Hybrid beam design method

Abstract

To provide a design method of a hybrid beam applicable even when the embedded length of a steel frame at the end of the SRC beam of a steel beam is less than 2.5 times the beam depth of the steel beam.SOLUTION: When calculating the allowable shear stress during long-term loading on an SRC beam structure 15 with the beam end of a steel beam 14 constituted of a steel frame 12 is buried in a reinforced concrete part 13, considering the residual crack width of the SRC beam structure 15, the calculated value is multiplied by a reduction coefficient β corresponding to the ratio of the embedded length of the steel frame 12 in the SRC beam structure 15 to the beam depth of the steel beam 12, with the SRC beam structure 15 as an RC member.SELECTED DRAWING: Figure 2

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, the structural performance of conventional hybrid beams was verified based on the case where the embedded length of the steel frame into the end of the SRC beam was 2.5 times or more the depth of the steel beam, and it was unclear how to properly evaluate the structural performance when the embedded length was less than 2.5 times. As a result, there was no design method for cases where the embedded length was less than 2.5 times the depth of the steel beam, and such hybrid beams were not used.

[0005] In view of the above, the present invention aims to provide a design method for hybrid beams that can be applied even when the embedded length of steel beams at the beam ends of SRC structures is less than 2.5 times the beam depth of the steel beams. [Means for solving the problem]

[0006] The hybrid beam design method of the present invention is characterized in that when calculating the allowable shear stress under long-term load of an SRC beam section constructed by embedding the beam end of a steel beam made of steel in a reinforced concrete section, the residual crack width of the SRC beam section is taken into account and a reduction coefficient β corresponding to the ratio of the embedded length of the steel frame into the SRC beam section to the beam depth of the steel beam is multiplied by the calculated value obtained for the SRC beam section as an RC member.

[0007] According to the present invention, even if the embedment length of the steel beam into the beam end of an SRC structure is less than 2.5 times the beam depth of the steel beam and the allowable shear stress of the beam end of the SRC structure is not equal to or greater than that of the beam end of an RC structure, by introducing the reduction coefficient β, it is possible to calculate the allowable shear stress taking into account the residual crack width of the SRC beam.

[0008] Furthermore, in the design method for hybrid beams of the present invention, based on the test results described below, it is preferable to set the reduction coefficient β to 0.85 when the embedded length of the steel frame in the SRC beam section is more than 2 times but less than 2.5 times the beam depth of the steel beam, and to set the reduction coefficient β to 1.0 when the embedded length of the steel frame in the SRC beam section is 2.5 times or more the beam depth of the steel beam.

[0009] Furthermore, in the hybrid beam design method of the present invention, based on the test results described below, it is preferable to set the reduction coefficient β to 1.0 when the steel frame is an H-beam or I-beam and steel plates are provided at the start and end of the steel frame to connect the upper and lower flanges. The thickness of the steel plates is preferably equal to or greater than the thickness of the steel frame web. [Brief explanation of the drawings]

[0010] [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] A graph showing the relationship between the calculated long-term allowable shear force of SRC beams and the experimental shear crack load. [Figure 5] A graph showing the relationship between residual crack width and shear stress level in SRC beams. [Figure 6] A graph showing the relationship between the residual crack width in SRC beams multiplied by the reduction coefficient β and the shear stress level. DETAILED DESCRIPTION OF THE INVENTION

[0011] 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.

[0012] 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.

[0013] 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.

[0014] 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.

[0015] 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.

[0016] 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.

[0017] Furthermore, if necessary, steel rib plates (closing plates) 21 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, connecting the upper and lower flanges on the left and right sides. The thickness of the rib plates 21 is preferably equal to or greater than the thickness of the web of the steel frame 12. The rib plates 21 correspond to the steel plates of this invention.

[0018] The SRC beams 15 are made of cast-in-place concrete. The concrete may be ordinary concrete or fiber-reinforced concrete.

[0019] In order to determine a formula for calculating the shear force of the SRC beam section 15 in the hybrid beam 10 described above, a test specimen described below was prepared.

[0020] 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. A total of 15 specimens, No. 4-1 to No. 4-4, No. 5-10, and No. 5-12, were of the bending yield type, and a total of three specimens, No. 4-5, No. 4-6, and No. 5-11, were of the shear failure type.

[0021] [Table 1]

[0022] [Table 2]

[0023] [Table 3]

[0024] 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.

[0025] 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.

[0026] 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 SRC1075mm, and the design strength Fc is 36N / mm 2 It was formed using concrete.

[0027] 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.

[0028] 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.

[0029] 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.

[0030] 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.

[0031] 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.

[0032] 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.

