Design methods for steel beams

Abstract

To provide a steel beam design method that can design a stiffening area with consideration of the effect of sear buckling in the case of stiffening only with use of a horizontal stiffener.SOLUTION: A steel beam design method of this invention comprises a computation step of a first stiffening length, a computation step of a second stiffening length, and a computation step of a stiffening length in which the length of the stiffening area 6 is set to be the same as or greater than the sum of the length of the first stiffening part 61 and the length of the second stiffening part 62. In the computation step of the first stiffening length, the design is made in such a way that, assuming there is not installed any horizontal stiffener 5 to the second stiffening part 62, but only installed to the first stiffening part 61, the yield strength Ma0 of the web 4 at a non-stiffening part 71 where no horizontal stiffener 5 is installed to is greater than the bending moment M2 caused on the web at the second end part 61b of the first stiffening part 61. In the computation step of the second stiffening length, the length of the second stiffening part 62 is set to be the same as the beam depth (1.0H) of the steel beam 1.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] This invention relates to a method for designing steel beams. [Background technology]

[0002] For steel beams with a large web-to-thickness ratio, a thin-walled web stiffening method is known that reduces the amount of steel used while ensuring the necessary plastic deformation performance by stiffening only the web near the hinge formation position at the beam end with a horizontally extending horizontal stiffener (see, for example, Patent Documents 1 and 2). [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2020-094339 [Patent Document 2] Japanese Patent Publication No. 2021-183782 [Overview of the Initiative] [Problems that the invention aims to solve]

[0004] In this type of thin-walled web stiffener stiffening method, shear buckling is more likely to occur in the area of ​​the web on the span-center side where the ends of the horizontal stiffeners are located, due to the bending deformation of the horizontal stiffeners. When shear buckling occurs in the web, there is a concern that the shear buckling waveform will affect the surrounding load-bearing capacity and plastic deformation capacity. To suppress the effects of this web shear buckling, vertical stiffeners are installed in the area of ​​the web where the ends of the horizontal stiffeners on the span-center side are located. However, due to design constraints or the need to simplify manufacturing, it is sometimes impossible to install vertical stiffeners. In such cases, stiffening is performed using only horizontal stiffeners. When using only horizontal stiffeners for stiffening, it is necessary to install them to a extent that minimizes the effect of shear buckling, but a design that takes the effect of shear buckling into account has not yet been established.

[0005] Therefore, the present invention aims to provide a steel beam design method that allows for the design of a stiffening range that takes into account the effects of shear buckling when stiffening is performed using only horizontal stiffeners. [Means for solving the problem]

[0006] To achieve the above objective, the present invention provides a steel beam design method for calculating the length dimension of a stiffener stiffener in a steel beam provided with a stiffener The method includes a second stiffener stiffening length calculation step for calculating the length dimension of the stiffener stiffening section, and a stiffener stiffening length calculation step for setting the length dimension of the stiffener stiffening section to be greater than or equal to the sum of the length dimension of the first stiffener stiffening section and the length dimension of the second stiffener stiffening section, wherein the first stiffener stiffening length calculation step assumes that the horizontal stiffener is not provided in the second stiffener stiffening section but only in the first stiffener stiffening section, and the yield strength M of the unstiffened section where the horizontal stiffener is not provided in the web is greater than the bending moment M2 generated at the central end of the web in the longitudinal direction in the first stiffener stiffening section. a0 Designed to increase the load capacity M of the un-rigidified section. a0 The bending moment M2 is calculated by the following equations (1.1) and (1.2), and the bending moment M2 is calculated by reducing the bending moment M1 that occurs at the end of the web in the longitudinal direction by the ratio of the length of the unstiffened section to the internal length of the steel beam, and the bending moment M1 is calculated by the following equation (1.3), and in the second stiffener stiffening length calculation step, the length dimension of the second stiffener stiffening section is set to the same value as the beam depth dimension of the steel beam.

[0007]

