JP5399649B2 - Evaluation method of bending strength of reinforced concrete beams - Google Patents

Description

  The present invention relates to a method for evaluating the bending strength of a reinforced concrete beam, and more particularly to a method for evaluating the bending strength of a reinforced concrete beam in consideration of not only a balance of bending but also a shearing force.

  Usually, in high-rise buildings, the strength decreases in the order of column concrete, beam concrete, and floor concrete. Therefore, there is a need to separate the concrete. Generally, it takes time to install a formwork at the boundary between the beam and the floor. Therefore, when placing the concrete of the beam, the concrete is dripped at the boundary between the floor and the concrete does not solidify. Within the time, floor concrete is cast and mixed.

  At this time, in the “Building Construction Standard Specification / Explanation, JASS5, Reinforced Concrete Construction”, the time from mixing the concrete to stacking the concrete is defined as 2 to 2.5 hours. Subtracting the transportation time leaves almost no time, and a strict construction plan must be made.

  By the way, if it is possible to cast all the remaining beams and the back-placed part of the floor with only one kind of concrete and floor concrete that is cheaper than the pillar concrete after placing the concrete, it will greatly reduce the labor and material cost of construction. Can be reduced. In this case, the lower side of the beam has high strength with PCa, and the upper side of the beam has low strength with a post-casting portion made of floor concrete. Here, if the upper side of the beam is compressed, it will be necessary to consider concrete crushing, but the calculation based on the balance of cross-sectional force, which is widely used in general, can no longer be applied, and it is a convergence calculation assuming plane maintenance. Therefore, it is determined whether or not crushing has occurred. In this case, enormous time and labor are required to perform the cross-sectional analysis on all the beams.

  Moreover, as a measure for suppressing crushing, it is realistic to increase the number of shear reinforcement bars to enhance the concrete restraining effect, but since there is no formula for evaluating the effect, it cannot be actually designed.

  Therefore, a method for calculating the strength of a reinforced concrete beam in which concretes having different design standard strengths are cast up and down in consideration of the design standard strengths of both concretes is disclosed (see Patent Document 1). The technique described in this Patent Document 1 uses the conditional expressions related to the height of a reinforced concrete beam, the design standard strength of the concrete positioned below, and the design standard strength of the concrete positioned above, to determine the shear strength of the reinforced concrete beam. Is calculated.

JP 2006-225894 A

  By the way, in order to plan the building to make the building sticky by yielding the axial rebar of the beam except for the lowest floor and the top floor, which usually allow the yield of the column in the design of the building, the horizontal strength per layer is It is determined by the bending strength due to the reinforcement of the beam. However, when calculating the bending strength, it is a precondition that the concrete on the compression side does not collapse. In order to examine whether or not this crushing occurs, there is a method of making it equal to or less than the balanced rebar ratio. However, the calculation of the balanced rebar ratio is based on the theory of elasticity and does not confirm the behavior of the compression region in the final state, so it is a simple but fairly safe evaluation, and as a result the axis is constrained ( The beam strength is reduced), the beam cross-sectional area is increased, or the concrete strength is required to be increased.

  As described above, in order to calculate the bending strength in detail, there is a method of determining whether a reinforcing bar yields or concrete reaches a crushing strain by a cross-sectional analysis using a computer. However, in practice, it is not realistic to perform a cross-sectional analysis for each beam because it takes time and effort. In fact, not only the compressive force caused by bending but also the compressive force generated to bear the shear force is generated in the compression area at the end of the beam. Originally, it is necessary to evaluate these combined forces at the same time. There is.

  The present invention has been proposed in view of the above-described circumstances, and in a construction method for placing concrete having different design reference strengths at the lower and upper portions of a reinforced concrete beam, compared to conventional techniques, it is much simpler and more accurate. An object of the present invention is to provide an evaluation method capable of evaluating the bending strength of a reinforced concrete beam, and to use this evaluation method to appropriately design a reinforced concrete beam.

