Method for Evaluating Member Elastic Rigidity of Beam Member

Abstract

To provide a method for evaluating member elastic stiffness of a beam member, in which a widened end portion of the beam member is provided with a joint for friction bonding by means of a high-strength bolt, to enable increase in the member elastic stiffness to be evaluated appropriately.SOLUTION: A method for evaluating member elastic stiffness of a beam member in which a widened joint for friction bonding by means of a high-strength bolt connecting a central member and a bracket is provided at an end of the member, comprises the steps of: modeling a central member section of only the central member 3, a bracket section of only the bracket 13, and a joint section of a joint 12 connecting those sections based on the cross-sectional shapes representative of each section; deriving deflection δ when a load Q acts on the leading edge of a free end of a calculated model, in which beam elements of the central member section, joint section, and bracket section are rigidly connected in the material axis direction to form a cantilevered beam; and expressing the member elastic stiffness SMθ of the beam member as a relationship between bending moment M and a member deformation angle θ, based on the derived deflection δ.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a method for evaluating the member elastic rigidity of a beam member provided with an extended joint by friction joining with high-strength bolts that connect a central member and a bracket to the end of the member.

Background Art

[0002] In steel frame structures, as disclosed in Patent Documents 1 and 2, a construction method is known in which the through diaphragm of the column-beam joint is extended planarly to form a bracket. In the joints at the ends of the beam members described in these documents, the design is such that the bolt hole position of the high-strength bolt joint farthest from the column becomes the starting point of the plasticized region. That is, only the central member side of the beam member is plasticized during an earthquake load.

[0003] On the other hand, Non-Patent Document 1 discloses a construction method in which the flange that becomes the end of the steel beam is widened at the joint between a square steel pipe column and a steel beam. Generally, when the flange at the end is widened, the member elastic rigidity of the beam member becomes higher compared to the case where there is no widening of the end, and the deformation of the structure when a horizontal force acts becomes smaller.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Patent Document 2

Non-Patent Documents

[0005]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0006] When performing the structural design of a steel frame structure, it is necessary to evaluate "how much deformation will occur with how much force" when horizontal forces such as seismic forces act on the steel frame structure. However, for beam members with widened material ends and joints with friction joints using high-strength bolts provided, a method for appropriately evaluating the increase in member elastic rigidity due to widening and incorporating it into a consistent structural calculation program has not been established.

[0007] Therefore, an object of the present invention is to provide a method for evaluating the member elastic rigidity of a beam member that can appropriately evaluate the increase in the member elastic rigidity of a beam member with a widened joint of friction joint using high-strength bolts at the material end.

Means for Solving the Problems

[0008] In order to achieve the above object, the method for evaluating the member elastic rigidity of a beam member according to the present invention is a method for evaluating the member elastic rigidity of a beam member provided with a widened joint of friction joint using high-strength bolts connecting a central member and a bracket at the material end, comprising the steps of: modeling a central member section of only the central member, a bracket section of only the bracket, and a joint section connecting these sections, based on the cross-sectional shapes representing each section; deriving the deflection δ when a load Q acts on the free end of a calculation model that becomes a cantilever beam with the beam elements of the central member section, the joint section, and the bracket section rigidly joined in the material axis direction; and expressing the member elastic rigidity S Mθ of the beam member in terms of the relationship between the bending moment M and the member deformation angle θ.

Effects of the Invention

[0009] In the method for evaluating the member elastic rigidity of a beam member according to the present invention configured as described above, in order to evaluate the member elastic rigidity of a beam member provided with a widened joint of friction joint using high-strength bolts at the material end, sections with different cross-sectional shapes are modeled as a central member section, a joint section, and a bracket section, respectively.

[0010] Then, the deflection δ is derived using a calculation model that results in a cantilever beam with three beam elements rigidly joined in the material axis direction, and based on this, the member elastic stiffness S of the beam member is determined. Mθ By doing so, it becomes possible to appropriately evaluate the increase in the member elastic stiffness of a beam member in which the material end is widened and a friction joint using high-strength bolts is provided.

Brief Description of the Drawings

[0011]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Embodiments for Carrying Out the Invention

[0012] Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is an explanatory diagram showing an outline of a method for evaluating the member elastic rigidity of the beam member according to the present embodiment. Further, FIG. 2 is a perspective view showing the configuration of the steel column-beam joint structure 1 described in the present embodiment. Furthermore, FIGS. 3 and 4 are an explanatory diagram and a side view showing the configuration of the material end portion of the beam connected to the steel column 2 of the steel column-beam joint structure 1 and the plasticized region.

