JP2024089289A - Reinforcement member design method - Google Patents

Abstract

The present invention provides a method for designing a reinforcing member that evaluates reinforcing performance suited to actual conditions.
[Solution] This is a design method for a reinforcing member consisting of a reinforcing steel plate and an anchor, in the case where an opening is made in an existing beam, a reinforcing steel plate is bonded around the opening on both sides of the beam, and the reinforcing steel plate is joined to the side of the beam with an anchor to reinforce the beam. The required reinforcing shear strength Q _R,need of the reinforcing member is obtained from the difference between the shear strength Q _su0 of the beam before the opening is made and the shear strength Q _suR of the beam after the opening is made, the joint surface shear strength q _j per joint surface is calculated from the material type and diameter of the anchor and the effective bonding area a _b of the reinforcing steel plate, and the shape of the reinforcing steel plate is determined so that the joint surface shear strength q _j per joint surface is equal to or greater than the required joint surface shear strength q _j,need per joint surface calculated from the required reinforcing shear strength Q _R ,need of the reinforcing steel plate, and the reinforcing steel plate does not break under pressure at the bolt hole, does not yield at the upper and lower parts of the opening, and does not buckle at the upper and lower parts of the opening at the maximum strength.
[Selected figure] Figure 7

Description

Application for application of Article 30, Paragraph 2 of the Patent Act Publication date: September 1, 2022 Publication: Okamura Gumi Technical Annual Report No. 48, No. 6, pp. 75-80, Okamura Gumi Technical Research Institute, Inc.

This invention relates to a method for designing reinforcing members when openings are made in existing reinforced concrete beams.

During the life of a building, new holes may be created in existing reinforced concrete beams to change or install new equipment piping. Since the holes do not exist in the original design, a reinforcing structure must be added to compensate for the reduction in cross-section caused by the holes.

As a reinforcing structure for such an opening, there is a method of installing reinforcing steel plates on both sides of the beam around the opening (see, for example, Patent Document 1). In this method, an opening for passing piping is provided in the existing beam, and four anchor holes for fixing the reinforcing steel plate are provided around it. The reinforcing steel plate is provided with an opening of the same diameter as the opening in the beam, and four holes for passing anchors to fix the reinforcing steel plate to the side of the beam.

Japanese Patent Application Laid-Open No. 55-042965

However, the reinforcement performance of the above reinforcement methods has not been fully verified, and no design method has been established. For this reason, there is a demand for a method of evaluating reinforcement performance that is suited to actual conditions.

In view of the above, the present invention aims to provide a method for designing reinforcing members that evaluates reinforcing performance suited to actual conditions.

The design method of the reinforcing member of the present invention is a design method of a reinforcing member consisting of a reinforcing steel plate and the bolt when an opening is made in an existing reinforced concrete beam, a reinforcing steel plate is attached around the opening on both sides of the beam, and the reinforcing steel plate is bolted to the side of the beam through bolt holes made in at least the four corners of the reinforcing steel plate. The required reinforcing shear strength of the reinforcing member is calculated from the difference between the shear strength of the beam before the opening is made and the shear strength of the beam after the opening is made, the joint shear strength per joint surface is calculated from the material type and diameter of the bolt and the effective adhesive area of the reinforcing steel plate, and the joint shear strength per joint surface is equal to or greater than the required joint shear strength per joint surface calculated from the required reinforcing shear strength of the reinforcing steel plate, and the shape of the reinforcing steel plate is determined so that the reinforcing steel plate does not break at the bolt hole, does not yield at the upper and lower parts of the opening, and does not buckle at the upper and lower parts of the opening at the maximum strength.

As can be seen from the results of the structural experiments described below, the reinforcing member design method of the present invention makes it possible to obtain a reinforcing member design method that evaluates reinforcing performance suited to actual conditions.

Since the shear force of the joint surface acts in the diagonal direction of each of the four divided reinforcing steel plate portions, in the design method of the reinforcing member of the present invention, it is preferable to determine the sine value of the angle between the line connecting two diagonally positioned bolts, among the bolts arranged near the four corners of the reinforcing steel plate, and the axial direction of the beam material, and to determine the joint surface shear strength per joint surface as the required reinforcing shear force of the reinforcing steel plate divided by four times the sine value.

In addition, the results of the structural experiments described below have shown that the shear strength of the joint surface decreases according to the aperture ratio, which is the ratio of the beam depth to the aperture diameter. Therefore, in the design method of the reinforcing member of the present invention, it is preferable to determine the joint surface shear strength per joint surface as the minimum value between the required shear force per joint surface at the joint surface when the fastening strength is sufficient and the shear force per joint surface at the joint surface when the fastening strength is insufficient, multiplied by a reduction coefficient based on the ratio of the beam depth to the aperture diameter.

In the design method of the reinforcing member of the present invention, for example, the shear strength of the beam before the opening is provided is calculated using the Ohno-Arakawa formula, and the shear strength of the beam before reinforcement after the opening is provided is calculated using the modified Hirosawa formula, which is a modified version of the Ohno-Arakawa formula.

1 is a schematic perspective view showing an existing RC beam having an opening to which a method for designing a reinforcing member according to an embodiment of the present invention is applied; Front view showing test specimen #21/3. Top view showing test specimen #21/3. FIG. 4 is a cross-sectional view taken along line IV-IV in FIG. FIG. 4 is a cross-sectional view taken along line V-V in FIG. 3 . FIG. 13 is an enlarged cross-sectional view showing the fixed state of the reinforcing steel plate of test specimen #21/3. 4 is a flowchart showing a method for designing a reinforcing member according to an embodiment of the present invention. FIG. 13 is a diagram explaining the effective range c of the shear reinforcement around the opening. FIG. 2 is a diagram for explaining the effective adhesive area a _b of one bonding surface of the reinforcing steel plate. 1 is a diagram for explaining the concept of buckling that occurs in a reinforcing steel plate. A graph showing the relationship between shear force and component deformation angle for all test specimens, along with the main occurrences of various cracks, etc. 1 is a graph showing the relationship between τ·Σa _p and the measured value Q _ex,R of the reinforcing effect. 1 is a graph showing the relationship between σ·Σa _p and the measured value Q _ex,R of the reinforcing effect. Graph showing the progress of each crack occurrence event. Graph showing the relationship between the design value Q _suR of maximum shear strength and the experimental value Q _max .

