JP4581729B2 - Calculation method of shear stress of reinforced concrete beam, design method of reinforced concrete beam, reinforced concrete beam - Google Patents

Description

  The present invention relates to a method for calculating a shear stress acting on a joint surface of a reinforced concrete beam in which concrete is jointed up and down and an opening is provided across the joint surface, and design of a reinforced concrete beam using this method. The present invention relates to a method and a reinforced concrete beam designed by this design method.

In recent years, PC members such as precast concrete (hereinafter referred to as PC) columns and beams have been widely used in order to improve the quality of construction of reinforced concrete structures and shorten the construction period. When constructing reinforced concrete beams and slabs using half PC beam members, it is necessary to place concrete on the upper half PC beam at the site.
Therefore, in Patent Document 1, in order to shorten the construction period, a shear reinforcement bar that surrounds the main bar of the upper half PC beam and a main bar of the slab are perpendicular to the main bar of the PC beam and sheared into the slab. A method is disclosed in which a force transmission bar is provided and concrete is placed on the upper half PC beam and the slab at once.
JP 7-305443 A

The reinforced concrete beam constructed by the above method has a structure in which the concrete is handed up and down, and when an external force is applied to the reinforced concrete beam, there is a risk of causing slip failure on the joint surface. Therefore, it is necessary to calculate the shear stress applied to the joint surface and the slip strength of the joint surface, and to design the structure so that the slip strength is greater than the degree of shear stress generated on the joint surface.
However, when the opening is applied to the joint surface, the shear stress generated on the joint surface is increased, and there is a risk of inducing a slip failure. However, the calculation method of the shear stress degree when the opening is applied to the joint surface has not been established, and if it is designed using the conventional structure design method of the joint surface, a slip fracture occurs from the opening. .

  Therefore, the present invention can prevent slip failure on the joint surface by properly calculating the shear stress degree generated in the reinforced concrete beam in which the concrete is jointed up and down and an opening is provided across the joint surface. The purpose is to.

なお、式（２）の右辺におけるΣは、前記鉄筋コンクリート梁の有効幅内に存在する梁主筋またはスラブ筋の合計であることを示している。以下の記載においても同様である。 The method for calculating the degree of shear stress of the present invention is a method for calculating the degree of shear stress acting on the joint surface of a reinforced concrete beam in which concrete is handed up and down and an opening is provided across the joint surface. The cross-sectional area of the beam main bar is As, the maximum stress acting on the main beam subjected to tension is σ _st , the cross-sectional area of the slab bar subjected to tension within the effective width of the reinforced concrete beam is a _sl , and the maximum stress of the slab bar is When the degree is σ _sl , the length of the section excluding the hinge region from the section from the edge or center of the opening to the point where the stress of the reinforcing bar is maximum is Δl ′, and the width of the joint surface is b The shear stress τ ′ _xy applied to the joint surface is calculated by the following equation.

Note that Σ on the right side of Equation (2) indicates the sum of the beam main bars or slab bars existing within the effective width of the reinforced concrete beam. The same applies to the following description.

Further, the design method of the reinforced concrete beam of the present invention is a design method of the reinforced concrete beam in which the concrete is handed up and down, and an opening is provided across the joint surface. It is characterized in that the shear stress degree τ ′ _xy acting on the joining surface is calculated and designed so that the shear stress degree τ ′ _xy does not exceed the sliding strength τ _u of the joining surface.
Further, the present invention includes a reinforced concrete beam characterized by being designed by the above design method. The reinforced concrete beam may be constructed by in-situ concrete casting on a precast concrete member.
Since the shear stress obtained by the above calculation method takes into account the effect of providing an opening on the joint surface, it opens on the joint surface of a reinforced concrete beam jointed with concrete of a different design standard strength. When providing, it is possible to prevent slippage of the joint surface.

  According to the present invention, it is possible to appropriately calculate the shear stress generated in a reinforced concrete beam in which concrete is cast up and down and an opening is provided across the joint surface, thereby preventing slip failure on the joint surface.