[0013] As shown in FIG. 2, the steel column-beam joint structure 1 used in the description of the present embodiment is provided at an intersection where a central member 3 having a width narrower than the column width is connected to a steel column 2 which is a column member. Here, the beam 11 serving as a beam member is mainly composed of a joint 12 connecting a bracket 13 protruding from the steel column 2 and the central member 3, and the central member 3 extending from the joint 12 toward the other column or the like. In FIGS. 3 and 4, for the sake of simplicity of explanation, only the beam 11 in one direction in FIG. 2 and the steel column 2 are extracted and shown.

[0014] For the steel column 2, steel structures such as a rectangular steel pipe including a substantially square shape in plan view, a circular steel pipe, and a welded fabricated box-shaped cross section can be used. Further, a concrete filled steel tube column (CFT: Concrete Filled Tube) in which the inside of the steel tube is filled with concrete can also be used as the steel column 2.

[0015] At the intersection with the beam 11, the inside of the steel column 2 is closed by a continuous diaphragm 4 formed of a steel plate. The continuous diaphragms 4 are arranged at intervals above and below the intersection. The intersection of the steel column 2 provided with the continuous diaphragm 4 may use a ready-made product or can also be assembled by welding.

[0016] The continuous diaphragm 4 is formed of a single integral steel plate with a through portion 41 penetrating the inside of the steel column 2 and a bracket flange 42 protruding to the outside (see FIG. 2). For example, in the continuous diaphragm 4 formed of a steel plate having a substantially octagonal shape in plan view, an annular portion protruding to the side of the steel column 2 with an inner edge being substantially square and an outer edge being substantially octagonal serves as the bracket flange 42.

[0017] The spaces between the bracket flanges 42 of the continuous diaphragm 4 projecting from above and below the intersection of the steel columns 2 are connected by a bracket web 43 formed of a steel plate that is substantially rectangular in side view (see FIGS. 2 and 4).

[0018] The bracket web 43 projects from the side of the steel column 2 by the same amount as the bracket flange 42 and is disposed on each side of the steel column 2. The bracket web 43 is joined to the side of the steel column 2, the lower surface of the upper bracket flange 42, and the upper surface of the lower bracket flange 42 by fillet welding. A plurality of bolt holes for passing high-strength bolts or ultra-high-strength bolts are drilled in the bracket flange 42 and the bracket web 43. The number and position of the bolt holes can be set arbitrarily.

[0019] The bracket flange 42 and the bracket web 43 are provided in accordance with the positions of the respective parts of the web member 3 of the connecting beam 11. The web member 3 is a beam body (steel beam) formed of a steel structure such as an H-shaped steel, and includes an upper flange 31, a lower flange 32, and a web 33 connecting them (see FIG. 2). Here, the thickness of the bracket flange 42 is made equal to or greater than the thickness of the flange (31, 32) of the web member 3, and the thickness of the bracket web 43 is made equal to or greater than the thickness of the web 33 of the web member 3.

[0020] The bracket flange 42 of the upper continuous diaphragm 4 is provided at a position where it abuts against the upper flange 31 of the web member 3, and the bracket flange 42 of the lower continuous diaphragm 4 is provided at a position where it abuts against the lower flange 32 of the web member 3. The bracket web 43 is provided at a position where it abuts against the web 33 of the web member 3.

[0021] That is, the continuous diaphragm 4 of the present embodiment has a general "function as a continuous diaphragm" in the prior art and a "function as a beam bracket" for connecting the web member 3. Therefore, the bracket flange 42 and the bracket web 43 are collectively referred to as a bracket 13.

[0022] A plurality of bolt holes for passing high-strength bolts or ultra-high-strength bolts are drilled in the upper flange 31, the lower flange 32, and the web 33 at the axial end of the central member 3. The number and position of the bolt holes can be set arbitrarily.

[0023] The bracket flange 42 and the flange (31, 32) of the central member 3 that are butt-joined in this way are friction-joined by high-strength bolts 6 including ultra-high-strength bolts via packing plates (5, 51). In short, the end of the packing plate (5, 51) on the steel column side is joined to the bracket flange 42 of the continuous diaphragm 4, and the end of the packing plate (5, 51) on the central member side is joined to the end of the flange (31, 32) of the central member 3.

