Shear strength evaluation method and structure for beams with slabs

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

Technical Field

[0001] The present invention relates to a method for evaluating the shear strength of a beam with a slab and a structure provided with a beam with a slab evaluated using the same.

Background Art

[0002] After installing the lower part of a beam formed of precast concrete at a predetermined position of a structure, reinforcement of the upper part of the beam and a slab connected thereto is performed, and in-situ concrete is integrally placed, whereby a beam with a slab in which the beam and the slab are integrated is formed as a half-precast beam.

[0003] In a half-precast beam, concretes with different strengths can be used for the upper and lower parts of the beam. Therefore, high-strength concrete is required for the beam as a structural member, but for the slab as a secondary member, it is sufficient if it has the strength to function as a slab. Therefore, using normal-strength concrete for the slab and the upper part of the beam is effective in reducing the material cost. However, in this case, it is necessary to appropriately judge the structural bearing capacity (mainly shear bearing capacity) of the beam, and a design method with no strength excess or deficiency is required.

[0004] 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 of the overall height D of the beam (D / 2 ≧ t), only the part above 1 / 2 of the beam is considered, and the shear strength of the beam is calculated based on the average strength of the concrete according to the ratio of the heights of the upper and lower parts of the beam. On the other hand, when D / 2 < t, the concrete strength of the upper part of the beam is directly used as the shear strength of the beam.

[0005] However, in the technique described in Patent Document 1, only the part above 1 / 2 of the height of the beam is considered when obtaining the shear strength of the entire beam. Also, no consideration is given to the improvement in the shear strength of the beam due to the slab integrated with the upper part of the beam.

[0006] Therefore, for example, in the technique described in Patent Document 2, the shear strength of the beam is obtained by multiplying the concrete strength at the upper part of the beam by a value obtained by dividing it by a value corresponding to the ratio of the cooperation width of the slab to the width of the beam. Here, the cooperation width B of the slab is determined from the inner length L of the beam, the compressive strength σc2 of the concrete at the upper part of the beam, and the shear strength σs2 so that the compressive force borne by the slab part does not exceed the shear force that can be transmitted at the interface between the slab and the upper part of the beam, and the cooperation width B is obtained within the range of B < L / (2×σc2 / σs2).

Prior Art Documents

Patent Documents

[0007]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0008] However, the inventor of the present application has found that even in the technique described in Patent Document 2 above, the shear strength of the beam with a slab is underestimated, and the shear resistance of the beam with a slab is improperly evaluated to be low.

[0009] In view of the above points, an object of the present invention is to provide a method for evaluating the shear strength of a beam with a slab that can appropriately determine the shear strength of the beam with a slab, and a structure including a beam with a slab evaluated using this method.

Means for Solving the Problems

[0010] The method for evaluating the shear strength of a beam with a slab according to the present invention is a method for evaluating the shear strength of a beam with a slab including a beam lower part formed using a 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. The design standard strength of the first concrete is Fcd [N / mm 2], the design 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 joint width of the slab is ba [mm], the thickness of the slab is t [mm], the height of the top of the beam is Tu [mm], and the width of the bottom and top of the beam is b [mm]. The average strength of concrete when evaluating the shear strength of the beam with slab is Fce [N / mm 2 ] is expressed by formula (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 / Tu and b'=ba / b.

[0011] According to the method for evaluating the shear strength of a slab beam of the present invention, the concrete strength of a slab beam is theoretically examined and experimentally confirmed, and then the average concrete strength Fce is proposed, as described below. By using this average concrete strength Fce when evaluating the shear strength, it is possible to avoid a design that is on the safe side and has an excessively large shear resistance.

[0012] The shear strength of a structure having a slab-attached beam of the present invention is evaluated using the shear strength evaluation method of the slab-attached beam of the present invention. did It is characterized by:

[0013] According to a structure provided with a slab-attached beam of the present invention, it is possible to reduce the construction costs of the structure while ensuring the necessary shear strength. [Brief description of the drawings]

[0014] [Figure 1] 1 is a schematic side view of a structure according to an embodiment of the present invention. [Diagram 2] FIG. 2 is a schematic cross-sectional view taken along line II-II in FIG. [Diagram 3] 13 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. [Figure 4] 13 is a graph showing the relationship between the degree of margin in a test specimen in which a bending hinge occurred. [Diagram 5] FIG. 11 is a longitudinal sectional view of a slab-attached beam according to a modified embodiment of the present invention. [Figure 6] FIG. 11 is a longitudinal sectional view of a slab-attached beam according to another modified embodiment of the present invention. [Figure 7] 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. [Figure 8] 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. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] A structure 100 to be evaluated by the evaluation method according to an embodiment of the present invention will be described with reference to FIGS.