The method for evaluating the bending strength of a reinforced concrete beam according to the present invention and the reinforced concrete beam designed using the evaluation method have the following characteristics in order to achieve the above-described object.
That is, the method for evaluating the bending strength of a reinforced concrete beam according to the present invention is a method for evaluating the bending strength of a reinforced concrete beam in a construction method in which concrete having different design standard strength is placed between the lower part and the upper part of the reinforced concrete beam. ,
The bending strength of the reinforced concrete beam is evaluated using the following conditional expression 1.

ただし、
Ｍ_u ： コンクリート梁の曲げ耐力
Ｔ_y2 ： 下端筋の引張力
Ｄ ： 梁成
ｄ_t ： 引張鉄筋の面積重心までの最小被り
Ｃ_c ： コンクリート圧縮力
β ： コンクリート強度の低減係数
Ｘ_n : 圧縮縁から中立軸までの距離
Ｃ_s1 ： 圧縮鉄筋による圧縮力
ｄ_c ： 圧縮鉄筋の面積重心までの最小被り

However,
M _u : Bending strength of concrete beam T _y2 : Tensile force of bottom bar D: Beam formation d _t : Minimum covering to center of gravity of tensile bar C _c : Concrete compressive force β: Reduction factor of concrete strength X _n : Compression edge the distance to the neutral axis from C _s1: compression force by the compression rebar d _c: suffers minimal up centroid of the compression rebar

  The method for evaluating the bending strength of a reinforced concrete beam according to the present invention is such that the bending strength of the concrete beam obtained by the conditional expression 1 is smaller than the bending strength of the concrete beam obtained by the following conditional expression 2. It is characterized in that it is judged that crushing occurs.

ただし、
Ｍ ： 梁主筋の降伏で決まるコンクリート梁の曲げ耐力
Ｔ_y ： 引張鉄筋の降伏時引張力
ｄ_j ： 引張鉄筋の面積重心から圧縮縁までの距離

However,
M: Beam longitudinal reinforcement Flexural Strength T _y of concrete beams determined by the yielding of: at yield tensile force of the tensile reinforcement d _j: distance to the compressed edge from the area centroid of the tensile reinforcement

  Conditional expression 1 is a conditional expression derived based on an assumption regarding the stress state of the beam end when an antisymmetric moment is applied by the building horizontal force. That is, when an antisymmetric moment is applied to the beam when an earthquake occurs, the bending section force and the compressive force of the truss mechanism and arch mechanism, which are shear load-bearing mechanisms, are concentrated in the compression region of the beam end. To do. Conditional expression 1 was obtained by assuming a resistance cross-sectional area according to the ratio of the magnitudes of the respective force components and solving a series of simultaneous equations. Conditional expression 2 is a conditional expression that is generally used for the bending strength determined by the yield of the beam main reinforcement.

  The method for evaluating the bending strength of a reinforced concrete beam according to the present invention considers not only the balance of bending but also the shearing force as a method of evaluating the bending strength when placing concrete having different design reference strengths at the lower and upper parts of the reinforced concrete beam. Therefore, the bending strength of reinforced concrete beams can be evaluated easily and accurately. Moreover, a reinforced concrete beam can be designed appropriately by using this evaluation method.

  Specifically, by using the method for evaluating the bending strength of a reinforced concrete beam according to the present invention, when the reinforced concrete beam is precast and all the post-casting parts other than columns are cast with floor concrete, the strength of the reinforced concrete beam is measured at the top and bottom of the reinforced concrete beam. It is possible to easily calculate the bending crush strength of cross sections using different concrete using general spreadsheet software without performing cross section analysis. In addition, for concrete crushing on reinforced concrete beams, the reinforcement effect when reinforcing by increasing the shear reinforcement can be evaluated numerically as an increase in crushing strength.

