JP2018154996A - Design method for composite beam and composite beam - Google Patents

Abstract

PROBLEM TO BE SOLVED: To optimize a torsional rigidity ratio between a concrete slab and a beam while suppressing the lateral buckling of the beam.SOLUTION: In a design method of a composite beam 10 having a beam 12 of an H-shaped steel joined to a column 14 and a concrete slab 20 joined to an upper flange 12A of the beam 12, a torsional rigidity ratio of the concrete slab 20 and the beam 12 is set so that the beam 12 does not collapse laterally when a design member angle is given to the beam 12.SELECTED DRAWING: Figure 2

Description

  The present invention relates to a composite beam design method and a composite beam.

  A method of designing a composite beam having an H-shaped cross-section beam and a concrete slab joined to the flange of the beam, taking into account the restraining force (restraint effect) against lateral buckling deformation of the flange of the beam by the concrete slab A synthetic beam design method for obtaining the elastic lateral buckling strength of a beam is known (for example, see Patent Document 1).

JP 2012-012788 A

  In the method of designing a composite beam disclosed in Patent Document 1, the torsional rigidity ratio between the concrete slab and the beam is set to a predetermined value or more to secure a restraining force against the lateral buckling deformation of the flange caused by the concrete slab. Suppresses bending.

  However, further optimization of the torsional stiffness ratio between the concrete slab and the beam is desired.

  An object of the present invention is to optimize the torsional rigidity ratio between a concrete slab and a beam while suppressing the lateral buckling of the beam in consideration of the above facts.

  The method for designing a composite beam according to claim 1 includes a pair of flanges facing each other in the vertical direction and a web connecting the pair of flanges, the beam joined to a column, and joined to the flange. A composite slab design method comprising: a torsional rigidity ratio between the concrete slab and the beam so that the beam does not buckle when a design member angle is given to the beam. .

  According to the composite beam designing method of the first aspect, when the design member angle is given to the beam, the torsional rigidity ratio between the concrete slab and the beam is set so that the beam does not laterally buckle.

  Here, the torsional rigidity of the concrete slab required for restraining the rotation of the flange of the beam varies depending on the design member angle of the beam (the required member angle of the beam). That is, when the design member angle of the beam is reduced, the torsional rigidity of the concrete slab necessary for restraining the rotation of the flange of the beam is also reduced. On the other hand, as the design member angle of the beam increases, the torsional rigidity of the concrete slab required to constrain the rotation of the flange of the beam also increases.

  Therefore, in the present invention, when the design member angle is given to the beam, the torsional rigidity ratio between the concrete slab and the beam is set so that the beam does not buckle laterally. Thereby, the torsional rigidity ratio between the concrete slab and the beam can be optimized while suppressing the lateral buckling of the beam.

  In the composite beam designing method according to claim 2, the torsional rigidity ratio is set so as to satisfy the formula (1).

  According to the composite beam designing method of the second aspect, the torsional rigidity ratio between the concrete slab and the beam is set so as to satisfy the formula (1). Thereby, the torsional rigidity ratio between the concrete slab and the beam can be easily optimized.

  The composite beam design method according to claim 3 is the composite beam design method according to claim 1 or 2, wherein the concrete slab has a slab thickness of 140 mm or more, or between the concrete slab and the beam. When there is a deck plate between them, it is 130 mm or more.

  According to the composite beam designing method of the third aspect, the torsional rigidity ratio between the concrete slab and the beam can be further optimized by setting the slab thickness of the concrete slab within a practical range.

  The composite beam according to claim 4 has a pair of flanges facing each other in the vertical direction and a web connecting the pair of flanges, a beam joined to a column, and a concrete slab joined to the flange. When the design member angle is given to the beam, the torsional rigidity ratio between the concrete slab and the beam is set so that the beam does not laterally buckle.

  According to the composite beam of the fourth aspect, when the design member angle is given to the beam, the torsional rigidity ratio between the concrete slab and the beam is set so that the beam does not laterally buckle.

  Here, as described above, the torsional rigidity of the concrete slab required to restrain the rotation of the flange of the beam varies depending on the design member angle of the beam (the necessary member angle of the beam).

  Therefore, in the present invention, when the design member angle is given to the beam, the torsional rigidity ratio between the concrete slab and the beam is set so that the beam does not buckle laterally. Thereby, the torsional rigidity ratio between the concrete slab and the beam can be optimized while suppressing the lateral buckling of the beam.