number

[0008] In this invention, the bending moment M2 generated at the central end in the longitudinal direction of the first stiffener stiffening section, i.e., at the boundary with the unstiffened section, is greater than the yield strength M of the unstiffened section. a0 If the bending moment M2 generated at the boundary between the first stiffener stiffened section and the unstiffened section reaches the yield strength Ma0 of the unstiffened section, a plastic hinge may form at the boundary between the first stiffener stiffened section and the unstiffened section, resulting in a double-hinged state and a deformation state in which the plastic deformation capacity rapidly decreases. In contrast, in the present invention, in the first stiffener stiffening length calculation process, the length dimension of the first stiffener stiffener is designed such that the yield strength Ma0 of the unstiffened section is greater than the bending moment M2 generated at the boundary between the first stiffener stiffener stiffener section and the unstiffened section. Therefore, there is no risk of the above-mentioned deformation state occurring, and it is possible to design the first stiffener stiffening length considering the increase in yield strength due to the stiffening of the horizontal stiffener. Furthermore, if shear buckling occurs in the web, there is concern that the shear buckling waveform may affect the surrounding load-bearing capacity and plastic deformation capacity. In response to this, in the present invention, in the second stiffener stiffening length calculation step, the second stiffener stiffening length is calculated so that the area affected by the shear buckling waveform at the central end of the horizontal stiffener in the longitudinal direction is stiffened by the second stiffener stiffening section. In the stiffener stiffening length calculation step, the length dimension of the stiffener stiffening section is calculated to be greater than or equal to the combined value of the length dimension of the first stiffener stiffening section and the length dimension of the second stiffener stiffening section. Assuming that the shear buckling waveform occurs at an angle of 45° with respect to the beam axis direction (height direction), within the range not exceeding the beam cross-sectional dimension from the end on the center side in the length direction of the horizontal stiffener toward the end of the steel beam, it is considered to be within the range affected by the shear buckling waveform. On the other hand, the range exceeding the beam cross-sectional dimension from the end on the center side in the length direction of the horizontal stiffener toward the end of the steel beam can be considered as a range that is not significantly affected by shear buckling even when web shear buckling occurs. For the above reasons, by setting the length dimension of the second stiffener bracing to the same value as the beam cross-sectional dimension and setting the length dimension of the stiffener bracing portion to be equal to or greater than the sum of the length dimensions of the first stiffener bracing portion and the second stiffener bracing portion, it is possible to prevent the mutual influence of the stiffener bracing portion and the non-braced portion.

[0009] In the design method of the steel beam according to the present invention, the horizontal stiffener may be provided only on one surface of the web.

[0010] By doing so, the design and manufacture of the steel beam become easy and steel material reduction can be achieved.

Effect of the Invention

[0011] According to the present invention, it is possible to design a bracing range considering the influence of shear buckling when bracing is performed using only horizontal stiffeners.

Brief Description of the Drawings

[0012] [Figure 1] It is a perspective view of a steel beam according to an embodiment of the present invention. [Figure 2] It is a side view of a steel beam according to an embodiment of the present invention. [Figure 3] It is a table showing the specifications of the analysis case used for verifying the design formula of the stiffener bracing length by FEM analysis. [Figure 4] It is a graph of the analysis result of Case1. [Figure 5] It is an image of the analysis result of Case1. [Figure 6] It is a graph of the analysis result of Case2. [Figure 7] This is an image showing the analysis results for Case 2. [Figure 8] This is a graph showing the analysis results for Case 3. [Figure 9] This is an image showing the analysis results for Case 3. [Modes for carrying out the invention]

[0013] The design method for steel beams according to embodiments of the present invention will be described below with reference to Figures 1-9. As shown in Figure 1, the steel beam design method according to this embodiment is as follows: As shown in Figures 1 and 2, the steel beam 1 according to this embodiment is an H-shaped steel. The steel beam 1 has an upper flange 2, a lower flange 3, and a web 4. The steel beam 1 extends horizontally, and both ends are joined to columns 12. Hereinafter, the horizontal direction in which the steel beam 1 extends will be referred to as the length direction. The horizontal direction perpendicular to the length direction will be referred to as the width direction. In the description of the steel beam 1, the vertical direction will be referred to as the height direction. Figures 1 and 2 show the vicinity of one end 1a in the length direction of the steel beam 1.

[0014] Two horizontal stiffeners 5 are joined to a predetermined area of ​​the web 4 of the steel beam 1, extending from the longitudinal end 4a towards the longitudinal center. The web 4 of the steel beam 1 is stiffened by the two horizontal stiffeners 5. The two horizontal stiffeners 5 are joined to only one face of the web 4. The two horizontal stiffeners 5 are positioned one above the other with a gap between them. The two horizontal stiffeners 5 are of the same length.

[0015] The area in the web 4 where the horizontal stiffeners 5 are joined and stiffened is referred to as the "stiffener stiffening area 6". The stiffener stiffening area 6 is provided near both ends in the longitudinal direction of the web 4. The area in the web 4 other than the stiffener stiffening area 6, i.e., the area where the horizontal stiffeners 5 are not provided, is referred to as the "unstiffened area 7". The unstiffened area 7 is provided in the middle of the longitudinal direction of the web 4. The end of the stiffener stiffener 6 that is closest to the column 12 is referred to as the first end 6a. The end of the stiffener stiffener 6 that is further away from the column 12, i.e., the end on the side of the unstiffened section 7, is referred to as the second end 6b. The first end 6a is located at the end 4a of the web 4 in the longitudinal direction.

