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WO2018151298A1 - Procédé d'analyse, procédé de conception, procédé de production et programme - Google Patents

Procédé d'analyse, procédé de conception, procédé de production et programme Download PDF

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Publication number
WO2018151298A1
WO2018151298A1 PCT/JP2018/005768 JP2018005768W WO2018151298A1 WO 2018151298 A1 WO2018151298 A1 WO 2018151298A1 JP 2018005768 W JP2018005768 W JP 2018005768W WO 2018151298 A1 WO2018151298 A1 WO 2018151298A1
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WIPO (PCT)
Prior art keywords
analysis method
steel
axis direction
lateral buckling
load
Prior art date
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Application number
PCT/JP2018/005768
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English (en)
Japanese (ja)
Inventor
聡 北岡
半谷　公司
菅野　良一
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Nippon Steel Corp
Original Assignee
Nippon Steel and Sumitomo Metal Corp
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Application filed by Nippon Steel and Sumitomo Metal Corp filed Critical Nippon Steel and Sumitomo Metal Corp
Priority to MYPI2019003867A priority Critical patent/MY178003A/en
Priority to SG11201906406YA priority patent/SG11201906406YA/en
Priority to JP2018540902A priority patent/JP6414374B1/ja
Publication of WO2018151298A1 publication Critical patent/WO2018151298A1/fr
Anticipated expiration legal-status Critical
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/20—Investigating strength properties of solid materials by application of mechanical stress by applying steady bending forces
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]

Definitions

  • the present invention relates to an analysis method for evaluating the lateral buckling strength of a steel beam, a steel beam design method, a steel beam manufacturing method, and a program.
  • This application claims priority based on Japanese Patent Application No. 2017-028462 for which it applied to Japan on February 17, 2017, and uses the content here.
  • the following formula (91) has been proposed as a conventional evaluation formula for lateral buckling strength of steel beams in buildings. Further, it is disclosed in Patent Document 1 for the purpose of making the design of a steel beam highly accurate by using an evaluation formula for lateral buckling strength using two moment correction factors according to the torsion conditions of the steel beam. Steel beam design methods have been proposed.
  • the conventional basic equations for buckling are often not known correctly or are too complex, so the energy method is generally used to calculate the buckling load. Is used.
  • the correct energy formula for lateral buckling when an intermediate load is applied has not been known so far, and the buckling load was calculated using an approximate energy formula. It could not be provided.
  • the design method disclosed in Patent Document 1 is a steel beam design method for preventing lateral buckling of a steel beam in which the lateral movement of the upper flange is constrained.
  • Design method disclosed in Patent Document 1 as an evaluation formula for elastic Lateral Buckling force M e of steel beam, below (93) below, using (94) below, by the torsional resistance and San safe by twisting Wagner the resistance, respectively by multiplying a different moment correction factors C 1 and C 2, and calculates the elastic Lateral Buckling force M e.
  • E Young's modulus
  • moment of inertia of area is I f the lower flange
  • G is the shear modulus
  • l is the beam length
  • d b is This is the distance between the plate thickness centers of the upper flange and the lower flange.
  • the (91) equation the evaluation formula of Lateral Buckling force M e of the beam by (92) below, has the following problems. That is, the above equation (91) is an approximate solution based on experiments and analysis because the buckling load M 0 when the equal bending moment is applied is multiplied by the moment correction coefficient C b that takes into account the effect of the moment gradient. Since the approximation accuracy is low, a large safety factor is required for use as a design method, and there is room for improvement in that respect.
  • the (91) equation is a evaluation formula using the single moment correction coefficient C b. That is, it is an attempt to express the load condition as a linear influence coefficient, which is a factor that has low evaluation accuracy and hinders economic structural design.
  • the (93) equation (94) evaluation formula Lateral Buckling force M e of the beam by the formula is an evaluation formula using two moment correction factors C 1 and C 2, high precision steel beam You can design with.
  • this evaluation formula corresponds only to the inverse symmetric moment, and cannot cope with the load on the steel beam of the actual building in which the vertical load and the horizontal load act in various ways.
  • the present invention has been devised in view of the above-described problems, and the object of the present invention is an analysis method, a design method, and a method that can evaluate the lateral buckling strength of a steel beam with high accuracy. It is to provide a manufacturing method and a program.