  As described above, according to the composite beam designing method and composite beam according to the present invention, the torsional rigidity ratio between the concrete slab and the beam can be optimized while suppressing the lateral buckling of the beam.

It is an elevation view which shows the composite beam which concerns on one Embodiment. FIG. 2 is a sectional view taken along line 2-2 of FIG. It is a model figure of the concrete slab which comprises a composite beam. It is a perspective view which shows the composite beam used by the analysis. (A) And (B) is a perspective view which shows the analysis model of a composite beam. Elastic Lateral Buckling force of the beam and _{(M cre /} M _cr0), is a graph showing the relationship between the torsional rigidity ratio x of the concrete slab and the beam. It is a table | surface which shows the dimension of the test body of the beam used by the loading experiment, and an analysis result. (A) shows the relationship between the beam strength increase coefficients α ₁ and α ₂ due to the restraining force of the concrete slab and the web side length ratio λ _W when the support conditions at both ends of the beam are fixed support at both ends. (B) is a graph showing the beam strength increase coefficients α ₁ and α ₂ due to the restraining force of the concrete slab and the beam web when the support conditions at both ends of the beam are fixed support at one end and pin support at the other end. It is a graph which shows the relationship with side length ratio (lambda) _W. (A) is a graph obtained by dividing the web edge length ratio lambda _w in web width-thickness ratio d / t _w shown in FIG. 8 (A), (B), the web side shown in FIG. 8 (B) it is a graph obtained by dividing the length ratio λ _w in the web width thickness ratio d / t _w. Elastic Lateral Buckling force of the beam and _{(M cre /} M _cr0), is a graph showing the relationship between the torsional rigidity ratio x of the concrete slab and the beam. It is a table | surface which shows the dimension of the test body of the beam used by the loading experiment, and an analysis result. It is an elevation view which shows a loading experiment apparatus. (A) shows the skeleton curve used in the loading experiment, and (B) is a graph showing the relationship between the moment M of the beam and the member angle R obtained from the experiment. It is a table | surface which shows the comparison result of the calculated value of a plasticity factor of a beam, and an experimental value. (A) And (B) is a graph which shows the relationship between the calculated value of the plasticity factor μ of a beam, and an experimental value.

(One embodiment)
Hereinafter, an embodiment will be described with reference to the drawings.

(Composite beam)
As shown in FIGS. 1 and 2, the composite beam 10 in this embodiment includes a beam 12 and a concrete slab 20. The beam 12 has an H-shaped cross section. The beam 12 includes a pair of flanges 12A and 12B that face each other in the vertical direction, and a web 12C that connects the pair of flanges 12A and 12B. For example, the beam 12 is installed on a pair of pillars 14.

  The beam 12 may be, for example, a roll H formed by roll forming, or may be a build H assembled by welding a pair of flanges 12A and 12B and the web 12C. Further, the cross-sectional shape of the beam 12 may be a deviated cross-sectional shape in which the thickness and width of the pair of flanges 12A and 12B and the web 12C are different.

Further, the support conditions for both ends 12E1 and 12E2 in the material axis direction of the beam 12 may be fixed support at both ends, or may be fixed at one end and supported at the other end pin. Further, a generalized lateral buckling slenderness ratio λ _b of the beam 12 described later is set to 150 to 250. Note that “lower limit value to upper limit value” in the present embodiment means a value that is greater than or equal to the lower limit value and less than or equal to the upper limit value.

The concrete slab 20 is, for example, a reinforced concrete structure or a PCa concrete structure. The slab thickness t _c (see FIG. 2) of the concrete slab 20 is, for example, 140 mm or more. When the concrete slab is a deck slab (synthetic slab), that is, when there is a deck plate (not shown) between the concrete slab 20 and the beam 12, the slab thickness t _c of the concrete slab is, for example, 130 mm or more.

The concrete slab 20 is joined to the upper flange 12 </ b> A of the beam 12 via a plurality of studs 22, and constitutes the composite beam 10 together with the beam 12. The plurality of studs 22 are, for example, headed studs. Each stud 22 protrudes upward from the upper surface of the flange 12A. These studs 22 are arranged at intervals in the material axis direction (longitudinal direction) of the beam 12. In addition, as shown in FIG. 2, the plurality of studs 22 are arranged at intervals in the width direction of the flange 12A. The number of studs 22 arranged in the width direction of the flange 12A may be one.

