defined as the x-axis direction, the depth direction as the y-axis direction, and the width direction of the flanges 11 and 12 as the z-axis direction. At this time, the nodes at both ends of the analysis model in the x-axis direction were rigidly connected to the representative nodes at the center of the cross-sections at both ends. Then, the analysis model was given the following constraints as geometric boundary conditions: (1) to (3). (1) The displacement in the z-axis direction is constrained at the nodes on the joint line between flanges 11, 12 and web 13. (2) At one of the representative nodes at both ends of the H-shaped steel beam 10 in the x-axis direction, the displacement in the y-axis direction and the z-axis direction, and the rotation around the x-axis and the y-axis are constrained. (3) At the other representative node of both ends of the H-shaped steel 10 in the direction of the material axis, displacement in the y-axis direction, z-axis direction, and x-axis direction, and rotation around the x-axis and y-axis are constrained. Then, a uniform bending moment in the axial direction of the material was applied to the analytical model as a mechanical boundary condition, and the analysis was carried out.

[0073] When the H-shaped steel beam 10 shown in Figure 8 satisfies equation (61), the thickness t f For 1928 cases of H-shaped steel 10 with varying values, the buckling stress σ cr,cal and buckling stress σ cr,FEM This was compared with the following. The values ​​of the constants a1, a2, b1, and b2 used in this comparison were the optimal values ​​for the constants a1, a2, b1, and b2 when the H-shaped steel 10 satisfies equation (61) (constant a1 is 0.645, constant a2 is 83.247, constant b1 is 1.495, and constant b2 is 6.000). Buckling stress degree σcr,FEM Buckling stress σ cr,cal The maximum error was approximately 3.6%. Figure 8 shows that the buckling stress σ is calculated with sufficient accuracy for practical use. cr,cal It was found that this could be estimated.

[0074] When the H-shaped steel beam 10 shown in Figure 9 satisfies equation (62), the thickness t f For 589 cases of H-shaped steel 10 with varying values, the buckling stress σ cr,cal and buckling stress σ cr,FEM This was compared with the following. The values ​​of the constants a1, a2, b1, and b2 used in this comparison were the optimal values ​​for the constants a1, a2, b1, and b2 when the H-shaped steel 10 satisfies equation (62) (constant a1 is 0.756, constant a2 is 5004649, constant b1 is 9.142, and constant b2 is 12.031). Buckling stress degree σ cr,FEM Buckling stress σ cr,cal The maximum error was approximately 3.4%. From Figure 9, the buckling stress σ was calculated with sufficient accuracy for practical use. cr,cal It was found that this could be estimated.

[0075] When the H-shaped steel beam 10 shown in Figure 10 satisfies equation (63), the thickness t f For 116 cases of H-shaped steel 10 with varying parameters, the buckling stress σ cr,cal and buckling stress σ cr,FEM This was compared with the following. The values ​​of the constants a1, a2, b1, and b2 used in this comparison were the optimal values ​​for the constants a1, a2, b1, and b2 when the H-shaped steel 10 satisfies equation (63) (constant a1 is 8622949, constant a2 is 5506.458, constant b1 is -7.987, and constant b2 is -6.453). Buckling stress degree σ cr,FEM Buckling stress σ cr,cal The maximum error was approximately 1.8%. From Figure 10, the buckling stress σ was calculated with sufficient accuracy for practical use. cr,cal It was found that this could be estimated.

[0076] When the H-shaped steel beam 10 shown in Figure 11 satisfies equation (64), the thickness t fFor 384 cases of H-shaped steel 10 with varying parameters, the buckling stress σ cr,cal and buckling stress σ cr,FEM This was compared with the following. The values ​​of the constants a1, a2, b1, and b2 used in this comparison were the optimal values ​​for the constants a1, a2, b1, and b2 when the H-shaped steel 10 satisfies equation (64) (constant a1 is 4176.84, constant a2 is 444.227, constant b1 is -3.188, and constant b2 is -4.022). Buckling stress degree σ cr,FEM Buckling stress σ cr,cal The maximum error was approximately 4.3%. From Figure 11, the buckling stress σ was calculated with sufficient accuracy for practical use. cr,cal It was found that this could be estimated.

[0077] As described above, in any case where the H-shaped steel 10 satisfies equation (61) to (64), the buckling stress σ is obtained with sufficient accuracy for practical purposes. cr,cal It was found that this could be estimated.

