JP4412196B2 - Calculation method of shear strength of reinforced concrete beam, design method using this calculation method, reinforced concrete beam designed by this design method and beam / floor structure of reinforced concrete - Google Patents

Description

  The present invention relates to a method for calculating the shear strength of a reinforced concrete beam in which concretes having different design reference strengths are cast up and down, a design method using this calculation method, and a reinforced concrete beam and a reinforced concrete beam designed by this design method. -Regarding floor structure.

  Conventionally, reinforced concrete beams and slabs have been constructed using half precast (hereinafter referred to as half PC) members. In that case, concrete must be placed on the half PC beam member upper part and the slab at the site. Usually, the design standard strength of the concrete used for the beam is higher than the design standard strength used for the slab, so a construction method that takes this into consideration is required.

When placing concrete on the half PC beam member upper part and the slab at the site, after joining the main bars of the half PC beam member 8 to shorten the work period, the upper part of the half PC beam member 8 and the concrete 2 of the slab 7 are attached at once. A method of placing is used. FIG. 11 is a sectional view of a reinforced concrete beam 1 constructed by placing concrete 2 on the half PC beam member 8 and the slab 7 at a time. As shown in FIG. 11, the reinforced concrete beam 1 constructed by the above-described method has a configuration in which concretes 2 and 3 having different design reference strengths are spliced up and down. However, there is no established method for calculating the shear strength of reinforced concrete beams in which concrete 2 and 3 with different design standard strengths are cast up and down, so the entire cross section is reinforced concrete composed of concrete with lower design standard strength. Had to be designed as a beam.
Therefore, when the reinforced concrete beam 1 is designed using the above method, the designed shear strength is lowered, and the number of shear reinforcement bars is increased, or the strength of the shear reinforcement bars is used. It was necessary to improve the shear strength. In addition, there is a method to make the cast-in-place concrete equal to or higher than the half PC beam member, but in that case, the concrete will be stronger than necessary for the slab, increasing the cost and labor of pressing the top end. The problem of increasing will occur.

As one method for improving the shear strength of a reinforced concrete beam, for example, in Patent Document 1, as shown in FIG. 12, a beam main bar 5 is also arranged in a slab 7, and the beam main bar inside the half PC beam member 8 is arranged. A shear reinforcement bar 11 surrounding the lower bar 4 and the upper beam main bar (upper bar) 5 of the half PC beam member 8 is provided, and the half PC beam member goes straight between the beam main bar 5 of the slab 7. 8 discloses a method of improving the shear strength of the reinforced concrete beam 1 by providing shear force transmission bars 12 in the upper part and the slab 7.
Further, for example, in Patent Document 2, in a reinforced concrete beam in which shear reinforcement bars wound around the beam upper main bar and the beam lower bar are embedded at predetermined intervals in the longitudinal direction of the beam, adjacent shear reinforcement bars are disclosed. In the meantime, there is disclosed a method for improving the shear strength of a reinforced concrete beam by providing an inverted U-shaped reinforcing bar that is attached to the upper main bar of the beam and whose lower end enters the lower concrete part.
JP 7-305443 A JP 2000-336746 A

  However, in order to reinforce a reinforced concrete beam by the method described in Patent Document 1, it is necessary to arrange the shear force transmission bar 12 before placing concrete. Moreover, in order to reinforce by the method described in Patent Document 2, it is necessary to arrange a shear reinforcement bar and an inverted U-shaped reinforcement bar. For this reason, the construction period is extended and the construction cost increases.

  Conventionally, in the case of reinforced concrete beams in which concrete with different design standard strength has been handed over, it was designed using the value of the smaller design standard strength. It was overdesigned.

  However, in the first place, the reinforced concrete beam 1 in which the concretes 2 and 3 having different design standard strengths are handed over is stronger than the reinforced concrete beam in which the concrete having the same strength as the lower design standard strength is cast in all sections. Obviously, it is high, and when it is handled as a reinforced concrete beam in which concrete having a strength equal to the lower design standard strength is cast on the entire cross section, it will be excessively reinforced and the construction cost will increase.