[0024] Among the packing plates (5, 51), the outer-flange packing plate 5 is formed of a steel plate such that the side of the steel column is widened and the side of the central member has the width of the central member. That is, the outer-flange packing plate 5 spanned between the upper surface of the bracket flange 42 of the upper continuous diaphragm 4 and the upper flange 31 of the central member 3 is formed in a substantially trapezoidal shape in plan view in which the width of the edge adjacent to the steel column 2 is wider than the width of the central member and the edge on the central member side has the width of the central member. The outer-flange packing plate 5 spanned between the lower surface of the bracket flange 42 of the lower continuous diaphragm 4 and the lower flange 32 of the central member 3 is also formed in a similar substantially trapezoidal shape in plan view.

[0025] On the other hand, the inner-flange packing plate 51 (see FIG. 4) that faces the outer-flange packing plate 5 with the upper flange 31 or the lower flange 32 interposed therebetween is formed to have a width of half or less of the width of the outer-flange packing plate 5 so that it can be disposed on both sides of the web 33 of the central member 3. The inner-flange packing plate 51 does not have to have the same thickness as the outer-flange packing plate 5 and can be set to an arbitrary thickness.

[0026] In addition, the web-side packing plates 52 spanned between both side surfaces of the bracket web 43 and the web 33 of the central member 3 are formed of steel plates into substantially rectangular shapes in side view with a height lower than that of the web 33 of the central member 3.

[0027] A plurality of bolt holes for passing high-strength bolts or ultra-high-strength bolts are drilled in the flange outer reinforcing plate 5, the flange inner reinforcing plate 51, and the web side reinforcing plate 52. The number and position of the bolt holes are made to match those of the bolt holes in the upper flange 31, the lower flange 32, the web 33, the bracket flange 42, and the bracket web 43 of the central member 3.

[0028] As shown in FIGS. 3 and 4, the beam 11 of the steel frame column-beam joint structure 1 is designed to yield at the first bolt position (A-section position, the bolt hole position of the high-strength bolt joint by the high-strength bolt 6 farthest from the steel frame column 2) of the central member 3. Then, a plasticized region is formed toward the center of the span in a portion of the central member 3 adjacent to the first bolt position (the first row on the central member side).

[0029] Here, with respect to the A-section of the first bolt position of the central member 3, among the high-strength bolts 6 joining the flanges (31, 32) of the central member 3 and the reinforcing plates (5, 51), the cross-section at the bolt position closest to the end of the central member 3 is defined as the B-section. Further, among the high-strength bolts 6 joining the bracket flange 42 and the reinforcing plates (5, 51), the cross-section at the bolt position of the joint 12 closest to the end of the central member 3 is defined as the D-section, and the cross-section at the midpoint between the B-section and the D-section is defined as the C-section. And the cross-section at the bolt position of the high-strength bolt 6 closest to the steel frame column 2 is defined as the E-section.

[0030] As described in this embodiment, since the reinforcing plates (5, 51) of the beam 11 are widened with respect to the width of the central member 3, it has been clarified by experiments that the member elastic rigidity becomes larger than that of the beam member of the conventional construction method without flange widening. FIG. 5 is an explanatory diagram of the experimental results confirming that the elastic rigidity of the beam member with the widened member end is higher than that without widening.

[0031] Here, the test specimen No. 1 is a test specimen of the conventional method, and the test specimen No. 3 is a test specimen that simulates the beam 11 described in this embodiment. Since the cross-sections of the beam members of the No. 1 test specimen and the central member 3 of the No. 3 test specimen are the same, according to the load-deformation relationship shown in Fig. 5, it becomes possible to grasp the change in the elastic rigidity when the beam 11 described in this embodiment is used without changing the cross-section of the beam member of the conventional method.

[0032] In short, as for the beam member provided with the joint 12 widened by the frictional joint with the high-strength bolt 6 at the member end like the beam 11 described in this embodiment, an increase in the member elastic rigidity can be expected as is clear from this experimental result. However, as of the current situation before this application, there is no means to consider this effect in design.

[0033] In structural design, the member elastic rigidity has a great influence on the calculation results of "the stress of the members constituting the structure" and "the deformation of the structure". If an incorrect member elastic rigidity is used during the analysis of stress and deformation, the design will be for a phenomenon that deviates from the behavior of the actual structure. Therefore, it is very important to accurately evaluate the elastic rigidity of the member to be designed in order to grasp the behavior of the actual structure.

