JP2022012546A - Analytic model and design method for reinforced concrete beam - Google Patents

Abstract

To provide an analytic model capable of evaluating rigidity of a reinforced concrete beam including a hole by modeling the reinforced concrete beam including the hole, and a design method for the reinforced concrete beam.SOLUTION: The present invention relates to an analytic model for which a reinforced concrete beam 10 including a hole 15 penetrating a side face is modeled. Regarding the analytic model, when performing the modeling on the basis of non-hole beam elements (a first non-hole beam element 11A and a second non-hole beam element 14A) in non-hole regions (a first non-hole region 21 and a second non-hole region 23) of the reinforced concrete beam 10 in a length direction U of the reinforced concrete beam 10 and a hole beam element in a hole beam region (a hole beam region 22) of the reinforced concrete beam 10 in the length direction U, the hole beam element consists of an upper chord material 12 disposed above the hole 15 and a lower chord material 13 disposed below the hole 15.SELECTED DRAWING: Figure 4

Description

The present invention relates to an analysis model that models a reinforced concrete beam having an opening penetrating a side surface and a method for designing a reinforced concrete beam having an opening.

Conventionally, it has been known that a reinforced concrete beam is provided with an opening for the purpose of passing equipment piping or allowing people to pass through during inspection after completion (see, for example, Non-Patent Document 1).

Non-Patent Document 1 shows a method of shearing reinforcement of an open hole, and even if sufficient shear reinforcement is performed, the decrease in the rigidity of the beam is not compensated for, so that a large through hole is provided. It is stated that the provision of continuous through holes should be avoided. Further, in Non-Patent Document 1, in order to reduce the influence of the decrease in rigidity due to the opening, the diameter of the circular hole and the side length of the rectangular hole in the beam direction may be set to 1/3 or less of the beam. Are listed.

"Reinforced Concrete Structure Calculation Criteria / Explanation", Architectural Institute of Japan, March 1, 2010

In the conventional structural design, the diameter of the circular hole and the side length of the rectangular hole in the beam direction are set to 1/3 or less of the beam, so that the member rigidity is equivalent to that of the beam without a hole. However, the member rigidity has been evaluated ignoring the influence of the opening. Therefore, there is a problem that the rigidity of the reinforced concrete beam having an opening cannot be appropriately evaluated.

Therefore, an object of the present invention is to provide an analysis model capable of modeling a reinforced concrete beam having an opening and evaluating the rigidity of the reinforced concrete beam having an opening, and a method for designing the reinforced concrete beam.

In order to achieve the above object, the analysis model of the present invention is an analysis model that models a reinforced concrete beam having an opening penetrating a side surface, and is a non-opening hole of the reinforced concrete beam in the longitudinal direction of the reinforced concrete beam. In modeling based on the non-perforated beam element of the region and the perforated beam element of the perforated region of the reinforced concrete beam in the longitudinal direction, the perforated beam element is of said perforation. It is characterized in that it is composed of an upper chord member arranged above and a lower chord member arranged below the opening.

Further, in the analysis model of the present invention, the non-perforated beam element may be arranged on both sides of the perforated beam element.

Further, in the analysis model of the present invention, the perforated beam element may be set based on the moment of inertia of area of the upper chord member and the moment of inertia of area of the lower chord member.

Further, in the analysis model of the present invention, the amount of reinforcing bars for calculating the moment of inertia of area of the upper chord member and the lower chord member may be based on the main bar and the reinforcing bar arranged around the opening.

Ｑ：せん断力
ｒ_ｂ：低減係数
Ｋ_ｂ：無開孔の鉄筋コンクリート梁の弾性部材曲げ剛性
δ_ｂ（Ｌ）：たわみ量
Ｌ：鉄筋コンクリート梁の全長
Ｅ_ｃ：コンクリートのヤング率
Ｉ_ｅ：鉄筋コンクリート梁の無開孔領域の断面２次モーメント
_０Ｉ_ｅ：鉄筋コンクリート梁の有開孔領域の等価断面２次モーメント
_ｉｌ：鉄筋コンクリート梁の一端から開孔までの長さ
_０ｌ：開孔の長さ
_ｉｌ_Ｍ：鉄筋コンクリート梁の一端から反曲点までの長さ Further, the design method of the reinforced concrete beam may be performed by using the analysis model and the following equation.