A method for designing a reinforcing member according to an embodiment of the present invention will be described with reference to the drawings. Note that the drawings are for the purpose of explaining the present embodiment in a schematic manner, and the dimensions have been exaggerated.

As shown in Figure 1, this reinforcing member design method is a method for designing the reinforcing steel plate 20 and anchor 32, which are reinforcing members, in a perforated beam steel plate reinforcement method in which an opening 11 is made in an existing RC (reinforced concrete) beam 10, a reinforcing steel plate (hereinafter referred to as reinforcing steel plate) 20 is placed in the part including the opening 11 (hereinafter referred to as the opening part), and reinforcement is performed by fixing it using epoxy resin 31 (see Figure 6) and anchor bolts (hereinafter referred to as anchors) 32. Note that the anchors 32 correspond to the bolts of this invention.

The beam 10 to which this reinforcing member design method is applied is made of reinforced concrete and has a rectangular cross section with its long sides extending in the vertical direction (Z-axis direction), and both ends in the beam axial direction (X-axis direction) are integrated with reinforced concrete columns 40. The beam 10 may also be integrated with reinforced concrete slabs that protrude outward in the beam width direction (Y-axis direction) from both sides of its upper part.

Referring also to Figures 2 to 6, in the beam 10, multiple upper end beam main bars 12 and multiple lower end beam main bars 13 are embedded in the beam axial direction as beam main bars. The upper end beam main bars 12 are embedded in the upper part of the beam 10 at intervals in the beam width direction. Meanwhile, the lower end beam main bars 13 are embedded in the lower part of the beam 10 at intervals in the beam width direction. Here, five upper end beam main bars 12 and five lower end beam main bars 13 are arranged, but the number and arrangement of these can be changed as appropriate.

The upper end beam main reinforcement 12 and the lower end beam main reinforcement 13 are bound by multiple shear reinforcement bars (stirrups) 14, 15. The shear reinforcement bars 14, 15 are formed in a rectangular frame shape surrounding the upper end beam main reinforcement 12 and the lower end beam main reinforcement 13, and are embedded in the beam 10 at intervals in the beam axial direction. These shear reinforcement bars 14, 15 are configured to transmit shear force between the upper end beam main reinforcement 12 and the lower end beam main reinforcement 13. To prevent shear failure at the ends of the beam 10, the shear reinforcement bars 15 are arranged at narrower intervals than the shear reinforcement bars 14 in the center and nearby areas.

The reinforcing steel plate 20 is a rectangular steel plate with a thickness of t [mm], and has an opening 21 in the center with the same diameter as the opening 11 in the beam 10. The reinforcing steel plate 20 is installed on both sides of the beam 10 in the beam width direction, and is fixed by at least four anchors 32. The anchors 32 are arranged symmetrically in the beam axis direction and in the up-down direction, centered on the opening 11. Note that the reinforcing steel plate 20 may be fixed by four penetrating anchors instead of a total of eight anchors 32.

The material of the reinforcing steel plate 20 is SS400, S490 as specified in JIS G 3101, SM400A, SM400B, SM400C, SM490A, SM490B, SM490C as specified in JIS G 3106, or SN400A, SN400B, SN400C, SN490A, SN490B, SN490C as specified in JIS G 3136.

The beam 10 is made of ordinary concrete with a concrete strength _σBD of 15 N/ ^mm2 to 30 N/mm2. This design method is applicable to beams 10 having a depth D [mm], beam width b of 2/ ³ ·D or less, inner span length L of 3D or more, diameter H of opening 11 of D/3 or less and 250 mm or less, vertical positions of opening 11 in a range other than D/4 from the upper end and lower end of beam 10, and intervals between openings 11 of 3 times or more the average of diameter H of adjacent openings 11.

The anchor 32 is fixed using a hexagonal nut 33 and flat washer 34 (see Figures 5 and 6) with a capsule-type or injection-type adhesive. The anchor 32, hexagonal nut 33 and flat washer 34 are made of steel material that belongs to strength classes 4.6, 4.8, and 5.6 specified in JIS B 1051, and the material is the same as that of the reinforcing steel plate 20, or SR235, SR295, SD295, and SD345 specified in JIS G 3112. The embedded part of the anchor 12 is threaded over its entire length or is a deformed bar.

The adhesive 31 is an epoxy resin adhesive, and under test conditions of 23° C., the compressive strength according to the test method specified in JIS K 7181 is 50.0 N/ ^mm2 or more, the tensile strength according to the test method specified in JIS K 7161 is 19.6 N/ ^mm2 or more, the compressive elastic modulus according to the test method specified in JIS K 7181 is 9.8× ¹⁰² N/ ^mm2 or more, and the viscosity according to the test method specified in JIS K 7117 is 2500 mPa·s or less. However, the viscosity of the adhesive 31 is not limited to the above values if good filling properties are confirmed by experiments or the like.

A sealant 35 (see FIG. 6) is used to prevent leakage when the adhesive 31 is injected. The sealant 35 is an epoxy resin putty, and under test conditions of 23° C., the compressive strength according to the test method specified in JIS K 7181 is 50.0 N/mm2 ^or more, the tensile strength according to the test method specified in JIS K 7161 is 19.6 N/ ^mm2 or more, and the compressive elastic modulus according to the test method specified in JIS K 7181 is 9.8× ¹⁰² N/mm2 or ^more .

This embodiment relates to a method for designing a reinforcement structure in which a through hole 11 is provided in an existing reinforced concrete beam 10, and reinforcing steel plates 20 are installed on both sides of the through hole 11 and secured with anchors (or through bolts) 32. This design method assumes that only shear stress acts on the reinforcing steel plates 20, and that no bending stress acts on them.