  The number and strength of the plurality of studs 22 are set such that the lateral movement of the flange 12A of the beam 12 can be restricted by the concrete slab 20, for example. Further, the flange 12A of the beam 12 and the concrete slab 20 are not limited to the stud 22 and may be joined by other joining members.

  Here, at the time of an earthquake, there is a possibility that a lateral buckling occurs in which the web 12C of the beam 12 protrudes in the out-of-plane direction. As a countermeasure, for example, a lateral stiffener (lateral buckling suppression member) (not shown) may be attached to the beam 12 to provide out-of-plane rigidity to the web 12C of the beam 12. However, it takes time to attach the lateral stiffener to the beam 12.

  Therefore, in the present embodiment, the ratio between the torsional rigidity of the concrete slab 20 and the torsional rigidity of the beam 12 (hereinafter simply referred to as “twisting”) so that the beam 12 is not laterally buckled by the restraining force (constraint effect) of the concrete slab 20. Stiffness ratio x ”) is set. Thereby, in this embodiment, the lateral buckling of the beam 12 can be suppressed while making the lateral stiffener unnecessary.

  Here, the torsional rigidity of the concrete slab 20 required to constrain the rotation of the flange 12A of the beam 12 varies depending on the design member angle θ of the beam 12 (the necessary member angle of the beam). That is, when the design member angle θ of the beam 12 is reduced, the torsional rigidity of the concrete slab 20 required for restricting the rotation of the flange 12A of the beam 12 is also reduced. On the other hand, when the design member angle θ of the beam 12 is increased, the torsional rigidity of the concrete slab 20 required for restricting the rotation of the flange 12A of the beam 12 is also increased.

  Therefore, in this embodiment, the torsional rigidity ratio x between the concrete slab 20 and the beam 12 is set so that the beam 12 does not buckle when the design member angle θ is given to the beam 12. More specifically, the torsional rigidity ratio x between the concrete slab 20 and the beam 12 is set so as to satisfy the following formula (1). Thereby, the torsional rigidity ratio x between the concrete slab 20 and the beam 12 can be optimized while suppressing the lateral buckling of the beam 12. When the torsional rigidity ratio x is negative (x <0), no lateral buckling occurs in the beam 12 regardless of the torsional rigidity of the concrete slab 20.

However,
b: Constant determined by support conditions at both ends of beam <Support conditions at both ends of beam: In the case of fixed support at both ends>
b = 1.82 to 8.15
<Supporting conditions at both ends of the beam: When one end is fixed and the other end is pin supported>
b = 2.67-4.69
_θ M: End bending moment generated at the end of the beam when the design member angle θ is given to the beam M _cr0 : Elastic lateral buckling strength of the beam due to equal bending moment α ₁ , α ₂ : Restraint force of the concrete slab Coefficient of increase in beam strength due to the beam <Supporting conditions at both ends of the beam: In the case of fixed support at both ends>
α ₁ = 2.74 to 3.91
α ₂ = 3.40-7.47
<Supporting conditions at both ends of the beam: When one end is fixed and the other end is pin supported>
α ₁ = 2.43 to 2.59
α ₂ = 3.99 to 6.61
It is.

(Calculation method of torsional rigidity ratio between concrete slab and beam)
Hereinafter, a method for calculating the torsional rigidity ratio x between the concrete slab 20 and the beam 12 will be described while examining the necessity of the lateral stiffener.

The necessity of the horizontal stiffener is determined based on the plastic deformation performance of the beam 12, for example. The plastic deformation performance of the beam 12, that is, the plastic rate (retained plastic rate) μ of the beam 12 is expressed by the following formulas (2) and (3).

However,
λ _b : Generalized lateral buckling slenderness ratio M _cre : Elastic lateral buckling strength of the beam considering the restraining force of the concrete slab M _p : Total plastic yield strength of the beam

In order to improve the accuracy of the above equations (2) and (3), it is necessary to accurately obtain the elastic lateral buckling strength M _cre of the beam 12 in consideration of the restraining force of the concrete slab 20. Restraining force of the concrete slab 20 is, for example, as shown in FIG. 3, the lateral movement restraining spring k _u for restraining lateral movement of the flange 12A of the beam 12, the rotation restraint for restraining the rotation of the flange 12A of the beam 12 It is modeled on a spring k _beta.

Here, when the beam 12 and the concrete slab 20 are integrally joined to form the composite beam 10, the lateral movement of the flange 12 </ b> A of the beam 12 is basically restrained by the concrete slab 20. Therefore, in this embodiment, the lateral movement of the flange 12A is intended to be fully constrained by the lateral movement restraining spring k _u of the concrete slab 20, the rotation restraining force of the flange 12A by the rotation restraining spring k _beta of the concrete slab 20 consider.

