Design methods for steel beams

Abstract

This invention provides a steel beam design method that can accurately evaluate the lateral buckling resistance of a steel beam with its upper flange constrained for arbitrary boundary and load conditions. [Solution] The steel beam design method is a steel beam design method for preventing lateral buckling of a steel beam 10 in which the lateral movement and rotation of the upper flange 11 are constrained, wherein the lateral buckling strength M of the steel beam e This is evaluated by a formula that is the sum of the values ​​obtained by multiplying the terms representing 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 separate moment correction factors C1, C2, and C3, respectively.

Description

Technical Field

[0001] The present invention relates to Design methods for steel beams .

Background Art

[0002] Conventionally, in steel frame structures, H-shaped cross-section members are used for girders, joists, etc. Although the H-shaped cross-section member has high cross-sectional performance around the strong axis, its cross-sectional performance around the weak axis is low. Therefore, lateral buckling may occur in which the H-shaped cross-section member deforms in the out-of-plane direction. When lateral buckling occurs, the load-bearing capacity is lost. Therefore, in a general design, lateral bracing members for preventing lateral buckling are installed on the H-shaped cross-section members. However, the installation of such lateral bracing members has problems such as an increase in construction costs such as an increase in material costs and processing costs due to an increase in the number of members, and a decrease in the efficiency of construction work.

[0003] Regarding such problems of steel beams, as in Patent Documents 1 to 4, design methods for omitting lateral bracing members have been studied by considering the buckling restraint effect by a floor slab or the like attached to the upper flange.

[0004] In Patent Document 1, the lateral buckling strength is theoretically derived under the condition that the lateral movement of the upper flange of the steel beam is restrained but rotation is allowed. Since the lateral buckling strength formula of Patent Document 1 only anticipates the lateral movement restraint effect of the upper flange by the floor slab, even in the case where rotational restraint cannot be expected due to damage to the local floor slab around the headed stud joint, the lateral buckling strength can be evaluated on the safe side. On the other hand, when local damage to the floor slab does not occur, the rotation of the upper flange is also generally restrained by the floor slab. Therefore, in that case, the lateral buckling strength is underestimated by the lateral buckling strength formula of Patent Document 1. That is, in the case where rotation is restrained in addition to the lateral movement of the upper flange, efficient design cannot be achieved.

[0005] 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 constrained. However, the lateral buckling resistance formulas in patent documents 2 and 3 are approximate formulas that use coefficients obtained by regression analysis of the results of FEM analysis on a main beam subjected to seismic forces. Therefore, there are limitations on the cross-sectional dimensions and length of the beam to which the resistance formula can be applied, and the application is limited to cases where an inversely symmetric bending moment is acting under the load conditions. In other words, the inventions disclosed in Patent Documents 2 and 3 are approximate formulas that are applicable under limited conditions and cannot be applied to the various boundary conditions and load conditions that may occur in actual structures.

[0006] Patent Document 4 theoretically derives the lateral buckling resistance under the condition that the lateral movement and rotation of the upper flange of a steel beam are constrained. [Prior art documents] [Patent Documents]

[0007] [Patent Document 1] Japanese Patent Publication No. 2016-23446 [Patent Document 2] Japanese Patent Publication No. 2019-56220 [Patent Document 3] Japanese Patent Publication No. 2020-158953 [Patent Document 4] Japanese Patent Publication No. 2022-144692 [Overview of the project] [Problems that the invention aims to solve]

[0008] However, the lateral buckling resistance formula in Patent Document 4 evaluates lateral buckling resistance under conditions where bending moment acts, such as when the lower flange, which minimizes lateral buckling resistance, is compressed. Therefore, while it provides a conservative evaluation for the bending moment distribution acting on beam members that constitute an actual building, it does not allow for precise evaluation according to the boundary conditions and load conditions of each beam member, thus preventing efficient design that conforms to the actual conditions. In other words, a design method for lateral buckling resistance assuming that the lateral movement and rotation of the upper flange of an H-shaped cross section member are constrained by the floor slab attached to the upper flange has not yet been established. The reason for this is that the lateral buckling deformation of a beam with constrained lateral movement and rotation of the upper flange is complex, and it is difficult to express it mathematically and obtain the lateral buckling resistance as a closed-form solution.

