JP7322078B2 - Structure design method - Google Patents

Description

One embodiment of the present invention relates to a structure and its design method.

In recent years, in structures such as office buildings, hospitals, and commercial facilities that require a large interior space, steel frames are used as beams that connect a pair of columns, and both ends of the steel frames are covered with reinforced concrete. Beams (mixed structural beams or hybrid beams) are employed. By using hybrid beams, it is possible to greatly reduce the number of columns compared to constructing all beams with reinforced concrete. As a result, structures with large spaces can be designed and constructed (patent Reference 1).

JP 2013-170386 A

An object of one embodiment of the present invention is to provide a structure with a hybrid beam that can be constructed at a lower cost. Alternatively, an object of one of the embodiments of the present invention is to provide a method for designing a structure with hybrid beams.

One embodiment of the invention is a method of designing a structure including a hybrid beam. A hybrid beam comprises a steel frame and reinforced concrete covering the ends of the steel frame. Reinforced concrete includes multiple beam main bars, multiple transverse reinforcing bars, multiple insert bars, beam concrete, and slab concrete. The plurality of beam main bars extend in the extension direction of the steel frame. The plurality of transverse reinforcing bars intersects the steel frame and the plurality of beam main bars and surrounds the steel frame and the plurality of beam bars. The plurality of insert bars intersects the steel frame and the plurality of beam bars and surrounds a portion of the steel frame and the plurality of beam bars. The beam concrete embeds a portion of the steel frame, a portion of the plurality of beam main bars, a portion of the plurality of transverse reinforcing bars, and a portion of the plurality of insert bars. The slab concrete sits on top of and contacts the beam concrete, another part of the steel frame, another part of the beam main bars, the other part of the transverse reinforcing bars, and the insert bars. embed another part of The plurality of horizontal reinforcing bars are a plurality of beam end side concentrated horizontal reinforcing bars arranged at a first density on the beam end side, and a plurality of beam center side concentrated horizontal reinforcing bars arranged at a second density on the beam center side. Reinforcing bars, and a plurality of intermediate lateral reinforcements arranged at a density lower than the first density and the second density between the plurality of beam end side concentrated lateral reinforcing bars and the plurality of beam center side concentrated lateral reinforcing bars. Consists of muscle. This design method does not consider the contribution of the beam end-side concentrated horizontal reinforcing bars, but the contributions of multiple beam center-side concentrated horizontal reinforcing bars, multiple intermediate horizontal reinforcing bars, and multiple insertion bars, as well as the beam concrete and the above-mentioned It includes calculating the ultimate strength of the joint surface considering the vertical stress component applied to the joint surface between slab concrete.

（１）
式（１）において、μ_ｅｑは接合面の等価摩擦係数であり、_ｓａ_ｗは複数の中間横補強筋の断面積の総和であり、_ｓσ_ｗｙは複数の横補強筋の降伏強度または基準強度（Ｆ値）であり、_ｓｗａ_ｗは複数の差し筋の断面積の総和であり、_ｓｗσ_ｗｙは複数の差し筋の降伏強度または基準強度（Ｆ値）であり、_Ａａ_ｗは複数の梁中央側集中横補強筋の断面積の総和であり、_Ａσ_ｗｙは複数の梁中央側集中横補強筋の降伏強度または基準強度（Ｆ値）であり、σ_０は鉄筋コンクリートに生じる平均外部鉛直応力であり、ｂ´はフランジの位置における鉄筋コンクリートの有効幅であり、ｌ_ｃは鉄骨が延伸する方向における鉄筋コンクリートの長さである。 One embodiment of the invention is a method for designing a structure including hybrid beams. A hybrid beam comprises a steel frame having a web and a pair of flanges connected to the web, and reinforced concrete covering both ends of the steel frame. Reinforced concrete includes beam main bars, multiple transverse reinforcing bars, multiple insert bars, beam concrete, and slab concrete. The beam main reinforcement extends in the extension direction of the steel frame. The plurality of lateral reinforcing bars intersects the steel frame and the plurality of beam main bars and surrounds the steel frame and the plurality of beam main bars. The plurality of insert bars intersects the steel frame and the plurality of beam bars and surrounds a portion of the steel frame and the plurality of beam bars. The beam concrete embeds a portion of the steel frame, a portion of the plurality of beam main bars, a portion of the plurality of transverse reinforcing bars, and a portion of the plurality of insert bars. The slab concrete sits on top of and contacts the beam concrete, another part of the steel frame, another part of the beam main bars, the other part of the transverse reinforcing bars, and the insert bars. embed another part of The plurality of horizontal reinforcing bars are a plurality of beam end side concentrated horizontal reinforcing bars arranged at a first density on the beam end side, and a plurality of beam center side concentrated horizontal reinforcing bars arranged at a second density on the beam center side. From the reinforcing bars and a plurality of intermediate transverse reinforcing bars arranged at a density lower than the first density and the second density between the plurality of beam end side concentrated transverse reinforcing bars and the beam center side concentrated transverse reinforcing bars Configured. This design method includes calculating the ultimate strength q _fr of the joint surface between beam concrete and slab concrete according to the following equation (1).

(1)
In equation (1), μ _eq is the equivalent friction coefficient of the joint surface, _s a _w is the sum of the cross-sectional areas of multiple intermediate lateral reinforcing bars, and _s σ _wy is the yield strength or standard of multiple lateral reinforcing bars. is the strength (F-value), _sw a _w is the sum of the cross-sectional areas of the multiple insert bars, _sw σ _wy is the yield strength or reference strength (F-value) of the multiple insert bars, and _A a _w is the multiple _wy is the yield strength or reference strength (F-value) of multiple concentrated transverse reinforcements on the beam center side, and _σ0 is _the average external stress generated in reinforced concrete. is the vertical stress, b' is the effective width of the reinforced concrete at the location of the flange, and _lc is the length of the reinforced concrete in the direction in which the steel frame extends.