First, the relationship between the rotational restraining force of the concrete slab 20, that is, the torsional rigidity of the concrete slab 20, and the lateral buckling strength M _cre of the beam 12 is obtained by analysis.

(Analysis model)
4 and 5A show an analysis model of the beam 12. The support condition of both ends 12E1 and 12E2 in the material axis direction of the beam 12 is fixed. That is, at both ends 12E1 and 12E2 of the beam 12, the rotation and warpage around the strong axis and the weak axis are restricted. In this analysis, three types of beams 12 having different beam spans (total beam lengths) 1 are used.

The analysis model of the concrete slab 20 is modeled as a beam element having only torsional rigidity. Slab width B _e in this concrete slab 20 is set to, for example, a pillar width of the pillar 14 the beam 12 is joined.

  FIG. 5B shows an analysis model in which the support conditions of both ends 12E1 and 12E2 of the beam 12 are one end fixed support and the other end pin support.

(analysis method)
In this analysis, an inverse symmetrical bending moment M (see FIG. 5A) is given to three types of beams 12 having different beam spans l using the torsional rigidity of the concrete slab 20 as a parameter, and the elastic lateral buckling strength of each beam 12 is given. M _cre was determined respectively.

Further, the elastic lateral buckling strength M _cr0 of each beam 12 when an equal bending moment is applied to the beam 12 from which the concrete slab 20 is omitted, that is, the beam 12 in which the lateral movement and rotation of the flange 12A are _{unconstrained.} Was calculated not by analysis but by calculation (manual calculation). In addition, the support conditions of both ends 12E1 and 12E2 of the beam 12 when _{obtaining the} elastic lateral buckling strength M _cr0 are the same as those for the elastic lateral buckling strength M _cre .

(Analysis results, support conditions at both ends of the beam: fixed support)
FIG. 6 shows an analysis result when the support condition of both ends 12E1 and 12E2 of the beam 12 is fixed support. The vertical axis in FIG. 6 is a value _obtained by dividing the elastic lateral buckling strength M _cre of the beam 12 obtained by analysis by the elastic lateral buckling strength M _cr0 . Further, the horizontal axis of FIG. 6 is the torsional rigidity ratio x between the concrete slab 20 and the beam 12.

As shown in FIG. 6, the elastic lateral buckling strength (M _cre / M _cr0 ) _{approaches the} lower limit value when the torsional rigidity ratio x between the concrete slab 20 and the beam 12 is 0.01 or less, and the torsional rigidity ratio When x is 100 or more, it gradually approaches the upper limit.

Here, when the elastic lateral buckling strength (M _cre / M _cr0 ) is a lower limit value, that is, when the torsional rigidity ratio x of the concrete slab 20 to the beam 12 is 0.01 or less, the torsional rigidity of the concrete slab 20 is small. Therefore, the rotational restraining force of the flange 12A of the beam 12 by the concrete slab 20 is also reduced. Therefore, basically, the rotation of the flange 12A of the beam 12 is not constrained by the concrete slab 20, and only the lateral movement of the flange 12A is constrained.

On the other hand, when the elastic lateral buckling strength (M _cre / M _cr0 ) is the upper limit, that is, when the torsional rigidity ratio x of the concrete slab 20 to the beam 12 is 100 or more, the torsional rigidity of the concrete slab 20 is large. The rotational restraining force of the flange 12A of the beam 12 by the slab 20 is also increased. Therefore, basically, the rotation of the flange 12 </ b> A is restricted by the concrete slab 20. That is, the concrete slab 20 is in a state in which the rotation and lateral movement of the flange 12A are completely restricted.

A function in which the elastic lateral buckling strength (M _cre / M _cr0 ) converges to the lower limit value and the upper limit value as described above can be expressed by a logistic function represented by the following formula (4).

However,
f: Lower limit value f + a: Upper limit value a, b, c, f: Unknown (constant)
It is.

Here, y in equation (4) is the elastic lateral buckling strength M _cre of the beam 12, and x in equation (4) is the torsional rigidity ratio x between the concrete slab 20 and the beam 12. In this case, the lower limit f of the elastic lateral buckling strength M _cre is the lateral buckling strength M _cr1 of the beam 12 in which the rotation of the flange 12A is unconstrained and only the lateral movement of the flange 12A is completely restrained. The upper limit f + a resilient Lateral Buckling force _{M cre} is next _{M cr2} the Lateral Buckling force of the beam 12 to rotate and lateral movement of the flange 12A is fully constrained, represented by the following formula (5).

