JP7590268B2 - Calculation method for eccentricity distance in joint structure between CFT column and RC column - Google Patents

Description

The present invention relates to a method for calculating the eccentricity distance in a joint structure between a CFT column and an RC column.

The joint structure described in Patent Document 1 below has been proposed as a structure (construction method) for joining RC columns and CFT columns.

JP 2019-138137 A

However, Patent Document 1 does not go so far as to determine the reaction force (axial force) at the bottom of a CFT-RC column and its position of action (eccentric distance from the material axis) when an axial force (long-term load) and a horizontal force (short-term load [earthquake load] are assumed, and this horizontal force gradually increases while repeatedly alternating between positive and negative) act on a column in which an RC column and a CFT column are joined (hereinafter referred to as a CFT-RC column).

In consideration of the above circumstances, the present invention provides a method for calculating the eccentricity distance in a joint structure between a CFT column and an RC column, which calculates the eccentricity distance required when determining the reaction force at the bottom surface of the CFT-RC column.

前記直線によって規定される平面は終局時まで保持されるものと仮定して、下記式（１－２）より、

前記偏心距離ｅを算定する。 In order to achieve the above object, the present invention employs the following means.
That is, the method for calculating the eccentricity distance in a joint structure between a CFT column and an RC column according to the present invention is a method for calculating the eccentricity distance in a joint structure between a CFT column and an RC column, which calculates the eccentricity distance, which is the distance from the axis required when calculating the reaction force of the bottom surface of a column where a CFT column is joined to an RC column arranged above the CFT column, and comprises the steps of: connecting the values of _ε1 and _ε2 with a straight line based on the strain measurement values _ε1 and _ε2 of the two outermost edges of the steel pipe of the CFT column; and calculating the slope φ of the straight line from the following formula (1-1);

Assuming that the plane defined by the straight line is maintained until the end, from the following formula (1-2),

The eccentric distance e is calculated.

In the method for calculating the eccentricity distance in a joint structure between a CFT column and an RC column configured in this way, the measured strain values _ε1 and _ε2 at two outermost points of the steel pipe of the CFT column are used to connect the values _ε1 and _ε2 with a straight line, and the inclination φ of said line is calculated. Based on this inclination φ, the eccentricity distance e from the axis, which is necessary to calculate the reaction force (axial force) at the bottom surface of the CFT-RC column, can be calculated.

各前記直線によって規定される平面は終局時まで保持されるものと仮定して、下記式（２－２）より、

前記偏心距離ｅを算定する。 The method for calculating the eccentricity distance in a joint structure between a CFT column and an RC column according to the present invention is a method for calculating the eccentricity distance, which is the distance from the axis required when calculating the reaction force of the bottom surface of a column joined to a CFT column and an RC column arranged above the CFT column, and comprises the steps of: connecting the values of ε ₀ and ε ₁ and the values of ε _{0 and ε 2 with straight lines from the strain measurement values ε 1 and ε 2 of the two outermost edges of the steel pipe of the CFT column and the strain ε 0 at the center of the measurement values ε 1 and ε 2 ; and calculating the slopes φ 1 and} φ ₂ of _the straight lines according to the following formulas (2-1a) and (2-1b),

Assuming that the plane defined by each of the straight lines is maintained until the end, from the following formula (2-2),

The eccentric distance e is calculated.

In the method for calculating the eccentricity distance in a joint structure between a CFT column and an RC column configured in this way, the strain measurements _ε1 , _ε2 at two outermost points of the steel pipe of the CFT column and the strain _ε0 at the center of the measurements _ε1 , _ε2 are used to connect the values of _ε0 and _ε1 , and the values of _ε0 and _ε2 with straight lines, respectively, and the slopes _φ1 , _φ2 of each of the straight lines are calculated. Based on these slopes _φ1 , _φ2 , the eccentricity distance e from the axis, which is necessary when calculating the reaction force (axial force) at the bottom of the CFT-RC column, can be calculated.

The method for calculating the eccentricity distance in a joint structure between a CFT column and an RC column according to the present invention makes it possible to calculate the eccentricity distance required to determine the reaction force at the bottom surface of a CFT-RC column.