In this method for designing a reinforcement structure, as shown in FIG. 7, first, a required reinforcement shear force Q _R,need , which is a shear force required for reinforcement by the reinforcement structure, is calculated (STEP 1).

The shear strength Q _suR of the reinforced beam 10 is calculated as the sum of the shear strength Q _su0 around the opening 11 of the beam 10 (hereinafter also referred to as a perforated beam) before reinforcement and the increase in shear strength Q _R due to the reinforcement structure, as shown in formula (1).
Q _suR = Q _su0 + Q _R ... (1)

The shear strength Q _suR of the reinforced beam 10 is designed to be equal to or greater than the shear strength Q su of the beam 10 before the holes 11 are provided (hereinafter also referred to as a non-perforated beam), as shown in formula ₍₂ ).
Q _suR ≧Q _su ... (2)

Equation (3) is derived from equation (1).
Q _R = Q _suR - Q _su0 ... (3)

The increment in shear strength Q _R due to the reinforcement structure needs to be equal to or greater than the required reinforcement shear strength Q _R,need , as shown in equation (4).
Q _R ≧Q _R,need ... (4)

The required reinforcement shear force Q _R,need is calculated using equation (5).
Q _R,need =α(Q _su -Q _su0 ) ... (5)

Here, α is the surcharge coefficient according to the aperture ratio (H/D), which is 1.2 when H/D<1/4 and 1.0 when H/D≧1/4.

This value of the premium coefficient α is derived from structural experiments using test specimens, which will be described later. Specifically, in these structural experiments, the maximum strength of the test specimens with an aperture ratio of 1/4 generally met the expected value, but fell short of the expected value for the test specimens with an aperture ratio of 1/3. From this, it can be assumed that designs with a small aperture ratio relative to beam depth D are on the safe side. However, taking into consideration the overall influences that could not be confirmed in experiments, such as the smaller the aperture ratio, the greater the freedom to decenter vertically, and changes in the position of aperture 11, the premium coefficient α was set to 1.2 when the aperture ratio is less than 1/4.

Q _su is the shear strength of the beam 10 before the opening 11 is provided, and is calculated by the Ohno-Arakawa min formula shown in formula (6). This formula is described in "Reinforced Concrete Structure Calculation Standards and Commentary" published by the Architectural Institute of Japan.

Here, k _u is a coefficient based on the effective depth d of the beam 10, and k _u = (160/d) ^0.37 . However, when d ≧ 400 [mm], k _u = 0.72, and when d ≦ 160 [mm], k _u = 1.0. k _p is a coefficient based on the tensile reinforcement ratio p _r , and k _p = 2.36p _r ^0.23 . F _cR is the reinforcement design strength standard of concrete [N/mm ² ]. M is the maximum bending moment [Nmm], and Q is the maximum shear force [N]. b is the beam width [mm] of the beam 10, D is the beam depth [mm] of the beam 10, d is the effective depth [mm] of the beam 10, and j is the stress center distance [mm]. p _w is the shear reinforcement ratio. However, when p _w exceeds 0.012, p _w is set to 0.012, and σ _wy is the standard yield point [N/mm ² ] of the shear reinforcement bars 14 and 15 .

Q _su0 is the shear strength around the opening of the beam 10 with a hole before reinforcement, and is calculated using the modified Hirosawa formula, which is a modified version of the Ohno-Arakawa formula shown in formula (7). This formula is also described in "Reinforced Concrete Structure Calculation Standards and Commentary" published by the Architectural Institute of Japan.

ただし、ｐ_s＝Σ｛a_ｓ（ｓｉｎθ＋ｃｏｓθ）／（ｂ・ｃ）｝ ・・・（８）

Here, p _s =Σ{a _s (sin θ + cos θ) / (b·c)} (8)

Here, H is the diameter [mm] of the opening 11. p _s is the reinforcement ratio within the effective range c of the shear reinforcement 14, 15 around the opening. However, if p _s exceeds 0.012, p _s is set to 0.012. σ _sy is the standard yield point F [N/mm ² ] of the shear reinforcement around the opening. With reference to Figures 8 and 9, c is the effective range of the shear reinforcement 14, 15 around the opening, and is the distance [mm] between the position where a straight line drawn in a 45° direction from the center of the opening intersects with the center of gravity of the tensile reinforcement (main reinforcement). _{a s} is the cross-sectional area [mm ² ] of one set of shear reinforcement 14, 15 within the range of c. θ is the angle that the shear reinforcement 14, 15 around the opening makes with the beam axis.

In the design method of this reinforcement structure, next, the material type and diameter of the anchor 32 and the effective bonding area a _b of the reinforcing steel plate 20 are selected (STEP 2).

Next, the joint surface shear force q _j per joint surface is determined (STEP 3).

This reinforcement structure is constructed by fixing the reinforcing steel plate 20 to the concrete using anchors 32 and bonding it with adhesive 31 so that it becomes one with the concrete. Therefore, the adhesive strength of the joint surface with the reinforcing steel plate 20 is important in preventing damage to the concrete.

When concrete is subjected to a shear force, the joint surface on the concrete side deforms, but the reinforcing steel plate 20 is sufficiently harder than concrete that it does not deform even when subjected to a shear force. Therefore, the amount of deformation between the joint surface between the reinforcing steel plate 20 and the concrete increases the further away from the opening 11, so the shear stress on the joint surface of the reinforcing steel plate 20 is greater at the edge than in the vicinity of the opening 11. Therefore, in order to efficiently exert the reinforcing effect, the fixing strength of the anchors 32 at the four corners is important.

Referring to the results of the structural experiment described below, it is believed that the failure of the beam 10 was due to the destruction of the concrete around the anchors 32, accompanied by shear cracks, which caused the anchors 32 to lose their adhesion resistance and the progression of peeling at the joint surface, resulting in a loss of strength.