  • An analysis method is an analysis method for evaluating the lateral buckling strength of a steel beam.
  • both ends of the beam in the axial direction of the beam are fixed, and the width of the upper flange at the intermediate portion in the axial direction of the beam.
  • the lateral buckling strength M cr of the beam is expressed as follows under the condition that the lateral movement in the direction is constrained, an intermediate load is applied to the upper flange from above, and end loads are applied to both ends of the beam in the axial direction. It is calculated from the equations (12) to (16).
  • ⁇ and ⁇ are coefficients determined from the following equations (1) and (2) depending on the presupposed load conditions V and w.
  • V is a shearing force acting on the end of the beam in the material axis direction
  • w is an intermediate load acting on an intermediate portion of the beam in the material axis direction.
  • L is the length of the beam in the axial direction
  • E is the Young's modulus
  • I is the secondary moment of inertia around the weak axis of the lower flange
  • G is the shear elastic modulus
  • J is the torsion of Saint-Bennan.
  • d b is the thickness center distance between the upper and lower flanges
  • z is the length of up to any point in the timber axis direction of the beam from one end to the timber axis direction of the reference beam.
  • ⁇ is a torsion angle generated in the beam by lateral buckling.
  • ⁇ ′ represents the first derivative of ⁇
  • ⁇ ′′ represents the second derivative of ⁇ .
  • t is an auxiliary variable for integration.
  • ⁇ and ⁇ are determined as real numbers in a range according to the following equations (3a) and (3b).
  • a n is the unknown coefficients of the n items, in representing the ⁇ a (10a) type or (10b) equation and represents the weight of each term constituting the series in these series.
  • a method of designing a steel beam according to one embodiment of the present invention is based on the analysis method according to any one of the above (1) to (3), a step of calculating the M cr, based on the M cr Determining a cross-sectional dimension of the steel beam.
  • the manufacturing method of the steel beam which concerns on 1 aspect of this invention is based on the process of calculating Mcr based on the analysis method as described in any one of said (1) to (3), and Mcr .
  • the method includes a step of determining a cross-sectional dimension of the steel beam and a step of manufacturing the steel beam based on the determined cross-sectional dimension of the steel beam.
  • the analysis method for evaluating the lateral buckling strength of a steel beam, the design method of the steel beam, the manufacturing method of the steel beam, and the program according to the present invention can evaluate the lateral buckling strength of the steel beam with high accuracy. It is possible to design a steel beam and to manufacture a steel beam based on this.
  • FIG. 1 is a perspective view showing a steel beam that is an object of the analysis method according to the present embodiment.
  • Fig.2 (a) is a front view which shows the free body of the steel beam used as the object of the analysis method which concerns on this embodiment
  • FIG.2 (b) is the side view.
  • FIG. 3A is a front view showing a state in which both ends of the steel beam to be subjected to the analysis method according to the present embodiment are fixed and the lateral movement of the upper flange is restricted.
  • FIG. 3B is a side view of the steel beam shown in FIG. 3A.
  • FIG. 3C is a front view showing an example in which an opening is provided in a part of the floor slab above the steel beam to be an object of the analysis method according to the present embodiment.
  • FIG. 4A is a perspective view showing an example of a linear buckling analysis result by FEM of a steel beam in which the lateral movement of the upper flange is constrained
  • FIG. 4B is a steel frame in which the lateral movement of the upper flange is not constrained.
  • It is a perspective view which shows the example of a linear buckling analysis result by FEM of a beam.
  • Fig.5 (a) is a side view which shows an example of the virtual displacement of the steel beam used as the object of the analysis method concerning this embodiment
  • FIG.5 (b) is the bottom view
  • FIG. 6 is a cross-sectional view taken along line AA ′ of FIG. FIG.
  • FIG. 6A is a schematic side view showing a bending moment distribution in the material axis direction when both ends of the steel beam to be subjected to the analysis method according to the present embodiment are equally bent
  • FIG. FIG. 6 (d) is a schematic side view showing a reverse symmetric moment or the like when both ends are not bent equally
  • FIG. 7A is a graph showing a calculation result using ⁇ approximated by a predetermined series in the analysis method according to this embodiment
  • FIG. 7B is a graph showing the fourth term approximation of the Fourier cosine series. It is a graph which shows the calculation result using (phi) approximated.