[0009] This 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 lateral buckling resistance of a steel beam in which the lateral movement and rotation of the upper flange are constrained under arbitrary boundary conditions and load conditions, and a steel beam evaluated by this steel beam design method. [Means for solving the problem]

[0010] To solve the aforementioned problems, this invention proposes the following means. (1) One aspect of the present invention is a method for designing a steel beam to prevent lateral buckling of a steel beam in which the lateral movement and rotation of the upper flange are constrained, wherein the lateral buckling strength of the steel beam is M e This is a design method for steel beams, which evaluates the resistance force using equation (1), which is the sum of the values ​​obtained by multiplying the terms representing 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 plate by different moment correction coefficients C1, C2, and C3, respectively. Here, E is Young's modulus, I f d is the second moment of area of ​​the flange, 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 and lower flanges are Saint-Venant and J. w D is the Saint-Venant torsion constant of the aforementioned web. w This is the bending stiffness of the web plate.

[0011]

number

[0012] In this invention, as a result of intensive studies, the inventors have found that the lateral buckling resistance M of a steel girder is expressed as the sum of values obtained by multiplying terms representing the resistance due to Wagner torsion, the resistance due to Saint-Venant torsion, and the resistance due to web plate bending by different moment correction coefficients C1, C2, and C3 respectively. e By evaluating it according to formula (1), it has been found that the lateral buckling resistance with the lateral movement and rotation of the upper flange restricted can be evaluated with high accuracy under arbitrary boundary conditions and load conditions. Therefore, the lateral buckling resistance with the lateral movement and rotation of the upper flange restricted can be evaluated with high accuracy under arbitrary boundary conditions and load conditions.

[0013] (2)Aspect 2 of the present invention may be a design method for a steel girder according to (1), in which both ends of the steel girder are rigidly connected to a main girder respectively, bending moments act on both ends of the steel girder, a vertical uniformly distributed load acts on the upper flange, and values given by formulas (6) to (8) are used as the moment correction coefficients C1, C2, and C3. Here, M b is the resistance due to the Wagner torsion, M t is the resistance due to the Saint-Venant torsion, M w is the resistance due to the web plate bending, and they are given by formulas (9) to (11) respectively.

[0014]

Equation

[0015] In this invention, when the steel girder corresponds to a secondary girder where both ends of the steel girder are rigidly connected to a main girder respectively, bending moments act on both ends, and a vertical uniformly distributed load acts on the upper flange, the lateral buckling resistance can be evaluated with higher accuracy by using formulas (6) to (11).

[0016] (3) Embodiment 3 of the present invention is a design method for a steel beam as described in (1), wherein the first end of the steel beam is rigidly connected to a main beam and the second end is pinned to a main beam, a bending moment is applied to the end of the steel beam on the first end side, and a vertically uniformly distributed load is applied to the upper flange, and the moment correction coefficients C1, C2, and C3 are values ​​given by equations (16) to (18). Here, M b This is the resistance force due to the Wagner torsion, M t The resistance force due to the torsion of Saint-Venant, M w is the resistance force due to the bending of the web plate, and is given by equations (19) to (21), respectively.

[0017]

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[0018] In this invention, in a steel beam, when the steel beam is a secondary beam in which the first end is rigidly connected to the main beam and the second end is pin-connected to the main beam, and when a bending moment acts on the end on the first end side and a vertically uniformly distributed load acts on the upper flange, the lateral buckling strength can be evaluated with higher accuracy using equations (16) to (21).

[0019] (4) Embodiment 4 of the present invention is the steel beam design method described in (1), wherein both ends of the steel beam are rigidly connected to columns, inversely symmetric bending moments act on both ends of the steel beam, and the moment correction coefficients C1, C2, and C3 are values ​​given by equations (26) to (28). Here, M b This is the resistance force due to the Wagner torsion, M t The resistance force due to the torsion of Saint-Venant, M w is the resistance force due to the bending of the web plate, and is given by equations (29) to (31), respectively.