Q: Shear force r _b : Reduction coefficient K _b : Elastic member of non-perforated reinforced concrete beam Flexural rigidity δ _b (L): Deflection amount L: Total length of reinforced concrete beam E _c : Young ratio of concrete I _e : Reinforced concrete beam Secondary moment of cross section of non-perforated area
₀ I _e : Equivalent moment of inertia of area in the perforated area of the reinforced concrete beam
_il : Length from one end of the reinforced concrete beam to the opening
₀ l: Length of opening
_{il M} : Length from one end of the reinforced concrete beam to the inflection point

The analytical model of the present invention configured as described above is a perforated beam element in a non-perforated region of a reinforced concrete beam in the longitudinal direction of a reinforced concrete beam and a perforated hole in a perforated region of a reinforced concrete beam in the longitudinal direction. In modeling based on the beam element, the perforated beam element is composed of an upper chord member located above the perforation and a lower chord member located below the perforation. Therefore, the reinforced concrete beam can be modeled after considering the existence of openings. As a result, the rigidity of the reinforced concrete beam having an opening can be evaluated based on the modeled reinforced concrete beam having an opening.

Further, in the analysis model of the present invention, a reinforced concrete beam having an open hole can be faithfully modeled so that the non-perforated beam element is arranged on both sides of the perforated beam element.

Further, in the analysis model of the present invention, the perforated beam element is set based on the moment of inertia of area of the upper chord member and the moment of inertia of area of the lower chord member. Therefore, it becomes possible to appropriately model a reinforced concrete beam having an opening, and it is possible to evaluate the rigidity of a reinforced concrete beam having various types of openings.

Further, in the analysis model of the present invention, the amount of reinforcing bars for calculating the moment of inertia of area of the upper chord member and the lower chord member can be based on the main bar and the reinforcing bar arranged around the opening. Therefore, it is possible to model a reinforced concrete beam having an opening close to the actual physical properties.

It is a perspective view which shows the reinforced concrete beam of Example 1. FIG. It is a side view which shows the reinforced concrete beam of Example 1. FIG. FIG. 3A is a cross-sectional view showing a reinforced concrete beam of Example 1, FIG. 3A shows a cross section taken along the line AA in FIG. 2, and FIG. 3B shows a cross section taken along the line BB in FIG. It is a figure for demonstrating the modeling of the reinforced concrete beam of Example 1. FIG. It is a figure which shows the distribution of the stress when the shearing force acts on the reinforced concrete beam of Example 1, FIG. 5 (a) is a figure which shows the bending moment distribution, and FIG. 5 (b) is a figure which shows the deflection distribution. be. It is a figure for demonstrating the calculation method of the moment of inertia of area of a reinforced concrete member. It is a graph which shows the result of the variable analysis of the reduction coefficient of Example 1, FIG. 7 (a) is a graph which shows the transition when the height of a hole is changed, and FIG. 7 (b) is a graph which shows the transition of the hole. It is a graph which shows the transition when the length is changed, and FIG. 7C is the graph which shows the transition when the position of an opening is changed in the longitudinal direction. It is a flowchart explaining the design flow of a reinforced concrete beam. It is a side view which shows the reinforced concrete beam of Example 2. FIG. It is a figure explaining the evaluation of the shear rigidity of the reinforced concrete beam of Example 4. FIG.

Hereinafter, embodiments for realizing the analysis model and the design method for the reinforced concrete beam according to the present invention will be described with reference to Example 1 shown in the drawings.

[Structure of reinforced concrete beams]
FIG. 1 is a perspective view showing a reinforced concrete beam of the first embodiment. FIG. 2 is a side view showing the reinforced concrete beam of the first embodiment. 3A and 3B are cross-sectional views showing a reinforced concrete beam of the first embodiment, FIG. 3A shows a cross-sectional view taken along the line AA in FIG. 2, and FIG. 3B shows a cross-sectional view taken along the line BB in FIG. .. Hereinafter, the configuration of the reinforced concrete beam of the first embodiment will be described.

As shown in FIG. 1, the reinforced concrete beam 10 in the first embodiment is applied to a reinforced concrete foundation beam having an opening 15 that allows a worker to enter under the floor when performing maintenance / inspection of a building or the like. Will be done. In Example 1, the bending rigidity of the elastic member of the reinforced concrete beam 10 is evaluated.

The foundation 1 is composed of an independent foundation 3 that supports the columns 2 and a reinforced concrete beam 10 that connects the columns 2.

The side surface of the reinforced concrete beam 10 is provided with a penetrating rectangular opening 15 that allows a worker to enter.

As shown in FIG. 2, in the reinforced concrete beam 10, one end i is connected to one column 2 and the other end j is connected to the other column 2.

The reinforced concrete beam 10 is provided with an opening 15 on the j-end side of the central CL in the longitudinal direction U of the reinforced concrete beam 10.