  Hereinafter, an embodiment of a method for evaluating the bending strength of a reinforced concrete beam according to the present invention will be described with reference to the drawings. FIG. 1 is a schematic diagram showing a cross section of a PCa portion and a post-casting portion in a reinforced concrete beam, FIG. 2 is a schematic diagram showing a resistance mechanism of the entire reinforced concrete beam, and FIG. 3 is a diagram of Fan and Strut at a compression end portion of a reinforced concrete beam. It is a schematic diagram which shows the burden of.

<Strength of concrete used for beams>
The method of evaluating the bending strength of a reinforced concrete beam (hereinafter abbreviated as “beam”) according to the present invention is a method for placing a concrete having different design reference strengths at the lower and upper portions of the beam. Apply. This method uses different concrete in the vertical direction within the cross section of the beam. That is, as shown in FIG. 1, high-strength concrete is used for the PCa portion 11 located on the lower side in the cross section of the beam 10, and low-strength floor concrete is used for the back-placed portion 12 located on the upper side. In FIG. 1, 10 indicates a beam, 11 indicates PCa portions 11 and 12 and a post-striking portion, 13 indicates a shearing rebar, and 20 indicates a floor.

At this time, since the bending strength in which the upper side of the beam 10 is compressed is compared with the bending strength in which the lower side of the beam 10 is compressed, it is considered that the strength is lowered. If it will be in such a state, it will be uselessly because the shaft reinforcement arranged with much effort will not fully demonstrate performance. Further, the fracture mode is not preferable because it is weaker than the reinforcement yield. Furthermore, since the damage of concrete is conspicuous in appearance, it is not preferable. It has been confirmed from structural experiments that such collapse of the beam end can be improved by slightly increasing the number of shear reinforcement bars at the very end only. The evaluation of the bending strength of the reinforced concrete beam according to the present invention is a general spreadsheet software, which is intended to calculate the crushing strength simply by incorporating the reinforcing effect of the shear reinforcement.
The Strut & Fan Mode used to assume the stress state at the beam end was referred to “ACI JOURNAL January-February 1985 pp46-56”.

<Stress state of beam end when reverse symmetric moment is applied by building horizontal force>
As shown in FIG. 2, it is assumed that an arch mechanism (Strut) and a truss mechanism (Fan) act on the compression region of the beam end. In the following description, T _y is the tensile yield tensile force of the reinforcing bar, V _f is the shear force of the Fan of when all shear reinforcement in the beam surrendered, V _s is the concrete beam compressive ultimate strength of Strut The shearing force at the point of reaching

  In FIG. 2, the following equation (1) is established from the balance in the horizontal direction on the broken line extending from the upper left to the lower right.

ただし、
Ｔ_y1 ： 上端筋の引張力
Ｔ_y2 ： 下端筋の引張力
Ｃ_c1 ： Strutと釣り合うコンクリート圧縮力
Ｃ_c2 ： Fanと釣り合うコンクリート圧縮力
ここで、曲げ降伏が先行する場合には、せん断補強筋が降伏する前に圧壊するので、下記式（２）が成立する。

However,
T _y1 : Tensile force of upper end muscle T _y2 : Tensile force of lower end muscle C _c1 : Concrete compressive force balanced with Strut C _c2 : Concrete compressive force balanced with Fan Here, when bending yielding precedes, shear reinforcement Since it collapses before yielding, the following formula (2) is established.

ただし、
_bＶ_u ： 梁の保有せん断耐力
Ｖ_f ： 梁内のすべてのせん断補強筋が降伏した時点のFanのせん断力
Ｖ_s ： Strutのコンクリート束が圧縮終局強度に達した時点のせん断力
ここで、Ｖｓがせん断補強筋による拘束効果を考慮した保有コンクリート強度に達した時点を梁の圧壊点とし、力と幾何学的な釣り合いからＶ_ｓ、Ｖ_ｆを求めると、下記式（３−１）、式（３−２）、式（３−３）、式（３−４）、式（４）が成立する。

However,
_b V _u : Shear strength of the beam V _f : Shear force of Fan when all the shear reinforcements in the beam yield V _s : Shear force when the Strut concrete bundle reaches the ultimate compressive strength When Vs reaches the retained concrete strength in consideration of the restraining effect by the shear reinforcement, the collapse point of the beam is used, and V _s and V _f are calculated from the force and geometrical balance, the following equations (3-1), Expressions (3-2), (3-3), (3-4), and (4) are established.