  Therefore, the present invention calculates the shear strength of a reinforced concrete beam in which concrete of different design standard strength is cast up and down in consideration of the design standard strength of both concretes so that the reinforced concrete beam can be designed appropriately. With the goal.

The method for calculating the shear strength of the present invention is a method for calculating the shear strength of a reinforced concrete beam in which concretes having different design reference strengths are cast up and down, wherein the height of the reinforced concrete beam is D [mm], the lower side. When the design standard strength of the concrete located at Fc ₁ [N / mm ² ] and the design standard strength and height of the concrete located above are Fc _t [N / mm ² ] and t [mm], respectively, Assuming that the reinforced concrete beam has an equivalent design reference strength F _Ce [N / mm ² ] calculated by the following formula (1) or (2) according to the magnitude relationship between D / 2 and t, The shear strength of a reinforced concrete beam is calculated.
For _{D / 2 ≧ t Fc e =} {Fc t × t + Fc 1 × (D / 2-t)} / (D / 2)
... (1)
In the case of _{D / 2 <t Fc e =} Fc t ... (2)

Further, the present invention calculates the shear strength of a reinforced concrete beam in which concretes having different design reference strengths are handed over by the above method, and designs the reinforced concrete so as to be equal to or higher than the shear force generated in the reinforced concrete beam. A reinforced concrete beam design method characterized by the above and a reinforced concrete beam designed by the design method are also included.
Further, the reinforced concrete beam may be a reinforced concrete beam constructed by placing concrete on the half precast concrete member. Furthermore, it is good also as a reinforced concrete beam constructed by placing concrete into the upper part of the half precast concrete member and the slab.
Furthermore, in the reinforced concrete beam, a part of the beam upper end main reinforcement may be arranged over the slab, and the shear force transmission reinforcement for transmitting the shear force from the beam web portion into the slab may be omitted.
Further, the present invention provides a beam / floor structure including the reinforced concrete beam, a beam composed of a lower high-strength concrete portion having a lower end main reinforcement, and an upper ordinary strength concrete portion having a beam upper end reinforcement, A floor slab formed of the same normal strength concrete as the normal strength concrete portion, and the high strength concrete portion and the normal strength concrete portion are sheared around the beam upper main bar and the beam lower main bar. It also includes a reinforced concrete beam / floor structure in which reinforcing bars are embedded at predetermined intervals in the longitudinal direction of the beam.

  According to the present invention, since the shear strength of a reinforced concrete beam can be appropriately calculated by considering the design standard strength of each of the concrete cast up and down, it is possible to reduce the shear reinforcement that has been excessively performed conventionally. . For this reason, measures such as increasing the shear transmission bars of Patent Document 1 and the reinforcing bars of Patent Document 2 more than necessary are unnecessary, and the cost can be reduced. Moreover, when constructing a reinforced concrete beam using a half precast beam, the concrete can be placed on the half PC beam member upper part and the slab at a time, so the construction period can be shortened.

  According to the present invention, it is possible to calculate the shear strength of a reinforced concrete beam in which concrete with different design standard strength is cast up and down in consideration of the design standard strength of both concretes, so it is possible to appropriately design a reinforced concrete beam It becomes.

  First, a reinforced concrete beam that is an object of the present invention will be described. FIG. 1 is a view showing a reinforced concrete beam 1, FIG. 1 (a) is an axial sectional view of the reinforced concrete beam 1, and FIG. 1 (b) is a lateral sectional view of the reinforced concrete beam 1. As shown in FIG. 1, a reinforced concrete beam 1 to be calculated according to the present invention includes concrete 2 and 3 which are cast up and down with a joint surface as a boundary, and beam main bars 4 and 5 embedded in concrete 2 and 3. And the shear reinforcement 6. Here, the upper concrete 2 is made of concrete having a design standard strength lower than that of the lower concrete 3. Moreover, in FIG. 2, another embodiment of the reinforced concrete beam 1 used as the calculation object of this invention is shown. The reinforced concrete beam 1 to be calculated according to the present invention includes a structure in which the concrete 2 on the upper side of the reinforced concrete beam 1 is integrated with the slab 7 as shown in FIG.