[0020]

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[0021] In this invention, when a steel beam is a main beam, with both ends of the steel beam rigidly connected to columns, and when inversely symmetrical bending moments act on both ends, the lateral buckling resistance can be evaluated with higher accuracy using equations (26) to (31).

[0022] (5) Embodiment 5 of the present invention relates to the design method for a steel beam described in any one of (1) to (4), wherein the lateral buckling strength M e This is a steel beam that was evaluated highly. This invention provides a steel beam design method that can evaluate with high accuracy the lateral buckling strength of a steel beam with its upper flange lateral movement and rotation constrained under arbitrary boundary and load conditions, thereby enabling evaluation of the lateral buckling strength M e We can provide steel beams that have been evaluated. [Effects of the Invention]

[0023] The steel beam design method of the present invention allows for highly accurate evaluation of the lateral buckling resistance of a steel beam with constrained lateral movement and rotation of the upper flange under arbitrary boundary and load conditions. Furthermore, the steel beam design method of the present invention, which allows for highly accurate evaluation of the lateral buckling resistance of a steel beam with constrained lateral movement and rotation of the upper flange under arbitrary boundary and load conditions, enables the evaluation of the lateral buckling resistance M e We can provide steel beams that have been evaluated. [Brief explanation of the drawing]

[0024] [Figure 1] This is a side view of the steel beam to be designed according to the design method of a steel beam according to one embodiment of the present invention. [Figure 2] This is a plan view of the steel beam. [Figure 3] This is a cross-sectional view along the cutting line A1-A1 in Figure 1. [Figure 4] This figure shows the bending moment distribution of a steel beam when a uniform bending moment is applied to the end of the steel beam and a uniformly distributed vertical load is applied to the upper flange. [Figure 5]This figure shows the bending moment distribution of a steel beam when a bending moment is applied to one end and a vertically uniformly distributed load is applied to the upper flange. [Figure 6] This figure shows the bending moment distribution of a steel beam when inversely symmetrical bending moments act on each end. [Figure 7] This is a perspective view showing the analytical model and boundary conditions for a steel beam. [Figure 8] This figure shows the relationship between l / H and MFEM or Me under boundary condition 1 and load condition 1. [Figure 9] This figure shows the relationship between l / H and MFEM or Me under boundary condition 1 and load condition 2. [Figure 10] This figure shows the relationship between l / H and MFEM or Me under boundary condition 2 and load condition 3. [Modes for carrying out the invention]

[0025] 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 10.

[0026] [1. Structure of steel beams] In the steel beam design method of this embodiment (hereinafter simply referred to as the design method), the steel beam (steel beam) 10 shown in Figures 1 to 3 is the subject of design (evaluation). In Figures 1 to 3, the undeformed shape of the 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 steel beam 10 after these external forces are applied is shown by dashed lines. The steel beam 10 extends in the direction of the material axis z, which is along the horizontal plane. The 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.

[0027] 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.

[0028] The steel beam 10 is formed from an H-shaped cross-section member. That is, the steel beam 10 exhibits an H shape when viewed along the material axis z (viewed along the material axis z). The steel beam 10 may be formed from H-shaped steel. In this case, the steel beam 10 may be formed from rolled H-shaped steel or from welded H-shaped steel.

[0029] The steel beam 10, configured as described above, supports a retaining member (not shown), such as a floor slab, from below the retaining member. In this case, the 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. In this way, the upper flange 11 of the steel beam 10 is tightly connected to the retaining member by the shear force transmission member.

[0030] The steel beam 10 is then used as described below by the (boundary condition 1) and (boundary condition 2) by the members to which both ends of the steel beam 10 in the material axis direction z are joined. (Boundary condition 1) The steel beam 10 is used as a secondary beam by connecting both ends of the steel beam 10 in the direction of the material axis z to the main beam. (Boundary condition 2) The steel beam 10 is used as a main beam by connecting both ends of the steel beam 10 in the direction of the material axis z to the columns. The structure comprises a steel beam 10, a holding member, a shear force transmission member, and two main beams (or columns) to constitute a holding member support structure. 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.

