Structure of continuous composite beams and evaluation method for maximum deflection of continuous composite beams

Abstract

To provide a structure such that a continuous composite beam in which a plurality of steel beams whose ends are rigidly joined to girders are continuous in series is integrated with a concrete slab through a shear connector, wherein each of a region PB where positive bending is generated in long-term load action, and a region NB where negative bending is generated in the long-term load action form a more rational structure, and an evaluation method for maximum deflection of a continuous composite beam.SOLUTION: A structure of a continuous composite beam is a structure of a continuous composite beam in which steel beams whose both ends are rigidly joined to girders, and steel beams composed of composite beams having a concrete slab integrated with the steel beams through a shear connector provided on the upper surface of the steel beams are continuously configured in series with two or more spans, wherein in only a region where positive bending is generated in long-term load action among each span of the continuous composite beam, the shear connector is provided.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a structure of a continuous composite beam and a method for evaluating the maximum deflection of a continuous composite beam. [Background technology]

[0002] In steel-framed buildings, the ends of steel sub-girders are often connected to the main steel girder using pin joints, which connect only the web of the steel sub-girder to the main steel girder. However, with this type of structure, the sub-girders are prone to large deflections.

[0003] Therefore, by using a rigid connection method in which not only the web at the end of the steel sub-girder but also the upper and lower flanges are joined to the steel main girder, and by making multiple steel sub-girders into a continuous beam in series, the rotational rigidity of the end of the steel sub-girder is increased and deflection of the sub-girder is suppressed.

[0004] In addition, a shear connector such as a headed stud is provided on the upper flange of a steel beam, and the concrete slab placed on top of the steel beam is integrated with the steel beam via this shear connector to create a composite beam, which increases the bending rigidity of the beam and suppresses deflection of the beam.

[0005] For example, as disclosed in Patent Document 1, the above two types of structures are combined to form a composite beam in which a steel beam and a concrete slab are integrated, and the ends of the steel beams are rigidly connected to the steel beams, forming a continuous composite beam structure in which a plurality of such beams are connected in series. As shown in Fig. 35, in the conventional continuous composite beam CBP structure, a shear connector 84 is provided on an upper flange 82 over the entire length of a steel beam 8, and the steel beam is integrated with a concrete slab 9. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] JP 2017-053102 A [Patent Document 2] Patent Publication No. 2021-082153 [Non-patent literature]

[0007] [Non-Patent Document 1] Architectural Institute of Japan (ed.), "Guidelines and Commentary on Composite Structure Design", Architectural Institute of Japan, November 2010, pp. 51-133 Summary of the Invention [Problem to be solved by the invention]

[0008] Here, as shown in FIG. 35, in the structure of the conventional continuous composite beam CBP as disclosed in Patent Document 1, positive bending occurs in the center of each span of the continuous composite beam CBP when a long-term load is applied, and negative bending occurs near the end of the sub-beam that is rigidly connected to the main beam 1 so as to straddle the main beam 1. In the region PB where positive bending occurs when a long-term load is applied, compression occurs on the concrete slab 9 side on the inside of the bend, and the concrete slab 9 bears the compressive stress, so that the bending rigidity of the composite beam becomes large. In contrast, in the region NB where negative bending occurs when a long-term load is applied, tension occurs on the concrete slab 9 side on the outside of the bend, but the concrete slab 9 bears almost no tensile stress, so that the composite effect of the concrete slab 9 and the steel sub-beam 8 is low. Therefore, the bending rigidity of the composite beam in the region NB where negative bending occurs when a long-term load is applied is smaller than that of the region PB where positive bending occurs when a long-term load is applied. In this way, in the structure of the continuous composite beam CBP, the region PB where positive bending occurs and the region NB where negative bending occurs occur in each span when a long-term load is applied, and the bending rigidity is different between these two regions PB and NB.

[0009] In addition, as shown in Fig. 36, in the structure of the conventional continuous composite beam CBP, near the end of the sub-beam that is rigidly joined to the main girder 1 so as to straddle the main girder 1, that is, in the area NB where negative bending occurs under the action of a long-term load, tensile stress is transmitted from the shear connector 84 provided on the upper flange 82 on the outside of the bending of the steel sub-girder 8 to the concrete 91 of the concrete slab 9. In order to achieve a safe design that can fully withstand this tensile stress, it becomes necessary to increase the amount of reinforcing bars 92 in the concrete slab 9, which is uneconomical.

[0010] In consideration of the above problems, the present invention aims to provide a continuous composite beam structure and a method for evaluating the maximum deflection of a continuous composite beam, which is formed by integrating a continuous beam consisting of multiple steel beams in series, each of which has its end portions rigidly connected to a main beam, with a concrete slab via a shear connector, and which can have a more rational structure in each of the region PB where positive bending occurs under long-term load and the region NB where negative bending occurs under long-term load. [Means for solving the problem]

[0011] In order to solve the above problems, the present invention has the following features.

[0012] [1] A continuous composite beam structure in which sub-beams made of composite beams each having a steel sub-beam rigidly connected to a main beam at both ends and a concrete slab integrated with the steel sub-beam via a shear connector provided on the upper surface of the steel sub-beam are arranged in series in two or more spans, A continuous composite beam structure, in which the shear connectors are provided only in areas of each span of the continuous composite beam where positive bending occurs under long-term load.

[0013] Here, the term "long-term load" refers to the load that constantly acts on the floor frame including the above-mentioned continuous composite beam structure, and includes fixed load (self-weight) and live load. Depending on the use of the structure, dynamic loads such as wheel pressure loads when vehicles are traveling and impact loads associated with unloading may act on the floor frame. If such dynamic loads act on the structure on a daily basis, they are included in the live load.

[0014] [2] The continuous composite beam structure described in [1] is installed at a location in each span that is subjected to long-term concentrated loads from n points (n is an integer between 2 and 5), and the length L1 [mm] of the area in which the shear connector is installed in each span of the continuous composite beam satisfies the following formula (1).

[0015] (β-0.05)L≦L1≦(β+0.05)L …(1) however, L [mm] is the length of each span of the continuous composite beam, and β is expressed by the following formula (2). β = A1 × log e α+A2…(2) In the above formula (2), α is the ratio of the bending rigidity of the composite beam to the bending rigidity of the steel beam, and is set to 1.0≦α≦3.5. A1 and A2 are coefficients determined by the number of spans m (m is an integer of 2 or more).

[0016] [3] A method for evaluating the maximum deflection of a continuous composite beam in the structure of the continuous composite beam described in [2], comprising: calculating an evaluation value δ of the maximum deflection of the continuous composite beam by the following formula (3): eq A method for evaluating the maximum deflection of a continuous composite beam, calculating the value in mm.

[0017] δ eq =B1×δ s / {(α-1)×β+1}-B2…(3) However, in the above formula (3), δ s[mm] is the maximum deflection value of the continuous composite beam calculated by evaluating that only the steel sub-beam portion functions as a structural member over the entire length of the continuous composite beam, and B1 and B2 are coefficients determined by the number of spans m (m is an integer of 2 or more). Effect of the Invention

[0018] According to the structure of the continuous composite beam of the present invention, shear connectors are provided only in the areas of each span of the continuous composite beam where positive bending occurs under long-term load, and no shear connectors are provided in the areas where negative bending occurs. Therefore, in the areas where negative bending occurs under long-term load, almost no tensile force acts on the concrete slab from the upper flange, which is on the outside of the bending of the steel beam, and there is no need to increase the amount of reinforcing bars in the concrete slab.

[0019] For this reason, in areas where positive bending occurs under long-term load, the steel beams and concrete slabs are integrated to form a composite beam, which increases the flexural rigidity and strength of the beam and suppresses deflection of the beam, while in areas where negative bending occurs, the steel beams can resist tensile forces on the outside of the bend. In this way, the amount of reinforcing bars in the concrete slab is not excessively large, resulting in a structurally rational and economical structure.