  FIG. 3 is a diagram illustrating an example of a method for constructing the reinforced concrete beam 1 using the half PC beam member 8 which is a half precast member. The half PC beam member 8 is composed of concrete 3, a shear reinforcement bar 6 whose lower part is embedded in the concrete 3 and whose upper part is exposed, and a beam main bar 4 embedded in the concrete 3.

As shown in FIG. 3, the reinforced concrete beam 1 has the half PC beam member 8 built therein, the upper end bar 5 and the slab bar (not shown) are arranged, and the post-cast concrete 2 is hit on the upper part of the half PC beam member 8. It is built by setting. Here, when concrete having a design standard strength different from that of the concrete 3 of the half PC beam member 8 is used for the post-cast concrete 2, the reinforced concrete beam 1 constructed by the concrete has a design standard strength different from that above and below. The concrete 3 of the half PC beam member 8 is the lower concrete 3 and the post-cast concrete 2 is the upper concrete 2.
In order to shorten the construction period, a method of placing concrete 2 on the half PC beam member upper portion 8 and the slab 7 at once may be used. In this way, the reinforced concrete beam 1 constructed by placing the concrete 2 on the half PC beam member 8 and the slab 7 at a time, the concrete 2 on the upper side of the reinforced concrete beam 1 is slab 7 as shown in FIG. It becomes the composition united with. The calculation method of the shear strength of the present invention is also effective when calculating the shear strength of the reinforced concrete beam 1 constructed as described above.

  Next, the shear strength calculation method of the present invention will be described. The formula for calculating the shear strength of a reinforced concrete beam includes, for example, the shear strength formula described in the “Guidelines for Strengthening Assurance Design of Reinforced Concrete Buildings / Description” of the Architectural Institute of Japan. However, these equations are intended for reinforced concrete beams in which concrete of a certain design standard strength is cast on the entire cross section, and not for reinforced concrete beams in which concretes having different design standard strengths are cast up and down.

Accordingly, the shear strength calculation method of the present invention is a method for calculating the shear strength of a reinforced concrete beam in which concretes having different design standard strengths are cast up and down, wherein the height of the reinforced concrete beam is D [mm], When the design standard strength of the concrete located on the lower side is Fc ₁ [N / mm ² ] and the design standard strength and height of the concrete located on the upper side are Fc _t [N / mm ² ] and t [mm], respectively to the reinforced concrete beams, is regarded as having a calculated by the equivalent design strength Fc e _[N / mm ^2] by the following equation in accordance with the magnitude relationship between D / 2 and t (1) or (2) The shear strength of the reinforced concrete beam is calculated.
For _{D / 2 ≧ t Fc e =} {Fc t × t + Fc 1 × (D / 2-t)} / (D / 2)
... (3)
In the case of _{D / 2 <t Fc e =} Fc t ... (4)

  Here, if the obtained shear strength is less than the shear force generated in the reinforced concrete beam obtained by structural calculation etc., to increase the shear strength, increase the number of shear reinforcement bars, or replace the high strength reinforcement bars with shear reinforcement bars. Design to use for.