  • FIG. 8 is a flowchart for explaining the flow of the analysis method according to the present embodiment.
  • FIG. 9 is a flowchart for explaining the flow of the design method according to the embodiment of the present invention.
  • the analysis method according to the present embodiment targets a steel beam that is a structural material such as a floor structure such as a building, a soil structure, or a frame structure as illustrated in FIG.
  • the analysis method according to the present embodiment is used for evaluating the lateral buckling strength of a steel beam, and mainly uses an H-section steel 20 in which an upper flange 21 and a lower flange 22 are connected by a web 23. This is intended to calculate the lateral buckling strength of the beam 2 with high accuracy.
  • the beam 2 includes a pair of upper and lower flanges 21 and 22 extending in the width direction X, and a pair of upper and lower upper flanges 21 and 22 is a web 23.
  • the beam 2 is, for example, a steel beam having a substantially H-shaped cross section by connecting the upper and lower ends of the web 23 to the approximate center in the width direction X of the upper flange 21 and the lower flange 22.
  • the entire beam 2 extends in the material axis direction Z and has a predetermined length L, as shown in FIG.
  • the distance in the height direction Y from the center of the plate thickness of the upper flange 21 to the center of the plate thickness of the lower flange 22 is the distance d b between the plate thickness centers of the upper flange 21 and the lower flange 22.
  • the distance d b between the thickness center distance in the height direction Y from the upper surface of the upper flange 21 to the upper surface of the lower flange 22, or from the lower surface of the upper flange 21 and the lower surface of the lower flange 22 in the height direction Y It can also be handled as the same as the distance.
  • the thickness center distance d b is the distance in the height direction Y from the lower surface of the upper flange 21 to the upper surface of the lower flange 22, or the RyoNaru in the height direction Y of the beam 2, treated as approximately the same You can also
  • the beam 2 is formed such that the upper flange 21 and the lower flange 22 extend in the width direction X and the web 23 extends in the height direction Y, as shown in FIG. X is a strong axis (therefore, the rotation direction about the width direction X is around the strong axis), and the height direction Y is the weak axis (therefore, the rotation direction about the height direction Y is around the weak axis). .
  • the beam 2 is laterally buckled when the lower flange 22 protrudes in the width direction X with respect to the material axis direction Z and the height direction Y.
  • the beam 2 that is the object of the analysis method according to the present embodiment has both ends 2a, 2a of the beam 2 in the material axis direction Z fixed to the column 3 or the like by rigid joining.
  • the both end portions 2 a and 2 a of the beam 2 are welded to the diaphragm 30 provided on the side surface of the square steel pipe, thereby being rigidly joined to the column 3. It will be fixedly supported.
  • both end portions 2a, 2a of the beam 2 may be welded to steel beams substantially orthogonal to each other inside the column 3 when a reinforced concrete column or an unreinforced concrete column is used as the column 3. Furthermore, both ends 2a and 2a of the beam 2 may be welded to a steel column extending in the height direction Y inside the column 3 when a steel reinforced concrete column is used as the column 3.
  • Both ends 2a, 2a of the beam 2 are fixed ends against lateral buckling deformation. That is, the beam 2 is joined to the column so that it does not rotate around the Y axis at its end, and the upper flange 21 of the beam 2 is joined to the column 3 so as not to rotate around the Z axis. .
  • This condition is that the upper flange 21 is joined to the steel column at the end of the beam 2 by welding or the like, or a part including the end 2a of the beam 2 is embedded in the concrete column. It is realized by doing.
  • the beam 2 that is the object of the analysis method according to the present embodiment may be fixed to the pillar 3 or the like at both ends 2a and 2a in the material axis direction Z by semi-rigid bonding or pin bonding.
  • the semi-rigid joint is a joint type in which the rotational movement of the beam 2 with respect to the column 3 is restricted to some extent, and the bending stress that can be transmitted between the column 3 and the beam 2 is smaller than that of a complete rigid joint.
  • the pin joint refers to a joint type that does not restrict the rotational movement of the beam 2 with respect to the column 3 and means that there is no or minimal bending stress that can be transmitted between the column 3 and the beam 2.