[0020] In addition, according to the method for evaluating the maximum deflection of a continuous composite beam of the present invention, the evaluation value of the maximum deflection of a continuous composite beam can be accurately and easily calculated by the explicit function shown in the above equation (3) without the need for numerical analysis or convergence calculation. [Brief description of the drawings]

[0021] [Figure 1] FIG. 1 is a side view showing an example of the structure of a continuous composite beam of the present invention. [Diagram 2] FIG. 2 is a schematic diagram showing the bending moment distribution occurring in a three-span continuous composite beam subjected to a long-term load. [Diagram 3] FIG. 3 is an enlarged view of a composite beam having shear connectors. [Figure 4]FIG. 4 is an enlarged view of the case where no shear connector is provided. [Diagram 5] FIG. 5 is a diagram showing a schematic structure of the continuous composite beam of the present invention. [Figure 6] 6(a) to 6(d) are diagrams showing a procedure for deriving the bending moment at the end of each span of a three-span continuous composite beam. [Figure 7] 7(a) and 7(b) are diagrams showing the deflection angles at the ends of each span of a three-span continuous composite beam. [Figure 8] 8(a) to 8(c) are diagrams showing the superposition of the end bending moment and the concentrated load acting on a three-span continuous composite beam. [Figure 9] 9(a) to 9(d) are diagrams showing a procedure for deriving the bending moment at the end of each span of a three-span continuous composite beam. [Figure 10] FIG. 10 is a diagram showing the ratios β1 and β2 of the region where positive bending occurs and the end bending moment M in each span of a three-span continuous composite beam. [Figure 11] FIG. 11 is a diagram showing a schematic diagram of the ratio β of the region where positive bending occurs and the end bending moment M in each span of a two-span continuous composite beam. [Figure 12] Figure 12(a) is a diagram showing the reaction forces generated at each support point of a three-span continuous composite beam, and Figures 12(b) and 12(c) are diagrams showing the balance of bending moments at each position of the three-span continuous composite beam. [Figure 13] Figures 13(a) and 13(b) are graphs showing the analysis results and regression equations for the proportion of the area where negative bending occurs in the spans at both ends of a three-span continuous composite beam when a long-term load is applied. [Figure 14] FIG. 14 is a graph showing the analysis results and regression equation for the ratio of the area in which positive bending occurs in each span of a two-span continuous composite beam when subjected to a long-term load. [Figure 15] FIG. 15 is a diagram showing the ratios β1 and β2 of the region where positive bending occurs and the end bending moment M in each span of a four-span continuous composite beam. [Figure 16]FIG. 16 is a diagram showing the ratios β1 to β3 of the region where positive bending occurs and the end bending moment M in each span of a five-span continuous composite beam. [Figure 17] FIG. 17 is a diagram showing the ratios β1 to β3 of the region where positive bending occurs and the end bending moment M in each span of a 6-span continuous composite beam. [Figure 18] FIG. 18 is a diagram showing the ratios β1 to β4 of the region where positive bending occurs and the end bending moment M in each span of a 7-span continuous composite beam. [Figure 19] FIG. 19 is a diagram showing the ratios β1 to β4 of the region where positive bending occurs and the end bending moment M in each span of an 8-span continuous composite beam. [Figure 20] FIG. 20 is a diagram showing the ratios β1 to β5 of the region where positive bending occurs and the end bending moment M in each span of a 9-span continuous composite beam. [Figure 21] FIG. 21 is a diagram showing the ratios β1 to β5 of the region where positive bending occurs and the end bending moment M in each span of a 10-span continuous composite beam. [Figure 22] 22(a) and 22(b) are graphs showing the analysis results and regression equations for the ratio of the area where negative bending occurs in the spans at both ends of a four-span continuous composite beam when a long-term load is applied. [Figure 23] 23(a) to 23(c) are graphs showing the analysis results and regression equations of the ratio of the area where negative bending occurs in the spans at both ends of a five-span continuous composite beam when a long-term load is applied. [Figure 24] 24(a) to 24(c) are graphs showing the analysis results and regression equations of the ratio of the area where negative bending occurs in the spans at both ends of a 6-span continuous composite beam when a long-term load is applied. [Diagram 25] 25(a) to 25(d) are graphs showing the analysis results and regression equations of the ratio of the area where negative bending occurs in the spans at both ends of a 7-span continuous composite beam when a long-term load is applied. [Figure 26]26(a) to 26(d) are graphs showing the analysis results and regression equations for the ratio of the area where negative bending occurs in the spans at both ends of an 8-span continuous composite beam when a long-term load is applied. [Figure 27] 27(a) to 27(e) are graphs showing the analysis results and regression equations for the ratio of the area where negative bending occurs in the spans at both ends of a 9-span continuous composite beam when a long-term load is applied. [Figure 28] 28(a) to 28(e) are graphs showing analysis results and regression equations for the ratio of areas where negative bending occurs in spans at both ends of a 10-span continuous composite beam when a long-term load is applied. [Figure 29] FIG. 29 is a conceptual diagram of an equivalent secondary bending moment. [Diagram 30] 30(a) and 30(b) are diagrams showing the frame and loading conditions for a numerical analysis to verify the effect of the structure of the continuous composite beam of the present invention. [Diagram 31] FIG. 31 is a diagram showing the second moment of area set in the numerical analysis. [Diagram 32] FIG. 32 is a flowchart showing a procedure for determining an area in which positive bending occurs when a long-term load is applied. [Diagram 33] FIG. 33 is a graph showing the analysis results and regression equation for the maximum deflection of a three-span continuous composite beam. [Diagram 34] FIG. 34 is a graph showing the analysis results and regression equation for the maximum deflection of a two-span continuous composite beam. [Diagram 35] FIG. 35 is a side view showing an example of the structure of a conventional continuous composite beam. [Diagram 36] FIG. 36 is a side view showing a main portion of an example of the structure of a conventional continuous composite beam. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022] Hereinafter, with reference to the drawings, an embodiment of the structure of a continuous composite beam and a method for evaluating the maximum deflection of a continuous composite beam of the present invention will be described in detail. [Continuous composite beam structure] A side view of an example of the structure of the continuous composite beam of this embodiment is shown in Fig. 1. As shown in Fig. 1, the structure of the continuous composite beam CB of this embodiment is composed of two or more spans of composite beams in which a steel frame sub-beam 2 made of H-shaped steel and a concrete slab 4 are integrated in series.

[0023] In each span of the continuous composite beam CB, both ends of the steel beam 2 are rigidly connected to the steel girder 1 made of H-shaped steel. Specifically, at both ends of the steel beam 2, the web 21 of the steel beam 2 is bolted to a gusset plate provided on the steel girder 1 via a splice plate 25, and the upper flange 22 and the lower flange 23 of the steel beam 2 are welded to the steel girder 1. Then, by forming a continuous composite beam CB in which the beams made of such composite beams are continuous in series for two or more spans so as to straddle the steel girder 1, the rotational rigidity of both ends of the steel beam 2 is increased and the deflection of the continuous composite beam CB is suppressed.

[0024] As shown in Fig. 1, in the structure of the continuous composite beam CB of this embodiment, only in the region PB where positive bending occurs during long-term loading among the spans of the continuous composite beam CB, a shear connector 24 made of a headed stud is provided on the upper surface of the steel beam 2. The steel beam 2 and the concrete slab 4 are integrated through this shear connector 24. In other words, in the region NB where negative bending occurs during long-term loading among the spans of the continuous composite beam CB, no shear connector 24 is provided on the upper surface of the steel beam 2, and the steel beam 2 and the concrete slab 4 are not integrated.

[0025] The concrete slab 4 is constructed by laying a flat deck (not shown) on the steel beams 2, arranging reinforcing bars 42 on top of the flat deck at prescribed intervals, and pouring concrete 41. Alternatively, a composite slab may be constructed by laying a composite slab deck plate (not shown) on the steel beams 2, arranging reinforcing bars 42 on top of the flat deck, and pouring concrete 41.

[0026] Fig. 2 shows a schematic diagram of the bending moment distribution occurring in a three-span continuous composite beam CB3 subjected to a long-term load. As shown in Fig. 2, the region NB in ​​the continuous composite beam CB3 where negative bending occurs when a long-term load is applied is near the end of the sub-beam that is rigidly connected to the steel frame girder 1 so as to straddle the steel frame girder 1. As described above, in the structure of the continuous composite beam CB of this embodiment, no shear connector 24 is provided in the region NB in ​​each span of the continuous composite beam CB where negative bending occurs when a long-term load is applied (see Fig. 1). This configuration will be described below.

[0027] 3 and 4 show enlarged views of a composite beam with shear connectors 24 and a composite beam without shear connectors 24, respectively.