ただし、
Ｃ_c1 ： Strutと釣り合うコンクリート圧縮力
Ｃ_c2 ： Fanと釣り合うコンクリート圧縮力
Ｆ ： 垂直方向単位長さ当たりの拘束効果を考慮したコンクリート強度×梁幅
Ｙ ： Strutが負担するｙ方向の成分
Ｂ ： Fanが負担するｙ方向の成分
Ｃ_c ： コンクリート圧縮力
Ｃ_s1 ： 梁の圧縮鉄筋による圧縮力
Ｔ_y2 ： 下端筋の引張力

However,
C _c1 : Concrete compressive force balanced with Strut C _c2 : Concrete compressive force balanced with Fan F: Concrete strength x beam width considering the restraining effect per unit length in the vertical direction Y: Y-direction component borne by Strut B: Fan Component in the y direction borne by C _c : Concrete compressive force C _s1 : Compressive force due to compression _{bar of} beam T _y2 : Tensile force of lower end

ただし、
Ｆ ： 垂直方向単位長さ当たりの拘束効果を考慮したコンクリート強度×梁幅
β ： コンクリート強度の低減係数（０．８５）
_cσ_B ： 保有コンクリート強度（せん断補強筋の拘束効果を考慮した強度）
Ｂ ： Fanが負担するｙ方向の成分
また、図２において、Ｓｔｒｕｔの帯が梁の軸方向となす角をθとすると、下記式（５）が成立する。

However,
F: Concrete strength considering the restraining effect per unit length in the vertical direction x beam width β: Reduction factor of concrete strength (0.85)
_c σ _B : Strength of retained concrete (strength considering the restraining effect of shear reinforcement)
B: y-direction component borne by Fan Further, in FIG. 2, when the angle formed by the Strut band and the beam axial direction is θ, the following equation (5) is established.

ただし、
θ ： Strutの帯が梁の軸方向となす角
Ｘ ： Strutが負担するｘ方向の成分
Ｙ ： Strutが負担するｙ方向の成分
Ｄ ： 梁成
Ｌ₀ ： 梁の内法スパン
式（５）から、Ｙについて連立方程式を解き、幾何学的に正号は棄てて、負号を採ると、下記式（６）となる。

However,
theta: axial and angle swath beam of Strut X: Strut the component of x-direction to bear Y: Strut the component of the y direction to bear D: RyoNaru L _0: Beams inner size span formulas (5) , Y solving the simultaneous equations, geometrically discarding positive signs and taking negative signs, the following equation (6) is obtained.

ただし、
Ａ ： Fanが負担するｘ方向の成分
Ｂ ： Fanが負担するｙ方向の成分
Ｄ ： 梁成
Ｘ ： Strutが負担するｘ方向の成分
Ｙ ： Strutが負担するｙ方向の成分
Ｌ₀ ： 梁の内法スパン
また、図３に示すように、下記式（７）が成立する。

However,
A: component in x direction Fan be borne B: component in the y direction Fan to bear D: RyoNaru X: component in x direction Strut be borne Y: component in the y direction Strut be borne L _0: Of the beams Legal span As shown in FIG. 3, the following equation (7) is established.

ただし、
Ａ ： Fanが負担するｘ方向の成分
Ｂ ： Fanが負担するｙ方向の成分
Ｄ ： 梁成
Ｘ ： Strutが負担するｘ方向の成分
Ｙ ： Strutが負担するｙ方向の成分
Ｌ₀ ： 梁の内法スパン

However,
A: component in x direction Fan be borne B: component in the y direction Fan to bear D: RyoNaru X: component in x direction Strut be borne Y: component in the y direction Strut be borne L _0: Of the beams Law span

Here, with reference to FIG.4 and FIG.5, Formula (5), Formula (6), and Formula (7) are demonstrated in more detail. FIG. 4 is an explanatory diagram for explaining how to derive the equations (5) and (6), and FIG. 5 is an explanatory diagram for explaining how to derive the equation (7).
As shown in FIG. 4, when attention is paid to Strut in the compression region at the beam end, the following equation (5-1) is established. Further, since the following formula (5-2) is established, the formula (5) is derived.