[0034] Therefore, in the method for evaluating the member elastic rigidity of the beam member of this embodiment, a mathematical formula for evaluating the member elastic rigidity of the beam 11 is derived and will be described below. In the method for evaluating the member elastic rigidity of the beam member of this embodiment, the "member elastic rigidity" required at the time of design is evaluated. First, as shown in Fig. 1, after modeling the cantilever beam member into three beam elements of a "bracket section", a "joint section", and a "central member section", the member elastic rigidity is calculated for a cantilever beam model (hereinafter referred to as the "calculation model") in which the beam elements of each section are rigidly joined in the material axis direction.

[0035] In the bracket section, it is modeled as a beam element with a uniform cross-section having the same width as the maximum width max b fs1 of the flange external attachment plate 5 (refer to the right end of Fig. 6). The joint section has the same width as the maximum width of the flange external attachment plate 5 at the E cross-section position (refer to Figs. 3 and 4)max b fs1 is set as the width of the central member 3 at the A cross-section position, and the beam member with a variable cross-section with the width bc b is modeled (refer to the center in Fig. 6). And the central member section is modeled as a cross-section beam of an H-shaped steel with a width bc b (refer to the left end in Fig. 6).

[0036] As shown in Fig. 1, the boundaries of these three sections are set as follows: the boundary between the bracket section and the joint section is set at the first bolt position (E cross-section position) on the steel column side of the bracket 13, and the boundary between the joint section and the central member section is set at the first bolt position (A cross-section position) on the central member side (refer to Figs. 3 and 4). This boundary setting is carried out considering the stress transmission from the base material to the gusset plate in the flange. That is, since the axial force of the flange (31, 32) of the central member 3 starts to be transmitted to the gusset plate (5, 51) starting from the A cross-section position, it is set that the flange (31, 32) of the central member 3 bears the total axial force of the flange until the A cross-section position. And since the axial force of the gusset plate (5, 51) starts to be transmitted to the bracket flange 42 starting from the D cross-section position, it is set that the bracket flange 42 bears the total axial force of the flange from the E cross-section position to the material end.

[0037] For the cantilever beam (refer to the lowermost part in Fig. 1) with the three-section beam elements modeled as above rigidly joined in the material axis direction, the deflection δ at the free end is derived when a concentrated load Q acts on the tip of the free end. In the subsequent derivation process of the deflection angle θ and the deflection δ, the cross-section loss due to the high-strength bolt holes is not considered.

[0038] Fig. 7 is an explanatory diagram schematically showing the deformation of the bracket section of the calculation model. As shown in this figure, in the bracket section that receives the concentrated load Q at the tip which is the free end of the cantilever beam, since the bending moment distribution is as shown in the upper part of the figure, the second moment of area of the bracket section is br I, and the Young's modulus is br E. Then, the deflection angle curve br θ(x) and the deflection curve br δ(x) can be expressed as follows respectively.

[0039] [Number] Here, bc l is the length of the central member section (the length from the A-section position to the free end tip), J l' is the length from the surface of the steel column 2 to the A-section position (see FIGS. 3 and 4).

[0040] Substituting x = J l into the above two equations, the deflection angle br θ = br θ( J l) and the deflection br δ = br δ( J l) at the tip of the bracket section can be obtained and expressed as follows. [Number]

[0041] As shown in FIG. 1, since the joint section has a variable cross-section whose width changes linearly with respect to the material axis x direction, in deriving the deformation of the joint section, first, a function of the cross-sectional second moment needs to be obtained. Based on the cross-section of the joint section shown in FIG. 6, the cross-sectional second moment I fs1 (x) of the flange external attachment plate 5 can be expressed as follows. [Number] Here, b fs1 (x) is a function of the width of the flange external attachment plate 5, br H is due to the bracket 13, and t fs1 is the thickness of the flange external attachment plate 5.

[0042] b fs1 (x) is J γ = ( max b fs1 - bc b) / J l is set, and then the cross-sectional second moment I fs2 (x) of the flange internal attachment plate 51 can be expressed as follows.

Number

[0043] Also, b fs2 (x), when the interval between the inner flange plates 51 is g fs2 is as follows.

Number

[0044] And, based on the above formulation, when each constant is arranged as follows, the second moment of area of the joint section J I(x) can be expressed as follows.