[0028] In the region NB where negative bending occurs under long-term load, if a shear connector 24 is provided as shown in Fig. 3, tensile stress is transmitted from the upper flange 22, which is on the outer side of the bending of the steel beam 2, to the concrete 41 of the concrete slab 4 via the shear connector 24. This tensile stress is then borne by the reinforcing bars 42 in the concrete slab 4. To achieve a safe design that can adequately bear this tensile stress, it would be necessary to increase the amount of reinforcing bars 42 in the concrete slab 4, which would be uneconomical.

[0029] In contrast, in the continuous composite beam CB of this embodiment, no shear connector 24 is provided in the region NB where negative bending occurs under long-term load, as shown in Fig. 4. Therefore, almost no tensile stress is transmitted from the upper flange 22, which is the outer side of the bending of the steel beam 2, to the concrete 41 of the concrete slab 4, and the upper flange 22 of the steel beam 2 bears the tensile stress. Therefore, there is no need to increase the amount of reinforcing bars 42 in the concrete slab 4.

[0030] In this way, in the structure of the continuous composite beam CB of this embodiment, in the region PB where positive bending occurs under long-term load, the steel frame sub-girders 2 and the concrete slab 4 are integrated to form a composite beam, thereby increasing the bending rigidity and strength of the beam and suppressing deflection of the beam. Also, in the region NB where negative bending occurs under long-term load among the spans of the continuous composite beam CB, the shear connectors 24 are not provided, so that the upper flange 22 on the outer side of the bending of the steel frame sub-girders 2 bears the tensile stress, and there is no need to increase the amount of reinforcing bars 42 in the concrete slab 4. This results in a structurally rational and economical structure.

[0031] For example, in the case of a three-span continuous composite beam CB3 as shown in Figure 2, when the ratio of the bending rigidity of the composite beam to the bending rigidity of the steel sub-beam 2 is 2.0, as shown in Table 1 described later, the area PB where positive bending occurs under long-term load in both end spans is approximately 83% of the span length L. Therefore, compared to providing shear connectors 24 over the entire length of the continuous composite beam, the amount of shear connectors 24 installed can be reduced by approximately 17%.

[0032] FIG. 5 shows a schematic diagram of the structure of the continuous composite beam CB of this embodiment. As described above, in the structure of the continuous composite beam CB of this embodiment, the shear connector 24 is provided only in the region PB where positive bending occurs during long-term load application among the spans of the continuous composite beam CB. Therefore, the region PB where positive bending occurs during long-term load application among the continuous composite beams CB is evaluated as a composite beam in which the steel beam 2 and the concrete slab 4 are integrated, and the region NB where negative bending occurs is evaluated as only the steel beam 2 portion functions as a structural member, and the continuous composite beam CB is designed. In other words, the continuous composite beam CB is designed to have different bending rigidities at the inflection point position F between the region PB where positive bending occurs during long-term load application and the region NB where negative bending occurs. <Area where positive bending occurs when a long-term load is applied> In the structure of the continuous composite beam CB of this embodiment, the shear connector 24 is provided only in the area PB where positive bending occurs under long-term load. This area PB where positive bending occurs under long-term load may be determined by performing detailed numerical analysis or convergence calculation, but can be determined accurately and simply by the following method, for example.

[0033] As described above, the structure of the continuous composite beam CB of this embodiment is such that the sub-beams made of composite beams are arranged in series in two or more spans so as to straddle the steel beam 1, and it is assumed that the beams are installed in locations that receive long-term concentrated loads from about two to five grandchild beams. Therefore, it is assumed that the lengths of the spans of the continuous composite beam CB of this embodiment are equal to each other, and that the beams are installed in locations that receive long-term concentrated loads P [N] of the same magnitude at equal intervals from n points (n is an integer between 2 and 5). In this case, it is preferable that the length L1 [mm] of the area where the shear connectors 24 are provided in each span of the continuous composite beam CB satisfies, for example, the following formula (1).

[0034] (β-0.05)L≦L1≦(β+0.05)L …(1) In the above formula (1), L [mm] is the length of each span of the continuous composite beam CB, and β is a value indicating the proportion of the area PB where positive bending occurs in each span of the continuous composite beam CB when a long-term load is applied, and is expressed by the following formula (2): β = A1 × log e α+A2…(2) It is calculated as follows.

[0035] In the above formula (2), α is the ratio of the bending rigidity of the composite beam to the bending rigidity of the steel beam 2, and is set to 1.0≦α≦3.5. Additionally, A1 and A2 are coefficients determined by the number of spans m (m is an integer of 2 or more) of the continuous composite beam CB. For example, when m=3, A1=0.1265, A2=0.5015, and when m=2, A1=0.0586, A2=0.7624.

[0036] As shown in the above formula (2), β in the above formula (1) is expressed by a simple explicit function, specifically, a linear function of the natural logarithm of the ratio α of the bending rigidity of the composite beam to the bending rigidity of the steel beam 2. The method of deriving the values ​​of the coefficients A1 and A2 in the above formula (2) will be described later.

[0037] Conventionally, detailed numerical analysis and convergence calculations were required to determine the proportion β of the area PB where positive bending occurs and the position of the inflection point, and these analyses and calculations required a great deal of effort. In contrast, in this embodiment, the proportion β of the area PB where positive bending occurs can be calculated accurately and easily using an explicit function in the form shown in the above formula (2). In other words, by using the above formulas (1) and (2), the area PB where positive bending occurs under long-term load, i.e., the area where the shear connector 24 should be provided in each span of the continuous composite beam CB, can be determined accurately and easily.

[0038] The method for deriving the coefficients A1 and A2 in the above equation (2) will be explained below using as an example a mechanical model in which a three-span continuous composite beam CB3, each span of which is equal in length, is subjected to a concentrated load P of the same magnitude at equal intervals from three points on each span, as shown in Figure 6(a).

[0039] In each span of a continuous composite beam CB, the area PB where positive bending occurs when a long-term load is applied can be determined by deriving the end bending moment M of the span end located within the area NB where negative bending occurs, and then using this end bending moment M to derive the inflection point position F within each span. <Derivation of end bending moment> In each span of a continuous composite beam CB, the end bending moment M of the span end located within the region NB where negative bending occurs under long-term load can be derived as follows.

[0040] First, as shown in Fig. 6(b) to Fig. 6(d), the three-span continuous composite beam CB3 is separated into three simple beams at intermediate supports B and C. Then, in each of the three separated simple beams, bending moments M are applied to supports B and C so that the same stress distribution state as before separation is maintained. B , M CConsider applying the following.

[0041] Here, as shown in Figures 7(a) and 7(b), the deflection angle θ at support B of the simple beam on the left side of support B is l is the deflection angle θ at support B of the simple beam to the right of support B r is equal to.

[0042] In addition, the deflection angle θ at the support point B of the simple beam on the right side of the support point B shown in Figure 8(a) r is the deflection angle θ caused by the simple beam being subjected to a concentrated load P from three points, as shown in Figure 8(b). e r As shown in Figure 8(c), this simple beam is subjected to bending moment M at supports B and C. B , M C The deflection angle θ caused by the action of m r The sum of θ e r +θ m r Although not shown in the figure, the deflection angle θ at the support point B of the simple beam on the left side of the support point B is l The deflection angle θ caused by a concentrated load P on this simple beam from three points is e l And this simple beam is subjected to bending moment M at support B. B The deflection angle θ caused by m l The sum of θ e l +θ m l In other words, the following equation (4) holds true.

[0043] θ e l +θ m l =θ e r +θ m r …(4) Next, as shown in Figure 9(a), in the simple beam on the left side of the support B, the proportion of the area in which positive bending occurs in the span length L [mm] is β1, that is, the length L of the area in which positive bending occurs. 11 L 11 = β1 × L. In this simple beam, the bending moment M acting on the support B is B The deflection angle θ at the fulcrum B is m l can be calculated by the unit load method (principle of virtual work) as shown in the following formula (5). In this example, the lengths of the spans of the continuous composite beam CB3 are equal to each other, and each span receives a concentrated load P of the same magnitude at equal intervals from three points. Therefore, due to symmetry, M B =M C In the following, M B and M. C is written as M.

[0044]

number

[0045] (When α=1, θ m l =ML / 3EI) Here, α is the ratio of the bending rigidity of the composite beam in which the steel beam 2 and the concrete slab 4 are integrated to the bending rigidity of only the steel beam 2. Also, E [N / mm 2 ] is the Young's modulus of the steel material that constitutes the steel beam 2, and I [mm 4 ] is the second moment of area of ​​steel beam 2.