[0016] The stiffener stiffener portion 6 has a first stiffener stiffener stiffener portion 61 on the first end 6a side and a second stiffener stiffener stiffener stiffener portion 62 on the second end 6b side. The first stiffener stiffener stiffener stiffener portion 61 and the second stiffener The portion of the horizontal stiffener 5 that is provided in the first stiffener stiffening section 61 will be referred to as the first horizontal stiffener 51.

[0017] Of the longitudinal ends of the horizontal stiffener 5, the end closest to the column 12 is denoted as the first end 5a, and the end further away from the column 12 is denoted as the second end 5b. The first end 5a of the horizontal stiffener 5 is located at the position of the longitudinal end 4a of the web 4, that is, at the position of the first end 6a of the stiffener stiffening section 6. The second end 5b of the horizontal stiffener 5 is located at the position of the second end 6b of the stiffener stiffening section 6.

[0018] The steel beam design method according to this embodiment includes a first stiffener stiffening length calculation step for calculating the length dimension of the first stiffener stiffening section, a second stiffener stiffening length calculation step for calculating the length dimension of the second stiffener stiffening section, and a stiffener stiffening length calculation step for setting the length dimension of the stiffener stiffening section to be greater than or equal to the sum of the length dimensions of the first stiffener stiffening section and the second stiffener stiffening section.

[0019] (First stiffener stiffening length calculation process) The length dimension of the first stiffener reinforcing portion 61 is calculated assuming that the horizontal stiffener 5 is provided only on the first stiffener reinforcing portion 61 and not on the second stiffener reinforcing portion 62. That is, it is assumed that the horizontal stiffener 5 consists only of the first horizontal stiffener 51. When assuming in this way, the region where the first horizontal stiffener 51 is not provided is denoted as the non-reinforced portion 71. The non-reinforced portion 71 also includes the second stiffener reinforcing portion 62. The required length dimension of the first stiffener reinforcing portion 61 is denoted as "stiffener reinforcement length L st ". The stiffener reinforcement length L st is designed such that the yield strength M a0 of the non-reinforced portion 71 is greater than the bending moment M2 generated at the second end portion 61b of the first stiffener reinforcing portion 61. The yield strength M a0 of the non-reinforced portion 71 is calculated by the following equations (1.1) and (1.2). As the width-to-thickness ratio of the web 4 increases, and the maximum yield strength (W F0 of the steel beam 1 for the yield strength M max ) of the non-reinforced portion is less than the full plastic moment M p of the non-reinforced portion cross-section, an appropriate yield strength evaluation is possible.

[0020]

Equation

[0021] ]>The bending moment M2 generated at the second end portion 61b of the first stiffener reinforcing portion 61 is calculated by reducing the bending moment M1 at the end portion 1a of the steel beam 1 by the ratio of the length of the non-reinforced portion 71 of the steel beam 1 (inner length L0 of the steel beam 1 - stiffener reinforcement length L st ×2) to the inner length L0 of the steel beam 1. Here, the bending moment M1 at the end portion 1a of the steel beam 1 for the design of the stiffener reinforcement length L st is calculated using the maximum yield strength evaluation equation using the width-to-thickness ratio index W F according to the following reference 1. Reference 1: Kikuo Igarashi, Ryota Suekuni, Takuma Shinohara, and Tao Wang: Novel width-to-thickness ratio index and width-to-thickness ratio classification for evaluating the load-bearing capacity and plastic deformation capacity of steel H-shaped beams, Journal of Structural Engineering, Architectural Institute of Japan (668), pp. 1865-1872, 2011.10) Stiffener stiffening length L st In calculating this, in order to overestimate end stresses and design on the safe side, the maximum load-bearing capacity evaluation formula from Reference 1, which was derived by taking the lower limit of the maximum load-bearing capacity, is modified to take the upper limit of the maximum load-bearing capacity, and is calculated using the following formula (1.3).

[0022]

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[0023] (Second stiffener stiffening length calculation process) The length dimension of the second stiffener bracing section 62 shall be the same as the beam depth dimension (H) of the steel beam 1 (1.0H).

[0024] (Stiffener stiffening length calculation process) The length dimension of the stiffener stiffening section 6 is the length dimension of the first stiffener stiffening section 61 calculated in the first stiffener stiffening length calculation step, i.e., the stiffener stiffening length L. st This value is the sum of the length dimension of the second stiffener stiffening section 62 calculated in the second stiffener stiffening length calculation process, that is, the beam depth dimension (1.0H) of the steel beam 1.

