Design method

Abstract

To provide a design method that can appropriately evaluate an elastic lateral buckling proof stress of a steel beam in a floor in-process structure.SOLUTION: The present invention relates to a design method of a floor in-process structure 45A comprising H-shaped steel made steel beams 25 having both ends joined to supporting members 15 by pins, and a deck plate 36 placed on upper flanges 26 of the steel beams and joined to the upper flanges. An elastic lateral buckling proof stress of the steel beam is designed when the steel beam is affected by constraint from in-plane rigidity of the deck plate as to the state before hardening concrete 37A placed on the deck plate.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to Design method Regarding. [Background technology]

[0002] Generally, H-shaped steel beams with pin joints at both ends are used as sub-beams (steel beams) in steel-frame construction. A floor slab, such as a deck composite slab or a reinforced concrete slab, is poured onto the top flange of the sub-beam. The top flange and the floor slab are then fastened together via a shear connector, forming an integrated structure of the sub-beam and the floor slab (see, for example, Patent Document 1). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent No. 5885911 Summary of the Invention [Problem to be solved by the invention]

[0004] When a vertical load acts on a sub-beam with pin joints at both ends, a compressive force acts on the top flange and a tensile force acts on the bottom flange, resulting in a so-called positive bending stress state. Normally, when designing a beam, lateral buckling stiffeners are considered to prevent the phenomenon of lateral buckling (elastic lateral buckling), in which the flange subjected to compressive force deforms outward from the structural plane. However, in the case of a sub-beam with pin joints at both ends, the top flange is in compression over the entire length of the beam. And because a sufficiently rigid floor slab is joined to the top flange of the sub-beam to restrain deformation, lateral buckling of the sub-beam is not considered to be a problem, and lateral buckling stiffeners are not required.

[0005] However, the upper flange is restrained by the floor slab only after the concrete of the floor slab has hardened. During construction, when the concrete of the floor slab is poured and before it hardens, the floor work structure is made up of the joists, deck plates, and unhardened concrete. During construction, the weight of the sub-beam, the mass of the deck plate, concrete, and rebar, and the load during construction act as vertical loads on the sub-beam, so it is necessary to design the upper flange so that lateral buckling does not occur when it is not restrained. Therefore, in order to prevent lateral buckling from occurring due to the load during construction, methods such as using wide H-shaped steel with low cross-sectional efficiency for the sub-beam and attaching horizontal braces to the upper flange as lateral buckling stiffening during construction are used. This makes it difficult to use H-shaped steel with a narrow cross-sectional area that has good cross-sectional efficiency, and also creates problems such as increased effort and costs in processing and construction. As described above, in the case of small beams with pin joints at both ends, lateral buckling during construction can sometimes be a bottleneck.

[0006] The present invention has been made in consideration of such problems, and aims to provide a design method and an evaluation method that can appropriately evaluate the elastic lateral buckling strength of steel beams in a floor-work structure. [Means for solving the problem]

[0007] In order to solve the above problems, the present invention proposes the following means. The design method of the present invention is a design method for a floor-in-progress structure comprising an H-shaped steel beam with both ends pin-joined to support members, and a deck plate placed on the upper flange of the steel beam and joined to the upper flange, and is characterized in that the elastic lateral buckling strength of the steel beam is designed assuming that the steel beam is restrained by the in-plane rigidity of the deck plate before the concrete poured on the deck plate has hardened. In addition, the evaluation method of the present invention is a method for evaluating a floor-in-progress structure comprising a steel beam made of H-shaped steel with both ends pin-jointed to support members, and a deck plate placed on the upper flange of the steel beam and joined to the upper flange, and is characterized in that the elastic lateral buckling strength of the steel beam is evaluated before the concrete poured on the deck plate has hardened, assuming that the steel beam is restrained by the in-plane rigidity of the deck plate.

[0008] When concrete is poured onto the steel beam and the deck plate after the upper flange of the steel beam is joined to the deck plate, the steel beam is actually restrained by the in-plane rigidity of the deck plate even before the concrete hardens, improving the elastic lateral buckling strength of the steel beam. Therefore, by designing and evaluating the elastic lateral buckling strength of the steel beam assuming that the steel beam is restrained by the in-plane rigidity of the deck plate, it is possible to appropriately evaluate the elastic lateral buckling strength of the steel beam in a floor work structure without underestimating the elastic lateral buckling strength of the steel beam to which the deck plate is joined.

[0009] In the design method, the elastic lateral buckling moment M of the steel beam calculated by the formulas (1) to (4) is e may be designed to exceed the bending moment generated in the steel beam due to the mass of the steel beam, the deck plate, the concrete, the reinforcing bars embedded in the concrete, and the load during construction. where G is the shear modulus of elasticity of the steel beam, J is the Saint-Venant torsional constant of the steel beam, and d b : Distance between the center of thickness of the lower flange and the upper flange of the steel beam, K H : horizontal spring rigidity based on the in-plane rigidity of the deck plate, E: Young's modulus of the steel beam, I: second moment of area of ​​a pair of flanges of the steel beam about the weak axis of the steel beam.

[0010]

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[0011] According to this invention, the bending moment generated in the steel beam due to the loads actually acting on the steel beam during construction, such as the weight of the steel beam, the deck plate, the reinforcing bars, the mass of the concrete before hardening, and the live load during construction, is calculated as the elastic lateral buckling moment M e Therefore, it is possible to prevent the steel beam from undergoing elastic lateral buckling against the bending moment that actually occurs in the steel beam. Furthermore, the elastic lateral buckling moment M is calculated from only the cross-sectional dimensions of the steel beam and the horizontal spring stiffness of the deck plate, without depending on the length of the steel beam. e Since it is possible to calculate the above equation, it is possible to confirm that the steel beam will not elastically buckle laterally when the H-shaped steel and deck plate are combined, enabling efficient design.

[0012] In the design method, the elastic lateral buckling moment M of the steel beam calculated by the formulas (5) to (8) is e may be designed to exceed the yield moment of the steel beam. where G is the shear modulus of elasticity of the steel beam, J is the Saint-Venant torsional constant of the steel beam, and d b : Distance between the center of thickness of the lower flange and the upper flange of the steel beam, K H : horizontal spring rigidity based on the in-plane rigidity of the deck plate, E: Young's modulus of the steel beam, I: second moment of area about the weak axis of the steel beam of a pair of flanges of the steel beam.