Number

[0045] Using the second moment of area obtained as above, the deformation of the joint section shown in Fig. 8 is derived. Let the Young's modulus of the steel material in the joint section be fs E, then the relationship between the bending moment and the curvature J φ(x) in the joint section can be expressed as follows.

Number

[0046] After arranging the above formula with D5 = D4 / D3 and then integrating with respect to x, considering the continuity condition at the boundary (x = J l) between the bracket section and the joint section, the deflection angle curve J θ(x) and the deflection curve J δ(x) are as follows.

Equation

[0047] Substituting x = 0 into the above formula, the deflection angle J θ = J θ(0) and the deflection J δ = J δ(0) at the tip of the joint section can be expressed as follows.

Equation

[0048] Figure 9 is an explanatory diagram schematically showing the deformation of the central member section of the calculation model. Let the second moment of area of the central member section be bc I and the Young's modulus be bc E. Then, considering the continuity condition at the boundary (x = 0) between the joint section and the central member section, the deflection angle curve bc θ(x) and the deflection curve bc δ(x) of the central member section subjected to a concentrated load Q at the free end tip can be expressed as follows respectively.

Equation

[0049] By substituting x = - bc θ(x) and the deflection curve bc δ(x) of the central member section derived as above, the deflection angle bc θ = bc at the tip of the central member section can be obtained. bcθ(- bc l) and deflection bc δ = b δ(- bc l) can be obtained. However, since the tip of the central member section is synonymous with the tip of a cantilever beam, the deflection angle θ and the deflection δ at the free end of the "cantilever beam type beam member that receives a concentrated load Q at the free end tip" are the same as those of the central member section. That is, θ and δ can be expressed as follows, respectively.

Equation

[0050] Based on the deflection δ derived in this way, when expressing the member elastic rigidity S Mθ of the beam 11 in terms of the relationship between the bending moment M and the member deformation angle θ, it becomes as follows.

Equation

[0051] In the above equation, each term in [ ] -1 represents the influence of the central member section, the joint section, and the bracket section. The E of each term is the Young's modulus of the steel used in each section. That is, the above equation can evaluate the member elastic rigidity even for a beam member with different Young's moduli of the materials used in each section.

[0052] Also, in the evaluation formula of the member elastic rigidity shown in the above equation (Equation 12), there are terms for the central member section, the joint section, and the bracket section from the beginning, and it can be said that the member elastic rigidity of the beam 11 can be evaluated precisely.

[0053] On the other hand, in order to express the above-mentioned "calculation model" in a program, it is necessary to provide nodes at the boundary positions of each section, and a plurality of intermediate nodes will be provided for one beam 11. Also, although the above equation is for evaluating the member elastic rigidity of a cantilever beam type beam member, when performing stress analysis using a consistent structural calculation program in actual structural design, it is common to input the member cross-section.

[0054] Specifically, in the practice of structural design, the member elastic stiffness is defined so as to specify the "end moment and rotation angle", and in a consistent structural calculation program, it is commercially available in a state constructed according to this. Therefore, in order to design the structure including the beam 11 using a consistent structural calculation program, an evaluation method must be provided in a form with high affinity for structural design practice so that the member elastic stiffness of the beam 11 can be considered in the program.

[0055] Therefore, below, the case where a "beam with a uniform cross-section equivalent to the calculation model" as shown in FIG. 10 is introduced will be described. The "beam with a uniform cross-section equivalent to the calculation model" means a beam in which the deflection δ when a concentrated load Q acts on the tip of the free end is equivalent to the calculation model. Below, this "beam with a uniform cross-section equivalent to the calculation model" will be referred to as the "evaluation model".

[0056] The second moment of area of each section of the calculation model is I for the bracket section, br I(x) (a function of the coordinate x in the material axis direction) for the joint section, J and I for the central member section. Although they are different in each section, the second moment of area of the evaluation model is the same bc I bc throughout the entire section. eq It becomes as follows.

[0057] Generally, in a cantilever beam, the following equation holds for the relationship between the bending moment M at the beam end and the member deformation angle θ.

Equation

[0058] Utilizing the fact that the "member stiffness when this relationship is applied to a beam with a uniform cross-section equivalent to the calculation model" is equivalent to the "formula (Equation 12) showing the member stiffness of a beam member in the cantilever beam form", and assuming that the Young's modulus is the same throughout the entire section, the second moment of area bc I eq of the evaluation model can be expressed as follows.