[0016] The structure 100 is a structure having a beam with slab 30 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.

[0017] The entire beam 10 is made up of the lower beam section 11 and the upper beam section 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 Japanese Patent No. 4021588.

[0018] 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.

[0019] The width of the beam 10 is b [mm]. The cross-sectional area of ​​the vertical cross section perpendicular to the longitudinal direction of the lower beam portion 11 is Ad [mm 2 ](=Td·b), and the cross-sectional area of ​​the vertical section perpendicular to the longitudinal direction of the upper part of the beam 12 is Au [mm 2 ](=Tu ·b).

[0020] The height Tu of the beam upper portion 12 is lower than the thicknesses t1, t2 [mm] of the slab 20. That is, there is no contact between the beam lower portion 11 and 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.

[0021] The first concrete used in forming the lower part 11 of the beam is, for example, high-strength concrete, and its design standard strength is Fcd [N / mm 2 The second concrete used to form the upper part 12 of the beam and the slab 20 is, for example, normal strength concrete, and its design standard strength is Fcu [N / mm 2 The design strengths Fcu and Fcd of the first and second concretes are preferably 24 to 60 N / mm 2 and it is preferable that the standard design strength Fcu of the second concrete is equal to or greater than 1 / 2 of the standard design strength Fcd of the first concrete.

[0022] 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 vertical section of the beam 10 and the slab 20 as a whole forms a T-shape. The slab 21 on one side has a total width of ba1 [mm] and a thickness of t1 [mm], and the slab 22 on the other side has a total width of ba2 [mm] and a thickness of t2 [mm]. The total 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.

[0023] The joint widths ba1 and ba2 of the slabs 21 and 22 are calculated in accordance with the "Standards and Commentary for Calculating Reinforced Concrete Structures (2010)" compiled by the Architectural Institute of Japan. The sum of the joint widths ba1+ba2 of the slabs 21 and 22 is preferably 0.1 times or more, and more preferably 0.1 to 0.83 times, of the inside dimension L0.

[0024] Reinforcing bars such as beam main bars 13 and shear reinforcement bars 14 are arranged in the beam 10 (beam lower section 11 and beam upper section 12). Note that the arrangement of the reinforcing bars shown in Fig. 2 is one example, and the reinforcing bars may be arranged in other ways, for example, anti-slip bars, bond reinforcement bars, etc. may be arranged. It is preferable to use reinforcing bars 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 bars is 295 to 590 N / mm 2 The yield points of the shear reinforcement, slip prevention reinforcement 15, and bond reinforcement are preferably 295 to 1275 N / mm 2 It is preferable that:

[0025] 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 reinforcement 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 distance equal to or greater 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.

[0026] Here, the lower beam portion 11 is made of precast reinforced concrete, the upper beam portion 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 beam portion 11 may be made of cast-in-place concrete. Also, the slab 20 may be formed by a ribbed precast concrete plate (FR plate) slab construction method, a void slab construction method, or the like.

[0027] On pages 51 and 52 of the "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., a method is shown 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.

[0028] The inventors of the present application thus calculated the average strength (equivalent average strength) Fce [N / mm of the concrete of the beam with slab 30 by 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. 2 It is proposed to calculate the concrete strength Fcd of the lower part 11 of the beam by the following formula (1): Fce=(Fcd·Ad+αs·Fcu·Au) / (Ad+Au) ··· (1)

[0029] Here, the premium coefficient αs for the slab 20 is calculated by the following formula (2). αs=1+t1'·b1'+t2'·b2' ··· (2)

[0030] And, t1'=t1 / Tu, t2'=t2 / Tu, b1'=ba1 / b, and b2'=ba2 / b. When the slab 20 is only the slab 21 on one side, the formula (2) becomes the formula (3). αs=1+t1'·b1' (3)

[0031] Thus, 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 slab 20 for the cooperative width ba.

