Design methods for steel beams

Abstract

This invention provides a design method for steel beams that allows for highly accurate evaluation of the perforated lateral buckling resistance of a steel beam in which through holes are formed in the web and the lateral movement and rotation of the upper flange are constrained. [Solution] A steel beam design method for preventing lateral buckling of a steel beam 10 in which a through hole 13a is formed in the web 13 and the lateral movement and rotation of the upper flange 11 are constrained, wherein a steel beam in which no through hole is formed is defined as a non-perforated steel beam 10A, and the perforated lateral buckling strength of the steel beam is calculated by multiplying the resistance force due to plate bending of the web, which constitutes the evaluation formula for the non-perforated lateral buckling strength, which is the lateral buckling strength of the non-perforated steel beam, by a reduction coefficient corresponding to the through hole.

Description

[Technical Field]

[0001] The present invention Design methods for steel beams Regarding. [Background technology]

[0002] Traditionally, H-shaped members have been used in steel-framed buildings for main beams and secondary beams. While H-shaped members have high cross-sectional performance around their strong axis, their cross-sectional performance around their weak axis is low, which can lead to lateral buckling, a deformation of the H-shaped member in the out-of-plane direction. Since lateral buckling results in a loss of load-bearing capacity, lateral stiffeners are typically installed in H-shaped members in general designs to prevent lateral buckling. However, installing such lateral bracing members presents challenges such as increased construction costs due to the increased number of members, resulting in higher material and processing costs, as well as decreased efficiency in construction work.

[0003] To address these challenges with steel beams, methods have been investigated to suppress lateral buckling and eliminate the need for lateral stiffeners by considering the restraining effect on the lateral movement and rotation of the upper flange by a floor slab or the like attached to the upper flange, as described in Patent Documents 1 to 3.

[0004] Patent Document 1 describes a design method for beams in which a concrete slab is joined to a flange, setting the torsional stiffness ratio of the concrete slab and beam to restrain the rotation of the upper flange and prevent lateral buckling. Patent Documents 2 and 3 derive the lateral buckling resistance when the lateral movement and rotation of the upper flange of a steel beam are restrained. These patent documents 1 to 3 describe methods for restraining the lateral movement and rotation of the upper flange of an H-shaped cross section member by a floor slab attached to the upper flange, and evaluate the lateral buckling resistance in such cases. However, they assume that the steel beam is made of a uniform H-shaped cross section member with no cross-sectional defects. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2018-154996 [Patent Document 2] Japanese Patent Publication No. 2019-56220 [Patent Document 3] Japanese Patent Publication No. 2020-158953 [Overview of the project] [Problems that the invention aims to solve]

[0006] On the other hand, in actual building steel beams, through-holes are sometimes formed in the web to allow equipment piping and other components to pass through. In this case, a cross-sectional defect occurs in the web. When the lateral movement and rotation of the upper flange are constrained, the bending resistance of the web contributes to the resistance to lateral buckling deformation. Therefore, when through-holes are provided, the web becomes more susceptible to deformation compared to a cross-section without through-holes, potentially reducing its lateral buckling resistance. In other words, when through-holes are provided in the web, their effect must be considered when evaluating the lateral buckling resistance.

[0007] As described above, conventionally, it is not possible to evaluate the lateral buckling strength (perforated lateral buckling strength) of a steel beam in which through holes are formed in the web and the lateral movement and rotation of the upper flange are constrained.

[0008] The present invention has been made in view of the above problems, and aims to provide a steel beam design method that can evaluate with high accuracy the perforated lateral buckling resistance of a steel beam in which through holes are formed in the web and the lateral movement and rotation of the upper flange are restrained, and a steel beam designed by this steel beam design method. [Means for solving the problem]

[0009] To solve the aforementioned problems, this invention proposes the following means. (1) Embodiment 1 of the present invention is a design method for a steel beam in which through holes are formed in the web and the lateral movement and rotation of the upper flange are constrained, wherein a steel beam in which the through holes are not formed is defined as a non-perforated steel beam, and the perforated lateral buckling capacity of the steel beam is calculated by multiplying the resistance force due to plate bending of the web, which constitutes the evaluation formula for the non-perforated lateral buckling capacity, which is the lateral buckling capacity of the non-perforated steel beam, by a reduction coefficient corresponding to the through holes.

[0010] In this invention, the inventors, after diligent study, found that the evaluation formula for the lateral buckling resistance of a non-perforated steel beam includes the resistance force due to the bending of the web. Furthermore, they found that the lateral buckling resistance of a perforated steel beam, in which through holes are formed in the web and the lateral movement and rotation of the upper flange are constrained, can be calculated by multiplying the resistance force due to the bending of the web (as in the non-perforated lateral buckling resistance) by a reduction coefficient corresponding to the through holes. Therefore, the perforated lateral buckling strength of a steel beam with a through hole in the web and restrained lateral movement and rotation of the upper flange can be evaluated with high accuracy.

