Hybrid beam design method

Abstract

To provide a method for designing a hybrid beam. which can calculate a deformation amount of a beam end of an RC structure in consideration of burying of a steel frame.SOLUTION: When a deformation amount of an RC beam part 31 formed by burying a beam end of a steel frame S beam 32 in the RC beam part 31 with respect to a load is calculated through elastoplastic analysis, rigidity calculated regarding the RC beam part 31 as an RC structure is changed in consideration of a shearing force generated due to burying of the steel frame in the RC beam part 31.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a method for designing a hybrid beam. [Background technology]

[0002] In recent years, there has been an increase in buildings that use composite beams (hybrid beams) with a steel frame (S) in the center and steel frames covered with reinforced concrete (RC) at both ends as the beam skeleton (see, for example, Patent Documents 1 to 3). Because the center of a hybrid beam is made of steel, it is possible to reduce the beam's own weight and beam depth compared to RC beams, which has the advantages of allowing for longer beam spans, cost reductions, and increased freedom in floor plan design. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2021-113464 [Patent Document 2] Patent Publication No. 2021-113465 [Patent Document 3] Japanese Patent Publication No. 2021-113466 Summary of the Invention [Problem to be solved by the invention]

[0004] However, in the past, when a building was represented as a three-dimensional frame and elastic-plastic analysis was performed to calculate the deformation of the beams in response to load, the embedding of steel at the end of the reinforced concrete beam into which the end of the steel beam of the hybrid beam was embedded was not taken into account.

[0005] In view of the above, the present invention aims to provide a design method for hybrid beams that can calculate the deformation of the end of a reinforced concrete beam taking into account the embedded steel frame. [Means for solving the problem]

[0006] The hybrid beam design method of the present invention is characterized in that when calculating the deformation amount against load of a steel-reinforced concrete beam section formed by embedding the beam end of a steel beam made of steel in a reinforced concrete section using elastic-plastic analysis, the rigidity calculated by treating the steel-reinforced concrete beam section as reinforced concrete is changed to take into account the generation of shear force due to the embedding of the steel in the reinforced concrete beam section.

[0007] According to the present invention, it is possible to take into consideration the apparent decrease in rigidity in a reinforced concrete beam section due to shear forces generated by the lever reaction force of steel frames embedded in the reinforced concrete beam section.

[0008] In the design method of the hybrid beam of the present invention, from the test results described below, the distance between the point where the load acts on the steel beam as a concentrated load and the base end of the steel-reinforced concrete beam section is defined as L0, and the length of the steel-reinforced concrete beam section is defined as L rc When the above-mentioned reduction rate β of the stiffness to be changed is y A(2L0-L rc ) / (3L0-2L rc ) is preferable.

[0009] Furthermore, in the hybrid beam design method of the present invention, when rib plates are provided at both longitudinal ends of the steel frame within the steel-reinforced concrete beam section, it is preferable to calculate the deformation amount in response to the load by taking into account the deformation and rotation of the steel-reinforced concrete beam section due to the elastic rigidity of the steel frame within the steel-reinforced concrete beam section.

[0010] In this case, even when a rib plate is installed, it is possible to take into account the apparent decrease in rigidity in the reinforced concrete beam due to the shear force generated by the lever reaction force of the steel frame embedded in the reinforced concrete beam. [Brief explanation of the drawings]

[0011] [Figure 1]1 is a schematic front view showing an example of a hybrid beam to which a hybrid beam design method according to an embodiment of the present invention is applied; [Figure 2] Schematic longitudinal cross-section of the test specimen. [Figure 3] 3 is a schematic cross-sectional view taken along line III-III in FIG. 2. [Figure 4] Schematic diagram showing deformation of reinforced concrete beams and steel beams. [Figure 5] 1 is a graph schematically showing the relationship between deformation and load. [Figure 6] 1 is a graph showing the relationship between deformation and load in the test results of test specimen No. 4-1. [Figure 7] Graph showing the relationship between deformation and load in the test results for test specimen No. 5-6. DETAILED DESCRIPTION OF THE INVENTION

[0012] An example of a hybrid beam 10 to which the hybrid beam design method according to the embodiment of the present invention is applied will be described with reference to the drawings. Hybrid beams to which this design method is applied are, for example, those described in Patent Documents 1 to 3. Note that Figures 1 to 3 are diagrams for schematic explanation, and the dimensions are exaggerated.