Hereinafter, the calculation method of the shear strength of the reinforced concrete beam will be described in detail.
First, a method for calculating the shear strength of a reinforced concrete beam in which concrete having a constant design standard strength is cast on the entire cross section will be described. FIG. 4 is a diagram showing a balance of forces in a state where the reinforced concrete beam receives bending moment, shearing force, and axial force at both ends thereof. As shown in FIG. 4, the cross section A of the reinforced concrete beam receives a load V having a magnitude equal to the compressive force and the shearing force acting on the beam vertically downward on the upper end reinforcement and the surrounding concrete from the outside. Is under tensile load. Moreover, the upper end reinforcement of the cross section B receives a tensile load, and the lower end reinforcement and the surrounding concrete receive a compressive load and a load V having a magnitude equal to the shear force acting on the beam vertically upward.

  Reinforced concrete beams receive bending moment, shearing force, and axial force and reach the ultimate state. As a stress transmission mechanism in the member, a stress transmission mechanism called a compression strut or arch mechanism that diagonally connects the compression regions at both ends of the member, It is transmitted by a stress transmission mechanism called a truss mechanism in which the compressive force at the end is transmitted after being converted into the tensile force of the lateral reinforcement. Therefore, the stress transmitted by each mechanism is considered separately.

  FIG. 5 is a schematic diagram showing a stress transmission mechanism of a reinforced concrete force in which an arch mechanism is formed. As shown in FIG. 5, the arch mechanism has a shear force applied to the reinforced concrete beam in a section A that receives a compressive load in the upper end and its vicinity in section A, and a section that receives a compressive load in the section B and its lower end in the vicinity. The concrete located between the two is a mechanism for transmitting as compressive stress. Actually, the region forming the arch mechanism seems to have a bulging shape at the center of the reinforced concrete beam, but here, a prismatic region connecting the upper half of the section A and the lower half of the section B, To do.

Here, when considering the balance of forces in the vertical direction and the horizontal direction in the cross section A, the following expression is derived. H ′ is the sum of horizontal loads received by the concrete and the reinforcing bar of the arch mechanism in section A, N ′ is the axial compression force of the arch mechanism, θ is the inclination of the arch mechanism with respect to the horizontal direction, and F c _e [N / mm ² ] indicates the design standard strength of the concrete placed in the reinforced concrete beam, D [mm] indicates the height of the reinforced concrete beam, and b [mm] indicates the width of the reinforced concrete beam.
V _a '−N′sin θ = 0 (5)
H′−N′cos θ = 0 (6)

When N ′ is eliminated from the equations (5) and (6), the following equation is derived.
V _a '= H'tan θ (7)

Here, when the compressive stress of concrete is σ _e [N / mm ² ], the following equation is derived.
H ′ = bσ _e D / 2 (8)

Substituting Eq. (8) into Eq. (7) and considering the final state, substitute the compressive strength of concrete σ _e [N / mm ² ] and the concrete design standard strength F _e [N / mm ² ] of concrete. In this case, the shear strength V _a ′ borne by the arch mechanism in the reinforced concrete beam in which the concrete having the same design standard strength is cast on the entire cross section is obtained, and is expressed by the following equation.
V _a ′ = bFc _e Dtan θ / 2 (9)

Next, similarly, the shear strength of the reinforced concrete beam in which concretes having different design standard strengths are cast up and down is derived. FIG. 6 is a diagram showing a balance of forces in a state where a bending moment, a shearing force and an axial force are received at both ends of the reinforced concrete beam. Similar to the case where concrete of a certain design standard strength is placed on the entire cross section, the cross section A of the reinforced concrete beam has the same size as the compressive force and the vertical downward shear force on the upper end reinforcement and the surrounding concrete. and under a load V _a, undergoing tensile load on the lower end muscle. Moreover, under load pulling the upper end muscle section B, and subjected to shearing load V _a shear force equal in magnitude to the compressive load and vertically upward to the concrete and surrounding the lower end muscle.
In FIG. 6, D [mm] is the height of the reinforced concrete beam, b [mm] is the width of the reinforced concrete beam, t [mm] is the height of the upper concrete, and Fc _t [N / mm ² ] is the upper side of the reinforced concrete beam. The design standard strength of concrete, Fc ₁ [N / mm ² ], represents the design standard strength of the lower concrete.

