WO2020246524A1

WO2020246524A1 - Method for designing column-beam joint, method for manufacturing column-beam joint, and column-beam joint structure

Info

Publication number: WO2020246524A1
Application number: PCT/JP2020/022018
Authority: WO
Inventors: 政樹有田; 涼平桑田; 慧木村; 聡北岡
Original assignee: 日本製鉄株式会社
Priority date: 2019-06-03
Filing date: 2020-06-03
Publication date: 2020-12-10
Also published as: JPWO2020246524A1; JP7074260B2

Abstract

In this method for designing a column-beam joint: rotational rigidity is defined as the rotational resistance per unit rotation angle of a section of a steel beam inside concrete in a column-beam joint; the load supported by the steel beam and the rotational rigidity are used to calculate the required moment capacity acting on the column from the steel beam; and the distance between both ends of the steel beam and/or the cross-sectional shape of the steel beam is adjusted such that the calculated required moment capacity does not exceed the maximum moment capacity that can be resisted by the column-beam joint.

Description

Beam-column joint design method, beam-column joint manufacturing method and beam-column joint structure

This disclosure relates to a method for designing a beam-column joint, a method for manufacturing a beam-column joint, and a structure for a beam-column joint.

Japanese Unexamined Patent Publication No. 2016-142062 (Patent Document 1) discloses a column-beam joint structure in which a reinforced concrete column and a steel beam are joined. In the column-beam joint structure described in Patent Document 1, a recess is formed in the reinforced concrete column, the end portion of the steel beam is inserted and arranged in the formed recess, and concrete is filled.

In the column-beam joint structure described in Patent Document 1, the degree of fixation of the steel beam is adjusted by adjusting the embedding length of the end portion of the steel beam in the concrete filled in the recess. In addition, by adjusting the degree of fixation, the end of the steel beam is semi-rigidly joined to the reinforced concrete column, and the joint between the reinforced concrete column and the steel beam and the bending moment acting on the steel beam are adjusted. There is. Further, by adjusting the degree of fixation, the deflection at the center of the beam is reduced as compared with the case where the ends of the steel beam are pin-joined. That is, the rotational rigidity of the joint between the reinforced concrete column and the steel beam is adjusted. Hereinafter, the joint portion between the column and the beam is also referred to as a “column-beam joint portion” or simply a “joint portion”.

However, Patent Document 1 does not mention anything about the yield strength of the beam-column joint. Therefore, when the rotational rigidity of the column-beam joint is secured for the purpose of adjusting the deflection and the bending moment of the steel frame beam, the bearing capacity may be insufficient and Patent Document 1 may not be implemented.

Further, in Patent Document 1, even when the embedding length of the end portion of the steel frame beam in concrete approaches zero, the degree of fixation does not approach zero. For this reason, the degree of fixation is overestimated or underestimated when Patent Document 1 is carried out beyond the range of the ratio of the embedded length to the beam length in the experiments and analyzes shown in Patent Document 1. There is a fear. Therefore, there is a concern that the deflection of each beam is underestimated or the moment acting on the joint is underestimated.

The moment acting on the joint is calculated according to the load supported by the beam, the span of the beam, the flexural rigidity of the beam, and the rotational rigidity of the joint. However, if the acting moment exceeds the moment strength of the joint, the joint will be plasticized, the degree of fixation will be lower than the calculated value, the deflection of the beam will be larger than the calculated value, and there is a concern that the column will be damaged. is there. This means that when Patent Document 1 is implemented, there is a possibility that a case that does not satisfy the required performance in design may be overlooked.

The degree of fixation also changes depending on the distance between the joints at both ends of the steel beam, that is, the length of the beam, but Patent Document 1 does not consider the influence of the distance between the joints.

Further, in Patent Document 1, the fixedness of the joint is adjusted by adjusting the embedding length, but in the actual design, the diameter of the column is determined by the required performance of the column and also by the diameter of the column. , The maximum length that a beam can be embedded is restricted. In particular, when a plurality of beams are embedded from two or more directions so that the beams intersect the concrete columns, the plurality of beams are arranged so that the beams do not overlap each other.

In addition, it will be necessary to ensure the filling property of concrete and the predetermined cover thickness. For this reason, the maximum length that can be embedded in concrete in a beam is severely restricted. In this case, in order to secure the rotational rigidity and moment strength of the joint, the length of the beam of the embedded part needs to be the maximum length that can be adopted in construction, so the embedded length is adjusted. There is also the possibility that it cannot be done.

From the above, the joint structure of Patent Document 1 includes the possibility that it cannot be actually implemented. Further, Patent Document 1 includes room for improvement from the viewpoint of accurately evaluating the rotational rigidity of the beam-column joint and imparting the required moment strength according to the rotational rigidity of the joint.

In the present disclosure, in consideration of the above facts, a method for designing a column-beam joint, a method for manufacturing a column-beam joint, and a column capable of satisfying the moment resistance while ensuring the rotational rigidity of the joint between the column and the beam. It is an object of the present invention to provide a beam joint structure.

The method for designing a beam-column joint according to the present disclosure is provided for a concrete beam, a steel beam in which at least one end in the longitudinal direction is embedded in the concrete of the column in a semi-rigid joint state, and a steel beam. It is a method of designing a beam-beam joint having a resistance element that generates a reaction force against the rotation of the steel beam, and is a rotation resistance per unit rotation angle of the part of the steel beam inside the concrete at the beam-beam joint. was defined as the rotational stiffness S _j, by using the rotational stiffness S _j and load the steel beam supporting and calculate the required moment capacity to act from steel beam in Column joints, it is calculated required moment capacity Column Adjust at least one of the distance between both ends of the steel beam and the cross-sectional shape of the steel beam so that the maximum moment strength that the joint can resist is not exceeded.

Further, other methods for designing a beam-beam joint according to the present disclosure include a concrete beam and a steel beam in which at least one end in the longitudinal direction is embedded in the concrete of the column in a semi-rigid joint state. It is a method of designing a beam-column joint provided with a resistance element provided on a steel beam and generating a reaction force against the rotation of the steel beam, and is a unit rotation angle of a part of the steel beam inside concrete at the beam-beam joint. It is defined as rotational stiffness S _j rotational resistance per the necessary moment capacity to act from steel beam in Column joints with the rotational stiffness S _j the steel beam is set by the following process a and the load supporting calculate.
<Process A>
Table by the product of the total number of resistive elements n, as a natural number of 1 to n and i, the resistive element and resistive element i, the reaction force of the resistance element i is rigid k _i and the amount of deformation of the resistance element i The center of rotation of the steel beam part inside the concrete of the pillar is set as the point where the reaction force of the resistance element i and the external force are balanced, and the distance between the action line of the representative displacement of the resistance element i and the center of rotation is x _{d, i.} Let the distance between the center of gravity of the reaction force of the resistance element i and the center of rotation be x _{l, i} , and the rotational rigidity S _j be set based on the evaluation of the value obtained by the following equation 1.

Further, in the method for manufacturing a column-beam joint according to the present disclosure, at least one end in the longitudinal direction of a steel frame beam is provided with a resistance element designed by using the above-mentioned method for designing a column-beam joint. It is embedded inside the concrete in a semi-rigid joint state.

Further, the beam-column joint structure according to the present disclosure is provided on a concrete column, a steel beam in which at least one end in the longitudinal direction is embedded in the concrete of the column in a semi-rigid joint state, and a steel beam. It has a resistance element that generates a reaction force against the rotation of the steel beam, and the rotation resistance per unit rotation angle of the steel beam part inside the concrete at the beam-column joint is defined as the rotational rigidity _Sj. When the moment generated by the maximum resistance of the resistance element is defined as the maximum moment strength that can be resisted by the beam-beam joint, the required moment strength that acts from the steel beam to the beam-beam joint is the steel beam. At least one of the distance between both ends of the steel beam and the cross-sectional shape of the steel beam is such that the required moment strength calculated using the load supported by and the rotational rigidity _Sj does not exceed the maximum moment strength. It has been adjusted.

In addition, other beam-column joint structures according to the present disclosure include a concrete column, a steel beam in which at least one end in the longitudinal direction is embedded in the concrete of the column in a semi-rigid joint state, and a steel beam. It has a resistance element that is provided in the above and generates a reaction force against the rotation of the steel beam, and the rotation resistance per unit rotation angle of the steel beam part inside the concrete at the column-beam joint is defined as the rotational rigidity _Sj. Then, as the required moment strength acting on the beam-column joint from the steel beam, the required moment strength is set by using the load supported by the steel beam and the rotational rigidity _Sj set by the following process B.
<Process B>
Table by the product of the total number of resistive elements n, as a natural number of 1 to n and i, the resistive element and resistive element i, the reaction force of the resistance element i is rigid k _i and the amount of deformation of the resistance element i The center of rotation of the steel beam part inside the concrete of the pillar is set as the point where the reaction force of the resistance element i and the external force are balanced, and the distance between the action line of the representative displacement of the resistance element i and the center of rotation is x _{d, i.} The distance between the center of gravity of the reaction force of the resistance element i and the center of rotation is x _{l, i} , and the rotational rigidity S _j is set to a value satisfying the following equation 3.

According to the present disclosure, a method for designing a column-beam joint, a method for manufacturing a column-beam joint, and a column-beam joint structure capable of satisfying the moment resistance while ensuring the rotational rigidity of the joint between the column and the beam. Can be provided.

FIG. 1 is a side view showing a model of a joint between a column and a beam. FIG. 2 is a side view showing a model of a joint between a column and a beam, and shows a section up to an inflection point in the length direction of the steel beam. FIG. 3 is a side view showing a model for calculating the rotational rigidity of the joint between the column and the beam, and is a bearing resistance at the interface between the concrete of the column and the upper and lower flanges in the portion of the steel beam embedded in the column concrete. The stress distribution of the reaction force is shown. FIG. 4 is a perspective view schematically showing the bearing pressure resistance at the interface between the concrete of the column and the upper and lower flanges, and shows a state in which the reaction force due to the bearing pressure resistance has a linear stress gradient. FIG. 5 is a perspective view schematically showing the bearing pressure resistance at the interface between the concrete of the column and the upper and lower flanges, and shows a state in which the reaction force due to the bearing pressure resistance is a uniform stress. FIG. 6 is a side view showing a model for calculating the rotational rigidity of the joint between the column and the beam. The reaction force due to the bearing pressure resistance at the interface between the face bearing plate and the concrete of the column, and the pull-out resistance of the stud in the column. The reaction force due to the resistance of the reinforcing bar in the slab is shown. FIG. 7 is a perspective view for explaining the cone-shaped fracture of the concrete of the column due to the pulling out of the stud in the column when the stud in the column is installed as an additional member in the portion of the steel beam embedded in the concrete of the column. FIG. 8A is a side view showing a model for calculating the strength of the joint between the column and the beam, and is a vertical support of the interface between the column concrete and the upper and lower flanges in the portion of the steel beam embedded in the column concrete. It is a side view which shows typically the situation that the maximum reaction force by a pressure resistance acts on a steel beam. FIG. 8B is a side view showing a model for calculating the moment strength of the joint between the column and the beam, and is a bearing resistance at the interface between the concrete of the column and the upper and lower flanges in the portion of the steel beam embedded in the column concrete. It is a side view for demonstrating the actual stress distribution and conversion to a stress block when the maximum proof stress is applied. FIG. 9A is an explanatory diagram for explaining the effective bearing area and the maximum bearing stress distribution area, and shows the case where the entire projection surface is in the concrete. FIG. 9B is an explanatory diagram for explaining the effective bearing area and the maximum bearing stress distribution area, and shows a case where a part of the projection surface is outside the concrete. FIG. 10A is a side view showing a model for calculating the moment strength of the joint between the column and the beam, in the horizontal direction of the portion of the steel beam embedded in the column concrete and the additional member provided at the peripheral edge thereof. It is a side view which shows the situation which the maximum reaction force by resistance acts on a steel beam. Additional members are face bearing plates, column studs and reinforcing bars in slabs. FIG. 10B is a side view showing a model for calculating the moment strength of the joint between the column and the beam, and shows the maximum stress distribution of the effective bearing area of the interface between the face bearing plate and the concrete of the column, the stud in the column. It is a side view for demonstrating the maximum reaction force by the pull-out resistance of, and the maximum reaction force by the resistance of a reinforcing bar in a slab. FIG. 11 is an explanatory diagram for explaining the effective bearing area and the maximum bearing stress distribution area at the interface between the face bearing plate and the concrete of the column. FIG. 12 is a diagram for explaining the relationship between the moment and the angle of rotation of the joint, and the rotational rigidity and the proof stress of the joint. FIG. 13A is a side view showing a model for calculating the rotational rigidity of the joint between the column and the beam, and shows the reaction force due to the bearing resistance at the interface between the portion of the steel beam embedded in the column concrete and the column concrete. It is a side view which shows the stress distribution. FIG. 13B is a side view showing a model for calculating the strength of the joint between the column and the beam, and is a bearing resistance at the interface between the concrete of the column and the upper and lower flanges in the portion of the column steel beam embedded in the column concrete. It is a side view which shows the effective region of the bearing pressure when the maximum reaction force by is acting on a steel beam, and the actual stress distribution and conversion to a stress block. FIG. 14 is a graph showing the moment-rotation angle relationship at the column face position of the joint portion, and the experimental results and the calculation results according to the present disclosure are shown together. FIG. 15 is a graph showing a comparison between the experimental results of the rotational rigidity of the joint with respect to the repeatedly acting load and the calculation results according to the present disclosure. FIG. 16 is a diagram showing a calculation result of the degree of fixation α _rig according to the present disclosure. FIG. 17 is a diagram showing the ratio of the generated moments M _{j, Ed} of the joint portion and the proof stress M _{j, Rd} of the joint portion calculated by the present disclosure.

The beam-column joint structure according to the embodiment of the present disclosure will be described with reference to FIGS. 1 and 2. In the description of the drawings below, the same parts and similar parts are designated by the same reference numerals or similar reference numerals. However, the relationship between the thickness and the plane dimension in the drawing, the ratio of the thickness of each device and each member, etc. are different from the actual ones. Therefore, the specific thickness and dimensions should be determined in consideration of the following explanation. In addition, there are parts where the relationships and ratios of the dimensions of the drawings are different from each other.

As shown in FIGS. 1 and 2, the beam-column joint structure of the present embodiment is applied to the joint 14 between the column 10 and the beam 12. The vertical direction of the building is indicated by the arrow Z direction, and one side of the beam 12 extending direction and one horizontal direction of the building is indicated by the arrow X direction. The arrow Z direction is the vertical direction in FIG. 1, and the arrow X direction is the horizontal direction in FIG.

In the following description of each direction of XYZ, the signs of "positive (+)" and "negative (-)" are reversed between one direction extending to the opposite side and the other direction. For example, in the vertical direction in FIG. 1, when the vertical direction is simply described as a whole without distinguishing between the upper + Z direction and the lower −Z direction, the term “Z direction” is used. The explanation will be given without adding the “positive (+)” and “negative (-)” symbols.

The pillar 10 is formed in a substantially rectangular shape in a cross-sectional view cut along the horizontal direction of the building (a plane parallel to the XY plane). The column 10 is realized as a steel-framed reinforced concrete (SRC) column by arranging a reinforcing bar 16 (see FIG. 2) and a steel frame 18 inside the concrete 32. The present disclosure can also be applied to a joint between a reinforced concrete (RC) column and a steel beam.