  In Equation (5), x is represented by a natural logarithm for simplification. Further, the torsional rigidity ratio x is expressed by the following formula (6).

However,
_{C G:} shear modulus of elasticity of the concrete slab
_C J: Torsional constant of Sambunan of concrete slab
_S G: Shear elastic modulus of the beam
_S J: The torsional constant of the sambunan of the beam.

Further, the torsion constant _C J of Saint-Venant of the concrete slab 20 is represented by the following formula (7).

However,
B _e : Slab width of concrete slab (effective width)
t _c : slab thickness of concrete slab.

Further, torsional constant _S J of Saint-Venant beam 12 is expressed by the following equation (8).

However,
H: RyoNaru t _f: thickness t _w of the beam flanges: the thickness of the web B: is the width of the beam.

Next, the coefficients b and c of the above equation (4) are obtained by the least square method based on the analysis result. FIG. 7 shows the dimensions of the specimen of the beam 12 and the analysis results. Note that _a M _cr1 and _a M _cr2 in FIG. 7 are analysis values, and M _cr0 , M _cr1 , and M _cr2 are calculated values of Equation (9) and the like. The same applies to FIG.

  As shown in FIG. 7, the coefficient c was around 1.0 regardless of the shape and size of the beam 12. Therefore, in this embodiment, as an example, the coefficient c is set to 1.0 (c = 1.0). Next, the coefficient b was in the range of 1.82 to 8.15. Therefore, in this embodiment, as an example, the coefficient b is set to 4.31 (b = 4.31) which is an average value of the plurality of beams 12.

  The coefficient b is not limited to the average value 4.31 and may be in the range of 1.82 to 8.15. Similarly, the coefficient c is not limited to 1.0 and may be around 1.0.

Next, buckling strength (elastic lateral buckling strength) M _cr1 and M _cr2 are _defined as in the following formulas (9a) and (9b).

However,
α ₁ , α ₂ : Beam strength increase coefficient due to restraint force of concrete slab (lateral buckling strength increase coefficient)
It is.

_Further , as described above, the elastic lateral buckling strength _Mcr0 is the elastic lateral buckling strength of the beam 12 due to the equal bending moment (the lateral movement and rotation of the flange 12A are unconstrained), and is represented by the following formula (10). .

However,
E: Elastic modulus of the beam I _y : Secondary moment of inertia around the weak axis of the beam I _w : Beam bending torsional constant l _b : Effective buckling length of the beam (in the case of fixed support at both ends, l _b = 0.5 × l)
l: Beam span.

In addition, the bending torsional constant of the beam is expressed by the following formula (11).

However,
t _f : plate thickness of the flange of the beam b _f : width of the flange of the beam h: distance between centers of the upper and lower flanges.

Further, the web side length ratio λ _w of the beam 12 is expressed by the following formula (12).

However,
l: Beams span H: RyoNaru t _f: is the thickness of the flange.

Next, FIG. 8 (A) shows the relationship between the yield strength increase coefficients α ₁ and α ₂ of the beam 12 and the web side length ratio λ _w . The yield strength coefficients α ₁ and α ₂ were obtained by dividing the lateral buckling strength M _cr1 and M _cr2 of the beam 12 obtained from the eigenvalue analysis by the elastic lateral buckling strength M _cr0 of the above equation (10). .

As can be seen from FIG. 8A, the yield strength increase coefficient α ₁ is substantially linearly related to the web side length ratio λ _w , but the yield strength increase coefficient α ₂ varies. Therefore, as shown in FIG. 9 (A), it was organized by dividing the web edge length ratio lambda _w in web width-thickness ratio d / t _w. Incidentally, d is the height of the web 12C of the beam 12 (see FIG. 2), _{t w} is the thickness of the web 12C.

As shown in FIG. 9A, the yield strength increase coefficients α ₁ and α ₂ of the beam 12 are approximately linearly related to the web side length ratio λ _w / (web width thickness ratio d / t _w ). Therefore, the yield strength increase coefficients α ₁ and α ₂ are defined as in the following formulas (13a) and (13b).

However,
λ _W : Web side length ratio of beam d: Web composition (web height)
_tw : web thickness.