[0032] The equivalent average strength Fce in the present invention is proposed after theoretically examining the concrete strength of the slab beam 30 and verifying it through experiments as described below. This equivalent average strength Fce is on the safe side as described below, and can prevent a design having an excessively large shear resistance. This makes it possible to reduce the construction cost of the structure 100 while ensuring the necessary shear resistance.

[0033] Figure 3 is a graph showing the relationship between the margin of safety for specimens that failed in shear before bending failure. The X-axis shows the margin of safety Qsu / Qfu, which is calculated by dividing the ultimate shear strength Qsu based on the truss-arch theory by the bending strength Qfu, which is the shear strength of beam 10 at 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 calculated by dividing the maximum strength Qmax when the specimen fails in shear or bond cracks 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 diameter of beam 10. Mu=0.9 at σy d (4) Qfu=2 Mu / L0 (5)

[0034] In Fig. 3, the cross marks and square marks indicate that the test specimens were shear-fractured, and the white circle marks and diagonal-lined circle marks indicate that the test specimens were bond-fractured. The square marks and diagonal-lined circle marks indicate the results of tests actually conducted by the inventors of the present application, while the cross marks and white circle marks indicate experimental data published in existing literature.

[0035] Figure 4 is a graph showing the relationship between the margin of safety for specimens that 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 the case where the specimen fails in shear or bond failure.

[0036] In Fig. 4, the open squares and diagonal lined squares indicate that the test specimens broke in shear after yielding, the + marks and + marks in black squares indicate that the test specimens broke in bond after yielding, and the open diamonds and diagonal lined diamonds indicate that the test specimens 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.

[0037] 3 and 4, in a region where the shear margin Qsu / Qfu is 1 or more, the ultimate shear strength Qsu is greater than the bending strength Qfu, and theoretically, bending failure will occur instead of shear failure.

[0038] 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.

[0039] 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 and fail.

[0040] When calculating the equivalent average strength Fce, it is preferable to perform the calculation based on the following assumptions.

[0041] First, when the top end of the beam upper part 12 is located higher than the top end of the slab 20, as in the case of a slab-attached beam 30A shown in Figure 5, the beam upper part 12 is regarded as excluding the part that is higher than the top end of the slab 20 (the shaded part in Figure 5), and the equivalent average strength Fce is calculated.

[0042] 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 lower than the horizontal joint surface A (the shaded area in Figure 6) is excluded, and the equivalent average strength Fce is calculated.

[0043] Thirdly, when there is a part formed of the first concrete in the upper part 12 of the beam like the slab-attached beam 30C shown in Fig. 7, that part (the part with the same hatching as the lower part 11 of the beam in Fig. 7) is regarded as the upper part 12 of the beam, not as the lower part 11 of the beam, to calculate the equivalent average strength Fce. In other words, the part regarded as the lower part 11 of the beam is limited to the part formed entirely of the first concrete in the horizontal cross section.

[0044] Fourth, when the slab 20 has a portion formed using a concrete having a higher design standard strength than the second concrete, such as the first concrete, as in the case of the slab-equipped beam 30C shown in Fig. 7, the slab 20 is considered to be made of the second concrete, including that portion (the portion hatched in the same manner as the beam lower portion 11 in Fig. 7), and the equivalent average strength Fce is calculated. For example, this is the case when a portion of the slab 20 is made of precast concrete.

[0045] Fifth, when a void (air gap) 23 exists in the slab 20, as in the case of a slab-attached beam 30D shown in Fig. 8, the portion of the slab 20 (shaded area in Fig. 8) outside the void 23 closest to the beam upper portion 12 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.

[0046] The present invention is not limited to the above-mentioned method for evaluating the shear strength of the slab-attached beam 30 and the structure including the slab-attached beam evaluated using the same, and may be modified as appropriate. [Explanation of symbols]

[0047] 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

[Claim 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: The design strength of the first concrete is Fcd [N / mm 2 ], the design 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 joint 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 of the beam and the upper part of the beam is b [mm]. The average strength of the concrete when evaluating the shear strength of the beam with the slab is Fce [N / mm 2 ] is represented by formula (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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