  First, a description will be given of a reinforced concrete beam that is an object of calculation of the shear stress degree of the present invention. 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, in a reinforced concrete beam 1 to be calculated according to the present invention, concrete 2 and 3 are handed up and down. When shear stress acts on the reinforced concrete beam 1 in which the concrete 2 and 3 are joined up and down, if the shear stress level exceeding the slip strength is applied to the joint surface 4, slip failure occurs. Therefore, it is necessary to design against slippage failure of the joining surface 4. In particular, when the opening 9 is provided in the joint surface 4, the shear stress applied to the joint surface 4 is increased, so that slip failure is easily induced. Note that the reinforced concrete subjected to the calculation of the degree of shear stress of the present invention includes a reinforced concrete beam in which concrete having different design reference strengths is cast up and down.

  By the way, the reinforced concrete beam 1 having such a configuration is often constructed using, for example, a half PC beam member. FIG. 2 is a diagram showing a method of constructing the reinforced concrete beam 1 using the half PC beam member 5 which is a half precast member. The half PC beam member 5 is installed, the upper end reinforcement 6 and the slab reinforcement (not shown) are arranged, and the post-cast concrete 7 is constructed on the half PC beam member upper part and the slab at once. The upper surface of the concrete body 8 of the half PC beam member 5 is provided with a concave portion in order to reduce the weight and improve the workability. The reinforced concrete beam 1 constructed using such a half PC beam member 5 often passes through the joint surface 4 of the concrete body 8 and the post-cast concrete 7 when the opening 9 is provided.

Therefore, in the method for calculating the degree of shear stress according to the present invention, when the joint surface 4 has the opening 9, the degree of shear stress τ _xy applied to the joint surface 4 is determined as follows.

Τ ′ _xy is the shear stress applied to the joint surface, b is the width of the reinforced concrete beam 1, Δl ′ is the length of the section excluding the hinge region from the section from the maximum stress position to the end or center of the opening. It is. As is the cross-sectional area of the beam main bar 6, σ _st is the maximum stress acting on the beam main bar 6 subjected to tension, a _sl is the cross-sectional area of the slab bar subjected to tension within the effective width of the reinforced concrete beam 1, and σ _sl is the reinforced concrete beam This is the maximum stress level of the slab reinforcement that is subject to tension within the effective width.

  Hereinafter, a mechanism for calculating the degree of shear stress will be described using Equation (3) and Equation (4). First, let us consider a method of calculating the degree of shear stress in the ultimate limit state when concrete is handed up and down via a joint surface parallel to the material axis and the opening does not cross the joint surface. Fig. 3 shows the distribution of the stress level of the cross section of the beam end and the distribution of the stress level of the top bar embedded in the post-cast concrete when bending moment, shear force and axial force are applied to the reinforced concrete beam. FIG. As shown in FIG. 3, in the cross section A, a compressive force is applied to the upper end reinforcement and the surrounding concrete, and a tensile force is applied to the lower end reinforcement. In section B, a tensile force is applied to the upper end reinforcement, and a compressive stress is applied to the lower end reinforcement and the surrounding concrete. Thus, the stress of the upper end reinforcement changes from compression to tension between the end A and the end B, and the changed stress is transmitted to the lower end reinforcement through the concrete. In order for stress to be transmitted and force balance within the member to occur, the joint surface of the concrete must also be transmitted by the adhesive force between the concrete.

Therefore, consider the balance of forces in the ultimate limit state. When the ultimate limit is reached, the steel yields, the concrete cracks, and the joint surface slips. For this reason, a locally high stress portion occurs, but stress redistribution occurs, and it is possible to withstand locally high stress. Therefore, the average value of the joint surface is used as the shear stress of the joint surface. When the final state is reached, the main beam of the beam undergoes plastic deformation, and a hinge region having a length almost equal to that of the beam is formed from the end of the beam. In the final state, the stress level of the reinforcing bar can be made constant, assuming that the hinge region has yielded and is completely plastic. Therefore, the following formula is derived when considering the balance of stress at the joint surface of the portion excluding the hinge region from the section between the position of the maximum stress and the position where the moment becomes zero.
τ _xy · (b · Δl) = ΔT (5)

Here, τ _xy represents the average value of the shear stress at the joint surface, b is the width of the joint surface, Δl is the length excluding the hinge region from the section where the position of the maximum stress and the moment becomes zero, ΔT Is the amount of change in stress borne by the reinforcing bar. However, in the equation (5), as shown in FIG. 3, the stress T is regarded as zero at the point where the bending moment becomes zero, and the stress T is continuously increased in the interval between the point of maximum stress and the point where the moment becomes zero. It is assumed to change.