[0011] (2) Embodiment 2 of the present invention is the perforated lateral buckling strength M e The resistance force due to the bending of the web plate is reduced by the reduction coefficient κ. w The design method for steel beams described in (1) may also be the one calculated by formula (1), which has a term multiplied by . Here, E is Young's modulus, I f d is the second moment of area of ​​the upper flange and the lower flange, respectively. b l is the distance between the center thicknesses of the upper and lower flanges, l is the length of the steel beam, G is the shear modulus, J f The torsional constants of the upper flange and the lower flange, respectively, are J w D is the Saint-Venant torsion constant of the aforementioned web. w This is the bending stiffness of the web plate.

[0012]

number

[0013] In this invention, the perforated lateral buckling resistance M e can be calculated more accurately using Equation (1).

[0014] (3)Aspect 3 of the present invention may be a design method for a steel beam according to (1) or (2), wherein the reduction coefficient κ w is calculated by Equation (5) using Equations (2) to (4). Here, φ w is the diameter of the through-hole, e w is the vertical distance between the center of the through-hole and the central axis of the steel beam, and l w is the pitch in the material axis direction of the through-hole in the steel beam.

[0015] [Number]

[0016] In this invention, the reduction coefficient κ w can be calculated more accurately by Equation (5) using Equations (2) to (4).

[0017] (4)Aspect 4 of the present invention is a steel beam designed by the design method for a steel beam according to any one of (1) to (3). In this invention, a steel beam can be designed by a design method for a steel beam that can evaluate with high accuracy the perforated lateral buckling resistance of a steel beam in which through-holes are formed in the web and the lateral movement and rotation of the upper flange are restricted. [Advantages of the Invention]

[0018] The steel beam design method of the present invention allows for highly accurate evaluation of the perforated lateral buckling resistance of a steel beam in which through holes are formed in the web and the lateral movement and rotation of the upper flange are constrained. Furthermore, the present invention provides a steel beam designed using a steel beam design method that allows for highly accurate evaluation of the perforated lateral buckling resistance of a steel beam in which through holes are formed in the web and the lateral movement and rotation of the upper flange are constrained. [Brief explanation of the drawing]

[0019] [Figure 1] This is a side view of a perforated steel beam designed by a design method for a steel beam according to one embodiment of the present invention. [Figure 2] This is a plan view of the perforated steel beam. [Figure 3] This is a cross-sectional view along the cutting line A1-A1 in Figure 1. [Figure 4] This is a cross-sectional view illustrating the specifications of the perforated steel beam. [Figure 5] This figure shows the bending moment distribution of a perforated steel beam when a uniform bending moment is applied to the end of the perforated steel beam and a uniformly distributed vertical load is applied to the upper flange. [Figure 6] This figure shows the bending moment distribution of a perforated steel beam when a bending moment is applied to one end and a vertically uniformly distributed load is applied to the upper flange. [Figure 7] This figure shows the bending moment distribution of a perforated steel beam when inversely symmetrical bending moments act on each end. [Figure 8] This is a perspective view showing the analytical model and boundary conditions for a perforated steel beam. [Figure 9] This figure shows the relationship between l / H and MFEM or Me under boundary condition 1, load condition 1, αw = 0.5, and βw = 0.0. [Figure 10] This figure shows the relationship between l / H and MFEM or Me under boundary condition 1, load condition 1, αw = 0.3, and βw = -0.2. [Figure 11]This figure shows the relationship between l / H and MFEM or Me under boundary condition 1, load condition 1, αw=0.3, and βw=0.2. [Figure 12] This figure shows the relationship between l / H and MFEM or Me under boundary condition 1, load condition 2, αw = 0.5, and βw = 0.0. [Figure 13] This figure shows the relationship between l / H and MFEM or Me under boundary condition 1, load condition 2, αw = 0.3, and βw = -0.2. [Figure 14] This figure shows the relationship between l / H and MFEM or Me under boundary condition 1, load condition 2, αw = 0.3, and βw = 0.2. [Figure 15] This figure shows the relationship between l / H and MFEM or Me under boundary condition 2, load condition 3, αw = 0.5, and βw = 0.0. [Figure 16] This figure shows the relationship between l / H and MFEM or Me under boundary condition 2, load condition 3, αw = 0.3, and βw = -0.2. [Figure 17] This figure shows the relationship between l / H and MFEM or Me under boundary condition 2 and load condition 3, αw = 0.3, and βw = 0.2. [Modes for carrying out the invention]

[0020] The design method for steel beams and an embodiment of a steel beam according to the present invention will be described below with reference to Figures 1 to 17.

