Stiffness evaluation method for steel beams in mixed structural beams

Abstract

To provide a rigidity evaluation method for a steel beam in a mixed construction beam for expecting a composite effect of the steel beam and a RC building in the mixed construction beam and evaluating the rigidity of the steel beam by an effective clear span.SOLUTION: It is assumed that virtual horizontal external force acts at three locations at a central position and both sides of a steel beam, the virtual horizontal external force is separated into torsion moment and horizontal component force of the steel beam in a cross section of the steel beam, a torsion angle θse of the center of the steel beam due to the virtual horizontal external force is evaluated, rigidity of the steel beam is evaluated by an effective clear span Le of the steel beam, the torsion angle θse is shown by formula (1), it is assumed that an assumed beam made only in the same steel as the steel beam is stretched between columns, an equivalent rigid zone length ΔL from a position where the torsion angle θse is 0 to an end of the assumed beam satisfies formula (2) and the effective clear span Le of the steel beam is obtained by subtracting 2ΔL which is double of the equivalent rigid zone length from a clear span L of the steel beam as Le=L-2ΔL.SELECTED DRAWING: None

Description

[Technical Field]

[0001] The present invention relates to a method for evaluating the stiffness of a steel beam in a mixed structure beam. [Background technology]

[0002] As a beam erected between reinforced concrete (hereinafter referred to as RC) columns, a mixed structure beam is known in which both ends of a steel beam erected between RC columns are joined to the RC columns via RC end sections in which the ends of the steel beam are embedded (see, for example, Patent Document 1). In such a mixed structure beam, sufficient plastic deformation capacity can be expected from the steel beam by tightly connecting the upper flange of the steel beam to an RC slab that has in-plane rigidity and strength, or by providing separate lateral stiffeners to the steel beam. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2014-190102 Summary of the Invention [Problem to be solved by the invention]

[0004] Because both ends of the steel beams with the inside span are surrounded by the end reinforced concrete sections, the rigidity of the beams can be expected to be enhanced by the combined effect of the reinforced concrete structure. However, at present, this effect is not taken into consideration during the design.

[0005] The present invention aims to provide a method for evaluating the rigidity of steel beams in mixed structural beams, which is based on the effective interior span and takes advantage of the combined effect of steel beams and reinforced concrete in mixed structural beams. [Means for solving the problem]

[0006] In order to achieve the above object, the method for evaluating the rigidity of a steel beam in a mixed structural beam according to the present invention is a method for evaluating the rigidity of a steel beam in a mixed structural beam, the steel beam having a steel beam installed between reinforced concrete columns and reinforced concrete end RC sections provided at both ends of the steel beam in the longitudinal direction, joined to the columns, and having the ends of the steel beam embedded therein, in an interior effective span. The method assumes that a virtual horizontal external force acts on three positions, namely, a position that is the center of the steel beam in the material axis direction and positions on both sides of the center in the material axis direction, and separates the virtual horizontal external force into a torsional moment and a horizontal component force in the weak axis direction of the steel beam within the cross section of the steel beam, and calculates the torsion angle θ at the center of the steel beam in the material axis direction due to the virtual horizontal external force. se The rigidity of the steel beam is evaluated by the effective interior span Le of the steel beam, and the torsion angle θ se is expressed by the following formula (1), and it is assumed that a hypothetical beam made of only steel, the same as the steel beam, is installed between the columns, and the torsion angle θ se The equivalent rigid zone length ΔL from the position where ΔL becomes 0 to the end of the assumed beam satisfies the following formula (2), and the effective interior span Le of the steel beam is set to Le = L - 2ΔL, which is the interior span L of the steel beam minus 2ΔL, which is twice the equivalent rigid zone length.