Number

[0059] Furthermore, the moment of inertia of the evaluation model represented by the above formula (Equation 14) bc I eq is divided by the moment of inertia of the central member section bc I and arranged, and can be expressed as the following formula.

Number

[0060] That is, the ratio φ bc of "the moment of inertia of the beam (evaluation model) with a uniform cross-section equivalent to the calculation model" to "the moment of inertia of the central member section bc I eq " can be obtained. When performing stress analysis on the steel frame structure used for the beam 11 in this embodiment, in the consistent structural calculation program, after inputting "the cross-section of the central member 3 throughout the entire section" for the beam 11, by inputting the "moment of inertia increase rate (ratio φ bc )" represented by the above formula (Equation 15), it becomes possible to consider the increase in rigidity due to the friction joint by the high-strength bolts 6 with widened member ends. bc )" can be input, it becomes possible to consider the increase in rigidity due to the friction joint by the high-strength bolts 6 with widened member ends.

[0061] In short, by multiplying the moment of inertia bc I of the central member 3 by the ratio φ bc , it is possible to consider "the increase in member rigidity accompanying the adoption of the beam 11 in this embodiment while keeping the beam width constant". Therefore, in the rigidity evaluation of the beam 11 in this embodiment, the "framework of the rigidity evaluation of the composite beam" on the program constructed on the premise of "a beam with a constant width" can be utilized as it is without special processing.

[0062] Next, the method for evaluating the member elastic rigidity of the beam member in this embodiment will be described. In this embodiment, taking the beam 11 having the joint 12 of the steel frame column-beam joint structure 1 described above as an example, a method for evaluating the member elastic rigidity of the beam member of the beam 11 will be described.

[0063] In the first step, as shown in FIG. 1, the central member section with only the central member 3, the bracket section with only the bracket 13, and the joint section of the joint 12 connecting these sections are modeled based on the cross-sectional shapes representing the respective sections as shown in FIG. 6.

[0064] In the subsequent step, a calculation model is set as a cantilever beam in which the beam elements of the central member section, the joint section, and the bracket section are rigidly joined in the material axis direction, and the deflection δ when a concentrated load Q acts on the tip of the free end of the calculation model is derived (see Equation (11)).

[0065] In the next step, based on the derived deflection δ, the member elastic rigidity S of the beam 11 Mθ is expressed by the relationship between the bending moment M and the member deformation angle θ. Details have been described above as Equation (12).

[0066] Furthermore, in the next step, when performing stress analysis using a consistent structural calculation program, the second moment of area bc I eq of the evaluation model in which the cross-sectional shape of the beam member equivalent to the calculation model is uniform in the material axis direction is obtained (see Equation (14)).

[0067] In the subsequent step, the ratio φ bc I eq of the second moment of area bc I of the evaluation model divided by the second moment of area of the central member section bc I is obtained (see Equation (15)). By doing so, when using a general-purpose program, it is input as a beam with the same cross-section as the central member 3 over the entire length, and the ratio φ bc I obtained from the above Equation (15) for the increase rate of the second moment of area bc of the central member 3 is input, so that the member elastic rigidity of the beam 11 provided with the joint 12 of the friction joint by the high-strength bolt 6 with the material end widened can be appropriately considered.

[0068] Next, the operation of the method for evaluating the member elastic rigidity of the beam member of the present embodiment will be described. In the method for evaluating the member elastic rigidity of the beam member of the present embodiment configured as described above, in order to evaluate the member elastic rigidity of the beam 11 provided with the joint 12 with the widened frictional joint by the high-strength bolts 6 at the member end, sections with different cross-sectional shapes are modeled as a central member section, a joint section, and a bracket section, respectively.

[0069] Then, the deflection δ is derived by a calculation model that becomes a cantilever beam in which the beam elements (3, 12, 13) of the three sections are rigidly joined in the member axis direction, and based on this, the member elastic rigidity S of the beam member Mθ is represented.

[0070] By doing so, it becomes possible to appropriately evaluate the increase in the member elastic rigidity of the beam 11 provided with the joint 12 with the widened frictional joint by the high-strength bolts 6 at the member end. In short, since the flange external attachment plate 5 of the beam 11 of the present embodiment is widened, an increase in member elastic rigidity can be expected compared to the beam of the conventional method, so it becomes possible to reduce the cross-section used for the central member 3 compared to the case of using the conventional method. And this can be achieved only when the member elastic rigidity of the beam 11 of the present embodiment can be correctly considered in structural design practice. That is, by applying the method for evaluating the member elastic rigidity of the beam member of the present embodiment to perform structural design, it becomes possible to optimize the structural cost.

