JP7747571B2 - 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, the structural performance of conventional hybrid beams was verified based on cases 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 structural performance when the embedded length was less than 2.5 times. As a result, there was no design method available 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.

In light of the above, the present invention aims to provide a hybrid beam design method that can be applied even when the embedded length of the steel frame at the end of an SRC beam is less than 2.5 times the beam depth of the steel beam.

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 formed by embedding the beam ends of a steel beam made of steel in reinforced concrete, 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.

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

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 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.

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 connecting the upper and lower flanges are provided at the start and end of the steel frame within the SRC beam section. It is also preferable that the thickness of the steel plates is equal to or greater than the thickness of the steel frame web.

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 . 10 is a graph showing the relationship between the calculated long-term allowable shear strength of an SRC beam and the experimental value of the shear crack load. 1 is a graph showing the relationship between residual crack width and shear stress level in an SRC beam. 10 is a graph showing the relationship between the residual crack width of an SRC beam multiplied by the reduction coefficient β and the shear stress level.

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 rib plates 21 correspond to the steel plates in this invention.

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

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, as described below, was prepared.

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. 5-10, 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 test 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. 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. Strain gauges were also attached at 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.

The loading was repeated for seven cycles, with the deflection angle at the tip of the steel beam 14 being ±(2.5, 5, 10, 15, 20, 30, 40) x ^10-3 rad, and then monotonically loaded in one direction up to +100 x ^10-3 rad. The direction in which the top end of the steel beam 14 is in tension is considered the positive direction. Displacement in the frame experiment was measured using an electric displacement meter, and the deflection angle was calculated from the measurement results.

Then, during the loading test, the shear force when the strain increase in the shear reinforcement 17 suddenly increased was calculated as the experimental value of the shear crack load.

On the other hand, the long-term allowable shear force 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)

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 length 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)

where Md is the maximum bending moment due to long-term load of the RC member being designed, and is calculated based on Article 15 of the RC Code. Qd is the maximum shear due to long-term load of the RC member being designed, and is calculated based on Article 15 of the RC Code.

Next, we consider applying Equation (1) to the SRC beam section 15. The relationship between the calculated long-term allowable shear strength QaL of the SRC beam section 15 based on Equation (1) and the experimental value of the shear crack load obtained in a loading test is shown in the graph in Figure 4. Note that material testing 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.

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

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

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

Furthermore, for specimens No. 5-7 to No. 5-12, in which the embedded length _L3 is 2.5 times or more the beam depth _Hs of the steel beam section 14, the experimental values all exceed the calculated values. Therefore, it can be seen that when the embedded length _L3 is 2.5 times or more the beam depth _Hs of the steel beam section 14, the reduction coefficient β can be set to 1.0, and the calculated value based on formula (1) can be used as the long-term allowable shear force QaL of the SRC beam section 15.

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)

However, the reduction coefficient β is 1.0 when the rib plate 21 is present or when the embedded length _L3 is 2.5 times or more the beam depth _Hs of the steel beam section 14, and is 0.85 when the rib plate 21 is not present and the embedded length _L3 is 2.0 times or more but less than 2.5 times the beam depth _Hs of the steel beam section 14. Note that when the embedded length _L3 is less than 2.0 times the beam depth _Hs of the steel beam section 14, formula (3) does not apply.

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

Specifically, from the results of visual inspection of crack width, the average crack width (peak crack width) 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 (unloaded crack width) 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.

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 section 15 divided by the cross-sectional area A of the SRC beam section 15 to the concrete strength Fc of the SRC beam section 15.

Note that the concrete strength Fc here is the concrete strength at the time of the experiment. Therefore, the shear stress levels of each test specimen in Figures 5 and 6 differ slightly from the values calculated based on the concrete strength in the mix plan listed in Tables 1 to 3.

This graph shows that the residual crack width exceeded 0.3 mm in specimen No. 4-2, which yielded in bending. Since 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.

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 in actual buildings it is less than 0.4 mm, meaning that the damage level does not exceed the yielding of the rebar. This shows that the setting of the reduction coefficient β is appropriate.

Furthermore, similar to the long-term allowable shear force QaL of the SRC beam section 15 for the usability study described above, if shear cracking due to long-term load is 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)

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

On the other hand, the short-term allowable shear force Qas of the SRC beam section 15 for repairability consideration 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)

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 Code. 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)

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...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 (2)

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. 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.