In addition, when the horizontal deformation of the anchor 32 is small, less than about 0.5 mm, a fracture line appears at the concrete interface directly below the joint surface of the adhesive 31. At maximum strength, no fracture occurs in the area from the anchor 32 to the opening 11 side, and it is thought that shear stress is transmitted as adhesion resistance and friction resistance at the joint surface around this anchor 32.

The frictional resistance here is considered to be a shear resistance accompanied by compressive surface pressure due to the reaction force of the anchor 32, which acts as frictional resistance inside the object even before the concrete interface is destroyed. The bearing resistance of the anchor 32 and the reinforcing steel plate 20 is sufficiently small compared to the adhesion resistance and frictional resistance, so it can be ignored, and it is considered possible to evaluate the shear strength by the combination of frictional resistance and adhesion resistance.

(Required shear force in the diagonal direction of the anchor due to beam shear)
From the results of structural experiments described later, it is found that in this reinforced structure, the maximum strength is determined by the shear fracture of the joint surface of the reinforcing steel plate 20. Therefore, the increment Q _R in shear force due to reinforcement is determined according to the reinforcing force due to the vertical component in the shear direction of the joint surface between the side surface of the beam 10 and the reinforcing steel plate 20. In other words, the shear force of the joint surface acts on the parts of the reinforcing steel plate 20 that are divided into the upper and lower parts of the opening 11, respectively.

Therefore, the required increase in shear strength due to reinforcement Q _R,need is calculated as four times the shear force Q p _,need that needs to be borne by each part of the reinforcing steel plate 20 between one joint surface that is divided into the upper and lower parts of the opening 11 at the ultimate strength of the beam 10, as shown in equation (9).
Q _R,need =4Q _p,need ... (9)

At this time, the shear force of the joint surface acts in the diagonal direction of each of the four divided parts of the reinforcing steel plate 20. If it is considered that bending is not applied, this required shear force Q _p,need is calculated by formula (10) using the required shear force q _j,Q of the anchor 32 in the diagonal direction per joint surface due to the shear of the beam 10.
Q _p,need =q _j,Q · sinφ ... (10)

Here, φ is the angle between the beam axial direction and the diagonal of the anchor 32 at the edge. However, since bending is not applied, the shear direction of the joint surface is the diagonal direction of the anchor 32 at the edge, and therefore φ is calculated from the distance H _a [mm] between the anchors 32 in the direction perpendicular to the beam axis and the distance L _a [mm] between the anchors 32 in the beam axial direction by formula (11). Note that, since the angle between the beam axial direction and the diagonal of the anchor 32 at the edge is 32.5° for all test specimens whose performance was confirmed in the structural experiment described later, the upper limit of φ is set to 32.5°.
φ=tan ⁻¹ (H _a /L _a ) (11)

Then, equation (12) is obtained from equations (5), (9), and (11).
q _j,need =α(Q _su -Q _su0 )/4 sin φ (12)

(Shear strength of each joint surface)
The joint surface shear strength q _j [N] per joint surface is calculated by the smaller of the strength q _j1 when the bonded joint area is sufficient and the strength q _j2 when the bonded joint area is insufficient, using formula (13). Here, the strength q _j1 is the strength determined by the yield of the reinforcing steel material 20 when the anchor 32 effectively works up to the shear strength because the fixing strength is sufficient. On the other hand, the strength q _j2 is the strength determined by the bearing failure of the concrete around the anchor 32 when the fixing strength is insufficient and peeling occurs at the joint surface.
q _j =β _H · min (q _j1 , q _j2 ) ... (13)

Here, β _H is a reduction coefficient of the reinforcing effect according to the hole opening ratio (H/D), and is expressed by the formula (14), with 1 as the upper limit.
β _H =-4.8H/D+2.2 ... (14)

From the results of the structural experiment described later, it is clear that the shear strength of the joint surface decreases according to the aperture ratio. Therefore, when the aperture ratio is 1/3, the shear strength of the joint surface is reduced, and the reduction coefficient _βH shown in formula (14) is introduced.

The strength q _j1 determined by the yield of the reinforcing steel 20 is calculated by formula (15) in accordance with the anchor joint surface strength formula Q _a in the "Japan Building Disaster Prevention Association, 2017 Revised Edition, Seismic Diagnosis Standards, Seismic Retrofit Design Guidelines, and Commentary for Existing Reinforced Concrete Buildings."
q _j1 =0.7σ _ay · a _a ... (15)

Here, σ _ay is the standard yield strength [N/mm ² ] of the anchor 32, with the upper limit being 300 N/mm ² , and _{a a} is the nominal cross-sectional area [mm ² ] of the anchor 32.

The strength _qj2 determined by the bearing failure of the concrete around the anchor 32 is obtained by formula (16) following "Toshiaki Komiya, Kiyoshi Masuo: Ultimate Strength of Adhesive Joints and Indirect Joints for Steel Frame Additional Brace Reinforcement (Seismic Reinforcement)", Proceedings of the Japan Concrete Institute, Vol. 22 (3), 2000".
q _j2 = 0.08σ _B a _b + 0.5σ _{a y} a _a ... (16)

Here, σ _B is the compressive strength of concrete [N/mm ² ], and _{a b} is the effective bonding area [mm ² ] per joint surface due to bonding of the reinforcing steel plate 20, which is the range indicated by diagonal lines in Fig. 9 and is calculated by formula (17).
a _b = (H _a · L _a - πH ² / 4) / 4 ... (17)

Then, in the design method of this reinforcement structure, it is confirmed whether the joint surface shear strength q _j per joint surface calculated by equation (13) is equal to or greater than the required shear force q _j,need in the anchor diagonal direction per joint surface due to shear of the beam 10 calculated by equation (12) (STEP 4).
q _j ≧q _j,need ... (18)

If the formula (18) is not satisfied (STEP 4: NO), at least one of the diameter of the anchor 32 and the effective adhesive area a _b of the reinforcing steel plate 20 is reselected (STEP 2).

If the formula (18) is satisfied (STEP 4: YES), the thickness t _p of the reinforcing steel plate 20 is selected (STEP 5).

