JP2021155941A - Method for evaluating shear strength of beam with slab and structure - Google Patents

Abstract

To provide a method for evaluating the shear strength of a beam with a slab.SOLUTION: In a beam 30 with a slab comprising of a beam lower part 11 made of first concrete, a beam upper part 12 made of second concrete, and a slab 20, when the design reference strength of the first concrete is Fcd [N/mm2], the design reference strength of the second concrete is Fcu [N/mm2], the cross-sectional area of the beam lower part 11 is Ad [mm2], the cross-sectional area of the beam upper part 12 is Au [mm2], the cooperation width of the slab 20 is ba [mm], the thickness of the slab 20 is t [mm], the height of the beam upper part 12 is Tu [mm], and the width of the beam 10 is b [mm], the average strength Fce [N/mm2] of the concrete in evaluating the shear strength of the beam 30 with the slab is expressed by the formula: Fce=(Fcd×Ad + αs×Fcu×Au)/(Ad + Au) ...(1), and the overdesign factor αs in the formula (1) is expressed by the formula: αs=1 + t '×b' ...(2),where t '=t/Tu, b'=ba/b.SELECTED DRAWING: Figure 2

Description

The present invention relates to a method for evaluating the shear strength of a beam with a slab and a structure including a beam with a slab evaluated using the method.

After installing the lower part of the beam made of precast concrete at a predetermined position in the structure, the upper part of the beam and the slab connected to it are laid out and the on-site concrete is placed integrally, so that the beam and the slab are integrated. It is known to form a beam with a slab as a half precast beam.

Half precast beams can use concrete of different strengths at the top and bottom of the beam. Therefore, high-strength concrete is required for the beam, which is the structural material, but since the slab, which is the secondary member, only needs to have the strength to be established as a slab, normal-strength concrete is used for the slab and the upper part of the beam. If this is done, it is effective in reducing the material cost. However, in this case, it is necessary to properly judge the structural strength (mainly shear strength) of the beam, and a design method with just enough strength is required.

For example, in the technique described in Patent Document 1, when the height t of the upper part of the beam is 1/2 or more (D / 2 ≧ t) of the height D of the entire beam, the portion above 1/2 of the beam. The shear strength of the beam is calculated based on the average strength of concrete based on the ratio of the height of the upper part to the lower part of the beam. On the other hand, when D / 2 <t, the concrete strength at the top of the beam is used as it is as the shear strength of the beam.

However, in the technique described in Patent Document 1, when determining the shear strength of the entire beam, only the portion above 1/2 of the height of the beam is considered. In addition, no consideration is given to the improvement of the shear strength of the beam by the slab integrated with the upper part of the beam.

Therefore, for example, in the technique described in Patent Document 2, the value obtained by dividing the concrete strength of the upper part of the beam by a value corresponding to the ratio of the cooperation width of the slab and the width of the beam is obtained as the shear strength of the beam. Here, the cooperation width B of the slab is the inner length L of the beam so that the compressive force borne by the slab portion does not exceed the shear force that can be transmitted at the interface between the slab and the upper part of the beam. From the compressive strength σc2 and shear strength σs2 of the concrete above the beam, the cooperation width B is obtained so that it is within the range of B <L / (2 × σc2 / σs2).

Japanese Unexamined Patent Publication No. 2006-225894 Japanese Unexamined Patent Publication No. 2006-097320

However, the inventor of the present application has found that the shear strength of the slab-attached beam is underestimated even in the technique described in Patent Document 2, and the shear strength of the slab-attached beam is unreasonably evaluated as low.

In view of the above points, the present invention provides a method for evaluating the shear strength of a beam with a slab capable of appropriately determining the shear strength of the beam with a slab, and a structure including the beam with a slab evaluated using the method. The purpose is.

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

According to the method for evaluating the shear strength of a beam with a slab of the present invention, as will be described later, the concrete strength of the beam with a slab is theoretically examined and confirmed by experiments, and then the average strength Fce of the concrete is proposed. By using this average strength Fce in the evaluation of the shear strength, it is possible to suppress the design from being on the safe side and having an excessive shear strength.