Further, in the present embodiment, H-shaped steel is used as the steel frame 18. The H-shaped steel is formed in an H-shaped cross section in a cross-sectional view cut along the horizontal direction of the building. Further, in the present embodiment, as shown in FIG. 2, a plurality of reinforcing bars 16 extending in the vertical direction of the building are provided as the main reinforcing bars 16A. Further, reinforcing bars 16 surrounding the plurality of main bars 16A are provided as band bars 16B above, below, and sideways of the beam 12 in a plurality of steps in the vertical direction of the building.

In this embodiment, the four beams 12 are joined to the columns 10 at the same positions in the vertical direction of the building. For example, the four beams 12 are arranged around the pillar 10 at a distance of 90 ° from each other when viewed from the upper side of the building. Since the configurations of the four beams 12 are the same as each other, in the following description, one beam 12 out of the four beams 12 will be exemplified.

The beam 12 is a composite beam composed of a steel beam 20 and a reinforced concrete slab 22. The steel frame beam 20 is formed in an H-shaped cross section in a cross-sectional view cut in the vertical direction. The vertical direction is a direction orthogonal to the longitudinal direction of the beam 12. That is, the steel beam 20 is cut at a plane parallel to the YZ plane. The slab 22 extends horizontally at the upper part of the steel beam 20 and is integrated with the steel beam 20. The horizontal direction is parallel to the XY plane. The present disclosure can also be applied to a beam that is not integrated with the slab 22 (that is, a steel beam).

As shown in FIGS. 1 and 2, the steel beam 20 has a rectangular plate-shaped upper flange 20A whose thickness direction is the vertical direction (that is, the Z direction) of the building, and the upper flange 20A on the lower side of the upper flange 20A. It is provided with a lower flange 20B that extends parallel to the 20A. Further, the steel beam 20 includes a web 20C. The web 20C connects the central portion of the upper flange 20A in the width direction and the central portion of the lower flange 20B in the width direction to each other in the vertical direction of the building. The width direction of the upper flange 20A and the lower flange 20B is one direction in the horizontal direction of the building and the Y direction orthogonal to the X direction. The web 20C is formed in a rectangular plate shape with the Y direction as the thickness direction.

The beam end portion 24, which is the end portion in the longitudinal direction of the steel frame beam 20, is joined to the steel frame 18 of the column 10 via a fastening member such as a bolt 34 and a fin plate 36. The “beam end portion 24” means a portion of the steel frame beam 20 embedded in the concrete 32 of the column 10. Further, in the steel frame beam 20, the beam end portion 24 of the steel frame beam 20 is embedded in the concrete 32 of the column 10. In the present embodiment, the steel beam 20 is joined to the column 10 in a semi-rigid joint state.

The steel frame beam 20 is provided with an upper flange end 20Aa, a lower flange end 20Ba, and a web end 20Ca at the beam end 24, respectively. The upper flange end portion 20Aa refers to a region of the upper flange 20A embedded in the concrete 32 of the pillar 10. The lower flange end portion 20Ba refers to a region of the lower flange 20B embedded in the concrete 32 of the pillar 10. The web end 20Ca refers to a region of the web 20C embedded in the concrete 32 of the pillar 10.

The upper flange end portion 20Aa is formed on the outer surface 24A of the upper flange 20A located on the + Z direction side in FIG. 1 and the inner surface 24B of the upper flange 20A located on the −Z direction side in FIG. It is in contact with the concrete 32.

Further, the lower flange end portion 20Ba is a pillar on each of the inner surface 24C of the lower flange 20B located on the + Z direction side in FIG. 1 and the outer surface 24D of the lower flange 20B located on the −Z direction side in FIG. It is in contact with 10 concretes 32.

Further, as shown in FIG. 7, the web end portion 20Ca is in contact with the concrete 32 of the pillar 10 on each of the web surface on the + Y direction side and the web surface on the −Y direction side.

Further, the steel frame beam 20 of the present embodiment includes a plurality of studs 26 fixed to the upper flange 20A constituting the upper part of the steel frame beam 20. The plurality of studs 26 project from the upper flange 20A toward the upper side of the building, and are arranged so as to be spaced apart from each other along the longitudinal direction of the steel frame beam 20. In FIG. 1, only the two studs 26A at the beam end 24 are illustrated by way of example. The stud 26A at the beam end portion 24 is an additional member that acts as a “resistance element” against rotation when the beam end portion 24 rotates about the rotation center 24E described later.

Further, in the present embodiment, the joint reinforcing bar 28 is included in the diameter of the column 10 along the longitudinal direction of the steel frame beam 20, along the upper end of the stud 26, and on the Y axis. Is provided so as to penetrate the pillar 10 in the X direction. Of the arranged joint reinforcing bars 28 and studs 26, a part of the joint reinforcing bars 28 and the stud 26B other than the portion located at the beam end 24 are embedded inside the slab 22. The stud 26B in the slab 22 connects the steel beam 20 and the slab 22. The joint reinforcing bar 28 is an additional member that acts as a "resistance element" against rotation when the beam end portion 24 rotates about the rotation center 24E.

Further, the steel frame beam 20 includes a face bearing plate 30 formed in a rectangular plate shape with the longitudinal direction of the steel frame beam 20 as the thickness direction. In the present embodiment, the two face bearing plates 30 are fixed at the same position in the longitudinal direction of the steel frame beam 20 on the + Y direction side and the −Y direction side with the web 20C in between, respectively.

The dimension measured along the + Y direction of the face bearing plate 30 is the range in which the face bearing plate 30 does not protrude toward the + Y direction or the −Y direction from the area surrounded by the upper flange 20A, the lower flange 20B and the web 20C. It is set to the inside dimension. Further, in the state where the steel beam 20 is embedded in the concrete 32 of the column 10, the surface of the face bearing plate 30 opposite to the axial side of the column 10 is substantially the same surface as the outer surface of the column 10. It has become. The axial side of the pillar 10 is the right side in FIG. 1, and the side opposite to the axial side of the pillar 10 is the outer surface of the pillar 10.

On the other hand, the inner surface 30A of the face bearing plate 30 located on the axial side of the pillar 10 is in contact with the concrete 32 of the pillar 10.

As shown in FIG. 1, when a vertical load in the −Z direction is applied to the steel beam 20, the steel beam 20 is centered on the rotation center 24E of the beam end 24 in the XZ plane, and the steel beam 20 is shown in FIG. Inside, it rotates counterclockwise by φ _j , and the steel beam 20 is displaced to the position of the steel beam 20a shown by the broken line in FIG.

Here, the first axis 24F passing through the rotation center 24E and parallel to the Z direction and the second axis 24G passing through the rotation center 24E and parallel to the X direction are set. Further, of the inner surface 30A of the face bearing plate 30 when the beam end portion 24 rotates about the rotation center 24E, the portion in the −Z direction with the second shaft 24G sandwiched is the first inner surface 30Aa of the face bearing plate. Is defined as.

When the steel beam 20 rotates toward the position of the steel beam 20a, a reaction force due to bearing pressure acts from the concrete 32 of the column 10, so that the first inner surface 30Aa of the face bearing plate 30 with respect to the rotation of the beam end 24. Rotational resistance occurs. That is, the first inner surface 30Aa of the face bearing plate 30 serves as a "resistance element" against rotation when the beam end portion 24 arranged inside the concrete 32 of the column 10 in the steel frame beam 20 rotates about the rotation center 24E. It is an additional member that acts.

Further, when a vertical load in the −Z direction acts on the steel beam 20 and the steel beam 20a rotates about the rotation center 24E, a reaction force due to bearing pressure acts from the concrete 32 of the column 10. Therefore, on the outer surface 24A and the inner surface 24B of the upper flange 20A at the upper flange end portion 20Aa, rotational resistance with respect to the rotation of the beam end portion 24 occurs. Further, the inner surface 24C and the outer surface 24D of the lower flange 20B at the lower flange end 20Ba also generate rotational resistance with respect to the rotation of the beam end 24.

That is, the outer surface 24A of the upper flange end 20Aa acts as the upper flange end outer surface resistance element 24Aa and as a "resistance element" that resists the rotation of the beam end 24. Further, the inner surface 24B of the upper flange end portion 20Aa acts as an upper flange end inner surface resistance element 24Ba as a "resistance element" that resists the rotation of the beam end portion 24.

Further, the inner surface 24C of the lower flange end portion 20Ba acts as a lower flange end inner surface resistance element 24Ca and a "resistance element" that resists the rotation of the beam end portion 24. Further, the outer surface 24D of the lower flange end portion 20Ba acts as a lower flange end portion outer surface resistance element 24Da as a “resistance element” that resists the rotation of the beam end portion 24.

More specifically, of the outer surface 24A of the upper flange end portion 20Aa, the portion on the + X direction side from the first shaft 24F is set as the upper flange end portion outer surface resistance element 24Aa. Further, of the inner surface 24B of the upper flange end portion 20Aa, the portion on the −X direction side of the first shaft 24F is set as the upper flange end inner surface resistance element 24Ba.

Further, of the inner surface 24C of the lower flange end portion 20Ba, the portion on the + X direction side from the first shaft 24F is set as the lower flange end portion inner surface resistance element 24Ca. Further, of the outer surface 24D of the lower flange end portion 20Ba, the portion on the side in the −X direction from the first shaft 24F is set as the lower flange end portion outer surface resistance element 24Da.

The upper flange end outer surface resistance element 24Aa, the upper flange end inner surface resistance element 24Ba, the lower flange end inner surface resistance element 24Ca, and the lower flange end outer surface resistance element 24Da are inside the concrete 32 of the column 10 in the steel beam 20. When the beam end portion 24 arranged in the above is rotated around the rotation center 24E, there are four "resistance elements" that generate a reaction force against the rotation.

Further, in the present embodiment, when the steel beam 20 rotates to the position of the steel beam 20a, the stud 26A, which is one of the additional members, is displaced in the −X direction on the left side in FIG. 1, depending on the amount of displacement. , Receives a reaction force from the concrete 32 of the pillar 10. That is, the stud 26A is a "resistance element" that generates a reaction force against the rotation when the beam end portion 24 arranged inside the concrete 32 of the column 10 in the steel frame beam 20 rotates around the rotation center 24E. Is.

Further, in the present embodiment, when the steel frame beam 20 rotates to the position of the steel frame beam 20a, the first inner surface 30Aa of the face bearing plate 30 which is one of the additional members is displaced toward the + X direction on the right side in FIG. .. The displaced first inner surface 30Aa receives a reaction force from the concrete 32 of the pillar 10 and the opposing joint portion 14 on the + X direction side of the pillar 10 according to the amount of displacement. That is, the first inner surface 30Aa of the face bearing plate 30 has a reaction force that opposes the rotation when the beam end 24 arranged inside the concrete 32 of the column 10 in the steel beam 20 rotates about the rotation center 24E. It is a "resistance element" that causes

Further, in the present embodiment, when the steel beam 20 rotates to the position of the steel beam 20a, the joint reinforcing bar 28, which is one of the additional members, is stretched and displaced in the −X direction on the left side in FIG. The displaced joint reinforcing bar 28 exerts a reaction force (in other words, tensile force) from the concrete 32 of the column 10 and the joint reinforcing bar 28 of the joint portion 14 on the opposite side existing in the + X direction according to the amount of displacement. receive. That is, the joint reinforcing bar 28 generates a reaction force against the rotation when the beam end portion 24 arranged inside the concrete 32 of the column 10 in the steel frame beam 20 rotates around the rotation center 24E. It is a resistance element.

As described above, in the present embodiment, the upper flange end outer surface resistance element 24Aa, the upper flange end inner surface resistance element 24Ba, the lower flange end inner surface resistance element 24Ca, the lower flange end outer surface resistance element 24Da, the stud 26A, and the face bearing. Seven "resistance elements" of the first inner surface 30Aa of the plate 30 and the joint reinforcing bar 28 are set. Therefore, in the present embodiment, the total number of resistance elements “n” is n = 7.

Here, "i" is defined as a natural number of 1 or more and n or less. In the case of this embodiment, the resistance element 1 (i = 1) is the upper flange end outer surface resistance element 24Aa. Further, the resistance element 2 (i = 2) is an upper flange end inner surface resistance element 24Ba. Further, the resistance element 3 (i = 3) is the lower flange end inner surface resistance element 24Ca. Further, the resistance element 4 (i = 4) is a lower flange end outer surface resistance element 24Da. Further, the resistance element 5 (i = 5) is a stud 26A. Further, the resistance element 6 (i = 6) is the first inner surface 30Aa of the face bearing plate. Further, the resistance element 7 (i = 7) is a joint reinforcing bar 28. These resistance elements are collectively referred to as "resistance element i".

Further, in this embodiment, the reaction force of the resistance element i is defined as those represented by the product of the stiffness k _i and the amount of deformation of the resistance element i. Further, the elastic rotation center 24Ea of the beam end 24 arranged inside the concrete 32 of the column 10 is the sum of the reaction forces of the resistance element i accumulated for i = 1 to 7 in consideration of the action direction, and the steel frame. It can be obtained as a point at which the shearing force (that is, external force) acting on the joint portion due to the vertical load in the −Z direction supported by the beam 20 is balanced.

When an axial force in the X direction as an external force acts on the beam, the elastic rotation center 24Ea also satisfies the balance between the axial force and the X-direction component of the reaction force of the resistance element i. Can be sought. The "elastic rotation center 24Ea" means the rotation center 24E in a state where the reaction force of the resistance element i and the external force are balanced.

Further, in the present embodiment, the elastic rotation center 24Ea is set as a point where the following two types of balance are simultaneously realized.

Specifically, first, in the elastic rotation center 24Ea, the upper flange end outer surface resistance element 24Aa, the upper flange end inner surface resistance element 24Ba, the lower flange end inner surface resistance element 24Ca, and the lower flange end outer surface resistance element 24Da. On the other hand, the sum of the reaction forces in the Z direction due to the bearing pressure acting on the concrete 32 of the column 10 is balanced with the shearing force acting on the joint due to the vertical load in the −Z direction acting on the steel beam 20. The vertical load is an external force.

At the same time, at the elastic rotation center 24Ea, the sum of the reaction force in the X direction due to the bearing pressure acting from the concrete 32 of the column 10 and the reaction force of the joint reinforcing bar 28 with respect to the stud 26A is the sum of the reaction force of the joint reinforcing bar 28, which is the face bearing plate 30. It balances with the reaction force in the X direction due to the bearing pressure acting on the concrete 32 of the pillar 10 with respect to the first inner surface 30Aa of

Further, the distance between the action point of the representative displacement of the resistance element i and the elastic rotation center 24Ea is set as "x _{d, i} ". The distances x _{d and i} are not illustrated in FIGS. 1 to 17, but specific settings will be described in detail in FIGS. 6 and 2.31 which will appear later.

The "representative displacement" will be explained later. Although not shown, the "representative displacement point of action" is the upper flange end outer surface resistance element 24Aa, the upper flange end inner surface resistance element 24Ba, the lower flange end inner surface resistance element 24Ca, and the lower flange end outer surface. The center point of each of the resistance elements 24Da in the X direction can be adopted.

For example, when the total length of the upper flange end outer surface resistance element 24Aa illustrated in FIG. 1 in the X direction is 200 mm, both ends are set as the "representative displacement action point" of the upper flange end outer surface resistance element 24Aa. A center point 100 mm away from the X direction can be adopted.