The yield strength increase coefficient α ₁ of the beam 12 is not limited to the above formula (13a), and may be in the range of 2.74 to 3.91 (see FIG. 7). Similarly, yield strength increased coefficient alpha ₂ of the beam 12 is not limited to the above formula (13b), may range from 3.40 to 7.47 (see FIG. 7).

By the way, from the formula (9a) and the formula (9b), the formula (8) is expressed by the following formula (14).

From the above formula (14), the restraining force of the flange 12A of the beam 12 by the concrete slab 20 is represented by the following formula (15).

Further, in FIG. 10, the elastic Lateral Buckling force of the beam 12 obtained from the equation (14) and _(M cre _{/ M cr0),} elastic Lateral Buckling force of the beam 12 obtained from the analysis _(M cre _{/ M cr0)} is It is shown. Note that plot (solid circles) in Fig. 10, the slab width (effective width) B _e of the concrete slab 20 shows the torsional rigidity ratio x in the case where the pillar width.

  As shown in FIG. 10, the calculated value graph (solid line) and the analytical value graph (broken line) correspond well. From this, it can be seen that the equation (14) is appropriate.

(Support conditions for both ends of the beam: one end fixed and other end pin support)
In the same manner as described above, the case where the support conditions of the both ends 12E1 and 12E2 of the beam 12 are one end fixed support and the other end pin support was also examined.

Supporting conditions across 12E1,12E2 beam 12, when the other end a pin supported at one end fixed support, the effective seat屈長of _{l b} of the beam 12, a 0.7l _(l b = 0.7l). Also, as shown in FIG. 11, the coefficient b is in the range of 2.67 to 4.69, and the average value is 3.92 (b = 3.92). The coefficient c is around 1.0 (c = 1.0).

  The coefficient b is not limited to the average value of 3.92, and may be in the range of 2.67 to 4.69. Similarly, the coefficient c is not limited to 1.0 and may be around 1.0.

Furthermore, as shown in FIG. 8 (B), yield strength increases the coefficient alpha ₁ of the beam 12, there is a generally linear relationship between the web edge length ratio lambda _w, the yield strength increased coefficient alpha _2, there are variations. Therefore, as shown in FIG. 9 (B), and organized by dividing the web edge length ratio lambda _w in web width-thickness ratio d / t _w.

As shown in FIG. 9B, the proof stress increase coefficients α ₁ and α ₂ are substantially linearly related to the web side length ratio λ _w / (web width thickness ratio d / t _w ). Therefore, the yield strength coefficients α ₁ and α ₂ are defined as in the following formulas (13a ′) and (13b ′).

However,
λ _W : Web side length ratio of beam d: Web composition (web height)
_tw : web thickness.

The yield strength increase coefficient α ₁ of the beam 12 is not limited to the above formula (13a ′), and may be in the range of 2.43 to 2.59 (see FIG. 11). Similarly, yield strength increased coefficient alpha ₂ of the beam 12 is not limited to the above formula (13b '), may range from 3.99 to 6.61 (see FIG. 11).

(Confirmation of validity of formula (14))
Next, the validity of the equation (14) is verified. Specifically, the plastic modulus μ of the beam 12 is calculated from the elastic lateral buckling strength M _cre of the beam 12 obtained by the equation (14). Then, the validity of the equation (14) is verified by comparing the calculated plasticity factor μ of the beam 12 with the plasticity factor μ ′ of the beam 12 obtained from the experimental value.

First, when Expression (14) is substituted into Expression (3), the generalized lateral buckling slenderness ratio (generalized slenderness ratio) λ _b of the beam 12 is represented by the following Expression (16).

Further, when the above equation (16) is substituted into the equation (2), the plasticity ratio μ of the beam 12 is expressed by the following equation (17). From this equation (17), the plastic modulus μ of the beam 12 was obtained.

(Outline of loading experiment)
In the loading experiment, a load was repeatedly applied to the beam 12 by the loading device 30 shown in FIG. 12, and the plasticity ratio μ was obtained from the relationship between the obtained moment M and the member angle R.

(Loading device)
As shown in FIG. 12, the loading device 30 includes a pair of columns 38 and a force beam 46 supported by the pair of columns 38. The pair of pillars 38 are supported by the floor 56 via the foundation 58. Further, the column bases of the pair of columns 38 are connected to the foundation 58 via the rotation shaft 50, and the column heads of the columns 38 are made to the force beam 46 via the rotation shaft 51. Thereby, the pair of pillars 38 can be tilted. The composite beam 10 is installed between the pair of columns 38. A weight 48 that applies a long-term load to the composite beam 10 is appropriately placed on the composite beam 10.