[0013] As shown in Fig. 1, the hybrid beam 10 is a beam in which both ends of a steel frame 12 made of steel such as H-shaped steel or I-shaped steel that is spanned between opposing columns 11 are embedded in a reinforced concrete (RC) structure 13. Although not shown, the hybrid beam 10 may also be one in which the ends of the steel frame 12 are embedded in an RC structure that is integrated with the RC foundation.

[0014] The hybrid beam 10 has a steel beam section (S beam section) 14 in the center with the steel frame 12 exposed, and both ends are SRC beam sections 15 with the steel frame 12 covered by a reinforced concrete structure 13.

[0015] The column 11 is made of reinforced concrete, and although not shown in detail, a plurality of main column reinforcements and shear reinforcement bars surrounding the main column reinforcements are arranged inside.

[0016] 2 and 3, the SRC beam section 15 is provided with a steel frame 12, a plurality of main beam reinforcements 16 arranged above and below the steel frame 12 and extending along the longitudinal direction of the hybrid beam 10, and a plurality of shear reinforcement bars 17 surrounding these main beam reinforcements 16. The main beam reinforcements 16 extend into the column 11. The main beam reinforcements 16 are fixed to the beam-column joints by means of fixing hardware or bent fixing. An fixing piece 18 is provided at the tip of the main beam reinforcement 16. The fixing piece 18 consists of a nut part that screws into the threaded part at the tip of the main beam reinforcement 16 and a steel plate fixed to this nut part.

[0017] At the base end (the end on the column 11 side) and tip end (the end on the steel beam 14 side) of the SRC beam 15, concentrated reinforcement (shear reinforcement) 19 is arranged at closer intervals and more densely than in the middle area where shear reinforcement 17 is arranged. Furthermore, core reinforcement 20 is arranged in each shear reinforcement 17 and concentrated reinforcement 19.

[0018] Furthermore, if necessary, steel rib plates (closing plates) 21 that connect the upper and lower flanges on the left and right sides may be provided by fillet welding at the end (the end on the column 11 side) and the start (the end on the steel beam 14 side) of the steel frame 12 inside the SRC beam 15. The thickness of the rib plates 21 is preferably equal to or greater than the thickness of the web of the steel frame 12.

[0019] The SRC beams 15 are made of cast-in-place concrete. The concrete may be ordinary concrete or fiber-reinforced concrete.

[0020] Incidentally, a building may be represented as a three-dimensional frame and subjected to elastic-plastic analysis to calculate the deformation of beams against loads and confirm structural safety.

[0021] Here, as shown in Figure 4, we will explain how to calculate the deformation amount at point A of a cantilever type hybrid beam 30, which has a reinforced concrete beam section 31 at the fixed end and a steel beam section 32 at the free end, when a concentrated load Q is applied to point A on the free end side. A The relationship between δ and the load Q is trilinear, as shown in FIG.

[0022] As explained below, the first bending point P1 is determined from the elastic rigidity of the RC beam section 31 and the S beam section 32, and the bending crack resistance of the RC cross section at the end of the RC beam section 31. However, it is assumed that the steel frame embedded in the RC beam section 31 will not slip out, shear failure will not occur at the junction between the RC beam section 31 and the S beam section 32, and bearing failure (compression failure) of the RC beam section 31 will not occur.

[0023] Deformation at free end point A A δ is the deformation of the RC beam 31 rc δ, deformation of steel beam 32 due to rotation of RC beam 31 rc θ, deformation of the steel beam 32 itself S It is calculated from equation (1) as the sum of δ. A δ = rc δ+ rc θ L s + s δ (1) where L s is the length of the steel beam section 32.

[0024] Deformation δ during bending crack e is determined from equation (2) according to the theory of elasticity. δ e = rc δ e + rc θ e L s + s δ e (2)

[0025] The first term on the right side of equation (2) is the deformation of the RC beam 31 at the time of bending cracking. rc δ eis calculated from equation (3). rc δ e =Q hc / rc K e (3)

[0026] Here, Q hc is the shear force at the time of bending cracking [N], and the bending cracking moment is M bc [N / mm], and the shear span length of the hybrid beam 30 is L0 [mm], Q hc =M bc / L0. Note that M bc is the section modulus e Z [mm 3 ], compressive strength of concrete [N / mm 2 ]of c σ B When M bc =0.56√ c σ B · e It can be found from Z.