[0021] [1. Structure of perforated steel beams] In the steel beam design method of this embodiment (hereinafter simply referred to as the design method), the perforated steel beam (steel beam; beam made of steel) 10 shown in Figures 1 to 3 is the subject of design (evaluation). In Figures 1 to 3, the undeformed shape of the perforated steel beam 10 before external forces such as bending moment and vertically uniformly distributed load are applied is shown by solid lines. The buckled shape of the perforated steel beam 10 after these external forces are applied is shown by dashed lines. The perforated steel beam 10 extends in the direction of the material axis z, which is along the horizontal plane. The perforated steel beam 10 comprises an upper flange 11, a lower flange 12, and a web 13. The upper flange 11, the lower flange 12, and the web 13 are each formed in a flat shape from steel plate or the like.

[0022] The upper flange 11 and the lower flange 12 face each other in the vertical direction y. The upper flange 11 is positioned above the lower flange 12. The web 13 is positioned between the upper flange 11 and the lower flange 12. The width direction x of the steel beam 10, which is the thickness direction of the web 13, intersects (is perpendicular to) the material axis direction z and the vertical direction y. The web 13 is joined to the middle portion of the upper flange 11 in the width direction x, and to the middle portion of the lower flange 12 in the width direction x.

[0023] As shown in Figure 1, the web 13 has a plurality of through holes 13a. Each through hole 13a penetrates the web 13 in the width direction x. In this example, each through hole 13a has a circular shape when viewed in the width direction x (viewed along the width direction x). Note that the shape of the through-hole when viewed in the width direction x is not limited to a circular shape, but may be rectangular or other shapes. The number of through-holes formed in the web 13 may be one.

[0024] The perforated steel beam 10 is formed from an H-shaped cross-section member. That is, when viewed in the direction z along the material axis, the perforated steel beam 10 exhibits an H shape. The perforated steel beam 10 may be formed from H-shaped steel. In this case, the perforated steel beam 10 may be formed from rolled H-shaped steel or from welded H-shaped steel.

[0025] As shown in Figure 4, the perforated steel beam 10 configured as described above supports a retaining member 16, such as a floor slab, from below the retaining member 16. In this case, the perforated steel beam 10 is provided with a shear force transmission member (not shown) that protrudes upward from the upper flange 11. For example, a shear connector is used as the shear force transmission member. The shear force transmission member is embedded in the retaining member 16. In this way, the upper flange 11 of the perforated steel beam 10 is tightly connected to the retaining member 16 by the shear force transmission member.

[0026] Furthermore, the perforated steel beam 10 is used as described below in (boundary condition 1) and (boundary condition 2) by joining the members to which both ends of the perforated steel beam 10 in the material axis direction z are joined. (Boundary condition 1) The perforated steel beam 10 is used as a secondary beam by joining both ends of the perforated steel beam 10 in the direction of the material axis z to the main beam. (Boundary condition 2) The perforated steel beam 10 is used as a main beam by joining both ends of the perforated steel beam 10 in the direction of the material axis z to the columns. Furthermore, the retaining member support structure 17 (see Figure 4) is comprised of a perforated steel beam 10, a retaining member 16, a shear force transmission member, and two main beams (or columns). A main beam is a beam whose ends are connected to columns. A secondary beam is a beam whose ends are connected to main beams.

[0027] The lateral movement and rotation of the upper flange 11 of the perforated steel beam 10 are restrained by the holding member 16 and the shear force transmission member. Here, as shown in Figure 3, for example, the intersection line of a first reference plane passing through the center of the upper flange 11 in the vertical direction y and perpendicular to the vertical direction y, and a second reference plane passing through the center of the web 13 in the width direction x and perpendicular to the width direction x, is defined as the reference line O1. In this context, lateral movement of the upper flange 11 refers to movement of the upper flange 11 in the width direction x. For example, rotation of the upper flange 11 refers to rotation of the upper flange 11 around the reference line O1. This design method is for preventing lateral buckling of a perforated steel beam 10 in which the lateral movement and rotation of the upper flange 11 are constrained.

[0028] Here, the specifications of the perforated steel beam 10 are defined. The distance between the center thicknesses of the upper flange 11 and the lower flange 12 is d b (mm) is specified (see Figure 3). Distance d between the centers of the plate thickness b This is the distance in the vertical direction y between the center of the vertical direction y of the upper flange 11 and the center of the vertical direction y of the lower flange 12. The length of the perforated steel beam 10 in the axial direction z is defined as l (mm) (see Figure 2). The Young's modulus of the perforated steel beam 10 is E(N / mm²). 2 The shear modulus of the perforated steel beam 10 is defined as G(N / mm²). 2 ) is stipulated.