  In addition, one end of the force beam 46 and the reaction force wall 57 are connected via the jack 40 and the load cell 42. By applying a horizontal force to one end of the force beam 46 by the jack 40, an antisymmetric bending moment is applied to the composite beam 10.

(Experimental result)
A skeleton curve is created in accordance with FIG. 13A, and the deformation of the beam 12 when the proof stress of the beam 12 is reduced to the total plastic proof strength of the composite beam 10 calculated by the above-described loading test (the proof stress of the beam 12 is calculated). (If the total plastic yield strength of the composite beam 10 obtained in the above is not reduced, the maximum deformation of the beam 12), as shown in FIG. 13B, the elastic stiffness of the experimental value and the total plastic yield strength by the general yield method by dividing the elastic deformation R _p at full plastic strength obtained from was determined ductility factor mu.

  Here, FIG. 14, FIG. 15 (A), and FIG. 15 (B) show the relationship between the plasticity ratio μ obtained from the above equation (17) and the plasticity ratio μ ′ obtained from the experimental value. Yes. In FIG. 15A, a positive / negative average value is employed for the plasticity ratio μ ′, and FIG. 15B employs a positive / negative maximum value for the plasticity ratio μ ′. That is, in this embodiment, the formula (14) is evaluated with two types of indices.

  From FIG. 15A, it can be seen that the plasticity factor μ of the beam 12 obtained from the above equation (17) corresponds well with the plasticity factor μ ′ of the beam 12 obtained from the experimental value. On the other hand, it can be seen from FIG. 15B that the plasticity factor μ of the beam 12 obtained from the above equation (17) is slightly larger than the plasticity factor μ ′ of the beam 12 obtained from the experimental value. That is, it can be seen from the above formula (17) that the plasticity ratio μ of the beam 12 is evaluated on the safe side.

  FIG. 15B shows a comparison result when the support conditions of both ends 12E1 and 12E2 of the beam 12 are one end fixed support and the other end pin support. Also in this case, it can be seen that the plasticity factor μ of the beam 12 obtained from the above equation (17) is slightly larger than the plasticity factor μ ′ of the beam 12 obtained from the experimental value. That is, it can be seen from the above formula (17) that the plasticity ratio μ of the beam 12 is evaluated on the safe side.

  In the loading experiment in the case of one end fixed support and the other end pin support, in the loading history in which the lower flange 12B is compressed, the proof stress of the beam 12 is reduced to the total plastic proof stress of the composite beam 10 obtained by calculation. Based on the deformation at the time, the plasticity ratio μ of the beam 12 was obtained.

  As described above, it can be seen from FIG. 15A and FIG. 15B that Expression (14) is appropriate.

(Necessity of horizontal stiffeners)
Next, the necessity of a horizontal stiffener will be examined.

First, the relationship between the design member angle θ of the beam 12 and the plasticity ratio μ of the beam 12 will be described. The relationship between the design member angle θ of the beam 12 and the plasticity ratio μ _rq is expressed by the following formula (18) and formula (19).

However,
θ _p : Elastic member angle when the total plastic yield strength of the beam is reached I _x : Cross-sectional second moment around the strong axis of the beam.

  The beam 12 that needs to be examined for lateral buckling generally has a large slenderness ratio, and bending deformation is often excellent. Therefore, in the above equation (18), the shear deformation of the beam 12 is not considered, and only the bending deformation of the beam 12 is considered.

Here, Yokoho Tsuyoshizai is Naru required conditions, ductility factor of equation (17) mu is the ductility factor mu _rq above equations (18), represented by the following formula (20). From this equation (20), it can be seen that the necessity of the horizontal stiffener does not depend on the steel type of the beam 12.

Further, in the beam 12 (elastic member) that receives the antisymmetric bending moment, the end bending moment _θ M generated at the end of the beam 12 when the member angle of the beam 12 is a predetermined member angle (designed member angle) θ. Is represented by the following formula (21).

Then, the above formula (20) is represented by the following formula (22).

When the support conditions of both ends 12E1 and 12E2 of the beam 12 are one end fixed support and the other end pin support, the end bending moment _θ M of the beam 12 is expressed by the following formula (21 ′).

The above equation (22) indicates that the elastic lateral buckling strength M _{cre of} the beam 12 considering the restraining force by the concrete slab 20 is equal to or greater than the end bending moment _θ M generated at the end of the beam 12 given the design member angle θ. In this case, it is shown that the lateral stiffener is unnecessary. Therefore, by setting the elastic lateral buckling strength M _cre of the beam 12 so as to satisfy the above formula (22), the lateral stiffener can be made unnecessary.

