Method of estimating natural period of low-rise building

Abstract

To provide a low-rise building natural period estimation method which enables simple and accurate estimation of a natural period of a low-rise building without the need for structural calculation.SOLUTION: A low-rise building natural period estimation method is provided, involving estimating the natural period of a low-rise building using a formula below.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a method for estimating the natural period of a low-rise building. [Background technology]

[0002] A building (or structure) is subject to constant vibrations caused by so-called environmental vibrations, such as the earth's own vibrations, traffic vibrations caused by trains and other vehicles, vibrations during the operation of factory equipment, and vibrations caused by wind loads. During an earthquake, vibrations with a larger amplitude than the constant vibrations generally occur depending on the magnitude of the earthquake motion. When constructing a building, it is important to consider not only the vibrations of the building during an earthquake, but also the presence or absence of building damage at the constant vibration levels and their impact on the living environment, and in that case, it is necessary to calculate the (horizontal) primary natural period of the building (hereinafter, the primary natural period and the natural period are synonymous). The ground on which a building stands is prone to vibrating at a period that is specific to the ground due to this environmental vibration, so if a design can be made to shift the natural period of the ground from the primary natural period of the building, it will be possible to avoid resonance of the building's constant vibrations caused by environmental vibrations, and to reduce the constant vibrations as much as possible.

[0003] Incidentally, for mid- to high-rise buildings and super-high-rise buildings, the primary natural period of the building at the microtremor level is generally almost equal to the primary natural period calculated by structural calculation. In this structural calculation, first, a two-dimensional model or a three-dimensional model of the mid- to high-rise building is created in a computer, and various static and dynamic loads are applied to this analytical model to verify the structural stability of the analytical model. The analytical model used in such structural calculation is formed by connecting columns and beams (which are called structural members or primary members that constitute the structural body) that are the structural body as beam members with rigidity and weight. That is, in the design of a mid- to high-rise building or super-high-rise building with six or more floors, for example, secondary members (members other than the primary members, also called non-structural members) such as exterior walls, partition walls (including parting walls), and studs are generally not included in the analytical model, since the analytical results are generally governed by the structural body.

[0004] However, in low-rise buildings, such as those with five stories or less (for example, ordinary detached houses and low-rise apartment buildings), the influence of secondary members such as exterior walls other than the structural frame on the rigidity of the entire building becomes large, and the inventors have identified that, depending on the building specifications, the rigidity of the building is dominated by the secondary members, and in some cases the rigidity of the structural frame can be ignored. Therefore, when calculating the natural period of a low-rise building, it is necessary to estimate the natural period taking into account the influence of the secondary members.

[0005] Regarding a method of estimating (predicting) the natural period (natural frequency in Patent Document 1) of such a low-rise building, a prediction method has been proposed in which the natural frequency Va of the building's skeleton during an earthquake is calculated based on the results of structural calculations of the building, a correction coefficient C is calculated based on the building's external shape and the number of openings in the first floor of the building, and the natural frequency Vb of the building during micro-vibrations is calculated based on the natural frequency Va of the building's skeleton during an earthquake and the correction coefficient C (see, for example, Patent Document 1). [Prior art documents] [Patent documents]

[0006] [Patent Document 1] JP 2004-27679 A Summary of the Invention [Problem to be solved by the invention]

[0007] However, the method for predicting the natural frequency of a building described in Patent Document 1 is a prediction method that presupposes structural calculations, and therefore requires a lot of time and effort to predict the natural period of a low-rise building.

[0008] The present invention has been made in consideration of the above-mentioned problems, and aims to provide a method for estimating the natural period of a low-rise building, which can estimate the natural period of a low-rise building simply and with high accuracy without the need for structural calculations. [Means for solving the problem]

[0009] In order to achieve the above object, one aspect of a method for estimating a natural period of a low-rise building according to the present invention includes: The method is characterized in that the natural period of the low-rise building is estimated using the following equation (X):

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[0010] According to this aspect, the natural period of a low-rise building can be estimated simply and accurately based on a new estimation formula that takes into account the building's rigidity (rigidity of both primary and secondary members), which is a particularly important factor for low-rise buildings, in addition to the estimation formula for the primary natural period prescribed in the Building Standards Act. Here, low-rise buildings include low-rise buildings made of steel frame construction and low-rise buildings made of reinforced concrete.

[0011] The Building Standards Act prescribes an estimation formula for the primary natural period (Ministry of Land, Infrastructure, Transport and Tourism Notification No. 597 of 2007), and this estimation formula uses the height of the building and the structural specifications of the building (steel frame construction, reinforced concrete construction, etc.) as variables. Therefore, if the structural specifications are set to steel frame construction or reinforced concrete construction, the primary natural period of the building will be determined only by the height of the building.

[0012] However, in reality, as is clear from the well-known relationship that the primary natural period of a building is inversely proportional to the square root of the building's rigidity, in order to accurately estimate the primary natural period of a building, it is necessary to evaluate the influence of the building's rigidity as well, and in the case of a low-rise building, the accuracy of the estimation formula can be further improved by taking into account the influence of secondary members when estimating the primary natural period. Therefore, in the estimation method of this aspect, an estimation formula is used that takes into account the rigidity of secondary members such as exterior walls in addition to the rigidity of the primary members.