[0029] The second moment of area of ​​the upper flange 11 and the lower flange 12 are defined as I f (mm 4 ) is defined as follows. The Saint-Venant torsional constants of the upper flange 11 and the lower flange 12 are defined as J f (mm 4 ) is defined as follows. The Saint-Venant torsion constant of Web 13 is J w (mm 4 ) is stipulated. The bending stiffness (plate rigidity) of the web 13 plate is D w (Nmm) is specified. Note that the bending stiffness D w The thickness of the web 13 is t w (mm), and using the Poisson's ratio ν(-) of the perforated steel beam 10 (web 13), D w =E·t w 3 / (12(1-ν 2 It can be calculated as follows: ))

[0030] As shown in Figure 4, the diameter of the through hole 13a is φ w (mm) is specified. At this time, the opening ratio α of the through hole 13a w (-) is (φ w / d b ) is defined as follows. The vertical distance (eccentricity distance) between the center of the through-hole 13a and the central axis O6 of the perforated steel beam 10 is, e w(mm) is specified. Note that the distance e w Let's assume that it takes positive values ​​below the central axis O6 and negative values ​​above the central axis O6. At this time, the eccentricity β w (-) is (e w / d b ) is defined as follows.

[0031] The pitch in the material axis direction z of adjacent through holes 13a in the material axis direction z is l w (mm) is defined as follows. At this time, ratio p w (-) is (l w / φ w ) is defined as follows.

[0032] Here, in each configuration of the perforated steel beam 10, a beam in which multiple through-holes 13a are not formed in the web 13 is defined as a non-perforated steel beam 10A (see Figure 1). In other words, the non-perforated steel beam 10A differs from each configuration of the perforated steel beam 10 only in that multiple through-holes 13a are not formed in the web 13. Below, we will first derive the lateral buckling resistance of the non-perforated steel beam 10A.

[0033] [2. Derivation of the lateral buckling resistance of non-perforated steel beams] In the following, the lateral buckling strength of a non-perforated steel beam 10A, in which the lateral movement and rotation of the upper flange 11 are constrained, is derived using the energy method. In the following, the width direction x will also be referred to as the x-axis. Similarly, the vertical direction y will be referred to as the y-axis, and the direction z in the material axis direction will be referred to as the z-axis. The x, y, and z axes define a right-handed xyz coordinate system. Rotations around the x, y, and z axes are defined with the direction in which a right-handed screw advances as positive. The origin O of the xyz coordinate system is set at the end 10a1 on the first end (end) 10a side (left side in Figure 1) of the non-perforated steel beam 10A in the material axis direction z. Note that the xyz coordinate system is shown separated from the origin O in order to make the figure clearer. Here, in the non-perforated steel beam 10A, the end on the opposite side of the material axis z from the first end 10a (the right side in Figure 1) is defined as the second end (end) 10b.

[0034] Assume that the lateral movement of the upper flange 11 is constrained, thereby constraining its movement in the x-axis direction, and the rotation of the upper flange 11 is constrained, thereby constraining its rotation around the z-axis. The boundary conditions for ends 10a and 10b of the non-perforated steel beam 10A are as follows: At ends 10a1 and 10b1, movement in the x-axis and y-axis directions was fixed, and rotation around the z-axis was also fixed. • Movement in the z-axis direction was fixed only at end 10a1. Furthermore, the following assumptions were made: The degree of fixity for rotation around the y-axis of each end 10a1 and 10b1 is determined by a displacement function that assumes lateral buckling deformation, as described later. The connection between the upper flange 11 and the web 13, and the connection between the lower flange 12 and the web 13, maintain a right angle even after buckling.

[0035] Here, the deformation due to lateral buckling of the non-perforated steel beam 10A, in which the lateral movement and rotation of the upper flange 11 are constrained, is represented by the lateral movement u in the x-axis direction (see Figure 3) occurring in the lower flange 12. The lateral movement u is given by n displacement functions f, as shown in equation (41). i Expressed as a linear combination of , where i is a natural number and a i This is an undetermined coefficient. At this time, the torsional angle φ (see Figure 3) generated in the lower flange 12 is expressed as a function of the lateral movement u in equation (42). Lateral movement u in the x-axis direction generated in the web 13 w This is expressed in equation (43) as a function of the horizontal movement u.

[0036]

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[0037] Displacement function f i Any function that satisfies the boundary conditions at the ends 10a and 10b can be used for this, and an example of this is shown in equations (44) to (47).

[0038]

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[0039] Equations (44) and (45) are displacement functions assuming boundary conditions where the degree of fixation of both ends 10a and 10b of the non-perforated steel beam 10A is low, such as a secondary beam where both ends 10a and 10b are joined to a main beam, and rotation around the y-axis is not constrained. Equation (44) is a displacement function assuming that lateral buckling deformation is dominant symmetrically at both ends 10a1 and 10b1 in the material axis direction z of the non-perforated steel beam 10A. Equation (45) is a displacement function assuming that lateral buckling deformation is dominant at the first end 10a of the non-perforated steel beam 10A.