[0025] If shear buckling occurs in web 4, there is concern that the shear buckling waveform will affect the surrounding load-bearing capacity and plastic deformation capacity. Therefore, the range affected by the shear buckling waveform of the second end 5b of the horizontal stiffener 5 is defined. Assuming that the shear buckling waveform occurs at an angle of 45° with respect to the beam depth direction (height direction), the range from the second end 5b of the horizontal stiffener 5 toward the first end 5a (end 1a of the steel beam 1) to a beam depth dimension (1.0H) or less is considered to be the range affected by the shear buckling waveform. On the other hand, the range from the second end 5b of the horizontal stiffener 5 toward the first end 5a to a beam depth dimension (1.0H) or more is considered to be a range that is not significantly affected by shear buckling, even if shear buckling occurs in web 4. For the reasons above, the required stiffener stiffening length L is calculated based on the length dimension of the horizontal stiffener 5. st In addition, extending the beam depth (1.0H) prevents the stiffened section and the unstiffened section 7 from influencing each other.

[0026] (Verification of design methods using FEM analysis) To verify the validity of the calculation of the length dimension of the stiffener stiffening section 6 of the steel beam 1 described above using the above-described steel beam design method, a large deformation nonlinear analysis (FEM analysis) was performed. Figure 3 shows the analysis cases. In all cases, the steel beam is an H-shaped steel. The beam cross section was set to H-650×200×8×13, and the shear span was set to 5000 mm. In this analysis, the stiffener stiffening length l st We conducted an analysis using the following parameters. Required stiffener stiffening length L st Based on the above calculation formula, the design would result in approximately 1430mm.

[0027] Analysis Case 1: Stiffener stiffening length l st Required stiffener length L st The length dimension does not meet the requirements, and the stiffener stiffening length l st The required stiffener length is L st It is 0.91 times that. Analysis Case 2 involves stiffener stiffening length l st Required stiffener length Lst The dimension obtained by adding 0.1 times the beam depth (L st +0.1H) and stiffener stiffening length l st The required stiffener length is L st It is 1.05 times that. Analysis Case 3: Stiffener stiffening length l st Required stiffener length L st The dimension obtained by adding 0.5 times the beam depth (L st (+0.5H), and stiffener stiffening length l st The required stiffener length is L st This is 1.19 times that amount.

[0028] Figures 4-9 show the load-deformation relationship and deformation characteristics of the analysis results. As shown in Figures 4 and 5, in Analysis Case 1, coupled buckling of the flange and web occurs at the boundary between the stiffened and unstiffened sections because the stiffener stiffening length is shorter than the required stiffener stiffening length. As shown in Figures 6 and 7, in Analysis Case 2, stiffener stiffening is applied to near the position exceeding the required stiffener stiffening length, so it can be confirmed that failure due to coupled buckling of the flange and web at the end of the steel beam is dominant. As shown in Figures 8 and 9, in Analysis Case 3, stiffener stiffening is applied to near the position exceeding the required stiffener stiffening length by a longer distance than in Analysis Case 2, so it can be confirmed that failure due to coupled buckling of the flange and web at the end of the steel beam is dominant. This analysis determined that the stiffener stiffening length is L st Even in analysis Case 3, where +0.5H was used, it was confirmed that stable hysteresis behavior was observed. Therefore, a stiffener stiffening length (L) that is safer than in analysis Case 3 was determined. st The design method for the steel beam described above, which uses +1.0H, can be validated based on the results of this analysis.