Then, consider whether the conditions for bearing strength, combined stress, and buckling are met (STEP 6).

(Consideration of bearing strength)
First, it is confirmed by formula (19) that the reinforcing steel plate 20 does not undergo bearing failure at the through holes for the anchors 32.
1.9F _p t _{p da} ≧α _d q _j ... (19)

Here, _Fp is the F-value [N/ ^mm2 ] of the steel plate according to the "2018 Edition of the Architectural Institute of Japan, Reinforced Concrete Structural Calculation Standards and Commentary. _{" tp} is the thickness [mm] of the reinforcing steel plate 20. _da is the diameter [mm] of the shaft of the anchor 32, which is the name [mm] for deformed bars. _αd is the bearing coefficient taking safety into consideration, which is 1 here.

(Combined stress considerations)
Next, it is confirmed that the upper and lower parts of the opening 21 in the reinforcing steel plate 20 do not yield by checking using equation (20) that the stress σ _p,need [N/mm ² ] generated in those parts is within the standard yield point σ _py [N/mm ² ] of the reinforcing steel plate 20.
σ _py ≧σ _p,need・・・ (20)

Here, the stress σ _p,need generated in the reinforcing steel plate 20 is calculated from equations (21) to (24) taking into account the respective stresses acting due to shear and bending of the beam 10.
σ _p,need ² ＝σ _x ² ＋３τ _xy ^{2 ・・}・ (21)
σ _x =q _j,M /a _p ... (22)
τ _xy = Q _p,need / a _p ... (23)
a _p =t _p (H _p -H)/2 (24)

Here, σ _x is the axial stress [N/mm ² ] generated in the reinforcing steel plate 20 between one joint surface in the vertical cross section of the hole core. _{q j,M} is the necessary joint surface shear force [N] in the beam material axial direction per one joint surface due to bending of the beam 10. Note that since it is assumed that bending does not act, q _j,M = 0. τ _xy is the shear stress [N/mm ² ] generated in the reinforcing steel plate 20 between one joint surface in the vertical cross section of the hole core. _{a p} is the cross-sectional area [mm ² ] of the reinforcing steel plate 20 between one joint surface in the vertical cross section of the hole core. H _p is the height [mm] of the reinforcing steel plate 20, and H is the diameter [mm] of the opening 11.

(Buckling considerations)
Next, it is confirmed that the reinforcing steel plate 20 does not buckle at the upper and lower parts of the opening 21 by checking using equation (25) that the joint surface shear strength q _j is equal to or less than the elastic buckling load P _cr [N] of the reinforcing steel plate 20 .
P _cr ≧q _j (25)

Referring to FIG. 10 which shows the concept of buckling occurring in the reinforcing steel plate 20, it is assumed that elastic buckling does not occur even when a joint surface shear force acts as a compressive force on the reinforcing steel plate 20 in the hatched rectangular portion in the figure, and the buckling load P _cr is calculated by equations (26) and (27).
P _cr = π ² E _s · I _P / l _k ² ... (26)
I _P = b _P · t _P ³ / 12 ... (27)

Here, E _s is the Young's modulus [N/mm ² ] of the reinforcing steel plate 20, I _p is the second moment of area [mm ⁴ ] outside the plane of the reinforcing steel plate 20 between one joint surface in the vertical cross section of the hole core, l _k is the buckling length [mm] of the reinforcing steel plate 20 between one joint surface in the vertical cross section of the hole core, which is represented as H here, and b _p is the width [mm] of the reinforcing steel plate 20 between one joint surface in the vertical cross section of the hole core.

When all of the formulas (19), (20), and (25) are satisfied (STEP 6: YES), it is determined that the selection of the thickness _tp of the reinforcing steel plate 20 is appropriate, and the design of the reinforcing structure is terminated. On the other hand, when any one of these formulas is not satisfied (STEP 6: NO), the thickness _tp of the reinforcing steel plate 20 is reselected (STEP 5).

(Structural experiment)
(Test specimen)
A total of eight specimens were prepared as test specimens. For each test specimen, a beam 10 having a beam width b of 300 mm, a beam depth D of 450 mm, and an inside span length L of 1,350 mm was prepared.

As shown in Figures 2 to 6, the upper end beam main reinforcement 12 and the lower end beam main reinforcement 13, which are arranged in five pieces each, are reinforcing bars of 19 mm diameter made of SD490, and the main reinforcement ratio p _t was 1.19%. The shear reinforcement 14 in the center and its vicinity is a reinforcing bar of 6 m diameter made of SD295A, and the interval in the beam axis direction is 100 mm in the general part, and 200 mm around the opening 11 because the shear reinforcement 14 is cut by the opening 11, the reinforcement ratio p _s in the general part is 0.21%, and the reinforcement ratio p _s around the opening 11 is 0.12%. And the shear reinforcement 15 at the ends located 325 mm away from both ends is a reinforcing bar of 6 m diameter made of SD295A, the interval in the beam axis direction is 50 mm, and the reinforcement ratio p s at both ends is 0.85%.

The upper support part 41 and the lower support part 42, which imitated the column part 40 (see FIG. 1), each had a width of 550 mm, a height of 740 mm, and a depth of 450 mm. The upper support part 41 and the lower support part 42 were internally arranged with main reinforcement and shear reinforcement to ensure sufficient shear strength. The beam 10, the upper support part 41, and the lower support part 42, which were arranged as described above, were formed by pouring concrete with a target compressive strength of 21 N/ ^mm2 .

After that, an opening 11 with a diameter H of 150 mm (1/3 of the beam depth D) was created, centered at a position 250 mm from the top end, which was the center of the beam 10 in the width direction. Then, four M20 bolt holes were created, centered at positions 155 mm away from the center in the beam width direction and 99 mm away in the beam height direction.

Two auxiliary steel plates 20 made of SS400 and having a height of 274 mm, a width of 386 mm, and a thickness _tp of 4.5 mm were prepared. An opening 21 having a diameter H of 150 mm was provided at the center of each auxiliary steel plate 20. Four openings were provided, each 3 mm larger than the bolt diameter, at positions 155 mm away from the center in the beam width direction and 99 mm away from the center in the beam height direction.

