JP7747572B2 - Hybrid beam design method - Google Patents

Description

The present invention relates to a method for designing hybrid beams.

In recent years, there has been an increase in buildings with beam skeletons made of composite beams (hybrid beams) with a steel frame (S) in the center and steel frames covered with reinforced concrete (RC) at both ends (see, for example, Patent Documents 1 to 3). Because hybrid beams have a steel center, they can reduce the beam's own weight and beam depth compared to RC beams, offering advantages such as longer beam spans, reduced costs, and greater freedom in floor planning.

Japanese Patent Application Laid-Open No. 2021-113464 Japanese Patent Application Laid-Open No. 2021-113465 Japanese Patent Application Laid-Open No. 2021-113466

However, in the past, when a building was represented as a three-dimensional frame and elastic-plastic analysis was performed to calculate the amount of beam deformation due to load, the embedded steel beams at the ends of the reinforced concrete beams into which the ends of the steel beams of the hybrid beams were embedded were not taken into account.

In light of the above, the present invention aims to provide a design method for hybrid beams that can calculate the deformation of the end of reinforced concrete beams, taking into account the embedded steel frame.

The hybrid beam design method of the present invention is characterized in that when calculating, by elastic-plastic analysis, the deformation amount due to load of a steel-reinforced concrete beam section formed by embedding the beam ends of a steel beam made of steel in a reinforced concrete section, the rigidity calculated by treating the steel-reinforced concrete beam section as being made of reinforced concrete is modified to take into account the shear force generated by embedding the steel in the reinforced concrete beam section.

This invention makes it possible to take into account the apparent decrease in rigidity in reinforced concrete beams due to shear forces generated by the lever reaction force of steel beams embedded in the beams.

Furthermore, in the design method of the hybrid beam of the present invention, based on the test results described below, _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 _L0 and the length of the steel-reinforced concrete beam section is Lrc, it is preferable that the rigidity reduction rate _βy to be changed is ( _2L0 - _Lrc ) / (3L0 _{- 2Lrc} ).

Furthermore, in the hybrid beam design method of the present invention, if 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 amount of deformation in response to the load by taking into account the amount of deformation and rotation of the steel-reinforced concrete beam section, as well as the deformation and rotation due to the elastic rigidity of the steel frame within the steel-reinforced concrete beam section.

In this case, even when rib plates are installed, it is possible to take into account the apparent decrease in rigidity of 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.

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; Schematic longitudinal cross-section of the test specimen. 3 is a schematic cross-sectional view taken along line III-III in FIG. 2. Schematic diagram showing deformation of reinforced concrete beams and steel beams. 1 is a graph schematically showing the relationship between deformation and load. 10 is a graph showing the relationship between deformation and load in the test results of test specimen No. 4-1. 10 is a graph showing the relationship between deformation and load in the test results of specimen No. 5-6.

An example of a hybrid beam 10 to which the hybrid beam design method according to an 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 listed above. Note that Figures 1 to 3 are diagrams for schematic illustration, and the dimensions have been exaggerated.

As shown in Figure 1, the hybrid beam 10 is a beam in which both ends of a steel frame 12 made of steel beams such as H-beams or I-beams are embedded in a reinforced concrete (RC) structure 13, spanning opposing columns 11. Although not shown, the hybrid beam 10 may also be formed by embedding the ends of the steel frame 12 in a RC structure integrated with a RC foundation.

The hybrid beam 10 has a steel-framed beam section (S-beam section) 14 in its center, where the steel frame 12 is exposed, and its ends are SRC beam sections 15, where the steel frame 12 is covered with a reinforced concrete structure 13.

Column 11 is made of reinforced concrete, and although details are not shown, it is internally fitted with multiple main column reinforcements and shear reinforcement surrounding the main column reinforcements.