[0031] The lateral movement and rotation of the upper flange 11 of the steel beam 10 are restrained by the holding member 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 steel beam 10 in which the lateral movement and rotation of the upper flange 11 are constrained.

[0032] Here, the specifications of the 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 steel beam 10 in the axial direction z is defined as l (mm) (see Figure 2). The Young's modulus of steel beam 10 is E(N / mm²). 2 The shear modulus of the steel beam 10 is defined as G(N / mm²). 2 ) is stipulated.

[0033] The second moment of area of ​​the upper flange 11 and the lower flange 12 (flanges) 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 tw (mm), and using the Poisson's ratio ν(-) of the steel beam 10 (web 13), D w =E·t w 3 / (12(1-ν 2 It can be calculated as follows: ))

[0034] [2. Derivation of the lateral buckling resistance of steel beams] In the following section, the lateral buckling strength of a steel beam 10 with its upper flange 11's lateral movement and rotation 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-axis, y-axis, and z-axis define a right-handed xyz coordinate system. Rotations around the x-axis, y-axis, and z-axis 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 steel beam 10 in the material axis direction z. Note that the xyz coordinate system is shown separated from the origin O for clarity in the figure. Here, in the steel beam 10, 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.

[0035] 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 steel beam 10 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.

[0036] Here, the deformation of the steel beam 10 due to lateral buckling, 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.

[0037]

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[0038] 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).

[0039]

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[0040] Equations (44) and (45) are displacement functions assuming boundary conditions where the degree of fixation of both ends 10a and 10b of the steel beam 10 is low, and rotation around the y-axis is not constrained, such as when the ends 10a and 10b of the steel beam 10 are joined to the main beam. 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 steel beam 10. Equation (45) is a displacement function assuming that lateral buckling deformation is dominant at the first end 10a of the steel beam 10.

[0041] Equations (46) and (47) are displacement functions assuming boundary conditions in which the degree of fixation of both ends 10a and 10b of the steel beam 10 is high and rotation around the y axis is constrained, such as in a main beam where both ends 10a and 10b are joined to columns. Equation (46) is a displacement function assuming that lateral buckling deformation is predominant symmetrically at both ends of the steel beam 10. Equation (47) is a displacement function assuming that lateral buckling deformation is predominant at the first end 10a of the steel beam 10. Note that in equations (44) to (47), j is any real number greater than or equal to 1.

[0042] As shown in Figure 1, the load condition is a bending moment M at the end 10a1 of the steel beam 10. a A bending moment M acts on 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 moment distribution acting on the steel beam 10. a M b , and the vertically uniformly distributed load w, and the lateral buckling resistance M cr The relationship can be expressed by equations (51) to (53). The bending moment distribution M acting on the steel beam 10 is expressed by equation (54) using α, β, and γ. Also, the stress function σ of the web 13 is w This is expressed by equation (55) using the bending moment distribution M and the section modulus Z.

[0043]

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[0044] 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 the steel beam 10, as well as the load conditions shown in Figures 4 to 6. Figure 4 shows the bending moment distribution M of the steel beam 10 when the ends 10a1 and 10b1 of the steel beam 10 are subjected to equal bending moments and a vertically uniformly distributed load is applied to the upper flange 11, as is the case when the beam is a secondary beam rigidly connected to the 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.

[0045] Figure 5 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 pin-connected 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 6 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.

[0046] Under these conditions, the total potential energy Π of the steel beam 10 is expressed by equation (56).

[0047]

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[0048] Here, θ a (rad) is the angle of rotation that occurs at the end 10a1 of the steel beam 10, θ b (rad) is the angle of rotation occurring at end 10b1 of the steel beam 10. v is the vertical displacement function at the point where the distributed load is applied. Rotation angle θ a ,θ bThe displacement functions v and u are expressed using the horizontal movement u, respectively.

[0049] 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.

[0050]

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[0051] From the neutral equilibrium in the energy principle, equation (64) is obtained.