[0071] As described above, the embodiments of the present invention have been described in detail with reference to the drawings. However, the specific configuration is not limited to this embodiment, and design changes that do not deviate from the gist of the present invention are included in the present invention.

[0072] For example, in the above-described embodiment, the method for evaluating the member elastic rigidity of the beam 11 in the steel column-beam joint structure 1 in which the center member 3 is connected to the brackets 13 projecting in all four directions of the steel column 2 via the joints 12 has been described, but the present invention is not limited thereto. The present invention can also be applied when evaluating the member elastic rigidity of a beam member having a friction joint by high-strength bolts in a form different from the above-described joint 12.

Explanation of Signs

[0073] 11: Beam (beam member) 12: Joint 13: Bracket 2: Steel column (column) 3: Center member 5: Flange external attachment plate (attachment plate) 6: High-strength bolt

Claims

1. A method for evaluating the member elastic rigidity of a beam member, which appropriately evaluates an increase in member elastic rigidity due to widening of the beam member provided with a friction joint by high-strength bolts connecting a central member and a bracket at the end of the member, comprising: modeling a central member section of only the central member, a bracket section of only the bracket, and a joint section connecting these sections, based on the cross-sectional shape representing each section; deriving a deflection δ when a load Q acts on the tip of the free end of a calculation model that becomes a cantilever beam in which beam elements of the central member section, the joint section, and the bracket section are rigidly joined in the material axis direction; Based on the derived deflection δ, the member elastic rigidity S of the beam member Mθ comprises a step of expressing it by the relationship between the bending moment M and the member deformation angle θ, The member elastic rigidity SMθ of the beam member is characterized by being expressed by the following formula. Here, bc E, fs E, and br E are the Young's moduli of the steel materials in the central member section, the joint section, and the bracket section, respectively. bc I is the second moment of area of the central member section. bc l is the length of the central member section, and l is the length of the beam member. J l is the length of the joint section. br I is the second moment of area of the bracket section. br l' is the length of the bracket section, D 3 and D 5 are as shown below. As a premise shown by the above formulas D1 - D5, the beam member includes a bracket flange protruding from a steel column, a flange outer attachment plate and a flange inner attachment plate that are opposed to each other with the flange of the central member interposed therebetween, where the steel column side is widened and the central member side is formed to the width of the central member, and a plurality of high-strength bolts that join the ends of the flange outer attachment plate and the flange inner attachment plate on the steel column side to the bracket flange and join the ends of the flange outer attachment plate and the flange inner attachment plate on the central member side to the flange of the central member. The meanings of each symbol are as follows. Jγ is (max bfs1 - bcb) / Jl, max bfs1 is the maximum width of the flange outer attachment plate, bcb is the width of the central member, brH is the eccentricity of the bracket, tfs1 is the thickness of the flange outer attachment plate, brtf is the thickness of the bracket flange, tfs2 is the thickness of the flange inner attachment plate, Abfs1 is the width of the flange outer attachment plate at the bolt hole position of the high-strength bolt farthest from the steel column, gfs2 is the interval between the flange inner attachment plates, and bcIw is the sectional secondary moment of inertia of the web of the central member.

2. The second moment of area of the evaluation model in which the cross-sectional shape of the beam member equivalent to the calculation model is uniform in the material axis direction bc I eq The step of obtaining The second moment of area of the evaluation model bc I eq is divided by the second moment of area of the central member section bc I to obtain the ratio φ bc The method for evaluating the member elastic rigidity of the beam member according to claim 1, characterized by comprising the step of obtaining the ratio φ.

3. The second moment of area of the evaluation model in which the cross-sectional shape of the beam member equivalent to the calculation model is uniform in the material axis direction bc I eq The step of obtaining, and The second moment of area of the evaluation model bc I eq is divided by the second moment of area of the central member section bc I to obtain the ratio φ bc A method for evaluating the member elastic stiffness of the beam member according to claim 1, characterized by comprising the step of obtaining The second moment of area of the evaluation model bc I eq and the ratio φ bc are characterized by being expressed by the following formula, which is an evaluation method for the member elastic stiffness of a beam member.

Images