Referring to Figures 2 and 3, the SRC beam section 15 contains steel frames 12, multiple main beam reinforcement bars 16 arranged above and below the steel frames 12 and extending along the longitudinal direction of the hybrid beam 10, and multiple shear reinforcement bars 17 surrounding these main beam reinforcement bars 16. The main beam reinforcement bars 16 extend into the column 11. The main beam reinforcement bars 16 are fixed to the beam-column joint using fixing hardware or bent fixing. Fixing pieces 18 are attached to the ends of the main beam reinforcement bars 16. The fixing pieces 18 consist of a nut portion that screws onto the threaded portion at the end of the main beam reinforcement bars 16 and a steel plate fixed to the nut portion.

At the base end (the end closest to the column 11) and tip end (the end closest to the steel beam 14) of the SRC beam section 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.

Furthermore, if necessary, steel rib plates (closing plates) 21 may be fillet welded to the end (the end on the column 11 side) and start (the end on the steel beam 14 side) of the steel frame 12 inside the SRC beam section 15, connecting the left and right upper and lower flanges. It is preferable that the thickness of the rib plates 21 be equal to or greater than the thickness of the web of the steel frame 12.

The SRC beam section 15 is made of cast-in-place concrete. The concrete may be either ordinary concrete or fiber-reinforced concrete.

By the way, buildings are sometimes represented as three-dimensional frames and elastic-plastic analysis is performed to calculate the deformation of beams under load and confirm structural safety.

Here, we will explain an example of how to calculate the deformation amount at point A when a concentrated load Q is applied to point A on the free end side of a cantilever 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, as shown in Figure 4. The relationship between the vertical deformation _Aδ at the free end point A of the hybrid beam 30 and the load Q is trilinear, as shown in Figure 5.

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 there will be no slippage of the steel frame embedded in the RC beam section 31, no shear failure at the transition between the RC beam section 31 and the S beam section 32, and no bearing failure (compression failure) of the RC beam section 31.

The deformation _Aδ at the free end point A is calculated from equation (1) as the sum of the deformation _rcδ of the RC beam section 31, the deformation _rcθ of the S beam section 32 due to the rotation of the RC beam section 31, and the deformation _Sδ of the S beam section 32 itself.
_A δ= _rc δ+ _rc θ・L _s + _s δ... (1)
Here, L _s is the length of the steel beam section 32 .

The deformation δ _e at the time of bending cracking is determined by the formula (2) according to the theory of elasticity.
δ _e = _rc δ _e + _rc θ _e・L _s + _s δ _e ... (2)

The deformation _rc δ _e of the RC beam portion 31 at the time of bending cracking, which is the first term on the right side of equation (2), can be found from equation (3).
_rc δ _e = Q _hc / _rc K _e ... (3)

Here, Q _hc is the shear force [N] at the time of bending cracking, and can be calculated from Q _hc = M _bc / L ₀ when the bending cracking moment is M _bc [N/mm] and the shear span length of the hybrid beam 30 is L ₀ [mm]. Note that M _bc can be calculated from M _bc = 0.56√c _{σ B} · _e Z when the section modulus is _{e Z} [mm ³ ] and the compressive strength of the concrete [N/mm ² ] is _c σ B.

_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)

Here, _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 (3L ₀ −2L _rc )} ... (5)

Here, _c E 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 second moment of area [N/mm] of the RC beam section 31, which does not take into account the steel frame but does take into account the main beam reinforcement, and is found from equation (6).
_rc I _e =Φ _r・I _o ... (6)

Here, Φ _r is the increase rate of the moment of inertia of area, and 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)

Here, 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)

Here, n is the ratio of the Young's modulus of concrete _cE [N/ ^mm2 ] to the Young's modulus of the beam main reinforcement _sE [N/ ^mm2 ], and is found from n = _sE / _cE . And _p1 is the tensile reinforcement ratio, and is found from _{p1 = amal} / (rcb · rcD), where _amal is the cross-sectional area of the tension side reinforcement [ ^mm2 ], _rcb is the beam width of the _RC beam section ₃₁ [mm], and _rcD is the _beam depth of the _RC beam section 31 [ _mm ].

And, γ can be calculated from _m a _c / _m a _l when _m a _c is the cross-sectional area of the compression side rebar [mm]. _rc d _l1 can be calculated from _rc d _l / _rc D when _rc d _l is the distance from the tension edge to the center of gravity of the tension side rebar. _rc d _c1 can be calculated from _rc d _c / _rc D when _rc d _c is the distance from the compression edge to the center of gravity of the compression side rebar.