[0027] and, rc K e is the equivalent rigidity [N / mm] of the RC beam portion 31, and is calculated from equation (4). rc K e =1 / {(1 / rc K em )+(1 / re K es )} (4)

[0028] where: rc K em is the elastic bending rigidity [N / mm] of the RC beam portion 31, and is calculated from equation (5). rc K em =6 c E. rc I e / {L rc 2 (3L0-2L rc )} (5)

[0029] where: cE is the Young's modulus of concrete [N / mm 2 ], L rc is the length [mm] of the RC beam section 31. rc I e is the equivalent moment of inertia [N / mm] of the RC beam 31, which does not take into account the steel frame but does take into account the main beam reinforcement, and is calculated from equation (6). rc I e =Φ r I o ··· (6)

[0030] where Φ r is the increase rate of the moment of inertia of area, which is calculated from equation (7). Φ r =12(1 / 3-g ol +g 0l 2 ) +12n·p l {(1-g ol - rc d ol ) 2 +(g ol - rc d l1 ) 2 γ} (7)

[0031] where g ol is calculated from equation (8). g ol ={0.5+n·p l (1- rc d c1 + rc d cl ·γ)} / {1+n·p l (1+γ)} ··· (8)

[0032] where n is the Young's modulus of concrete mentioned above c E [N / mm 2 ] and Young's modulus of the beam main reinforcement s E [N / mm 2 ], and n = s E / c It can be found from E. And, p l is the tension reinforcement ratio, ama l is the cross-sectional area of ​​the tension side rebar [mm 2 ], rc b is the beam width [mm] of the RC beam section 31, rc When D is the beam depth [mm] of the RC beam section 31, p l = am a l / ( rc b· rc D) can be found from

[0033] And γ is m a c When the cross-sectional area of ​​the compression side rebar is [mm], m a c / m a l It can be found from rc d l1 teeth, rc d l When is the distance from the tension edge to the center of gravity of the tension side rebar, rc d l / rc It can be found from D. rc d c1 teeth, rc d c When is the distance from the compression edge to the center of gravity of the compression side rebar, rc d c / rc It can be found from D.

[0034] Furthermore, I in Eq. (6) o is the moment of inertia [N m] for a plain RC section, and I o = rc b· rc D 3 This can be calculated from / 12.

[0035] Also, in equation (4), re K es is the elastic deformation shear stiffness [N / mm] of the RC beam portion 31, and is calculated from equation (9). re K es = c G. rc A es / ( rc κ·L rc) (9) where: c G is the shear modulus of concrete [N / mm], rc A es is the shear deformation equivalent cross-sectional area [mm 2 ] and rc κ is the shape factor of the RC cross section.

[0036] The second term on the right side of equation (2) is the rotation angle of the RC beam 31 at the time of bending cracking. rc θ e is calculated from equation (10). rc θ e =Q hc / θ K e ··· (10)

[0037] where: θ K e is the elastic rotational rigidity [N / rad] of the RC beam portion 31, and is calculated from equation (11). θ K e =2 c E. rc I e / {L rc (2L0-L rc )} (11)

[0038] The third term on the right side of equation (2) is the deformation of the steel beam 32 at the time of bending cracking. s δ e is calculated from equation (12). s δ e =Q hc / s K e ··· (12)

[0039] where: s K e is the equivalent rigidity [N / mm] of the steel beam section 32, and is calculated from equation (13). s K e =1 / (1 / s K em +1 / s K es ) (13)

[0040] where: s K em is the elastic bending shear stiffness [N·m] of the steel beam section 32, and is calculated from equation (14). s K em =3E s I s / L s 3 ··· (14) Here, I s is the moment of inertia of the steel beam 32 [mm 4 ] and L s is the length [m] of the steel beam section 32.

[0041] on the other hand, s K es is the elastic shear stiffness [N·m] of the steel beam section 32, and is calculated using equation (15). s K es = s G. s A / ( s κ·L s ) (15) where: s G is the shear modulus of elasticity of the steel beam 32 [N / mm 2 ] and s A is the cross-sectional area of ​​the steel beam 32 [mm 2 ] and s κ is the shape factor of the cross section of the steel beam portion 32, which is 1.2 in the case of H-shaped steel.

[0042] As will be explained below, the second bending point P2 is determined by the rigidity reduction rate α y and ultimate bending strength M hy It is determined from.