[0046] In addition, as shown in Figure 9(b), the simple beam on the left side of the support B is subjected to a concentrated load P from three points, and the deflection angle θ e l is calculated by the unit load method using the following formula (6).

[0047]

number

[0048] (When α=1, θ e l =-(5 / 32)PL 2 / EI) In addition, as shown in Fig. 9(c), in the simple beam on the right side of the support B, the ratio of the area where positive bending occurs in the span length L [mm] is β2, that is, the length L of the area where positive bending occurs. 12 L 12 = β2 × L. In this simple beam, the bending moment M (M B , M C ) causes a deflection angle θ at the support B. m r is calculated by the unit load method using the following formula (7).

[0049]

number

[0050] (When α=1, θ m r =-ML / 2EI) In addition, as shown in Figure 9(d), the simple beam on the right side of the support B is subjected to a concentrated load P from three points, and the deflection angle θ e r can be calculated by the unit load method using the following formula (8).

[0051]

number

[0052] (When α=1, θ e r =(5 / 32)PL 2 / EI) By substituting the above formulas (5) to (8) into the above formula (4), the relational expression for the end bending moment M of the three-span continuous composite beam CB3 as shown in FIG. 10 is derived as the following formula (9).

[0053]

number

[0054] The relational expression for the end bending moment M of the two-span continuous composite beam CB2 as shown in FIG. 11 can also be derived by the same procedure as above, as shown in the following equation (10).

[0055]

number

[0056] Furthermore, even when the loading conditions differ for each span, when the span lengths differ, or when the number of supports (spans) increases, a relational equation can be derived for the end bending moment M of the span end located within the region NB where negative bending occurs under long-term load by using the same procedure as above. <Derivation of inflection point position> As shown in Figure 12(a), let R1 be the reaction force generated at supports A and D at both ends of the three-span continuous composite beam CB3, and let R2 be the reaction force generated at intermediate supports B and C. Then, as shown in Figures 12(b) and 12(c), consider cutting the three-span continuous composite beam CB3 at a position x [mm] away from support A at the left end, and applying a bending moment to the cut position so that the same stress distribution state as before the cut is maintained in the part to the left of the cut position.

[0057] As shown in Fig. 12(b), when the cutting position is to the left of fulcrum B, the balance of bending moment M1(x) at the cutting position is expressed by the following formula (11). Also, as shown in Fig. 12(c), when the cutting position is between fulcrum B and fulcrum C, the balance of bending moment M2(x) at the cutting position is expressed by the following formula (12).

[0058] M1(x)=(3P-R1)x-(3 / 2)PL…(11) M2(x)=(3P-R1-R2)x-(3 / 2)PL+R2…(12) Here, when x = L, M1(L) in the above equation (11) is equal to the end bending moment M in the above equation (9), so the following equation (13) can be derived from equations (9) and (11).

[0059] (3P-R1)L-(3 / 2)PL=PL×φ…(13) However, in the above formula (13),

[0060]

number

[0061] It is.

[0062] By rewriting the above equation (13), the reaction force R1 is expressed as the following equation (15).

[0063] R1 = (3 / 2) PP × φ … (15) Moreover, the sum of the reaction forces R1, R2 at the supports A to D is equal to the sum of the concentrated loads P acting from nine points, and this relationship is expressed by the following equation (16).

[0064] 2R1+2R2=9P …(16) Therefore, from the above equations (15) and (16), the reaction force R2 is expressed as shown in the following equation (17).

[0065] R2 = 3P + P × φ … (17) Substituting the reaction forces R1, R2 expressed by equations (15) and (17) into the above equations (11) and (12) and rearranging, we obtain the following equations (18) and (19).

[0066] M1(x)={(3 / 2)+φ}Px-(3 / 2)PL…(18) M2(x)=-(3 / 2)Px+{(3 / 2)+φ}PL …(19) As described above, β1 indicates the proportion of the area where positive bending occurs in the span length L [mm] in the span to the left of support B, and β2 indicates the proportion of the area where positive bending occurs in the central span between supports B and C. Therefore, the inflection point position where M1(x) or M2(x) becomes 0 is x = β1 × L, or x = L + (L - β2 × L) / 2 = (3 / 2)L - (L / 2) β2.

[0067] From this, for the inflection point position F, the simultaneous equations expressed as in the following equation (20) are derived.

[0068]

number

[0069] Considering that the range of bending stiffness ratio α actually used in architectural design is 1.0 to 3.5, values ​​of α from 1.0 to 3.5 in 0.1 intervals (1.0, 1.1, 1.2, ..., 3.4, 3.5) were substituted into the above equation (20) as the value of α, to create 26 simultaneous equations.

[0070] By solving these 26 simultaneous equations, the values ​​of β1 and β2 were calculated. In addition, using the same procedure as above, the ratio β of the area where positive bending occurs in each span of the two-span continuous composite beam CB2 under long-term load was also calculated. 1、 The values ​​of β2 and β are shown in Table 1. Table 1 also shows the value of β in the two-span continuous composite beam CB2, calculated using a similar method.

[0071] [Table 1]

[0072] Furthermore, Tables 2 to 7 show the results of calculating the percentage of the area where positive bending occurs in the span length L [mm] for the case where the number of spans m of the continuous composite beam CB is 4 to 10 as shown in Figures 15 to 21. Here, the percentage of the area where positive bending occurs was calculated based on a mechanical model in which continuous composite beams CB4 to CB10 with 4 to 10 spans, each of which has the same span length, are subjected to a concentrated load P of the same magnitude at equal intervals from three points on each span.

[0073] As shown in Fig. 15, when m=4, that is, in the case of a 4-span continuous composite beam CB4, β1 indicates the proportion of the area where positive bending occurs in the span length L [mm] in the span to the left of support B or the span to the right of support D. Also, β2 indicates the proportion of the area where positive bending occurs in the span length L [mm] in the span between support B and support C or the span between support C and support D.

[0074] As shown in Fig. 16, when m=5, that is, in the case of a 5-span continuous composite beam CB5, β1 indicates the proportion of the area in the span length L [mm] where positive bending occurs in the span to the left of support B or the span to the right of support E. β2 indicates the proportion of the area in the span length L [mm] where positive bending occurs in the span between support B and support C or the span between support D and support E. β3 indicates the proportion of the area in the span length L [mm] where positive bending occurs in the central span between support C and support D.

[0075] As shown in Fig. 17, when m=6, that is, in the case of a 6-span continuous composite beam CB6, β1 indicates the proportion of the area in the span length L [mm] where positive bending occurs in the span to the left of support B or the span to the right of support F. β2 indicates the proportion of the area in the span length L [mm] where positive bending occurs in the span between support B and support C or the span between support E and support F. β3 indicates the proportion of the area in the span length L [mm] where positive bending occurs in the span between support C and support D or the span between support D and support E.

[0076] As shown in FIG. 18, when m=7, that is, in the case of a 7-span continuous composite beam CB7, β1 indicates the proportion of the area in the span length L [mm] where positive bending occurs in the span to the left of support B or the span to the right of support G. β2 indicates the proportion of the area in the span length L [mm] where positive bending occurs in the span between support B and support C or the span between support F and support G. β3 indicates the proportion of the area in the span length L [mm] where positive bending occurs in the span between support C and support D or the span between support E and support F. β4 indicates the proportion of the area in the span length L [mm] where positive bending occurs in the central span between support D and support E.

[0077] As shown in FIG. 19, when m=8, that is, in the case of an 8-span continuous composite beam CB8, β1 indicates the ratio of the area in the span length L [mm] where positive bending occurs in the span to the left of support B or the span to the right of support H. β2 indicates the ratio of the area in the span length L [mm] where positive bending occurs in the span between support B and support C or the span between support G and support H. β3 indicates the ratio of the area in the span length L [mm] where positive bending occurs in the span between support C and support D or the span between support F and support G. β4 indicates the ratio of the area in the span length L [mm] where positive bending occurs in the span between support D and support E or the span between support E and support F.

[0078] As shown in FIG. 20, when m=9, that is, in the case of a 9-span continuous composite beam CB9, β1 indicates the ratio of the area in the span length L [mm] where positive bending occurs in the span to the left of support B or the span to the right of support I. β2 indicates the ratio of the area in the span length L [mm] where positive bending occurs in the span between support B and support C or the span between support H and support I. β3 indicates the ratio of the area in the span length L [mm] where positive bending occurs in the span between support C and support D or the span between support G and support H. β4 indicates the ratio of the area in the span length L [mm] where positive bending occurs in the span between support D and support E or the span between support F and support G. β5 indicates the ratio of the area in the span length L [mm] where positive bending occurs in the central span between support E and support F.