[0007]

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[0008] Here, T1: Torsional moment due to P1 (= P1·H / 2, H: Torsional moment due to steel beam) β RC : Ratio of effective length Lj of end RC structure to inside span L β1: Ratio of the acting distance of the virtual horizontal external force (other than the center of the span) from the end of the mixed structure beam 1 to the inside span G·Jc: Torsional rigidity of the end RC section (product of concrete shear modulus G and polar moment of inertia Jc) G·Js: Torsional rigidity of steel beam (product of shear modulus of elasticity G and polar moment of inertia Js of steel material (for H-shaped steel: Js=Σti 3si / 3, ti: plate thickness, si: constituent plate length)

[0009]

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[0010] In order to achieve the above-mentioned object, the method for evaluating the rigidity of a steel beam in a mixed structural beam according to the present invention is a method for evaluating the rigidity of a steel beam in a mixed structural beam, which has a steel beam installed between reinforced concrete columns, and reinforced concrete end RC sections provided at both ends of the steel beam in the longitudinal direction, joined to the columns, and in which the ends of the steel beam are embedded, in an interior effective span. The method assumes that a virtual horizontal external force acts on three positions, namely, a position that is the center of the steel beam in the material axis direction and positions on both sides of the center in the material axis direction, and separates the virtual horizontal external force into a torsional moment and a horizontal component force in the weak axis direction of the steel beam within the cross section of the steel beam, and calculates the lateral deflection δ of the steel beam in the material axis direction due to the virtual horizontal external force. se The rigidity of the steel beam is evaluated by the effective internal span Le of the steel beam, and the lateral deflection δ se is expressed by the following formulas (3) to (8), and it is assumed that a hypothetical beam made of only steel, the same as the steel beam, is installed between the columns, and the end position in the material axis direction is used as a parameter to calculate the lateral deflection δ at the center in the material axis direction when the virtual horizontal external force is applied to the hypothetical beam. so and the lateral deflection δ se The equivalent rigid zone length ΔL from the position where these are equal to the end position of the assumed beam satisfies the following formula (9), and the effective interior span Le of the steel beam is set to Le = L - 2ΔL, which is the interior span L of the steel beam minus 2ΔL, which is twice the equivalent rigid zone length.

[0011]

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[0012] In this invention, by assuming a hypothetical horizontal external force on the steel beam in a mixed structural beam and taking into account either the torsion angle or lateral deflection or both, the rigidity of the steel beam embedded in the end reinforced concrete section can be evaluated in terms of the effective internal span. [Effects of the Invention]

[0013] According to the present invention, the composite effect of the beam and the reinforced concrete structure can be expected, and the rigidity of the beam can be evaluated by the effective interior span. [Brief explanation of the drawings]

[0014] [Figure 1]FIG. 1 is an elevation view of a mixed construction beam according to an embodiment of the present invention. [Figure 2] FIG. 10 is an elevation view showing details of a mixed structural beam. [Figure 3] This is a plan of a mixed structural beam. [Figure 4] 10A and 10B are diagrams illustrating a torsional moment of a virtual horizontal external force. [Figure 5] FIG. 10 is a diagram showing the torsion angle distribution of a mixed structure beam due to a torsional moment. [Figure 6] FIG. 10 is a diagram showing the bending moment and lateral deflection of a mixed structure beam due to a virtual horizontal external force. [Figure 7] FIG. 10 is a diagram showing the deformation state and equivalent rigidity zone of an assumed beam. [Figure 8] 1 is a table showing a list of coefficients relating to torsion of a rectangular cross section. [Figure 9] This is the calculation result of ΔL (β1=0.25). [Figure 10] 10 is a table and graph showing the effect of the virtual horizontal external force position ratio (β1) on ΔL in H-2. [Figure 11] 10 is a table and graph showing the effect of the virtual horizontal external force position ratio (β1) on ΔL at L-2. DETAILED DESCRIPTION OF THE INVENTION

[0015] Hereinafter, a method for evaluating the rigidity of a steel beam in a mixed structural beam according to an embodiment of the present invention will be described with reference to FIGS. As shown in Fig. 1, a mixed structural beam 1 according to this embodiment is erected between reinforced concrete columns 2. The mixed structural beam 1 has a steel beam 3 erected between the columns 2, and reinforced concrete end sections 4 provided at both ends of the beam length, joined to the columns 2, and in which the ends of the steel beam 3 are buried. The steel beam 3 is joined to the columns 2 via the reinforced concrete end sections 4.