[0043] Deformation at bending yield δ y is determined from equation (16) according to the theory of elasticity. δ y = rc δ y + rcθ y L s + s δ y ··· (16)

[0044] The first term on the right side of equation (16) is the deformation of the RC beam 31 at the time of flexural yielding. rc δ y is calculated from equation (17). rc δ y =Q hy / (α y · rc K e ) (17) Here, Q hy is the shear force [N] at bending yield of the RC beam 31, and Q hy =M hy / L0, where M hy is the ultimate bending strength of the RC beam 31. y is the reduction rate of rigidity of the RC beam.

[0045] The second term on the right side of equation (16) is the rotation angle of the RC beam 31 at the time of flexural yielding. rc θ y is calculated from equation (18). rc θ y =Q hy / (α y β y · θ K e ) (18)

[0046] The third term on the right side of equation (2) is the deformation of the steel beam 32 at bending yield. s δ y is calculated from equation (19). s δ y =Q hy / s K e ··· (19)

[0047] The stiffness reduction rate α of the RC beam 31 in Equation (17) and Equation (18) y In the commonly used Sugeno formula, rcWhen D≧2.0, it is calculated by the formula (20). Note that a is the shear span length L [mm], and here, it is the length L of the RC beam part 31. rc is. α y =(0.043+1.64n·p l +0.043·a / ( rc d / rc D) 2 ··· (20)

[0048] In addition, in the Sugano method, the rigidity reduction rate α of the RC beam 31 y is a / rc When D<2.0, it is calculated using equation (21). α y =(-0.0836+0,159d / rc D)( rc d / rc D) 2 ··· (twenty one)

[0049] The inventors calculated the stiffness reduction rate α at bending yield using the Sugeno formula of the above formulas (21) and (22). y In order to confirm whether this is also valid for the hybrid beam 10, a test specimen as described below was prepared.

[0050] A total of 18 specimens, No. 4-1 to No. 4-6 and No. 5-1 to No. 5-12, were prepared. The specifications of each specimen are summarized in Tables 1 to 3. Fifteen specimens, No. 4-1 to No. 4-4, No. 5-1 to No. 5-10, and No. 5-12, were of the bending yield type, and three specimens, No. 4-5, No. 4-6, and No. 5-11, were of the shear failure type.

[0051] [Table 1]

[0052] [Table 2]

[0053] [Table 3]

[0054] The dimensions of the test specimen were determined by assuming it was a half to two-thirds smaller than an actual building. Referring to Figures 2 and 3, the distance L1 to the load point of the cantilevered test specimen was 2,425 mm, and the distance L2 between the inflection points was 2,350 mm.

[0055] In specimen No. 4-1, the steel frame 12 has a height (height of the steel beam 14) H s 500mm, side length (beam width of steel beam section 14) B s The steel frame 12 was embedded into the SRC beam 15 to a length L3 of 1000 mm, and no rib plate 21 was provided.

[0056] In specimen No. 4-1, the SRC beam part 15 has a height (beam depth) H SRC 800mm, width (beam width) B SRC 650mm, length L SRC 1075mm, and the design strength Fc is 36N / mm 2 It was formed using concrete.

[0057] In specimen No. 4-1, the SRC beam section 15 consisted of eight 19mm diameter SD390 rebars arranged horizontally in the upper and lower sections as the main beam reinforcement 16, with two rebars arranged inside each of them. The intermediate shear reinforcement 17 consisted of 8mm diameter KSS785 rebars arranged at 60mm intervals (s1) surrounding the main beam reinforcement 16. Furthermore, at the beginning of the SRC beam section 15, five sets of 10mm diameter KSS785 rebars were arranged at 30mm intervals (s2) surrounding the main beam reinforcement 16 as concentrated reinforcement 19. At the end of the SRC beam section 15, five sets of 8mm diameter KSS785 rebars were arranged at 30mm intervals (s2) surrounding the main beam reinforcement 16 as concentrated reinforcement 19.

[0058] In the test specimen No. 4-1, the shear margin of the end of the SRC beam 15 (= shear strength at bending strength) J Q U_vu / Shear strength at shear load J Q U_mu ) is greater than 1, and the failure mode is bending failure mode.

[0059] Test specimen No. 4-2 is different from test specimen No. 4-1 in that the beam depth H of the SRC beam part 15 SRC The only difference is that the height is lower at 670 mm and the number of concentrated reinforcement bars 19 has been reduced to four sets.