[0033] 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.

[0034] 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.

[0035] 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.

[0036] 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.

[0037] 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 2 The 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

[0038] Loading tests were conducted using each of the above-mentioned specimens. In this test, each specimen was configured as a cantilever beam with its base end fixed, and a load was applied with a jack to the load application point (distance L1 from the base end) on the free end of the steel frame 12. 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. In addition, strain gauges were attached to multiple locations on the webs and flanges of the steel frame 12, as well as on the main beam reinforcement 16 and shear reinforcement 17.

[0039] 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 Monotonous loading was carried out in one direction up to rad. The direction in which the upper end of the steel beam 14 was in tension was the positive direction. Displacements in the frame experiments were measured using an electric displacement meter, and the deflection angle was calculated from the measurement results.

[0040] Then, during the loading test, the shear force when the increment in the strain of the shear reinforcement 17 suddenly increased was obtained as the experimental value of the shear crack load.

[0041] On the other hand, the long-term allowable shear strength QaL of RC members for usability consideration is calculated using the following formula (1) based on Article 15, Paragraph 2 (1) of the Reinforced Concrete Structural Calculation Standards (RC Standards). QaL=b·j·α·fs (1)

[0042] Here, b is the beam width of the RC member. j is the stress center distance of the RC member, which can be expressed as 7 / 8·d. However, d is the effective strength of the RC member. fs is the long-term allowable shear stress of concrete. α is the shear span ratio of the RC member, which can be calculated using the following formula (2). α=4 / ((Md / Qd d)+1) and 1≦α≦2 (2)

[0043] where Md is the maximum bending moment due to long-term load of the RC member to be designed, calculated based on Article 15 of the RC Standards. Qd is the maximum shear due to long-term load of the RC member to be designed, calculated based on Article 15 of the RC Standards.

[0044] Next, consider applying formula (1) to the SRC beam section 15. The relationship between the calculated value of the long-term allowable shear strength QaL of the SRC beam section 15 based on formula (1) and the experimental value of the shear crack load obtained in the loading test is shown in the graph in Figure 4. Note that a material test was conducted on the concrete actually used in the SRC beam section 15 to determine the compressive strength σ, and the value obtained by multiplying this compressive strength σ by 1 / 30 was used as the long-term allowable shear stress.

[0045] In this graph, to make it easier to see whether the experimental values ​​of each test specimen are higher or lower than the calculated values ​​from equation (1), dashed lines are drawn at positions where the values ​​on the horizontal and vertical axes are equal, and β is introduced as a reduction coefficient for the calculated values, with the cases where β is 1.1 and 0.85 also plotted.

[0046] From this graph, it can be seen that for all test specimens, the experimental values ​​exceeded the calculated values ​​multiplied by 0.85. Therefore, by multiplying the calculated value based on formula (1) by 0.85 as a reduction coefficient β and setting this value as the long-term allowable shear force QaL of the SRC beam 15, it is possible to obtain a design value with a margin of error.

[0047] Furthermore, the experimental values ​​for specimens No. 4-4, No. 5-2, No. 5-4, No. 5-6, and No. 5-10, which have rib plates 21, all exceeded the calculated values. Therefore, when rib plates 21 are present, it is clear that the reduction coefficient β should be set to 1, and the calculated value based on equation (1) should be used as the long-term allowable shear force QaL of the SRC beam section 15.

[0048] Furthermore, the embedded length L3 is the beam depth H of the steel beam part 14. S In the test specimens No. 5-7 to No. 5-12, the experimental values ​​are all greater than the calculated values. S If the long-term allowable shear force QaL is 2.5 times or more, the reduction coefficient β can be set to 1.0, and the value calculated based on equation (1) can be used as the long-term allowable shear force QaL of the SRC beam section 15.

[0049] From the above, the long-term allowable shear force QaL of the SRC beam section 15 for usability consideration can be calculated from the following equation (3) using the reduction coefficient β. QaL=β·b·j·α·fs ··· (3)

[0050] However, the reduction coefficient β is the value when the rib plate 21 is provided or when the embedded length L3 is the beam depth H of the steel beam portion 14. S If the embedded length L3 is 2.5 times or more, the value is 1.0. ... S If the embedded length L3 is 2.0 times or more but less than 2.5 times, the value is 0.85. S If it is less than 2.0 times, formula (3) does not apply.

[0051] To confirm the validity of equation (3), the crack width that occurred in each specimen when it was unloaded from the short-term load for damage control to the long-term load for ensuring serviceability was confirmed.