[0079] As shown in FIG. 21, when m=10, that is, in the case of a continuous composite beam CB10 with 10 spans, β1 indicates the ratio of the area in the span length L [mm] where positive bending occurs in the span to the left of fulcrum B or the span to the right of fulcrum J. β2 indicates the ratio of the area in the span length L [mm] where positive bending occurs in the span between fulcrum B and fulcrum C or the span between fulcrum I and fulcrum J. β3 indicates the ratio of the area in the span length L [mm] where positive bending occurs in the span between fulcrum C and fulcrum D or the span between fulcrum H and fulcrum I. β4 indicates the ratio of the area in the span length L [mm] where positive bending occurs in the span between fulcrum D and fulcrum E or the span between fulcrum G and fulcrum H. β5 indicates the ratio of the area in the span length L [mm] where positive bending occurs in the span between fulcrum E and fulcrum F or the span between fulcrum F and fulcrum G.

[0080] [Table 2]

[0081] [Table 3]

[0082] [Table 4]

[0083] [Table 5]

[0084] [Table 6]

[0085] [Table 7]

[0086] In addition, Figures 13(a), 13(b) and 14 show graphs with the values ​​of β1, β2 or β, the proportion of the area where positive bending occurs, on the vertical axis and the value of the bending rigidity ratio α on the horizontal axis, in which the values ​​of β1, β2 or β shown in Table 1 are plotted, respectively.

[0087] In Figures 22(a) and 22(b), the values ​​of β1 and β2 when m = 4 shown in Table 2 are plotted on a graph with the values ​​of the proportions of the area where positive bending occurs, β1 and β2, on the vertical axis and the value of the bending rigidity ratio α on the horizontal axis.

[0088] Figures 23(a) to 23(c) show the values ​​of β1 to β3 when m = 5 shown in Table 2, plotted on a graph with the values ​​of the proportions of the area where positive bending occurs, β1 to β3, on the vertical axis and the value of the bending rigidity ratio α on the horizontal axis.

[0089] Figures 24(a) to 24(c) show the values ​​of β1 to β3 when m = 6 shown in Table 3, plotted on a graph with the values ​​of the proportions of the area where positive bending occurs, β1 to β3, on the vertical axis and the value of the bending rigidity ratio α on the horizontal axis.

[0090] Figures 25(a) to 25(d) show the values ​​of β1 to β4 when m = 7 shown in Table 4, plotted on a graph with the values ​​of the proportions of the area where positive bending occurs, β1 to β4, on the vertical axis and the value of the bending rigidity ratio α on the horizontal axis.

[0091] Figures 26(a) to 26(d) show the values ​​of β1 to β4 when m = 8 shown in Table 5, plotted on a graph with the values ​​of the proportions of the area where positive bending occurs, β1 to β4, on the vertical axis and the value of the bending rigidity ratio α on the horizontal axis.

[0092] Figures 27(a) to 27(e) show the values ​​of β1 to β5 when m = 9 shown in Table 6, plotted on a graph with the values ​​of the proportions of the area where positive bending occurs, β1 to β5, on the vertical axis and the value of the bending rigidity ratio α on the horizontal axis.

[0093] Figures 28(a) to 28(e) show the values ​​of β1 to β5 when m = 10 shown in Table 7, plotted on a graph with the values ​​of the proportions of the area where positive bending occurs, β1 to β5, on the vertical axis and the value of the bending rigidity ratio α on the horizontal axis.

[0094] Figures 13(a), 13(b), 14, and 22(a) to 28(e) also show the regression equations obtained by performing regression analysis on the distribution of values ​​of β or β1 to β5, using a linear function of the common logarithm of the bending stiffness ratio α as the regression equation. The coefficients A1 and A2 in the above equation (2) can be derived by performing such regression analysis. As shown in Figures 13(a) and 13(b), A1 = 0.0434 and A2 = 0.7998 for both side spans when m = 3, and A1 = 0.1265 and A2 = 0.5015 for the center span when m = 3. Also, as shown in Figure 14, when m = 2, A1 = 0.0586 and A2 = 0.7624. As shown in Figures 22(a) and 22(b), the values ​​of (A1, A2) in each span when m = 4 are (0.0494, 0.7892) or (0.0998, 0.5567). As shown in Figures 23(a) to 23(c), the values ​​of (A1, A2) in each span when m = 5 are (0.0477, 0.7919), (0.1089, 0.5421), or (0.0800, 0.6031). As shown in Figures 24(a) to 24(c), the values ​​of (A1, A2) in each span when m = 6 are (0.0482, 0.7912), (0.1064, 0.5458), or (0.0875, 0.5905). As shown in Figures 25(a) to 25(d), the values ​​of (A1, A2) in each span when m = 7 are (0.0481, 0.7914), (0.1071, 0.5449), (0.0853, 0.5937), or (0.0953, 0.5774). As shown in Figures 26(a) to 26(d), the values ​​of (A1, A2) in each span when m = 8 are (0.0481, 0.7913), (0.1069, 0.5451), (0.0859, 0.5929), or (0.0930, 0.5807). Also, as shown in Figures 27(a) to 27(e), the values ​​of (A1, A2) in each span when m = 9 are (0.0481, 0.7914), (0.1070, 0.5451), (0.0857, 0.5931), (0.0936, 0.5798) or (0.0907, 0.5838).Also, as shown in Figures 28(a) to 28(e), the values ​​of (A1, A2) in each span when m = 10 are (0.0481, 0.7913), (0.1069, 0.5451), (0.0858, 0.5930), (0.0935, 0.5800) or (0.0914, 0.5830).

[0095] As shown in Figures 13(a) to 28(e), the coefficient of determination R 2 is a value close to 1. Therefore, it can be seen that the proportions β, β1 to β5 of the region PB where positive bending occurs under long-term load can be calculated accurately and easily by the regression equations shown in Figs. 13(a) to 28(e), that is, the explicit function in the form shown in the above equation (2).

[0096] Furthermore, the number m of spans of the continuous composite beam CB and the number n (n is an integer between 2 and 5) of points of application of the long-term concentrated load acting on each span of the continuous composite beam CB may be different from those described above. Even in such a case, if the bending stiffness ratio α is within the range of 1.0 to 3.5, the proportion β of the area PB where positive bending occurs can be calculated accurately and simply by the explicit function in the form shown in the above formula (2).

[0097] The pitch of the shear connectors 24 is usually set to a dimension such as 100 mm, 150 mm, or 200 mm. The length L of each span of the continuous composite beam CB is often set to a different dimension within a range of about 9000 mm to 12500 mm. When these dimensions change, the value of β calculated by the above formula (2) changes accordingly. Therefore, in the above formula (1), the value of the proportion β of the region PB where positive bending occurs under long-term load is given a ±5% range, and the length x [mm] of the region where the shear connectors are provided is limited to a range of (β-0.05)L or more and (β+0.05)L or less. [Evaluation method for maximum deflection of continuous composite beams] The method for evaluating the maximum deflection of a continuous composite beam according to this embodiment evaluates the maximum deflection of the continuous composite beam CB in the structure of the continuous composite beam CB described above.

[0098] Specifically, in the region NB where negative bending occurs under long-term load in the continuous composite beam CB of this embodiment, only the steel beam 2 portion is evaluated as functioning as a structural member. The moment of inertia I [mm 4 ] is used as is.

[0099] In addition, in the region PB of the continuous composite beam CB in this embodiment where positive bending occurs under long-term load, it is evaluated as a composite beam in which the steel beam 2 and the concrete slab 4 are integrated. The second moment of area of ​​the entire continuous composite beam CB in this region is calculated by using the ratio α of the bending rigidity of the composite beam to the bending rigidity of the steel beam 2, and is expressed as α×I [mm 4 ] is expressed as follows.

[0100] The second moment of area I [mm 4 ] and the second moment of area α×I [mm 4 ] and the equivalent secondary bending moment I of the entire span of the continuous composite beam CB eq [mm 4 ] is defined as shown in the following equation (21).