[0060] Test specimen No. 4-3 is different from test specimen No. 4-2 in that the beam width B of the SRC beam section 15 SRC The only difference between specimen No. 4-4 and specimen No. 4-2 is that the width of the shear reinforcement bars 17 was narrowed to 500 mm, and the spacing S1 of the shear reinforcement bars 17 was widened to 75 mm. Specimen No. 4-4 differs from specimen No. 4-2 only in that rib plates 21 made of steel plates of the same thickness as the webs of the steel frame 12 were fixed to the steel frame 12 by fillet welding at the start and end of the SRC beam section 15.

[0061] Specimen No. 4-5 differs from Specimen No. 4-3 only in that the number of main beam reinforcement bars 16 in the upper and lower sections of the SRC beam section 15 has been reduced to six each. Specimen No. 4-6 differs from Specimen No. 4-5 in that the design strength Fc of the SRC beam section 15 has been reduced to 30 N / mm 2 The only difference is that concrete with reduced strength was used.

[0062] Test specimen No. 5-1 differs from test specimen No. 4-5 in that the thickness of the steel frame 12 web is increased to 10 mm, and the SRC beam 15 has a design strength Fc of 24 N / mm 2 The only differences are that low-strength concrete is used, the diameter of the main beam reinforcement 16 is reduced to 16 mm and made of low-strength material SD345, the shear reinforcement 17 is also reduced to 6 mm in diameter and made of low-strength material SD345, the spacing S1 of the shear reinforcement 17 is narrowed to 50 mm, and the arrangement of the concentrated reinforcement 19 is reduced to three sets.

[0063] Specimens No. 5-2, No. 5-4, and No. 5-6 differ from specimens No. 5-1, No. 5-3, and No. 5-5 only in that rib plates 21 made of steel plates of the same thickness as the webs of the steel frame 12 are fixed to the steel frame 12 by fillet welding at the beginning and end of the SRC beam section 15, respectively.

[0064] Specimen No. 5-3 differs from specimen No. 4-5 only in that the thickness of the steel frame 12 web is increased to 10 mm, the material of the main beam reinforcement 16 is low-strength SD390, and the arrangement of the concentrated reinforcement bars 19 is reduced to three sets. Specimen No. 5-5 differs from specimen No. 5-3 only in that the spacing S1 of the shear reinforcement bars 17 is widened to 125 mm.

[0065] Specimen No. 5-7 differs from specimen No. 5-5 only in that the spacing S1 of the shear reinforcement 17 is widened to 150 mm. Specimen No. 5-8 differs from specimen No. 5-7 in that the design strength Fc of the SRC beam 15 is 48 N / mm 2 The only difference is that high-strength concrete is used and the spacing S1 of the shear reinforcement 17 is narrowed to 75 mm.

[0066] Test specimen No. 5-9 is different from test specimen No. 5-7 in that it is a steel frame 12 with a height of H S 350mm, side length B S The H-shaped steel beams made of SN490B with a thickness of 175 mm, a web thickness of 7 mm, and a flange thickness of 11 mm are used, and the embedment depth L3 of the steel frame 12 is set to 750 mm. The cross section of the SRC beam part 15 is set to a height (beam depth) H SRC 400mm, width (beam width) B SRC The only differences are that the diameter of the beam main reinforcement 16 is reduced to 16 mm, the diameter of the shear reinforcement 17 is reduced to 6 mm, the spacing S1 of the shear reinforcement 17 is narrowed to 50 mm, and the diameter of the concentrated reinforcement 19 at the starting end is reduced to 8 mm and the diameter of the concentrated reinforcement 19 at the starting end is reduced to 6 mm.

[0067] Test specimen No. 5-10 differs from test specimen No. 5-9 in that the SRC beam 15 has a design strength Fc of 30 N / mm 2The only difference between specimen No. 5-11 and specimen No. 5-7 is that the concrete used was lowered to the beam depth H of the SRC beam 15. SRC The only difference between specimen No. 5-12 and specimen No. 5-8 is that the design strength Fc of the SRC beam 15 is 36 N / mm. 2 The only difference is that concrete of

[0068] A loading test was conducted using each of the above-mentioned specimens. In this test, the base end of each specimen was fixed as a cantilever beam, and a load was applied with a jack to the load application point (distance L1 from the base end) on the free end side of the steel frame 12. In addition, although not shown, an out-of-plane vibration prevention device (not shown) was attached to the tip of the steel beam 14 to prevent twisting of the steel beam 14 due to deformation caused by the load.