Embodiments of the present invention facilitate the calculation of the ultimate strength of a hybrid beam, thereby allowing more precise design of structures including hybrid beams.

1 is a schematic perspective view of a structure that is one embodiment of the present invention; FIG. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic side view showing the appearance and internal structure of a hybrid beam of a structure that is one embodiment of the present invention; 1 is a schematic side view of a hybrid beam of a structure that is one embodiment of the present invention; FIG. 1 is a schematic cross-sectional view of a hybrid beam of a structure that is one embodiment of the present invention; FIG. 1 is a schematic cross-sectional view of a hybrid beam of a structure that is one embodiment of the present invention; FIG. Schematic side view of a specimen used in Examples. Plot of lateral reinforcement strain versus beam tip deflection angle of the specimen. Plot of sliding displacement at the joint position versus beam tip deformation angle of the specimen. Friction coefficient between steel frame and slab concrete in each specimen.

Hereinafter, each embodiment of the present invention will be described with reference to the drawings and the like. However, the present invention can be implemented in various aspects without departing from the gist thereof, and should not be construed as being limited to the description of the embodiments illustrated below.

In order to clarify the description, the drawings may schematically represent the width, thickness, shape, etc. of each part compared to the actual embodiment, but this is only an example and does not limit the interpretation of the present invention. not something to do. In this specification and each drawing, elements having the same functions as those described with respect to the previous drawings may be denoted by the same reference numerals, and redundant description may be omitted. When notating a part of a numbered element, the number is accompanied by a lowercase letter. When a plurality of elements having the same or similar structure are separately described, a hyphen and a natural number are added after the symbol. When collectively denoting a plurality of elements having the same or similar structure, only symbols are used.

Hereinafter, the expression "a certain structure is exposed from another structure" means a mode in which a part of a certain structure is not covered by another structure. A part also includes the aspect covered with another structure.

Hereinafter, concrete refers to a material that does not exhibit fluidity due to the hardening of hydrates formed by the reaction of cement, one of the raw materials, with water. It is distinguished from the fluid state (ready-mixed concrete, fresh concrete).

<First embodiment>
The structure of the structural body 100, which is one of the embodiments of the present invention, will be described below. In the drawings shown below, for the sake of convenience, the xy plane is the plane parallel to the horizontal ground surface, and the z direction is the vertical direction perpendicular to the xy plane.

1. Overall Structure A schematic perspective view of a structure 100 is shown in FIG. As shown in FIG. 1, a structure 100 includes a plurality of columns 110 extending in the vertical direction (z direction), a plurality of beams 120 connected to a pair of columns 110 and extending in the horizontal direction (x direction or y direction), and a floor slab 150 provided on the beam 120 as a basic configuration. Each beam 120 is connected with a pair of adjacent columns 110 .

At least one of the beams 120 provided in the structure 100 is a hybrid beam. All of the beams 120 provided in the structure 100 may be hybrid beams, or part of the beams 120 may be hybrid beams, and the other beams 120 may be entirely made of reinforced concrete (reinforced concrete beams, hereinafter referred to as RC beams). note) may be used. For example, in the structure 100 shown in FIG. 1, the first beam 120-1 and the third beam 120-3 are hybrid beams, and the second beam 120-2 and the fourth beam 120-4 are RC beams. is. Here, a pair of pillars 110 (for example, a pair of first pillar 110-1 and second pillar 110-2, a third pillar 110-3 and a fourth pillar 110-4) provided at a long interval (span) A hybrid beam is used as the beam 120 connected to the pair of the fifth column 110-5 and the pair of the sixth column 110-6), and the pair of columns 110 (for example, the first column 110 -1 and the third pillar 110-3, the second pillar 110-2 and the fourth pillar 110-4, the third pillar 110-3 and the fifth pillar 110-5, the third RC beams are used for the pair of the 4th column 110-4 and the 6th column 110-6). Although the arrangement of the hybrid beam and the RC beam can be determined arbitrarily, it is preferable to use the hybrid beam between a pair of pillars 110 provided at a long interval, as in the example shown in FIG. This is because hybrid beams are lighter than RC beams, so the use of hybrid beams for beams with a large span (here, first beam 120-1, third beam 120-3, etc.) results in a large indoor space. This is because sufficient strength can be imparted to the structure 100 while ensuring the

2. Columns Schematic side views of a pair of columns 110 (a first column 110-1 and a second column 110-2) and a beam 120 connected thereto are shown in FIGS. 2(A) and 2(B). In FIG. 2B, the concrete of the pillars 110 and the beams 120 is indicated by dotted lines to show the internal structure. Also, the floor slab 150 is not shown in FIGS. 2A and 2B.

The number of pillars 110 is not particularly limited as long as it is four or more, and the number and arrangement thereof may be appropriately determined according to the size and shape of the structure 100 . The pillars 110 are connected to piles and foundation beams (not shown). The shape of the pillar 110 (cross-sectional shape in the xy plane) is also arbitrary, and may be appropriately selected from rectangular, circular, elliptical, and the like. The length of the pillar 110 is also appropriately designed according to the size of the structure 100 and the height of each story.

Each column 110 is provided with a reinforcing bar unit including at least one column main bar 112 extending in the vertical direction and a plurality of tie bars 114 intersecting the column main bar 112 and surrounding the column main bar 112. Concrete 116 is poured so as to surround the unit (FIG. 2(B)). The number of column main reinforcements 112 and the arrangement density of the ties 114 are also appropriately determined according to the length and thickness of the column 110 and the required strength.