  An arch mechanism with the same shape is also formed in a reinforced concrete beam in which concrete with different design reference strengths is cast up and down. FIG. 7 is a diagram illustrating the transmission of the force of the arch mechanism in a reinforced concrete beam in which concretes having different design reference strengths are laid up and down.

Here, the position for determining the shear strength of a reinforced concrete beam in which concretes having different design reference strengths are cast up and down is equal to the position for determining the strength of the arch mechanism. Since the design standard strength Fc ₁ [N / mm ² ] of the lower concrete is larger than the design standard strength Fc _t [N / mm ² ] of the upper concrete, the strength of the arch mechanism is in a cross section perpendicular to the compressive stress. The upper design reference strength is determined in the cross section where the proportion of the concrete having Fc _t [N / mm ² ] is the largest, that is, the cross section A. Considering the balance of forces in the section A, the following two formulas are derived.
V _a −N _a sin θ = 0 (10)
H-N _a cos θ = 0 (11)
Here, the vertical downward load applied to the cross section A (= V _a is the shearing force borne by the arch mechanism), N _a is the compressive stress in the axial direction of the arch mechanism, and H is the concrete in the vicinity of the upper and upper bars in the cross section A. The sum of compressive loads acting on, θ represents the angle of the arch mechanism with respect to the horizontal plane.

When N is eliminated from the equations (10) and (11), the following equation is derived.
V _a = Htanθ (12)

Considering the balance of forces in section A, if the compressive stress applied to the upper concrete is σ _t [N / mm ² ] and the compressive stress applied to the lower concrete is σ ₁ [N / mm ² ], The following formula is derived.
H = b · {σ _t × t + σ ₁ × (D / 2−t)} (13)

The following expressions are derived from Expressions (12) and (13).
V _a = {σ _t · bt + σ ₁ · b (D / 2−t)} tan θ (14)

Further, when considering the final state, if σ _t = Fc _t and σ ₁ = Fc ₁ , the maximum shear strength that can be borne by the arch mechanism of the reinforced concrete beam is obtained.
V _a = {Fc _t · bt + Fc ₁ · b (D / 2−t)} tan θ (15)

Here, the above reinforced concrete beam is compared with the case where it is regarded as a beam in which concrete having the same design reference strength F _Ce [N / mm ² ] is placed in all sections. The shear strength of a beam in which concrete having the same design standard strength is cast on the entire cross section is expressed by Equation (9). Therefore, the following formula is derived by setting V _a = V _a ′.
{Fc _t · bt + Fc ₁ · b (D / 2−t)} tan θ = Fc _e bDtan θ / 2
... (16)
Fc _e = {Fc _t · bt + Fc ₁ · b (D / 2−t)}} / (D / 2)
... (17)

  The left side of equation (16) is the compressive strength of the concrete when all sections are considered constant, and the right side is the average obtained by multiplying each design standard strength by the proportion of each concrete in the upper half of the cross section of the reinforced concrete beam Strength (hereinafter referred to as equivalent strength). When calculating the shear strength of a beam borne by the arch mechanism of a reinforced concrete beam in which concrete with two types of compressive strength is spun in the height direction from Equation (16), each design criterion is applied to the entire reinforced concrete beam. It can be seen that each concrete can be treated as a reinforced concrete beam having an equivalent strength obtained by multiplying the strength by the proportion of the area in the upper half of the cross section of the reinforced concrete beam.

Next, the shear strength borne by the truss mechanism will be described.
FIG. 8 is a diagram illustrating a stress transmission mechanism of the truss mechanism, and FIG. 9 is a diagram illustrating in detail a region surrounded by IFGH in FIG. In the truss mechanism, stress is applied by a compressive stress field (region surrounded by CDEF in FIG. 8) spreading from the ends on both sides of the member and an oblique compressive stress field (region surrounded by IFGH in FIG. 8) having a constant angle φ. It is thought to convey. Therefore, the shear strength of the reinforced concrete beam is the lowest value among the shear strengths obtained in the region surrounded by CDEF and the region surrounded by IFGH.

