JP7621064B2 - Shear strength evaluation method for beams with slabs and structures - Google Patents

Description

The present invention relates to a method for evaluating the shear strength of a slab-attached beam and a structure equipped with a slab-attached beam that has been evaluated using the method.

It is known that after placing the lower part of a beam made of precast concrete in a designated position on the structure, reinforcement is arranged for the upper part of the beam and the slab connected to it, and then concrete is poured in situ to form a half-precast beam in which the beam and slab are integrated.

Half-precast beams allow the use of concrete of different strengths in the upper and lower parts of the beam. Therefore, while high-strength concrete is required for the beam, which is a structural member, the slab, which is a secondary member, only needs to be strong enough to function as a slab, so using normal-strength concrete for the slab and upper part of the beam is effective in reducing material costs. However, in this case, the structural strength of the beam (mainly shear strength) must be properly determined, and a design method that is neither too strong nor too weak is required.

For example, in the technology described in Patent Document 1, when the height t of the top of the beam is 1/2 or more of the height D of the entire beam (D/2≧t), only the part of the beam above 1/2 is taken into consideration, and the shear strength of the beam is calculated based on the average strength of the concrete according to the height ratio of the top and bottom of the beam. On the other hand, when D/2<t, the concrete strength of the top of the beam is used as the shear strength of the beam.

However, in the technology described in Patent Document 1, only the portion above half the beam height is taken into account when calculating the shear strength of the entire beam. In addition, no consideration is given to the improvement of the beam's shear strength by the slab integrated with the upper part of the beam.

For example, in the technology described in Patent Document 2, the concrete strength of the upper part of the beam is multiplied by a value according to the ratio of the beam width to the beam width to determine the beam shear strength. Here, the slab's cooperative width B is determined so that it falls within the range of B < L/(2 x σc2/σs2) based on the beam's inside length L and the concrete's compressive strength σc2 and shear strength σs2 at the upper part of the beam, so that the compressive force borne by the slab does not exceed the shear force that can be transmitted at the boundary between the slab and the upper part of the beam.

JP 2006-225894 A JP 2006-097320 A

However, the inventors of the present application found that even in the technology described in Patent Document 2, the shear strength of the slab-attached beams was underestimated, and the shear resistance of the slab-attached beams was unfairly underestimated.

In view of the above, the present invention aims to provide a method for evaluating the shear strength of a slab-attached beam that can accurately determine the shear strength of the slab-attached beam, and a structure equipped with a slab-attached beam that has been evaluated using the method.

The shear strength evaluation method of a beam with slab of the present invention is a method for evaluating the shear strength of a beam with slab, which comprises a lower part of a beam formed using a first concrete, and an upper part of a beam and a slab which are integrated with the lower part of the beam and formed using a second concrete different from the first concrete, wherein, when the design standard strength of the first concrete is Fcd [N/ ^mm2 ], the design standard strength of the second concrete is Fcu [N/ ^mm2 ], the cross-sectional area of the lower part of the beam is Ad [ ^mm2 ], the cross-sectional area of the upper part of the beam is Au [ ^mm2 ], the overall width of the slab is ba [mm], the thickness of the slab is t [mm], the height of the upper part of the beam is Tu [mm], and the widths of the lower part of the beam and the upper part of the beam are b [mm], the average strength of the concrete Fce [N/ ^mm2 ] when evaluating the shear strength of the beam with slab is expressed by equation (1):
Fce=(Fcd・Ad+αs・Fcu・Au)/(Ad+Au)... (1)
The premium coefficient αs in formula (1) is expressed by formula (2):
αs=1+t'・b'... (2)
Here, it is characterized in that t'=t/T u and b'=ba/b.

According to the method for evaluating the shear strength of a slab-attached beam of the present invention, as described below, the concrete strength of a slab-attached beam is theoretically examined and experimentally confirmed, and then the average concrete strength Fce is proposed. By using this average concrete strength Fce when evaluating the shear strength, it is possible to be on the safe side and prevent the design from having excessive shear resistance.

The structure having a slab-attached beam of the present invention is characterized in that its shear strength has been evaluated using the shear strength evaluation method for a slab-attached beam of the present invention.

The structure equipped with the slab-attached beam of the present invention makes it possible to reduce the construction costs of the structure while ensuring the necessary shear strength.

1 is a schematic side view of a structure according to an embodiment of the present invention. FIG. 2 is a schematic cross-sectional view taken along line II-II in FIG. 1 is a graph showing the relationship between the margin of error in a test specimen that underwent shear failure before the occurrence of a bending hinge. 13 is a graph showing the relationship between the degree of margin in a test specimen in which a bending hinge occurred. FIG. 11 is a longitudinal sectional view of a slab-attached beam according to a modified embodiment of the present invention. FIG. 11 is a longitudinal sectional view of a slab-attached beam according to another modified embodiment of the present invention. FIG. 11 is a longitudinal sectional view of a slab-attached beam according to yet another modified example of the embodiment of the present invention. FIG. 11 is a longitudinal sectional view of a slab-attached beam according to yet another modified example of the embodiment of the present invention.