Further, the distance between the center of gravity of the reaction force of the resistance element i and the elastic rotation center 24Ea is set as "xl _{, i} ". Then, in the present embodiment, the rotational rigidity of the joint portion 14 is calculated by the following equation 1.

Here, the "center of gravity of the reaction force" in the setting of the distances x _{l and i} is the moment acting on the center of rotation by the distributed load w acting on the region s having a certain length or a certain area. It refers to the line of action of a virtual concentrated load p that gives an equivalent moment. However, for the virtual concentrated load p, the distance from the center of rotation to the action line is set, assuming that the distributed load w is the same as the value integrated in the region s. For example, the joint reinforcing bar 28 as the resistance element i intersects the plane parallel to the XY plane at the position dr-shifted from the upper surface of the slab 22 in the −Z direction in the XZ plane shown in FIG. The line can be set as the center of gravity of the reaction force. According to Equation 1, for a joint portion of an arbitrary detail having a plurality of resistance elements, the characteristics of each resistance element and the rotational rigidity of the joint portion can be uniquely associated with each other. The distances x _{l and i} will be specifically described later with reference to FIG. 1 and Equation 1.21.

By the above procedure, the rotational rigidity _Sj of the joint can be obtained from the characteristics of each resistance element of the joint. The bending moment acting on the joint is uniquely determined from the obtained rotational rigidity of the joint, the bending rigidity of the beam, the span of the beam, and the load supported by the beam. The bending moment acting on this joint is defined as the required moment proof stress _{Mj, Ed} of the joint. In order not to damage the joint, it is necessary that the required moment strengths _{Mj and} _Ed do not exceed the maximum moment strengths _{Mj and Rd} possessed by the joint described later. Here, by adjusting the beam cross-sectional shape, each resistive element of the joint, to adjust the rotational stiffness S _j of the joint portion, by adjusting the span of the rotational stiffness S _j and the beam joints, the joint The required moment proof stress _{Mj, Ed} can be adjusted.

Further, in the present embodiment, the reaction force of the resistance element i is regarded as the maximum reaction force _{Fi, Rd} that can be borne by the resistance element i. Further, the moment strength of the joint portion 14 is expressed as " _{Mj, Rd} ". Further, an arbitrary rotation center 24E is assumed, and the distance between the assumed rotation center 24E and the action point of the reaction force is set as "x _{u, i} ". Further, " _{Mj, Rd} " is calculated using the following equation 2 with the two variables, the X coordinate and the Y coordinate, which are the positions of the rotation center 24E.

Then, the moment strength of the joint portion 14 is set to be the same as the minimum value of the maximum moment strength _{Mj and Rd} calculated by the following equation 2. In the calculation of Equation 2, one or more values of proof stress _{Mj and Rd} are calculated by using two X-coordinates and Y-coordinates of the rotation center 24E as variables. Finally, the minimum value is selected from the calculated maximum moment proof stress _{Mj and Rd} values. Therefore, as described above, the rotation center 24E can be arbitrarily assumed in the calculation.

According to Equation 2, the maximum proof stress of each resistance element and the maximum proof stress of the joint can be uniquely associated with each other at the joint of any detail having a plurality of resistance elements.

In Equation 2, the rotation center 24E at the position where the values of the maximum moment proof stress Mj and _Rd are minimized is defined as the "ultimate rotation center 24Eb". That is, in the process of calculation of Equation 2, the rotation center 24E shifts from the state of the "elastic rotation center 24Ea" to the state of the "ultimate rotation center 24Eb". Further, in the "ultimate rotation center 24Eb", the balance between the reaction force of the resistance element i and the external force is not always established.

Like the joint portion 14 between the column 10 and the beam 12 described above, the steel frame beam 20 is joined to the column 10 in a semi-rigid joint state, and the cross-sectional dimensions of the additional member and the beam 12 including the resistance element. And, if the length of the beam 12 is set appropriately, it is possible to impart appropriate rotational rigidity and strength to the beam end portion 24. Next, a method of designing the beam-column joint will be described. The beam-column joint is a joint 14 between the column 10 and the beam 12.

(Evaluation method of rotational rigidity of joint portion 14)
First, a method for quantitatively evaluating the rotational rigidity of the joint portion 14 will be described. Based on the evaluation of the rotational rigidity of the joint portion 14, the dimensions of each portion of the steel frame beam 20, additional members, and the like can be designed. Then, the rotational rigidity of the joint portion 14 can be set to a desired value by constructing the joint portion 14 using the dimensions of each portion of the designed steel frame beam 20, additional members, and the like.

Here, if the rotational rigidity S _j (Nmm / rad) of the joint portion 14 is defined as the rotational resistance (N mm) per unit rotation angle (rad) of the beam end portion 24 at the joint portion 14, the rotational rigidity S _j is defined. Is expressed by the following equation 1.1. Incidentally, _{"M j"} in formula 1.1 is a rotational resistance of the beam-portion 24 (Nmm). Further, “φ _j ” in the equation 1.1 is the rotation angle (rad) of the beam end portion 24.

As shown in FIG. 1, the deformation state of the joint portion 14 includes the rigid body rotation of the beam end portion 24 of the steel frame beam 20 and the deformation of each resistance element that restrains (that is, opposes the rotation) the rotation of the steel frame beam 20. The amount of deformation δ _i (mm) of the resistance element i is expressed by the following equation 1.2, assuming that it is composed of.

“X _{d, i} ” in Equation 1.2 is the distance (mm) from the action line of the representative displacement of the resistance element i to the elastic rotation center of the beam end 24, that is, the action line of the representative displacement of the resistance element i. And the distance from the elastic rotation center of the portion of the steel beam arranged inside the concrete of the column. Here, the representative displacement represents the displacement at the point of action of the reaction force when the reaction force of the resistance element acts on one point. When the reaction force of the resistance element acts as a stress distributed linearly or planarly, the representative displacement is a uniform stress distribution equivalent to the value obtained by dividing the distributed reaction force by line integral or surface integral, respectively. Represents a virtual displacement at the center of action of a uniform stress distribution, assuming.

Reaction force _{F i} of the resistive element i can be calculated by the product of the amount of deformation of the resistance element i [delta] _i and stiffness _k i (N / mm), the formula 1.3 below.

A reaction force F _i in all of the resistive elements, the distance x _l from the center of gravity of the reaction force of the resistance element i to be described later to the elastic rotation center of the beam end _24, the sum of the product of _{i (mm),} the joint It is obtained as the rotation resistance M _j (N mm) and is represented by the following equation 1.4. The distances x _{l and i} are the distances between the center of gravity of the reaction force of the resistance element i and the elastic center of rotation of the portion of the steel beam arranged inside the concrete of the column.

Further, by substituting Equation 1.2 and Equation 1.3 into Equation 1.4, the following Equation 1.5 is obtained.

Further, from the relationship between the formula 1.5 and the formula 1.1, the following formula 1.6 (that is, the formula 1) is established.

In order to obtain the rotational rigidity of the joint portion 14 by the above method, it is necessary to specify the position of the elastic rotation center of the rigid body rotation of the beam end portion 24 of the steel frame beam 20 in the model. Since the object is elastic, it is assumed that each resistance element of the joint 14 undergoes reversible deformation with a linear load deformation relationship for any angle of rotation. Then, the balance condition between the sum and the external force of the internal forces F _i junction 14, it is possible to obtain the elastic rotation center. As the external force, at least one of the beam axial force N (N) and the beam shear force V (N) can be applied.

The resistance element in the joint portion 14 is an element that generates a reaction force against the rotation of the beam end portion 24 of the steel frame beam 20. Specifically, as the resistance elements, as described above, the tensile resistance of the joint reinforcing bar 28 arranged in the concrete 32 of the slab 22 and the column 10, and the pulling out of the stud 26 in the joint 14 (inside the column). The resistance, the bearing resistance between the upper and lower surfaces of the upper and lower flanges 20A of the steel beam 20 and the upper and lower surfaces of the lower flange 20B and the concrete 32 of the column 10, and the bearing resistance between the face bearing plate 30 and the concrete 32 of the column 10 are set. it can.

In addition, slip resistance due to friction at the bolt joint connecting the web 20C of the steel beam 20 and the fin plate 36 of the column 10, shear deformation resistance of the bolt 34 due to bearing pressure, local deformation resistance of the bolt hole into which the bolt 34 is inserted, The shear resistance of the fin plate 36 and the like can also be set. In this embodiment, an elastic load-deformation relationship (elastic rigidity) is assumed for each resistance element.

In the present embodiment, among the above, the tensile resistance of each joint reinforcing bar 28 arranged in the slab 22 and the concrete 32 of the column 10, the pull-out resistance of the stud 26 in the joint 14 (inside the column), and the steel frame. The bearing resistance between the upper and lower surfaces of the upper flange 20A of the beam 20 and the concrete 32 of the column 10, the bearing resistance between the upper and lower surfaces of the lower flange 20B and the concrete 32 of the column 10, and the concrete of the face bearing plate 30 and the column 10. The bearing resistance with 32 was set as the main resistance element. Hereinafter, the elastic rigidity of each resistance element will be described.

(Elastic rigidity of joint reinforcing bar 28)
The elastic rigidity with respect to the tensile resistance of the joint reinforcing bar 28 arranged in the slab 22 or the concrete 32, that is, the elastic rigidity _kr (N / mm) of the joint reinforcing bar 28 is the elongation of the joint reinforcing bar 28. u _r (mm), the tensile force _T r (N), and, using the _{k slip,} which will be described later, can be expressed by the formula 1.7 below. Note that in FIG. 1, the elongation u _r of the joint reinforcement 28 is illustrated.

Further, a _{r (mm} 2) the entire cross-sectional area of the joint reinforcement 28 within the effective width of the slab ^22, the Young's modulus E _r of the joint reinforcement _28, the stress of the reinforcing bars corresponding to the elongation u _r sigma _{When r} (N / mm ² ) and strain are set as ε _r , respectively, the following equations 1.8 and 1.9 are further established.

Here, within the effective width of the joint reinforcement 28, strain epsilon _r and elongation u _r is assumed to be constant irrespective of the position in the width direction. Therefore, Similarly, the effective length h _r of the joint reinforcement 28, defines a constant length irrespective of the slab 22 widthwise position. This definition, elongation _{u r} and strain epsilon _r is associated with formula 1.10 or less.

In formula 1.10, in the range of the effective length h _r around the core of the pillar 10, the strain of the joint reinforcement 28 is assumed to be uniform, and. “Α” in the formula 1.10 is a correction coefficient of the joint length according to the moments on both sides.

The value of the correction coefficient α is based on "Appendix A.2" of Public Document 1 "EN1994-1-1: 2004 Eurocode 4: Design of composite steel and concrete structures Part 1-1: General rules and rules for buildings". Set. For example, when a symmetrical negative bending moment (M _{j, Ed1} = M _{j, Ed2} ) acts on both sides, the value of the correction coefficient α is 0.5. When the moment on one side is zero (M _{j, Ed1} > M _{j, Ed2} = 0), the value of the correction coefficient α is 3.6. Further, 0.5 is adopted as the lower limit value of the correction coefficient α, and 3.6 is adopted as the upper limit value. Then, the calculation is performed by the following equations 1.11 to 1.15 according to the ratio of the moments on both sides (M _{j, Ed1} > M _{j, Ed2} ).

(I) Correction coefficient α for _{Mj and Ed1}

(Ii) Correction coefficient α for _{Mj and Ed2}

Here, the moment is positive in the direction of negative bending (that is, the direction in which the beam becomes convex upward).

As shown in FIG. 2, in the strain history of the joint reinforcing bar 28, among the studs 26 connecting the steel beams 20 and the slab 22 on both sides of the joint 14, the distance between the studs 26 closest to the column 10 is determined. It is set to be equal to the effective length h _r. Further, since a substantially symmetrical negative bending moment acts on both sides of the joint portion 14, the correction coefficient α is set to 0.5. As a result, the strain ε _{r, calc} of the joint reinforcing bar 28 calculated under the assumption of plane holding (Navier Hypothesis) and the experimental strain in the range where the moment-rotation angle relationship of the joint 14 shows elastic behavior. However, it was confirmed that they were almost the same. Based on this result, the effective length h _r, of the stud 26 connecting the steel beams 20 and the slab 22 can be set as a distance between the closest to the pillar.

From the above, by substituting Expression 1.8 to Formula 1.10 Formula 1.7, the elastic stiffness _{k r,} can be calculated by Equation 1.16 below.

“K _slip ” in the formula 1.16 is a reduction coefficient (0 ≦ k _slip ≦ 1) of the rigidity of the joint reinforcing bar 28 in consideration of the deformation of the stud 26, and the slab 22 and the steel beam due to the deformation of the stud 26. The larger the relative deviation of 20, the smaller the value. The reduction coefficient k- _slip is based on "Appendix A.2" of Public Document 1 "EN1994-1-1: 2004 Eurocode 4: Design of composite steel and concrete structures Part 1-1: General rules and rules for buildings". It can be calculated by the formulas 1.17 to 1.20 of.

Here, in the formulas 1.17 to 1.20, “l _h ” is the length of the section (negative bending section) from the joint portion 14 to the inflection point in the length direction of the steel frame beam 20. Further, "N" is the number of studs 26 (shear connectors) included in the concrete 32a of the slab 22 within _{l h.} Further, "k _sc " is the shear rigidity (N / mm) per stud 26.

Further, "h _s " is the distance from the center of action of the compressive force (compressive force due to the bearing pressure between the face bearing plate 30 and the concrete 32 of the column 10 described later) to the joint reinforcing bar 28 ( mm). Further, "d _s" is the distance from the junction reinforcement 28 to the center of gravity of the cross section of the steel beam 20 (mm). Further, “I _a ” is the moment of inertia of area (mm ⁴ ) of the steel frame beam 20. Moreover, _{"E a"} is the Young's modulus of the steel beam 20 (N / mm ^2).

Further, the distance x _{d, i} for calculating the displacement of the joint reinforcing bar 28, that is, the action line of the representative displacement of the resistance element i, and the elastic rotation of the portion of the steel beam arranged inside the concrete of the column. The distance from the center is expressed by the following equation 1.21. Further, the length of the arm for calculating the moment resistance due to the reaction force, that is, the distance between the center of gravity of the reaction force of the resistance element i and the elastic rotation center of the portion of the steel beam arranged inside the concrete of the column. Similarly _, x _{l and i} are represented by the following equation 1.21.

Here, as shown in FIG. 1, “x _n ” in the equation 1.21 is between the elastic rotation center of the joint portion 14 and the surface of the slab 22 (that is, the upper surface of the slab 22 in FIG. 1). It is a component (mm) parallel to the vertical axis (Z axis) at the distance of. Further, "d _r" in the equation 1.21 is the center of the cross section of the joint reinforcement 28 (In the case of multi-layer reinforcement, their center of gravity) at a distance from to the surface of the slab 22, the vertical direction It is a component (mm) parallel to the axis (Z axis) of. As can be seen from Equation 1.21, in the present embodiment, the distance x _{d, i} and the distance x _{l, i} are equal.

(Elastic rigidity against shear of studs in columns)
The elastic rigidity with respect to the pull-out resistance of the stud 26 in the joint portion 14 (inside the pillar), that is, the elastic rigidity k _st (N / mm) with respect to the shear of the stud in the pillar is determined by the pull-out resistance T _st (N) of the stud 26. It can be obtained based on the deviation u _st (mm) of the stud 26. The pull-out resistance T _st of the stud 26 is represented by the following formula 1.22, and the displacement _{ust of the} stud 26 is represented by the following formula 1.23.