[0040] Equations (46) and (47) are displacement functions assuming boundary conditions in which the degree of fixation of both ends 10a and 10b of the non-perforated steel beam 10A is high, such as a main beam where both ends 10a and 10b are joined to columns, and rotation around the y axis is constrained. Equation (46) is a displacement function assuming that lateral buckling deformation is predominant symmetrically at both ends of the non-perforated steel beam 10A. Equation (47) is a displacement function assuming that lateral buckling deformation is predominant at the first end 10a of the non-perforated steel beam 10A. Note that in equations (44) to (47), j is any real number greater than or equal to 1.

[0041] As for the load conditions, as shown in Figure 1, a bending moment M is applied to the end 10a1 of the non-perforated steel beam 10A. a A bending moment M acts upon the end 10b1. b Assume that a vertically uniformly distributed load (a uniformly distributed load directed downwards) w acts on the intersection line (reference line O1) between the upper flange 11 and the web 13 in the middle part of the steel beam 10 in the z-axis direction. Bending moment M a M b By combining the bending moment M with a vertically uniformly distributed load w, it is possible to reproduce approximately any arbitrary moment distribution acting on the non-perforated steel beam 10A. a M b , and the uniformly distributed vertical load w, and the non-perforated lateral buckling resistance M crThe relationship can be expressed by equations (51) to (53). The bending moment distribution M acting on the non-perforated steel beam 10A is expressed by equation (54) using α, β, and γ. Also, the stress function σ of the web 13 is given by w This is expressed by equation (55) using the bending moment distribution M and the section modulus Z.

[0042]

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[0043] Here, α=1 is used as the base value, and the bending moment at the end 10b1 is determined by changing β, while the change in the bending moment in the intermediate section can be adjusted by the magnitude of γ. This makes it possible to reproduce the bending moment distribution under various boundary conditions assumed for a non-perforated steel beam 10A, as well as the load conditions shown in Figures 5 to 7. Figure 5 shows the bending moment distribution M of the non-perforated steel beam 10A when equal bending moments are applied to both ends 10a1 and 10b1 of the non-perforated steel beam 10A, and a vertically uniformly distributed load is applied to the upper flange 11, as if it were a secondary beam rigidly connected to a main beam at both ends (hereinafter referred to as load condition 1). By setting "α=1, β=-1, γ=1.5" in equation (54), the bending moment distribution M of load condition 1 can be reproduced.

[0044] Figure 6 shows the bending moment distribution M when a bending moment is applied to the end 10a1 and a vertically uniformly distributed load is applied to the upper flange 11, such as in a secondary beam where the first end 10a is rigidly connected to the main beam and the second end 10b is pinned to the main beam (hereinafter referred to as load condition 2). By setting "α=1, β=0, γ=1" in equation (54), the bending moment distribution M for load condition 2 can be reproduced. Figure 7 shows the bending moment distribution M when inversely symmetrical bending moments act on each end 10a1, 10b1, such as in a main beam rigidly connected to columns at both ends (hereinafter referred to as load condition 3). By setting "α=1, β=1, γ=0" in equation (54), the bending moment distribution M for load condition 3 can be reproduced.

[0045] Under these conditions, the total potential energy Π of the non-perforated steel beam 10A is expressed by equation (56).

[0046]

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[0047] Here, θ a (rad) is the angle of rotation that occurs at the end 10a1 of the non-perforated steel beam 10A, θ b (rad) is the angle of rotation occurring at end 10b1 of the non-perforated steel beam 10A. v is the vertical displacement function at the point of application of the distributed load. Rotation angle θ a ,θ b The displacement functions v and u are expressed using the horizontal movement u, respectively.

[0048] Substitute equations (42) and (43), equations (51) through (53), and equation (55) into equation (56). Then, using A, B, C, D, F, and I shown in equations (57) through (62), rearrange the definite integrals and the total potential energy Π is expressed in equation (63). Note that in equation (63), the infinitesimal term in the strain energy of web 13 is treated as zero.

[0049]

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[0050] From the neutral equilibrium in the energy principle, equation (64) is obtained.

[0051]

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[0052] Here, we set a part of the right-hand side of equation (64) to K as shown in equation (71), and the non-perforated lateral buckling resistance M cr Solving for this, we get the lateral buckling resistance of a non-porous material. crEquation (72) is obtained as the basic formula. Of the right-hand side of equation (72), the first term represents the resistance force against lateral movement of the lower flange 12 of the non-perforated steel beam 10A (the so-called resistance force due to Wagner torsion), the second term represents the resistance force against twisting of the cross section of the non-perforated steel beam 10A (the so-called resistance force due to Saint-Venant torsion), and the third term represents the resistance force against plate bending of the web of the non-perforated steel beam 10A.