3. Floor Slab The floor slab 150 is reinforced concrete that forms the floor surface of each layer and is provided on the beams 120 (FIG. 1). A floor slab 150 is provided on each floor. Note that only a portion of the floor slab 150 is shown in FIG. 1 for ease of viewing. Although not shown, the floor slab 150 has a wooden board or a metal deck plate that forms the floor surface, and a plurality of reinforcing bars or reinforcing bar units called reinforcing bar trusses that are arranged in a mesh pattern on the board or deck plate. , is formed by placing concrete (slab concrete 128b, which will be described later) so as to embed this reinforcing bar unit.

4. Hybrid Beam As shown in FIGS. 2A and 2B, a beam 120 that is a hybrid beam has a steel frame 122 connected to a pair of columns 110 and reinforced concrete placed at both ends of the steel frame 122 . A portion where the reinforced concrete is arranged is called an RC section 120a. On the other hand, since reinforced concrete is not provided between the two RC sections 120a, this section is also called a steel frame section 120b. As will be described below, the reinforced concrete includes various rebars and concrete 128 covering both ends of the steel frame 122 and the rebars. The reinforced concrete placed at both ends of the steel frame 122 is separated from each other, and the steel frame 122 is exposed between them, that is, in the steel frame section 120b.

The steel frame 122 contains iron, and its cross-sectional shape may be H-shaped, I-shaped, T-shaped, L-shaped, or the like. Typically, H-steel with an H-shaped cross section can be used. When using H steel, the steel frame 122 is arranged so that the upper surfaces of the two flanges extend horizontally. The steel frame 122 is provided so as not to enter the reinforcing bar unit of the column 110 constructed by the column main reinforcing bars 112 and the tie bars 114 .

A schematic side view of one RC section 120a is shown in FIG. As shown in FIGS. 2(B) and 3, reinforcing bars such as a plurality of beam main bars 126 and a plurality of horizontal reinforcing bars 124 are arranged in each RC section 120a. A fixing plate 126a having a larger cross-sectional area than the beam main reinforcement 126 may be formed on the beam center side of each beam main reinforcement 126 (FIG. 2(B)). A plurality of inserts 125 may be further arranged in the RC section 120a. The plurality of insert bars 125 may be provided so as to be in contact with the plurality of lateral reinforcing bars 124 . These rebars firmly fix the beam main bars 126 to the rebar units of the column 110 . Steel frame 122 may contact column 110 . More specifically, each end of the steel frame 122 may contact the ties 114 of the pair of columns 110 or may contact or be embedded in the concrete 116 .

The beam main reinforcement 126 extends in a direction (horizontal direction) parallel to the longitudinal direction of the steel frame 122 and partially inserted into the reinforcement unit of the column 110 . The beam main bars 126 are arranged above and below the steel frame 122 . The beam main reinforcement 126 may be separated from the steel frame 122 or may be in contact therewith.

The lateral reinforcing bars 124 intersect the steel frames 122 and the beam main bars 126 . As shown in the cross-sectional schematic diagram (FIG. 4(B)) along chain line AA' in FIG. The lateral reinforcing bars 124 may be arranged so as to surround all the beam main bars 126 . Here, as shown in FIG. 3, the horizontal reinforcing bars 124 are arranged at a high density on the pillar 110 side (that is, the end portion side of the beam 120) and the central portion side of the beam 120. FIG. Hereinafter, the lateral reinforcing bars 124 arranged at high density on the pillar 110 side and the central part side of the beam 120 are referred to as beam end side concentrated lateral reinforcing bars 124a and beam center side concentrated lateral reinforcing bars 124b, respectively. On the other hand, between the beam end side concentrated horizontal reinforcing bar 124a and the beam center side concentrated horizontal reinforcing bar 124b, the horizontal reinforcing bar 124 is separated from the beam end side concentrated horizontal reinforcing bar 124a and the beam center side concentrated horizontal reinforcing bar 124b. Placed at a density lower than the placement density. The lateral reinforcing bars 124 arranged at a low density are hereinafter referred to as intermediate lateral reinforcing bars 124c. The lateral reinforcing bar 124 farthest from the column 110 among the beam end side concentrated lateral reinforcing bars 124a, the lateral reinforcing bar 124 closest to the column 110 among the beam center side concentrated lateral reinforcing bars 124b, and a plurality of intermediate lateral reinforcing bars 124c. may be arranged at a constant pitch S. Due to the difference in arrangement density of the horizontal reinforcing bars 124, compared with the interval between two adjacent beam end side concentrated horizontal reinforcing bars 124a and the gap between two adjacent beam center side concentrated horizontal reinforcing bars 124b, The interval between the intermediate lateral reinforcing bars 124c is small. The interval between two adjacent beam end side concentrated horizontal reinforcing bars 124a and the interval between two adjacent beam center side concentrated horizontal reinforcing bars 124b may be the same or different. The beam end side concentrated horizontal reinforcing bars 124a, the beam center side concentrated horizontal reinforcing bars 124b, and the intermediate horizontal reinforcing bars 124c may have any number and may be different or the same.

As shown in FIG. 3 and a schematic cross-sectional view (FIG. 4(B)) along the dashed line BB' in FIG. 122 intersects two or more beam main bars 126, surrounds the steel frame 122 and part of the beam main bars 126, and is arranged so that the U-shaped opening faces downward. Each insert 125 can be sandwiched between, for example, two adjacent lateral reinforcing bars 124 and arranged so as to be in contact with one of the lateral reinforcing bars 124 . The number, arrangement density, and length of the streaks 125 may also be determined arbitrarily.