The structure 100 to be evaluated using the evaluation method according to an embodiment of the present invention will be described with reference to Figures 1 and 2.

The structure 100 is a structure that includes a beam 30 with a slab formed using dissimilar concrete, in which the lower part 11 of the beam is formed using a first concrete, and the upper part 12 of the beam integrated with the lower part 11 and the slab 20 integrated with the upper part 12 of the beam are both formed using a second concrete.

The entire beam 10 is made up of the lower beam part 11 and the upper beam part 12. The beam 10 is located between columns 40, and the inside dimension between the columns 40 is L0. This structure 100 is constructed, for example, by the construction method described in Patent Publication No. 4021588.

The height (thickness) of the lower beam portion 11 is Td [mm], the height of the upper beam portion 12 is Tu [mm], and the height (beam depth) of the entire beam 10 is D [mm] (= Td + Tu). The height Tu of the upper beam portion 12 is preferably 0.5 times or less the beam depth D, and more preferably 0.25 to 0.5 times. The beam depth D is preferably 1/2.5 or less of the inside dimension L0, and more preferably 1/6 to 1/2.5.

The width of the beam 10 is b [mm]. The cross-sectional area of the lower beam part 11 in a vertical section perpendicular to its longitudinal direction is Ad [ ^mm2 ] (= Td · b), and the cross-sectional area of the upper beam part 12 in a vertical section perpendicular to its longitudinal direction is Au [ ^mm2 ] (= Tu · b).

The height Tu of the upper part 12 of the beam is lower than the thicknesses t1, t2 [mm] of the slab 20. In other words, the lower part 11 of the beam is not in contact with the slab 20. The thicknesses t1, t2 of the slab 20 are preferably 0.19 times or more the beam depth D, and more preferably 0.19 to 0.5 times.

The first concrete used in forming the lower beam section 11 is, for example, high-strength concrete, and its design standard strength is Fcd [N/ ^mm2 ]. The second concrete used in forming the upper beam section 12 and the slab 20 is, for example, normal-strength concrete, and its design standard strength is Fcu [N/ ^mm2 ], which is smaller than Fcd. The design standard strengths Fcu and Fcd of the first and second concretes are preferably 24 to 60 N/ ^mm2 , and the design standard strength Fcu of the second concrete is preferably 1/2 or more of the design standard strength Fcd of the first concrete.

Here, slabs 20 (21, 22) are present on both sides of the upper part of the beam 12, the top ends of the upper part of the beam 12 and the slab 20 are located on the same plane, and the beam 10 and the slab 20 as a whole have a T-shaped vertical section. The slab 21 on one side has a cooperative width ba1 [mm] and a thickness t1 [mm], and the slab 22 on the other side has a cooperative width ba2 [mm] and a thickness t2 [mm]. The cooperative widths ba1, ba2 and the thicknesses t1, t2 may be the same or different. The thicknesses of both slabs 21, 22 may be the same or different.

The cooperative widths ba1 and ba2 of the slabs 21 and 22 are calculated in accordance with the "Standards and Commentary for Reinforced Concrete Structural Calculation (2010)" compiled by the Architectural Institute of Japan. The total cooperative widths ba1 + ba2 of the slabs 21 and 22 are preferably 0.1 times or more the inside dimension L0, and more preferably 0.1 to 0.83 times.

The beam 10 (beam lower part 11 and beam upper part 12) is provided with reinforcing bars such as beam main reinforcing bars 13 and shear reinforcing bars 14. The reinforcing bars shown in FIG. 2 are only an example, and reinforcing bars may be provided in other ways, such as slip prevention bars and bond reinforcement bars. These reinforcing bars are preferably those specified in JIS G3112 steel bars for reinforced concrete or those certified by the Minister of Land, Infrastructure, Transport and Tourism. The yield point of the beam main reinforcing bars is preferably 295 to 590 N/ ^mm2 , and the yield points of the shear reinforcement bars, slip prevention bars 15, bond reinforcement bars, etc. are preferably 295 to 1275 N/ ^mm2 .

As shown by the two-dot chain line in Figure 2, slip prevention bars 15 are reinforcing bars that contribute to stress transmission (prevention of slip failure) at the horizontal joint surface, excluding shear reinforcement bars, and are arranged to connect the lower part 11 of the beam with the upper part 12 of the beam. Specifically, slip prevention bars 15 are downward U-shaped reinforcing bars, with the horizontal part of the upper end hanging on the upper end bar of the upper part 12 of the beam, and the lower end of the vertical part being buried in the lower part 11 of the beam for a length longer than the general anchorage length. Slip prevention bars 15 are arranged as necessary after calculating the shear strength taking into account the slippage of the horizontal joint surface between the lower part 11 of the beam and the upper part 12 of the beam.