ただし、
θ ： Strutの帯が梁の軸方向となす角
Ｘ ： Strutが負担するｘ方向の成分
Ｙ ： Strutが負担するｙ方向の成分

However,
θ: Angle formed by the Strut band and the axial direction of the beam X: The x-direction component borne by Strut Y: The y-direction component borne by Strut

ただし、
θ ： Strutの帯が梁の軸方向となす角
Ｘ ： Strutが負担するｘ方向の成分
Ｙ ： Strutが負担するｙ方向の成分
Ｄ ： 梁成
Ｌ₀ ： 梁の内法スパン
そして、式（５）から、下記式（６−１）、下記式（６−２）が導き出される。ここで、Ｙについて解くと、下記式（６−３）となり、Ｙ＜Ｄであるから負号を採ると、式（６）が導き出される。

However,
theta: axial and angle swath beam of Strut X: component in x direction Strut be borne Y: component in the y direction Strut be borne D: RyoNaru L _0: clear width span of the beam and the formula (5 ), The following formula (6-1) and the following formula (6-2) are derived. Here, when solving for Y, the following expression (6-3) is obtained. Since Y <D, the expression (6) is derived by taking a negative sign.

ただし、
Ｘ ： Strutが負担するｘ方向の成分
Ｙ ： Strutが負担するｙ方向の成分
Ｄ ： 梁成
Ｌ₀ ： 梁の内法スパン

However,
X: Strut the component of x-direction to bear Y: Strut the component of the y direction to bear D: RyoNaru L _0: clear width span of the beam

ただし、
Ｘ ： Strutが負担するｘ方向の成分
Ｙ ： Strutが負担するｙ方向の成分
Ｄ ： 梁成
Ｌ₀ ： 梁の内法スパン

However,
X: Strut the component of x-direction to bear Y: Strut the component of the y direction to bear D: RyoNaru L _0: clear width span of the beam

ただし、
Ｘ ： Strutが負担するｘ方向の成分
Ｙ ： Strutが負担するｙ方向の成分
Ｄ ： 梁成
Ｌ₀ ： 梁の内法スパン
また、図５に示すように、梁端部の圧縮領域でＦａｎに注目すると、下記式（７−１）が成立する。また、下記式（７−２）が成立するため、式（７）が導き出される。

However,
X: Strut the component of x-direction to bear Y: Strut the component of the y direction to bear D: RyoNaru L _0: clear width span of the beam As shown in FIG. 5, the Fan in the compressed region of the beam end When attention is paid, the following formula (7-1) is established. Moreover, since the following formula (7-2) is established, the formula (7) is derived.

ただし、
γ ： Fanの帯が梁の軸方向となす角
Ａ ： Fanが負担するｘ方向の成分
Ｂ ： Fanが負担するｙ方向の成分

However,
γ: Angle formed by the band of the fan and the axial direction of the beam A: Component in the x direction borne by the fan B: Component in the y direction borne by the fan

ただし、
γ ： Fanの帯が梁の軸方向となす角
Ａ ： Fanが負担するｘ方向の成分
Ｂ ： Fanが負担するｙ方向の成分
Ｘ ： Strutが負担するｘ方向の成分
Ｙ ： Strutが負担するｙ方向の成分
Ｄ ： 梁成
Ｌ₀ ： 梁の内法スパン
そして、式（７）から、Ｂについて連立方程式を解き、幾何学的に正号は棄て、負号を採ると、下記式（８）となる。

However,
γ: Angle between the band of the fan and the axial direction of the beam A: x-direction component borne by the fan B: y-direction component borne by the fan X: x-direction component borne by Strut Y: y borne by Strut direction component D: RyoNaru L _0: clear width span of the beam and, from equation (7), solving simultaneous equations for B, geometrically plus sign is discarded, when taking the negative sign, the following formula (8) It becomes.