Furthermore, I _o in equation (6) is the second moment of area [N·m] in the case of an unreinforced RC cross section, and is calculated from I _o = _rc b· _rc D ³ /12.

Furthermore, _re K _es in equation (4) is the elastic deformation shear stiffness [N/mm] of the RC beam section 31, and is calculated from equation (9).
_re K _es = _c G・_rc A _es /( _rc κ・L _rc ) ... (9)
Here, _c G is the shear modulus of elasticity of concrete [N/mm], _rc A _es is the shear deformation equivalent cross-sectional area [mm ² ] of the RC beam section 31, and _rc κ is the shape factor of the RC cross section.

The rotation angle _rc θ _e of the RC beam section 31 at the time of bending cracking, which is the second term on the right side of equation (2), can be calculated from equation (10).
_rc θ _e = Q _hc / _θ K _e ... (10)

Here, _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 (2L ₀ −L _rc )} ... (11)

The deformation _s δ _e of the steel beam portion 32 at the time of bending cracking, which is the third term on the right side of equation (2), can be found from equation (12).
_s δ _e = Q _hc / _s K _e ... (12)

Here, _s K _e is the equivalent rigidity [N/mm] of the steel beam portion 32, and is calculated from equation (13).
_s K _e =1/(1/ _s K _em +1/ _s K _es ) ... (13)

Here, _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 second moment of area [mm ⁴ ] of the steel beam section 32 , and L _s is the length [m] of the steel beam section 32 .

On the other hand, _s K _es is the elastic shear stiffness [N·m] of the steel beam section 32, and is calculated from equation (15).
_s K _es = _s G・_s A/( _s κ・L _s ) ... (15)
Here, _s G is the shear modulus of elasticity [N/mm ² ] of the steel beam section 32, _s A is the cross-sectional area [mm ² ] of the steel beam section 32, and _s κ is the shape coefficient of the cross section of the steel beam section 32, which is 1.2 in the case of H-shaped steel.

As will be explained below, the second bending point P2 is determined by the rigidity reduction rate _αy and the ultimate bending strength _Mhy of the RC beam portion 31, which are the restoring force characteristics.

The deformation δ _y at bending yield is determined by equation (16) according to the theory of elasticity.
δ _y = _rc δ _y + _rc θ _y・L _s + _s δ _y ... (16)

The deformation _rc δ _y of the RC beam portion 31 at the time of flexural yielding, which is the first term on the right side of equation (16), can be found 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 portion 31, and is calculated by Q _hy = M _hy / L _0. Here, M _hy is the ultimate bending strength of the RC beam portion 31. α _y is the rigidity reduction rate of the RC beam portion.

The rotation angle _rc θ _y of the RC beam section 31 at the time of bending yielding, which is the second term on the right side of equation (16), can be determined from equation (18).
_rc θ _y = Q _hy / (α _y・β _y・_θ K _e ) ... (18)

The deformation _s δ _y of the steel beam portion 32 at the time of bending yielding, which is the third term on the right side of equation (2), can be found from equation (19).
_s δ _y = Q _hy / _s K _e ... (19)

In the commonly used Sugeno formula, the rigidity reduction rate _αy of the RC beam section 31 in formulas (17) and (18) is calculated by formula (20) when a/ _rc D≧2.0, where a is the shear span length L [mm], which is the length _Lrc of the RC beam section 31 in this case.
α _y = (0.043+1.64n・p _l +0.043・a/( _rc d/ _rc D) ²
... (20)

In addition, in the Sugano method, the rigidity reduction rate α _y of the RC beam portion 31 is calculated by equation (21) when a/ _rc D<2.0.
α _y = (-0.0836+0,159d/ _rc D) ( _rc d/ _rc D) ² ... (21)

The inventors prepared the test specimen described below to confirm whether the stiffness reduction rate _αy at bending yielding calculated using the Sugeno formula (21) and (22) above is also valid for the hybrid beam 10.