In the formula (5), the left side shows the stress transmitted at the joint surface between the position of the maximum stress of the reinforcing bar and the position where the moment becomes zero, and the right side is the amount of change of the stress borne by the reinforcing bar, Derived from being equal. In addition, the amount of change ΔT of the stress borne by the reinforcing bar is the amount of change in the stress of the main beam of the beam and the amount of change in the stress of the slab reinforcement within the range (referred to as the effective width) of the stress applied to the beam in the slab near the beam. It is sum. Δl is the length of a section obtained by excluding the length of the hinge region from the section from the position where the moment becomes zero to the position where the stress becomes maximum. Here, since it is difficult to model ΔT simply, it is considered that the stress borne by the reinforcing bar becomes zero at a position where the moment becomes zero, and changes linearly. Then, the amount of change in stress between Δl becomes equal to the difference between the maximum stress and zero, that is, the maximum stress value, and can be determined as follows.

In addition, As is the cross-sectional area of the beam main bar, σ _st is the maximum stress acting on the main beam subjected to tension, a _sl is the cross-sectional area of the slab bar subjected to tension within the effective width of the reinforced concrete beam, and σ _sl is the effective _strength of the reinforced concrete beam. This is the maximum stress level of the slab reinforcement that is subject to tension within the width. From the above equations (5) and (6), the degree of shear stress τ _xy applied to the joint surface is expressed by the following equation.

When the adhesion design is performed, the shear stress degree τ _xy obtained by this equation is designed so as not to exceed the slip strength τ _u of the joint surface. In addition, as a formula for obtaining the sliding strength τ _u of the joining surface, for example, the following formula proposed by Furuya et al.

τ _u = 0.075fc ′ + (1.12−0.0012fc ′) · p _w f _ws <0.3 fc ′ (9)
Note that fc ′ is the design standard strength of concrete, p _w is the shear reinforcement ratio, and f _ws is the yield point of the shear reinforcement.

As shown in Expression (9), it is understood that the slip strength τ _u of the joint surface can be increased by increasing the shear reinforcement ratio p _w and the yield point f _ws of the shear reinforcement. Therefore, if the shear stress τ _xy of the joint surface exceeds the slip strength τ _u , reinforcement such as increasing the shear reinforcement strength or using a high strength shear reinforcement strength is performed, and the slip strength of the joint surface is achieved. The design is performed so that τ _u exceeds the shear stress τ _xy .

Next, a description will be given of a method for calculating the shear stress level of the joint surface when an opening is provided so as to straddle the joint surface of the concrete in the reinforced concrete beam in which the concrete is handed up and down. Fig. 4 shows the stress distribution in the cross section of the beam end when the shear force is applied to the reinforced concrete beam having an opening at the position passing through the joint surface of the concrete, and the stress level of the upper bar embedded in the post-cast concrete It is a figure which shows distribution.
Because no stress is transmitted on the joint surface where the opening is provided, the stress transmission from the upper end to the lower end when the shear force is applied is the part where the tensile stress of the reinforcing bar is maximized from the end of the opening. This is performed at a portion excluding the hinge region. For this reason, it is considered that the stress distribution of the upper end muscle becomes zero at the opening as shown in FIG. Therefore, Δl in the equations (7) and (8) is the following equation in which Δl ′ is the length Δl ′ of the section excluding the hinge region from the section from the maximum stress position to the end or center of the opening. In this case, τ ′ _xy can be calculated as the shear stress degree of the joint surface.

Here, as shown in FIG. 4, since Δl> Δl ′, the degree of shear stress τ ′ _xy generated on the joint surface when the opening is provided is equal to the degree of shear stress τ _xy generated on the joint surface when no opening is provided. Become bigger. Conventionally, there was no method for calculating the shear stress level of the joint surface with such an opening, so even if the shear stress level applied to the joint surface is increased by providing the opening, it is not possible to design for it. In addition, sliding failure occurred at the joint surface. However, 'by using the _xy calculation method, shear stress intensity τ occurs striking joint surface' Shear Stress τ of the present invention it is possible to calculate the _xy, advance, such as increasing the number of shear reinforcement It is possible to design to increase the slip strength τ _u of the joint surface, and to prevent slip failure.