The reinforced concrete beam 10 has a perforated region 22 provided with an opening 15 in the longitudinal direction U, a first non-perforated region 21 as an unopened region on the i-end side of the opening 15, and an opening 15. It can be divided into a second non-perforated region 23 as a non-perforated region on the j-end side of the above.

The reinforced concrete beam 10 has a first non-perforated material 11 arranged in the first non-perforated region 21, a second non-perforated material 14 arranged in the second non-perforated region 23, and a perforated hole. It is composed of an upper chord member 12 arranged in the region 22 and a lower chord member 13 arranged in the perforated area 22.

The first non-perforated lumber 11 is formed so as to extend from the i-end to one end of the perforation 15 in the longitudinal direction U. The second non-perforated member 14 is formed so as to extend from the other end of the opening 15 to the j end in the longitudinal direction U.

The upper chord member 12 is arranged above the opening 15. The lower chord member 13 is arranged below the opening 15.

As shown in FIGS. 2, 3 (a) and 3 (b), the reinforced concrete beam 10 includes an upper end bar 16 as a main bar, a lower end bar 17 as a main bar, and an upper end reinforcing bar 18 as a reinforcing bar. A lower end reinforcing bar 19 as a reinforcing bar is provided.

Four upper end bars 16 are arranged side by side in the width direction so as to extend from the i-end to the j-end in the longitudinal direction U. Four lower end bars 17 are arranged side by side in the width direction so as to extend from the i-end to the j-end in the longitudinal direction U.

The upper end reinforcing bar 18 is installed above the opening 15 and on the opening 15 side of the upper end bar 16. The upper end reinforcing bar 18 is arranged so as to extend in the longitudinal direction U from the middle of the first non-perforated region 21 to the middle of the second non-perforated region 23 through the perforated region 22. Four upper end reinforcing bars 18 are arranged side by side at equal intervals in the width direction of the reinforced concrete beam 10.

The lower end reinforcing bar 19 is installed below the opening 15 and on the opening 15 side of the lower end bar 17. The lower end reinforcing bar 19 is arranged so as to extend in the longitudinal direction U from the middle of the first non-perforated region 21 to the middle of the second non-perforated region 23 through the perforated region 22. Four lower end reinforcing bars 19 are arranged side by side at equal intervals in the width direction of the reinforced concrete beam 10.

Here, the length of the reinforced concrete beam 10 in the longitudinal direction U is defined as the length L. In the longitudinal direction U, the length from the _i -end to one end of the opening 15 is defined as the length il. In the longitudinal direction U, the length of the opening 15 is ₀ l. In the longitudinal direction U, the length from the other end of the opening 15 to the j end is defined as the length _j l.

As shown in FIG. 3A, the height of the reinforced concrete beam 10 is defined as the beam beam D. The width of the reinforced concrete beam 10 is defined as the width b.

As shown in FIG. 3B, the height of the upper chord member ₁₂ is defined as the height D1. The height of the _lower chord member 13 is the height D2. The height of the opening 15 is defined as the height H.

[Evaluation model]
FIG. 4 is a diagram for explaining the modeling of the reinforced concrete beam 10 of the first embodiment. Hereinafter, modeling of the reinforced concrete beam 10 of the first embodiment will be described.

In the first embodiment, the bending rigidity of the elastic member of the reinforced concrete beam 10 is determined through the steps of FIGS. 4 (a) and 4 (b), respectively, in the non-perforated region (21, 23) and the perforated region 22. The elements are set as an aggregate, and the aggregate is aggregated and abstracted and replaced with an evaluation model expressed as one beam element.

Specifically, first, as shown in FIG. 4A, the reinforced concrete beam 10 is modeled as an aggregate of beam elements. That is, the first non-perforated material 11 is set as the first non-perforated beam element 11A as the non-opened beam element. The second non-perforated lumber 14 is set as the second non-perforated beam element 14A as the non-perforated beam element. The upper chord member 12 is set as the upper chord member beam element 12A. The lower chord member 13 is set as the lower chord member beam element 13A. The upper chord member beam element 12A and the lower chord member beam element 13A are joined in parallel by the rigid bar element 16A.

In other words, the reinforced concrete beam 10 is an assembly of a first non-perforated beam element 11A, a second non-perforated beam element 14A, an upper chord member beam element 12A, a lower chord member beam element 13A, and a rigid rod element 16A. Can be modeled into.

Since the upper chord beam element 12A and the lower chord beam element 13A are joined in parallel by the rigid rod element 16A, the equivalent moment of inertia of area _{0 Ie} of the perforated beam element is the cross section 2 of the upper chord beam element 12A. It is obtained as the sum of the moment of inertia and the moment of inertia of area of the lower chord member beam element 13A. As a result, the perforated beam element in which the upper chord member beam element 12A and the lower chord member beam element 13A are equivalently replaced can be obtained.