Further, the following formula (23) is obtained from the above formula (22) and formula (14).

  When the above equation (23) is solved for the torsional rigidity ratio x, the above equation (1) is obtained. Therefore, by setting the torsional rigidity ratio x between the concrete slab 20 and the beam 12 so as to satisfy the expression (1), it is possible to suppress the lateral buckling of the beam 12 while eliminating the need for a lateral stiffener.

  Here, for example, an interlayer deformation angle at the end of the structure is adopted as the design member angle θ of the beam 12. This facilitates selection of the design member angle θ of the beam 12. In general, the member angle (deformation amount) of the beam 12 is about 40 to 60% of the interlayer deformation angle of the structure. Therefore, the beam 12 can be evaluated on the safe side by adopting the interlayer deformation angle at the end of the structure (at the time of ultimate proof stress) as the design member angle θ of the beam 12.

  Note that the design member angle θ of the beam 12 is not limited to the interlayer deformation angle at the end of the structure, and can be changed as appropriate.

(Supplement)
Supplementing Formula (20), both sides of Formula (20) are divided by the total plastic yield strength M _p of the beam 12, and further, the plastic rate μ) of Formula (1) and the plastic rate μ _rq of Formula (15) are _expressed as _follows . When substituted, the plasticity ratio μ of the beam 12 can be expressed by the following formula (24).

(Modification)
Next, a modification of the above embodiment will be described.

  In the above embodiment, the concrete slab 20 is joined to the upper flange 12 </ b> A of the beam 12, but the concrete slab 20 may be joined to the lower flange 12 </ b> B of the beam 12.

  Moreover, in the said embodiment, although Formula (1) was used for calculation of the torsional rigidity ratio x of the concrete slab 20 and the beam 12, the said embodiment is not restricted to this. The torsional rigidity ratio between the concrete slab 20 and the beam 12 only needs to be set so that the beam 12 does not laterally buckle when the design member angle θ is given to the beam 12, and the calculation method thereof can be changed as appropriate. is there.

  As mentioned above, although one embodiment of the present invention was described, the present invention is not limited to such an embodiment, and one embodiment and various modifications may be used in combination as appropriate, and the gist of the present invention will be described. Of course, various embodiments can be implemented without departing from the scope.

12 beam 12A flange 12E1 one end (one end of the beam in the material axis direction)
12E2 The other end (the other end in the beam axis direction of the beam)
14 Pillar 20 Concrete slab

Claims (4)

A method of designing a composite beam, comprising a pair of flanges facing each other in the vertical direction and a web connecting the pair of flanges, the beam being joined to a column, and a concrete slab joined to the flange. And
When the design member angle is given to the beam, the torsional rigidity ratio between the concrete slab and the beam is set so that the beam does not buckle laterally.
How to design composite beams. The torsional rigidity ratio is set so as to satisfy the formula (1).
The method for designing a composite beam according to claim 1.

However,
b: Constant determined by support conditions at both ends of beam <Support conditions at both ends of beam: In the case of fixed support at both ends>
b = 1.82 to 8.15
<Supporting conditions at both ends of the beam: In the case of one end fixed support and the other end pin support>
b = 2.67-4.69
_θ M: End bending moment generated at the end of the beam when the design member angle θ is given to the beam M _cr0 : Elastic lateral buckling strength of the beam due to equal bending moment α ₁ , α ₂ : Restraint force of the concrete slab Coefficient of increase in beam strength due to the beam <Supporting conditions at both ends of the beam: In the case of fixed support at both ends>
α ₁ = 2.74 to 3.91
α ₂ = 3.40-7.47
<Supporting conditions at both ends of the beam: When one end is fixed and the other end is pin supported>
α1 = 2.43-2.59
α2 = 3.99 to 6.61
It is. The slab thickness of the concrete slab is 140 mm or more, or 130 mm or more when there is a deck plate between the concrete slab and the beam.
The method for designing a composite beam according to claim 1 or 2. A composite beam having a pair of flanges facing each other in the vertical direction and a web connecting the pair of flanges, and comprising a beam joined to a column and a concrete slab joined to the flange,
When the design member angle is given to the beam, the torsional rigidity ratio between the concrete slab and the beam is set so that the beam does not buckle laterally,
Composite beam.