[0013]

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[0014] According to this invention, the elastic lateral buckling moment M of a steel beam e The yield moment of the steel beam, which is the subject of comparison, is determined based on the cross-sectional shape perpendicular to the material axis direction of the steel beam and the physical properties of the steel beam. Generally, sub-beams are used in a range below this yield moment, and the bending moment generated in the steel beam during construction is also below this value. For this reason, the elastic lateral buckling moment M e Since the condition exceeds the yield moment of the steel beam, there is no need to consider the load conditions during construction, and the elastic lateral buckling moment M e The required value of can be determined.

[0015] In the design method, the in-plane stiffness of the deck plate is calculated by the first required stiffening stiffness K req1 may be designed to exceed where G is the shear modulus of elasticity of the steel beam, J is the Saint-Venant torsional constant of the steel beam, and d b : Distance between the center of thickness of the lower flange and the upper flange of the steel beam, K H : horizontal spring rigidity based on the in-plane rigidity of the deck plate, E: Young's modulus of the steel beam, I: second moment of area of ​​the flange of the steel beam about the weak axis of the steel beam, Z: section modulus of the steel beam about the strong axis, F: standard strength of the steel beam.

[0016]

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[0017] According to the present invention, the first required stiffening stiffness K req1 Because the steel beams are restrained by the in-plane rigidity of the deck plate, which is designed to exceed this, it is possible to prevent lateral buckling of the steel beams even if a moment is generated in the steel beams during construction due to the loads that actually act on the steel beams, such as the weight of the steel beams, the deck plate, the mass of the concrete before hardening, and the live load during construction.

[0018] In the design method, the in-plane stiffness of the deck plate is calculated by the second required stiffening stiffness K req2 may be designed to exceed

[0019]

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[0020] According to the present invention, the second required stiffening stiffness K req2 Because the steel beams are restrained by the in-plane rigidity of the deck plate, which is designed to exceed this rigidity, it is possible to prevent elastic lateral buckling of the steel beams even if a moment is generated in the steel beams during construction due to the loads that actually act on the steel beams, such as the weight of the steel beams, the deck plate, the reinforcing bars, the mass of the concrete before hardening, and the live load during construction. Furthermore, the required in-plane stiffness of the deck plate is determined using the relatively easily obtained dimensions of the depth and width of the steel beam, without depending on the length of the steel beam. Therefore, the second required stiffening stiffness K required to prevent the steel beam from elastically buckling laterally is req2 can be easily obtained.

[0021] In addition, in the design method, the steel beam may be designed so that no lateral buckling stiffener is attached to the steel beam. According to this invention, it is possible to more reliably prevent the need to attach lateral buckling stiffeners to steel beams, and further reduce the costs required for constructing floor work structures. Effect of the Invention

[0022] According to the design method and evaluation method of the present invention, the elastic lateral buckling strength of steel beams in a floor construction can be appropriately evaluated. [Brief description of the drawings]

[0023] [Figure 1] FIG. 1 is a perspective view of a building having a floor work structure to which the design method of the first embodiment of the present invention is applied. [Diagram 2] 2 is a cross-sectional view taken along line A1-A1 in FIG. [Diagram 3] This is a front view of the steel beam of the same floor-in-progress structure. [Figure 4] FIG. [Diagram 5] FIG. 2 is a plan view of a building, showing a schematic diagram of a horizontal spring. [Figure 6] 5 is a view taken in the direction of the arrow B1 in FIG. 4. [Figure 7] 5 is a view taken in the direction of the arrow B2 in FIG. 4. [Figure 8] This is a diagram showing the change in elastic lateral buckling moment depending on the length of a steel beam. [Figure 9] This is a graph showing the change in elastic lateral buckling strength versus the (l / H) value when subjected to uniform bending and long-term load. [Figure 10]FIG. 13 is a diagram showing the change in bending moment with respect to the non-dimensional coordinates of a steel beam when subjected to uniform bending and long-term loads. [Figure 11] This is a graph showing the change in elastic lateral buckling strength versus the value of (l / H) when horizontal stiffening stiffness is used as a variable. [Figure 12] This figure shows the change in (MFEM / Mp) or (Mcr / Mp) with respect to the non-dimensional lateral buckling slenderness ratio when the horizontal stiffening stiffness is used as a variable. [Figure 13] This is a graph showing the change in elastic lateral buckling strength versus (l / H) value for H-shaped steel with different cross-sectional shapes, when the horizontal stiffening stiffness is used as a variable. [Figure 14] This figure shows the change in (MFEM / Mp) or (Mcr / Mp) versus the non-dimensional lateral buckling slenderness ratio when the horizontal stiffening stiffness is used as a variable for H-shaped steel with different cross-sectional shapes. [Figure 15] FIG. 13 is a diagram showing a change in (Me / My) relative to stiffening rigidity K in the design method according to the third embodiment of the present invention. [Figure 16] FIG. 13 is a graph showing the change in (Me / My) relative to the stiffening coefficient k. [Figure 17] 1 is a graph showing the change in (Me / My) relative to stiffening stiffness K, based on the formula for stiffening stiffness K. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0024] (First embodiment) Hereinafter, a floor work structure to which a first embodiment of a design method and an evaluation method according to the present invention is applied will be described with reference to FIGS.

[0025] [1. Floor work structure configuration] In a floor in-progress structure, the concrete of the floor slab is in a fluid state before hardening. When the concrete in a floor in-progress structure hardens, it becomes a floor structure. The floor structure is used in a building 1 shown in FIG. 1. The building 1 comprises a plurality of columns 10, a plurality of girders (support members) 15, steel beams 25 which are minor beams, and a floor slab 35. 1, the floor slab 35 is indicated by a two-dot chain line. The steel beams 25 and the floor slab 35 constitute a floor structure 45.