[0078] [6. Effects of this embodiment] As described above, in the estimation device 50, estimation method S1, and estimation program 61 of this embodiment, the inventors have carefully considered the buckling restraint effect of flanges 11 and 12 on the web 13, expressed using the first ratio and the second ratio. w / t w Based on this, the buckling stress can be estimated for an H-shaped steel beam 10 subjected only to a bending moment F1 without performing convergence calculations. cr We found that it is possible to estimate this. Therefore, for an H-shaped steel beam 10 acting only on a bending moment F1, the buckling stress σ can be calculated without performing a convergence calculation. cr It is possible to estimate this.

[0079] Furthermore, the estimation unit 52 (in estimation process S5) calculates the variable X using the first ratio and the second ratio according to equation (56) when the H-shaped steel 10 satisfies equation (61), and this variable X and the width-to-thickness ratio (b w / t w Equation (57) using ) gives the buckling stress σcr This is estimated. Thus, using equations (56) and (57), the buckling stress σ for the H-shaped steel 10 subjected only to bending moment F1 can be estimated without performing convergence calculations. cr It is possible to estimate this accurately. The estimation unit 52 calculates the variable X using the first ratio and the second ratio according to equation (56) when the H-shaped steel 10 satisfies equation (62), and this variable X and the width-to-thickness ratio (b w / t w Equation (57) using ) gives the buckling stress σ cr This is estimated. Thus, using equations (56) and (57), the buckling stress σ for the H-shaped steel 10 subjected only to bending moment F1 can be estimated without performing convergence calculations. cr It is possible to estimate this accurately.

[0080] The estimation unit 52 calculates the variable X using the first ratio and the second ratio according to equation (56) when the H-shaped steel 10 satisfies equation (63), and this variable X and the width-to-thickness ratio (b w / t w Using equation (58), the buckling stress σ cr This is estimated. Thus, using equations (56) and (58), the buckling stress σ for the H-shaped steel 10 subjected only to bending moment F1 can be estimated without performing convergence calculations. cr It is possible to estimate this accurately. The estimation unit 52 calculates the variable X using the first ratio and the second ratio according to equation (56) when the H-shaped steel 10 satisfies equation (64), and this variable X and the width-to-thickness ratio (b w / t w Using equation (58), the buckling stress σ cr This is estimated. Thus, using equations (56) and (58), the buckling stress σ for the H-shaped steel 10 subjected only to bending moment F1 can be estimated without performing convergence calculations. cr It is possible to estimate this accurately.

[0081] 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 modifications, combinations, deletions, etc., of the configuration are also included without departing from the spirit of the present invention. For example, in the above embodiment, it is not necessary to use equations (56) to (58) when estimating the buckling stress. The H-shaped cross-sectional member is assumed to be an H-shaped steel beam 10. However, the H-shaped cross-sectional member is not limited to an H-shaped steel beam 10; it may have a pair of flanges and a web. [Explanation of symbols]

[0082] 10 H-shaped steel (H-shaped cross-section member) 11. First flange 12. Second flange 13 Web 50 Estimation device (device for estimating buckling stress) 52 Estimation part 61. Estimation Program (Program for estimating buckling stress) F1 Bending moment L5 Reference axis S1 Estimation Method (Method for Estimating Buckling Stress) S5 Estimation process

Claims

1. A buckling stress estimation device for estimating the buckling stress of an H-shaped cross section member having a pair of flanges and a web, wherein the only external force acting is a bending moment around a reference axis extending in the thickness direction of the web, The system includes an estimation unit that estimates the buckling stress based on the width-to-thickness ratio of the web, taking into account the buckling restraint effect of the pair of flanges on the web. The buckling restraint effect is due to the distance b between the center thicknesses of the pair of flanges. ｗ The first ratio is the ratio of the width B of each of the pair of flanges, and the thickness t of each of the pair of flanges. ｆ and the thickness t of the web ｗ A device for estimating buckling stress, expressed using the second ratio, which is the ratio of [the two factors].

2. The estimation unit calculates the buckling stress σ using equation (2), which uses the first ratio and the second ratio to calculate the variable X when the H-shaped cross section member satisfies equation (1), and equation (3), which uses the variable X and the width-to-thickness ratio. ｃｒ An apparatus for estimating buckling stress according to claim 1, which estimates the following: Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a １ is a constant between 0.620 and 0.685, and a ２ b is a constant between 77.747 and 88.247, １ b is a constant between 1.445 and 1.550, and ２ This is a constant between 5.950 and 6.