That is, the perforated beam element can be set based on the moment of inertia of area of the upper chord member 12 and the moment of inertia of area of the lower chord member 13.

Then, as shown in FIG. 4B, the bending rigidity of the first non-perforated beam element 11A can be set to the bending rigidity E _c I _e . The bending rigidity of the second non-perforated beam element 14A can be the bending rigidity E _c I _e . The bending rigidity of the perforated beam element can be the bending rigidity _{E c0} Ie.

That is, in the longitudinal direction U of the reinforced concrete beam 10, the first non-perforated beam element 11A of the first non-perforated region 21, the second non-perforated beam element 14A of the second non-perforated region 23, and the perforated hole. Based on the perforated beam element of the region 22, it can be modeled as an evaluation model for evaluating the bending rigidity of the elastic member of the reinforced concrete beam 10 having the perforation 15.

The first non-perforated beam element 11A and the second non-perforated beam element 14A are arranged on both sides of the perforated beam element in the longitudinal direction U.

[Derivation of equation for shear force-bending deformation]
5A and 5B are diagrams showing the distribution of stress when a shear force acts on the reinforced concrete beam 10 of Example 1, FIG. 5A is a diagram showing a bending moment distribution, and FIG. 5B is a diagram showing deflection. It is a figure which shows the distribution. Hereinafter, the derivation of the equation for the shear force-bending deformation relationship of Example 1 will be described.

A shear force Q that generates a bending moment distribution as shown in FIG. 5 (a) acts on the reinforced concrete beam 10 modeled as shown in FIG. 4 (b), and as shown in FIG. 5 (b), the bending force Q acts on the beam. It is assumed that δ _b (x) is exhibited.

The bending moment _i M applied to the i end is expressed by the following equation.
_i M = Q _i l _M
il _M is the distance from the _i end to the inflection point P.

The bending moment _j M applied to the j end is expressed by the following equation.
_j M = Q _j l _M
j l _M is the distance from the inflection point P to the j end.

The deflection δ _b (x) is defined by the following equation (1).

The first non-perforated beam element 11A, the second non-perforated beam element 14A, and the perforated beam element are considered to be configured in a row. Therefore, when x = il and x = _{il + 0 l ,} the continuous condition is satisfied.

Then, the first non-perforated beam element 11A, the second non-perforated beam element 14A, and the perforated beam element have a deflection δ _b ( _il ) and a deflection angle θ _b ( _il ) which is a fine coefficient thereof. ), And the deflection δ _b (il + _{0 l} ) and its fine coefficient, the deflection angle θ _b (il + _{0 l} ).

By utilizing this continuous condition and solving the system of FIG. 5 as an elementary beam, the deflection _i δ _b (x) in the equation (1) can be obtained as the following equation (2).

The deflection ₀ δ _b (x) in the equation (1) can be obtained as the following equation (3).

なお、_０Ｉ_ｅ＝Ｉ_ｅのとき、_ｉδ_ｂ（ｘ）＝_０δ_ｂ（ｘ）＝_ｊδ_ｂ（ｘ）となる。 The deflection _j δ _b (x) in the equation (1) can be obtained as the following equation (4).

When ₀ I _e = I _e , _i δ _b (x) = ₀ δ _b (x) = _j δ _b (x).

The deflection angle _i θ _b (x), which is a derivative of the deflection _i δ _b (x), can be obtained by the following equation (5).

The deflection angle ₀ θ _b (x), which is a derivative of the deflection ₀ δ _b (x), can be obtained by the following equation (6).

The deflection angle _j θ _b (x), which is a derivative of the deflection _j δ _b (x), can be obtained by the following equation (7).

As described above, since ₀ θ _b ( _i l + ₀ l) = _j θ _b ( _il + ₀ l) is established under continuous conditions, the equations (6) and (7) are solved for _i M. And the following equation (8) is obtained.

ここで、ｒ_ｂを低減係数とする。
Ｋ_ｂを無開孔の鉄筋コンクリート梁１０の弾性部材曲げ剛性とする。 By substituting the equation (8) into the equation (4), as shown in FIG. 5A, the deflection at the i-end of the reinforced concrete beam 10 on which the shear force Q acts can be obtained as the following equation (9). ..

Here, r _b is used as a reduction coefficient.
Let K _b be the flexural rigidity of the elastic member of the reinforced concrete beam 10 having no holes.