[0052] Specifically, from the results of visual inspection of crack width, the average values ​​of cracks (crack width at peak) when the deflection angle of the test specimen was 1 / 400, 1 / 200, 1 / 100, and 1 / 67 rad, and the average crack width when unloaded from 1 / 100 rad (crack width at unloading) were calculated, and from these the residual crack width when unloading from short-term loading to long-term loading was estimated. However, cracks occurring at the end of the SRC beam section 15 were excluded.

[0053] The relationship between this residual crack width and shear stress level is shown in the graph in Figure 5. The shear force level is a value that represents the ratio of the shear force Q acting on the SRC beam 15 divided by the cross-sectional area A of the SRC beam 15 to the concrete strength Fc of the SRC beam 15.

[0054] The concrete strength Fc here is the concrete strength during the experiment. Therefore, the shear stress levels of each specimen in Figures 5 and 6 are slightly different from the values ​​calculated based on the concrete strength in the mix plan listed in Tables 1 to 3.

[0055] This graph shows that the residual crack width exceeded 0.3 mm in specimen No. 4-2, which yielded in bending. Because each specimen is assumed to be approximately 1 / 2 to 2 / 3 the size of an actual building, it is estimated that in an actual building, the residual crack width would exceed 0.4 mm, the damage level at which rebar yields.

[0056] The relationship between the value obtained by multiplying the residual crack width by the reduction coefficient β and the shear stress level is shown in the graph in Figure 6. From this graph, it can be inferred that the maximum value obtained by multiplying the residual crack width by the reduction coefficient β is less than 0.3 mm, and that in an actual building it is less than 0.4 mm, so the damage level does not exceed the yielding of the rebar. This shows that the setting of the reduction coefficient β is appropriate.

[0057] Furthermore, similar to the long-term allowable shear force QaL of the SRC beam section 15 for the usability study described above, if shear cracks due to long-term loads are allowed, the long-term allowable shear force of the SRC beam section 15 can be calculated from the following formula (4) by referring to Article 15, Paragraph 2 (1) of the Reinforced Concrete Structural Calculation Standards (RC Standards). QaL=β·b·j·{α·fs+0.5·wfl(pw-0.002)} ··· (4)

[0058] where wfl is the long-term allowable tensile stress of the shear reinforcement. And pw is the stirrup ratio (= aw / (b·x)) of the RC beam, which is 0.6% or less. Here, aw is the cross-sectional area of ​​one set of shear reinforcement 17, and x is the spacing between the shear reinforcement 17.

[0059] On the other hand, the short-term allowable shear force Qas of the SRC beam section 15 for the purpose of examining repairability can be calculated using the following formula (5), with reference to Article 15, Paragraph 2 (2) of the RC Standards. Qas=β b j {2 / 3 α fs+0.5 wfl(pw-0.002)} (5)

[0060] Furthermore, the short-term allowable shear force QA of the SRC beam section 15 for the purpose of examining safety against large earthquake motions can be calculated using the following formula (6) with reference to Article 15, Paragraph 2 (3) of the RC Standards. Note that if short-term design is performed using formula (5) and safety against shear failure is examined based on the ultimate shear strength QaL of the SRC beam section 15, calculation using formula (6) may be omitted. QA=β·b·j·{α·fs+0.5·wfl(pw-0.002)} ··· (6)

[0061] 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]

[0062] 10...Hybrid beam, 11...Column, 12...Steel frame, 13...Reinforced concrete (RC) structure, 14...Steel beam section (S beam section), 15...SRC beam section, 16...Main beam reinforcement, 17...Shear reinforcement, 18...Anchor piece, 19...Concentrated reinforcement, 20...Core reinforcement, 21...Rib plate (steel plate).

Claims

1. When calculating the allowable shear stress of an SRC beam section formed by embedding the beam end of a steel beam made of steel in a reinforced concrete section under long-term load, the residual crack width of the SRC beam section is taken into consideration and a reduction coefficient β corresponding to the ratio of the embedding length of the steel frame into the SRC beam section to the beam depth of the steel beam is multiplied by the calculated value obtained for the SRC beam section as an RC member, A design method for hybrid beams, characterized in that the reduction coefficient β is set to 0.85 when the embedded length of the steel frame into the SRC beam section is more than 2 times but less than 2.5 times the beam depth of the steel beam, and the reduction coefficient β is set to 1.0 when the embedded length of the steel frame into the SRC beam section is 2.5 times or more the beam depth of the steel beam.

2. A design method for a hybrid beam as described in claim 1, characterized in that when the steel frame is an H-shaped steel or an I-shaped steel and steel plates are provided at the start and end of the steel frame within the SRC beam section to connect the upper flange and the lower flange, the reduction coefficient β is set to 1.0.

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