In each RC section 120a, the ends of the steel frame 122, the beam main reinforcement 126, the lateral reinforcing reinforcement 124, and the insert reinforcement 125 are embedded in the concrete 128 (Fig. 3). Here, as shown in FIGS. 4(A) and 4(B), part of the concrete 128 includes the ends of the steel frame 122, part of the beam main reinforcement 126, part of the lateral reinforcement 124, and insert reinforcement. 125 is embedded. This concrete is hereinafter referred to as beam concrete 128a. At least a portion of the upper flange of steel frame 122 is exposed from beam concrete 128a. Another part of the concrete 128 is concrete that is placed on the beam concrete 128a, and this concrete is hereinafter referred to as slab concrete 128b. The slab concrete 128b is in contact with the upper surface of the beam concrete 128a and at least part of the flange on the upper side of the steel frame 122, and is in contact with the other part of the main beam reinforcement 126, the other part of the lateral reinforcement 124, and the rest of the insert reinforcement 125. embed part of The slab concrete 128b is concrete that constitutes the floor slab 150 and is integrated with the floor slab 150 .

Therefore, in addition to at least a portion of the upper flange of the steel frame 122, a portion of the beam main reinforcement 126, a portion of the lateral reinforcement 124, and a portion of the insert 125 are exposed from the beam concrete 128a. The portions exposed from the beam concrete 128a of these reinforcing bars are embedded in the slab concrete 128b. The beam concrete 128a may be provided so that its upper surface is flush with the upper surface of the upper flange of the steel frame 122, as shown in FIG. 4(A), or as shown in FIG. , may be provided so as to cover a portion of the upper surface of the flange and expose the other portion. That is, the beam concrete 128 a may be provided so that the upper surface is higher than the upper surface of the steel frame 122 . Alternatively, as shown in FIG. 5(B), the beam concrete 128a may be provided so that the upper surface is positioned lower than the upper surface of the flange and a part of the web connecting the pair of flanges is exposed from the beam concrete 128a. .

Although not shown, the upper surface of the beam concrete 128a may have irregularities formed by a brushing process or the like. The depth of the unevenness (that is, the height of the protrusion) may be 2 mm or more and 10 mm or less, or 3 mm or more and 7 mm or less. By forming the unevenness on the upper surface of the beam concrete 128a, it is possible to increase the friction coefficient of the joint surface (hereinafter referred to as the joint surface) 130 between the beam concrete 128a and the slab concrete 128b. The concrete 128b can be fixed to each other more firmly.

The beam concrete 128a and the slab concrete 128b may be cast so that the compressive strength is in the range of 21 N/mm ² or more and 150 N/mm ² or less, or 24 N/mm ² or more and 120 N/mm ² or less. The beam concrete 128a and the slab concrete 128b may or may not have the same composition and strength. In the latter case, beam concrete 128a may be stronger or weaker than slab concrete 128b. For example, one of the beam concrete 128a and the slab concrete 128b is cast so as to have a compressive strength of 21 N/mm ² or more and 33 N/mm ² or less, or 24 N/mm ² or more and 27 N/mm ² or less, and the other has a compressive strength is 27 N/mm ² or more and 150 N/mm ² or less, 36 N/mm ² or more and 120 N/mm ² or less, or 36 N/mm ² or more and 48 N/mm ² or less. By lowering the strength of one concrete (for example, the slab concrete 128b) than the other, the structure 100 can be constructed at low cost. The strength of beam concrete 128a and slab concrete 128b may be substantially the same as or different from the strength of concrete 116 used in column 110 .

As described above, the hybrid beam used in the structure 100 according to the present embodiment has a surface where the beam concrete 128a and the slab concrete 128b are jointed, that is, a joint surface 130 (see FIG. 4A). . In such a structure, by using the design method described in the second embodiment, the ultimate shear strength at the joint surface 130 can be accurately calculated. 128b can be effectively prevented from horizontal slip failure. Therefore, even if the low-strength slab concrete 128b is used for part of the RC section 120a and the floor slab 150, the structure 100 with excellent earthquake resistance can be provided.

<Second embodiment>
This embodiment describes a method for designing the structure 100 with the hybrid beams described in the first embodiment. More specifically, a design method for preventing horizontal slip failure from occurring due to an external force on the joint surface 130 of the RC section 120a of the beam 120 will be described. Descriptions of configurations that are the same as or similar to the configuration described in the first embodiment may be omitted.

（１） A detailed introduction process will be described in an embodiment, but as a method for effectively preventing horizontal sliding failure on the joint surface 130, the design method according to this embodiment uses the joint between the beam concrete 128a and the slab concrete 128b in the RC section 120a. Ultimate strength q _fr of surface 130 is calculated by the following equation (1).

(1)

Variables in the above formula are as follows (see FIGS. 4A, 6A, and 6B).