A total of 18 specimens, No. 4-1 to No. 4-6 and No. 5-1 to No. 5-12, were prepared. The specifications for each specimen are summarized in Tables 1 to 3. A total of 15 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, while a total of three specimens, No. 4-5, No. 4-6, and No. 5-11, were of the shear failure type.

The dimensions of the test specimen were determined assuming a scaled-down version of an actual building at approximately 1/2 to 2/3 the size. 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.

For specimen No. 4-1, an H-shaped steel beam made of SN490B with a height (beam depth of steel beam section 14) _Hs of 500 mm, a side length (beam width of steel beam section 14) _Bs of 200 mm, a web thickness of 9 mm, and a flange thickness of 16 mm was used as the steel frame 12. The embedded length _L3 of this steel frame 12 into the SRC beam section 15 was 1000 mm, and no rib plate 21 was provided.

In specimen No. 4-1, the SRC beam section 15 had a height (beam depth) H _SRC 800 mm, a width (beam width) B _SRC 650 mm, and a length L _SRC 1075 mm, and was formed using concrete with a design strength Fc of 36 N/mm ² .

In specimen No. 4-1, in the SRC beam section 15, eight 19mm diameter SD390 rebars were placed horizontally in the upper and lower sections as the main beam reinforcement 16, with two rebars placed inside each of them. As shear reinforcement 17 in the middle region, 8mm diameter KSS785 rebars were placed around the main beam reinforcement 16 at 60mm intervals s1. Furthermore, at the beginning of the SRC beam section 15, five sets of 10mm diameter KSS785 rebars were placed at 30mm intervals S2 to surround 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 placed at 30mm intervals S2 to surround the main beam reinforcement 16 as concentrated reinforcement 19.

In specimen No. 4-1, the shear margin (= shear strength at bending load capacity _J Q _{U_vu} / shear strength at shear load capacity _J Q _{U_mu} ) of the end of the SRC beam section 15 exceeds 1, and the failure mode is bending failure mode.

Specimen No. 4-2 differs from Specimen No. 4-1 only in that the beam depth H _SRC of the SRC beam section 15 is low at 670 mm and the number of concentrated reinforcement bars 19 is reduced to four sets.

Specimen No. 4-3 differs from Specimen No. 4-2 only in that the beam width B _SRC of the SRC beam section 15 is narrower at 500 mm and the spacing S1 of the shear reinforcement bars 17 is wider 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 are fixed to the steel frame 12 by fillet welding at the start and end of the SRC beam section 15.

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 was reduced to six each. Specimen No. 4-6 differs from Specimen No. 4-5 only in that the SRC beam section 15 was made of concrete with a design strength Fc reduced to 30 N/ ^mm2 .

Specimen No. 5-1 differs from Specimen No. 4-5 only in that the thickness of the web of the steel frame 12 is increased to 10 mm, low-strength concrete with a design standard strength Fc of 24 N/ ^mm2 is used for the SRC beam section 15, the diameter of the main beam reinforcement 16 is reduced to 16 mm and made of a low-strength material consisting of SD345, the diameter of the shear reinforcement 17 is also reduced to 6 mm and made of a low-strength material consisting of SD345, the spacing S1 of the shear reinforcement 17 is narrowed to 50 mm, and the number of sets of concentrated reinforcement 19 is reduced to three.

Test specimens No. 5-2, No. 5-4, and No. 5-6 differ from test 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 were fixed to the steel frame 12 by fillet welding at the beginning and end of the SRC beam section 15, respectively.

Specimen No. 5-3 differs from specimen No. 4-5 only in that the web thickness of the steel frame 12 is increased to 10 mm, the material of the main beam reinforcement 16 is low-strength SD390, and the number of 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 increased to 125 mm.

Specimen No. 5-7 differs from Specimen No. 5-5 only in that the spacing S1 of the shear reinforcement bars 17 was widened to 150 mm. Specimen No. 5-8 differs from Specimen No. 5-7 only in that high-strength concrete with a design strength Fc of 48 N/ ^mm2 was used for the SRC beam section 15, and the spacing S1 of the shear reinforcement bars 17 was narrowed to 75 mm.