  • the beam 2 to be a target in the analysis method according to the present embodiment is provided with a floor slab 4 made of concrete or the like above the upper flange 21 in the intermediate portion 2b of the beam 2 in the material axis direction Z.
  • a concrete slab whose main structure is concrete is used, and a deck synthetic slab whose main structure is a deck plate made of concrete or steel is used.
  • the floor slab 4 is illustrated, but a part of the member constituting the roof is provided above the upper flange 21, an intermediate load due to the roof's own weight and load load acts, and the upper flange 21.
  • the lateral movement in the width direction X may be constrained.
  • a portion excluding the end faces at both end portions 2a and 2a is defined as an intermediate portion of the beam 2.
  • one or a plurality of shear connectors 25 such as headed studs are provided on the upper surface of the upper flange 21 in the intermediate portion 2b of the beam 2 in the material axis direction Z. Provided at predetermined intervals.
  • the shear connector 25 is provided so as to protrude upward from the upper surface of the upper flange 21 of the beam 2 and is embedded in the concrete or the like of the floor slab 4 above the upper flange 21 of the beam 2.
  • the target beam 2 in the analysis method according to the present embodiment is shown in FIG. 3A in the intermediate portion 2b of the beam 2 in the material axis direction Z by the shear connector 25 being embedded in the floor slab 4 or the like. As described above, the lateral movement of the upper flange 21 in the width direction X is restricted.
  • lateral movement in the width direction X of the upper flange 21 of the beam 2 is restrained, such as punching plug welding when a deck composite slab is used as a driving rod or a floor slab 4.
  • punching plug welding when a deck composite slab is used as a driving rod or a floor slab 4.
  • the upper flange 21 of the beam 2 is fixed to the floor slab as much as possible, it can be used as the shear connector 25.
  • the analysis method according to the present embodiment can be applied.
  • the upper flange 21 of the beam 2 is appropriately restrained by the opening reinforcing material 41 and the straight beam on both sides of the opening 40 so that the upper flange 21 of the beam 2 does not move laterally around this section.
  • Such an analysis method can be preferably used.
  • the beam 2 that is the object of the analysis method according to the present embodiment has an intermediate load due to the weight of the floor slab 4 and the load load at the intermediate portion 2 b of the beam 2 in the material axis direction Z. Act. At this time, in the intermediate portion 2b of the beam 2 in the material axis direction Z, an intermediate load acts on the upper flange 21 from above as an equally distributed load on the beam 2 that is the object of the analysis method according to the present embodiment. Further, when each column 3 is inclined due to an earthquake or the like, an end load is applied from the column 3 to both ends 2 a and 2 a of the beam 2 in the material axis direction Z.
  • the bending moment about the axis in the width direction X, along the height direction Y, at each of both ends 2a and 2a of the beam 2 in the material axis direction Z is generated.
  • the magnitude of one or more of these forces may be zero.
  • the target beam 2 in the analysis method according to the present embodiment is not subjected to reinforcement by a reinforcing member such as a secondary beam, but the analysis method according to the present embodiment is reinforced by a reinforcing member. Since the buckling strength of the beam made is evaluated on the safe side, this can also be targeted. Note that the reinforcing bars are not included in the reinforcing member.
  • the lateral movement of the upper flange 21 in the width direction X is restricted by the floor slab 4, so that the beam 2 is buckled early. Not reach.
  • the analysis method according to the present embodiment is a method for evaluating the lateral buckling suppression effect of the beam 2 using such lateral movement constraints.
  • the beam 2 undergoes lateral buckling as shown in FIG.
  • both ends 2a and 2a of the beam 2 in the material axis direction Z are fixed with respect to the beam 2 in which the shape steel such as the H-section steel 20 is used.
  • the lateral movement of the upper flange 21 in the width direction X is restricted, so that an intermediate load acts on the upper flange 21 from above, and the beam 2 in the material axis direction Z at both ends 2a, under conditions that effect the end load 2a, and calculates the Lateral Buckling force M cr of the beam 2.
  • the rotation of the beam 2 is positive in the direction in which the right screw advances.
  • the solid line represents the free body of the beam 2
  • the broken line represents an example of a virtual displacement that occurs in the free body of the beam 2 due to lateral buckling.