[0101] I eq =β×(α×I)+(1-β)×I …(21) FIG. 29 shows the equivalent secondary bending moment I eq The conceptual diagram of the equivalent secondary bending moment I eq is evaluated by increasing the value of the moment of inertia of the entire continuous composite beam from the moment of inertia I of the steel beam 2 by the amount that the bending stiffness of the area PB where positive bending occurs in the continuous composite beam is greater than the bending stiffness of the area NB where negative bending occurs. This equivalent moment of inertia I eq By using this, the maximum deflection of a continuous composite beam can be calculated assuming that the effective cross section of the continuous composite beam consists of only two steel sub-beams over its entire length.

[0102] In addition, if the number of spans of a continuous composite beam is 3 or more, the equivalent secondary bending moment I eq The values ​​of the two are calculated, and the average value obtained by adding them up and dividing them by the number of spans can be used as the equivalent secondary bending moment of the entire continuous composite beam.

[0103] In the method for evaluating the maximum deflection of a continuous composite beam according to this embodiment, the area moment of inertia I of the steel beam 2 and the equivalent bending moment I obtained by the above formula (21) are eq Ratio of I / I eq Using the above, the evaluation value δ of the maximum deflection of the continuous composite beam is calculated as shown in the following formula (22). eq Calculate [mm].

[0104] δ eq =B1×(I / I eq )×δ s +B2…(22) However, in the above formula (22), δ s [mm] is the maximum deflection of the continuous composite beam CB, calculated assuming that only the steel beam 2 portion functions as a structural member over the entire length of the continuous composite beam CB, that is, the maximum deflection of a continuous steel beam consisting of two or more spans of steel beams 2 in series. For example, in the case of a three-span continuous composite beam CB3, δ s The value of [mm] can be calculated using the following formula (23).

[0105] δ s =0.02643×P×L 3 / (E×I s ) …(twenty three) In the above formula (23), E is the Young's modulus [N / mm 2 ].

[0106] Furthermore, I / I in the above equation (22) eq can be rewritten as the following equation (24) from the above equation (21).

[0107] I / I eq=I / {β×(α×I)+(1-β)×I}=1 / {(α-1)×β+1} …(24) Substituting the above equation (24) into the above equation (22) and rearranging it, the evaluation value of the maximum deflection of the continuous composite beam δ eq [mm] is calculated using formula (3) below.

[0108] δ eq =B1×δ s / {(α-1)×β+1}-B2…(3) In the above formulas (3) and (22), B1 and B2 are coefficients determined by the number of spans m (m is an integer equal to or greater than 2) of the continuous composite beam CB. For example, when m=3, B1=1.0061, B2=0.1334, and when m=2, B1=1.1790, B2=0.3631.

[0109] Conventionally, in order to evaluate the maximum deflection of a continuous composite beam, it is necessary to perform numerical analysis and convergence calculation, and this analysis and calculation require a great deal of effort. In this regard, Patent Document 2 discloses a method for calculating the maximum deflection of a composite beam subjected to a uniformly distributed load without performing convergence calculation. However, as described above, the continuous composite beam CB of this embodiment is configured such that the sub-beams made of composite beams are continuously arranged in series for two or more spans so as to straddle the steel frame girder 1, and it is assumed that the continuous composite beam CB is installed in a location that receives a long-term concentrated load from about two to five grandchild beams. The method described in Patent Document 2 cannot be applied to evaluate the maximum deflection of a continuous composite beam that receives such a long-term concentrated load.

[0110] In contrast, in this embodiment, the evaluation value δ of the maximum deflection of the continuous composite beam eq [mm] can be calculated accurately and easily using an explicit function of the form shown in equation (3) above.

[0111] As in the above formula (2), β in the above formula (3) is expressed as a simple explicit function, specifically, as a linear function of the natural logarithm of the ratio α of the bending rigidity of the composite beam to the bending rigidity of the steel beam 2. The method of deriving the values ​​of the coefficients B1 and B2 in the above formula (3) will be described later. By using the above formulas (3) and (2), the evaluation value δ of the maximum deflection of the continuous composite beam in the structure of the continuous composite beam according to this embodiment can be calculated. eq [mm] can be determined accurately and easily.

[0112] Here, the maximum deflection of the continuous composite beam of this embodiment was obtained by numerical analysis using the two-span continuous composite beam CB2 as an example.

[0113] In this numerical analysis, as shown in Fig. 30(a), the analysis target was a two-span continuous composite beam CB2 that is configured in series for two spans across a steel girder 1 and is installed at a location that receives long-term concentrated loads from three grandchild beams 3. Then, as shown in Fig. 30(b), a mechanical model was set up in which the two-span continuous composite beam CB2, whose spans are equal in length, receives concentrated loads P of the same magnitude at equal intervals from three points on each span.

[0114] As shown in Table 8, five types of cross-sectional size of the steel beam 2 and seven types of span length L [mm] of the beam were set as analysis parameters. As shown in Table 8, the five types of cross-sectional size of the steel beam 2 have a moment of inertia of 1000 to 3000 × 10 6 mm 4 The values ​​were selected so as to be distributed almost evenly within the range.

[0115] The second moment of area of ​​the composite beam in which the steel beam 2 and the concrete slab 4 are integrated, and the ratio α of the bending rigidity of the composite beam to the bending rigidity of the steel beam 2 are as shown in Table 8.

[0116] [Table 8]

[0117] The standard strength of the steel material that constitutes the steel beam 2 is 325N / mm2 , Young's modulus is 205000N / mm 2 The design strength Fc of the concrete 41 constituting the concrete slab 4 is 24 N / mm 2 The reinforcing bars 42 in the concrete slab 4 were equivalent to SD295 as specified in the Japanese Industrial Standard JISG3112 (steel bars for reinforced concrete). Based on this, the material properties of each material were set. The cross-sectional rigidity of the composite beam formed by integrating the steel beam 2 and the concrete slab 4 was calculated according to the calculation method described in Non-Patent Document 1.

[0118] The thickness of the concrete slab 4 is 180 mm. Assuming the use of a flat deck with truss reinforcement, the reinforcing bars 42 in the concrete slab 4 are D13, arranged in a single stage at 200 mm intervals.

[0119] The headed studs constituting the shear connectors 24 are φ19 mm in size and are provided at 100 mm intervals along the length of the continuous composite beam CB2. Two rows of headed studs are provided in the beam width direction for steel beams 2 with a flange width of 250 mm or more, and one row of headed studs are provided in the beam width direction for steel beams 2 with a flange width w of 200 mm or less.

[0120] The fixed load on the two-span continuous composite beam CB2 is 4320N / m for the concrete 41 of the concrete slab 4. 2 , deck plate is 200N / m 2 , the ceiling and piping fixed to the concrete slab 4 are 200N / m 2 , other fixed load is 4800N / m 2 It was decided.

[0121] In addition, the load on concrete slab 4 is 12750N / m 2 It was decided.

[0122] From the above, the uniformly distributed load w [N / mm] applied to the two-span continuous composite beam CB2 was set to 50N / mm. In addition, the magnitude of the concentrated load P [N] acting on the two-span continuous composite beam CB2 from each of the three grandchild beams 3 in each span of the two-span continuous composite beam CB2 was set as shown in Table 9.

[0123] [Table 9]

[0124] As described above, the maximum deflection of the continuous composite beam CB2 was calculated for each of the 35 combinations of the five cross-sectional sizes of the steel beam 2 and the seven span lengths L [mm] of the beam using the structural analysis software “cadtool” manufactured by Andor Co., Ltd.

[0125] Then, as shown in Figure 31, for the above-mentioned mechanical model, a bending stiffness equivalent to that of a composite beam was input into region PB where positive bending occurs under long-term load, and a value equivalent to the bending stiffness of a steel sub-beam 2 was input into region NB where negative bending occurs under long-term load, with the inflection point position F according to the bending moment distribution as the boundary, to numerically analyze the maximum deflection of the continuous composite beam CB2.

[0126] Here, when the bending stiffness is different between the area PB where positive bending occurs and the area NB where negative bending occurs in the continuous composite beam CB2, the bending stiffness at each position of the continuous composite beam CB2 changes according to the change in the bending moment distribution. Therefore, in the continuous composite beam CB2, the proportion β of the area PB where positive bending occurs under long-term load was identified by the procedure shown in FIG.