By modifying the equation (9), the following equation (10) is obtained.

Here, when the reinforced concrete beam 10 has no holes, the structural relationship of the reinforced concrete beam 10 is expressed by the following equation (11) under the stress conditions as shown in FIG.

As is clear from the comparison between the equation (10) and the equation (11), the elastic member bending rigidity of the reinforced concrete beam 10 having the opening 15 is reduced by the reduction coefficient r to the elastic member bending rigidity _Kb of the reinforced concrete beam 10 having no opening. Equal to the value multiplied by _b . This reduction coefficient r _b can be defined as a reduction coefficient for obtaining the bending rigidity of the elastic member of the reinforced concrete beam 10 having the opening 15.

The reduction coefficient r _b is expressed as the following equation (12).

As is clear from the calculation method of _{0 Ie} , since the moment of inertia of area of the upper chord member 12 and the lower chord member 13 is calculated and added independently, the beam of the upper chord member 12 and the lower chord member 13 The beams do not have to be the same. Therefore, the position of the opening 15 does not have to be at the center position in the beam direction, and even if it is unevenly distributed above or below the reinforced concrete beam 10, it can be faithfully modeled accordingly.

[Second moment of inertia of reinforced concrete member]
FIG. 6 is a diagram for explaining a method of calculating the moment of inertia of area of a reinforced concrete member. Hereinafter, the moment of inertia of area of the reinforced concrete member will be described.

As described in Non-Patent Document 1 (“Reinforced Concrete Structural Calculation Criteria / Explanation”, Architectural Institute of Japan, March 1, 2010), when dealing with minute deformation, minute vibration, self-strain stress, etc. of a reinforced concrete frame. It is better to consider the influence of the reinforcing bar on the concrete cross section so that it corresponds to the measured value. Therefore, consider the equivalent moment of inertia _Ie .

記号ｇ：断面縁から断面の重心までの距離 In FIG. 6, each reference numeral is as follows.

Symbol g: Distance from the cross-section edge to the center of gravity of the cross-section

Assuming that the geometrical moment of inertia I ₀ in the case of no reinforcement is equivalent to the geometrical moment of inertia Ie in the case of reinforcement, _φr is the rate of increase of the moment of inertia of area due to the _inclusion of reinforcing bars. become that way.

The equivalent moment of inertia of area _Ie in the case of streaks can be calculated based on the upper end streaks 16 and the lower end streaks 17. Further, the equivalent moment of inertia of area _Ie in the case of reinforcement is calculated based on the upper end reinforcement 16, the lower end reinforcement 17, the upper end reinforcing bar 18 and the lower end reinforcing bar 19 arranged around the opening 15. You can also do it. That is, the amount of reinforcing bars for calculating the moment of inertia of area of the upper chord member 12 and the lower chord member 13 is the upper end bar, the lower end bar 17, the upper end reinforcing bar 18 and the lower end reinforcing bar 19 arranged around the opening 15. May be based on.

[Variable analysis of reduction coefficient r _b ]
FIG. 7 is a graph showing the result of variable analysis of the reduction coefficient of Example 1, and FIG. 7 (a) is a graph showing the transition when the height of the opening 15 is changed, and FIG. 7 (b) is shown. ) Is a graph showing the transition when the length of the opening 15 is changed, and FIG. 7 (c) is a graph showing the transition when the position of the opening 15 is changed in the longitudinal direction. Hereinafter, the variable analysis of the reduction coefficient _rb of Example 1 will be described. As a test body, a reinforced concrete beam 10 having a height H of the opening 15 of 1/2 of the beam frame D was used. Further, as the test body, the one in which the opening 15 was formed in the center of the reinforced concrete beam 10 in the beam direction was used.

(Change the height of the opening)
As shown in FIG. 7A, it can be seen that the elastic flexural rigidity of the member tends to decrease at an accelerating rate as the height H of the opening 15 increases.

(Change the length of the hole)
As shown in FIG. 7B, it can be seen that even if the height H of the opening 15 is the same, the rigidity decreases as the length ₀ l of the opening 15 increases. Further, it can be reconfirmed that the length of the opening 15 is ₀ l = 0, and the reduction coefficient r _b when imitating the reinforced concrete beam 10 without a hole is 1.0.

(Change the position of the opening)
As shown in FIG. 7 (c), when the opening 15 was located at the central CL in the longitudinal direction U, the reduction coefficient r _b = 0.66, but when the opening 15 approaches the j-end side, It was found that the reduction coefficient r _b was reduced and the elastic flexural rigidity of the member was reduced.