Then, after blasting the two reinforcing steel plates 20, anti-rust paint (Metalact H-15 (manufactured by Kansai Paint Co., Ltd.), JIS K 5633) was applied to both side surfaces of the beam 10 in the beam width direction, and the reinforcing steel plates 20 were fastened to the concrete using four anchors 32 embedded with M20 and having a length _La of 140 mm, hexagonal nuts 33, and flat washers 34. After that, a sealant (S930 (manufactured by Toho Earth Tech Co., Ltd.) was applied to the edges of the reinforcing steel plates 20 and around the openings 21, and CP300 (manufactured by Toho Earth Tech Co., Ltd.) was injected as the epoxy resin 31.

Test specimen #21/3A was identical to test specimen #21/3, except that an M22 through bolt was used as the anchor 32.

Specimen #15/3 was identical to specimen #21/3, except that the beam 10, upper support portion 41 and lower support portion 42 were formed by pouring concrete with a target compressive strength of 15 N/ ^mm2 , the thickness _tp of the auxiliary steel plate 20 was 3.2 mm, and the anchors 32 were M16.

Specimen #21/4 was identical to specimen #21/3 except that the diameter H of the opening 11 was 113 mm, which was 1/4 of the beam depth D, the height of the auxiliary steel plate 20 was 220 mm, the width was 310 mm, the thickness _tp was 3.2 mm, and the anchor 32 was M16.

Specimen #21/4B was identical to specimen #21/3 except that the diameter H of the opening 11 was 113 mm, which was 1/4 of the beam depth D, the thickness _tp of the auxiliary steel plate 20 was 3.2 mm, and the anchor 32 was M16.

Specimen #21/4P was identical to specimen #21/3 except that the diameter H of the opening 11 was 113 mm, which was 1/4 of the beam depth D; the shear reinforcement bars 14 in the center and its vicinity were lined up in the beam width direction, with four bars spaced apart in the beam axis direction by 45 mm in the general part and 180 mm around the opening 11, the reinforcement ratio p _s in the general part was 0.94%, and the reinforcement ratio p _s around the opening 11 was 0.60%; and the shear reinforcement bars 15 at both ends were spaced apart in the beam axis direction by 35 mm, and the reinforcement ratio p _s at both ends was 1.21%.

Test specimen #21/3a was identical to test specimen #21/3, except that the width of the auxiliary steel plate 20 was 420 mm, the anchors 32 were M6 drive-in type, and the bolt holes in the auxiliary steel plate 20 were 2 mm larger than the bolt diameter.

Test specimen #21/3N was identical to test specimen #21/3 except that the auxiliary steel plate 20 was not glued or joined to the beam 10.

The specifications of the test specimen are summarized in Table 1.

(Experiment details)
The test specimen was fixed vertically to the Construction Research Institute type loading device with the upper support part 41 on top and the lower support part 42 on the bottom, and a push-pull type hydraulic jack was used to apply a horizontal load so that antisymmetric deformation occurred in the test specimen. The loading history consisted of one cycle at member deformation angle R = ±1.25 x ^10-3 rad, two cycles at R = ±(2.5, 5, 7.5, 10) x ^10-3 rad, and then one-way loading up to R = +30 x ^10-3 rad. In consideration of the damage state of the test specimen, two additional cycles of R = ±15 x ^10-3 rad were added to test specimen #21/4P only.

In addition to the shear force, which is the load of the loading device, and the member deformation angle, the rebar strain in the main part of the beam 10, the strain of the reinforcing steel plate 20, and the shear deformation angle of each part were measured. The shear deformation angle was calculated from the measurement value of the displacement meter installed diagonally within the range divided into the area around the hole of the beam 10 and the end.

(Destructive properties)
Regarding the nature of failure, only specimen #21/4P experienced bending failure at the end of the beam 10, while the other specimens experienced shear failure around the opening of the beam 10.

For example, in the case of specimen #21/3, as shown in Fig. 11, which shows the relationship between shear force and member deformation angle of all specimens, including the main occurrence of various cracks, bending cracks (FC) occurred in the general part at R = +0.16 x ^10-3 rad, bending shear cracks occurred at R = +0.48 x ^10-3 rad, bond splitting cracks along the main reinforcement occurred at R = +0.74 x ^10-3 rad, shear cracks (SC) occurred in the general part at R = +0.91 x ^10-3 rad, shear cracks (CSC) occurred in the chord material at R = +1.9 x ^10-3 rad, and cracks in the openings (HSC) occurred at R = +2.5 x ^10-3 rad.

After that, the rigidity decreased, and deformation progressed accompanied by the sound of the epoxy resin 31 peeling off, and a shear crack (HESC) occurred near the anchor 32 at R = +3.3 x ^10-3 rad (209 kN). As the shear cracks of the chord material and cracks inside the opening increased, a shear crack occurred near the anchor 32 across the joint surface of the reinforcing steel plate 20 (247 kN), the stirrups yielded (STY) at R = +5.1 x ^10-3 rad, bending of the reinforcing steel plate 20 was observed, and the maximum strength (256 kN) was reached. After the maximum strength, the load decreased with the progression of the shear slippage of the opening, and the reinforcing steel plate yielded (PY) at R = +10.5 x ^10-3 rad. From the above, it is considered that the failure mode at the maximum strength is a shear failure type at the opening.

In addition, for specimen #21/4P, bending failure was determined due to the following reasons: at the maximum strength, the shear reinforcement 15 had not reached the yield strain, but the main reinforcements 12 and 13 at the beam ends had reached the yield strain, and the decrease in strength after the maximum strength was small. However, the central part and the adjacent shear reinforcement 14 reached the yield strain during the negative load immediately after the maximum strength and the positive load in the second cycle at the same deformation angle. From this, it is believed that the maximum strength can also be evaluated as the strength at the time of shear failure for specimen #21/4P. From this, it was found that the maximum strength can be evaluated as the strength at the time of shear failure for all specimens.