[0016] Steel beam 3 is an H-shaped steel. The end RC section 4 is embedded only at the end 3a of the steel beam 3 in the beam length direction. The end reinforced concrete section 4 may be a precast concrete member, or may be constructed using conventional reinforced concrete construction methods.

[0017] A method for evaluating the rigidity of a steel beam in a mixed structure beam according to this embodiment will be described. A virtual horizontal external force is assumed to act on three points on the upper flange 31 of the steel beam 3. The three points on which the virtual horizontal external force acts are three points (A), (B), and (C) in the axial direction of the steel beam 3, including the center of the span (B) of the steel beam 3, as shown in Figures 2 and 3. As shown in Figures 3 and 4, within the cross section of steel beam 3, the virtual horizontal external force is separated into torsional moment T1 and horizontal component force (steel weak axis force) P1, and the torsional angle θ at the center of the span due to the virtual horizontal external force of mixed structural beam 1 is se and lateral deflection δ se When evaluating lateral deflection, shear deformation shall not be taken into consideration. It is assumed that the torsional moment from the steel beam 3 is transmitted entirely to the tip of the end RC section 4 (see Figure 5). The horizontal component is transmitted within the RC structure (see Figure 6). The same steel frame as steel beam 3 is used, and an assumed beam with only steel frame and no end RC structural part 4 is assumed. The lateral deflection δ at the center of the span when the same virtual horizontal external force is applied is calculated using the fixed end position (end position) as a parameter. so Evaluate δ so =δ se The equivalent rigid zone length ΔL that satisfies the above is calculated (see Figure 7). From the above, the effective internal span Le can be evaluated as Le = L - 2ΔL, where L is the internal span of the steel beam 3.

[0018] (Evaluation of twist angle) The formula for evaluating the torsion angle and equivalent rigid area due to the torsional moment will be explained below. From the twist angle distribution shown in Fig. 5, the θ se is expressed by the following equation:

[0019]

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[0020] Here, T1: Torsional moment due to P1 (= P1·H / 2, H: due to steel beam 3) β RC : Ratio of effective length Lj of end RC structural part 4 to inside span L β1: Ratio of the acting distance of the virtual horizontal external force (other than the center of the span) from the end of the mixed structure beam 1 to the inside span G·Jc: Torsional rigidity of the end RC section 4 (product of concrete shear modulus G and polar moment of inertia Jc (Jc: see table in Figure 8)) G·Js: Torsional rigidity of steel beam 3 (product of shear modulus of elasticity G of steel and polar moment of inertia Js (for H-shaped steel: Js = Σti 3 si / 3, ti: plate thickness, si: constituent plate length)

[0021] Using the same steel frame as steel beam 3, and assuming a hypothetical beam that does not have end RC section 4, and defining the distance from the end of mixed structural beam 1 to the position where the torsion angle is 0 as ΔL, the torsion angle distribution in Figure 5 can be evaluated using the following formula.

[0022]

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[0023] (Lateral deflection evaluation) The following explains the evaluation formulas for lateral deflection and equivalent rigid area due to virtual horizontal external force. FIG. 6 shows the bending moment distribution and deformation state (lateral deflection) that occur in the steel beam 3 and the end RC section 4 due to a hypothetical horizontal external force acting on the mixed structural beam 1. The following relational expression is obtained from the balance of the loads and bending moments acting on the steel beam 3.

[0024]

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[0025] Here, R1: Reaction force acting on the starting point of the embedded steel beam embedded in the end RC section (the transition point between the steel beam and the end RC section) Re: Reaction force acting on the end of the embedded steel beam (on the face side of the RC column) embedded in the end RC structure P1: Virtual horizontal external force M0: Bending moment acting at the center of the steel beam in a mixed structural beam M e : Bending moment acting on the end of a mixed structure beam (column side of RC structure) β1: Ratio of the acting distance of the virtual horizontal external force (other than the center of the span) from the end of the mixed structure beam 1 to the inside span β RC : Ratio of effective length Lj of end RC structural part 4 to inside span L The deformation of each part is expressed by the following equations based on the applied load and boundary conditions of each part.