As described above, the influence of having the opening 15 on the bending rigidity of the elastic member is appropriately evaluated according to the height H of the opening, the length ₀ l of the opening 15, and the position in the longitudinal direction U. I found that I could do it.

When ₀ I _e = I _e and mathematically it can be imitated as a reinforced concrete beam 10 without a hole, _i M = Q0.5 L from the equation (8). That is, the _{il M shown in FIG. 5 (a) is il M = 0.5} L, and the reinforced concrete beam 10 is subjected to antisymmetric bending.

₀ I _e ≠ _{I e} , and mathematically, when the reinforced concrete beam 10 has an opening 15, il _M ≠ 0.5 L depending on the conditions. That is, if there is no opening, the anti-inflection point P may move due to the influence of the opening 15 even under the condition of the inverse symmetric bending, and the inverse symmetric bending may not be established according to the equation (8). Proven in.

That is, it was possible to mathematically clarify that the opening 15 can upset the balance of the inverse symmetric bending. Further, the reduction coefficient r _b can be defined in consideration of the influence.

[Action of analysis model and design method of reinforced concrete beam with perforation]
Next, the operation of the analysis model of Example 1 and the design method of the reinforced concrete beam 10 having the opening 15 will be described. The analysis model of Example 1 is an analysis model that models a reinforced concrete beam 10 having an opening 15 penetrating a side surface. In this analysis model, the non-perforated beam element (first non-opening) of the non-perforated region (first non-perforated region 21, second non-perforated region 23) of the reinforced concrete beam 10 in the longitudinal direction U of the reinforced concrete beam 10 is obtained. Modeled based on the perforated beam element 11A, the second non-perforated beam element 14A) and the perforated beam element of the perforated hole region (perforated hole region 22) of the reinforced concrete beam 10 in the longitudinal direction U. The perforated beam element is composed of an upper chord member 12 arranged above the perforated hole 15 and a lower chord member 13 arranged below the perforated hole 15 (FIG. 4).

Thereby, the reinforced concrete beam 10 can be modeled in consideration of the existence of the opening 15. Therefore, the rigidity of the reinforced concrete beam 10 having the openings 15 can be evaluated based on the modeled reinforced concrete beam 10 having the openings 15.

As a result, as shown in FIG. 8, in the general structural design procedure of a building, the rigidity of the reinforced concrete beam 10 having the opening 15 can be evaluated by the stress calculation which is an upstream process.

In the analysis model of the first embodiment, the non-perforated beam elements (first non-perforated beam element 11A, second non-perforated beam element 14A) are arranged on both sides of the perforated beam element (FIG. 4).

As a result, the non-perforated beam element (first non-perforated beam element 11A, second non-perforated beam element 14A) has an opening 15 so as to be arranged on both sides of the perforated beam element. The reinforced concrete beam 10 can be faithfully modeled.

In the analysis model of the first embodiment, the perforated beam element is set based on the moment of inertia of area of the upper chord member 12 and the moment of inertia of area of the lower chord member 13 (FIG. 4).

This makes it possible to appropriately model the reinforced concrete beam 10 having the openings 15 and evaluate the rigidity of the reinforced concrete beams 10 having various types of openings.

In the analysis model of Example 1, the amount of reinforcing bars for calculating the moment of inertia of area of the upper chord member 12 and the lower chord member 13 is the main bar (upper end bar 16, lower end bar 17) and the reinforcing bar arranged around the opening 15. It is based on (upper end reinforcing bar 18, lower end reinforcing bar 19).

This makes it possible to model the reinforced concrete beam 10 having the openings 15 closer to the actual physical properties. Therefore, the rigidity of the reinforced concrete beam 10 having the openings 15 can be evaluated based on the modeled reinforced concrete beam 10 having the openings 15.

In the method for designing the reinforced concrete beam 10 having the holes 15 in the first embodiment, the reinforced concrete beam 10 having the holes 15 can be designed by using the analysis model and the above equations (10) and (12). can.

This makes it possible to know the bending rigidity of the elastic member of the reinforced concrete beam 10 having the opening 15. Therefore, it is possible to appropriately evaluate the decrease in rigidity of the reinforced concrete beam 10 due to the opening 15. As a result, the bending rigidity of the elastic member of the reinforced concrete beam 10 having the opening 15 can be easily evaluated.

In addition, the framework of a general-purpose structural design program can be used as it is.

Further, when I _e = _{0 Ie} and mathematically imitates the reinforced concrete beam 10 with no open hole, the reduction coefficient r _b = 1.0, and the equations (10) and (11) match. That is, in a broad sense, the equation (11) can be an evaluation equation that can accurately evaluate the bending rigidity of the elastic member of the reinforced concrete beam 10.