[0053]

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[0054] The accuracy of equation (72) depends on the correctness of the assumed displacement function. However, when the displacement function is expressed by equations (44) through (47), an approximation up to the fourth term (n=4) can be used to obtain a solution with practically sufficient accuracy for any bending moment distribution. However, when using up to the fourth term (n=4), it is necessary to solve a quartic equation to obtain the solution from equation (72), and although an explicit evaluation is possible, the process of obtaining the solution becomes somewhat complicated. Therefore, the inventors sought a formula that could more easily evaluate the lateral buckling strength of a non-perforated beam, and the lateral buckling strength of the non-perforated steel beam 10A shown in formula (73) is M en We found that it is possible to evaluate it with high accuracy using this method.

[0055]

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[0056] Equation (73) follows equation (72) in terms of the resistance forces that make up the right-hand side, but modifies the third term, the resistance force due to the bending of the web, taking into account the characteristic that, under all load conditions, when the length l of the non-perforated steel beam 10A is extremely long, the sum of the terms for the resistance force due to Wagner torsion and the resistance force due to the bending of the web in equation (72) converges to twice the value obtained by taking the square root of their product. Note that C1, C2, and C3 are so-called moment correction factors, and their values ​​vary depending on the boundary conditions and load conditions.

[0057] Thus, in this design method, the lateral buckling resistance M of the non-porous material en This is evaluated by equation (73), which is the sum of terms obtained by multiplying the resistance force due to Wagner torsion, the resistance force due to Saint-Venant torsion, and the resistance force due to the bending of the web by different moment correction factors C1, C2, and C3, respectively. Examples of moment correction factors C1, C2, and C3 are shown in equations (81) to (89) in Table 1.

[0058] [Table 1]

[0059] Table 1 shows examples of moment correction factors C1, C2, and C3 for three different combinations of boundary and load conditions. Each of the moment correction factors C1, C2, and C3 is given by equations (91) to (93) M b M t , and M w It can be calculated using [this method].

[0060]

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[0061] M b M t , and M w This is a non-porous lateral buckling resistance M en These are the various resistance forces that make up the system. Specifically, M b This is the resistance force due to the Wagner torsion. Similarly, M t This is the resistance force due to the torsion of Saint-Venant, M w This is the resistance force caused by the bending of the web plate. For example, in the combination of boundary condition 1 and load condition 1, the moment correction coefficients C1, C2, and C3 are the values ​​given by equations (81) to (83). In other words, in the design method of this embodiment, the lateral buckling resistance M of the non-porous material en The calculation of this value does not require complex calculations such as solving higher-order equations or convergence calculations, allowing for a simple evaluation. By changing the moment correction coefficients C1, C2, and C3 in this way, evaluation is possible for any load and boundary conditions, and it can be applied to load and boundary conditions other than those shown here.

[0062] [3. Derivation of the lateral buckling resistance of perforated steel beams] Next, we derive the perforated lateral buckling resistance, which is the lateral buckling resistance of the perforated steel beam 10. First, we will examine the effect of the through-hole 13a in the web 13 on the perforated lateral buckling resistance. When a through-hole 13a is provided in the web 13, it is thought that the strain energy of the web 13, expressed as the third term on the right-hand side of the total potential energy Π in equation (56), will decrease. Here, we will focus on this change in strain energy and attempt to evaluate the perforated lateral buckling resistance considering the effect of the through-hole 13a. From the third term on the right-hand side of equation (56), the strain energy U of web 13 is obtained. w This is expressed by equation (101). If we consider only the second term, which has the greatest influence, on the right-hand side of equation (101), the strain energy U of the web 13 of the non-perforated steel beam 10A without through holes 13a is wn This is expressed by equation (102). On the other hand, the strain energy U of the web 13 of the perforated steel beam 10 wo This is expressed by equation (103).

[0063]

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[0064] Here, h represents the start and end points of the missing region. t and h b The diameter of the through hole 13a is φ w , and distance e w It can be expressed as a function of equations (104) to (107).

[0065]

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[0066] The strain energy U of the web 13 of the perforated steel girder 10 wo and the strain energy U of the web 13 of the non-perforated steel girder 10A wn When the ratio therebetween is determined, Equation (108) is obtained.