[0026] The pillars 10 extend in the vertical direction. The pillars 10 are arranged at intervals from one another. The pillars 10 are made of steel, RC (Reinforced Concrete), SRC (Steel Reinforced Concrete), CFT (Concrete Filled Steel Tube), or the like. As shown in Fig. 1 and Fig. 2, for example, girder 15 is made of H-shaped steel. Girder 15 is provided with a pair of first upper flange 16 and first lower flange 17 at the top and bottom. In girder 15, first upper flange 16 and first lower flange 17 are connected to each other by first web 18. Gusset plates 19 are joined to first web 18 of girder 15 by welding or the like. The girder 15 is placed between the adjacent columns 10 and extends in a direction along the horizontal plane. Both ends of the girder 15 are joined to the columns 10 by welding or the like. The girder 15 may be made of RC or SRC.

[0027] 3 and 4, the steel beam 25 is made of H-shaped steel. In FIG. 4 and other figures, the girder 15 is shown diagrammatically as a member joined to the steel beam 25 by a pin. The steel beam 25 is provided with a pair of upper and lower second upper flanges (upper flange) 26 and second lower flanges (lower flange) 27. In the steel beam 25, the second upper flange 26 and the second lower flange 27 are connected to each other by a second web . The steel beam 25 extends in the material axis direction Z of the steel beam 25. The length of the steel beam 25 in the material axis direction Z is 1. The distance in the height direction Y between the plate thickness centers of the second lower flange 27 and the second upper flange 26 of the steel beam 25 is the plate thickness center distance d b It is. As shown in Fig. 3, in the steel beam 25, the width direction X is the strong axis (hence, the rotation direction around the width direction X is the strong axis), and in the steel beam 25, the height direction Y is the weak axis (hence, the rotation direction around the height direction Y is the weak axis).

[0028] 2, the steel beam 25 is placed between adjacent girders 15 and extends in a direction along the horizontal plane. Both ends of the steel beam 25 are pin-joined to the girders 15. Specifically, the second web 28 of the steel beam 25 and the gusset plate 19 are joined to each other by fastening members 29 including high-strength bolts or the like.

[0029] The floor slab 35 includes a deck plate 36 , hardened concrete 37 , reinforcing bars (rebars) 38 , and shear connectors 39 . The deck plate 36 is formed by bending a steel plate or the like. The deck plate 36 is disposed on the second upper flange 26 of the steel beam 25. The deck plate 36 and the second upper flange 26 are joined to each other at a joint 42 made by burn-out plug welding or the like. The deck plate 36 is preferably disposed so that the concave and convex shape of the deck plate 36 extends in a direction perpendicular to the steel beam 25. The concrete 37 is formed into a flat plate shape with its thickness direction aligned in the vertical direction. The concrete 37 is a mixture of cement, aggregates such as sand, and water that hardens through hydration. The concrete 37 is placed on the deck plate 36.

[0030] The mixture is fluid concrete 37A before hardening. The steel beams 25, the deck plate 36, the concrete 37A, and the reinforcing bars 38 constitute a floor work structure 45A. The concrete 37A is poured on the deck plate 36. The floor work structure 45A does not necessarily have to include the concrete 37A. When constructing the floor work structure 45A, for example, the second upper flange 26 of the steel beam 25 and the deck plate 36 are joined, and then concrete 37A is poured onto the deck plate 36.

[0031] The floor slab 35 includes a plurality of reinforcing bars 38. A first reinforcing bar 38a, which is a part of the plurality of reinforcing bars 38, extends along the steel beam 25. A second reinforcing bar 38b, which is the remaining part of the plurality of reinforcing bars 38, extends in a direction perpendicular to the first reinforcing bar 38a. The first reinforcing bar 38a and the second reinforcing bar 38b are embedded in the concrete 37. The shear connectors 39 are, for example, headed studs. The floor slab 35 is provided with a plurality of shear connectors 39. The lower ends of the plurality of shear connectors 39 are fixed to the upper surface of the second upper flange 26 of the steel beam 25 at intervals. The shear connectors 39 are embedded in the concrete 37 through the deck plate 36.

[0032] The process of deriving the elastic lateral buckling moment will be described below. In the following, the second upper flange 26, the second lower flange 27, and the second web 28 will also be referred to as the upper flange 26, the lower flange 27, and the web 28, respectively.

[0033] [2. Derivation of the formula for calculating elastic lateral buckling moment] In the following, the subject is a floor work structure 45A having unhardened concrete 37A, and the following assumptions 1 to 5 are made. 1. The ends of the steel beams do not restrain warping. 2. The load conditions for steel beams are for uniform bending moment when the upper flange is compressed. The reason for uniform bending moment will be explained later. 3. The cross section of the steel beam retains its original H shape. 4. The out-of-plane displacement of the upper flange (displacement in a direction perpendicular to the main plane of the upper flange) is given by an arbitrary function. 5. The out-of-plane displacement of the lower flange is expressed using the undetermined coefficient α described later.

[0034] Figures 5 to 7 show schematic diagrams of horizontal spring 36a due to the in-plane rigidity of deck plate 36. The in-plane rigidity of deck plate 36 referred to here means a force acting in a direction along the main surface of deck plate 36 due to the rigidity of deck plate 36. Figure 5 is a plan view of building 1. Figure 6 is a view seen from the direction of arrow B1 in Figure 4. Figure 7 is a view seen from the direction of arrow B2 in Figure 4. In Figure 5, of the multiple steel beams 25, steel beam 25A that has elastically buckled laterally is shown by a thick solid line.

[0035] When a deck plate 36 is attached to a steel beam 25 in which elastic lateral buckling may occur, horizontal movement of the upper flange 26 of the steel beam 25 out of the structural plane is restrained by the in-plane rigidity of the deck plate 36. The in-plane rigidity of the deck plate 36 can be considered to be rigidity due to two types of resistance mechanisms: the axial rigidity of the deck plate 36 which transmits load to the girder 15 arranged parallel to the steel beam 25, and the shear rigidity of the deck plate 36 which transmits load to the girder 15 arranged perpendicular to the steel beam 25. The deck plate 36 is fixed to the steel beams 25 and girders 15 at joints 42 by burn-out plug welding or the like during installation, so it can be expected to exhibit stable axial rigidity. On the other hand, in order to exhibit shear rigidity, it is necessary to rely on load transmission due to frictional forces at the overlapping parts of adjacent deck plates 36. However, since the load that can be transmitted at the overlapping parts is unknown, it is difficult to expect shear rigidity. Therefore, in the following, we will take a safe sided by considering only the axial rigidity of the deck plate 36 as a stiffening effect. In this embodiment, a horizontal spring model is applied to stiffening by the deck plate 36. A specific method for determining the horizontal spring stiffness (stiffening stiffness) will be described later.