(Maximum strength)
Table 2 shows a list of the strengths of the test specimens. The shear strength Q _su of the non-perforated beam was calculated using formula (6) assuming the state before the opening 11 was provided. The shear strength Q _su0 of the beam with a hole was calculated using formula (7). Q _max is the maximum strength in the loading experiment. The design value of the shear strength around the hole Q _suR of the reinforced beam with a hole was calculated using formula (1). The design value Q _R of the increment in shear strength due to reinforcement was calculated by replacing Q _R,need with Q _R and Q _p,need with Q _p in formula (9). The estimated value Q _ex,R of the increment in shear strength due to reinforcement based on the experiment was calculated using the following formula (28).
Q _ex,R = Q _max -α _su0 · Q _su0 ... (28)

Here, Q _max is the experimental value of the maximum strength. α _su0 is the margin of error, which is the ratio of the experimental value to the calculated value of the modified Hirosawa formula, and here is 1.22, which is a value based on the experimental results of the test specimen #21/3N. This value is almost equivalent to the average value of the ratio of the experimental value to the calculated value in the modified Hirosawa formula according to literature such as "Architectural Institute of Japan, Reinforced Concrete Structural Calculation Standards and Commentary, 2018,""Japan Construction Center, Building Letter October 1993, 1993," and "Ochiai et al., Kitayama Kazuhiro, "Study on the Shear Performance Evaluation of RC Beams and Beams with Holes that Destroy in Shear," Proceedings of the Annual Conference of the Concrete Engineering Society, Vol. 34, No. 2, 2012."

In all specimens except for specimen #21/3N, which is a non-perforated beam specimen, the experimentally estimated value Q _ex,R of the increment in shear strength due to reinforcement exceeded the design value Q _R of the increment in shear strength due to reinforcement. This shows that the increment in shear strength due to reinforcement Q _R by Equation (9) is evaluated on the safer side than the actual increment due to reinforcement. In addition, it was found that the maximum strength Q _max by the loading experiment exceeds the design value Q _suR of the shear strength around the hole of the reinforced perforated beam. This shows that the shear strength around the hole Q _suR of the perforated beam by Equation (1) is evaluated on the safer side than the actual maximum shear strength Q _max .

(Appropriateness of evaluation as shear resistance)
The validity of formula (9), which evaluates the reinforcement effect as the shear resistance of the steel plates above and below the hole, was verified.

The maximum principal stress and maximum shear stress occurring in the reinforcing steel plates 20 at the top and bottom of the opening 21 are roughly equal, so the shear resistance borne by the reinforcing steel plates 20 at the top and bottom of the opening 21 is calculated from the shear stress τ perpendicular to the beam axis and the stress σ at 45° to the beam axis, respectively.

In addition, τ [N/ ^mm2 ] is the shear stress perpendicular to the beam axis at maximum strength, as shown in equation (29), and was calculated as the average value of the shear force τ _(P0u) of the reinforcing steel plate 20 at the upper part of the opening 21 and the shear force τ _(P0l) of the reinforcing steel plate 20 at the lower part.
τ = (τ _(P0u) + τ _(P0l) ) / 2 ... (29)

σ [N/ ^mm2 ] is the stress in the 45° direction to the beam axis at maximum strength, as shown in equation (30), and was calculated as the average value of the stress σ _(P0u) of the reinforcing steel plate 20 at the upper part of the opening 21 and the stress σ _(P0l) of the reinforcing steel plate 20 at the lower part.
σ = (σ _(P0u) + σ _(P0l) ) / 2 ... (30)

The relationship between τ· _np · _ap and σ· _np · _ap and the measured value Q _ex,R of the reinforcing effect is shown in Figures 12A and 12B, respectively. Note that _np · _ap is the cross-sectional area [ ^mm2 ] of the reinforcing steel plate 20 at the center of the hole in the direction perpendicular to the beam axis, and is calculated by formula (31).
_np · _ap =2· _tp ( _Hp −H) (31)

Here, _np is the number of reinforcing steel plates 20, which is 2 in this example. _tp is the thickness [mm] of the reinforcing steel plate 20. _Hp is the height [mm] of the reinforcing steel plate 20, and H is the diameter [mm] of the opening 21.

The point furthest from the regression line shown by the dotted line in Figure 11 (a) is the point for specimen #21/4P, which was the only specimen that experienced preceding bending failure. Specimen #21/4P had more extensive damage to the beam section 10 overall than the other specimens. Therefore, it is believed that the compressive stress of the reinforcing steel plate 20 decreased before the maximum strength because the compressive stress that should have been transmitted to the reinforcing steel plate 20 was transmitted to the concrete side due to localized fluctuations in the flow of force caused by the damage.

Figure 12B shows a table in which the equivalent shear force is evaluated using tensile stress at a 45° angle to the beam axis, ignoring compressive stress. This regression line does not deviate significantly from each point, and the overall correlation is higher. The correlation is roughly 1:1.

Therefore, as shown in equation (32), it was found that the estimated value (actual measured value) Q _ex,R of the actual reinforcing effect based on the experimental results can be roughly evaluated as the shear resistance 4Q _ex,p generated in the reinforcing steel plate 20 at the upper and lower parts of the opening 21.
Q _ex,R ≒ 4Q _ex,p ≒ σ Σa _p ... (32)

As for specimen #15/3, due to the characteristics of specimens made using poorly mixed concrete, the vertical strength had a large variation compared to other specimens, and bond splitting failure had progressed in the upper end main reinforcement 12. From this, it is presumed that the shear strength of the unreinforced perforated beam was evaluated to be higher than the actual value, resulting in a lower evaluation of Q _ex,R .

(joint shear strength)
Considering that the bonding surface around the anchor 32 mainly resists at the maximum strength as described above, and further that there is no significant difference in the maximum strength between test body #21/4 and test body #21/4B, it is considered appropriate to set an upper limit for the bonding area of the reinforcing steel plate 20, which contributes to the design formula for the reinforcing effect. Therefore, we decided to use formula (15) to evaluate cases where the bonding area is sufficient, and formula (16) to evaluate cases where the bonding area is insufficient.