[0067] [Number]

[0068] Equation (108) means the reduction rate of the strain energy of the web 13 due to the provision of the through-hole 13a. Since Equation (108) is premised on the existence of a defect in the web 13 over the entire length of the perforated steel girder 10, the ratio p w obtained by Equation (111) requires correction according to it. Also, when the equation is corrected in consideration of the assumption that the defective area is rectangular and that the terms other than the second term are not considered in the strain energy of the web 13, the reduction in the lateral buckling resistance due to the through-hole 13a is represented by Equation (112) w as the reduction coefficient κ

[0069] [Number]

[0070] That is, the reduction coefficient κ w is calculated by Equation (112) using Equations (104), (105), and (111). Note that the larger the opening ratio α w is, the smaller the reduction coefficient κ w becomes, and the smaller the eccentricity β w (the larger the absolute value with a negative value) is, the smaller the reduction coefficient κ w becomes, and the smaller the ratio p w is, the smaller the reduction coefficient κ w becomes.

[0071] Since Equation (112) is the reduction coefficient resulting from the reduction of the plate bending resistance of the web in the perforated lateral buckling resistance, the perforated lateral buckling resistance Me is expressed by Equation (113) in a form where the third term of Equation (73) for the non-perforated lateral buckling resistance is multiplied by the reduction coefficient κ shown in Equation (112). w That is, the inventors considered calculating the perforated lateral buckling resistance M

[0072]

Equation

[0073] by Equation (113), which has a term obtained by multiplying the resistance due to web plate bending by the reduction coefficient κ e . Specifically, regarding the fourth term of the strain energy of the web 13 shown in Equation (101), by considering the influence of the through hole 13a, the reduction coefficient multiplied by the term of the resistance due to the sun-bunan torsion of the web in the second term on the right side of Equation (113) for the perforated lateral buckling resistance M w can be derived in the same way. However, since the influence on the perforated lateral buckling resistance M is small, here, for simplicity of evaluation, the reduction coefficient is only multiplied by the term of the resistance due to the web plate bending in the third term. e That is, the perforated lateral buckling resistance M e is calculated by multiplying the term of the resistance due to the web plate bending that constitutes the evaluation formula of the non-perforated lateral buckling resistance M by the reduction coefficient κ en corresponding to the through hole 13a. w In addition, when multiple through holes 13a are provided and the arrangement conditions such as the aperture ratio and eccentricity are different for each through hole 13a, the perforated lateral buckling resistance M e [ can be evaluated on the safe side by calculating the reduction coefficient κ

[0074] for each condition (through hole 13a) and using the smallest value. w Next, the accuracy verification of the derived perforated lateral buckling resistance is as follows. e Specifically, when the lateral movement and rotation of the upper flange 11 derived above are completely restricted, the perforated lateral buckling resistance M

[0075] 〔4. Verification of the accuracy of the derived perforated lateral buckling resistance〕 Next, for the perforated lateral buckling resistance M eTo verify the accuracy of the evaluation formula ((Equation 113)), we will perform an elastic buckling analysis (eigenvalue analysis) using FEM and compare the results with the evaluation formula.

[0076] Figure 8 shows the analysis model and boundary conditions for the perforated steel beam 10. The perforated steel beam 10 is composed of four-node shell elements. The displacement in the x-direction (ux), the displacement in the y-direction (uy), and the rotation around the z-axis (rotz) are constrained at both ends 10a1 and 10b1 of the perforated steel beam 10. Furthermore, the displacement in the z-direction (uz) is constrained only at end 10a1 of the perforated steel beam 10. The upper flange 11 of the perforated steel beam 10 is designed to be constrained by a concrete floor slab (holding member), and the lateral movement (ux) and rotation (rotz) of each node on the centroid line 11a are fixed. The load conditions are as follows: bending moments are applied to both ends 10a1 and 10b1, and vertically uniformly distributed loads are applied to each node on the centroid line 11a of the upper flange 11, thereby reproducing load conditions 1 to 3. In the case of load conditions 1 and 2, the rotation of ends 10a1 and 10b1 around the y-axis is not constrained as a condition corresponding to boundary condition 1, while in the case of load condition 3, the rotation of ends 10a1 and 10b1 around the y-axis is constrained as a condition corresponding to boundary condition 2.

[0077] The cross-sectional dimensions of the perforated steel beam 10 are as shown in Table 2, for two cross-sections, Sample No. 1 and 2. For each cross-section of Sample No. 1 and 2, the ratio of beam length to beam depth (length l of perforated steel beam 10 / depth H of perforated steel beam 10, l / H) was set to be between 2 and 100 times (in increments of 2).