ただし、
Ａ ： Fanが負担するｘ方向の成分
Ｂ ： Fanが負担するｙ方向の成分
Ｄ ： 梁成
Ｘ ： Strutが負担するｘ方向の成分
Ｙ ： Strutが負担するｙ方向の成分
Ｌ₀ ： 梁の内法スパン
これらの幾何学的な釣り合いから下記式（９−１）、式（９−２）、（９−３）、（９−４）が成立する。

However,
A: component in x direction Fan be borne B: component in the y direction Fan to bear D: RyoNaru X: component in x direction Strut be borne Y: component in the y direction Strut be borne L _0: Of the beams Legal span From these geometrical balances, the following formulas (9-1), (9-2), (9-3), and (9-4) are established.

ただし、
Ｘ ： Strutが負担するｘ方向の成分
Ｙ ： Strutが負担するｙ方向の成分
Ｆ ： 垂直方向単位長さ当たりの拘束効果を考慮したコンクリート強度×梁幅
Ａ ： Fanが負担するｘ方向の成分
Ｂ ： Fanが負担するｙ方向の成分
Ｄ ： 梁成
Ｌ₀ ： 梁の内法スパン
Ｖ_s ： Strutのコンクリート束が圧縮終局強度に達した時点のせん断力
Ｖ_f ： 梁内のすべてのせん断補強筋が降伏した時点のFanのせん断力

However,
X: x-direction component borne by Strut Y: y-direction component borne by Strut F: concrete strength x beam width considering the restraining effect per unit length in the vertical direction A: x-direction component borne by Fan B : component in the y direction Fan to bear D: RyoNaru L _0: beams inner size span V _s: shear force at the time the concrete bundle of Strut reaches the compression ultimate strength V _f: all shear reinforcement in the beam Fan's shear force at the time of yield

  Therefore, the bending strength is expressed by the following formula (10). This expression (10) is conditional expression 1 in the present invention. FIG. 6 shows a balance of bending moments in the cross section. FIG. 6 is an explanatory diagram for explaining the balance of bending moments in the cross section.

ただし、
Ｍ_u ： コンクリート梁の曲げ耐力
Ｔ_y2 ： 下端筋の引張力
Ｄ ： 梁成
ｄ_t ： 引張鉄筋の面積重心までの最小被り
Ｃ_c ： コンクリート圧縮力
β ： コンクリート強度の低減係数（０．８５）
Ｘ_n : 圧縮縁から中立軸までの距離
Ｃ_s1 ： 圧縮鉄筋による圧縮力
ｄ_c ： 圧縮鉄筋の面積重心までの最小被り

However,
M _u : Bending strength of concrete beam T _y2 : Tensile force of lower end reinforcement D: Beam formation d _t : Minimum covering to center of gravity of tensile reinforcement C _c : Concrete compression force β: Reduction factor of concrete strength (0.85)
X _n: distance from the compressed edge to the neutral axis C _s1: compression force by the compression rebar d _c: suffers minimal up centroid of the compression rebar

<Judgment of collapse of beam end>
The bending strength obtained by the equation (10) is a bending strength assuming that crushing and yielding of the beam main bar occur simultaneously. Therefore, if the calculated value of the bending strength is smaller than the bending strength determined by the yield of the main bar of the beam, such as the following formula (11), which is generally used, it is judged that the concrete collapse occurs. Can do. This expression (11) is the conditional expression (2) in the present invention.