[0013] It has been demonstrated that the natural period of a low-rise building can be estimated with high accuracy by the above estimation formula (X). Thus, according to the low-rise building natural period estimation method of this aspect, the natural period of a low-rise building can be accurately calculated without requiring any structural calculations of the building using a computer.

[0014] The method for estimating the natural period of a low-rise building according to the present embodiment enables the calculation of the natural period of a low-rise building quickly and easily at an even earlier stage in the design stage of a new low-rise building, for example, at a stage when only a rough sketch exists. If the natural period of the low-rise building can be calculated at this stage, and for example, if the natural period of the ground on which the low-rise building is to be constructed has been specified, the degree of agreement between the two can be confirmed in a short time, and the initial design of the low-rise building can be performed without the two matching (without resonance).

[0015] In other words, this method is clearly different from the time-consuming method used in the past, in which the design of a low-rise building was decided, this was modeled in a computer, structural calculations were performed, and the natural period based on the calculation results was compared with the natural period of the ground. If the two natural periods match, the design of the low-rise building was revised and re-structural calculations were performed to confirm the natural period. Effect of the Invention

[0016] As can be understood from the above description, the method for estimating the natural period of a low-rise building of the present invention makes it possible to estimate the natural period of a low-rise building easily and with high accuracy, without the need for structural calculations. [Brief description of the drawings]

[0017] [Figure 1] 1 is a perspective view illustrating an example of a low-rise building to which a natural period estimation method according to an embodiment is applied. FIG. [Diagram 2] This is a plot of the actual measured primary natural period against an estimated graph of the primary natural period of a steel-framed building based on the estimation formula (notification formula) prescribed in the Building Standards Act and the estimation formula by the Architectural Institute of Japan. [Diagram 3] 1 is a correlation graph between the estimated natural period based on the estimation formula (X) and the actually measured natural period. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0018] Hereinafter, a method for estimating the natural period of a low-rise building according to an embodiment will be described with reference to the accompanying drawings. In this specification and the drawings, substantially identical components are designated by the same reference numerals, and duplicated descriptions may be omitted.

[0019] [Method for estimating the natural period of a low-rise building according to the embodiment] First, an example of a method for estimating the natural period of a low-rise building according to an embodiment will be described with reference to Fig. 1 and Fig. 2. Fig. 1 is a perspective view that shows a schematic diagram of an example of a low-rise building to which the method for estimating the natural period according to the embodiment is applied. Fig. 2 is a diagram in which an actually measured primary natural period is plotted against an estimated graph relating to the primary natural period of a steel-framed building based on an estimation formula (notification formula) prescribed in the Building Standards Act and an estimation formula by the Architectural Institute of Japan.

[0020] The low-rise building 10 shown in Fig. 1 is a simulation of a low-rise building of about one to five stories in the shape of a rectangular parallelepiped. Actual low-rise buildings have various shapes in plan view and side view, such as an L-shape or a convex shape in plan view, but the method for estimating the natural period according to the embodiment is preferably used for quickly and easily calculating the natural period of a low-rise building without requiring structural calculations in the early stage of designing a new low-rise building, for example, when there are only rough sketches, so that a low-rise building with a simple shape as shown in Fig. 1 may be used for calculating the natural period.

[0021] The natural period estimation method according to the embodiment is applied to estimating the natural period of a low-rise building having five floors or less, but does not exclude application to medium- to high-rise buildings having six floors or more. However, as will be described below, the accuracy of the estimated natural period is very high when applied to a low-rise building, and therefore it is desirable to apply the natural period estimation method according to the embodiment to a low-rise building.

[0022] The low-rise building 10 may be a steel-framed building or a reinforced concrete building.

[0023] A low-rise building 10 shown in FIG. 1 has a rectangular parallelepiped shape, with Wp as the length in the vibration direction, Wo as the length in the direction perpendicular to the vibration direction, and H as the height.

[0024] For example, a low-rise steel-framed building 10 is formed by fixing primary components, including columns made of shaped steel materials such as H-shaped steel or square steel pipes, and beams made of shaped steel materials such as H-shaped steel, with bolt connections or the like to form a structural body, and then attaching secondary components such as walls (exterior walls, partition walls, etc.) and floors to the structural body.

[0025] In general, the Building Standards Act prescribes the estimation formula for the (horizontal) primary natural period (Ministry of Land, Infrastructure, Transport and Tourism Notification No. 597 of 2007) as shown in the following formula (Q1).

[0026]

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[0027] In steel-framed buildings, α in equation (Q1) can be set to 1, and therefore the formula proposed in the Building Standards Act, shown in Figure 2, becomes T = 0.03H.

[0028] On the other hand, the formula proposed by the Architectural Institute of Japan (AIJ, a general incorporated association) for steel-framed buildings is T = 0.0202H, as shown in Figure 2.