Here, "T _st " in the formula 1.22 represents the pull-out resistance (N) of the stud 26 (see FIG. 1). Further, “ _φst ” in Equation 1.22 represents the diameter of the stud 26 (in the case of a headed stud, the diameter of the shaft portion (mm)) (see FIG. 1). Further, "n _st " in the formula 1.22 represents the number of studs 26 (see FIG. 1). Further, “ _ust ” in the formula 1.22 represents the deviation (mm) of the stud 26 (see FIG. 1). Further, “D _s ” in the formula 1.23 represents the total thickness (mm) of the slab 22 including the deck (see FIG. 1).

The formula 1.22 relating to the shear rigidity of the stud 26 is an empirical formula presented by Inoue et al. In the published document 2 “Ichiro Inoue: Current Status and Prospects of Headed Studs, Concrete Engineering, Vol. 34, No. 4, 1996.4”. Is. The shear rigidity of the stud 26 is given in proportion to the diameter of the stud 26. The coefficient "9.8" in equation 1.22 has a dimension of "N / mm ² ".

As the shear modulus k _sc used in Equations 1.18 and 1.19, Public Document 1 "EN1994-1-1: 2004 Eurocode 4: Design of composite steel and concrete structures Part 1-1: General rules and rules for The value described in "Appendix A.3" of "buildings" (100 kN / mm for φ19 stud) may be used.

From equation 1.22, the elastic stiffness _kst (N / mm) due to shearing of the stud 26 in the column 10 is expressed by the following equation 1.24.

Further, a value for calculating the displacement of the stud 26 in the column 10, that is, the distance between the action line of the representative displacement of the resistance element and the elastic rotation center of the portion of the steel beam arranged inside the concrete of the column. x _{d and i} are represented by the following equation 1.25. Further, the length of the arm for calculating the moment resistance due to the reaction force of the stud 26 in the column 10, that is, the center of gravity of the reaction force of the resistance element and the elastic rotation arranged inside the concrete of the column in the steel beam. The distances x _{l and i from the} center are similarly expressed by the following equation 1.25.

(Elastic rigidity due to bearing pressure between beam flange surface and concrete)
Next, regarding the elastic rigidity of the upper and lower surfaces of the upper flange 20A of the steel beam 20 and the concrete 32 of the column 10, and the bearing resistance of the upper and lower surfaces of the lower flange 20B and the concrete 32 of the column 10. The elastic rigidity will be described. That is, the elastic rigidity due to the bearing pressure of the beam flange surface and concrete will be described.

First, the reaction force of the bearing surface and the displacement of the bearing surface in the compression direction when the steel plate and concrete are under uniform bearing stress are formulated.

In Publicly known Document 3 "EN1993-1-8: 2005 Eurocode 3: Design of steel structures Part 1-8: Design of joints, BSI, 2010", a steel plate when the steel plate and concrete are under uniform bearing stress. The elastic rigidity k _c (N / mm) due to the bearing pressure between the surface and the concrete is given by the following equation 2.1.

Here, “b _eff ” in Equation 2.1 is the width (mm) of the effective bearing region. Further, “l _eff ” in Equation 2.1 is the distance from the center of elastic rotation to the edge of the effective bearing region (the length of the effective bearing region (mm)). Further, “b _eff × l _eff ” in Equation 2.1 represents the effective bearing area (mm ² ) of the concrete 32 (see FIG. 5). Moreover, _{"E c"} in formula 2.1 is a Young's modulus of the concrete (N / mm ^2).

“Α _c ” in Equation 2.1 is, for example, a value that depends on the Poisson ratio in the publicly known document 4 “Lambe TW, Whitman RV: Soil Mechanics, MIT, John Wiley & Sons, Inc., New York, 1969”. is there. Further, "α _c " is, for example, the value of the following equation 2.2 in the publicly known document 5 "Martin Steenhuis et al .: Concrete in compression and base plate in bending, HERON Vol. 53, No. 1/2, 2008". Will be disclosed as. Further, for "α _c ", for example, a value calculated by the following equation 2.3 can be adopted in consideration of the rigidity reduction rate of 1.5 due to the filling property of the mortar between the steel material and the concrete.

When Equation 2.3 is transformed into the general Hooke's equation: P = kδ, the following Equation 2.4 is established.

Here, "P _cl " in the equation 2.4 is the total reaction force due to the bearing pressure (value (N) obtained by integrating the reaction force in the effective bearing pressure region with the effective bearing pressure area). Further, “δ _c ” in Equation 2.4 is the displacement (mm) of the bearing interface in the compression direction. If the uniform average bearing stress of the effective bearing area is set to σ _c (N / mm ² ), Equation 2.4 can be further transformed into the form of Equation 2.5 below.

In the half space of the concrete 32 that receives the bearing pressure, the actual strain of the concrete 32 becomes zero at infinity from the bearing surface of the concrete 32 with respect to the displacement δ _c . On the other hand, it is assumed that a constant strain acts in the range of effective depth D _{c, eff} (mm) equivalent to this. Then, the strain ε _{c, eff} of the concrete 32 and the displacement δ _c are associated with each other by the following equation 2.6.

Then, from Equation 2.5 and Equation 2.6, the effective depths D _{c and eff} can be defined by the following Equation 2.7, which does not depend on the magnitude of strain.

Regarding the bearing pressure between the steel beam 20 (beam end 24) embedded in the concrete 32 of the column 10 in the joint 14 and the concrete 32, the farther the distance from the elastic rotation center of the beam end 24 is, the more Subduction due to bearing pressure (displacement of bearing bearing interface) increases. Therefore, the formula of the above-mentioned publicly known document 3 “EN1993-1-8: 2005 Eurocode 3: Design of steel structures Part 1-8: Design of joints, BSI, 2010 cannot be used as it is. Here, FIG. 3 And, as shown in FIG. 4, when the bearing surface has a linear stress gradient, a method for calculating the rigidity using Eq. 2.1 is derived.

When the bearing interface has the displacement distributions shown in FIGS. 3 and 4, the total reaction force P _c2 (N) received by the bearing surface can be calculated by the following equation 2.8. Note that "P _{c2, t} " in FIG. 3 is the total reaction force on the upper flange side, and can be calculated by replacing "P _c2 " in the following equation 2.8 with "P _{c2, t} ". Further, "P _{c2, b} " in FIG. 3 is the total reaction force on the lower flange side, and similarly, "P _c2 " in the following equation 2.8 is replaced with "P _{c2, b} " for calculation. it can.

“Σ _c (y)” in Equation 2.8 is the reaction force distribution (N / mm ² ) per unit area of concrete on the bearing surface.

Further, from FIG. 4, it is assumed that the following equations 2.9 to 2.11.

Here, "ε _c (y)" in Equations 2.9 to 2.11 is the strain distribution of concrete on the bearing surface. Further, "δ _c (y)" in the formulas 2.9 and 2.10 is the displacement distribution (mm) of the bearing surface in the compression direction.

Substituting Equations 2.9 to 2.11 into Equation 2.8, the following Equation 2.12 holds.

Assuming that the reaction force according to equation 2.12 is equivalent to the reaction force according to equation 2.4, the following equation 2.13 holds.

“Δ _{cP, eff} ” in Equation 2.13 is the representative displacement (mm) of concrete on the bearing surface.

Therefore, even when the bearing surface has a linear stress gradient, the reaction force is obtained by applying Equation 2.4 in a uniform bearing state using the displacement calculated in Equation 2.13. Can be done.

Next, the moment (rotational resistance) _Mc2 (Nmm) due to the bearing reaction force when the bearing surface has a linear stress gradient can be calculated by the following equation 2.14.

Further, the moment (rotational resistance) _Mc1 (N mm) when a uniform stress distribution is assumed on the bearing surface can be calculated by the following equation 2.15.

Assuming that the moment according to equation 2.14 is equivalent to the moment according to equation 2.15, the following equation 2.16 holds.

“Δ _{cM, eff} ” in Equation 2.16 is the displacement (mm) of the bearing surface in the compression direction at the distance for moment calculation.

Therefore, even when the bearing surface has a linear stress gradient, the equation 2.15 in a uniform bearing state can be applied by using the displacement calculated by the equation 2.16. From the above, the rigidity k _{c of the} bearing surface can be evaluated from the equations 2.12 and 2.13 by the following equation 2.17, which is the same as the equation 2.1.

The width b _eff of the effective bearing capacity region, the reaction force due to bearing capacity as the edge of Bearing faces by bending a plate is set in consideration of being attenuated. Regarding the flange of the steel frame beam 20 (beam end 24) embedded inside the pillar 10, when concrete 32 is filled between the upper and

lower flanges

20A and 20B, the upper and

lower flanges

20A and 20B are bent. By assuming that it is restrained by the concrete 32, the entire widths of the upper and

lower flanges

20A and 20B are considered to be effective.

Further, a value for calculating the representative displacement due to the bearing pressure between the upper and

lower flanges

20A and 20B of the steel beam 20 (beam end 24) embedded in the column 10 and the concrete 32, that is, the representative displacement of the resistance element i. The distance x _{d, i} between the line of action and the elastic rotation center of the portion of the steel beam arranged inside the concrete of the pillar is the effective bearing pressure from the elastic rotation center from equations 2.13 and 2.14. It is expressed by the following equation 2.18 using the distance l _eff to the edge of the region.

Further, the length of the arm for calculating the moment resistance, that is, the distance between the center of gravity of the reaction force of the resistance element and the elastic rotation center of the portion of the steel beam arranged inside the concrete of the column x _{l, i.} Is expressed by the following equation 2.19 from equations 2.13 and 2.14 using the distance l _eff from the center of elastic rotation to the edge of the effective bearing region.

In the case of FIG. 3, the length of the effective bearing region of the upper flange end outer surface resistance element 24Aa of the upper flange 20A is exemplified by "l _{eff, t} ". Further, the length of the effective bearing region of the upper flange end inner surface resistance element 24Ba of the upper flange 20A is exemplified by "l _{eff, b} ". Further, the length of the effective bearing region of the lower flange end inner surface resistance element 24Ca of the lower flange 20B is exemplified by "l _{eff, t} ". Further, the length of the effective bearing region of the lower flange end outer surface resistance element 24Da of the lower flange 20B is exemplified by "l _{eff, b} ". In addition, the width of the effective bearing region is exemplified by " _beff ".

(Elastic rigidity due to bearing pressure of face bearing plate and concrete)
Next, the elastic rigidity related to the bearing resistance between the face bearing plate 30 and the concrete 32 of the column 10 will be described.

For the face bearing plate 30, it is necessary to properly consider the restraint conditions around the bearing surface. Here, the out-of-plane deformation restraint of the face bearing plate 30 by the web 20C is ignored. As shown in FIG. 6, on the axis of the lower flange 20B, referring to the above-mentioned publicly known document 3 “EN1993-1-8: 2005 Eurocode 3: Design of steel structures Part 1-8: Design of joints, BSI, 2010”. It is assumed that the compressive force acting is transmitted to the concrete 32 through the effective bearing area of the face bearing plate 30.

The length _{l eff} and a width _{b eff} of the effective bearing capacity region, the width _B f of the lower flange 20B of the steel beam 20 (mm), the thickness of the web 20C _t w (mm), thickness of the face bearing plate 30 t _{Using fb} (mm), the compressive strength _fjd (N / mm ² ) of the concrete 32 against the local bearing pressure, and the yield stress _fy (N / mm ² ) of the face bearing plate 30, the following equation 2.20 And it is calculated by Equation 2.21.

“Γ _M0 ” in Equation 2.21 is a reduction coefficient in consideration of the variation in the strength of the steel material. The value of the reduction coefficient γ _M0 is set here as “1.0”.

According to the above-mentioned publicly known document 4 “Lambe TW, Whitman RV: Soil Mechanics, MIT, John Wiley & Sons, Inc., New York, 1969”, in Equation 2.21, the maximum bending moment of the cantilever is elastic limit bending. It is the back calculation of the beam length when the moment is reached. Further, considering the bending of the steel plate having the bearing surface of the T stub with the concrete, a model in which the T stub receives an evenly distributed load equal to the bearing strength of the concrete as a cantilever is assumed. That is, Equation 2.21 represents the length of the effective bearing region used in the calculation of the bearing strength.

On the other hand, in the above-mentioned publicly known document 4 "Lambe TW, Whitman RV: Soil Mechanics, MIT, John Wiley & Sons, Inc., New York, 1969", the dimensions of the effective bearing region used for calculating the rigidity of the bearing surface are described. The length _Cfl (mm) of the net bearing region in consideration of the bending deformation (sinusoidal waveform) of the steel sheet is expressed by the following equation 2.23. The length _{C fl} and length of the effective pressure bearing area that is converted to an equivalent uniform bearing capacity deformed state _C r _{(mm) = l eff} can be expressed by equation 2.22 or less. The effective depth h _eq (mm) that defines the strain for bearing deformation is expressed by the following equation 2.24.

Here, "ξ" in the formulas 2.23 and 2.24 is a ratio of the effective depth h _{eq to} the length _Cfl . Further, “α _c ” in Equation 2.24 is used in the above-mentioned publicly known document 3 “EN1993-1-8: 2005 Eurocode 3: Design of steel structures Part 1-8: Design of joints, BSI, 2010” and the above-mentioned. In reference to the publicly known document 5 "Martin Steenhuis et al .: Concrete in compression and base plate in bending, HERON Vol. 53, No. 1/2, 2008", the coefficient was set to α, and the following equation 2.25 was used. expressed.

Therefore, Equation 2.24 is expressed by the following Equation 2.26.

Then, by substituting Equation 2.23 and Equation 2.26 into Equation 2.22, the following Equation 2.27 holds.

On the other hand, in the above-mentioned publicly known document 3 "EN1993-1-8: 2005 Eurocode 3: Design of steel structures Part 1-8: Design of joints, BSI, 2010", Equation 2.21 is used for strength calculation and rigidity calculation. It is said that it may be used for both. This is because the value of Equation 2.21 and the value of Equation 2.27 are obtained in the above-mentioned publicly known document 4 "Lambe TW, Whitman RV: Soil Mechanics, MIT, John Wiley & Sons, Inc., New York, 1969". , Because it is almost the same.

From the above, similarly to the formulas 2.1 and 2.4, the rigidity k _{c, fb} (N / mm) and the reaction force P _{c, fb} (N) of the bearing surface between the face bearing plate 30 and the concrete 32 are determined. It can be calculated by the following equations 2.28, 2.29 and 2.30.

In addition, "δ _{c, fb} " in equation 2.29 means the displacement of the face bearing plate 30.

In addition, "x _{c, fb} " in the formula 2.30 means the distance between the face bearing plate 30 and the concrete 32.

Further, a value for calculating the representative displacement due to the bearing pressure between the face bearing plate 30 and the concrete 32, that is, the action line of the representative displacement of the resistance element i and the portion of the steel beam arranged inside the concrete of the pillar. From FIG. 6 _, the distances x _{d and i} from the elastic rotation center are the thickness D _s (mm) of the slab 22, the height H (mm) of the steel beam 20, and the thickness t _f (thickness t _f ) of the lower flange 20 B of the steel beam 20. It is expressed by the following equation 2.31 using mm) and the distance x _n (mm) measured along the Z direction from the upper surface of the slab 22 to the center of elastic rotation.