（２）
ここで、μ_ｓは鉄骨１２２とコンクリート間の摩擦係数であり、μ_ｒｃはコンクリートとコンクリート間の摩擦係数である。μ_ｓは０．３０以上０．９０以下、０．４０以上０．９０以下、０．５０以上０．９０以下、または０．５６以上０．８０以下の範囲から選択され、例えば０．５６である。梁コンクリート１２８ａの上面に凹凸を設けない場合にはμ_ｒｃはそれぞれ０．６λであり、凹凸を設ける場合にはμ_ｒｃは１．０λとする。λはコンクリートの種類に依存する係数であり、軽量コンクリートの場合には０．７５が、普通コンクリートの場合には１．０が採用される。Ｂｓはフランジの幅（鉄骨幅とも呼ばれ、ウェブの法線に平行な方向における長さ）であり、ｂはＲＣ区間１２０ａの梁コンクリート１２８ａの幅ｂ（ウェブの法線に平行な方向における長さ）である。ｂ´は、鉄骨１２２のフランジ位置でのＲＣ区間１２０ａの梁コンクリート１２８ａの有効幅であり、幅ｂから幅Ｂｓを引いた値である。実施例で述べるように、等価摩擦係数μ_ｅｑを上述した仮定に従って計算することで、水平すべり破壊試験から得られる終局強度と計算結果から得られる終局強度の間に高い整合性が得られることが確認されている。 μ _eq is the equivalent coefficient of friction, which is the friction coefficient of the joint surface 130 . The joint surface 130 is mainly formed at the interface between the steel frame 122 and the _slab concrete 128b and the interface between the beam concrete 128a and the slab concrete 128b. is assumed to contribute according to the area ratio of Therefore, μ _eq is represented by the following equation (2).

(2)
Here, _μs is the coefficient of friction between the steel frame 122 and concrete, and _μrc is the coefficient of friction between concrete. _μs is selected from the range of 0.30 to 0.90, 0.40 to 0.90, 0.50 to 0.90, or 0.56 to 0.80. be. When the upper surface of the beam concrete 128a is not uneven, _μrc is 0.6λ, and when unevenness is provided, _μrc is 1.0λ. λ is a coefficient that depends on the type of concrete, and is 0.75 for lightweight concrete and 1.0 for normal concrete. Bs is the width of the flange (also called the steel frame width, the length in the direction parallel to the normal to the web), and b is the width b of the concrete beam 128a of the RC section 120a (the length in the direction parallel to the normal to the web). is). b' is the effective width of the beam concrete 128a of the RC section 120a at the flange position of the steel frame 122, and is the value obtained by subtracting the width Bs from the width b. As described in the examples, by calculating the equivalent coefficient of friction μ _eq according to the above assumptions, it is found that high consistency can be obtained between the ultimate strength obtained from the horizontal sliding fracture test and the ultimate strength obtained from the calculation results. Confirmed.

_s a _w is the total cross-sectional area of the horizontal reinforcing bars 124 excluding the beam end side centralized horizontal reinforcing bar 124a and the beam center side centralized horizontal reinforcing bar 124b among the horizontal reinforcing bars 124 arranged in the RC section 120a. .

Since _s σ _wy is the yield strength or reference strength (F-value) of the lateral reinforcement 124, the first term in parentheses ( _s a _w σ _wy ) in equation (1) is the intermediate lateral reinforcement for the ultimate strength q _fr It represents the contribution of muscle 124c.

_sw a _w is the sum of the cross-sectional areas of the insertion rebars 125, and _sw σ _wy is the yield strength or reference strength (F-value) of the insertion rebars 125 . Therefore, the second term ( _sw a _w · _sw σ _wy ) in the parenthesis of equation (1) represents the contribution of the lead-in 125 to the ultimate strength q _fr . Note that the second term is 0 when the insertion line 125 is not arranged.

_A a _w is the sum of the cross-sectional areas of the beam center side concentrated lateral reinforcing bars 124b. _A σ _wy is the yield strength or reference strength (F value) of the beam center side concentrated lateral reinforcement 124b. Therefore, the third term ( _A a _wA σ _wy ) in parentheses in Equation (1) represents the contribution of the beam center side concentrated lateral reinforcement 124b to the ultimate strength q _fr .

σ ₀ is the average external vertical stress occurring in RC section 120a. _Fc is the design basis strength of the concrete slab 128b. l _c is the length of the reinforced concrete in the direction in which the steel frame extends.

From equation (1), it can be seen that in the design method according to one embodiment of the present invention, the beam end side concentrated lateral reinforcing bars 124a are not considered in the calculation of the ultimate strength q _fr of the joint surface 130 . This is because the results of tests conducted by the inventors have revealed that the beam end side concentrated lateral reinforcing bars 124a hardly contribute to the ultimate strength q _fr of the joint surface 130, as will be described in the examples. Therefore, in calculating the ultimate strength q _fr of the joint surface 130, it is possible to ignore the contribution of the beam end side concentrated lateral reinforcing bars 124a when resisting the horizontal shear force, and the beam center side concentrated lateral reinforcing bars 124b, The contribution of the intermediate lateral reinforcing bar 124c and the insert bar 125 and the vertical stress component applied to the joint surface 130 should be considered. This provides high consistency between the test results and the calculated results, as will be described in the examples.

As described above, the method for designing the structure 100 including the hybrid beam according to the embodiment of the present invention is the interface (that is, the joint surface 130) between the beam concrete 128a and the slab concrete 128b existing in the RC section 120a. Calculating the ultimate strength q _fr . In calculating the ultimate strength q _fr , an equivalent friction coefficient μ _eq is used as the friction coefficient of the joint surface 130 . The equivalent friction coefficient μ _eq is a value obtained by multiplying the friction coefficient of the interface between the steel frame 122 and the slab concrete 128b and the interface between the beam concrete 128a and the slab concrete 128b that constitute the joint surface 130 by the area ratio of each interface. is calculated by adding From the test results, μ _eq is selected from the range of 0.40 or more and 0.9 or less or 0.56 or more and 0.8 or less, and when securing a wide margin for the ultimate strength q _fr , it may be 0.56, for example. . At the same time, the contribution of some of the reinforcing bars provided in the RC section 120a is not considered. More specifically, although the insert reinforcement 125, the beam center side concentrated lateral reinforcing bar 124b, and the intermediate lateral reinforcing bar 124c are considered for the calculation of the ultimate strength _qfr , the ultimate strength of the beam end side concentrated lateral reinforcing bar 124a is considered. Contributions to the intensity q _fr are not considered. This method makes it easier to calculate the ultimate strength q _fr that matches the test results.