055. [Math 1]

3. When the H-shaped cross-sectional member satisfies the formula (4), the estimation unit calculates the variable X using the first ratio and the second ratio, and calculates the buckling stress σ by the formula (6) using the variable X and the width-to-thickness ratio. ｃｒ The buckling stress estimation device according to claim 1, which estimates the buckling stress. Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a １ is a constant between 0.726 and 0.796, and a ２ is 4.71 x 10 ６ The above 5.50 x 10 ６ The constants are as follows: b １ b is a constant between 9.087 and 9.197, ２ This is a constant between 11.976 and 12.

086. [Math 2]

4. The estimation unit calculates the buckling stress σ using equation (8), which uses the first ratio and the second ratio to calculate the variable X when the H-shaped cross section member satisfies equation (7), and equation (9), which uses the variable X and the width-to-thickness ratio. ｃｒ An apparatus for estimating buckling stress according to claim 1, which estimates the following: Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a １ The absolute value is 8.10 × 10 ６ The above 9.10 x 10 ６ The constants are as follows: a ２ The absolute value is 5.306 × 10 ３ The above 6.206 × 10 ３ The constants are as follows: b １ b is a constant between -8.087 and -7.887, ２ is a constant between -6.553 and -6.

353. [Math 3]

5. The estimation unit calculates the buckling stress σ using equation (11), which uses the first ratio and the second ratio to calculate the variable X when the H-shaped cross section member satisfies equation (10), and equation (12), which uses the variable X and the width-to-thickness ratio. ｃｒ An apparatus for estimating buckling stress according to claim 1, which estimates the following: Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a １ The absolute value is 4.05 × 10 ３ The above 4.30 x 10 ３ The constants are as follows: a ２ b is a constant whose absolute value is between 430 and 460, １ b is a constant between -3.21 and -3.17, and ２ is a constant between -4.15 and -3.

95. [Math 4]

6. A method for estimating the buckling stress of an H-shaped cross section member having a pair of flanges and a web, wherein the only external force acting on it is a bending moment around a reference axis extending in the thickness direction of the web, Considering the buckling restraint effect of the pair of flanges on the web, an estimation step is performed to estimate the buckling stress based on the width-to-thickness ratio of the web. The buckling restraint effect is due to the distance b between the center thicknesses of the pair of flanges. ｗ The first ratio is the ratio of the width B of each of the pair of flanges, and the thickness t of each of the pair of flanges. ｆ and the thickness t of the web ｗ A method for estimating buckling stress, expressed using the second ratio, which is the ratio of [the two factors].

7. In the estimation step, when the H-shaped cross section member satisfies equation (21), the variable X is calculated using the first ratio and the second ratio in equation (22), the variable X and the width-to-thickness ratio (b ｗ / t ｗ The buckling stress σ is obtained by equation (23) using ). ｃｒ A method for estimating buckling stress according to claim 6, which estimates the following: Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a １ is a constant between 0.620 and 0.685, and a ２ b is a constant between 77.747 and 88.247, １ b is a constant between 1.445 and 1.550, and ２ This is a constant between 5.950 and 6.

055. [Math 5]

8. In the estimation step, when the H-shaped cross section member satisfies equation (24), the variable X is calculated using the first ratio and the second ratio, and the variable X and the width-to-thickness ratio (b ｗ / t ｗ The buckling stress σ is obtained by equation (26) using ). ｃｒ A method for estimating buckling stress according to claim 6, which estimates the following: Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a １ is a constant between 0.726 and 0.796, and a ２ is 4.71 x 10 ６ The above 5.50 x 10 ６ The constants are as follows: b １ b is a constant between 9.087 and 9.197, ２ This is a constant between 11.976 and 12.

086. [Math 6]

9. In the estimation step, when the H-shaped cross section member satisfies equation (27), the variable X is calculated using the first ratio and the second ratio, and the variable X and the width-to-thickness ratio (b ｗ / t ｗ The buckling stress σ is obtained by equation (29) using ). ｃｒ A method for estimating buckling stress according to claim 6, which estimates the following: Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a １ The absolute value is 8.10 × 10 ６ The above 9.10 x 10 ６ The constants are as follows: a ２ The absolute value is 5.306 × 10 ３ The above 6.206 × 10 ３ The constants are as follows: b １ b is a constant between -8.087 and -7.887, ２ is a constant between -6.553 and -6.