[0078] [Table 2]

[0079] Figures 9 to 17 show the analysis results. In Figures 9 to 17, the vertical axis represents the analysis results M for perforated lateral buckling resistance. FEM , or perforated lateral buckling strength M according to equation (113) eThe horizontal axis represents (l / H). In Figures 9 to 17, the legend is plotted separately for each sample. Figures 9 to 11, 12 to 14, and 15 to 17 show the results for boundary condition 1 and load condition 1, boundary condition 1 and load condition 2, and boundary condition 2 and load condition 3, respectively. Note that in Figures 9 to 17, the number of plots has been reduced for ease of explanation. From Figures 9 to 17, the perforated lateral buckling resistance M e The analysis results are shown in the plot. FEM This shows that it corresponds well to the region where the length l of the perforated steel beam 10 is long (large l / H), where lateral buckling is dominant. Therefore, it can be seen that equation (113) accurately evaluates the perforated lateral buckling resistance regardless of the cross-sectional shape, boundary conditions, load conditions, and through-hole conditions of the perforated steel beam 10.

[0080] Note: Analysis result M FEM The aperture ratio α w The larger β is, the smaller the eccentricity β. w The smaller the value, the smaller it is confirmed, and the reduction coefficient κ w aperture ratio α w and eccentricity β w This is consistent with the trend of the influence.

[0081] [5. Design equipment and steel beams] Furthermore, the design method of this embodiment can be performed by a computer. For example, this computer includes a CPU, memory, etc. By executing the design program stored in memory, the computer determines the perforated lateral buckling resistance M e It functions as a calculation unit or similar component that calculates [a certain value]. The design device is configured with this calculation unit or similar component. Furthermore, the perforated steel beam 10 of this embodiment has a perforated lateral buckling resistance M according to the design method of this embodiment. e This beam was designed (manufactured) based on the calculation of [the relevant parameters]. [6. Effects of this embodiment] As explained above, in the design method of this embodiment, the inventors, after diligent study, determined that the non-perforated lateral buckling strength M of the non-perforated steel beam 10A enWe found that the evaluation formula includes the resistance force due to the bending of the web plate. Furthermore, we found that the perforated lateral buckling strength M of a perforated steel beam 10 in which a through hole 13a is formed in the web 13 and the lateral movement and rotation of the upper flange 11 are constrained. e However, the lateral buckling resistance M of the non-porous material en We found that the resistance force due to the bending of the web can be calculated by multiplying it by a reduction factor corresponding to the through hole 13a. Therefore, the perforated lateral buckling strength M of the perforated steel beam 10 is formed in the web 13, and the lateral movement and rotation of the upper flange 11 are constrained. e This can be evaluated with high accuracy.

[0082] Hole lateral buckling strength M e The resistance force due to the bending of the web plate is reduced by a reduction factor κ. w It is calculated by equation (113), which has a term multiplied by . Therefore, perforated lateral buckling strength M e This can be calculated more accurately using equation (113). Reduction coefficient κ w This is calculated using equations (104), (105), and (111) and then by equation (112). This gives the reduction coefficient κ w This can be calculated more accurately using equations (104), (105), and (111), and then by equation (112).

[0083] 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, the perforated lateral buckling resistance M e This may be calculated using an equation other than equation (113). Reduction coefficient κ w This can also be calculated using a formula other than equation (112). [Explanation of Symbols]

[0084] 10. Perforated steel beam (steel beam) 10A Non-perforated steel beam 11 Upper flange 12 Lower flange 13 Web 13a Through hole O6 center axis

Claims

1. A method for designing a steel beam to prevent lateral buckling of a steel beam in which through holes are formed in the web and the lateral movement and rotation of the upper flange are constrained, In the aforementioned steel beam, when a beam in which no through-holes are formed is defined as a non-perforated steel beam, A steel beam design method for calculating the perforated lateral buckling resistance of a steel beam, which is the lateral buckling resistance of a steel beam without holes, by multiplying the resistance force due to plate bending of the web, which constitutes the evaluation formula for the lateral buckling resistance of a non-perforated steel beam, by a reduction coefficient corresponding to the through-holes.

2. Said perforated lateral buckling strength M ｅ The resistance force due to the bending of the web plate is reduced by the reduction coefficient κ. ｗ A method for designing a steel beam according to claim 1, which is calculated by formula (1), having a term multiplied by . Here, E is Young's modulus, I ｆ d is the second moment of area of ​​the upper flange and the lower flange, respectively. ｂ l is the distance between the center thicknesses of the upper and lower flanges, l is the length of the steel beam, G is the shear modulus, and J is the shear modulus. ｆ The torsional constants of the upper flange and the lower flange, respectively, are J. ｗ D is the Saint-Venant torsion constant of the aforementioned web. ｗ This is the bending stiffness of the web plate. [Math 1]

3. The reduction coefficient κ ｗ The design method for a steel beam according to claim 2, wherein the value is calculated using equations (2) to (4) and then by equation (5). Here, φ ｗ is the diameter of the through-hole, e ｗ is the vertical distance between the center of the through-hole and the central axis of the steel frame beam, l ｗ is the pitch in the material axis direction of the steel frame beam of the through-hole. [Math 2]

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