The analysis model of Example 2 and the design method of the reinforced concrete beam having a hole are different from the analysis model of Example 1 and the design method of the reinforced concrete beam having a hole in that the shape of the hole is different.

[Structure of reinforced concrete beams]
FIG. 9 is a side view showing the reinforced concrete beam of the second embodiment. Hereinafter, the configuration of the reinforced concrete beam of the second embodiment will be described. The same or equivalent parts as those described in the above Examples will be described using the same terms or the same reference numerals.

As shown in FIG. 9A, even when the opening 15A is circular when viewed from the side, the moment of inertia of area is used as the upper chord member 12 above the opening 15A and the lower chord member 13 below the opening 15A, respectively. (It is assumed that it is derived as an equivalent cross section in the case of a streak), and by adding the two, the equivalent geometrical moment of inertia _{0 Ie} of the perforated hole region 22 can be calculated.

In this case, as shown in FIG. 9B, the equivalent moment of inertia of area in the case of a single bar of the upper chord member 12 and the lower chord member 13 can be obtained by regarding each as an RC filling arch.

Further, as shown in FIG. 9 (c), it can be interpreted by approximating to an RC beam having a variable cross section having a vertical haunch. That is, the evaluation of the cross-sectional performance of the chord material can be appropriately selected depending on the accuracy conditions and the calculation environment required for the beam to be designed.

As described above, even when the opening 15A is circular, the influence of the opening 15A of the reinforced concrete beam 10 can be reflected through the same process as in the first embodiment. That is, even when the opening 15A is circular, the reduction coefficient can be obtained through the same process as in Example 1.

Since other configurations and actions and effects are substantially the same as those in the above embodiment, the description thereof will be omitted.

The analysis model of Example 3 and the design method of the reinforced concrete beam having holes are different from the analysis model of Example 1 and the design method of the reinforced concrete beam having holes in that the holes are different.

[Structure of reinforced concrete beams]
Hereinafter, the configuration of the reinforced concrete beam of the third embodiment will be described. The same or equivalent parts as those described in the above Examples will be described using the same terms or the same reference numerals.

Since the reinforced concrete beam 10 of the first embodiment had one opening 15, as shown in FIG. 4, the reinforced concrete beam 10 had the first non-perforated region 21-the perforated region 22-the first, as shown in FIG. The reduction coefficient is derived by dividing into two non-perforated regions 23, each region is modeled as a beam element, and the beam element is solved as a primary beam according to a continuous condition.

In the third embodiment, for example, when there are two openings 15, the reinforced concrete beam 10 is provided with the first non-perforated area-the first perforated area-the second non-perforated area-the second perforated area-the third. If the problem of the elementary beam is solved by dividing it into non-perforated areas, the reduction coefficient can be derived by a similar framework.

As described above, even when there are a plurality of openings 15, the influence of the openings 15 of the reinforced concrete beam 10 can be reflected through the same process as in the first embodiment. That is, even when there are a plurality of openings 15, the reduction coefficient can be obtained through the same process as in Example 1.

Since other configurations and actions and effects are substantially the same as those in the above embodiment, the description thereof will be omitted.

The analysis model of Example 4 and the design method of the reinforced concrete beam having holes are different from the analysis model of Example 1 and the design method of the reinforced concrete beam having holes in that the rigidity of interest is different.

[Structure of reinforced concrete beams]
FIG. 10 is a diagram illustrating the evaluation of the shear rigidity of the reinforced concrete beam of the fourth embodiment. Hereinafter, the configuration of the reinforced concrete beam of the fourth embodiment will be described. The same or equivalent parts as those described in the above Examples will be described using the same terms or the same reference numerals.

In Example 4, in the reinforced concrete beam 10 under the same stress conditions as in Example 1, focusing on the shear force distribution and the shear deformation, the same figures are drawn together as shown in FIG. 10.

In this case, the rigidity evaluation by the elastic member shear rigidity K _s is required instead of the elastic member bending rigidity K _b (strictly speaking, K in which the K _b spring and the K _s spring are joined in series is the reinforced concrete beam 10). True elastic member rigidity ").

Similarly, in the case of the elastic member shear rigidity K _s , the reinforced concrete beam 10 is divided into a first non-perforated region 21-a perforated region 22-a second non-perforated region 23, and each of them is used as a beam element. The framework for connecting and finding the overall shear deformation starting from continuous conditions does not change.

If the overall shear deformation is obtained, the reduction coefficient and the like can be derived from the contrast with _Ks in the case of no opening as in bending.