353. [Number 7]

10. In the estimation step, when the H-shaped cross section member satisfies equation (30), the variable X is calculated using the first ratio and the second ratio, and the variable X and the width-to-thickness ratio (b ｗ / t ｗ The buckling stress σ is obtained by equation (32) using ). ｃｒ A method for estimating buckling stress according to claim 6, which estimates the following: Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a １ The absolute value is 4.05 × 10 ３ The above 4.30 x 10 ３ The constants are as follows: a ２ b is a constant whose absolute value is between 430 and 460, １ b is a constant between -3.21 and -3.17, and ２ is a constant between -4.15 and -3.

95. [Number 8]

11. A buckling stress estimation program for an estimation device that estimates the buckling stress of an H-shaped cross section member having a pair of flanges and a web, wherein the only external force acting on it is a bending moment around a reference axis extending in the thickness direction of the web, The estimation device is configured to function as an estimation unit that estimates the buckling stress based on the width-to-thickness ratio of the web, taking into account the buckling restraint effect of the pair of flanges on the web. The buckling restraint effect is due to the distance b between the center thicknesses of the pair of flanges. ｗ The first ratio is the ratio of the width B of each of the pair of flanges, and the thickness t of each of the pair of flanges. ｆ and the thickness t of the web ｗ A program for estimating buckling stress, expressed using the second ratio, which is the ratio of [the two factors].

12. The estimation unit calculates the variable X using the first ratio and the second ratio when the H-shaped cross section member satisfies equation (41), using equation (42), the variable X and the width-to-thickness ratio (b ｗ / t ｗ The buckling stress σ is obtained by equation (43) using ). ｃｒ A program for estimating buckling stress according to claim 11, which estimates the following: Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a １ is a constant between 0.620 and 0.685, and a ２ b is a constant between 77.747 and 88.247, １ b is a constant between 1.445 and 1.550, and ２ This is a constant between 5.950 and 6.

055. [Number 9]

13. The estimation unit calculates the variable X using the first ratio and the second ratio when the H-shaped cross section member satisfies equation (44), using equation (45), the variable X and the width-to-thickness ratio (b ｗ / t ｗ The buckling stress σ is obtained by equation (46) using ). ｃｒ A program for estimating buckling stress according to claim 11, which estimates the following: Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a １ is a constant between 0.726 and 0.796, and a ２ is 4.71 x 10 ６ The above 5.50 x 10 ６ The constants are as follows: b １ b is a constant between 9.087 and 9.197, ２ This is a constant between 11.976 and 12.

086. [Number 10]

14. When the H-shaped cross-sectional member satisfies the (47) formula, the estimation unit calculates the variable X using the first ratio and the second ratio by the (48) formula, and uses the variable X and the width-to-thickness ratio (b ｗ / t ｗ ) to estimate the buckling stress σ ｃｒ by the (49) formula. The buckling stress estimation program according to claim 11. Here, E is the Young's modulus of the H-shaped cross-sectional member, ν is the Poisson's ratio of the H-shaped cross-sectional member, a １ is a constant with an absolute value of 8.10×10 ６ or more and 9.10×10 ６ or less, a ２ is a constant with an absolute value of 5.306×10 ３ or more and 6.206×10 ３ or less, b １ is a constant of -8.087 or more and -7.887 or less, b ２ is a constant of -6.553 or more and -6.353 or less. [Math 11]

15. The estimation unit calculates the variable X using the first ratio and the second ratio when the H-shaped cross section member satisfies equation (50), using equation (51), the variable X and the width-to-thickness ratio (b ｗ / t ｗ The buckling stress σ is given by equation (52) using ). ｃｒ A program for estimating buckling stress according to claim 11, which estimates the following: Here, E is the Young's modulus of the H-shaped cross-section member, ν is the Poisson's ratio of the H-shaped cross-section member, and a １ The absolute value is 4.05 × 10 ３ The above 4.30 x 10 ３ The constants are as follows: a ２ b is a constant whose absolute value is between 430 and 460, １ b is a constant between -3.21 and -3.17, and ２ is a constant between -4.15 and -3.

95. [Math 12]

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