[0036] As shown in Fig. 7, it is assumed that the second upper flange 26 of the steel beam 25 is not completely fixed in position relative to the deck plate 36, but is movable relative to the deck plate 36 while being influenced by the horizontal spring 36a. As shown in Fig. 5, a restoring force is applied by the horizontal spring 36a to the portion of the steel beam 25A that has been displaced along the horizontal plane (the portion that buckles laterally) to return the portion to its original position. In FIG. 6, the out-of-plane displacement of the second upper flange 26 is expressed as u (u B The torsion angle of the steel beam 25 is φ. The out-of-plane displacement of the second lower flange 27 is u A The ratio of the out-of-plane displacement of the second lower flange 27 to the out-of-plane displacement of the second upper flange 26 is defined as an undetermined coefficient α.

[0037] The torsion angle (φ) of the steel beam 25 and the out-of-plane displacement (u B ,u A ) is expressed as follows: From a model that takes into account the horizontal spring 36a of the deck plate 36, the torsion angle of the steel beam 25 and the out-of-plane displacement of the second upper and lower flanges 26, 27 are expressed by equations (21) to (23).

[0038]

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[0039] The torsion angle of the steel beam 25 is expressed as a function of the out-of-plane displacement u of the second upper flange 26, as shown in equation (24).

[0040]

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[0041] At this time, the total potential energy when the horizontal spring 36a is attached to the second upper flange 26 is expressed by equation (25). where E is the Young's modulus of the steel beam 25. I is the second moment of area about the weak axis of the steel beam of the second upper and lower flanges 26, 27. Z is the coordinate in the material axis direction of the steel beam 25 shown in Figure 3. G is the shear modulus of elasticity of the steel beam 25. J is the Saint-Venant torsional constant of the H-shaped cross section of the steel beam 25. K H is the horizontal spring stiffness due to the horizontal spring 36a based on the in-plane stiffness of the deck plate 36. How to determine the horizontal spring stiffness will be described later. M e is the elastic lateral buckling moment of the steel beam 25. For example, u ’ is the first derivative of u with respect to Z, u ’ ’ is the second derivative of u with respect to Z.

[0042]

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[0043] Substitute equations (22), (23), and (24) into equation (25). Then, rearrange the definite integrals into A through C in equations (28) through (30). Then, the total potential energy is expressed by equation (31).

[0044]

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[0045] From equation (31), equation (32) can be obtained based on the principle of minimum potential energy. Note that equation (32) can be transformed into equation (33).

[0046]

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[0047] From equation (33), the elastic lateral buckling moment M cr is obtained by equation (34).

[0048]

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[0049] Next, the out-of-plane displacement u of the upper flange 26 is rearranged using a sine wave as shown in Equation (37), where n represents the number of sine half waves (number of modes) and is given as a positive integer.

[0050]

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[0051] The first-order and second-order differential equations of the out-of-plane displacement u of the upper flange 26 are expressed by equations (38) and (39), respectively.

[0052]

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[0053] By rearranging equations (28) to (30) using equations (37) to (39), equations (40) to (42) can be obtained.

[0054]

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[0055] Substituting equations (40) to (42) into equation (34) and rearranging, the elastic lateral buckling moment M e is expressed by equation (43). In addition, the elastic lateral buckling moment M cr is the smallest value among the values ​​obtained in equation (43) according to the number n of half waves.

[0056]

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[0057] where α is an undetermined coefficient, and the elastic lateral buckling moment M crFind the α that minimizes. (The right-hand side of equation (43) is partially differentiated with respect to α, resulting in 0, so we obtain equation (44). Note that equation (44) can be transformed into equation (45).

[0058]

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[0059] Specifying A and B as in (48) and (49), and solving (45), α is expressed as in (50).

[0060]

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[0061] α takes a value in the range of 0 to 1. Therefore, by rearranging the smaller solution given by equation (50), α can be expressed by equation (51).

[0062]

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[0063] Here, in Fig. 8, the elastic lateral buckling moment M cr The results are shown in Fig. 8. In Fig. 8, the horizontal axis represents the length of the steel beam, and the vertical axis represents the elastic lateral buckling moment. The steel beam used is an H-shaped steel beam with a cross-sectional shape of H-700x200x9x19. In equation (43), the elastic lateral buckling moment when the number of half waves n is 1 to 10 is shown by thin dotted lines. The elastic lateral buckling moment M cr is the minimum value of the elastic lateral buckling moment calculated according to the number n of half waves, and is shown by the thick solid line in Figure 8. Fig. 8 shows the results of eigenvalue analysis using FEM (Finite Element Method) (elastic lateral buckling moment M FEM The elastic lateral buckling moment M crshows good correspondence with the eigenvalue analysis results by FEM.

[0064] Elastic lateral buckling moment M according to Eq. (43) cr depends on the number of sine half waves, n. However, the minimum value of the buckling load obtained by substituting any positive integer for n is a constant value regardless of n. The minimum value of the elastic lateral buckling moment M cr,min is given by equation (52).

[0065]

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[0066] In Fig. 8, the minimum elastic lateral buckling moment M cr,min is shown by a thick dotted line. The minimum elastic lateral buckling moment M cr,min accurately captures the lower limit of the eigenvalue analysis results using FEM.

[0067] Similarly, the minimum value M cr,min The value of α that minimizes is found. Since the equation obtained by partially differentiating the right-hand side of equation (52) with respect to α becomes 0, we obtain equation (53). Note that equation (53) can be transformed into equation (54).

[0068]

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[0069] By defining A and B as in equations (57) and (58) and rearranging equation (54), we obtain equation (59) for α.