[0026]

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[0027] or

[0028]

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[0029] Here, EIs: Bending stiffness of steel beam 3 about the weak axis EIc: Bending rigidity of the end RC section 4 about the weak axis The following relationship holds between formulas (5) to (7) or formula (8) due to the compatibility condition of the lateral deflection of the steel beam 3:

[0030]

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[0031] Furthermore, from equations (3) and (10), the reaction forces R1 and R e is given by the following equation:

[0032]

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[0033] As shown in Fig. 7, the same steel frame as steel beam 3 is used, and an assumed beam without end RC structural part 4 is assumed. δ so is evaluated as follows:

[0034]

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[0035] Le is δ so =δ se It is expressed by the following equation using ΔL calculated from

[0036]

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[0037] The ratio of the equivalent rigid zone length to the effective length of the end RC structure part 4 is ΔL / Lj or ΔL / β RC It is given by L.

[0038] The evaluation results of the equivalent rigid area and effective interior span from the test are explained below. The calculation results of ΔL for specimens H-2 and L-2 are shown in the table in Figure 9. For the evaluation, the ratio β1 of the acting position (A) of the virtual horizontal external force in the span direction to L was set to β1 = 0.25. As a result of evaluating ΔL for the torsional component, the ratio of ΔL to Lj was found to be close to 1.0 in all cases. Therefore, if ΔL = Lj in equation (15), it can be seen that Le of the steel beam 3 in the mixed structural beam 1 is the length obtained by subtracting Lj from L.

[0039]

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[0040] However, if Lj at the left and right ends is different, the average value of Lj on the left and right shall be used. Regarding the lateral deflection component, the ratio of ΔL to Lj was 0.777 to 0.874, which indicates that approximately 3 / 4 of Lj from the pillar face can be considered as a rigid zone. The effect of β1 on the equivalent rigid area is shown in Figures 10 and 11. In both cases, if the equivalent rigid area length ratio is set to 0.75, δ so / δ se >1(δ so >δ se ) which means that the lateral deflection is evaluated on the safe side. Therefore, the Le of the steel beam 3 for the lateral deflection component can be evaluated by the following formula:

[0041]

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[0042] Next, the operation and effect of the method for evaluating the stiffness of a steel beam in a mixed structure beam according to the present embodiment will be described. In the method for evaluating the rigidity of steel beams in mixed structural beams according to the present embodiment, the rigidity of steel beams 3 surrounded by reinforced concrete can be evaluated in terms of the effective interior span by assuming a virtual horizontal external force on the steel beams 3 in the mixed structural beam 1 and taking into account either the torsion angle or lateral deflection or both. The torsional angle component can be evaluated using equation (16), and the lateral deflection component can be evaluated using equation (17). The effective internal span of steel beam 3 in mixed structural beam 1 can be evaluated by regarding 3 / 4 of Lj as the rigid zone.

[0043] The above describes an embodiment of the method for evaluating the rigidity of steel beams in mixed structural beams according to the present invention, but the present invention is not limited to the above embodiment and can be modified as appropriate within the scope of its intent. [Explanation of symbols]