Further, the length of the arm for calculating the moment resistance, that is, the distance between the center of gravity of the reaction force of the resistance element and the elastic rotation center of the portion of the steel beam arranged inside the concrete of the column x _{l, i.} Is also expressed by the following equation 2.31 which is the distance measured along the thickness of 20B.

In the above description, the deformed state of the joint portion 14 between the column 10 and the beam 12 is modeled by the rigid body rotation of the beam end portion 24 of the steel frame beam 20 which is a steel frame portion, and moment resistance is generated between steel and concrete. The calculation method of the elastic rigidity (that is, the rotational rigidity) of the bearing portion is described.

(Method of evaluating the yield strength of the joint portion 14)
Next, a case where a beam-column joint is designed by evaluating the proof stress of the joint 14 will be described. The proof stress M _{j, Rd} of the joint portion 14 is the product of the distance x _{u, i} (mm) from the resistance element i to the rotation center of the beam end portion 24 and the maximum reaction force _{Fi, Rd} (N) of the resistance element i. It is calculated by the following equation as the sum of. Further, in the present embodiment, the distance x _u from resistive element i to the rotational center of the beam end _{24, i} is the distance x _u from the center of gravity of the reaction force of the resistance element i to the rotational center of the beam end _{24, i} Is. In the final state of the joint portion 14 between the column 10 and the beam 12, the reaction force of each resistance element that restrains the rotation of the beam end portion 24 of the steel frame beam 20 due to the rigid body rotation of the beam end portion 24 of the steel frame beam 20 All are assumed to have reached maximum capacity.

In Equation 3.1, it is set that each resistance element in the joint portion 14 has a load deformation relationship of perfect rigid plasticity. It is also assumed that all resistance elements are in a state (ie, mechanism) that produces a plastic flow. The moment resistance obtained by this assumption gives a value larger than the true collapse load as the upper bound. Therefore, for an arbitrary center of rotation, a calculation for obtaining the moment resistance is performed using Equation 3.1. Further, in the calculation, the rotation center that minimizes the collapse load is obtained as the ultimate rotation center. The moment resistance when the ultimate center of rotation is obtained is set as the moment proof stress of the joint portion 14 (that is, the maximum moment proof stress M _{j, Rd of the} joint portion 14).

The resistance elements in the joint portion 14 include the tensile resistance of the joint portion reinforcing bar 28 arranged in the slab 22, the pull-out resistance of the stud 26 in the joint portion 14, and the support between the face bearing plate 30 and the concrete 32 of the column 10. The pressure resistance, the bearing resistance between the upper flange 20A of the steel beam 20 and the concrete 32 of the column 10, and the bearing resistance between the lower flange 20B and the concrete 32 of the column 10 can be set.

Other resistance elements include sliding resistance due to friction at the bolt joint connecting the web 20C of the steel beam 20 and the fin plate 36 of the column 10, shear deformation resistance of the bolt 34 due to bearing pressure, local deformation resistance of the bolt hole, and , The shear resistance of the fin plate 36 can be set.

For each resistance element, the proof stress _{Fi and Rd} as the reaction force that causes the plastic flow are required, but among the above-mentioned resistance elements, the proof stress is relatively large and cannot be ignored in the calculation of the moment resistance. , Tension resistance of the joint reinforcing bar 28 arranged in the slab 22, pull-out resistance of the stud 26 in the joint 14, bearing pressure resistance between the face bearing plate 30 and the concrete 32 of the column 10, and the upper flange of the steel beam 20. The proof stress of 20A and the concrete 32 of the pillar 10 and the proof stress of the lower flange 20B and the concrete 32 of the pillar 10 will be described. The moment resistance may be obtained by appropriately considering other resistance elements.

(Strength of joint reinforcement)
As shown in FIG. 10A, the proof stress of the joint reinforcing bar 28 arranged in the slab 22 corresponding to the reaction forces _Fi and _Rd , that is, the proof stress of the joint reinforcing bar 28 Fr _{, Rd} (N). ) Is expressed by the following equation 3.2 using the total cross-sectional area a _r (mm ² ) of the joint reinforcing bar 28 within the effective width of the slab 22 and the yield stress fr _{, y} (N / mm ² ). it can.

Alternatively, the tensile strength _{fr, u} may be used instead of the yield stress _{fr, y} .

Further, the length of the arm for calculating the moment resistance due to the reaction force of the joint reinforcing bar 28, that is, the distance between the rotation center of the portion of the steel beam arranged inside the concrete of the column and the action line of the reaction force. x _{u and i} are represented by the following equation 3.3. The distances x _{u and i} are the distances from the center of gravity of the reaction force of the resistance element i to the center of rotation of the beam end portion 24.

“X _{u, n} ” in Equation 3.3 is a component (mm) of the distance between the center of rotation of the joint portion 14 and the surface of the slab 22 parallel to the vertical axis (Z axis). Further, " _dr " in Equation 3.3 is from the center of the cross section of the joint reinforcing bar 28 (when the joint reinforcing bar 28 is a multi-layered reinforcing bar, the center of gravity of the multi-layered reinforcing bar) to the slab 22. It is a component (mm) of the distance to the surface parallel to the vertical axis (Z axis).

(Shear strength of studs in columns)
Next, as shown in FIG. 10A, the shear strength with respect to the pull-out resistance of the stud 26 in the joint 14 (inside the column) corresponding to the reaction forces _Fi and _Rd , that is, the maximum proof stress F of the stud 26 in the column. _{st and Rd} (N) will be described. The maximum yield strength F _{st, Rd} (N) is described in "Volume 4, Section 4.2, 4.2" of Architectural Institute of Japan 6 "Architectural Institute of Japan: Guidelines for Designing Various Synthetic Structures and Explanations, 2nd Edition, 2010.11". The formula for calculating the shear strength of anchor bolts with anchor bolts is used.

The maximum yield strengths F _{st and Rd} are the yield strength T _st1 determined by the shear strength of the stud 26, the yield strength T _st2 determined by the bearing strength of the concrete 32, and the yield strength T determined by the cone-shaped fracture of the concrete 32 of the pillar 10 on the front surface of the stud 26. _The smaller value of _st3 is adopted.

(I) Shear strength determined by the shear strength of the studs The shear strength T _st1 (N) is the following equation 3. Using the number n _st of the studs 26 and the shear strength q _a1 (N) per stud 26. Given in 4.

“Φ ₁ ” in Equation 3.4 is the reduction coefficient. The value of the reduction factor phi ₁ is herein set to "1.0". “ _S σ _qa ” in Equation 3.4 is the shear strength (N / mm ² ) of the stud 26. As the value of the shear strength _s σ _qa, a value of 1/3 ^1/2 of the 0.2% yield strength of the material test is used. “ _Sca ” in Equation 3.4 is the cross-sectional area (mm ² ) of the shaft portion of the stud 26.

(Ii) Shear strength proof stress T _st2 (N) determined by the bearing strength of concrete is determined by using the number n _st of the studs 26 and the bearing strength q _a2 (N) of the concrete 32 per stud 26. , Given by Equation 3.5 below.

In Formula 3.5 "phi _2" is the reduction factor of the concrete strength, the value of the reduction factor phi ₂ is herein set to "1.0". “F _cd ” in the formula 3.5 is the compressive strength (N / mm ² ) of the concrete 32 of the column 10. Further, "E _c " in the formula 3.5 is the Young's modulus (N / mm ² ) of concrete. The values of and Young's modulus E _c of compressive strength f _cd, both the value of the material testing is used.

(Iii) Shear strength proof stress T _st3 (N) determined by the cone-shaped fracture of column concrete is given by the following equation 3.6 using the cone-shaped fracture strength q _a3 (N).

“ _C σ _t ” in the formula 3.6 is the tensile strength (N / mm ² ) of the concrete 32 with respect to the cone fracture. In setting the tensile strength _c σ _t , the following equation 3.7 given in Architectural Institute of Japan: Architectural Institute of Japan: Guidelines for Designing Various Synthetic Structures and Explanations, 2nd Edition, November 2010 is used.

“A _qc ” in the formula 3.6 is the effective projected area (mm ² ) of the cone-shaped fracture surface, and is obtained by the following formula 3.8.

“C” in the formula 3.8 is the distance (mm) from the axis of the stud 26, which is the innermost part of the concrete 32 surface of the pillar 10, to the concrete 32 surface of the pillar 10 (see FIG. 7). Further, "s" in the formula 3.8 is the distance (mm) of the studs 26 in the same depth row (see FIG. 7). Further, "n _r " in the equation 3.8 is the number of studs 26 in the same depth row (see FIG. 7).

Further, the length of the arm for calculating the moment resistance due to the reaction force of the stud 26 in the column 10, that is, the rotation center of the portion of the steel beam arranged inside the concrete of the column and the action line of the reaction force. The distances x _{u and i} are expressed by the following equation 3.9.

(Beam flange surface and concrete bearing capacity)
Next, regarding the bearing capacity of the upper flange 20A and the lower flange 20B of the steel beam 20 and the concrete 32 of the column 10, that is, the bearing capacity Fc _{, Rd} (N) of the beam flange surface and the concrete. explain. In the above-mentioned publicly known document 3 "EN1993-1-8: 2005 Eurocode 3: Design of steel structures Part 1-8: Design of joints, BSI, 2010", when the base plate and concrete are under uniform bearing pressure. , The bearing capacity F _{c, Rd} is given by the following equation 3.10.

Here, "b _eff " in the formula 3.10 represents the width (mm) of the effective bearing area of concrete. Further, "l _eff " in the formula 3.10 represents the length (mm) of the effective bearing area of concrete. The width _beff is the same as in the case of the calculated rigidity of the elastic rigidity. On the bearing surface between the upper and

lower flanges

20A and 20B of the steel beam 20 and the concrete 32 of the pillar 10, the out-of-plane deformation of the upper and

lower flanges

20A and 20B by the concrete 32. In consideration of restraint, the entire widths of the upper and

lower flanges

20A and 20B are adopted.

In addition, the length l _eff has a uniform bearing deformation in the above-mentioned publicly known document 3 "EN1993-1-8: 2005 Eurocode 3: Design of steel structures Part 1-8: Design of joints, BSI, 2010". Since it is assumed, the length of the total bearing surface is used (β = 1).

On the other hand, in the case of rotational deformation as shown in FIG. 8A, a stress block in which the stress is in a uniform state is assumed with respect to a state in which there is a stress gradient. Therefore, using the reduction coefficient β, as shown in FIGS. 8A and 8B, the length l _eff is converted into a bearing surface equivalent to the actual stress distribution. On the other hand, the reduction factor beta, for example, a known literature 7 "EN1992-1-1: 2004 Eurocode2: Design of concrete structures Part 1-1: General rules and rules for buildings " in, depending on the compression strength f _cd concrete 32 It is defined by the following equation 3.11.

Further, in the publicly known document 8 "Architectural Institute of Japan: Design and construction of reinforced concrete column / steel beam mixed structure, 1st edition, 2001.1", it is stated that the reduction coefficient β is in the range of 0.6 to 0.85. There is.

Further, “f _jd ” in the formula 3.10 is the compressive strength of the concrete 32 with respect to the local bearing pressure, and is defined by the following formula 3.12.

Here, “λ _c ” in Equation 3.12 is the yield strength addition coefficient with respect to the local bearing pressure. The yield strength premium coefficient λ _c is described in the above-mentioned publicly known document 7 “EN1992-1-1: 2004 Eurocode2: Design of concrete structures Part 1-1: General rules and rules for buildings” and publicly known document 8 “Architectural Institute of Japan: Reinforced concrete columns ・Design and construction of steel beam mixed structure, 1st edition, 2001.1 ”. For example, according to Known Document 7, it can be calculated by the following formula 3.13.

Here, " _Ac0 " in Equation 3.12 is the local effective bearing area (mm ² ). Further, “ _Ac1 ” in the equation 3.12 is the maximum bearing stress distribution area (mm ² ). In the half-space, a projection plane having a similar shape with an effective bearing area A _c0 and having the same normals at the center of the plane is assumed (see FIGS. 9A and 9B). If the outer portion from the edge of the concrete 32 in the projection plane is present, the minus the outer portion is set to the maximum bearing capacity stress distribution area A _c1 (e.g. Model see Figure 9B).

“Β _j ” in Equation 3.12 is a reduction coefficient depending on the material of the bearing surface. The value of the reduction coefficient β _j is set here as “1.0”. When a spread mortar or the like is used, the value of the reduction coefficient β _j can be set to, for example, “2/3”.

Further, the distances x _{u and i} as the lengths of the arms for calculating the moment resistance due to the stress block are the distances l _eff from the center of rotation to the line of action of the resultant force due to the bearing stress from the models of FIGS. 8A and 8B. Is expressed by the following equation 3.14.

In FIGS. 8A and 8B, the length of the effective bearing region of the upper flange end outer surface resistance element 24Aa of the upper flange 20A is exemplified by "l _{eff, t} ". Further, the length of the effective bearing region of the lower flange end outer surface resistance element 24Da of the lower flange 20B is illustrated by "l _{eff, b} ". The upper flange end outer surface resistance elements 24Aa of the effective Bearing region having a width, and the width of the effective Bearing region of the lower flange edge outer face resistance element 24Da, which are all exemplified in the "b _eff".

With respect to the initial rigidity, the concrete 32 inside the upper and

lower flanges

20A and 20B and the concrete 32 outside the upper and

lower flanges

20A and 20B of the concrete 32 of the column 10 are kept integrated, and the inner side of the upper and

lower flanges

20A and 20B also has bearing resistance. Has.

However, at the time of the ultimate proof stress, the upper flange end inner surface resistance element 24Ba of the upper flange 20A and the lower flange end inner surface resistance element 24Ca of the lower flange 20B are set not to be considered in the derivation of the ultimate proof stress.

This is because the concrete 32 is destroyed by the twist between the rectangular portion surrounding the steel beam 20 and the outside of the rectangular portion at the time of the ultimate yield strength, and between the upper and

lower flanges

20A and 20B of the column 10 and the concrete 32 inside. Based on the idea that it is not possible to maintain the unity of. The outside of the rectangular portion is the end portion in the width direction of the upper and

lower flanges

20A and 20B. Further, it is based on the idea that the insides of the upper and

lower flanges

20A and 20B are not effective as resistance elements.

In FIGS. 8A and 8B, the length corresponding to the distance x _{u, i} is exemplified by "x _{u, ct} " for the upper flange end outer surface resistance element 24Aa of the upper flange 20A. Further, with respect to the lower flange end outer surface resistance element 24Da of the lower flange 20B, the length corresponding to the distance x _{u, i} is exemplified by "x _{u, cb} ".

Similarly, in FIGS. 8A and 8B, the reaction force _{F i,} yield strength corresponding to _Rd, for flange end outer face resistive elements 24Aa on the upper flange 20A is exemplified in "Bearing Strength _{F ct, Rd".} Further, the bearing capacity of the lower flange end outer surface resistance element 24Da of the lower flange 20B is illustrated in "F cc _{, Rd} ".

(Concrete bearing capacity of face bearing plate and column)
Then, the reaction force _{F i,} corresponding to _Rd, Bearing Strength _{F c} for Bearing resistance between the concrete 32 of the face bearing plate 30 and the bar _{10, fb,} explaining Rd (N). The bearing capacity F _{c, fb, and Rd} are the same as in the case of the bearing capacity of the beam flange surface and concrete, as described in the above-mentioned publicly known document 3 "EN1993-1-8: 2005 Eurocode 3: Design of steel structures Part 1-8: It is set using the following equation 3.15 of "Design of joints, BSI, 2010". Further, as shown in FIGS. 10A and 10B, it is assumed that the face bearing plate 30 and the concrete 32 are under a uniform bearing pressure state.