FIG. 1 is a diagram showing a joint structure between a CFT column and an RC column according to one embodiment of the present invention. FIG. 1 is a front view showing strain measurement positions of a CFT column steel pipe in a CFT-RC column specimen according to one embodiment of the present invention. FIG. 1 is a side view showing strain measurement positions of a CFT steel column pipe in a CFT-RC column specimen according to one embodiment of the present invention. Shows a straight line distribution assuming plane retention. The plane-preserving bilinear distribution is shown. A longitudinal cross-sectional view of test specimen No. 1 is shown. 7 is a cross-sectional view taken along line AA' in FIG. 6. 7 is a cross-sectional view taken along line BB' in FIG. 6. The calculation results of the eccentric distance are shown below.

Below, a method for calculating the eccentricity distance in a joint structure between a CFT column and an RC column according to an embodiment of the present invention will be explained with reference to the drawings.

(Joint structure between CFT column and RC column)
First, the joint structure between a CFT column and an RC column will be described.
FIG. 1 is a diagram showing a joint structure between a CFT column and an RC column according to one embodiment of the present invention.
The joint structure 20 between a CFT column and an RC column of this embodiment shown in Fig. 1 is applied to, for example, the framework of a warehouse in a multi-story logistics facility. The warehouse is configured, for example, with a floor with a height of more than 10 m on the lower floors, and with a multi-story and complex material handling rack.

The joint structure 20 between CFT columns and RC columns can be used not only in multi-story logistics facilities, but also in facilities where the lower floors of the CFT structure are used as offices or commercial facilities, and the upper floors of the RCS structure or RC structure are used as a complex with residences and a hotel. There is no need to limit the scope of application as long as the lower floors are equipped with CFT columns 2 and the upper floors are equipped with RC columns 3.

In the joint structure 20 between the CFT column and the RC column of this embodiment, the steel pipe 5 of the CFT column 2 in the lower layer is extended upward from the top 2a of the CFT column 2 to the root wrapping level (approximately 1.5 m). The main reinforcement 7 of the RC column 3 in the upper layer is inserted into the inside of the connecting steel pipe (root wrapping steel pipe) 6, which is the extended part of the steel pipe 5, and concrete 8 is poured and filled in, so that the main reinforcement 7 is fixed to the concrete 8.

The joining steel pipe 6 is in the shape of a square tube. On the top 6a side of the joining steel pipe 6, a ring-shaped rib plate is provided as a stiffening part 9, which protrudes inward from the inner surface of the upper end part of the joining steel pipe 6 and extends circumferentially. The stiffening parts 9 are provided on the four sides of the joining steel pipe 6. The stiffening parts 9 stiffen the joining steel pipe 6, suppressing out-of-plane deformation.

An anchor plate 10 is attached to the lower end 7d of the main reinforcement 7 of the RC column 3 where it is inserted into the connecting steel pipe 6. The anchor plate 10 integrates the main reinforcement 7 with the concrete 8 inside the connecting steel pipe 6, preventing the main reinforcement 7 from slipping out of the concrete 8 inside the connecting steel pipe 6 as deformation increases. A beam 4 is joined to the top 2a of the CFT column 2.

(Method 1 for calculating eccentricity distance in joint structure between CFT column and RC column)
Next, a first method for calculating the eccentricity distance in a joint structure between a CFT column and an RC column will be described.
Fig. 2 is a front view showing the strain measurement positions of the CFT steel column pipe in the CFT-RC column specimen according to one embodiment of the present invention. Fig. 3 is a side view showing the strain measurement positions of the CFT steel column pipe in the CFT-RC column specimen according to one embodiment of the present invention.
2 and 3 show an example of the strain measurement positions of the CFT steel column pipe in the CFT-RC column specimen.
Calculation method 1 of the eccentric distance is a method based on the "flat-maintaining straight-line distribution" using strain measurement values ε ₁ and ε ₂ at two outermost points of the CFT steel pipe column.

FIG. 4 shows the relationship between the strain measurement position x according to this method and the strains ε ₁ and ε ₂ at the outermost edge of the CFT steel pipe column obtained from the strain gauge at that position. The procedure for calculating the eccentricity distance is described below.

(1) Connect the values of _ε1 and _ε2 with a straight line, and calculate φ (the slope of the line) from the following formula (1-1).

The plane defined by this line is assumed to be maintained until the end (plane maintenance assumption).

(2) Calculate the strain ε _xi at the outermost edge of the steel pipe of a CFT-RC column when a compressive axial force is applied to the CFT-RC column.
When a compressive axial force acts on a CFT-RC column and an axial strain ε ₀ occurs in the CFT column steel pipe, ε _xi is expressed by the following formula (1-2).