[0044] 1 Mixed structural beam 2 pillars 3 Steel beams 4 End RC structure

Claims

1. Steel beams are installed between reinforced concrete columns, A method for evaluating the rigidity of a steel beam in a mixed structural beam having a reinforced concrete end portion provided at each end of the steel beam in the longitudinal direction, joined to the column, and burying the end of the steel beam, in an internal effective span, It is assumed that a virtual horizontal external force acts on three locations: the center of the steel beam in the material axis direction and positions on both sides of the center in the material axis direction. The virtual horizontal external force is separated into a torsional moment and a horizontal component force in the weak axis direction of the steel beam within the cross section of the steel beam, and the torsion angle θ at the center of the steel beam in the material axis direction due to the virtual horizontal external force is calculated. ｓｅ Evaluate The rigidity of the steel beam is evaluated by the effective interior span Le of the steel beam, The twist angle θ ｓｅ is expressed by the following formula (1): Assuming that an assumed beam consisting of only steel, the same as the steel beam, is installed between the columns, the twist angle θ ｓｅ The equivalent rigid zone length ΔL from the position where is 0 to the end of the assumed beam satisfies the following formula (2): A method for evaluating the rigidity of a steel beam in a mixed structure beam, in which the effective interior span Le of the steel beam is calculated by subtracting 2ΔL, which is twice the equivalent rigid zone length, from the interior span L of the steel beam, so that Le = L - 2ΔL. [Equation 1] Here, T １ : Torsional moment due to P1 (= P １ ・H / 2, H: due to steel beams) β ＲＣ : Ratio of effective length Lj of end RC structural part to inside span L β １ : Ratio of the acting distance of the virtual horizontal external force (other than the center of the span) from the end of the mixed structure beam 1 to the inside span G・Jc: Torsional rigidity of the end RC structure (product of concrete shear modulus G and polar moment of inertia Jc) G・Js: Torsional rigidity of steel beam (product of shear modulus of elasticity G of steel material and polar moment of inertia Js (for H-shaped steel: Js = Σti ３ si / 3, ti: plate thickness, si: constituent plate length) [Equation 2]

2. Steel beams are installed between reinforced concrete columns, A method for evaluating the rigidity of a steel beam in a mixed structural beam having a reinforced concrete end portion provided at each end of the steel beam in the longitudinal direction, joined to the column, and burying the end of the steel beam, in an internal effective span, Assuming that a virtual horizontal external force acts on three locations, namely, the center position in the steel beam in the material axis direction and positions on both sides of the center in the material axis direction, the virtual horizontal external force is separated into a torsional moment and a horizontal component force in the weak axis direction of the steel beam within the cross section of the steel beam, and the lateral deflection δ of the center of the steel beam in the material axis direction due to the virtual horizontal external force is calculated. ｓｅ Evaluate The rigidity of the steel beam is evaluated by the effective interior span Le of the steel beam, The lateral deflection δ ｓｅ is expressed by the following equations (3) to (8): Assuming that a hypothetical beam consisting of only steel, the same as the steel beam, is installed between the columns, and the end position in the material axis direction is used as a parameter, the lateral deflection δ at the center in the material axis direction when the virtual horizontal external force is applied to the hypothetical beam is calculated. ｓｏ and the lateral deflection δ ｓｅ The equivalent rigid zone length ΔL from the position where the distances are equal to the end position of the assumed beam satisfies the following formula (9): A method for evaluating the rigidity of a steel beam in a mixed structure beam, in which the effective interior span Le of the steel beam is calculated by subtracting 2ΔL, which is twice the equivalent rigid zone length, from the interior span L of the steel beam, so that Le = L - 2ΔL. [Equation 3] [Equation 4] R １ : Reaction force acting on the starting point of the embedded steel beam embedded in the end RC section (the transition point between the steel beam and the end RC section) Re: Reaction force acting on the end of the embedded steel beam (on the face side of the RC column) embedded in the end RC section P １ : Imaginary horizontal external force M ０ : Bending moment acting at the center of the steel beam in a mixed structural beam M ｅ : Bending moment acting on the end of a mixed structure beam (RC column side) β １ : Ratio of the acting distance of a virtual horizontal external force (other than the center of the span) from the end of a mixed structural beam to the inside span β ＲＣ : Ratio of effective length Lj of end RC structural part to inside span L [Equation 5] EIs: Bending stiffness of the steel beam about the weak axis EIc: Bending rigidity of the end RC structural part about the weak axis [Equation 6] [Equation 7] or [Equation 8] [Equation 9]

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