  • ⁇ Geometric boundary conditions> The upper flange 21 of the beam 2 is assumed to be restrained from displacement (lateral movement) in the X direction on the center line 0-0 ′.
  • the geometric boundary condition of the end 2a of the beam 2 is defined by a series of terminal conditions approximating lateral buckling deformation.
  • the beam 2 undergoes bending torsion with 0-0 ′ as a predetermined rotation axis due to lateral buckling, and deflection occurs as a secondary minute deformation.
  • the upper flange 21, the lower flange 22 and the web 23 are treated as flat plates.
  • the strength of the beam 2 against lateral buckling is determined by the bending rigidity in the plane of the upper flange 21 and the lower flange 22, the upper flange 21, and the lower flange. It is assumed that it is governed by the torsional rigidity of the flange 22 and the web 23.
  • L is the length of the beam 2 in the material axis direction Z
  • z is the beam 2 from one end (the left end 2a in the case of FIG. 5) which serves as a reference in the material axis direction Z of the beam 2.
  • ⁇ and ⁇ are coefficients determined by the load conditions of the material end load and the intermediate load, and represent the bending moment distribution of the beam 2. It can be obtained Lateral ⁇ heavy M cr considering a load condition of the beam by using ⁇ and gamma.
  • FIG. 6A when the bending moment distribution in the range of the real beam is equal bending at the left and right ends of the beam 2 (symmetric buckling), ⁇ is set to 0, and ⁇ It can be expressed by adjusting the value.
  • FIGS. 6B to 6D when equal bending is not achieved at the left and right member ends of the beam 2 (asymmetric buckling), ⁇ is a real number in the range of 1 to 3 (however, FIGS. 6B to 6D illustrate cases where ⁇ is 1, 2, and 3, respectively, and can be expressed by adjusting the value of ⁇ .
  • the deformation of each part of the beam 2 due to the lateral buckling is determined by the coordinate value in the material axis direction Z (that is, an arbitrary value in the material axis direction of the beam 2 from the left end 2a of the beam 2). It is expressed as a continuous function of (length to point) z.
  • the torsion angle ⁇ of the cross section generated in the beam 2 by the lateral buckling should be smoothly continuous in the material axis direction Z as shown in FIG.
  • an analytical solution of the lateral buckling strength is derived by approximating the series deformation of each part of the beam 2 due to the lateral buckling. Since the lateral buckling does not involve the distortion of the cross section of the beam 2, other deformations necessary for deriving the analytical solution, that is, the deflection v of the beam 2 shown in FIG. 5 (the left side of the following equation (3)), the right end of the beam 2 And the deflection ⁇ at the right end of the beam 2 can be expressed by the following equations (3) to (5), respectively. Thus, deformation of each part of the beam 2 due to lateral buckling can be uniquely expressed by ⁇ .
  • d b is the thickness center distance between the upper flange 21 and lower flange 22.
  • ⁇ ′ represents the first derivative of ⁇ .
  • t is an auxiliary variable for integration.
  • ⁇ U is the strain energy of the beam 2 and ⁇ T is the potential energy of the external force.
  • ⁇ U is given by the following equation (7) as the sum of strain energy by bending torsion and strain energy by pure torsion.
  • E is the Young's modulus
  • I is the secondary moment of inertia about the weak axis of the lower flange 22
  • G is the shear elastic modulus
  • J is the torsional constant of Saint-Bennan.
  • ⁇ ′′ represents the second derivative of ⁇ .
  • ⁇ T is given by the following equation (8) as the sum of potential energy of M cr , V, and w.
  • a n is the unknown coefficients of the n items, in representing the ⁇ a (10a) type or (10b) equation and represents the weight of each term constituting the series in these series.
  • the beam 2 having both ends 2a and 2a as fixed ends with respect to lateral buckling is targeted, and a cosine function (cosine) is used for each term of the series to represent this.
  • a cosine function cosine
  • A, B, C and D are functionals of ⁇ shown in the following equations (13) to (16).
  • ⁇ and ⁇ are coefficients determined from the following equations (1) and (2) depending on the presupposed load conditions V and w.
  • V is a shearing force acting on the end 2a of the beam 2 in the material axial direction Z
  • w is an intermediate load acting on the intermediate portion 2b of the beam 2 in the material axial direction Z.