[0029] Next, the operation and effects of the steel beam design method according to this embodiment will be described. In the steel beam design method according to this embodiment, the bending moment M2 generated at the central end (second end 61b) in the longitudinal direction of the first stiffener stiffening section 61, i.e., at the boundary with the unstiffened section 71, is greater than the load-bearing capacity M of the unstiffened section.a0 If the bending moment M2 generated at the boundary between the first stiffener stiffened section and the unstiffened section reaches the yield strength Ma0 of the unstiffened section, a plastic hinge may form at the boundary between the first stiffener stiffened section 61 and the unstiffened section 71, resulting in a double-hinged state and a deformation state in which the plastic deformation capacity rapidly decreases. In contrast, in this embodiment, in the first stiffener stiffening length calculation process, the length dimension of the first stiffener stiffened section 61 is designed such that the yield strength Ma0 of the unstiffened section 71 is greater than the bending moment M2 generated at the boundary between the first stiffener stiffened section 61 and the unstiffened section 71. Therefore, there is no risk of the above-mentioned deformation state occurring, and it is possible to design the first stiffener stiffened section 61 considering the increase in yield strength due to the stiffening of the first horizontal stiffener 51. Furthermore, if shear buckling occurs in the web 4, there is concern that the shear buckling waveform may affect the surrounding load-bearing capacity and plastic deformation capacity. In response to this, in this embodiment, in the second stiffener stiffening length calculation step, the second stiffener stiffening length is calculated so that the area affected by the shear buckling waveform of the second end 5b of the horizontal stiffener 5 is stiffened by the second stiffener stiffening section 62. In the stiffener stiffening length calculation step, the length dimension of the stiffener stiffening section 6 is calculated to be greater than or equal to the combined value of the length dimension of the first stiffener stiffening section 61 and the length dimension of the second stiffener stiffening section 62. Assuming that the shear buckling waveform occurs at a 45° angle with respect to the beam depth, the range from the second end 5b of the horizontal stiffener 5 towards the first end 5a (end 1a of the steel beam 1) to a beam depth dimension of 1.0H or less is considered to be affected by the shear buckling waveform. On the other hand, the range from the second end 5b of the horizontal stiffener 5 towards the first end 5a to a beam depth dimension of 1.0H or more is considered to be a range that is not significantly affected by shear buckling, even if shear buckling occurs in the web 4. For these reasons, the required stiffener stiffening length L was calculated based on the length dimension of the horizontal stiffener 5. st In addition, extending the beam depth (1.0H) prevents the stiffened section and the unstiffened section 7 from influencing each other. As a result, the steel beam design method according to this embodiment allows for the design of a stiffening range that takes into account the effect of shear buckling when stiffening is performed using only the horizontal stiffener 5.

[0030] In this embodiment, the horizontal stiffener 5 is joined to only one side of the web 4. This facilitates the design and fabrication of the steel beam 1 and reduces the amount of steel material used.

[0031] Although embodiments of the steel beam design method according to the present invention have been described above, the present invention is not limited to the above embodiments and can be modified as appropriate without departing from the spirit of the invention. For example, in the above embodiment, two horizontal stiffeners 5 are provided in one stiffener stiffener section 6, but the number of horizontal stiffeners 5 provided in one stiffener stiffener section 6 may be set as appropriate.

[0032] In the above embodiment, the horizontal stiffener 5 is joined to only one side of the web 4, but it may be joined to both sides of the web 4, taking rigidity into consideration. [Explanation of Symbols]

[0033] 1. Steel beam 4 Web 5 Horizontal stiffeners 5b Second end 6. Stiffener stiffening section 6a First end 6b Second end 7,71 Unstiffened part 51. No. 1 Horizontal Stiffener 61. First stiffener stiffening section 62. Second stiffener stiffening section

Claims

1. In a steel beam design method for calculating the length dimension of a stiffener stiffener in a steel beam provided with a stiffener The stiffener stiffening portion is, The first stiffener stiffening portion is located at the end of the web in the longitudinal direction, It has a second stiffener stiffener that is continuous with the first stiffener stiffener and is located on the central side in the longitudinal direction of the web, A first stiffener stiffening length calculation step for calculating the length dimension of the first stiffener stiffening section, A second stiffener stiffening length calculation step for calculating the length dimension of the second stiffener stiffening section, The process includes a stiffener stiffening length calculation step, which sets the length dimension of the stiffener stiffening portion to be greater than or equal to the sum of the length dimension of the first stiffener stiffening portion and the length dimension of the second stiffener stiffening portion. In the first stiffener stiffening length calculation process, Assuming that the horizontal stiffener is not provided in the second stiffener stiffening section but only in the first stiffener stiffening section, the bending moment M generated at the end of the web in the longitudinal direction of the first stiffener stiffening section is ２ The load-bearing capacity M of the un-rigidified section where the horizontal stiffener is not provided on the web is greater than that of the web. ａ０ Designed to increase in size, The load-bearing capacity M of the unreinforced section ａ０ This is calculated using the following formulas (1.1) and (1.2): The aforementioned bending moment M ２ This is the bending moment M generated at the end of the web in the longitudinal direction. １ The bending moment M is calculated by reducing it by the ratio of the length of the un-rigidified section to the inner length of the steel beam. １ This is calculated using the following formula (1.3): In the second stiffener stiffening length calculation process, A design method for a steel beam in which the length dimension of the second stiffener stiffening portion is set to the same value as the beam depth dimension of the steel beam. [Math 1]

2. The design method for a steel beam according to claim 1, wherein the horizontal stiffener is provided on only one side of the web.

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