First, when the shear strength V _t is determined in the region surrounded by CDEF, the following equation is derived from the balance of forces in the cross section EF.

Here, V _t is the shear stress to bear the truss mechanism, a _w is the cross-sectional area of the pair of transverse reinforcement, sigma _wy reliable strength of the transverse reinforcement, b _e the effective width of the cross-section involved in truss mechanism, j _e is the effective cross section involved in the truss mechanism. Here, the effective width and the effective width are the width and height of the area surrounded by the lateral reinforcement bars because the compressive load exists only within the area surrounded by the lateral reinforcement bars. This is the width and height.
As shown in Expression (18), when the shear strength V _t borne by the truss mechanism is determined in a compressive stress field (region surrounded by CDEF in FIG. 8) that spreads in a fan shape from both ends of the member, the shear strength V _It can be seen that _t is determined only by the conditions relating to the lateral reinforcement, and the design standard strength of the concrete does not depend on it.

Next, in FIG. 8, consider the conditions to determine the shear strengths _{V t} in the region surrounded by IFGH. As in the case of the arch mechanism, the condition for determining the shear strength V _{t in the} region surrounded by IFGH is the cross section in which the concrete whose design reference strength is F _Ct [N / mm ² ] is the largest in the cross section. The balance condition in S may be considered. Here, when comparing the reinforced concrete in which concrete of different strength is divided up and down with the shear strength of reinforced concrete in which concrete of a certain design standard strength is cast in all sections, it is determined by the region surrounded by ACGH. shear strength V _t of the truss mechanism, similar to that of a can be determined shear strength using the equivalent strength arch mechanisms, which concrete equivalent strength Fc _e 'in the cross section S is Da設the entire cross-section Can be calculated as

Here, according to the Japan Architectural Institute's "Toughness Guarantee Design Guidelines for Reinforced Concrete Buildings and Explanation", considering the angle φ of the truss mechanism, the angle φ is not an arbitrary value. The smaller the is, the greater the compressive stress across the shear crack becomes and the more difficult the compression transmission is, so cot φ ≦ 2, that is, φ ≧ π / 4. For this reason, the lower end M of the cross section S is positioned below the central axis of the reinforced concrete beam, and the proportion of the lower concrete in the cross section S is such that the lower end M of the cross section S is at the height of the central axis of the reinforced concrete beam. The time is equal to the proportion of the lower concrete in the upper half of the cross section, and when the position of the lower end M of the cross section S is lower than that, it becomes equal to or greater than the proportion of the lower concrete in the upper half of the cross section. Since the design standard strength of the lower concrete is higher than the design standard strength of the upper concrete, the equivalent strength increases as the proportion of the lower concrete occupies more. Therefore, the equivalent strength Fc _e of the concrete in the cross section S 'is an equivalent intensity of the upper half of the cross section Fc _e above. Thus, truss mechanism can up if the shear strength calculation of the safety side design to bear as a reinforced concrete beam concrete is Da設the entire cross-section of equivalent strength Fc _e of the upper half of the cross section of the reinforced concrete beams even truss mechanism .

Thus, as a concrete reinforced concrete beam is Da設the entire cross section of the design strength equal to the equivalent strength Fc _e of the upper half of the cross section of the reinforced concrete beam, by calculating the shear strength to bear the truss mechanism and arch mechanism, In either case, the maximum shear strength lower than the shear force borne by each mechanism is calculated. Therefore, the shear strength of the reinforced concrete beam, which is the sum of the truss mechanism and the arch mechanism, is also a safe design.