(3) Calculate the axial force N _S of the CFT column steel pipe.
1) When ε _xi ≦ε _y (ε _y : yield strain of CFT steel column), assuming that the stress-strain relationship of the CFT steel column is within the elastic range, N _S is calculated using the following formula (1-3).

2) When ε _xi > ε _y , assuming that the stress-strain relationship of the CFT steel column follows the completely elastic-plastic hysteresis rule, ε _xi is converted to the stress intensity σs of the CFT steel column, and N _S is calculated by the following formula (1-4).
When a CFT-RC column is subjected to repeated, gradually increasing, positive and negative horizontal forces, the stress-strain relationship of the CFT steel column exceeds the elastic range and enters the plastic region, and the proportional relationship between stress and strain no longer holds. Therefore, it is believed that in most cases N _S will be calculated using the following formula (1-4).

(4) Calculate the bending moment _MS of the CFT column steel pipe.
1) When ε _xi ≦ε _y, calculate M _S using the following formula (1-5).

2) When ε _xi > ε _y Assuming that the stress-strain relationship of the CFT steel column follows the hysteresis rule of a completely elastic-plastic type, ε _xi is converted to the stress intensity σs of the CFT steel column, and _Ms is calculated by the following formula (1-6).

Note that σ _s1 and σ _s2 are obtained by converting the measured strain values ε ₁ and ε ₂ of the CFT steel column into stress levels, assuming that the stress-strain relationship of the CFT steel column follows the hysteresis rule of a completely elastic-plastic type. Therefore, σ _s1 and σ _s2 are the stress levels of the CFT steel column at the strain measurement positions.

The axial force _NRC of the RC column and the bending moment _MRC (the bending moment acting on the bottom surface of the RC column in the CFT steel pipe column) are calculated using the following formulas (1-7) and (1-8), respectively. N, P, and H are shown in Figure 2.

(6) Calculate the eccentric distance e.
e is calculated from the relationship in equation (1-8) using the following equation (1-9).

(Method 2 for calculating eccentricity distance in joint structure between CFT column and RC column)
Next, a second method for calculating the eccentricity distance in a joint structure between a CFT column and an RC column will be described.
Calculation method 2 of the eccentric distance is a method based on the "two-linear distribution assuming plane retention" using strain measurements ε ₁ and ε ₂ at the two outermost edges of the CFT steel pipe column and strain ε ₀ at the center.

The relationship between the strain measurement position x according to this method, the strains _ε1 , _ε2 at the outermost edge of the CFT steel pipe column obtained from the strain gauge at said position, and the axial strain (the midpoint between measured values _ε1 and _ε2 , the measured value) _ε0 is shown in Figure 4, and the calculation procedure for the eccentricity distance is described below. In this calculation method, the base point is _ε0 , and the area is divided into two sections: the _ε0 - _ε1 section and the _ε0 - _ε2 section.

(1) The curvatures φ ₁ and φ ₂ in the ε ₀ -ε ₁ section and the ε ₀ -ε ₂ section are calculated.
The values of ε ₀ and ε _1, and ε ₀ and ε ₂ are connected with straight lines, and the intervals φ ₁ and φ ₂ (the slopes of the straight lines) are found using the following equations (2-1a) and (2-1b).

The plane defined by each line is assumed to be maintained until the end (plane maintenance assumption).

(2) The strains ε _1Xi and ε _2Xi at the outermost edge of the steel pipe of the CFT column in each section when a compressive axial force acts on the CFT-RC column are calculated using the following formulas (2-2a) and (2-2b).

(3) Calculate the axial force N _S of the CFT column steel pipe.
1) When ε _xi ≦ε _y (ε _y : yield strain of CFT steel column), assuming that the stress-strain relationship of the CFT steel column is within the elastic range, N _S is calculated using the following formula (2-3).

2) When ε _xi > ε _y , assuming that the stress-strain relationship of the CFT steel column follows the completely elastic-plastic hysteresis rule, ε _xi is converted to the stress intensity σs of the CFT steel column, and N _S is calculated by the following formula (2-4).
When alternating positive and negative gradually increasing horizontal forces act on a CFT-RC column, the stress-strain relationship of the CFT steel column exceeds the elastic range and enters the plastic region, and the proportional relationship between stress and strain no longer holds. Therefore, it is believed that in most cases N _S will be calculated using the following formula (2-4).

(4) Calculate the bending moment _MS of the CFT column steel pipe.
1) When ε _xi ≦ε _y, calculate M _S using the following formula (2-5).