The structure provided with the slab-bearing beam of the present invention is characterized in that it is formed by evaluating the shear strength using the shear strength evaluation method of the slab-bearing beam of the present invention.

According to the structure provided with the beam with a slab of the present invention, it is possible to reduce the construction cost of the structure while ensuring the required shear strength.

The schematic side view of the structure which concerns on embodiment of this invention. FIG. 2 is a schematic cross-sectional view taken along the line II-II of FIG. The graph which shows the relationship of the margin degree in the specimen which sheared and fractured before the occurrence of a bending hinge. The graph which shows the relationship of the margin degree in the test body in the test body which generated the bending hinge. FIG. 3 is a vertical cross-sectional view of a beam with a slab according to a modified example of the embodiment of the present invention. FIG. 3 is a vertical cross-sectional view of a beam with a slab according to another modification of the embodiment of the present invention. FIG. 3 is a vertical cross-sectional view of a beam with a slab according to still another modification of the embodiment of the present invention. FIG. 3 is a vertical cross-sectional view of a beam with a slab according to still another modification of the embodiment of the present invention.

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

In the structure 100, the beam lower portion 11 is formed by using the first concrete, and the beam upper portion 12 integrated with the beam lower portion 11 and the slab 20 integrated with the beam upper portion 12 both form a second concrete. It is a structure including a beam 30 with a slab formed by using dissimilar concrete formed by using.

The entire beam 10 is composed of the lower beam 11 and the upper beam 12. The beam 10 exists between the columns 40 and 40, and the internal dimension between the columns 40 is L0. The structure 100 is constructed by, for example, the construction method described in Japanese Patent No. 4021588.

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

The width of the beam 10 is b [mm]. The lower beam 11 has a vertical cross-sectional area orthogonal to its longitudinal direction Ad [mm ² ] (= Td · b), and the upper beam 12 has a vertical cross-sectional area orthogonal to its longitudinal direction. Au [mm ² ] (= Tu ・ b).

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

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

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

The cooperation widths ba1 and ba2 of the slabs 21 and 22 are calculated according to "Reinforced Concrete Structure Calculation Criteria and Explanation (2010)" edited by the Architectural Institute of Japan. The total cooperation width of the slabs 21 and 22 is preferably 0.1 times or more, more preferably 0.1 to 0.83 times the internal dimension L0.

Reinforcing bars such as a beam main bar 13 and a shear reinforcing bar 14 are arranged on the beam 10 (beam lower part 11 and beam upper part 12). The arrangement mode of the reinforcing bars shown in FIG. 2 is an example, and the reinforcing bars may be arranged in other modes, for example, slip prevention bars, adhesive reinforcing bars, and the like may be arranged. .. As these reinforcing bars, those specified in JIS G3112 reinforced concrete steel bars or those approved by the Minister of Land, Infrastructure, Transport and Tourism are preferably used. The yield point of the beam main bar ^{is preferably 295 to 590 N / mm 2} , and the yield point of the shear reinforcing bar, the slip prevention bar 15, the adhesive reinforcing bar and the like is preferably ^{295 to 1275 N / mm 2.}

As shown by the alternate long and short dash line in FIG. 2, the slip prevention bar 15 is a reinforcing bar that contributes to stress transmission (prevention of slip failure) of the horizontal joint surface except for the shear reinforcing bar, and the lower beam 11 and the upper beam 12 It is arranged so as to connect. Specifically, the slip prevention bar 15 is a downward U-shaped reinforcing bar, the horizontal portion of the upper end is hung on the upper end bar of the beam upper portion 12, and the lower end of the vertical portion is equal to or longer than the general fixing length in the beam lower portion 11. It will be buried. The misalignment prevention bar 15 is arranged as necessary after calculating the shear strength in consideration of the misalignment of the horizontal joint surface between the beam lower portion 11 and the beam upper portion 12.

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

On pages 51 and 52 of the "Wall Rigid Frame Reinforced Concrete Design and Construction Guideline (2003)" edited by the National Land Technology Policy Research Institute, Ministry of Land, Infrastructure, Transport and Tourism, when calculating the shear deformation of structures such as beams 30 with slabs, etc. , The method of calculating by adding the cooperation width ba of the slab 20 and replacing it with an equivalent rectangular cross section having the same beam shear D is shown.