[0052]

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[0053] Here, we set a part of the right-hand side of equation (64) to K as shown in equation (71), and the lateral buckling resistance M cr Solving for this, we get lateral buckling resistance cr Equation (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 steel beam 10 (the so-called resistance force due to Wagner torsion), the second term represents the resistance force against twisting of the cross section of the steel beam 10 (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 steel beam 10.

[0054]

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[0055] 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, and derived the lateral buckling strength M of the steel beam 10 shown in formula (73). e We found that it is possible to evaluate it with high accuracy using this method.

[0056]

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[0057] 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 steel beam 10 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.

[0058] Thus, in this design method, the lateral buckling resistance M e This is evaluated by equation (73), which is the sum of multiple values ​​obtained by multiplying terms representing the resistance force due to Wagner torsion, 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.

[0059] [Table 1]

[0060] 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].

[0061]

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[0062] M b M t , and M w The lateral buckling resistance M e 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 e 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.

[0063] [3. Verification of the accuracy of the derived lateral buckling resistance] Next, the derived lateral buckling resistance M when the lateral movement and rotation of the upper flange 11 are completely restrained. e To verify the accuracy of the simplified evaluation formula (Equation (73)), we will perform an elastic buckling analysis (eigenvalue analysis) using FEM and compare the results with the evaluation formula.

[0064] Figure 7 shows the analysis model and boundary conditions for the steel beam 10. The 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 steel beam 10. Furthermore, the displacement in the z-direction (uz) is constrained only at end 10a1 of the steel beam 10. The upper flange 11 of the 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.

[0065] The cross-sectional dimensions of the 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 steel beam 10 / depth H of steel beam 10, l / H) was set to be between 2 and 200 times (in increments of 2).

[0066] [Table 2]

[0067] Figures 8 to 10 show the analysis results. In Figures 8 to 10, the vertical axis represents the analysis result M of the lateral buckling resistance. FEM , or the lateral buckling resistance M according to equation (73) eThe horizontal axis represents (l / H). In Figures 8 to 10, the legend is plotted separately for each sample. Figures 8, 9, and 10 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 8 to 10, the number of plots has been reduced for ease of explanation. From Figures 8 to 10, the 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 steel beam 10 is long (large l / H), where lateral buckling is dominant. Therefore, it can be seen that equation (73) accurately evaluates the lateral buckling resistance regardless of the cross-sectional shape, boundary conditions, and load conditions of the steel beam 10.

[0068] [4. 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 can determine the lateral buckling resistance M e It functions as a calculation unit or similar component that calculates [the value]. The design device is configured with this calculation unit or similar component. Furthermore, the steel beam 10 of this embodiment has a lateral buckling resistance M according to the design method of this embodiment. e This beam was evaluated as such.

[0069] [5. Effects of this embodiment] As explained above, in the design method of this embodiment, the inventors, after careful consideration, determined that the lateral buckling strength M of the steel beam 10 is the sum of the values ​​obtained by multiplying the term representing the resistance force due to Wagner torsion, the term representing the resistance force due to Saint-Venant torsion, and the term representing the resistance force due to the bending of the web plate by separate moment correction coefficients C1, C2, and C3, respectively. e We found that by evaluating this using equation (73), the lateral buckling resistance of the upper flange 11, with its lateral movement and rotation constrained, can be evaluated with high accuracy under arbitrary boundary and load conditions. Therefore, under arbitrary boundary and load conditions, the lateral buckling resistance M of the upper flange 11 is constrained to lateral movement and rotation. e It can be evaluated with high accuracy.

[0070] In the case of a combination of boundary condition 1 and load condition 1, the moment correction coefficients C1, C2, and C3 may be the values ​​given by equations (81) to (83). In this case, when the steel beam 10 is a secondary beam, with both ends 10a and 10b rigidly connected to the main beam, and bending moments act on both ends 10a1 and 10b1, and a vertically uniformly distributed load acts on the upper flange 11, equations (81) to (83) and equations (91) to (93) are used to determine the lateral buckling strength M e This allows for evaluation with higher accuracy.