Specimen No. 5-9 differs from Specimen No. 5-7 only in that the steel frame 12 uses an H-shaped steel made of SN490B with a height H _S of 350 mm, a side length B _S of 175 mm, a web thickness of 7 mm, and a flange thickness of 11 mm, the embedded depth L ₃ of the steel frame 12 is 750 mm, the cross section of the SRC beam section 15 has a height (beam depth) H _SRC of 400 mm and a width (beam width) B _SRC of 515 mm, the diameter of the main beam 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 6 mm.

Specimen No. 5-10 differs from Specimen No. 5-9 only in that concrete with a design strength Fc of 30 N/ ^mm2 was used for the SRC beam section 15. Specimen No. 5-11 differs from Specimen No. 5-7 only in that the beam depth H _SRC of the SRC beam section 15 was reduced to 450 mm, seven main beam reinforcement bars 16 were arranged in the upper and lower sections of the SRC beam section 16, and four main beam reinforcement bars 16 were arranged inside each of those, the spacing S1 of the shear reinforcement bars 17 was widened to 200 mm, and the number of concentrated reinforcement bars 19 was increased to four sets. Specimen No. 5-12 differs from Specimen No. 5-8 only in that concrete with a design strength Fc of 36 N/ ^mm2 was used for the SRC beam section 15.

Loading tests were conducted using each of the above-mentioned specimens. In this test, a load was applied by a jack to the load application point (distance _L1 from the base end) on the free end side of the steel frame 12, using a cantilever beam with the base end fixed. Note that, 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.

The loading was repeated for seven levels of deflection angle at the tip of the steel beam 14, ±(2.5, 5, 10, 15, 20, 30, 40) × ^10-3 rad, for two cycles each, and then monotonically loaded in one direction up to +100 × ^10-3 rad. During this loading, the vertical displacement _A δ [mm] at the pressure point was measured.

The relationship between displacement _Aδ and load Q for specimen No. 4-1 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 experimental displacement between the first break point P1 and the second break point P2. This indicates that when the Sugeno formula is applied, the stiffness after shear cracking is overestimated, resulting in a calculated displacement that is smaller than the actual displacement. In other words, the stiffness of the RC beam section 31 is calculated to be greater than it actually is.

The inventors therefore believe that the reason for this overcalculation of rigidity is that the Sugano method does not take into account the steel beams embedded in the RC beam section 31.

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 section 31. This is explained in detail below.

If we ignore the amplification of shear force in the RC beam section 31 due to the lever reaction force of the steel frame, referring to Figure 4, the bending deformation _{rc δem1} and deflection angle _{rc φem1} at point B, which is the center point of the boundary surface between the RC beam section 31 and the S beam section 32, are determined from general formulas of material mechanics by equations (23) and (24), respectively.
_rc δ _em1 = Q (L ₀ - _{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 (3L ₀ -L _rc )/6・_c E・_rc I _e } ... (23)
_rc φ _em1 = Q (L ₀ - _{L rc} )・L _rc / ( _c E・_rc I _e )+Q・L _rc ² / (2・_c E _rc・I _e )
=Q{L _rc (2L ₀ -L _rc )/2・_c E・_rc I _e } ... (24)

On the other hand, when taking into account the amplification of shear stress in the RC beam section 31 due to the lever action of the steel frame, Q in equations (23) and (24) becomes Q·L ₀ /L _rc , which becomes equations (25) and (26), respectively.
_rc δ _em2 = Q (L ₀ - _{L rc} )L _rc ² / (2 _c E・_rc I _e )+Q (L ₀ /L _rc )・L _rc ³ / (3 _c E・_rc I _e )
=Q{L _rc ² (5L ₀ -3L _rc )/6・_c E・_rc I _e } ... (25)
_rc φ _em2 = Q (L ₀ - _{L rc} )・L _rc / ( _c E・_rc I _e )+Q (L ₀ /L _rc )L _rc ² / (2 _c E _rc・I _e )
=Q{L _rc (3L ₀ -2L _rc )/2・_c E・_rc I _e } ... (26)