[0069] The load is applied at a deflection angle of ±(2.5, 5, 10, 15, 20, 30, 40) × 10 at the tip of the steel beam 14. -3 Repeat 7 levels of rad for 2 cycles, then +100×10 -3 The monotonic loading was carried out in one direction up to rad. During this loading, the vertical displacement at the pressure point A δ [mm] was measured.

[0070] Displacement in specimen No. 4-1 A The relationship between δ and load Q is shown in the graph in Figure 6. In Figure 6, whether Sugeno's formula (22) or (23) is applied, the load is smaller than the displacement amount in the experimental results between the first break point P1 and the second break point P2. This shows that the experimental results show that when Sugeno's formula is applied, the rigidity after shear cracking is overestimated, and the calculated displacement amount is smaller than the actual displacement amount. In other words, the rigidity of the RC beam section 31 is calculated to be higher than it actually is.

[0071] Therefore, the inventors thought that the reason for the overcalculation of rigidity was that the Sugano method did not take into account the steel frame embedded in the RC beam section 31.

[0072] In the hybrid beam 30 described above, it is assumed that the shear force is amplified by the lever reaction force of the steel frame inside the RC beam portion 31. This will be specifically explained below.

[0073] If the amplification of the shear force of the RC beam 31 due to the lever reaction force of the steel frame is ignored, referring to Figure 4, the bending deformation at point B, which is the center point of the boundary surface between the RC beam 31 and the S beam 32, is rc δ em1 and deflection angle rc φ em1 are determined from the general formulas of material mechanics by equations (23) and (24), respectively. rc δ em1 =Q(L0-L rc )L rc 2 / (2· c E. rc I e )+Q·L rc 2 / (3· c E. rc I e ) =Q{L rc 2 (3L0-L rc ) / 6· c E. rc I e} ··· (twenty three) rc φ em1 =Q(L0-L rc )·L rc / ( c E. rc I e )+Q·L rc 2 / (2· c E rc I e ) =Q{L rc (2L0-L rc ) / 2· c E.rc I e} ··· (twenty four)

[0074] On the other hand, when the amplification of shear stress in the RC beam 31 due to the lever action of the steel frame is taken into consideration, Q in Equation (23) and Equation (24) becomes Q·L0 / L rc These are expressed as equations (25) and (26), respectively. rc δ em2 =Q(L0-L rc )L rc 2 / (2 c E. rc I e )+Q(L0 / L rc )·L rc 3 / (3 c E. rc I e ) =Q{L rc 2 (5L0-3L rc ) / 6· c E. rc I e} ··· (twenty five) rc φ em2 =Q(L0-L rc )·L rc / ( c E. rc I e )+Q(L0 / L rc )L rc 2 / (2 c E rc I e ) =Q{L rc (3L0-2L rc ) / 2· c E. rc I e} (26)

[0075] Overall deformation when a concentrated load Q is applied to point A at the tip of the steel beam 32 A Since δ is mainly due to the rotation of the steel frame accompanying the rotation of the RC beam 31, the amplification rate β of the shear force due to the lever reaction force of the steel frame within the RC beam 31 yis calculated from equation (27). β y = rc φ em2 / rc φ em1 =(3L0-2L rc ) / (2L0-L rc ) (27)

[0076] β y It can be said that the apparent rigidity of the RC beam 31 is reduced by taking into consideration the increase in shear force due to the lever reaction force. y is called the apparent stiffness reduction rate. Note that the stiffness reduction rate β y corresponds to the reduction rate in the present invention.

[0077] And this apparent stiffness reduction rate β y Using this, the deformation of the RC beam 31 at the time of flexural yielding, which is the first term on the right side of equation (16), is rc δ y is calculated from equation (28). rc δ y =Q hy / (α y β y · rc K e ) ··· (28) This is what happens when lever pressure is taken into account in equation (17).

[0078] Apparent stiffness reduction rate β y By introducing the displacement A The relationship between δ and load Q was calculated. As shown in Figure 6, the results were similar to the experimental results between the first break point P1 and the second break point P2. Furthermore, the experimental results and calculated values ​​also roughly agreed for specimens other than specimen No. 4-1. This confirmed the validity of equation (28).