Here, "b _eff " in the formula 3.15 is the width (mm) of the effective bearing surface of the concrete 32. Further, "l _eff " in the formula 3.15 is the length (mm) of the effective bearing surface of the concrete 32. Setting the width _{b eff,} as with computation rigidity of the elastic stiffness, the upper and lower flanges 20A, in Bearing surface between the concrete 32 and 20B and the bar 10, the vertical by concrete 32 flange 20A, restraint of out-of-plane deformation of the 20B taken into account , The entire width of the upper and

lower flanges

20A and 20B is adopted.

The length l _eff is described in the above-mentioned public document 3 "EN1993-1-8: 2005 Eurocode 3: Design of steel structures Part 1-8: Design of joints, BSI, 2010" and the above-mentioned public document 5 "Martin Steenhuis". Others: Concrete in compression and base plate in bending, HERON Vol. 53, No. 1/2, 2008 ”can be set using the following equation 3.16.

Here, "t _fb " in the formula 3.16 is the plate thickness (mm) of the face bearing plate 30. Further, “f _jd ” in the formula 3.16 is the compressive strength (N / mm ² ) of the concrete 32 with respect to the local bearing pressure. The compressive proof stress _fjd is the same as that described by Equations 3.12 and 3.13. Further, “ _fy ” in the equation 3.16 is the yield stress (N / mm ² ) of the face bearing plate 30.

Further, "γ _M0 " in the formula 3.16 is a reduction coefficient for considering the variation in the strength of the steel material, and the value of the reduction coefficient γ _M0 is set to "1.0" here. .. For the effective bearing area A _c0 (mm ² ) and the maximum bearing stress distribution area A _c1 (mm ² ) described in Equation 3.13, the projection plane shown in FIG. 11 is assumed. Further, the value of the reduction coefficient β _j is set to “1.0”.

Further, the distances x _{u and i} as the lengths of the arms for calculating the moment resistance due to the stress block are the distances l _eff from the center of rotation to the line of action of the resultant force due to the bearing stress from the models of FIGS. 10A and 10B. Is expressed by the following equation 3.17.

In the above description, a method of predicting the moment proof stress of the joint portion 14 in the ultimate state from the upper bound by accumulating the maximum proof stress of each resistance element has been described. By setting the dimensions of each part of the steel beam 20 and the quantity (presence / absence, if any) and position of the resistance elements based on this method, the moment strength of the joint portion 14 between the column 10 and the beam 12 can be determined. The desired moment strength can be set. That is, it can be adjusted so that the required moment proof stress M _{j, Ed} or more.

(Example 1)
(Comparison of calculation results and experimental results)
In order to confirm the effect of the beam-column joint of the present disclosure, in order to confirm the effect of the beam-column joint of the present disclosure, a load is applied to the beam in the downward -Z direction in the vertical direction with respect to the beam-column joint of the embodiment shown in FIGS. The relationship between the rotation angle and the moment was obtained. Then, the results of calculating the rotational rigidity and the moment strength of the joint using Equations 1 to 3.17 were compared with the experimental results.

The relationship between the moment of the beam end 24 of the steel beam 20 and the angle of rotation at the joint 14 is the initial rotational rigidity _{Sj, ini} (Nmm / rad) and the maximum moment according to the procedures of equations 1 to 3.17. It can be defined by a bilinear model by finding the yield strength M _{j and Rd} (N mm). Here, the elastic limit is set to 2/3 times the maximum moment proof stress _{Mj and Rd} . It is stipulated that when a moment exceeding the set elastic limit acts, the rotational rigidity is lower than the initial rotational rigidity _{Sj, ini} .

Further, the secant rigidity S _j (Nmm / rad) when the maximum moment proof stress M _{j, Rd} (N mm) is established is a trilinear model defined by the value obtained by dividing S _{j, ini} by the rigidity reduction rate η (> 1). It was assumed that it was defined in (see FIG. 12). When the trilinear model is applied, the acting moment of the joint is calculated with the rotational stiffness _{Sj and ini} as the elastic rotational stiffness. Further, when a moment of 2/3 times or less of the maximum moment proof stress _{Mj and Rd} acts, it can be carried out as it is.

Then, the acting moment of the joint is calculated with the rotational rigidity S _{j and ini} as the elastic rotational rigidity, and when a moment exceeding 2/3 times the maximum moment bearing capacity M _{j and Rd} acts, a new split line rigidity S _j is added. The acting moment of the joint was calculated as the bullet rotation rigidity. If the calculated working moment is equal to or less than the maximum moment proof stress _{Mj, Rd} , it is determined that it is feasible, that is, it is within the scope of the claims of the present disclosure. Further, when the calculated action moment exceeds the maximum moment proof stress _{Mj, Rd} , it is determined that it is not feasible, that is, it is outside the scope of the claims of the present disclosure. The rotational rigidity S _{j, ini} and the maximum moment proof stress M _{j, Rd} , η are set by the following equations 4.1, 4.2, and 4.3.

The deformation performance φ _cd shown in FIG. 12 is the minimum value (rad) of the rotation angles φ _{cd and i} when each resistance element reaches the limit of the amount of deformation. When the product of the distance x _{u, i} from the ultimate rotation center to each resistance element and the rotation angle φ _j is equal to the limit of the amount of deformation of each resistance element δ _{u, i} (mm), the rotation angle φ _j is solved. , The minimum rotation angle φ _{cd, i} can be obtained by φ _{cd, i} = δ _{u, i} / x _{u, i} .

(Elastic rigidity and yield strength of joint reinforcement)
In the first embodiment, when the joint reinforcing bar 28 is set as the i = first resistance element, the elastic rigidity _kr (N / mm) and the distance from the elastic rotation center satisfying the balance of the elastic force ( Arm length) x _r (= x _{d, 1} , x _{l, 1} (mm)), distance from the center of rotation to the reinforcing bar at the time of ultimate yield strength (arm length) x _{u, r} (= x _{u, 1)} (Mm)) and the proof stress _{Fr, Rd} (N) were determined using the following formulas 4.4 to 4.11.

The definition of each parameter in the equation is the same as that described in Equations 1 to 3.17. In addition, Table 1 below shows each parameter used for calculating the rigidity and proof stress of the reinforcing bar. In the experiment in Example 1, the conditions shown in Table 1 ( _Er , a _r , h _r , α, N, k _sc , h _s , d _s , l _h , E _a , I _a , ξ, _dr , f using _{_{_{r, y, x n, x}}} u, a _n), _"k r of formula 4.4 to formula _{_{4.11, k slip, K sc,}} ν, ξ, x d, 1, F r, Rd, x _{u, 1} ”was calculated.

(Elastic rigidity and yield strength against shear of studs in columns)
In the first embodiment, when the stud 26 in the column 10 is set as the i = second resistance element, the elastic rigidity _kst (N / mm) due to shearing and the stud from the ultimate rotation center satisfying the balance of the force at the time of elasticity. Distance to root (ie, arm length) x _st (= x _{d, 2} , x _{l, 2} (mm)), distance from center of rotation to reinforcing bar at ultimate strength (ie, arm length) x _{u, st} (= x _{u, 2} (mm)) and proof stress F _{st, Rd} (N) can be obtained by using the following formulas 4.12 to 4.20.

The definition of each parameter in the equation is the same as that described in Equations 1 to 3.17. Table 2 shows the parameters used for calculating the rigidity and proof stress of the column studs. In the experiment in Example 1, the conditions shown in Table 2 (φ _st , n _st , x _n , D _s , φ ₁ , _s σ _qa , _sc a, φ ₂ , f _cd , E _c , c, s, n _r ) To "k ₂ , x _{d, 2} , F _{2, Rd} , x _{u, 2} , T _st1 , T _st2 , T _st3 , _c σ _t , A _qc " in equations 4.12 to 4.20. Was calculated.

(Elastic rigidity and yield strength against the bearing surface of the beam body and concrete)
As shown in FIGS. 13A and 13B, in the first embodiment, the initial rigidity is supported at all four locations (that is, i = 3, 4, 5, 6) on the inner and outer surfaces of the upper and

lower flanges

20A and 20B. It was assumed that pressure resistance would occur. Further, for the maximum proof stress, it was assumed that bearing resistance occurs at all two places (that is, i = 3, 6) only on the outer surfaces of the upper and

lower flanges

20A and 20B.

It is considered that the upper and

lower flanges

20A and 20B maintain the integrity of the inner concrete 32 and the outer concrete 32 with respect to the initial rigidity, and the inner side of the upper and

lower flanges

20A and 20B also has bearing resistance. based on. However, in the final state, the concrete 32 is destroyed by the twist between the rectangular portion surrounding the steel beam 20 and the outside thereof (that is, the upper and

lower flanges

20A, 20B width direction ends), and the inside of the upper and

lower flanges

20A, 20B is Based on the idea that it will not work as a resistance factor.

Elastic rigidity of the bearing pressure between the upper and

lower flanges

20A and 20B and the concrete 32 k _c (N / mm), the distance from the representative point of the bearing pressure displacement of the resistance element i during elasticity x _{d, c, i} ( mm), the distance from the center of rotation to the center of gravity of the supporting pressure (that is, the length of the arm) x _{l, c, i} (mm) that satisfies the balance of the force at the time of elasticity, the center of gravity of the supporting pressure from the center of rotation at the time of the ultimate endurance The distance to (that is, the length of the arm) x _{u, c, i} (mm) and the endurance F _{c, i, Rd} (N) are set using the following equations 4.21 to 4.35. it can. The resistance elements i are all four locations including the inner and outer surfaces of the upper and

lower flanges

20A and 20B (that is, i = 3, 4, 5, 6).

In addition, Table 3 shows each parameter used for calculating the rigidity and proof stress due to the bearing resistance at the interface between the portion of the steel beam embedded in the column concrete and the column concrete. The values shown in Table 3 were used as each parameter in Equations 4.21 to 4.35.

Here, in the formulas 4.21 to 4.35, “B _f ” is the width (mm) of the upper and

lower flanges

20A and 20B of the steel frame beam 20. Further, " _tw " is the plate thickness (mm) of the web 20C of the steel frame beam 20. Further, “t _fb ” is the plate thickness (mm) of the face bearing plate 30. Further, " _Lem " is the embedded length (mm) of the column 10 of the steel frame beam 20 in the concrete 32.

Further, "y _n " in the formulas 4.21 to 4.35 is parallel to the x-axis from the concrete 32 outer surface (face bearing plate 30 side) of the pillar 10 to the elastic rotation center that satisfies the balance of the elastic force. Horizontal distance (mm) in any direction. Further, " _{yu, n} " is a horizontal distance (mm) from the outer surface of the concrete 32 of the pillar 10 to the ultimate rotation center. The outer surface of the concrete 32 of the pillar 10 is the surface on the face bearing plate 30 side.

(Elastic rigidity and yield strength against bearing pressure of face bearing plate and concrete)
In Example 1, the out-of-plane deformation restraint of the face bearing plate 30 by the web 20C was ignored. Further, it is set that the compressive force acting on the axis of the lower flange 20B is transmitted to the concrete 32 as a uniform bearing pressure in the plane through the effective bearing pressure region of the face bearing plate 30. Further, the bearing pressure of the face bearing plate 30 and the concrete 32 was set as the i = 7th resistance element.

In addition, elastic rigidity k _{c, fb} (N / mm), distance from the action line of the representative displacement of the bearing pressure region during elasticity to the center of elastic rotation x _{d, c, fb} (= x _{d, 7} (mm)), The distance from the elastic center of rotation that satisfies the balance of force during elasticity to the center of gravity of the supporting pressure (that is, the length of the arm) x _{l, c, fb} (= x _{l, 7} (mm)), the center of rotation during the ultimate endurance The distance from to the center of gravity of the supporting pressure (that is, the length of the arm) x _{u, c, fb} (mm) and the endurance F _{c, fb, Rd} (N) are given by the following equations 4.36 to 4. It was set using 43.

The definition of each parameter in the equation is the same as that described in Equations 1 to 3.17. In addition, Table 4 shows each parameter used for calculating the rigidity and proof stress due to the bearing pressure between the face bearing plate and concrete. The experiment in Example 1 was carried out using the conditions shown in Table 4 (E _c , B _f , t _w , t _fb , f _y , γ _M0 , β _j , f _{cd, fb} , A _c0 , _Ac1 ). From 4.36 to 4.43, "k _{c, fb} , x _{d, c, fb} , x _{l, c, fb} , F _{c, fb, Rd} " were calculated.

(Comparison of elastic rigidity and yield strength of experimental and evaluation models)
In the first embodiment, regarding the elastic rigidity, “x _n ” and “y _n ” indicating the positions of the elastic rotation centers of the beam end portion 24 are obtained from the equilibrium conditions of the external force and the internal force in the vertical and horizontal directions, and the equation 4 The initial rotational stiffness _{Sj, ini} was determined using .1.

Further, for the ultimate moment capacity, and a simple cumulative strength and upper bound theorem total resistance element, the maximum moment capacity M _j, represents the position of the eventual rotation center to minimize _Rd "x _{u, n",} "y _{u , N} "was calculated. Since the rigidity reduction rate η was about 3.0, which corresponded well with the rigidity after the non-linearization of the experiment, the value of the rigidity reduction rate η was set to “3.0” here.

FIG. 14 shows a comparison between the experimental results and the trilinear by the evaluation model. The vertical axis in FIG. 14 is the moment of the joint, and the horizontal axis is the rotation angle of the joint. The solid line in FIG. 14 represents the history of the experimental results, and the dotted line represents the trilinear according to the evaluation model. The moment of the joint 14 in the experiment was defined by the face position of the concrete 32 of the column 10. The face position of the concrete 32 of the pillar 10 is the surface of the side surface of the concrete 32 of the pillar 10 orthogonal to the X-axis direction in FIG. 1 on the side opposite to the X-axis.

Looking at FIG. 14, it can be seen that the experiment and the evaluation model are in good agreement.

FIG. 15 shows a comparison between the rotational rigidity of the unloading cycle and the evaluation model for repeated loading in the elastic range. The vertical axis in FIG. 15 is the rotational rigidity of the joint in the unloading cycle, and the horizontal axis is the number of cycles (that is, the number of repetitions). The plot points in FIG. 15 represent the experimental results, and the dotted lines represent the evaluation model. The rotational rigidity of the evaluation model can be evaluated by roughly evaluating the lower limit of the experiment. Table 5 shows specific numerical values in the above comparison results.

Table 5 shows the experimental results of the rotational rigidity and the moment strength of the joint and the calculation results according to the present disclosure. The ultimate moment strength is 93% of the average value of the experiment. The rotational rigidity has an evaluation accuracy of 76 to 77%. The moment strength is a calculation result on the safety side that is not overestimated.

Further, regarding the rotational rigidity, an evaluation error of about 20% has almost no effect on the evaluation error of the moment acting on the joint. Therefore, it can be said that the evaluation model in the present disclosure has accuracy that does not cause any problem in practical use.