  Furthermore, when the shear strength calculated using this equivalent strength is smaller than the shear force applied to this reinforced concrete beam, use a higher design standard strength for the upper concrete, or increase the number of shear reinforcement bars, etc. Design and design to improve shear strength.

  As described above, the shear strength calculated using the equivalent strength of the present invention is a safe value and is closer to the actual shear strength than the conventional method. For this reason, when constructing a reinforced concrete beam in which concretes having different design reference strengths are handed over, it is possible to reduce excessive reinforcement performed to give strength exceeding shearing force. In addition, even when a reinforced concrete beam is constructed using a half PC beam member, an appropriate design can be performed by using a method in which the upper half PC beam member and the concrete of the slab are integrally placed. It is no longer necessary to use concrete with a design standard strength higher than necessary for cast concrete, or to increase the number of shear reinforcements more than necessary, and the construction cost can be reduced while shortening the construction period. In addition, when reinforcement is required, it is possible to reinforce the shear reinforcement bars of the half PC beam members in advance at the processing plant, so there is no need to arrange shear transmission bars on site and further shorten the construction period. be able to.

  Hereinafter, comparison between the shear strength obtained by the calculation method of the present invention and the shear strength obtained by numerical analysis using the finite element method (FEM) (Experiment 1), and the shear strength obtained by the calculation method of the present invention And a shear strength obtained by a numerical analysis using FEM and a shear strength obtained by a shear experiment using a real reinforced concrete beam (Experiment 2). It is confirmed that the shear strength does not exceed the actual shear strength.

Table 1 is a table showing cross-sectional views and various conditions of the beam member to be analyzed in Experiment 1.
[Table 1]

As shown in Table 1, in this numerical analysis, the cross section is a beam with a width of 350 mm x height 400 mm x length 2000 mm, and concrete with a design reference strength Fc of 42 N / mm ² is placed on the entire cross section (CASE-1), design strength Fc than the beam bottom to a thickness of 250mm is the concrete 42N / mm ² are pouring, design strength to a thickness of 150mm on the top of 24N / mm ² concrete When cast (CASE-2), concrete with a design standard strength Fc of 42 N / mm ² is cast to a thickness of 200 mm from the bottom of the beam, and the design standard strength is 200 mm to the top. If it is concreting of ^{24N / mm 2 (cASE-3} ), design strength Fc than the beam bottom to a thickness of 150mm is the concrete 42N / mm ² are pouring, the thickness of 150mm thereon The design standard strength is 24 N / mm ² The equivalent strength is used for the five conditions when concrete is cast (CASE-4), and when concrete with a design standard strength Fc of 24 N / mm ² is cast on the entire cross section (CASE-5). The shear strength (equivalent strength) calculated above and the shear strength (FEM) obtained by numerical analysis using FEM were compared.

Moreover, Table 2 is a table | surface which shows the various conditions of the test body used for the shear experiment.
[Table 2]

The test specimen is a beam member with a width of 350 mm and a height of 400 mm, and high-strength concrete with a compressive strength of 52.6 N / mm ² is placed from the bottom to a thickness of 250 mm, and the upper part is 150 mm thick A high-strength concrete with a compressive strength of 52.6 N / mm ² is applied to all cross sections of a beam (CASE-A) in which ordinary concrete with a compressive strength of 20.8 N / mm ² is cast and a beam member with a width of 350 mm and a height of 400 mm. For the cast beam (CASE-B), the shear strength (shear experiment) obtained from the shear experiment, the shear strength (FEM) obtained by FEM, and the shear strength (equivalent strength) obtained from the equivalent strength Compared.

  FIG. 10 is a graph showing the shear strength obtained in Experiment 1 and Experiment 2. As shown in FIG. 10, in both Experiment 1 and Experiment 2, the shear strength obtained from the equivalent strength is based on the shear strength obtained by FEM and the shear strength obtained by the shear strength experiment using an actual reinforced concrete beam. Is also small. Accordingly, it was confirmed that if the shear strength calculated using the method for calculating the shear strength of the present invention is larger than the shear force applied to the reinforced concrete beam, no shear failure occurs.