Here, the lower part of the beam 11 is made of precast reinforced concrete, the upper part of the beam 12 and the slab 20 are made of cast-in-place concrete, and the beam with slab 30 is a half-precast beam. However, the lower part of the beam 11 may also be made of cast-in-place concrete. Also, the slab 20 may be made by a ribbed precast concrete plate (FR plate) slab construction method, a void slab construction method, or the like.

Pages 51 and 52 of "Guidelines for the Design and Construction of Wall-type Rigid Frame Reinforced Concrete Structures (2003)" compiled by the National Institute for Land and Infrastructure Management, Ministry of Land, Infrastructure, Transport and Tourism, et al., show a method for calculating the shear deformation of a structure such as a slab-attached beam 30 by adding the cooperative width ba of the slab 20 and replacing it with an equivalent rectangular cross section with the same beam depth D.

The inventors of the present application thus propose to calculate the average strength (equivalent average strength) Fce [N/mm2] of the concrete of the beam with slab 30 by the following formula (1), taking into consideration not only the cross section of the beam 10 but also the cross section including the joint width ba of the slab ²⁰ integrated with the beam 10, with the upper limit set to the concrete strength Fcd of the lower part 11 of the beam.
Fce=(Fcd・Ad+αs・Fcu・Au)/(Ad+Au)... (1)

Here, the premium coefficient αs for the slab 20 is calculated using the following equation (2).
αs=1+t1'・b1'+t2'・b2'... (2)

In addition, t1'=t1/Tu, t2'=t2/Tu, b1'=ba1/b, and b2'=ba2/b. When the slab 20 is the slab 21 on one side only, formula (2) becomes formula (3).
αs=1+t1'・b1'... (3)

In this way, according to the evaluation method of the present invention, firstly, the average value of the design standard strength based on the cross-sectional area ratio of the lower beam 11 and the upper beam 12 is set as the equivalent average strength Fce as a basic value. Secondly, the design standard strength of the concrete in the upper beam 12 is set as the equivalent average strength Fce taking into account the cooperative width ba of the slab 20. And, thirdly, the design standard strength of the concrete in the upper beam 12 is increased by multiplying it by an increase coefficient αs based on the cross-sectional area and ratio of the upper beam 12 and the cooperative width ba of the slab 20.

The equivalent average strength Fce in the present invention was proposed after theoretically studying the concrete strength of the slab-attached beam 30 and verifying it through experiments as described below. This equivalent average strength Fce is on the safe side as described below, and makes it possible to prevent a design with excessive shear strength. This makes it possible to reduce the construction costs of the structure 100 while ensuring the necessary shear strength.

FIG. 3 is a graph showing the relationship of the margin of safety in a test specimen that has failed in shear before it has failed in bending. The X-axis shows the margin of safety Qsu/Qfu, which is obtained by dividing the ultimate shear strength Qsu based on the truss arch theory by the bending strength Qfu, which is the shear strength of the beam 10 at the time of bending strength calculated by formula (5) using the simplified formula for bending strength Mu shown in formula (4). The Y-axis shows the margin of safety Qmax/Qfu, which is obtained by dividing the maximum strength Qmax when the test specimen has failed in shear or bond cracked by the shear strength Qfu. When calculating the ultimate shear strength Qsu, the equivalent average strength Fce is used as the concrete strength. Also, at is the cross-sectional area of the tensile reinforcing bar, σy is the yield strength of the main bar, and d is the effective depth of the beam 10.
Mu=0.9・at・σy・d... (4)
Qfu=2・Mu/L0... (5)

In Figure 3, the cross marks and square marks indicate that the test specimens were fractured by shear, and the white circles and diagonal lines indicate that the test specimens were fractured by bond cracks. The square marks and diagonal lines indicate the results of tests actually conducted by the inventors, while the cross marks and white circles indicate experimental data published in previous literature.

Figure 4 is a graph showing the relationship between the margin of safety for specimens that have failed in bending. As in Figure 3, the X-axis shows the shear margin of safety Qsu/Qfu, and the Y-axis shows the margin of safety Qmax/Qfu. However, Qmax includes the maximum strength when the specimen fails in bending, in addition to when it fails in shear or bond failure.

In Figure 4, the open squares and diagonal lined squares indicate that the test specimens failed in shear after yielding, the + marks and + marks in black squares indicate that the test specimens underwent bond cracking after yielding, and the open diamonds and diagonal lined diamonds indicate that the test specimens were bent. The diagonal lined squares, + marks in black squares, and diagonal lined diamonds indicate the results of tests actually conducted by the inventors, while the open squares, + marks, and open diamonds indicate experimental data published in previous literature.