From the above, the trilinear model by the method of designing the beam-column joint of the present disclosure corresponds well with the results of this experiment in terms of both elastic rigidity and maximum moment resistance. Therefore, it was confirmed that the rotational rigidity _Sj and the maximum moment proof stress _{Mj, Rd} of the joint can be accurately evaluated by using the calculation method described in the present disclosure.

As a result, the estimated value of the moment acting from the steel beam to the column by the load supported by the steel beam and the rotational rigidity _{Sj of the} portion of the steel beam arranged inside the concrete of the column, and the column It is possible to accurately compare the maximum moment bearing capacity that the joint with the beam can withstand. As a result, in the column-beam joint of the present disclosure, it is possible to prevent significant irreversible deformation (that is, plasticization) from occurring at the joint between the columns and beams, and to stabilize the deflection of the steel beam and the soundness of the columns. Can be secured.

(Example 2)
Further, in the second embodiment as well, the beam-column joint was designed and the rotational rigidity and the moment strength of the joint were evaluated. The evaluation of the rotational rigidity and the moment proof stress of the joint portion was performed based on the evaluation method of the rotational rigidity and the moment proof stress of the joint portion described in Example 1 above. An example of the present disclosure that satisfies the conditions of the present disclosure is shown as an example. In the embodiment, the moments acting on the joint (required moment proof stress) M _{j, Ed} estimated from the rotational rigidity _Sj calculated according to the evaluation method of the present disclosure and the load supported by the steel beam are the maximum moment proof stress of the joint. (Holding moment proof stress) This is an example that does not exceed _Mj and _Rd .

Examples of examples that do not satisfy the conditions of the present disclosure The present disclosures are shown as comparative examples. In the comparative example, the moments M _{j and Ed} acting on the joint estimated from the rotational rigidity S _j calculated according to the evaluation method of the present disclosure and the load supported by the steel beam are _{equal to} or greater than the maximum moment strength M _{j and Rd of} the joint. This is an example of

The design conditions are the materials shown in Table 6, the load conditions shown in Table 7, the distance between both ends of the steel beam (that is, the beam length), and the control width in which the steel beam bears the load. The results of the design are shown in Table 8, Table 9, Table 10 and Table 11. As shown in Tables 8 to 11, No. 1 to No. 101 samples of 101 were designed. In Table 8, No. 1 to No. The design conditions of 48 samples of 48 are shown, and in Table 9, No. 49-No. The design conditions for 53 samples of 101 are shown. In addition, in Table 10, No. 1 to No. The design results of 48 samples of 48 are shown, and in Table 11, No. 49-No. The design results of 53 samples of 101 are shown.

In the second embodiment, when the maximum (holding) moment proof stress of the joint and the required moment proof stress are compared, the moment generated in the joint when the elastic rotational rigidity of the joint is assumed is the joint. The case where the value (M _{j, Ed} / M _{j, Rd} ) divided by the moment strength possessed by the above exceeds 1.00 was set as a comparative example.

The fixed load (SDL) in Table 7 is a load that always acts on the beam except for the own weight Sw of the structure. Further, the variable load (LL) is the maximum load that is considered to act during the common period of the building except for the own weight Sw of the structure and the fixed load. Further, the product of the fixed load, the variable load, the sum of the weights of the structure and the control width is set as the evenly distributed load w (see Tables 8 and 9).

Further, “ _Lem ” in Tables 8 and 9 is the embedded length of the beam in the column concrete. Further, "D _s " represents the thickness of the floor slab. Further, "H, B _f , t _w , t _f " represent the height of the cross section of the steel frame beam, the width of the flange, the thickness of the web, and the thickness of the flange, respectively. Further, "I _a " represents the moment of inertia of area of the steel beam. Further, "t _fb " represents the plate thickness of the face bearing plate.

The design conditions shown in Tables 6 and 7 were set to be invariant. The cross-sectional dimensions of the steel beam _{_{(H, B f, t w}} , t f), the embedded length of the beam relative to the pillar concrete _{L em,} and the presence or absence of the additional member (i.e., columns in the stud and the face bearing plate), As parameters, the rotational rigidity S _{j of} the joint, the maximum moment bearing capacity M _{j, Rd} of the joint, and the moments M _{j, Ed} generated at the joint are calculated using the joint design method proposed in the present disclosure. did. The embedding length _Lem was set as the maximum embedding dimension limited by the diameter of the column and the steel frame of the column.

Further, in the case where the additional member is provided, the diameter φ _st of the stud is set to 19 mm. The embedding depth c from the surface of the column to the axis of the stud in the length direction of the steel beam was set to 150 mm. The number of studs was two, and the two studs were arranged in a row in the Y-axis direction. The distance between the two studs was unified to 100 mm. Further, the plate thickness t _fb of the face bearing plate was unified to 12 mm. No joint reinforcement was set.

FIG. 16 is a graph in which data points are plotted for the design results shown in Tables 8, 9, 10 and 11. In FIG. 16, the horizontal axis is the embedded length ratio _Lem / H (= embedded length ÷ beam length), and the vertical axis is the fixedness α _rig (= moment generated at the joint in each design example ÷ joint). The moments generated at the joints when the parts are rigid joints) are set respectively.

Further, FIG. 17 is a graph in which data points are plotted for the design results shown in Tables 8, 9, 10 and 11. In FIG. 17, the horizontal axis is the embedded length ratio _Lem / H (= embedded length ÷ beam length), and the vertical axis is the bending moment ratio (= moment M _j, generated at the joint in each design example _{. Ed} ÷ Maximum moment strength _{Mj, Rd} ) of the joint in each design example is set.

In the embodiment of the present disclosure in FIG. 17, when the bending moment ratios M _{j, Ed} / M _{j, Rd} are 1.00 or less, the moments M _{j, Ed} of the joint generated by the rotational rigidity of the joint are used. On the other hand, the maximum moment proof stress _{Mj and Rd of} the joint are exceeded, indicating that the design requirements are satisfied. When the bending moment ratios M _{j, Ed} / M _{j, Rd} are 1.00 or less, the joint moments M _{j, Ed} calculated using the load supported by the steel beam and the rotational rigidity S _j. However, it means a state in which the maximum moment bearing capacity _{Mj, Rd} that the joint can withstand is not exceeded.

On the other hand, in the comparative example, when the bending moment ratio exceeds 1.00, the moment strength of the joint is insufficient with respect to the moment of the joint generated by the rotational rigidity of the joint, and the design requirement is satisfied. It shows that it is not.

Further, as shown in FIG. 17, especially when the embedded length ratio _Lem / H is 0.6 or less, the moment strength of the joint is insufficient as in the comparative example, and the additional member, the span of the beam, If the cross-sectional shape and the like are not adjusted, there is a high possibility that the moment bearing capacity may be insufficient. Therefore, by using the beam-column joint design method according to the present embodiment and setting the bending moment ratios M _{j, Ed} / M _{j, and Rd} to 1.00 or less, the joint moments M _j, The maximum moment proof stress _{Mj, Rd} of the joint exceeds _Ed , the occurrence of comparative examples is suppressed, and the design requirements can be satisfied as in the examples.

Further, in FIG. 17, in the region where the embedding length ratio _Lem / H is 0.5 or less, the probability of occurrence of a comparative example in which the moment strength of the joint is insufficient is further increased. Therefore, this embodiment is more advantageous in the region where the embedding length ratio _Lem / H is 0.5 or less.

As shown in Table 8, Table 9, Table 10, Table 11 and FIG. 17, the height of the cross section of the beam is 500 mm (beam) at the joint where the steel beam is simply embedded in the column concrete without having additional members. When the length is about 1/24) or less and the embedded length ratio _Lem / H is 0.4 or less, the moment bearing capacity of the joint is insufficient and it cannot be used as a beam-column joint ( No. 49, 50, 51).

In addition, No. in Table 8, Table 9, Table 10, and Table 11. As shown in 27, 28, 29 and FIG. 17, the joint portion in which the steel beam is only embedded in the column concrete without having an additional member has an embedding length ratio when the cross-sectional height of the beam is 600 mm or less. If _Lem / H is 0.33 or less, the moment strength of the joint is insufficient and it cannot be used as a beam-column joint. The height of the cross section of the beam of 600 mm is about 1/20 of the length of the beam of 12 m. However, No. 1 having an embedding length ratio _Lem / H of 0.33. No. 29 is a comparative example, whereas No. 29 has the same steel beam cross section and embedding length and is provided with an additional member. In No. 40, the moment strength of the joint portion satisfies the required value by adjusting the additional member. No. The additional members of 40 are an in-column stud and a face bearing plate. Therefore, No. Reference numeral 40 denotes a column-beam joint, which is an embodiment of the present disclosure.

Further, from FIGS. 16 and 17, it can be seen that the degree of fixation α _rig and the bending moment ratio change not only depending on the embedding length ratio _Lem / H but also on the cross-sectional shape of the beam and the presence or absence of studs. That is, even when the embedded length ratio _Lem / H is the same and the load conditions are the same, the moment strength of the joint satisfies the conditions of the present disclosure depending on the cross-sectional shape of the beam and the presence or absence of additional members such as studs. And there are cases where it is not satisfied.

In the above embodiment, an example is shown in which the total number n of the resistance elements is n = 7, but for the value of the total number n, the number of additional members and the like is adjusted to increase or decrease the number of resistance elements. It can be set as appropriate. For example, in the beam-column joint described in the above embodiment, when the reinforcing bars, studs, and face bearing plates as additional members are omitted, the total number of resistance elements is n = 4. In this case, the elastic rotation center of the beam end of the steel beam arranged inside the concrete of the column acts on the steel beam and the sum of the reaction forces of the resistance element i accumulated for i = 1 to 4 in the -Z direction. It can be obtained as a point that balances with the vertical load.

Further, in the above-described embodiment, the rotational rigidity and the moment strength of the joint are adjusted mainly by the additional member of the steel frame beam. However, the rotational rigidity and moment resistance of the joint can be increased only by adjusting the distance between both ends of the steel beam (that is, the beam length) and by adjusting the cross-sectional shape of the beam end in the longitudinal direction of the steel beam. It may be adjusted.

Further, for the additional member provided as the resistance element, at least one of the arrangement, shape, size and number of the additional member is adjusted. For example, the arrangement, shape, dimensions, or number of reinforcing bars and studs can be adjusted, and the position, shape, dimensions, or number of face bearing plates can be adjusted. The required moment proof stress and the maximum moment proof stress change and are adjusted depending on the presence or absence and amount of the additional member.

Further, as described above, with the resistance element designed by the method of designing the column-beam joint of the present disclosure provided, at least one end of the steel beam in the longitudinal direction is semi-rigidly joined to the inside of the concrete of the column. By embedding in a state, the method for manufacturing a beam-column joint according to the present disclosure can be realized. Although one embodiment of the present disclosure has been described above, the present disclosure is not limited to the above, and various modifications other than the above can be carried out within a range not deviating from the gist thereof. Of course.

10 Column 12 Beam 16 Reinforcing bar 18 Steel frame 20A Upper flange (resistance element)
20B lower flange (resistance element)
26 studs (resistive element)
28 Joint reinforcement (resistance element)
30 Face bearing plate (resistance element)
32 Concrete 32a Slab Concrete 34 Bolt (Resistance Element)
36 fin plate (resistance element)

≪Additional notes≫
From this specification, the following aspects are conceptualized.

That is, the first aspect is
A concrete column, a steel beam in which at least one end in the longitudinal direction is embedded in the concrete of the column in a semi-rigid joint state, and a reaction force provided on the steel beam to resist rotation of the steel beam. It is a method of designing a beam-column joint having a resistance element that causes
The rotational resistance per unit rotation angle of the steel beam portion inside the concrete at the column-beam joint is defined as the rotational rigidity _Sj .
Using the load supported by the steel beam and the rotational rigidity _Sj , the required moment resistance acting from the steel beam to the column-beam joint is calculated.
At least one of the distance between both ends of the steel beam and the cross-sectional shape of the steel beam so that the calculated required moment strength does not exceed the maximum moment strength that the column-beam joint can resist. To adjust,
How to design a beam-column joint.

Aspect 2 is
A concrete column, a steel beam in which at least one end in the longitudinal direction is embedded in the concrete of the column in a semi-rigid joint state, and a reaction force provided on the steel beam to resist rotation of the steel beam. It is a method of designing a beam-column joint having a resistance element that causes
The rotational resistance per unit rotation angle of the steel beam portion inside the concrete at the column-beam joint is defined as the rotational rigidity _Sj .
Using the load supported by the steel beam and the rotational rigidity _Sj set by the following process A, the required moment resistance acting from the steel beam to the column-beam joint is calculated.
How to design a beam-column joint.
<Process A>
The total number of the resistance elements is n, i is an arbitrary natural number of 1 or more and n or less, and the resistance elements are resistance elements i.
Wherein the reaction force of the resistance element i is represented by the product of the stiffness k _i and the amount of deformation of the resistive element i,
The center of rotation of the steel beam portion inside the concrete of the column is defined as a point at which the reaction force of the resistance element i and the external force are balanced.
Let x _{d and i} be the distances between the action line of the representative displacement of the resistance element i and the center of rotation.
Let the distance between the center of gravity of the reaction force of the resistance element i and the center of rotation be x _{l, i} .
The rotational rigidity _Sj is set based on the evaluation of the value obtained by the following equation 1.

Aspect 3 is
At least one of the distance between both ends of the steel beam and the cross-sectional shape of the steel beam is adjusted so that the required moment strength does not exceed the maximum moment strength that the column-beam joint can withstand. ,
The method for designing a beam-column joint according to aspect 2.

Aspect 4 is
The resistance element includes a portion of the steel beam inside the concrete and an additional member provided on the peripheral edge of the portion.
The required moment proof stress or the maximum moment proof stress of the beam-column joint is set by adjusting at least one of the arrangement, shape and dimensions of the additional member.
The method for designing a beam-column joint according to the first or third aspect.

Aspect 5 is
The maximum reaction force that can be borne by the resistance element i of the steel beam portion inside the concrete is set to _Fi and _Rd .
The maximum moment strength of the beam-column joint is set to M _{j and Rd} .
Let x _{u and i} be the distance between the center of rotation of the steel beam and the line of action of the reaction force.
With the position of the center of rotation as a variable _, the minimum values of _{Mj and Rd} calculated using the following equation 2 are set in the maximum moment proof stress.
The method for designing a beam-column joint according to any one of

aspects

1 and 3 to 4.

Aspect 6 is
The embedding length ratio obtained by dividing the embedding length of one end of the steel beam into concrete by the beam of the steel beam is 0.6 or less.
The method for designing a beam-column joint according to any one of aspects 1 to 5.

Aspect 7 is
In a state where the resistance element designed by using the method for designing a column-beam joint according to any one of aspects 1 to 6 is provided, at least one end of the steel beam in the longitudinal direction of the column is provided. Embedded in concrete in a semi-rigid joint state,
Manufacturing method of beam-column joints.

Aspect 8 is
With concrete pillars
A steel beam in which at least one end in the longitudinal direction is embedded in the concrete of the column in a semi-rigid joint state, and
It has a resistance element provided on the steel beam and generating a reaction force against the rotation of the steel beam.
The rotational resistance per unit rotation angle of the steel beam portion inside the concrete at the column-beam joint is defined as the rotational rigidity _Sj, and the moment generated by the maximum yield strength that the resistance element can resist is the column-beam. When defined as the maximum moment strength that a joint can withstand,
As the required moment bearing force acting on the column-beam joint from the steel beam, the required moment bearing calculated using the load supported by the steel beam and the rotational rigidity _Sj does not exceed the maximum moment bearing. In addition, at least one of the distance between both ends of the steel beam and the cross-sectional shape of the steel beam is adjusted.
Beam-column joint structure.