[0029] FIG. 2 plots actual measurements made by the inventors for a three-story building (H is about 10 m), a four-story building (H is about 12 m), and a five-story building (H is about 15 m).

[0030] Looking at the relationship between the measured values ​​and the two equations, it can be seen that the measured values ​​are not biased toward either of the two equations, but are scattered toward both equations.

[0031] This is because in both formulas, the natural period is uniquely determined by the height of a building, and they are (presumably) primarily intended for calculating the natural period of high-rise or ultra-high-rise buildings, whose height has a significant effect on the natural period.

[0032] However, in reality, as is clear from the well-known relationship that the primary natural period of a building is inversely proportional to the square root of its stiffness, in order to accurately estimate the primary natural period of a building, it is necessary to evaluate the effect of the stiffness of the building. Furthermore, in the case of a low-rise building 10 shown in the figure, the inventors have identified that not only the stiffness of the primary members but also the stiffness of the secondary members greatly affect the primary natural period.

[0033] Therefore, below, we derive an estimation equation for the natural period of a low-rise building by expanding the known general equation while taking into account the stiffness of each of the primary and secondary members.

[0034] It is generally known that the primary natural period of a building is proportional to the square root of the reciprocal of the building's stiffness, as shown in the following equation (Q2).

[0035]

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[0036] In the well-known general formula, the denominator in the square root is simply expressed as "K", but in equation (Q2), the stiffness of a building is expressed as the sum of the stiffness of the primary member: Ks and the stiffness of the secondary member: Kw.

[0037] Equation (Q3) can be derived by expanding equation (Q2) as follows:

[0038]

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[0039] Comparing equation (Q3) with the two equations shown in Figure 2, it is clear that in the two equations, the natural period is determined solely by the height: H, whereas equation (Q3) indicates that the mass of the building and the stiffness of each of the primary and secondary members contribute to the natural period.

[0040] As explained below, experiments to verify the accuracy of the estimation formula (Q3) have demonstrated that this estimation formula is capable of estimating the natural period of a low-rise building with high accuracy. Therefore, we decided to propose a method for estimating the natural period of a low-rise building using this estimation formula.

[0041] Furthermore, by storing the above formula (X) (or formula (Q3)) in a computer and running a program that causes the computer to execute formula (X), it becomes possible to quickly calculate the natural period of a low-rise building.

[0042] Although not shown, this computer has a CPU (Central Processing Unit), RAM (Random Access Memory), ROM (Read Only Memory), HDD (Hard Disc Drive), NVRAM (Non-Volatile RAM), an input device, a display device, etc., and these components are connected via a bus so that they can communicate with each other. The ROM stores various programs and data used by the programs. The RAM is used as a storage area for loading programs and a work area for the loaded programs. The CPU realizes various functions by processing the programs loaded into the RAM. The HDD stores programs and various data used by the programs, etc. The NVRAM stores various setting information, etc.

[0043] For example, when a designer inputs various conditions for a low-rise building into an input device (the height of the low-rise building, the length of the low-rise building in the direction perpendicular to the vibration direction: Wo, various coefficients α1, β, γ, etc.), equation (X) stored in ROM is read into RAM. Based on these input conditions, etc., equation (X) is read into RAM by the CPU, and the estimation equation is executed to calculate the natural period of the target low-rise building.

[0044] According to this method for estimating the natural period, the natural period can be calculated quickly without detailed structural calculations of the low-rise building, as long as, for example, the height of the low-rise building and the length in the direction perpendicular to the vibration direction (Wo) and the various coefficients α1, β, and γ are set. Therefore, if the natural period of the ground has already been specified, the height (H) and width (Wo) of the low-rise building, as well as the specifications of the exterior walls, can be set in an early stage of the design of the low-rise building in a form that does not resonate with the natural period of the ground.

[0045] [Experiments to verify the accuracy of the estimation formula (X) and their results] The inventors applied the above-mentioned estimation formula (X) to many existing low-rise buildings to calculate the estimated natural periods, and also measured the natural periods of existing low-rise buildings, conducting experiments to verify the correlation between these estimated natural periods and the actually measured natural periods.

[0046] In this experiment, all of the buildings to be verified were steel-framed, low-rise buildings of 3 to 5 stories. The experimental results are shown in Figure 3, which is a correlation graph between the estimated natural period based on the estimation formula (X) and the actually measured natural period.

[0047] As can be seen from Figure 3, the measured natural periods are concentrated within a range of approximately ±10% of the estimated formula, demonstrating that the estimated formula (X) estimates the natural period of low-rise buildings with extremely high accuracy.

[0048] In addition, the configurations and the like of the above-mentioned embodiment may be combined with other components to form other embodiments, and the present invention is not limited to the configurations shown here. In this respect, the present invention can be modified within the scope of the gist of the present invention, and can be appropriately determined according to the application form. [Explanation of symbols]

[0049] 10: Low-rise building

Claims

[Claim 1] A method for estimating a natural period of a low-rise building, comprising: A method for estimating the natural period of a low-rise building, comprising estimating the natural period of the low-rise building using the following equation (X): [0010]

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