  • L is the length of the beam 2 in the axial direction Z
  • E is the Young's modulus
  • I is the secondary moment of inertia around the weak axis of the lower flange 22
  • G is the shear elastic modulus
  • J is the sun torsional constant of safe
  • d b is the thickness center distance between the upper flange 21 and lower flange 22
  • z is from one end portion serving as a timber axis direction of the reference beam to any point of the timber axis beam length That's it.
  • ⁇ is a torsion angle generated in the beam 2 by lateral buckling.
  • ⁇ ′ represents the first derivative of ⁇
  • ⁇ ′′ represents the second derivative of ⁇ .
  • t is an auxiliary variable for integration.
  • the above equation (12) is a linear sum of the yield strength against bending torsion and the yield strength against pure torsion, and generally B ⁇ A.
  • the design method disclosed in Patent Document 1 gives different correction factors to these two proof stresses when an antisymmetric bending moment acts on the beam 2 in which the lateral movement of the upper flange 21 is restricted. A high-precision approximate solution of lateral buckling strength is found.
  • Equation (9), or (10a) below and in the case of approximating the ⁇ by (10b) where the series, undetermined coefficient sequence that minimizes the equation (12) based on the retention principle (a n )
  • the necessary condition for minimizing the above equation (12) is the following equation (17), and the following equation (18) is obtained as an analytical solution of the lateral buckling strength by performing differentiation.
  • F nm in the above formula (18) represents the following formula (19).
  • N and m in the equations (17) to (23) represent tensor notation numbers for calculation.
  • L nm , M nm , N nm , and O nm in the above formula (19) represent the following formulas (20) to (23).
  • L nm , M nm , N nm , and O nm are determined by integrating ⁇ in the equations (20) to (23).
  • phi n represents the n-th basis function of a power series that approximates the phi.
  • equation (24) is obtained with respect to the above equation (10a).
  • ⁇ n ′ and ⁇ n ′′ represent the first and second derivatives of ⁇ n , respectively.
  • n and m correspond to the n-th and m-th terms in the series according to the formula (10a) or (10b), respectively.
  • the above equation (17) represents an Nth order simultaneous equation.
  • the determinant of the coefficient matrix of the above equation (17) must be 0. That is, the analytical solution of the lateral buckling strength can be obtained by solving the n-order equation of the following equation (25).
  • Equation (32) By substituting ⁇ and ⁇ , which are load conditions at the time of design, into the equation (32), various conditions of the beam 2 are E (Young's modulus), I (second moment of section around the weak axis of the lower flange 22), L (the length of the timber axis Z of the beam 2), d b (the thickness center distance between the upper flange 21 and the lower flange 22), G (shear modulus), J (the torsional constant of San safe) ( By substituting into equation (33), an analytical solution for lateral buckling strength can be calculated. In the equations (26) to (33), n and m represent tensor notation numbers for calculation.
  • the minimum positive value in the actual solution of the equation (26) is the primary lateral buckling strength of the beam 2.
  • the analysis method according to this embodiment is directed to a beam 2 in which a shape steel in which an upper flange 21 and a lower flange 22 are connected by a web 23 is used, and both ends 2a and 2a of the beam 2 in the material axis direction Z are fixed.
  • the lateral movement of the upper flange 21 in the width direction X is restricted, so that an intermediate load acts on the upper flange 21 from above, and the material axis of the beam 2
  • the lateral buckling strength M cr of the beam 2 is calculated from the following formulas (12) to (16) under the condition that end loads act on both end portions 2a, 2a in the direction Z.
  • ⁇ and ⁇ are coefficients determined from the following equations (1) and (2) depending on the presupposed load conditions V and w.
  • V is a shearing force acting on the end 2a of the beam 2 in the material axial direction Z
  • w is an intermediate load acting on the intermediate portion 2b of the beam 2 in the material axial direction Z.
  • L is the length of the beam 2 in the axial direction Z
  • E is the Young's modulus
  • I is the secondary moment of inertia around the weak axis of the lower flange 22
  • G is the shear elastic modulus
  • J is the sun torsional constant of safe
  • d b is the upper flange 21
  • the plate thickness center distance z is the length of up to any point in the timber axis direction of the beam from one end to the timber axis direction of the reference beam and the lower flange 22 It is.
  • ⁇ is a torsion angle generated in the beam 2 by lateral buckling.