2) When ε _xi > ε _y Assuming that the stress-strain relationship of the CFT steel column follows the perfectly elastic-plastic hysteresis rule, ε _xi is converted to the stress intensity σs of the CFT steel column, and _Ms is calculated by the following formula (2-6).

Note that σ _s1 and σ _s2 are obtained by converting the measured strain values ε ₁ and ε ₂ of the CFT steel column into stress levels, assuming that the stress-strain relationship of the CFT steel column follows the hysteresis rule of a completely elastic-plastic type. Therefore, σ _s1 and σ _s2 are the stress levels of the CFT steel column at the strain measurement positions.

The axial force _NRC of the RC column and the bending moment _MRC (the bending moment acting on the bottom surface of the RC column in the CFT steel pipe column) are calculated using the following formulas (2-7) and (2-8), respectively. N, P, and H are shown in Figure 2.

(6) Calculate the eccentric distance e.
e is calculated from the relationship in equation (2-8) using the following equation (2-9).

Next, using the test results of test piece No. 1 shown in Table 1 below as an example, we will attempt to calculate the eccentricity distance e using the above calculation methods 1 and 2.

The specimen diagrams for specimen No. 1 are shown in Figures 6 to 8, and the calculation results for the eccentricity distance for specimen No. 1 using calculation methods 1 and 2 are shown in Figure 9.

As shown in Figure 9, both calculation methods 1 and 2 can calculate the eccentricity distance e from the axis (in this case, e ≒ 200 mm) required to determine the reaction force (axial force) at the bottom of a CFT-RC column with approximately the same accuracy.

In method 1 for calculating the eccentricity distance in a joint structure between a CFT column and an RC column configured in this way, the measured strain values _ε1 and _ε2 at two outermost points of the steel pipe of the CFT column are used to connect the values _ε1 and _ε2 with a straight line, and the inclination φ of said line is calculated. Based on this inclination φ, the eccentricity distance e from the axis, which is necessary to calculate the reaction force (axial force) at the bottom surface of the CFT-RC column, can be calculated.

In addition, in method 2 for calculating the eccentricity distance in a joint structure between a CFT column and an RC column, the strain measurements _ε1 , _ε2 at two outermost points of the steel pipe of the CFT column and the strain _ε0 at the center of the measurements _ε1 , _ε2 are used to connect the values of _ε0 and _ε1 , and the values of _ε0 and _ε2 with lines, respectively, and the inclinations _φ1 , _φ2 of each line are found. Based on these inclinations _φ1 , _φ2 , the eccentricity distance e from the axis, which is necessary when finding the reaction force (axial force) at the bottom of the CFT-RC column, can be calculated.

The above describes one embodiment of the method for calculating the eccentricity distance in a joint structure between a CFT column and an RC column according to the present invention, but the present invention is not limited to the above embodiment and can be modified as appropriate without departing from the spirit of the invention.

2 CFT column 3 RC column 5 Steel pipe 20 Joint structure between CFT column and RC column e Eccentricity distance

Claims (2)

A method for calculating an eccentric distance in a joint structure between a CFT column and an RC column, the method comprising the steps of: calculating an eccentric distance, which is a distance from an axis required for calculating a reaction force at the bottom surface of a column where a CFT column is joined to an RC column arranged above the CFT column;
From the strain measurements ε ₁ and ε ₂ at the two outermost points of the steel pipe of the CFT column, the values of ε ₁ and ε ₂ are connected by a straight line, and the slope φ of the straight line is calculated by the following formula (1-1):

Assuming that the plane defined by the straight line is maintained until the end, from the following formula (1-2),

A method for calculating the eccentricity distance in a joint structure between a CFT column and an RC column, which calculates the eccentricity distance e. A method for calculating an eccentric distance in a joint structure between a CFT column and an RC column, the method comprising the steps of: calculating an eccentric distance, which is a distance from an axis required for calculating a reaction force at the bottom surface of a column where a CFT column is joined to an RC column arranged above the CFT column;
From the strain measurements ε ₁ and ε ₂ at the two outermost points of the steel pipe of the CFT column and the strain ε ₀ at the center between the measurements ε ₁ and ε ₂ , the values of ε ₀ and ε ₁ and the values of ε ₀ and ε ₂ are connected by lines, respectively, and the slopes φ ₁ and φ ₂ of the lines are calculated by the following formulas (2-1a) and (2-1b),

Assuming that the plane defined by each of the straight lines is maintained until the end, from the following formula (2-2),

A method for calculating the eccentricity distance in a joint structure between a CFT column and an RC column, which calculates the eccentricity distance e.

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