[0070]

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[0071] α takes values ​​in the range of 0 to 1. By ignoring the higher-order terms of α in equation (59) as being infinitesimal and rearranging, we obtain equation (60). Furthermore, by solving equation (60), we obtain equation (61) as an approximate solution for α.

[0072]

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[0073] In general H-shaped steel, A < B. Therefore, the formula (62) where α is positive becomes the approximate solution.

[0074]

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[0075] Note that under special conditions such as when the horizontal spring stiffness K H is extremely small, the value inside the square root of the formula (62) (the value of "9A 2 - 3B 2 ") becomes negative, and there may be a case where α cannot be obtained. In that case, by treating the inside of the square root as 0 and obtaining α in the form of the formula (62 - 1), the minimum value M cr,min of the elastic lateral buckling moment according to the formula (52) can be obtained.

[0076]

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[0077] The right side of this formula (52) is defined as the new elastic lateral buckling moment M e used in the design as the formula (63). As a result, regardless of n, a constant value is obtained, and the elastic lateral buckling moment M e that is easy to calculate can be obtained.

[0078]

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[0079] The design method in this embodiment is applied to a floor work structure 45A before construction, before concrete 37A poured on the deck plate 36 hardens. In this design method, the elastic lateral buckling strength of the steel beam 25 is designed assuming that the steel beam 25 is restrained by the in-plane rigidity of the deck plate 36. More specifically, in this design method, the elastic lateral buckling moment M e Specifically, the elastic lateral buckling moment M e is designed to exceed the bending moment generated in the steel beams 25 due to the mass of the steel beams 25, the mass of the deck plate 36, the mass of the reinforcing bars 38, the mass of the concrete 37A before hardening, and the load during construction. The load during construction referred to here means the mass of the equipment and personnel used in the construction work, such as the hose and vibrating device that pump the concrete 37A loaded on the deck plate 36 when constructing the floor work structure 45A, and the load caused by a large amount of concrete 37A being temporarily loaded locally on one part of the floor work structure 45A immediately after the unhardened concrete 37A is discharged from the hose or hopper. Furthermore, in this design method, the steel beam 25 may be designed so that no lateral buckling stiffener is attached thereto. The evaluation method in this embodiment is applied to the completed floor work structure 45A. In this evaluation method, the elastic lateral buckling strength of the steel beam 25 is evaluated assuming that the steel beam 25 is restrained by the in-plane rigidity of the deck plate .

[0080] [3. Examination of the effect of using an approximate solution for α on the minimum elastic lateral buckling strength] A parametric study was conducted on H-shaped steel with a cross-sectional shape of approximately 600 mm. A comparison was made between α calculated using the solver in a spreadsheet software (hereafter referred to as "solver") and α calculated using equation (62) (hereafter referred to as "approximation"). The minimum elastic lateral buckling moment M calculated using these α values ​​was cr,min In this case, α and the minimum value of the elastic lateral buckling moment M cr,min is the horizontal spring stiffness K H Depending on, it will be as follows: (1) Horizontal spring stiffness K H When is 0.2 α(approximation) / α(solver)=1.0006~1.2404 M cr,min (approximate) / M cr,min (Solver)=1.0000~1.0084 (2) Horizontal spring stiffness K H If is 5 α(approximation) / α(solver)=1.0000~1.0047 M cr,min (approximate) / M cr,min (Solver)=1.0000 As described above, the smaller the horizontal spring stiffness, the greater the discrepancy between the results obtained by the solver and those obtained by equation (62). However, the minimum value M cr,min The impact on

[0081] [4. Consideration of uniform bending moment as a loading condition for steel beams] FIG. 9 shows the results of eigenvalue analysis of an H-shaped steel beam 25 using FEM (Finite Element Method). Here, the steel beam 25 is an H-shaped steel beam with a cross-sectional shape of H-700×200×9×19. Here, the width of the steel beam 25 is H. In FIG. 9, the horizontal axis represents the value of "l / H (shear span ratio)" and the vertical axis represents the elastic lateral buckling moment M FEM represents the stiffening rigidity (horizontal stiffening rigidity) K imparted to the upper flange 26 for each load condition, when uniform bending (uniform bending moment) is applied and when long-term load is applied, is used as a variable. The long-term load here means a uniformly distributed downward load. The stiffening rigidity means the rigidity imparted to the upper flange 26 by a deck plate or the like. Both the uniform bending and the long-term load are conditions under which the upper flange 26 is in compression.

[0082] Here, uniform bending and long-term load will be explained with reference to Fig. 10. In Fig. 10, the horizontal axis represents the non-dimensional coordinate in the axial direction of steel beam 25, and the vertical axis represents the bending moment of steel beam 25 non-dimensionalized by the maximum value of the bending moment. On line L1 representing uniform bending, a constant bending moment acts regardless of the non-dimensional coordinate of steel beam 25. On the other hand, on line L2 representing long-term load, the magnitude of the bending moment at the center in the axial direction of steel beam 25 is larger than the magnitude of the bending moment at both ends in the axial direction of steel beam 25.

[0083] In FIG. 9, stiffening stiffnesses K that are 20, 40, and 60 times a predetermined constant D0 are applied to the upper flange 26 of a steel beam 25, respectively. In both the uniform bending and long-term loads, as the stiffening rigidity K of the upper flange 26 increases, the elastic lateral buckling strength M FEM When subjected to a long-term load, if the length l of the steel beam 25 is short, the strength of the steel beam 25 is determined by shear buckling, but if the length l of the steel beam 25 is long, the strength of the steel beam 25 is determined by lateral buckling. When the length l of the steel beam 25 is relatively long, and the stiffening rigidity K is constant, the elastic lateral buckling strength M FEM is the elastic lateral buckling strength M when subjected to uniform bending FEM However, when subjected to long-term load, as the length l of the steel beam 25 increases, the elastic lateral buckling strength M FEM approaches . Therefore, when evaluating the strength against lateral buckling, it is possible to evaluate on the safe side by assuming that uniform bending is applied.