  • ⁇ ′ represents the first derivative of ⁇
  • ⁇ ′′ represents the second derivative of ⁇ .
  • t is an auxiliary variable for integration.
  • the lateral buckling deformation of the beam 2 constrained by the lateral movement is complicated, but the lateral movement of the beam 2 is constrained and an intermediate load acts on the upper flange 21 from above. and, and wood-axis direction Z of the both end portions 2a of the beam 2, under conditions which effect the end load 2a, the Lateral Buckling force M cr of the beam 2 by calculating from the equation (12) - (16)
  • the Lateral Buckling force M cr of the beam 2 by calculating from the equation (12) - (16)
  • ⁇ and ⁇ are determined as real numbers according to equations (3a) and (3b).
  • ⁇ is 0 when the intermediate load is equal in the material axial direction Z of the beam 2 (symmetric buckling), and the intermediate load is equal in the material axial direction Z of the beam 2. If it is not necessary (asymmetric buckling), ⁇ is a real number in the range of 1 to 3, so that the intermediate load is an equal bending moment where the bending is equal and the case where the intermediate load is an antisymmetric moment where the intermediate load is not equal. In any case, it is possible to evaluate the lateral buckling strength of the steel beam while considering various load conditions assumed for the actual steel beam by using the above equations (12) to (16). It becomes possible.
  • the analysis method according to the present embodiment avoids the calculation calculation of the lateral buckling strength from becoming more complicated than necessary by approximating ⁇ by the series of the above formula (10a) or (10b).
  • the lateral buckling strength of the steel beam can be evaluated with higher accuracy. For example, by approximating ⁇ by the series of the above formula (10a) or (10b), it is possible to evaluate the lateral buckling strength of the steel beam with higher accuracy without performing complicated calculations.
  • the lateral buckling strength M cr of the beam is calculated from the above equations (12) to (16) under the condition that an intermediate load acts on the beam from above and an end load acts on both ends of the beam in the material axis direction.
  • the design of a steel beam includes a step of calculating M cr based on the analysis method according to the above embodiment, and further includes a step of designing a steel beam based on M cr obtained by the analysis method.
  • a method is provided. According to the steel beam design method, both lateral ends of the beam are fixed and the lateral movement of the beam is constrained, even though the lateral buckling deformation of the beam is restricted. From the above formulas (12) to (16), the intermediate buckling strength M cr of the beam is calculated from the above formulas (12) to (16). Thus, it is possible to evaluate the lateral buckling strength of such a steel beam with high accuracy.
  • the method includes a step of calculating M cr and a step of determining a cross-sectional dimension of the steel beam based on M cr , and determined by these steps.
  • a method of manufacturing a steel beam is provided that includes a step of manufacturing a steel beam based on a cross-sectional dimension of the beam.
  • an appropriate steel beam can be designed by manufacturing the steel beam based on the determination items related to the above conditions.
  • FIG. 8 is a flowchart for explaining the flow of the analysis method according to the embodiment.
  • FIG. 9 is a flowchart for explaining the flow of the design method according to the embodiment of the present invention.
  • a structural plan of a target building is performed. That is, the arrangement of columns, beams, walls, floors, etc. and their joining method are determined (S801).
  • an assumed external force such as a load load, a wind load, an earthquake load, and a snow load is set (S802).
  • a cross section of a column, beam, wall, floor or the like is assumed (S803).
  • S804 based on the information of S801 to S803, a frame analysis is performed, and a basic design for calculating an end load acting on the target beam is performed (S804).
  • the order of S801 to S803 does not matter.
  • I second moment of inertia around the weak axis of the lower flange
  • L material axis direction Z of the beam
  • d b distance between the center thicknesses of the upper flange and the lower flange
  • M cr is calculated using these numerical values (S805).
  • the structural plan of the target building is performed in the same manner as the above analysis method. That is, the arrangement of columns, beams, walls, floors, etc. and their joining method are determined (S901). In addition, an assumed external force such as a load load, a wind load, an earthquake load, and a snow load is set (S902). In addition, a cross section of a column, beam, wall, floor or the like is assumed (S903). Next, based on the information in S901 to S903, frame analysis is performed, and a basic design for calculating an end load acting on the target beam is performed (S904). Note that the order of S901 to S903 does not matter.