In this example, the results of a destructive test of a hybrid beam will be described. Based on the test results, a method for designing the structure 100 including the hybrid beam, which is one embodiment of the present invention, was established.

1. Test Body and Test Method A schematic diagram showing the entire test body 200 is shown in FIG. 6A, and a schematic diagram centering on the RC section 120a is shown in FIG. 6B. A destructive test by repeated positive and negative loading was performed on the specimen 200 shown in FIG. 6(A). The load is applied to the steel frame 122 (see the white arrow), the upward load is compression of the slab concrete 128b (slab compression), and the downward load is tension of the slab concrete 128b (slab tension). In the RC section 120a, beam concrete 128a and slab concrete 128b were laminated. The slab concrete 128b was cast after removing the laitance from the upper surface of the beam concrete 128a and forming unevenness of about 5 mm on the upper surface. Ordinary concrete was used for both the beam concrete 128a and the slab concrete 128b, but as shown in Table 1, their strengths are different from each other. Also, as shown in FIG. 6B, strain gauges were attached to three locations (A, B, and C) near the joint surface 130 . A is the place where the beam end side concentrated horizontal reinforcing bar 124a is arranged, B is the place where the middle horizontal reinforcing bar 124c is arranged, and C is the place where the beam center side concentrated horizontal reinforcing bar 124b is arranged. be. Twenty-two specimens 200 were tested, and horizontal sliding failure occurred in four specimens 200 among them. The specifications of these four specimens 200 are summarized in Table 1.

2. Contribution of lateral reinforcement to ultimate strength Strain ε of lateral reinforcement 124 at each point A to C obtained from strain gauges of four specimens 200 that caused horizontal slip failure, i.e., beam end side concentrated lateral reinforcement The strain ε of the bar 124a, the intermediate lateral reinforcing bar 124c, and the beam center side concentrated lateral reinforcing bar 124b was calculated. Also, the tip deformation angle Rb of the beam 120 at the time of horizontal sliding failure was measured. A plot of strain ε versus tip deformation angle Rb is shown in FIG.

From FIG. 7, it can be seen that the intermediate lateral reinforcing bar 124c and the beam center side concentrated lateral reinforcing bar 124b yield when the tip deformation angle Rb reaches from 5×10 ⁻³ rad to 10×10 ⁻³ rad. On the other hand, the strain of the beam end side concentrated lateral reinforcement 124a is small. From this, it was confirmed that the beam end side concentrated lateral reinforcement 124a has a small resistance to the horizontal shear force and hardly contributes to the ultimate strength _fqr for the joint surface 130.

（３）
ただし、τ_ｕ＜０．３σ_Ｂであり、σ_Ｂは用いられるコンクリートの圧縮強度である。σ_Ｂτ_ｕはせん断摩擦を接合要素の応力伝達機構とする場合の単位面積当たりの終局強度であり、μは接合面を形成するコンクリート間の摩擦係数、Ｐｓは接合面を横切る鉄筋の単位面積当たりの断面積であり、σ_ｙは接合面を横切る鉄筋の降伏強度または基準強度である。σ_０は単位面積当たりの応力の鉛直方向成分であり、式（１）における括弧内の第４項と等価である。この式（３）を用いる終局強度の算出方法では、接合面を横切る鉄筋の全てが考慮される。すなわち、試験体２００の場合では、差し筋１２５や中間横補強筋１２４ｃ、梁中央側集中横補強筋１２４ｂのみならず、梁端部側集中横補強筋１２４ａも考慮される。 Conventionally, the ultimate strength of the joint surface 130 has been determined according to "Design Guideline for Cast-in-Place Reinforced Concrete Structural Design (Draft) and Commentary (2002)" (edited by Architectural Institute of Japan, 1st edition, published by Maruzen Co., Ltd., October 2002). 20, p.60) using the following intensity formula (hereinafter referred to as formula (3)).

(3)
where τ _u <0.3σ _B , where σ _B is the compressive strength of the concrete used. σ _B τ _u is the ultimate strength per unit area when shear friction is used as the stress transmission mechanism of the joint element, μ is the friction coefficient between the concrete forming the joint surface, and Ps is the unit area of the reinforcing bar crossing the joint surface _y is the yield strength or reference strength of the rebar across the joint plane. σ ₀ is the vertical component of stress per unit area and is equivalent to the fourth term in parenthesis in equation (1). In the method of calculating the ultimate strength using this formula (3), all of the reinforcing bars crossing the joint surface are considered. That is, in the case of the test piece 200, not only the insertion reinforcement 125, the intermediate horizontal reinforcement 124c, the beam center side concentrated horizontal reinforcement 124b, but also the beam end side concentrated horizontal reinforcement 124a are considered.

However, as described above, the destructive test revealed that the beam-end-side concentrated lateral reinforcing bars 124 a hardly contribute to the ultimate strength of the joint surface 130 . Therefore, as represented by the formula (1) of the second embodiment, it was found that the ultimate strength can be calculated by ignoring the beam end side concentrated lateral reinforcing bars 124a.