[0079] The above describes the case where the rib plate 21 is not provided. Below, we will explain the case where the rib plate 21 is provided. Note that it is preferable that the thickness of the rib plate 21 is equal to or greater than the thickness of the steel web that constitutes the steel beam section 32.

[0080] Equation (2) also holds true when rib plates 21 are installed, but it is necessary to take into account the presence of steel frames within the RC beam section 31. Therefore, the first term on the right-hand side of equation (2) is found from equation (29) instead of equation (3). rc δ e =Q hc / rc K e +Q hc / rcs K e ··· (29)

[0081] where: rcs K e is the equivalent stiffness [N / mm] of the steel frame in the RC beam section 31, and is calculated from equation (30). rcs K e =1 / {(1 / rcs K em )+(1 / res K es )} (30)

[0082] where: rcs K em is the elastic bending rigidity [N / mm] of the steel frame in the RC beam section 31, and is calculated from equation (31). rcs K em =6 s E. s I / {L rc 2 (3L0-2L rc )} (31) where: s E is the Young's modulus of the steel frame [N / mm 2 ] and s I is the equivalent moment of inertia of the steel frame [N / mm].

[0083] Also, in equation (30),res K es is the elastic deformation shear stiffness of the steel frame [N / mm], which is calculated from equation (32). res K es = s G. s A / ( s κ·L rc ) (32)

[0084] And the elastic rotational rigidity of the RC beam 31 θ K e [N / rad] is calculated from equation (33), and the rotation angle of the RC beam 31 at the time of bending cracking, which is the second term on the right side of equation (2), is calculated from this. rc θ e Asking for, θ K e =2 c E. rc I e / {L rc (2L0-L rc )}+2 s E. s I / {L rc (2L0-L rc )} (33)

[0085] Displacement in specimens No. 5-6 A The relationship between δ and load Q is shown in the graph in Figure 7. When formula (29) is applied in Figure 7, the load becomes larger relative to the experimental displacement between the first bending point P1 and the second bending point P2. This shows that applying formula (29) results in a larger calculated displacement than the actual displacement. Note that specimens No. 4-4, No. 5-2, 4, and 10, which were equipped with rib plates 21 other than specimen No. 5-6, also showed results similar to those in Figure 7.

[0086] When the rib plate 21 is provided in this way, the deformation and rotation of the RC beam 31 are calculated by the formula (29) which takes into account the deformation and rotation due to the elastic stiffness of the steel frame in the RC beam. A δ. Even when the rib plate 21 is provided, the apparent rigidity reduction rate β yDisplacement using A It is preferable to determine δ.

[0087] The design method of the present invention is not limited to the hybrid beam 10 specifically described in the above embodiment, but can be modified as appropriate within the scope of the claims. [Explanation of symbols]

[0088] 10...Hybrid beam, 11...Column, 12...Steel frame, 13...Reinforced concrete (RC) structure, 14...Steel beam section (S beam section), 15...Steel reinforced concrete beam section (SRC beam section), 16...Main beam reinforcement, 17...Shear reinforcement, 18...Anchor piece, 19...Concentrated reinforcement, 20...Core reinforcement, 21...Rib plate, 30...Hybrid beam, 31...RC beam section, 32...S beam section.

Claims

1. When calculating the deformation amount against the load of a steel-framed reinforced concrete beam section formed by embedding the end of a steel-framed beam in a reinforced concrete section by elastic-plastic analysis, the rigidity calculated by regarding the steel-framed reinforced concrete beam section as a reinforced concrete structure is modified by taking into account the occurrence of shear force due to the embedding of the steel frame in the steel-framed reinforced concrete beam section, A design method for a hybrid beam, characterized in that when the distance between the point where the load acts on the steel beam as a concentrated load and the base end of the steel reinforced concrete beam section is L 0 and the length of the steel reinforced concrete beam section is L rc , the stiffness reduction rate β y to be changed is (2L 0 - L rc ) / (3L 0 - 2L rc ).

2. The design method for a hybrid beam as described in claim 1, characterized in that when rib plates are provided at both longitudinal ends of the steel frame within the steel-reinforced concrete beam section, the deformation amount relative to the load is calculated by taking into account the deformation and rotation of the steel-reinforced concrete beam section due to the elastic rigidity of the steel frame within the steel-reinforced concrete beam section.

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