The overall deformation _Aδ when a concentrated load Q is applied to point A at the tip of the steel beam section 32 is mainly due to the rotation of the steel frame accompanying the rotation of the reinforced concrete beam section 31, so the amplification factor _βy of the shear force due to the lever reaction force of the steel frame within the reinforced concrete beam section 31 can be calculated from equation (27).
β _y = _rc φ _em2 / _rc φ _em1 = (3L _{0 -} 2L _rc ) / (2L ₀ - _{L rc} ) ... (27)

β _y can be said to reduce the apparent rigidity of the RC beam section 31 by taking into account the increase in shear force due to the lever reaction force. Therefore, β _y is referred to here as the apparent rigidity reduction rate. The rigidity reduction rate β _y corresponds to the reduction rate in this invention.

Then, using this apparent stiffness reduction rate β _y , the deformation _rc δ _y of the RC beam portion 31 at the time of flexural yielding, which is the first term on the right side of equation (16), is calculated from equation (28).
_rc δ _y = Q _hy / (α _y・β _y・_{rc Ke} ) ... (28)
This is what happens when lever pressure is taken into account in equation (17).

The relationship between the displacement _Aδ and the load Q was calculated by introducing the apparent stiffness reduction rate _βy . 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. Note that the experimental results and calculated values also roughly agreed for test specimens other than test specimen No. 4-1. This confirmed the validity of equation (28).

The above describes the case where rib plates 21 are not provided. Below, we will explain the case where rib plates 21 are provided. Note that it is preferable that the thickness of the rib plates 21 be equal to or greater than the thickness of the steel webs that make up the steel beam section 32.

When the rib plate 21 is provided, the formula (2) is also valid, but it is necessary to take into consideration the presence of steel frames within the RC beam section 31. Therefore, the first term on the right side of the formula (2) is obtained from the formula (29) instead of the formula (3).
_rc δ _e = Q _hc / _rc K _e +Q _hc / _rcs K _e ... (29)

Here, _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)

Here, _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 (3L ₀ -2L _rc )} ... (31)
Here, _s E is the Young's modulus of the steel frame [N/mm ² ], and _s I is the equivalent second moment of area of the steel frame [N/mm].

Furthermore, _res K _es in equation (30) is the elastic deformation shear stiffness [N/mm] of the steel frame, and is calculated from equation (32).
_res K _es = _s G・_s A/( _s κ・L _rc ) ... (32)

Then, the elastic rotational stiffness _θ K _e [N/rad] of the RC beam section 31 is calculated from equation (33), and the rotation angle _rc θ _e of the RC beam section 31 at the time of bending cracking, which is the second term on the right side of equation (2), is calculated from this.
_θ K _e =2 _c E・_rc I _e /{L _rc (2L ₀ −L _rc )}+2 _s E・_s I/{L _rc (2L ₀ −L _rc )} ... (33)

The relationship between the displacement _Aδ and the load Q for specimen No. 5-6 is shown in the graph in Figure 7. When equation (29) is applied in Figure 7, the load becomes larger relative to the displacement amount obtained from the experimental results between the first bending point P1 and the second bending point P2. This shows that applying equation (29) results in a larger calculated displacement amount than the actual displacement amount. Note that specimens No. 4-4, No. 5-2, 4, and 10, which were provided with rib plates 21 other than specimen No. 5-6, also obtained results similar to those shown in Figure 7.

When the rib plate 21 is provided in this way, the displacement _Aδ can be calculated using equation (29), which takes into account the deformation and rotation due to the elastic rigidity of the steel frame within the RC beam section in addition to the deformation and rotation of the RC beam section 31. Note that even when the rib plate 21 is provided, it is preferable to calculate the displacement _Aδ using the apparent rigidity reduction rate _βy .

Note that the design method of the present invention is not limited to application to the hybrid beam 10 specifically described in the above embodiment, but can be modified as appropriate within the scope of the claims.

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 (2)

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 hybrid beams, 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 L0 _and the length of the steel-reinforced concrete beam section is Lrc _, the stiffness reduction rate βy to be changed _is ( 2L0 _- Lrc ₎ /(3L0 _- 2Lrc ₎ . 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 .