3. Friction Coefficient As described above, in the conventional calculation method (equation (3)), the friction coefficient (that is, μ _rc ) between concretes forming the joint surface 130 is adopted as the friction coefficient μ of the joint surface 130. there is However, when the ultimate strength q _fr was calculated using μ _rc in place of the equivalent friction coefficient μ _eq in Equation (1), it was confirmed that the calculated value deviated greatly from the value obtained from the test results. This is because the joint surface 130 includes not only the interface between the beam concrete 128a and the slab concrete 128b, but also the interface between the steel frame 122 and the slab concrete 128b. This is probably because the latter coefficient of friction is not taken into consideration in formula (3).

Therefore, for each of the four specimens 200 in which horizontal sliding failure occurred, the sliding displacement δ of the joint under load (during slab tension) was calculated. The measurement points were substantially the same as the three points A to C where the strain gauges of each specimen 200 were provided. A plot of the sliding displacement δ versus the beam tip deformation angle Rb is shown in FIG. As shown in FIG. 8, when the beam tip deformation angle Rb reaches about 10×10 ⁻³ rad, the sliding displacement δ increases greatly. Here, as can be understood from FIG. 7, the beam center side concentrated lateral reinforcing bar 124b and the intermediate lateral reinforcing bar 124c also yield when the beam tip deformation angle Rb reaches about 10×10 ⁻³ rad. These results mean that the load when the beam tip deformation angle Rb is about 10×10 ⁻³ rad corresponds to the horizontal shear endurance q _exp at the joint surface 130 between the beam concrete 128a and the slab concrete 128b. ing.

Based on this result, the equivalent friction coefficient μ _eq was obtained by substituting the horizontal shear strength q _exp obtained from the test results into the ultimate strength q _fr in Equation (1). Furthermore, as described in the second embodiment, the coefficient of friction at the joint surface 130 is the sum of the values obtained by multiplying the coefficient of friction between concrete and the coefficient of friction between concrete and the steel frame by the respective area ratios. Under the assumption (equation (2)), the coefficient of friction _μs between concrete and steel frame, that is, between slab concrete 128b and steel frame 122 was calculated. The results are shown in FIG. It is understood from FIG. 9 that the coefficient of friction _μs between the slab concrete 128b and the steel frame 122 is generally in the range of 0.50 to 0.90. In order to secure a large margin against horizontal slip failure, it can be said that it is preferable to adopt the lower limit of this range or a value close to it (for example, 0.56) to design the hybrid beam.

From the above results, in designing the structure 100 including the hybrid beam having the RC section 120a where the concrete is jointed and the upper concrete (that is, the slab concrete 128b) contacts the steel frame, the hybrid beam is based on the following design method. The horizontal shear force of the beam can be calculated.

(1) In calculating the horizontal shear force, the contribution of the beam-end-side concentrated lateral reinforcing bars 124a among the lateral reinforcing bars 124 arranged in the RC section 120a is not considered. Therefore, the stress component in the vertical direction of the joint surface 130 with respect to the cross-sectional area and yield strength or reference strength (F-value) of the beam center side concentrated lateral reinforcing bar 124b, the intermediate lateral reinforcing bar 124c, and the insert bar 125, and the ultimate strength q _fr Formula (1), which is a strength formula considering

(2) A value selected from the range of 0.50 to 0.90, or 0.56 to 0.8 as the friction coefficient between the steel frame 122 and the concrete provided on the steel frame 122 (here, the slab concrete 128b). to adopt.

(3) As the friction coefficient of the joint surface 130, the friction coefficient between the beam concrete 128a and the slab concrete 128b forming the joint surface 130 and the friction coefficient between the steel frame 122 and the concrete provided on the steel frame 122 (here, the slab concrete 128b) Equivalent friction coefficient μ _eq obtained by multiplying each friction coefficient by the area ratio is used.

Each of the embodiments described above as embodiments of the present invention can be implemented in combination as appropriate as long as they do not contradict each other. Appropriate additions, deletions, or design changes made by those skilled in the art based on each embodiment are also included in the scope of the present invention as long as they have the gist of the present invention.

Even if there are other actions and effects different from the actions and effects brought about by each of the above-described embodiments, those that are obvious from the description of the present specification or those that can be easily predicted by those skilled in the art are, of course, the present invention. is understood to be brought about by

100: structure, 110: pillar, 110-1: first pillar, 110-2: second pillar, 110-3: third pillar, 110-4: fourth pillar, 110-5: third 5 column, 110-6: sixth column, 112: column main reinforcement, 114: ties, 116: concrete, 120: beam, 120-1: first beam, 120-2: second beam, 120 -3: Third beam, 120-4: Fourth beam, 122: Steel frame, 124: Horizontal reinforcing bar, 124a: Beam end side concentrated horizontal reinforcing bar, 124b: Beam center side concentrated horizontal reinforcing bar, 124c: Intermediate lateral reinforcing bar, 125: Insert bar, 126: Beam main bar, 126a: Fixing plate, 128: Concrete, 128a: Beam concrete, 128b: Slab concrete, 130: Joint surface, 150: Floor slab, 200: Specimen

Claims (12)