The inventor of the present application considers not only the cross section of the beam 10 but also the cross section including the portion of the cooperation width ba of the slab 20 integrated with the beam 10, and the average strength (equivalent) of the concrete of the beam 30 with the slab. It is proposed to obtain the average strength) Fce [N / mm ² ] by the following formula (1). However, the upper limit is 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 by the slab 20 is based on the following equation (2).
αs = 1 + t1'・ b1'+ t2'・ b2' ・ ・ ・ (2)

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

As described above, according to the evaluation method of the present invention, first, basically, the average value of the design reference 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. Secondly, the design standard strength of the concrete of the upper part 12 of the beam is set to the equivalent average strength Fce in consideration of the cooperation width ba of the slab 20. Thirdly, the design standard strength of the concrete of the beam upper part 12 is increased by multiplying the cross-sectional area of the beam upper part 12 and the slab 20 by the cooperation width ba and the premium coefficient αs based on the ratio.

The equivalent average strength Fce in the present invention has been proposed after theoretically examining the concrete strength of the beam 30 with a slab and confirming it by an experiment as described later. Then, as will be described later, this equivalent average strength Fce can be prevented from being designed on the safe side and having an excessive shear strength. As a result, it is possible to reduce the construction cost of the structure 100 while ensuring the required shear strength.

FIG. 3 is a graph showing the relationship between the margins in the test piece that was shear-fractured before bending fracture. The X-axis is the bending strength of the beam 10 at the time of bending strength calculated by the formula (5) using the approximate formula of the bending strength Mu shown in the formula (4) for the ultimate shear strength Qsu based on the truss arch theory. The shear margin Qsu / Qfu obtained by dividing by the strength Qfu is shown. The Y-axis shows the margin Qmax / Qfu obtained by dividing the maximum proof stress Qmax when the test piece is sheared or inferior in adhesion by the shear strength Qfu. When determining the ultimate shear strength Qsu, the equivalent average strength Fce is used as the concrete strength. Further, at is the cross-sectional area of the tensile reinforcing bar, σy is the yield strength of the main reinforcing bar, and d is the effectiveness of the beam 10.
Mu = 0.9 ・ at ・ σy ・ d ・ ・ ・ (4)
Qfu = 2 ・ Mu / L0 ・ ・ ・ (5)

In FIG. 3, the x mark and the square mark indicate that the test piece was shear-broken, and the white circle mark and the diagonal line mark indicate that the test piece was poorly adhered. The square mark and the diagonal circle mark indicate the test results actually performed by the inventor of the present application, and the x mark and the white circle mark indicate the experimental data described in the prior literature.

FIG. 4 is a graph showing the relationship between the margins of the test piece that has been bent and broken. Similar to FIG. 3, the X-axis shows the shear margin Qsu / Qfu, and the Y-axis shows the margin Qmax / Qfu. However, Qmax includes the maximum proof stress in the case of bending fracture in addition to the case where the test piece is sheared or inferior in adhesion.

In FIG. 4, the white square mark and the diagonal line square mark indicate that the test piece was shear-broken after yielding, and the + mark and the + mark in the black square indicate that the test piece was poorly adhered after yielding. The diagonal diamonds indicate that the specimen is bent. The diagonal square mark, the black square + mark, and the diagonal rhombus mark indicate the test results actually performed by the inventor of the present application, and the white square mark, + mark, and white rhombus mark indicate the experimental data described in the prior literature. There is.

With reference to FIGS. 3 and 4, in the region where the shear margin Qsu / Qfu is 1 or more, the ultimate shear strength Qsu is larger than the bending strength Qfu, and theoretically, bending fracture occurs instead of shear fracture.

Further, in the region where the shear margin Qsu / Qfu is less than 1, the margin Qmax / Qfu is larger than the shear margin Qsu / Qfu, so that the maximum proof stress Qmax at the time of shear failure or poor adhesion is the theoretical shear. Ultimate strength greater than Qsu. From this, it can be seen that the equivalent average strength Fce calculated by the equation (1) is evaluated on the safer side than the shear strength at which the actual beam 10 undergoes shear failure.