FIG. 1A is an axial sectional view of a reinforced concrete beam, and FIG. 1B is a lateral sectional view of the reinforced concrete beam. It is sectional drawing which shows other embodiment of a reinforced concrete beam. It is a figure which shows an example of the method of constructing a reinforced concrete beam using the half PC beam member which is a half precast member. It is a figure which shows the balance of the force in the state which has received bending moment, shearing force, and axial force at the both ends to the reinforced concrete beam. It is a schematic diagram which shows the transmission mechanism of the force of the reinforced concrete which formed the compressive force strut. It is a figure which shows the balance of the force in the state which has received the bending moment, the shear force, and the axial force at the both ends of the reinforced concrete beam. It is a figure which shows transmission of the force of the arch mechanism in the reinforced concrete beam by which the concrete from which design reference | standard intensity | strength differs was divided up and down. It is a figure which shows the stress transmission mechanism of a truss mechanism. It is the figure which showed in detail about the part enclosed by EGJH of FIG. 4 is a graph showing the shear strength obtained by Experiment 1 and Experiment 2. It is sectional drawing of the reinforced concrete beam which poured concrete into the half PC beam member upper part and slab at once on the site. It is sectional drawing of the reinforced concrete beam and slab which provided the shear reinforcement bar and the shear force transmission bar.

Explanation of symbols

1 Reinforced concrete beam 2 Upper concrete 3 Lower concrete 4 Beam main bar (lower bar)
5 Beam main bar (upper bar)
6 Shear reinforcement bar 7 Slab 8 Half PC beam member 11 Shear reinforcement bar 12 Shear force transmission bar

Claims (6)

A method for calculating the shear strength of a reinforced concrete beam in which concretes with different design standard strengths are handed up and down,
The height of the reinforced concrete beam is D [mm], the design standard strength of the concrete positioned below is Fc ₁ [N / mm ² ], and the design standard strength and height of the concrete positioned above is Fc _t [N / mm ² ] and t [mm]
The reinforced concrete beams, is regarded as having the following formula (1) or (2) an equivalent design strength Fc e is calculated by _[N / mm ^2] according to the magnitude relationship between D / 2 and t, the A method for calculating shear strength, comprising calculating the shear strength of a reinforced concrete beam.
For _{D / 2 ≧ t Fc e =} {Fc t × t + Fc 1 × (D / 2-t)} / (D / 2)
... (1)
When D / 2 <t Fc _e = Fc _t (2) A design method for a reinforced concrete beam in which concrete with different design standard strengths is handed up and down,
The shear strength of the reinforced concrete beam is calculated by the method according to claim 1, and the reinforced concrete is designed so that the calculated shear strength is equal to or greater than the shear force generated in the reinforced concrete beam. Method.   A reinforced concrete beam designed by the design method according to claim 2.   4. The reinforced concrete beam according to claim 3, wherein the half precast concrete member is constructed by hitting concrete on-site.   4. The reinforced concrete beam according to claim 3, wherein a part of the beam upper main bar is arranged over the slab, and a shear force transmission bar for transmitting a shear force from the beam web portion to the slab is omitted. Reinforced concrete beams. A beam / floor structure including the reinforced concrete beam according to claim 3, wherein the beam is composed of a lower high-strength concrete portion having a lower end main reinforcing bar and an upper ordinary strength concrete portion having a beam upper main reinforcing bar,
A floor slab formed of the same ordinary strength concrete as the ordinary strength concrete portion of the beam,
In the high-strength concrete part and the normal-strength concrete part, shear reinforcement bars wound around the beam upper main bar and the beam lower bar main bar are embedded at predetermined intervals in the longitudinal direction of the beam. Characteristic reinforced concrete beam / floor structure.

Images