[0127] First, in step S1 shown in FIG. 32, the bending moment distribution of the continuous composite beam CB2 is numerically analyzed assuming that the continuous composite beam CB2 has uniform cross-sectional rigidity over its entire length, and the proportion β of the area PB where positive bending occurs is recorded. Next, in step S2, the bending rigidity I of the steel frame sub-beam 2 is set to the length (1-β)×L of the area NB where negative bending occurs, and the second moment of area α×I of the composite beam is set to the length β×L of the area PB where positive bending occurs, and the bending moment distribution of the continuous composite beam is numerically analyzed. Furthermore, in step S3, it is determined whether or not the difference between the area where negative bending occurs in the bending moment distribution calculated in step S2 and the length (1-β)×L of the area NB where negative bending occurs calculated in step S1 is within a predetermined value. If the determination result in step S3 is No, the value of β is changed in step S4, and the process is continued by returning to step S2. If the determination result in step S3 is Yes, the value of β at this time is set as the proportion β of the area NB where negative bending occurs under long-term load action, thereby completing the identification of the area PB where positive bending occurs.

[0128] Figure 33 shows the maximum deflection of the continuous composite beam CB3 on the vertical axis, and the value {(α-1)×β+1} (=I / I eq ) on the horizontal axis, the maximum deflection values ​​of the three-span continuous composite beam CB3 obtained by the above numerical analysis are plotted. Figure 33 also shows the regression equation obtained by performing a regression analysis on the distribution of the plotted values ​​of the maximum deflection values ​​of the three-span continuous composite beam CB3 obtained by the above numerical analysis, using a linear function of the common logarithm of {(α-1)×β+1} as the regression equation.

[0129] In addition, Figure 34 plots the maximum deflection values ​​of the two-span continuous composite beam CB2 obtained by the above numerical analysis in a graph similar to that of Figure 33. Figure 34 also shows the regression equation obtained by performing a regression analysis on the distribution of plotted values ​​of the maximum deflection values ​​of the two-span continuous composite beam CB3 obtained by the above numerical analysis, using a linear function of the common logarithm of {(α-1)×β+1} as the regression equation.

[0130] The coefficients B1 and B2 in the above formula (3) can be derived by performing such a regression analysis. As shown in Figures 33 and 34, if the number of spans of the continuous composite beam CB is m (m is an integer of 2 or more), then when m=3, B1=1.0061, B2=0.1334, and when m=2, B1=1.1790, B2=0.3631.

[0131] As shown in Figures 33 and 34, the coefficient of determination R 2 is close to 1. Therefore, the evaluation value δ of the maximum deflection of the continuous composite beam under long-term load is eq It can be seen that it can be calculated with high accuracy by the regression equations shown in Figs. 33 and 34, that is, an explicit function in the form of the above equation (3).

[0132] In addition, the number m of spans of the continuous composite beam CB and the number n (n is an integer between 2 and 5) of points of application of the long-term concentrated load acting on each span of the continuous composite beam CB may be different from the above. Even in such a case, if the bending stiffness ratio α is within the range of 1.0 to 3.5, the evaluation value δ of the maximum deflection of the continuous composite beam when a long-term load acts on it can be calculated by the explicit function of the form shown in the above formula (3). eq can be calculated easily and accurately.

[0133] In the above embodiment, the length of each span of the continuous composite beam CB (CB3, CB2) is equal to each other, and each span is subjected to the same magnitude of long-term concentrated load at equal intervals from multiple points. However, the structure of the continuous composite beam and the evaluation method of the maximum deflection of the continuous composite beam according to the present invention are not limited to this, and the length of each span of the continuous composite beam may not be uniform, and the intervals of the application points of the long-term concentrated load acting from multiple points in each span and the magnitude of the long-term concentrated load may not be uniform. Specifically, the effect of the present invention can be obtained even when the variation in the length of each span of the continuous composite beam is within 20%, the variation in the magnitude of the long-term concentrated load acting from multiple points in each span is within 20%, and the variation in the intervals of the application points acting from multiple points in each span is within 25%. EXAMPLES

[0134] For a three-span continuous composite beam CB3, the following was conducted to investigate the extent to which the value of the end bending moment M of the three-span continuous composite beam CB3 calculated by the above formula (9) changes due to the influence of errors in the values ​​of the proportions β1 and β2 of the area PB where positive bending occurs under long-term load. This verified the extent to which the proportion β of the area PB where positive bending occurs calculated by the above formula (2) is affected by errors in the values ​​of the proportions β1 and β2 of the area PB where positive bending occurs under long-term load.

[0135] Specifically, the values ​​of the proportions β1 and β2 of the region PB where positive bending occurs under long-term load, calculated by the above formula (2), were changed in 21 ways at 1% intervals within the range of increase / decrease rate of -10% to +10%.

[0136] In addition, the change in the value of the bending moment M at the end of the three-span continuous composite beam CB3 was investigated for four ratios of the bending rigidity of the composite beam in which the steel beam 2 and the concrete slab 4 are integrated to the bending rigidity of the steel beam 2 alone: ​​1.5, 2.0, 3.0, and 3.5. The moment of inertia I of the steel beam 2 was 1000×10 6 mm 4 The moment of inertia of the composite beam is α×I [mm 4 ] was set.

[0137] The span length L of each span of the three-span continuous composite beam CB3 is 10,000 mm, and each span is subjected to a long-term concentrated load P of 250,000 N of the same magnitude at three equally spaced points.

[0138] When α = 1.5, the values ​​of β1 and β2 obtained from the above formula (2) are β1 = 0.8174 and β2 = 0.5526. Therefore, the length L of the region PB where positive bending occurs in the left span and center span of the three-span continuous composite beam CB3 under long-term load is 11 , L 12 are L 11 =β1×L=8174mm, L 12=β2×L=5526mm.

[0139] Corresponding to the increase / decrease rate of -10% to +10% for the proportions β1 and β2 of the area PB where positive bending occurs under long-term load, the value of β1 was changed in the range of 0.7174 to 0.9174 and the value of β2 in the range of 0.4526 to 0.6526 in 21 different ways, and the value of the end bending moment M was calculated for these combinations using the above formula (9).

[0140] Similarly, when α = 2.0, α = 3.0, and α = 3.5, the values ​​of β1 and β2 were changed in 21 ways, and the values ​​of the end bending moment M were calculated for these combinations using the above equation (9).

[0141] Tables 10 to 13 show the effect of errors in the values ​​of β1 and β2, the proportions of the area PB where positive bending occurs under long-term load, on the end bending moment M[×10 6 The change in the value of [N·mm] is shown when the bending stiffness ratio α is 1.5, 2.0, 3.0, and 3.5. In Tables 10 to 13, those where the change in the calculated end bending moment M is 2% or more compared to the case where the rate of increase / decrease of the proportions β1 and β2 of the area PB where positive bending occurs under long-term load is 0 are underlined.

[0142] [Table 10]

[0143] [Table 11]

[0144] [Table 12]

[0145] [Table 13]

[0146] As shown in Tables 10 to 13, regardless of whether the bending rigidity ratio α is 1.5, 2.0, 3.0, or 3.5, when the rate of change in the values ​​of β1 and β2 is in the range of -5% to +5%, the change in the calculated value of the end bending moment M is less than 2% compared to when the rate of change in the values ​​of β1 and β2 is 0.

[0147] From the above investigation, it was confirmed that it is appropriate to set a ±5% range for the proportion β of the area PB where positive bending occurs under long-term load and to limit the range of the length x [mm] of the area where the shear connector is provided as shown in the above formula (1). EXAMPLES

[0148] The following numerical analysis was conducted to investigate the extent to which the maximum deflection of a three-span continuous composite beam CB3 changes due to changes in the ratios β1 and β2 of the area PB where positive bending occurs under long-term load. As a result, the evaluation value δ of the maximum deflection of the continuous composite beam calculated by the above formula (3) changes due to the error in the values ​​of the ratios β1 and β2 of the area PB where positive bending occurs under long-term load. eq We examined the extent to which the value of

[0149] Specifically, the values ​​of the proportions β1 and β2 of the region PB where positive bending occurs under long-term load, calculated by the above formula (2), were changed to three different increase / decrease rates of -1.0507%, 0, and +1.0507%, respectively.

[0150] In addition, the maximum deflection of the three-span continuous composite beam CB3 was analyzed for four ratios of the bending rigidity of the composite beam, which is the combination of the steel beam 2 and the concrete slab 4, to the bending rigidity of the steel beam 2 alone: ​​1.5, 2.0, 3.0, and 3.5. The moment of inertia I of the steel beam 2 is 1000×10 6 mm 4 The moment of inertia of the composite beam is α×I [mm 4 ] was set.