[0071] In the case of a combination of boundary condition 1 and load condition 2, the moment correction coefficients C1, C2, and C3 may be the values ​​given by equations (84) to (86). In this case, when the steel beam 10 is a secondary beam, with the first end 10a rigidly connected to the main beam and the second end 10b pinned to the main beam, and a bending moment acts on the first end 10a1 and a vertically uniformly distributed load acts on the upper flange 11, the lateral buckling strength M can be calculated using equations (84) to (86) and equations (91) to (93). e This allows for evaluation with higher accuracy.

[0072] In the case of a combination of boundary condition 2 and load condition 3, the moment correction coefficients C1, C2, and C3 may be the values ​​given by equations (87) to (89). In this case, when the steel beam 10 is a main beam, with both ends 10a and 10b rigidly connected to the columns, and inversely symmetric bending moments act on both ends 10a1 and 10b1, the lateral buckling strength M can be calculated using equations (87) to (89) and equations (91) to (93). e This allows for evaluation with higher accuracy.

[0073] Furthermore, in the steel beam 10 of this embodiment, the lateral buckling strength M of the steel beam 10 is determined by the constraint on the lateral movement and rotation of the upper flange 11 under arbitrary boundary conditions and load conditions.e A design method that can evaluate the lateral buckling resistance M with high accuracy. e This allows us to provide a steel beam 10 that has been evaluated positively.

[0074] 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. [Explanation of symbols]

[0075] 10 Steel beams 10a 1st end (end) 10b Second end (end) 11 Upper flange 12 Lower flange 13 Web

Claims

1. A design method for a steel beam to prevent lateral buckling of a steel beam in which the lateral movement and rotation of the upper flange are constrained, The lateral buckling resistance M of the steel beam ｅ The terms representing the resistance force due to Wagner torsion, Saint-Venant torsion, and web plate bending are each given a different moment correction coefficient C. １ , C ２ , and C ３ A design method for steel beams evaluated by equation (1), which is the sum of the values ​​obtained by multiplying by . Here, E is the Young's modulus, I ｆ is the second moment of area of the flange, d ｂ is the distance between the plate thickness centers of the upper flange and the lower flange, l is the length of the steel beam, G is the shear modulus of elasticity, J ｆ is the Saint-Venant torsional constant of the upper flange and the lower flange, J ｗ is the Saint-Venant torsional constant of the web, D ｗ is the bending rigidity of the web plate. [Math 1]

2. Both ends of the aforementioned steel beam are rigidly connected to the main beams, Bending moments act on both ends of the steel beam, and a vertically uniformly distributed load acts on the upper flange. The moment correction coefficient C １ , C ２ , and C ３ The steel beam design method according to claim 1, wherein the values ​​given by equations (6) to (8) are used. Here, M ｂ This is the resistance force due to the Wagner torsion, M ｔ This is the resistance force due to the torsion of Saint-Venant, M ｗ is the resistance force due to the bending of the web plate, and is given by equations (9) to (11), respectively. [Math 2]

3. In the aforementioned steel beam, the first end is rigidly connected to the main beam, and the second end is pin-connected to the main beam. A bending moment acts on the first end of the steel beam, and a vertically uniformly distributed load acts on the upper flange. The moment correction coefficient C １ , C ２ , and C ３ The design method for a steel beam according to claim 1, wherein the values ​​given by equations (16) to (18) are used. Here, M ｂ This is the resistance force due to the Wagner torsion, M ｔ This is the resistance force due to the torsion of Saint-Venant, M ｗ is the resistance force due to the bending of the web plate, and is given by equations (19) to (21), respectively. [Math 3]

4. Both ends of the aforementioned steel beam are rigidly connected to the columns, An inversely symmetrical bending moment acts on both ends of the aforementioned steel beam. The moment correction coefficient C １ , C ２ , and C ３ The steel beam design method according to claim 1, wherein the values ​​given by equations (26) to (28) are used. Here, M ｂ This is the resistance force due to the Wagner torsion, M ｔ This is the resistance force due to the torsion of Saint-Venant, M ｗ is the resistance force due to the bending of the web plate, and is given by equations (29) to (31), respectively. [Math 4]

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