Further, in the region where the shear margin Qsu / Qfu is 1 or more, the margin Qmax / Qfu is 1 or more, so that the maximum proof stress Qmax at the time of bending fracture is larger than the bending strength Qfu. From this, it can be seen that the equivalent average strength Fce calculated by the equation (1) is evaluated on the safer side than the bending strength at which the actual beam 10 bends and breaks.

When calculating the equivalent average intensity Fce, it is preferable to consider it as follows.

First, when the top end of the beam upper portion 12 is located above the top end of the slab 20, as in the beam 30A with a slab shown in FIG. 5, the beam upper portion 12 is located higher than the top end of the slab 20. The equivalent average intensity Fce is calculated assuming that the existing portion (shaded portion in FIG. 5) is excluded.

Secondly, when the horizontal joint surface A between the lower beam 11 and the upper beam 12 is located above the bottom end of the slab 20, as in the beam 30B with a slab shown in FIG. 6, it is lower than the horizontal joint surface A. The equivalent average intensity Fce is calculated assuming that the portion of the slab 20 existing at the position (the shaded portion in FIG. 6) is excluded.

Thirdly, when there is a portion formed by using the first concrete in the beam upper portion 12 like the beam 30C with a slab shown in FIG. 7, that portion (the same hatched portion as the beam lower portion 11 in FIG. 7). ) Is regarded as the upper beam 12 instead of the lower beam 11, and the equivalent average strength Fce is calculated. That is, the portion regarded as the lower portion 11 of the beam is limited to the portion formed of the first concrete in the horizontal cross section.

Fourth, if there is a part of the slab 20, such as the first concrete, which has a higher design standard strength than the second concrete, such as the beam 30C with a slab shown in FIG. 7, that part. The equivalent average strength Fce is calculated by assuming that the slab 20 is made of the second concrete including (the same hatching portion as the beam lower portion 11 in FIG. 7). For example, a part of the slab 20 is made of precast concrete.

Fifth, when a void (void) 23 is present in the slab 20 as in the beam 30D with a slab shown in FIG. 8, the portion of the slab 20 outside the void 23 closest to the beam upper portion 12 (FIG. 8). The shaded area) does not include the slab 20 in the cooperation width ba, and the equivalent average strength Fce is calculated. That is, the cooperation width ba is defined as the slab 20 from the side end surface of the beam upper portion 12 to the position where the nearest void 23 exists.

The present invention is not limited to the above-described method for evaluating the shear strength of the beam with slab 30 and the structure provided with the beam with slab evaluated using the method, and can be appropriately modified.

10 ... beam, 11 ... lower beam, 12 ... upper beam, 13 ... beam main bar, 14 ... shear reinforcement, 15 ... slip prevention bar, 20 ... slab, 21 ... one slab, 22 ... other slab, 24 ... void , 30, 30A, 30B, 30C ... Beams with slabs, 40 ... Pillars, 100 ... Structures, A ... Horizontal joint surfaces.

Claims (2)

Shearing of a beam with a slab consisting of a beam lower part formed using the first concrete and a beam upper part and a slab integrated with the beam lower part and formed using a second concrete different from the first concrete. It is a strength evaluation method
The design standard strength of the first concrete is Fcd [N / mm ² ], the design standard strength of the second concrete is Fcu [N / mm ² ], the cross-sectional area of the lower part of the beam is Ad [mm ² ], and the above. The cross-sectional area of the upper part of the beam is Au [mm ² ], the cooperative 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], the lower part of the beam and the beam. When the width of the upper part of the beam is b [mm], the average strength Fce [N / mm ² ] of concrete when evaluating the shear strength of the beam with a slab is expressed by the equation (1).
Fce = (Fcd / Ad + αs / Fcu / Au) / (Ad + Au) ・ ・ ・ (1)
The premium coefficient αs in the equation (1) is expressed by the equation (2).
αs = 1 + t'・ b'・ ・ ・ (2)
Here, a method for evaluating the shear strength of a beam with a slab, characterized in that t'= t / Tu and b'= ba / b. A structure including a beam with a slab, which is formed by evaluating the shear strength using the method for evaluating the shear strength of a beam with a slab according to claim 1.

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