Referring to Figures 3 and 4, in regions where the shear margin Qsu/Qfu is 1 or greater, the ultimate shear strength Qsu is greater than the bending strength Qfu, and theoretically bending failure will occur instead of shear failure.

Furthermore, in the region where the shear margin Qsu/Qfu is less than 1, the margin Qmax/Qfu is greater than the shear margin Qsu/Qfu, so the maximum strength Qmax at the time of shear failure or bond cracking is greater than the theoretical ultimate shear strength Qsu. This shows that the equivalent average strength Fce calculated by formula (1) is evaluated to be on the safe side compared to the shear strength at which the actual beam 10 will fail in shear.

In addition, in the region where the shear margin Qsu/Qfu is 1 or more, the margin Qmax/Qfu is 1 or more, so the maximum strength Qmax at the time of bending failure is greater than the bending strength Qfu. This shows that the equivalent average strength Fce calculated by formula (1) is evaluated to be on the safe side compared to the bending strength at which the actual beam 10 will bend to failure.

When calculating the equivalent average strength Fce, it is preferable to calculate it as follows:

First, when the top of the beam upper part 12 is located above the top of the slab 20, as in the case of a slab-attached beam 30A shown in Figure 5, the equivalent average strength Fce is calculated by regarding the beam upper part 12 as excluding the part that is located above the top of the slab 20 (the shaded part in Figure 5).

Secondly, when the horizontal joint surface A between the lower part 11 and the upper part 12 of the beam is located above the bottom end of the slab 20, as in the case of a slab-attached beam 30B shown in Figure 6, the part of the slab 20 that is located lower than the horizontal joint surface A (the shaded area in Figure 6) is excluded, and the equivalent average strength Fce is calculated.

Thirdly, when there is a portion of the upper part 12 of the beam that is formed using the first concrete, such as the slab-attached beam 30C shown in Figure 7, that portion (the portion with the same hatching as the lower part 11 of the beam in Figure 7) is regarded as the upper part 12 of the beam, not as the lower part 11 of the beam, and the equivalent average strength Fce is calculated. In other words, the portion regarded as the lower part 11 of the beam is limited to the portion in the horizontal cross section that is entirely formed from the first concrete.

Fourth, when there is a portion of the slab 20 that is made of a concrete such as the first concrete that has a higher design standard strength than the second concrete, such as the slab-attached beam 30C shown in Figure 7, the slab 20, including that portion (the portion hatched in the same manner as the lower beam portion 11 in Figure 7), is considered to be made of the second concrete, and the equivalent average strength Fce is calculated. For example, this is the case when part of the slab 20 is made of precast concrete.

Fifth, when a void (air gap) 23 exists in the slab 20, as in the case of a slab-attached beam 30D shown in Figure 8, the portion of the slab 20 on the outer side of the void 23 closest to the beam upper portion 12 (the shaded portion in Figure 8) is not included in the cooperative width ba when calculating the equivalent average strength Fce. In other words, the cooperative width ba is the slab 20 from the side end face of the beam upper portion 12 to the position where the closest void 23 exists.

The present invention is not limited to the above-mentioned method for evaluating the shear strength of a slab-attached beam 30 and the structure equipped with a slab-attached beam evaluated using the method, but can be modified as appropriate.

10...beam, 11...lower part of beam, 12...upper part of beam, 13...main beam bar, 14...shear reinforcement bar, 15...anti-slip bar, 20...slab, 21...one slab, 22...other slab, 24...void, 30, 30A, 30B, 30C...beam with slab, 40...column, 100...structure, A...horizontal joint surface.

Claims (1)

A method for evaluating the shear strength of a beam with a slab, the beam comprising a lower part of a beam formed using a first concrete, and an upper part of a beam and a slab, which are integrated with the lower part of the beam and formed using a second concrete different from the first concrete, comprising:
When the design standard strength of the first concrete is Fcd [N/ ^mm2 ], the design standard strength of the second concrete is Fcu [N/ ^mm2 ], the cross-sectional area of the lower part of the beam is Ad [ ^mm2 ], the cross-sectional area of the upper part of the beam is Au [ ^mm2 ], the overall width of the slab is ba [mm], the thickness of the slab is t [mm], the height of the upper part of the beam is Tu [mm], and the width of the lower part and the upper part of the beam is b [mm], the average strength of concrete Fce [N/ ^mm2 ] when evaluating the shear strength of the beam with slab is expressed by equation (1):
Fce=(Fcd・Ad+αs・Fcu・Au)/(Ad+Au)...(1)
The premium coefficient αs in formula (1) is expressed by formula (2):
αs=1+t'・b'...(2)
A method for evaluating the shear strength of a beam with a slab, characterized in that t'=t/Tu and b'=ba/b.

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