For q _j , we referred to "Japan Building Disaster Prevention Association, 'Guidelines and Commentary on Seismic Retrofit Design for Existing Reinforced Concrete Buildings', 2017,""Prefabricated Construction Association, 'Precast Construction Technology Collection, Vol. 1, General Theory of Precast Construction', 2003," and "Toshiaki Komiya, Kiyoshi Masuo, 'Ultimate Strength of Adhesive Joints and Indirect Joints for Steel Frame Expansion Brace Reinforcement', Proceedings of the Japan Concrete Engineering Society, Vol. 22, No. 3, 2000." In addition, the reason why the effective adhesive area a _b is set inside the center of the anchor 32 is because cracks were generated at the adhesive joint interface at the edge of the reinforcing steel plate 20 at the maximum strength.

(Reduction factor according to aperture ratio)
In order to examine the effect of the aperture ratio (H/D) on the joint shear strength, only the shear deformation components around the aperture were considered, excluding the shear deformation and bending deformation components at the end of the beam 10, and the progression of each crack occurrence event is shown in Figure 13, with the deformation angle around the aperture γm on the horizontal axis and the ratio of shear force to maximum strength (Q/Q _max ) on the vertical axis.

"Matsushita Kiyoo and Uemura Katsuro, 'Study on Reinforced Concrete Beams with Holes: Part 6, Small-scale Test Specimen Experiments on Reinforced Lightweight Concrete Beams with Circular Holes', Proceedings of the Architectural Institute of Japan, No. 66, 1960," reports that "Stress concentration occurs at the edge of the hole, and diagonal cracks at 45 degrees to the axis of the material occur early, and the larger the hole diameter, the earlier this crack occurs." The same phenomenon was confirmed in this structural experiment.

It was confirmed that the specimens with an aperture ratio (H/D) of 1/3 had cracks at various locations at the aperture surrounding deformation angle γ _m , which was smaller than the aperture ratio of 1/4. In particular, the shear cracks (HESC) near the anchors 32 occurred at 80% or more of Q _max in all specimens, and are presumed to affect the maximum strength of the joint surface. This is clear when the shear cracks (HESC) near the anchors 32 are classified and compared according to the aperture ratio, and the reduction coefficient β _H according to the aperture ratio was set as shown in formula (14), taking into account the degree of damage to the anchorage of the anchor 32.

(Safety of design formula)
The relationship between the design value Q _suR of the maximum shear strength and the experimental value Q _max is shown in Figure 14. The ratio (Q _max /Q _suR ) was 1.22 for the unreinforced specimen #21/3N, while the average value for all reinforced specimens was 1.37, the median value was 1.35, and the minimum value was 1.24, confirming that this is a highly safe design formula that exceeds the average value of the margin of safety of the modified Hirosawa formula for all reinforced specimens.

The ratio (Q _max /Q _su ) of the target shear strength Q _su of the non-perforated beam 10 to the experimental maximum shear strength Q _max was 1.32 as shown in Table 2, which was generally a good result. Some test specimens were slightly below 1, but considering the introduction of the reduction coefficient β _H , the design value Q _suR was evaluated to be on the safe side.

The present invention is not limited to the embodiments. For example, other formulas may be applied to formulas (6), (7), (14) to (16), and (19) to (27).

10...RC beam, 11...opening, 12...upper end beam main bar, 13...lower end beam main bar, 14...shear reinforcement in the center and nearby areas, 15...shear reinforcement at the end of the beam, 20...reinforcing steel plate, 21...opening, 31...adhesive, epoxy resin, 32...anchor, anchor bolt, 33...hexagonal nut, 34...flat washer, 35...sealing material, 40...column, 41...upper support, 42...upper support.

Claims (4)

A method for designing a reinforcing member consisting of a reinforcing steel plate and a bolt, in a case where an opening is provided in an existing reinforced concrete beam, a reinforcing steel plate is attached around the opening on both sides of the beam, and the reinforcing steel plate is joined to the side of the beam with a bolt through a bolt hole provided in at least the vicinity of four corners of the reinforcing steel plate,
The required reinforcing shear force of the reinforcing member is calculated from the difference between the shear strength of the beam before the opening is provided and the shear strength of the beam after the opening is provided;
The joint shear strength per joint surface is calculated from the material type and diameter of the bolt and the effective adhesive area of the reinforcing steel plate,
The joint shear strength per joint surface is equal to or greater than the required joint shear strength per joint surface calculated from the required reinforcing shear strength of the reinforcing steel plate,
A method for designing a reinforcing member, comprising determining a shape of the reinforcing steel plate so that, at the maximum strength of the reinforcing steel plate, it does not undergo bearing failure at the bolt holes, does not yield at the upper and lower parts of the opening, and does not buckle at the upper and lower parts of the opening. The sine value of the angle between a line connecting two diagonally positioned bolts among the bolts arranged near the four corners of the reinforcing steel plate and the beam axial direction is calculated;
The method for designing a reinforcing member according to claim 1, characterized in that the required joint shear strength per joint surface is calculated as a value obtained by dividing the required reinforcing shear strength of the reinforcing steel plate by a value four times the sine value. The design method for a reinforcing member according to claim 1, characterized in that the joint shear strength per joint surface is calculated as the minimum value of the shear force per joint surface at the joint surface when the fastening strength is sufficient and the shear force per joint surface at the joint surface when the fastening strength is insufficient, multiplied by a reduction coefficient based on the ratio of the beam depth of the beam to the diameter of the opening. A method for designing a reinforcing member according to any one of claims 1 to 3, characterized in that the shear strength of the beam before the opening is provided is calculated using the Ohno-Arakawa formula, and the shear strength of the beam before reinforcement after the opening is provided is calculated using the modified Hirosawa formula, which is a modified version of the Ohno-Arakawa formula.

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