  • the M cr of the cross section of the beam assumed in S903 is calculated (S905).
  • the bending moment M as the end load obtained in S904 is compared with Mcr obtained in S905, and a determination is made (S906).
  • M and M cr are compared, and if the determination is “YES (M cr slightly exceeds M)”, the cross-sectional dimension of the beam is determined as a set value (S907).
  • determination may be performed by comparing M with a value obtained by multiplying M cr by the safety factor (or adding the safety factor) in consideration of the safety factor.
  • the analysis method or design method described above is preferably realized by a computer device (not shown) that executes a program recorded on a tangible recording medium (not shown) that is not temporary, by a CPU (not shown).
  • the computer device executes the analysis method described above in response to a command from the input device operated by the operator, and outputs the M cr calculated in S805 of FIG. 8 as the analysis result. .
  • the computer device preferably executes the design method described above in response to a command from an input device operated by an operator, and outputs the comparison result of the determination in S906 of FIG. 9 as the design result. Or it is preferable that the cross-sectional dimension of the beam of S907 of FIG. 9 is output as a design result.
  • the analysis result or the output design result is preferably output so as to be visible via an output device (not shown).
  • the analysis method, the design method, the manufacturing method, and the program according to the above embodiment are used in a building such as a house, a school, an office, or a hospital facility, or a building such as a low-rise building, a high-rise building, or a high-rise building.
  • Steel beams that are structural materials such as floor structures such as buildings, soil structures, or frame structures can be targeted.
  • the analysis method according to the present embodiment can be preferably applied to I-shaped steel as well as a steel beam using an H-shaped steel in which an upper flange and a lower flange are connected to a web at the approximate center in the width direction X.
  • the present invention it is possible to evaluate the lateral buckling strength of a steel beam with high accuracy while considering various load conditions assumed for a real steel beam, a method for designing a steel beam, Since a manufacturing method and a program can be provided, it is industrially useful.

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Abstract

L'invention concerne un procédé d'analyse, un procédé de conception, un procédé de production et un programme. Le procédé d'analyse est destiné à l'évaluation d'une limite d'élasticité de flambage à torsion latérale d'une poutre d'acier, et comprend le calcul d'une limite d'élasticité de flambage à torsion latérale Mcr d'une poutre, constituant un acier façonné formé par couplage d'une bride supérieure (21) et d'une bride inférieure (22) par une bande (23), à partir d'une formule prescrite dans une condition dans laquelle : les deux extrémités (2a, 2a) de la poutre (2) dans une direction axiale Z de matériau sont fixes ; au niveau d'une section médiane (2b) de la poutre (2) dans la direction axiale Z de l'élément, un mouvement latéral de la bride supérieure (21) dans la direction de la largeur X est limité, et une charge intermédiaire est exercée sur la bride supérieure (21) par le dessus ; et une charge d'extrémité est exercée sur les deux extrémités de la poutre (2) dans la direction axiale Z de l'élément.
PCT/JP2018/005768 2017-02-17 2018-02-19 Procédé d'analyse, procédé de conception, procédé de production et programme Ceased WO2018151298A1 (fr)

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JP2021006788A (ja) * 2019-06-28 2021-01-21 日本製鉄株式会社 変位の推定装置、変位の推定方法、及び変位の推定プログラム
JP2021006786A (ja) * 2019-06-28 2021-01-21 日本製鉄株式会社 座屈応力度の推定装置、座屈応力度の推定方法、及び座屈応力度の推定プログラム
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JP2021006789A (ja) * 2019-06-28 2021-01-21 日本製鉄株式会社 座屈応力度の推定装置、座屈応力度の推定方法、及び座屈応力度の推定プログラム
JP2021006962A (ja) * 2019-06-28 2021-01-21 日本製鉄株式会社 座屈応力度の推定装置、座屈応力度の推定方法、及び座屈応力度の推定プログラム
WO2020262306A1 (fr) * 2019-06-28 2020-12-30 日本製鉄株式会社 Dispositif d'estimation de déplacement, dispositif d'estimation de contrainte de flambage, procédé d'estimation de déplacement, procédé d'estimation de contrainte de flambage, programme d'estimation de déplacement et programme d'estimation de contrainte de flambage
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