A method of designing a structure including a hybrid beam,
The hybrid beam is
Equipped with a steel frame and reinforced concrete covering both ends of the steel frame,
The reinforced concrete is
a plurality of beam main bars extending in the extending direction of the steel frame;
a plurality of lateral reinforcing bars intersecting the steel frame and the plurality of beam main bars and surrounding the steel frame and the plurality of beam main bars;
a plurality of insert bars that intersect the steel frame and the plurality of main beam reinforcements and surround the steel frame and a portion of the plurality of beam main reinforcements;
a beam concrete embedding an end portion of said steel frame, a portion of said plurality of main beam reinforcements, a portion of said plurality of transverse reinforcements, and a portion of said plurality of insert reinforcements; a slab concrete that is in contact with the beam concrete and embeds another part of the plurality of main beam reinforcements, another part of the plurality of lateral reinforcements, and another part of the plurality of insert reinforcements;
The plurality of lateral reinforcing muscles are
A plurality of beam end side concentrated lateral reinforcing bars arranged at a first density on the beam end side;
a plurality of beam center side concentrated lateral reinforcing bars arranged at a second density on the beam center side; and a plurality of intermediate transverse reinforcing bars arranged at a density lower than the second density,
The design method does not consider the contributions of the beam end side concentrated lateral reinforcing bars, the contributions of the plurality of beam center side concentrated lateral reinforcing bars, the plurality of intermediate lateral reinforcing bars, and the plurality of insertion bars, and A method of designing a structure, including calculating the ultimate strength of the joint surface in consideration of a vertical stress component applied to the joint surface between the beam concrete and the slab concrete. The contribution of the plurality of beam center side concentrated lateral reinforcing bars includes the sum of the cross-sectional areas of the plurality of beam center side concentrated lateral reinforcing bars, the reference strength of the plurality of lateral reinforcing bars, and the beam concrete and the slab concrete. 2. The method of designing a structure according to claim 1, wherein the product of coefficients of friction between The contribution of the plurality of intermediate lateral reinforcing bars is expressed by the sum of the cross-sectional areas of the plurality of intermediate lateral reinforcing bars, the reference strength of the lateral reinforcing bars, and the product of the coefficient of friction between the beam concrete and the slab concrete. 2. The method of designing a structure according to claim 1, wherein: 3. The contribution of the plurality of interstitial rebars is represented by the sum of the cross-sectional areas of the plurality of interstitial rebars, the reference strength of the interstitial rebars, and the product of the coefficient of friction between the beam concrete and the slab concrete. 2. The method for designing the structure according to 1. The friction coefficient is defined as the friction coefficient between the beam concrete and the slab concrete and the friction coefficient between the steel frame and the slab concrete, respectively, the interface between the beam concrete and the slab concrete at the joint surface, the steel frame and the steel frame, and the friction coefficient between the steel frame and the slab concrete. 5. The method for designing a structure according to claim 2, wherein the sum of the products of the area ratios of interfaces between slab concrete. 6. The method of designing a structure according to claim 5, wherein the coefficient of friction between said steel frame and said slab concrete is selected from a range of 0.40 or more and 0.90 or less. 6. The structure designing method according to claim 5, wherein the coefficient of friction between said steel frame and said slab concrete is selected from a range of 0.56 or more and 0.80 or less. A method of designing a structure including a hybrid beam,
The hybrid beam is
a steel frame having a web and a pair of flanges connected to the web; and reinforced concrete covering both ends of the steel frame,
The reinforced concrete is
a plurality of beam main bars extending in the extending direction of the steel frame;
a plurality of lateral reinforcing bars intersecting the steel frame and the plurality of beam main bars and surrounding the steel frame and the plurality of beam main bars;
a plurality of insert bars that intersect the steel frame and the plurality of main beam reinforcements and surround the steel frame and a portion of the plurality of beam main reinforcements;
a beam concrete embedding an end portion of said steel frame, a portion of said plurality of main beam reinforcements, a portion of said plurality of transverse reinforcements, and a portion of said plurality of insert reinforcements; a slab concrete that is in contact with the beam concrete and embeds another part of the plurality of main beam reinforcements, another part of the plurality of lateral reinforcements, and another part of the plurality of insert reinforcements;
The plurality of lateral reinforcing muscles are
A plurality of beam end side concentrated lateral reinforcing bars arranged at a first density on the beam end side;
a plurality of beam center side concentrated lateral reinforcing bars arranged at a second density on the beam center side; and a plurality of intermediate transverse reinforcing bars arranged at a density lower than the second density,
The design method includes calculating the ultimate strength q _fr of the joint surface between the beam concrete and the slab concrete according to the following formula (1),

(1)
In formula (1),
μ _eq is the friction coefficient of the joint surface,
_s a _w is the sum of cross-sectional areas of the plurality of intermediate lateral reinforcing bars;
_s σ _wy is the reference strength of the plurality of lateral reinforcing bars;
_sw a _w is the sum of the cross-sectional areas of the plurality of insertion bars;
_sw σ _wy is the reference strength of the plurality of insertion bars;
_A a _w is the sum of the cross-sectional areas of the plurality of beam center side concentrated lateral reinforcing bars;
_A σ _wy is the reference strength of the plurality of beam center side concentrated lateral reinforcing bars;
σ ₀ is the average external vertical stress occurring in the reinforced concrete,
b′ is the effective width of the reinforced concrete at the position of the flange;
The method of designing a structure, wherein l _c is the length of the reinforced concrete in the direction in which the steel frame extends. The coefficient of friction μ _eq is expressed by the following formula,

In the above formula,
_μs is the friction coefficient between the steel frame and the slab concrete,
B _s is the length of the flange in the direction parallel to the normal of the web;
μ _rc is the coefficient of friction between the beam concrete and the slab concrete;
9. The method of designing a structure according to claim 8, wherein b is the length of the beam concrete in said direction parallel to said normal. 10. The structure designing method according to claim 9, wherein said coefficient of friction [mu _]s between said steel frame and said slab concrete is selected from a range of 0.40 or more and 0.90 or less. 10. The structure designing method according to claim 9, wherein said coefficient of friction [mu _]s between said steel frame and said slab concrete is selected from a range of 0.56 or more and 0.80 or less. The method of designing a structure according to claim 1 or 8, wherein the slab concrete has a lower strength than the beam concrete.

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