However, the continuous condition in this case is not both the deflection δ _b and the deflection angle θ _b as in the case of bending deformation. As shown in FIG. 10 (e), the shear deformation angle θ _s is constant in the first non-perforated region 21, the perforated region 22, and the second non-perforated region 23. Only shear deformation δ _s can be set. Since the shear deformation can be obtained without solving higher-order equations such as deflection, the continuous condition is satisfied only by the shear deformation angle θ _s .

As described above, the elastic member shear rigidity K _s can also reflect the influence of the opening 15 of the reinforced concrete beam 10 through the same process as in the first embodiment. That is, the reduction coefficient of the elastic member shear rigidity K _s can also be obtained through the same process as in the first embodiment.

Since other configurations and actions and effects are substantially the same as those in the above embodiment, the description thereof will be omitted.

The analysis model of the present invention and the design method of the reinforced concrete beam have been described above based on Examples 1 to 4. However, the specific configuration is not limited to these examples, and design changes and additions are permitted as long as they do not deviate from the gist of the invention according to each claim.

In Examples 1 to 4, the formulation was performed for the bending moment distribution according to the inverse symmetric bending, but all of them take a classical mechanical approach of solving the beam element. Therefore, for example, even in a parabolic bending moment distribution system, the reduction coefficient can be derived without changing the framework by solving the beam element according to the moment distribution map.

In Examples 1 to 4, the theory has been developed focusing on elasticity in both bending and shearing, but the framework does not change even in the inelastic region after the occurrence of cracks. The non-perforated area and the perforated area may be replaced with beam elements respectively (in the perforated area, the upper and lower chord members may be individually evaluated and added).

The relationship of each beam element is determined using the continuous condition. Deformation is calculated so that the continuous condition is satisfied while reflecting the condition of each inelastic region in each beam element. The deformation of each beam element is summed up to obtain the deformation of the entire beam. The reduction coefficient is derived from the comparison with the deformation in the case of no opening.

In Examples 1 to 4, the present invention is applied to a reinforced concrete foundation beam having an opening 15 that allows a worker to enter under the floor when performing maintenance / inspection of a building. Indicated. However, the invention can be applied even to a foundation beam having a small opening for piping or the like.

In Examples 1 to 4, examples of applying the present invention to a foundation beam are shown. However, the present invention can be applied to reinforced concrete beams in the superstructure of foundation beams.

10 Reinforced concrete beam 11A 1st non-perforated beam element (an example of non-opened beam element)
12 Upper chord material 13 Lower chord material 14A Second non-perforated beam element (an example of non-perforated beam element)
15 Fenestra 16 Upper end muscle (example of main muscle)
17 Lower end muscle (example of main muscle)
18 Upper end reinforcing bar (an example of reinforcing bar)
19 Lower end reinforcing bar (an example of reinforcing bar)
21 First non-perforated region (an example of non-perforated region)
23 Second non-perforated region (an example of non-perforated region)
22 Perforated area (an example of perforated area)
U longitudinal direction

Claims (5)

It is an analysis model that models a reinforced concrete beam with an opening that penetrates the side surface.
With the non-perforated beam element of the non-perforated region of the reinforced concrete beam in the longitudinal direction of the reinforced concrete beam,
In modeling based on the perforated beam element of the perforated area of the reinforced concrete beam in the longitudinal direction.
An analysis model characterized in that the perforated beam element is composed of an upper chord member arranged above the perforation and a lower chord member arranged below the perforation. The analysis model according to claim 1, wherein the non-perforated beam element is arranged on both sides of the perforated beam element. The perforated beam element is
The moment of inertia of area of the upper chord material and
The analysis model according to claim 1 or 2, wherein the analysis model is set based on the moment of inertia of area of the lower chord member. The amount of reinforcing bars for calculating the moment of inertia of area of the upper chord member and the lower chord member is based on the main bar and the reinforcing bar arranged around the opening, according to claims 1 to 3. The analysis model described in any one of the items. A method for designing a reinforced concrete beam having a hole, which is performed by using the analysis model according to any one of claims 1 to 4 and the following equation.

Q: Shear force r _b : Reduction coefficient K _b : Elastic member of non-perforated reinforced concrete beam Flexural rigidity δ _b (L): Deflection amount L: Total length of reinforced concrete beam E _c : Young ratio of concrete I _e : Reinforced concrete beam Secondary moment of cross section of non-perforated area
₀ I _e : Equivalent moment of inertia of area in the perforated area of the reinforced concrete beam
_il : Length from one end of the reinforced concrete beam to the opening
₀ l: Length of opening
_{il M} : Length from one end of the reinforced concrete beam to the inflection point

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