ただし、
Ｍ ： コンクリート梁の曲げ耐力（梁主筋の降伏で決まる場合）
Ｔ_y ： 引張鉄筋の降伏時引張力
ｄ_j ： 引張鉄筋の面積重心から圧縮縁までの距離

However,
M: Bending strength of concrete beam (determined by yield of beam main bar)
T _y : Tensile strength of tensile reinforcement at yield d _j : Distance from the center of gravity of the tensile reinforcement to the compression edge

<Evaluation of restraint effect by shear reinforcement at beam end>
Regarding the restraint effect at the end of the beam, refer to the apparent increase in concrete strength due to the restraint effect of the reinforcing bars on the column shaft strength of the New-RC High Strength Reinforcement Subcommittee Report of the Ministry of Construction General Technology Research and Development Project. did.

Note that _c σ _B in the equation (4) is calculated by the following equation (12).

ただし、
_cσ_cB ： コンファインドコンクリートの強度
β ： コンクリート強度の低減係数（０．８５）
σ_B ： プレーンコンクリートのシリンダー強度
ｄ'' ： 横補強筋の公称直径
ｃ ： 横補強筋の有効横支持長さ
ｓ ： 横補強筋のピッチ
ρ_n ： 横補強筋の体積比
σ_ny ： 横補強筋の信頼強度
ｂ_e ： 梁の外周せん断鉄筋の間隔

However,
_c σ _cB : Confined concrete strength β: Concrete strength reduction factor (0.85)
σ _B : Cylinder strength of plain concrete d ″: Nominal diameter of transverse reinforcement c: Effective lateral support length of transverse reinforcement s: Pitch of transverse reinforcement ρ _n : Volume ratio of transverse reinforcement σ _ny : Lateral reinforcement trust the strength of the muscle b _e: spacing of the outer circumferential shear reinforcement of the beam

  The reinforced concrete beam of the present invention can be designed using the above evaluation method. The above evaluation method is applied when the bending strength of a beam is evaluated in a construction method in which reinforced concrete beams are precast, all the post-casting parts other than columns are cast with floor concrete, and concrete with different strength is used above and below the reinforced concrete beams. To do. In the evaluation method of the present invention, it is possible to easily calculate the bending crush resistance of the cross section using a general spreadsheet software without performing cross section analysis, and the accuracy is confirmed by a 1/2 scale beam member model experiment. As a result, it was found that the method has sufficient accuracy as a method for evaluating the bending strength of the beam.

The schematic diagram which shows the beam cross section of the PCa part in a reinforced concrete beam, and a post-casting part. The schematic diagram which shows the resistance mechanism of the whole reinforced concrete beam. The schematic diagram which shows the burden of Fan and Strut in the compression end part of a reinforced concrete beam. Explanatory drawing for demonstrating how to derive | lead-out Formula (5) and Formula (6). Explanatory drawing for demonstrating how to guide | lead-form Formula (7). Explanatory drawing for demonstrating the balance of the bending moment in a cross section.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Beam 11 PCa part 12 Post-striking part 13 Shear reinforcement 20 Floor Strut Arch mechanism Fan truss mechanism

Claims (2)

In the method of placing concrete with different design standard strengths at the bottom and top of reinforced concrete beams, it is a method for evaluating the bending strength of reinforced concrete beams,
A method for evaluating the bending strength of a reinforced concrete beam, wherein the bending strength of the reinforced concrete beam is evaluated using the following conditional expression 1.

However,
M _u : Bending strength of concrete beam T _y2 : Tensile force of bottom bar D: Beam formation d _t : Minimum covering to center of gravity of tensile bar C _c : Concrete compressive force β: Reduction factor of concrete strength X _n : Compression edge the distance to the neutral axis from C _s1: compression force by the compression rebar d _c: suffers minimal up centroid of the compression rebar It is judged that concrete crushing occurs when the bending strength of the concrete beam obtained by the conditional expression 1 according to claim 1 is smaller than the bending strength of the concrete beam obtained by the following conditional expression 2. Evaluation method of bending strength of reinforced concrete beams.

However,
M: Beam longitudinal reinforcement Flexural Strength T _y of concrete beams determined by the yielding of: at yield tensile force of the tensile reinforcement d _j: distance to the compressed edge from the area centroid of the tensile reinforcement

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