[0084] [5. How to calculate the horizontal spring stiffness (stiffening stiffness) of the deck plate] Since only the axial stiffness is considered as the in-plane stiffness of the deck plate 36, the axial stiffness can be calculated if the cross-sectional area of ​​the deck plate in the direction perpendicular to the steel beams 25 (sub-beams) is known, regardless of the shape of the deck plate. However, considering that deck plates of various shapes are used, in equation (65), the horizontal spring stiffness K is calculated assuming that a steel plate of uniform thickness is laid on the vertical projection surface. His being sought. However, E d is the Young's modulus of the deck plate 36. t d is the thickness of the deck plate 36. N is the number of steel beams 25 in the area surrounded by the girder 15. d is the length of the deck plate 36 that contributes to the rigidity (the distance from a girder 15 parallel to a steel beam 25 to that steel beam 25).

[0085]

number

[0086] Using equation (65), the horizontal spring stiffness K H In addition, since it is common for multiple sub-beams to be placed between the main girders 15, the axial rigidity in formula (65) is divided by the number of steel beams 25.

[0087] Here, for the commonly used deck plate with a plate thickness of 0.8 mm, which is the thinnest, the horizontal spring stiffness K H The distance from the main girder 15 to the steel beam 25 is 10m, and the number of steel beams 25 placed in the area is three. In this case, t d =0.8mm, N=3, l d = 10m, and the horizontal spring stiffness of the deck plate is K H is 5.47N / mm / mm. For H-beam of about 600 size, horizontal spring stiffness K H The elastic lateral buckling moment is evaluated using equation (65) with the material strength of the steel as F = 325N / mm 2 Yield moment M in the case y The elastic lateral buckling moment is F=385N / mm, which is the highest strength of the steel material expected for a steel beam. 2 Yield moment M in the case yThe yield moment is 3.5 to 6.4 times that of the deck plate 36 in the horizontal spring stiffness test. The yield moment here refers to the bending moment at which the outermost edge of the cross section of the H-shaped steel in the material axis direction is in a yield state. Even in the evaluation using the thinnest deck plate 36 according to this safe evaluation formula, the deck plate 36 has a sufficient stiffening effect against lateral buckling of the steel beam 25. Even if the specifications of the deck plate, such as the length, which contribute to the horizontal spring stiffness, change slightly, a sufficient stiffening effect can be expected. Therefore, by considering the effect of the in-plane stiffness of the deck plate 36 regardless of the type and shape of the deck plate 36, lateral buckling will not occur in the steel beam 25 even if a lateral buckling stiffener is not attached to the steel beam 25, and the strength of the steel beam 25 will be 3.5 to 6.4 times that of the deck plate 36 in the horizontal spring stiffness test. y It is clear that it is possible to reach

[0088] 6. Results of Application of the Design Method of This Embodiment 1 11 and 12 show the results of eigenvalue analysis performed by FEM on an H-shaped steel with a cross-sectional shape of H-700×200×9×19, with the stiffening rigidity K of the upper flange 26 being used as a variable. In Fig. 11, the horizontal axis represents the value of "l / H" and the vertical axis represents the elastic lateral buckling moment M FEM The stiffening stiffness K was changed from 0 to 56 times the predetermined constant D0. From FIG. 11, the elastic lateral buckling strength M FEM You can see that it varies. In Fig. 12, the horizontal axis represents the non-dimensional lateral buckling slenderness ratio (√(M p / M cr )) where M p is the total plastic moment of the steel beam 25, and M cr is the elastic lateral buckling moment calculated by Eq. (43). The vertical axis is the elastic lateral buckling strength M obtained by eigenvalue analysis using FEM. FEM , or the elastic lateral buckling moment M according to Eq. (43) cr The total plastic moment M of the steel beam 25 p It represents the standardized value by dividing by . The closer the plot in the figure is to the solid line, the higher the accuracy of this design method. From the figure, it can be seen that this design method can achieve extremely high accuracy regardless of the magnitude of the stiffening stiffness K of the upper flange 26.

[0089] 7. Results of Application of the Design Method of This Embodiment 2 13 and 14 show the results of eigenvalue analysis using FEM for three sizes of H-shaped steel with different cross-sectional shapes, with the stiffening stiffness K of the upper flange 26 as a variable. The three cross-sectional shapes are H-500×200×10×16, H-700×300×13×24, and H-900×300×16×28. The vertical and horizontal axes in Fig. 13 and Fig. 14 are the same as those in Fig. 11 and Fig. 12. From Fig. 13, it can be seen that the elastic lateral buckling strength M FEM It can be seen that takes on various values. On the other hand, as shown in Figure 14, it can be seen that this design method can evaluate the elastic lateral buckling moment with high accuracy for a steel beam 25 of any length l and any stiffening stiffness K, regardless of the cross-sectional shape of the steel beam 25.

[0090] As described above, according to the design method and evaluation method of this embodiment, when concrete 37A is poured on the steel beam 25 and the deck plate 36 after the second upper flange 26 of the steel beam 25 is joined to the deck plate 36, the steel beam 25 is actually constrained by the in-plane rigidity of the deck plate 36 even before the concrete 37A hardens, and the elastic lateral buckling strength of the steel beam 25 is improved. Therefore, by designing and evaluating the elastic lateral buckling strength of the steel beam 25 assuming that the steel beam 25 is constrained by the in-plane rigidity of the deck plate 36, the elastic lateral buckling strength of the steel beam 25 in the floor work structure 45A can be appropriately evaluated without underestimating the elastic lateral buckling strength of the steel beam 25 joined to the deck plate 36.

[0091] In addition, the elastic lateral buckling moment M eis designed to exceed the bending moment generated in the steel beam 25 due to the mass of the steel beam 25, the deck plate 36, the reinforcing bar 38, the concrete 37A before hardening, and the load applied during construction. Therefore, the bending moment generated in the steel beam 25 due to the loads actually acting on the steel beam 25 during construction, namely, the weight of the steel beam 25, the deck plate 36, the reinforcing bar 38, the concrete 37A before hardening, and the load applied during construction, is defined as the elastic lateral buckling moment M e Therefore, it is possible to prevent the steel beam 25 from lateral buckling against the bending moment that actually occurs in the steel beam 25. Furthermore, the elastic lateral buckling moment M of the steel beam 25 is calculated based only on the cross-sectional dimensions of the steel beam 25 and the horizontal rigidity of the deck plate 36, without depending on the length of the steel beam 25. e Therefore, it is possible to confirm that the steel beam 25, which is made of H-shaped steel, will not undergo elastic lateral buckling in the combination of the steel beam 25 and the deck plate 36, enabling efficient design. In addition, in this design method, a design is made so that no lateral buckling stiffener is attached to the steel beam 25. This makes it possible to more reliably prevent the attachment of a lateral buckling stiffener to the steel beam 25, and further reduce the cost required for constructing the floor work structure 45A.