Next, an experiment for confirming that the degree of shear stress generated on the joint surface increases as the opening straddles the joint surface through an experiment will be described. Table 1 is a table | surface which shows the conditions of the test body used for experiment.
[Table 1]

  As shown in Table 1, in this experiment, a reinforced concrete beam (CASE-1) in which post-cast concrete was cast on the precast concrete beam member, and post-cast concrete was cast on the precast concrete beam member, and the opening was cast. A shearing experiment was conducted for the case of crossing the joint surface (CASE-2). In addition, the strength of the concrete of each test body is as shown in Table 1, and conditions other than the presence or absence of the opening are very close values.

As a result of the shearing experiment, CASE-1 did not break at the joint surface, but CASE-2 failed at the joint surface. FIG. 5 shows the reinforcing _bar amount p _w σ _wy crossing the joint surface and CASE-1 for the joint surface obtained from Equations (7) and (8) and CASE-2 for Equation (10) and (11). It is a graph which shows the relationship between shear stress degree (tau) _zy , (tau) ' _zy, and sliding strength (tau) _u . The slip strength τ _u shown as a comparative example is obtained from the formula proposed by Furuya et al. As shown in FIG. 5, the shear stress degree τ _zy of CASE-1 is lower than the slip strength τ _u obtained by the equation (9), but the shear stress degree τ ′ _zy of CASE-2 is obtained by the equation (9). It exceeds the sliding strength τ _u . That is, since the shear stress τ _zy is smaller than the sliding strength τ _u, no shear fracture occurred on the joint surface. However, in CASE-2, by providing an opening, the shear stress τ ′ _zy is _expressed by the formula (9 ) Is greater than the required sliding strength τ _u , and it is considered that the joint surface has broken from the opening. Also from this, when the opening straddles the joint surface, the shear stress acting on the joint surface increases, and if the shear stress degree τ ′ _xy generated on the joint surface of the present invention is calculated, It was confirmed that destruction could be predicted. Therefore, it can be understood that slip failure can be prevented by designing the slip strength τ _{u to} be larger than the shear stress τ ′ _xy calculated by the method of calculating the shear stress of the present invention.
In addition, this invention is applicable also when the design reference | standard intensity | strength of the concrete handed up and down differs.

(A) is an axial sectional view of a reinforced concrete beam, and (b) is a transverse sectional view of the reinforced concrete beam 1. It is a figure which shows the method of constructing a reinforced concrete beam using a half PC beam member. It is a figure which shows the stress intensity distribution of the cross section of the beam edge part when a shear force acts on a reinforced concrete beam, and the stress intensity distribution of the upper end reinforcement embed | buried in post-cast concrete. It is a figure showing the stress intensity distribution of the cross section of the beam end and the stress intensity distribution of the upper end reinforcement embedded in the post-cast concrete when shearing force is applied to the reinforced concrete beam with an opening across the joint surface of the concrete is there. Reinforcement amount across the striking joint plane _{(p w} σ _wy) and shear stresses (τ _zy, τ _'xy) is a graph showing the relationship between.

Explanation of symbols

1 Reinforced concrete beam 2, 3 Concrete 4 Joint surface 5 Half PC beam member 6 Top bar (beam main bar)
7 Post-cast concrete 8 Concrete body 9 Opening

Claims (4)

A method of calculating the shear stress acting on the joint surface of the reinforced concrete beam in which the concrete is handed up and down and an opening is provided across the joint surface,
The cross-sectional area of the beam main bar is As, the maximum stress acting on the beam main bar subjected to tension is σ _st , the cross-sectional area of the slab bar subjected to tension within the effective width of the reinforced concrete beam is a _sl , and the maximum stress of the slab bar is σ _sl , when the length of the section excluding the hinge region from the section from either the edge or the center of the opening to the point where the stress of the reinforcing bar is maximum is Δl ′ and the width of the joint surface is b,
A method for calculating the degree of shear stress, wherein the degree of shear stress τ ′ _xy applied to the joint surface is calculated by the following equation.

A method for designing a reinforced concrete beam in which concrete is handed up and down and an opening is provided across the joint surface, wherein the shear stress τ ′ _xy acting on the joint surface is determined by the method according to claim 1. A design method for a reinforced concrete beam, characterized by calculating and designing the shear stress τ ′ _xy so as not to exceed the sliding strength τ _u of the joint surface.   A reinforced concrete beam designed by the design method according to claim 2. 4. The reinforced concrete beam according to claim 3, wherein the precast concrete member is constructed by placing concrete on-site.

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