Aspect 9 is
With concrete pillars
A steel beam in which at least one end in the longitudinal direction is embedded in the concrete of the column in a semi-rigid joint state, and
It has a resistance element provided on the steel beam and generating a reaction force against the rotation of the steel beam.
When the rotational resistance per unit rotation angle of the steel beam portion inside the concrete at the column-beam joint is defined as the rotational rigidity _Sj , the required moment resistance acting from the steel beam to the column-beam joint is defined as The required moment resistance is set using the load supported by the steel beam and the rotational rigidity _Sj set by the following process B.
Beam-column joint structure.
<Process B>
The total number of the resistance elements is n, i is an arbitrary natural number of 1 or more and n or less, and the resistance elements are resistance elements i.
Wherein the reaction force of the resistance element i is represented by the product of the stiffness k _i and the amount of deformation of the resistive element i,
The center of rotation of the steel beam portion inside the concrete of the column is defined as a point at which the reaction force of the resistance element i and the external force are balanced.
Let x _{d and i} be the distances between the action line of the representative displacement of the resistance element i and the center of rotation.
Let the distance between the center of gravity of the reaction force of the resistance element i and the center of rotation be x _{l, i} .
The rotational rigidity S _j is set to a value that satisfies the following equation 3.

Aspect 10 is
At least one of the distance between both ends of the steel beam and the cross-sectional shape of the steel beam is adjusted so that the required moment strength does not exceed the maximum moment strength that the column-beam joint can withstand. ing,
The beam-column joint structure according to aspect 9.

Aspect 11 is
At least one of the distance between both ends of the steel beam and the cross-sectional shape of the steel beam is adjusted so that the required moment strength does not exceed the maximum moment strength that the column-beam joint can withstand. ing,
The beam-column joint structure according to aspect 8 or aspect 10.

Aspect 12
The resistance element includes a portion of the steel beam inside the concrete and an additional member provided on the peripheral edge of the portion.
The required moment proof stress or the maximum moment proof stress of the beam-column joint is set by adjusting at least one of the arrangement, shape, and dimensions of the additional member.
The column-beam joint structure according to any one of Aspect 8 and Aspect 10 to Aspect 11.

Aspect 13 is
The embedding length ratio obtained by dividing the embedding length of one end of the steel beam into concrete by the beam of the steel beam is 0.6 or less.
The beam-column joint structure according to any one of aspects 8 to 12.

≪Other aspects≫
Also, from this specification, the following other aspects are conceptualized.

That is, the other aspect 1 is
A column-beam joint structure having a concrete column and a steel beam having at least one end in the longitudinal direction arranged in the concrete of the column.
When the rotational resistance per unit rotation angle of the portion of the steel beam arranged inside the concrete of the column is the rotational rigidity _Sj , the load supported by the steel beam and the concrete of the column in the steel beam The force acting on the column from the steel beam is estimated by the rotational rigidity _{Sj of the} portion arranged inside, and the force acting on the column from the steel beam is resisted by the concrete of the column. It has a resistance element that generates a reaction force against the rotation of the portion of the steel beam arranged inside the concrete of the column so as not to exceed the maximum strength that can be achieved.
A column-beam joint structure in which the reaction force of the resistance element is adjusted at least by adjusting the distance between both ends of the steel beam and / or the cross-sectional shape of the steel beam.

Another aspect 2 is
The resistance element includes a portion of the steel beam that is arranged inside the concrete of the column and an additional member provided at the peripheral edge thereof, and adjusts at least one of the arrangement, shape, and dimensions of the additional member. The beam-column joint structure according to another aspect 1, wherein the reaction force of the resistance element is adjusted by the above.

Another aspect 3 is
When the total number of the resistance elements is n, i is an arbitrary natural number of 1 or more and n or less, and the resistance element provided on the steel beam is the resistance element i,
The reaction force of the resistance element i is assumed to be expressed by the product of the stiffness k _i and the amount of deformation of the resistive element i,
The center of elastic rotation of the portion of the pillar arranged inside the concrete is defined as the point where the reaction force of the resistance element i and the external force are balanced.
Let x _{d, i} be the distance between the action line of the representative displacement of the resistance element i and the elastic rotation center of the portion of the steel beam beam arranged inside the concrete of the column.
The distance between the center of gravity of the reaction force of the resistance element i and the elastic rotation center of the portion of the steel beam arranged inside the concrete of the column is defined as x _{l, i} .
The column-beam joint structure according to another aspect 1 or another aspect 2 in which the rotational rigidity _Sj is set to a value satisfying the following equation 1.

Another aspect 4 is
The maximum reaction force that the resistance element i can bear as the reaction force of the resistance element i of the portion of the steel beam arranged inside the concrete of the column is set to _Fi and _Rd .
The proof stress of the joint is defined as M _{j and Rd} .
Let x _{u, i} be the distance between the center of rotation of the portion of the steel beam arranged inside the concrete of the column and the line of action of the reaction force.
M _{j and Rd} are calculated using the following equation 2 with the position of the center of rotation as a variable, and the proof stress of the joint is set to the minimum value of M _{j and Rd} calculated by the following equation 2. The column-beam joint structure according to any one of the other aspects 1 to 3.

Another aspect 5 is
A method for designing a column-beam joint having a concrete column and a steel beam having at least one end in the longitudinal direction arranged in the concrete of the column.
When the rotational resistance per unit rotation angle of the portion of the steel beam arranged inside the concrete of the column is the rotational rigidity _Sj , the load supported by the steel beam and the concrete of the column in the steel beam The force acting on the column from the steel beam is estimated by the rotational rigidity _{Sj of the} portion arranged inside, and the force acting on the column from the steel beam is resisted by the concrete of the column. A resistance element is provided to generate a reaction force against the rotation of the portion of the steel beam arranged inside the concrete of the column so as not to exceed the maximum strength that can be achieved.
A method for designing a column-beam joint in which the reaction force of the resistance element is adjusted at least by adjusting the distance between both ends of the steel beam and / or the cross-sectional shape of the steel beam.

Another aspect 6 is
The resistance element includes a portion of the steel beam that is arranged inside the concrete of the column and an additional member provided at the peripheral edge thereof, and adjusts at least one of the arrangement, shape, and dimensions of the additional member. The method for designing a beam-column joint according to another aspect 5, wherein the reaction force of the resistance element is adjusted by the method.

In another aspect 7, when the total number of the resistance elements is n, i is an arbitrary natural number of 1 or more and n or less, and the resistance element provided on the steel beam is the resistance element i,
The reaction force of the resistance element i is assumed to be expressed by the product of the stiffness k _i and the amount of deformation of the resistive element i,
The center of elastic rotation of the portion of the pillar arranged inside the concrete is defined as the point where the reaction force of the resistance element i and the external force are balanced.
Let x _{d, i} be the distance between the action line of the representative displacement of the resistance element i and the elastic rotation center of the portion of the steel beam beam arranged inside the concrete of the column.
Let the distance between the center of gravity of the reaction force of the resistance element i and the elastic rotation center of the portion of the steel beam arranged inside the concrete of the column be x _{l, i,} and use the value obtained by the following equation 3 The method for designing a beam-column joint according to another aspect 5 or another aspect 6 for evaluating the rotational rigidity of the joint.

Another aspect 8 is
The reaction force of the resistance element i of the portion of the steel beam arranged inside the concrete of the column is defined as the maximum reaction force _{Fi, Rd} that can be borne by the resistance element i.
The proof stress of the joint is defined as M _{j and Rd} .
Let x _{u, i} be the distance between the center of rotation of the portion of the steel beam arranged inside the concrete of the column and the line of action of the reaction force.
Using the position of the center of rotation as a variable, M _{j and Rd} are calculated using the following equation 4, and the yield strength of the joint is the minimum value of M _{j and Rd} calculated by the following equation 4. The method for designing a beam-column joint according to any one of aspects 5 to 7.

In the above other aspects, the following effects are exhibited.

According to the beam-column joint structure and the design method of the beam-column joint according to the other aspects, the load supported by the steel beam and the rotational rigidity _{Sj of the} portion of the steel beam arranged inside the concrete of the column make the steel beam The estimated value of the moment acting on the column does not exceed the maximum moment bearing capacity that the joint between the column and the beam can resist. As a result, it is possible to prevent the joint between the column and the beam from causing remarkable irreversible deformation (plasticization), ensure the stability of the deflection of the steel beam and the soundness of the column, and satisfy the required performance. it can.

The disclosure of Japanese Patent Application No. 2019-103652 filed on June 3, 2019 is incorporated herein by reference in its entirety.

Also, all documents, patent applications and technical standards described herein are to the same extent as if it were specifically and individually stated that the individual documents, patent applications and technical standards would be incorporated by reference. Incorporated herein by reference.

Claims

A concrete column, a steel beam in which at least one end in the longitudinal direction is embedded in the concrete of the column in a semi-rigid joint state, and a reaction force provided on the steel beam to resist rotation of the steel beam. It is a method of designing a beam-column joint having a resistance element that causes
The rotational resistance per unit rotation angle of the steel beam portion inside the concrete at the column-beam joint is defined as the rotational rigidity Sj .
Using the load supported by the steel beam and the rotational rigidity Sj , the required moment resistance acting from the steel beam to the column-beam joint is calculated.
At least one of the distance between both ends of the steel beam and the cross-sectional shape of the steel beam so that the calculated required moment strength does not exceed the maximum moment strength that the column-beam joint can resist. To adjust,
How to design a beam-column joint.
A concrete column, a steel beam in which at least one end in the longitudinal direction is embedded in the concrete of the column in a semi-rigid joint state, and a reaction force provided on the steel beam to resist rotation of the steel beam. It is a method of designing a beam-column joint having a resistance element that causes
The rotational resistance per unit rotation angle of the steel beam portion inside the concrete at the column-beam joint is defined as the rotational rigidity Sj .
Using the load supported by the steel beam and the rotational rigidity Sj set by the following process A, the required moment resistance acting from the steel beam to the column-beam joint is calculated.
How to design a beam-column joint.
<Process A>
The total number of the resistance elements is n, i is an arbitrary natural number of 1 or more and n or less, and the resistance elements are resistance elements i.
Wherein the reaction force of the resistance element i is represented by the product of the stiffness k i and the amount of deformation of the resistive element i,
The center of rotation of the steel beam portion inside the concrete of the column is defined as a point at which the reaction force of the resistance element i and the external force are balanced.
Let x d and i be the distances between the action line of the representative displacement of the resistance element i and the center of rotation.
Let the distance between the center of gravity of the reaction force of the resistance element i and the center of rotation be x l, i .
The rotational rigidity Sj is set based on the evaluation of the value obtained by the following equation 1.
At least one of the distance between both ends of the steel beam and the cross-sectional shape of the steel beam is adjusted so that the required moment strength does not exceed the maximum moment strength that the column-beam joint can withstand. ,
The method for designing a beam-column joint according to claim 2.
The resistance element includes a portion of the steel beam inside the concrete and an additional member provided on the peripheral edge of the portion.
The required moment proof stress or the maximum moment proof stress of the beam-column joint is set by adjusting at least one of the arrangement, shape and dimensions of the additional member.
The method for designing a beam-column joint according to claim 1 or 3.
The maximum reaction force that can be borne by the resistance element i of the steel beam portion inside the concrete is set to Fi and Rd .
The maximum moment strength of the beam-column joint is set to M j and Rd .
Let x u and i be the distance between the center of rotation of the steel beam and the line of action of the reaction force.
With the position of the center of rotation as a variable , the minimum values of Mj and Rd calculated using the following equation 2 are set in the maximum moment proof stress.
The method for designing a beam-column joint according to any one of claims 1 and 3 to 4.
The embedding length ratio obtained by dividing the embedding length of one end of the steel beam into concrete by the beam of the steel beam is 0.6 or less.
The method for designing a beam-column joint according to any one of claims 1 to 5.
At least one end of the steel beam in the longitudinal direction is provided with the resistance element designed by using the method for designing a column-beam joint according to any one of claims 1 to 6. Embedded in the concrete of the column in a semi-rigid joint state,
Manufacturing method of beam-column joints.
With concrete pillars
A steel beam in which at least one end in the longitudinal direction is embedded in the concrete of the column in a semi-rigid joint state, and
It has a resistance element provided on the steel beam and generating a reaction force against the rotation of the steel beam.
The rotational resistance per unit rotation angle of the steel beam portion inside the concrete at the column-beam joint is defined as the rotational rigidity Sj, and the moment generated by the maximum yield strength that the resistance element can resist is the column-beam. When defined as the maximum moment strength that a joint can withstand,
As the required moment bearing force acting on the column-beam joint from the steel beam, the required moment bearing calculated using the load supported by the steel beam and the rotational rigidity Sj does not exceed the maximum moment bearing. In addition, at least one of the distance between both ends of the steel beam and the cross-sectional shape of the steel beam is adjusted.
Beam-column joint structure.
With concrete pillars
A steel beam in which at least one end in the longitudinal direction is embedded in the concrete of the column in a semi-rigid joint state, and
It has a resistance element provided on the steel beam and generating a reaction force against the rotation of the steel beam.
When the rotational resistance per unit rotation angle of the steel beam portion inside the concrete at the column-beam joint is defined as the rotational rigidity Sj , the required moment resistance acting from the steel beam to the column-beam joint is defined as The required moment resistance is set using the load supported by the steel beam and the rotational rigidity Sj set by the following process B.
Beam-column joint structure.
<Process B>
The total number of the resistance elements is n, i is an arbitrary natural number of 1 or more and n or less, and the resistance elements are resistance elements i.
Wherein the reaction force of the resistance element i is represented by the product of the stiffness k i and the amount of deformation of the resistive element i,
The center of rotation of the steel beam portion inside the concrete of the column is defined as a point at which the reaction force of the resistance element i and the external force are balanced.
Let x d and i be the distances between the action line of the representative displacement of the resistance element i and the center of rotation.
Let the distance between the center of gravity of the reaction force of the resistance element i and the center of rotation be x l, i .
The rotational rigidity S j is set to a value that satisfies the following equation 3.
At least one of the distance between both ends of the steel beam and the cross-sectional shape of the steel beam is adjusted so that the required moment strength does not exceed the maximum moment strength that the column-beam joint can withstand. ing,
The beam-column joint structure according to claim 9.
The resistance element includes a portion of the steel beam inside the concrete and an additional member provided on the peripheral edge of the portion.
The required moment proof stress or the maximum moment proof stress of the beam-column joint is set by adjusting at least one of the arrangement, shape, and dimensions of the additional member.
The beam-column joint structure according to claim 8 or 10.
The maximum reaction force that can be borne by the resistance element i of the steel beam portion inside the concrete is set to Fi and Rd .
The maximum moment strength of the beam-column joint is set to M j and Rd .
Let x u and i be the distance between the center of rotation of the steel beam and the line of action of the reaction force.
With the position of the center of rotation as a variable, the minimum values of Mj and Rd calculated using the following equation 4 are set in the maximum moment proof stress.
The beam-column joint structure according to any one of claims 8 and 10 to 11.
The embedding length ratio obtained by dividing the embedding length of one end of the steel beam into concrete by the beam of the steel beam is 0.6 or less.
The beam-column joint structure according to any one of claims 8 to 12.