[0092] In this embodiment, the elastic lateral buckling moment M e However, it may be designed to exceed the yield moment of the steel beam 25. Elastic lateral buckling moment M of steel beam 25 e The yield moment of the steel beam 25 to be compared is determined based on the cross-sectional shape perpendicular to the material axis direction of the steel beam 25 and the physical properties of the steel beam 25. Generally, small beams such as steel beams are used within a range below this yield moment, and the bending moment generated in the steel beam 25 during construction is also below this value. For this reason, the elastic lateral buckling moment M e Since the condition that exceeds the yield moment of the steel beam 25, the elastic lateral buckling moment M of the steel beam 25 is e The required value of can be determined.

[0093] Second embodiment Next, a second embodiment of the present invention will be described. The same components as those in the above embodiment are designated by the same reference numerals, and the description thereof will be omitted. Only the differences will be described. In the design method of this embodiment, the floor installation structure 45A is designed based on the stiffening stiffness of the deck plate 36. Specifically, in the floor installation structure 45A, the in-plane stiffness of the deck plate 36 is calculated based on the first required stiffening stiffness K req1 Designed to exceed. where Z is the section modulus of the steel beam about the strong axis, and F is the standard strength of the steel beam.

[0094]

number

[0095] The minimum elastic lateral buckling moment M according to Eq. (53) cr,min is the yield moment M of steel beam 25 y From the condition that the horizontal spring stiffness is equal to H Required stiffening stiffness K req1 More specifically, the product of the section modulus Z of the steel beam 25 around the strong axis and the reference strength F of the steel beam 25 is substituted into the left side of equation (53) as the yield moment, and the horizontal spring stiffness K H This can be obtained by solving In the evaluation method of this embodiment, the in-plane stiffness of the deck plate 36 is calculated using the first required stiffening stiffness K req1 Then, it may be evaluated whether the in-plane stiffness of the deck plate 36 exceeds the first required stiffening stiffness K req1 If it is determined that the strength does not exceed this, then lateral buckling stiffening materials may be attached to the steel beam 25.

[0096] As described above, according to the design method of this embodiment, the elastic lateral buckling resistance of the steel beams 25 in the floor work structure 45A can be appropriately evaluated. Furthermore, the first required stiffening stiffness K req1Because the steel beam 25 is restrained by the in-plane rigidity of the deck plate, which is designed to exceed this rigidity, even if a bending moment is generated in the steel beam 25 due to the loads that actually act on the steel beam 25 during construction, such as the weight of the steel beam 25, the deck plate 36, the reinforcing bars 38, the mass of the concrete 37A before hardening, and the live load during construction, the steel beam 25 can be prevented from lateral buckling.

[0097] Third embodiment Next, a third embodiment of the present invention will be described with reference to Figs. 15 to 17. The same components as those in the above embodiment are given the same reference numerals, and the description thereof will be omitted. Only the differences will be described. In the design method of this embodiment, extensive research was carried out to more easily obtain the stiffening rigidity required for the deck plate 36 in the design method of the second embodiment. Figure 15 shows the elastic lateral buckling moment M against the stiffening stiffness K for an H-shaped steel with a cross-sectional shape of approximately 600 mm. e and the yield moment M y The results of a parametric study of the ratio of stiffening stiffness K to the stiffening stiffness M are shown in Fig. 15. e / M y ) In this parametric study, the stiffening stiffness K was changed in increments of 0.1 N / mm / mm in the range of 0.1 to 0.5 N / mm / mm, and a total of about 3,000 cases were examined. Note that in Figure 15, the same legend is used for cases where the stiffening stiffness K is constant. In addition, the elastic lateral buckling moment M e The yield moment M used to divide y is the highest strength expected for a steel beam, F=385N / mm 2 Therefore, if the strength of the steel beam is lower than this, the elastic lateral buckling moment M e and the yield moment M y Since the ratio of is large, this is a conservative assessment.

[0098] In Fig. 15, if the stiffening stiffness K is 0.4N / mm / mm or more, for the H-shaped steel of the size under consideration, (M e / M y ) exceeds 1, i.e., the elastic lateral buckling moment M e is the yield moment M y However, even if the stiffening stiffness K is a constant value, the cross-sectional shape of the H-shaped steel can cause the stiffening stiffness to exceed (M e / M y ) varies widely, making it difficult to determine the required value of stiffening rigidity K. On the other hand, FIG. 16 shows the same case under consideration, with the horizontal axis representing the stiffening coefficient k given by equation (71). Here, W is the width of the steel beam 25.

[0099]

number

[0100] In Figure 16, regardless of the cross-sectional shape of the H-shaped steel, (M e / M y The value of ) and the stiffening coefficient k show a good correlation with little variation. Therefore, the elastic lateral buckling moment M e is the yield moment M y The stiffening coefficient K required to exceed the elastic lateral buckling moment M can be determined accurately using equation (71). e is the yield moment M y It can be confirmed that it exceeds

[0101] Figure 17 shows the relationship between stiffening stiffness K and (M e / M y ) value change.

[0102]

number

[0103] In equations (74) to (76), the stiffening coefficient k in equation (71) is set to 0.08, and three orders are set to 1.00, 1.25, and 1.50. From Figure 17, when the order is set to 1.25 and stiffening stiffness K is given, (M e / M y ) has the least variation. Note that a degree of 1.00 shows a downward trend, a degree of 1.50 shows an upward trend, and a degree of 1.25 shows a roughly flat trend. Table 1 shows the average value, minimum value, and standard deviation for each formula of stiffening stiffness K.