[0151] The span length L of each span of the three-span continuous composite beam CB3 is 10,000 mm, and each span is subjected to a long-term concentrated load P of 250,000 N at equal intervals from three points. The Young's modulus E of the steel material that constitutes the steel beam 2 is 205,000 N / mm 2 It was decided.

[0152] When α = 1.5, the values ​​of β1 and β2 obtained from the above formula (2) are β1 = 0.8174 and β2 = 0.5526. Therefore, the length L of the region PB where positive bending occurs in the left span and center span of the three-span continuous composite beam CB3 under long-term load is 11 , L 12 are L 11 =β1×L=8174mm, L 12 =β2×L=5526mm. However, in this numerical analysis, the second moment of area of ​​the composite beam, α×I, is calculated by dividing the above L by 11 , L 12 Since it is difficult to set the length of L exactly, we set it to a value close to this. 11 =8164mm, L 12 =5546mm was entered.

[0153] As mentioned above, the values ​​of β1 and β2, the proportions of the area PB where positive bending occurs under long-term load, were changed to three values ​​of increase / decrease rate -1.0507%, 0, and +1.0507%. In other words, the values ​​of β1×L were set to three values ​​of 7657mm, 8164mm, and 8671mm, and the values ​​of β2×L were set to three values ​​of 5039mm, 5546mm, and 6053mm, and the maximum deflection [mm] of the continuous composite beam CB2 was obtained by numerical analysis for nine combinations of these.

[0154] Similarly, when α = 2.0, α = 3.0, and α = 3.5, the values ​​of β1 and β2 were changed to three different values, and the maximum deflection [mm] of the continuous composite beam CB2 was obtained by numerical analysis for nine combinations of these values.

[0155] When α=2.0, from the above formula (2), the length L of the region PB where positive bending occurs under long-term load is 11 , L12 L 11 =β1×L=8299mm, L 12 =β2×L=5893mm. However, as mentioned above, in this numerical analysis, the second moment of area α×I of the composite beam is calculated by dividing the above L by 11 , L 12 Since it is difficult to set the length of L exactly, we set it to a value close to this. 11 =8281mm, L 12 =5938mm was entered.

[0156] Similarly, when α = 3.0, from the above formula (2), the length L of the region PB where positive bending occurs under long-term load is 11 , L 12 L 11 =β1×L=8475mm, L 12 =β2×L=6411mm, but as a value close to this, L 11 =8437mm, L 12 =6406mm was entered.

[0157] In addition, when α = 3.5, from the above formula (2), the length L of the region PB where positive bending occurs under long-term load is 11 , L 12 L 11 =β1×L=8542mm, L 12 =β2×L=6608mm, but as a value close to this, L 11 =8555mm, L 12 =6562mm was entered.

[0158] Under the above conditions, a numerical analysis was performed using the structural analysis software “cadtool” made by Andor Corporation, and the maximum deflection of the three-span continuous composite beam CB3 was calculated.

[0159] Tables 14 to 17 show the maximum deflection [mm] of the continuous composite beam CB2 due to the influence of errors in the values ​​of β1 and β2, the proportions of the area PB where positive bending occurs under long-term load, when the bending stiffness ratio α is 1.5, 2.0, 3.0, and 3.5. Tables 14 to 17 also show the rate of change in the maximum deflection of the continuous composite beam CB2, based on the case where the rate of increase or decrease in the values ​​of β1 and β2 is 0.

[0160] [Table 14]

[0161] [Table 15]

[0162] [Table 16]

[0163] [Table 17]

[0164] As shown in Tables 14 to 17, the rate of change in the maximum deflection of the continuous composite beam CB2, based on the case where the rate of increase or decrease in the values ​​of β1 and β2 is 0, is at most 0.8% (when the bending rigidity ratio α is 3.0).

[0165] From the above considerations, even if the value of β calculated by the above formula (2) contains an error of about ±1%, the evaluation value of the maximum deflection of the continuous composite beam δ calculated by the above formula (3) is eq The effect on the maximum deflection of the continuous composite beam is very small. eq It was confirmed that it can be calculated with high accuracy. EXAMPLES

[0166] The evaluation value δ of the maximum deflection of the continuous composite beam CB calculated by the above formula (3) eqBy comparing the maximum deflection of the continuous composite beam CB obtained by numerical analysis, the evaluation value of the maximum deflection of the continuous composite beam δ obtained by the above formula (3) is eq The accuracy of [mm] was verified.

[0167] The conditions for the numerical analysis in this third embodiment were the same as those in the first embodiment.

[0168] Table 18 shows the evaluation value of maximum deflection of 3-span continuous composite beams compared with the analytical value of maximum deflection. Table 19 shows the evaluation value of maximum deflection of 7-span continuous composite beams compared with the analytical value of maximum deflection.

[0169] [Table 18]

[0170] [Table 19]

[0171] As shown in Table 18, in the case of a three-span continuous composite beam, the evaluation value δ of the maximum deflection of the continuous composite beam CB calculated by the above formula (3) is eq The error in the maximum deflection value of the continuous composite beam CB calculated by numerical analysis is less than 1.00% (0.13 mm in absolute difference). In addition, as shown in Table 19, in the case of a 7-span continuous composite beam, the evaluation value δ of the maximum deflection of the continuous composite beam CB calculated by the above formula (3) is eq The error in the maximum deflection value of the continuous composite beam CB obtained by numerical analysis is less than 2.07% (absolute difference less than 0.59 mm). Therefore, the evaluation value δ of the maximum deflection of the continuous composite beam is calculated by the above formula (3). eq It was confirmed that the distance [mm] could be calculated with high accuracy. [Explanation of symbols]

[0172] 1 girder 2, 8 Steel beam CB, CB2~CB10, CBP Continuous composite beam 21 Web 22, 82 Top flange 23 Lower flange 24, 84 Headed stud (shear connector) 25 Splice Plate 3 Sun Liang 4, 9 Concrete slab 41, 91 Concrete 42, 92 Reinforced concrete PB Region where positive bending occurs when a long-term load is applied NB Region where negative bending occurs when a long-term load is applied F Inflection point position L is the span length of each span of the continuous composite beam L1, L 11 , L 12 Length of the area where the shear connector is provided α Stiffness ratio β Percentage of area where positive bending moment occurs I Moment of inertia of steel beam I eq Equivalent moment of area

Claims

1. A continuous composite beam structure in which a sub-beam consisting of a composite beam having a steel sub-beam whose both ends are rigidly connected to a main beam and a concrete slab integrated with the steel sub-beam via a shear connector provided on the upper surface of the steel sub-beam is continuously arranged in series for two or more spans, A continuous composite beam structure, in which the shear connectors are provided only in areas of each span of the continuous composite beam where positive bending occurs under long-term load.

2. The continuous composite beam is installed at a location in each span where it is subjected to long-term concentrated loads from n points (n is an integer of 2 to 5), In each span of the continuous composite beam, the length L of the area in which the shear connector is provided １ The structure of the continuous composite beam according to claim 1, wherein [mm] satisfies the following formula (1): (β-0.05) L≦L １ ≦(β+0.05)L …(1) however, L [mm] is the length of each span of the continuous composite beam, β is expressed by the following formula (2): β=A １ ×log ｅ a+A ２ …(2) In the above formula (2), α is the ratio of the bending rigidity of the composite beam to the bending rigidity of the steel beam, and 1.0≦α≦3.5; A １ and A ２ is a coefficient determined by the number m of spans (m is an integer of 2 or more).

3. A method for evaluating the maximum deflection of a continuous composite beam in the structure of the continuous composite beam according to claim 2, The evaluation value δ of the maximum deflection of the continuous composite beam is calculated by the following formula (3): ｅｑ A method for evaluating the maximum deflection of a continuous composite beam by calculating the maximum deflection in mm. d ｅｑ =B １ ×d ｓ / {(α-1)×β+1}-B ２ …(3) However, in the above formula (3), δ ｓ [mm] is the maximum deflection value of the continuous composite beam calculated by evaluating that only the steel beam portion functions as a structural member over the entire length of the continuous composite beam, B １ and B ２ is a coefficient determined by the number m of spans (m is an integer of 2 or more).

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