[0104] [Table 1]

[0105] From Table 1, it can be seen that the order of 1.25 has the smallest variation (standard deviation) and is stable (M e / M y ) is evaluated to exceed 1. That is, in the design method of this embodiment, the in-plane stiffness of the deck plate 36 is calculated by the second required stiffening stiffness K req2 Designed to exceed. In the evaluation method of this embodiment, the in-plane stiffness of the deck plate 36 is calculated using the second required stiffening stiffness K req2 Then, it may be evaluated whether the in-plane stiffness of the deck plate 36 exceeds the second required stiffening stiffness K req2 If it is determined that the strength does not exceed this, then lateral buckling stiffening materials may be attached to the steel beam 25.

[0106]

number

[0107] As described above, according to the design method of this embodiment, the elastic lateral buckling resistance of the steel beams 25 in the floor work structure 45A can be appropriately evaluated. And the second required stiffening stiffness Kreq2 Since the steel beam 25 is restrained by the in-plane rigidity of the deck plate 36 which is designed to exceed this, even if a bending moment occurs in the steel beam 25 due to the loads that actually act on the steel beam 25 during construction, such as the weight of the steel beam 25, the deck plate 36, the reinforcing bars 38, the mass of the concrete 37A before hardening, and the live load during construction, the steel beam 25 can be prevented from elastic lateral buckling. Furthermore, the required value of the in-plane stiffness of the deck plate 36 is determined using the relatively easily obtained dimensions of the depth H and width W of the steel beam 25, without depending on the length of the steel beam 25. Therefore, the second required stiffening stiffness K required to prevent the steel beam 25 from elastically buckling laterally is req2 can be easily obtained.

[0108] Although the first to third embodiments of the present invention have been described above with reference to the drawings, the specific configurations are not limited to these embodiments, and the present invention also includes modifications, combinations, deletions, etc. of the configurations within the scope of the gist of the present invention. Furthermore, it goes without saying that the configurations shown in each embodiment can be used in appropriate combinations. For example, in the first to third embodiments, the method of joining the second upper flange 26 of the steel beam 25 and the deck plate 36 is not limited to burn-out plug welding, and may be fillet welding, adhesive bonding, or the like. The floor slab 35 may not include reinforcing bars 38 and shear connectors 39 . [Explanation of symbols]

[0109] 15 Large beam (supporting member) 25 Steel Beam 26 Second upper flange (upper flange) 36 Deck Plate 37A Concrete 38 Reinforcing steel bars (reinforced bars) 45A Floor-mounted structure

Claims

1. A steel beam made of H-shaped steel, both ends of which are pin-connected to support members; A deck plate disposed on the upper flange of the steel beam and joined to the upper flange; A method for designing a floor work structure comprising: The elastic lateral buckling strength of the steel beam is designed before the concrete poured on the deck plate hardens, assuming that the steel beam is restrained by the in-plane rigidity of the deck plate; The elastic lateral buckling moment M of the steel beam calculated using equations (1) to (4) ｅ is designed to exceed the bending moment generated in the steel beam due to the mass of the steel beam, the deck plate, the concrete, the reinforcing bars embedded in the concrete, and the load applied during construction. where G is the shear modulus of elasticity of the steel beam, J is the Saint-Venant torsional constant of the steel beam, and d ｂ : Distance between the thickness centers of the lower flange and the upper flange of the steel beam, K Ｈ : horizontal spring rigidity based on the in-plane rigidity of the deck plate, E: Young's modulus of the steel beam, I: second moment of area of ​​a pair of flanges of the steel beam about the weak axis of the steel beam. [0010]

2. A steel beam made of H-shaped steel, both ends of which are pin-connected to support members; A deck plate disposed on the upper flange of the steel beam and joined to the upper flange; A method for designing a floor work structure comprising: The elastic lateral buckling strength of the steel beam is designed before the concrete poured on the deck plate hardens, assuming that the steel beam is restrained by the in-plane rigidity of the deck plate; The elastic lateral buckling moment M of the steel beam calculated using equations (5) to (8) ｅ is designed to exceed the yield moment of the steel beam. where G is the shear modulus of elasticity of the steel beam, J is the Saint-Venant torsional constant of the steel beam, and d ｂ : Distance between the thickness centers of the lower flange and the upper flange of the steel beam, K Ｈ : horizontal spring rigidity based on the in-plane rigidity of the deck plate, E: Young's modulus of the steel beam, I: second moment of area of ​​a pair of flanges of the steel beam about the weak axis of the steel beam. [0025]

3. A steel beam made of H-shaped steel, both ends of which are pin-connected to support members; A deck plate disposed on the upper flange of the steel beam and joined to the upper flange; A method for designing a floor work structure comprising: The elastic lateral buckling strength of the steel beam is designed before the concrete poured on the deck plate hardens, assuming that the steel beam is restrained by the in-plane rigidity of the deck plate; The in-plane stiffness of the deck plate is calculated by the first required stiffening stiffness K ｒｅｑ１ The design method includes designing the steel beam so that the elastic lateral buckling moment M cr exceeds the yield moment of the steel beam. where G is the shear modulus of elasticity of the steel beam, J is the Saint-Venant torsional constant of the steel beam, and d ｂ : Distance between the thickness centers of the lower flange and the upper flange of the steel beam, K Ｈ : horizontal spring rigidity based on the in-plane rigidity of the deck plate, E: Young's modulus of the steel beam, I: second moment of area of ​​a pair of flanges of the steel beam about the weak axis of the steel beam. [0030]

4. A steel beam made of H-shaped steel, both ends of which are pin-connected to support members; A deck plate disposed on the upper flange of the steel beam and joined to the upper flange; A method for designing a floor work structure comprising: The elastic lateral buckling strength of the steel beam is designed before the concrete poured on the deck plate hardens, assuming that the steel beam is restrained by the in-plane rigidity of the deck plate; The in-plane stiffness of the deck plate is calculated by the second required stiffening stiffness K ｒｅｑ２ The design method includes designing the steel beam so that the elastic lateral buckling moment M cr exceeds the yield moment of the steel beam. Here, H is the height of the steel beam, and W is the width of the steel beam. [0045]

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