Method for estimating the natural period of low-rise buildings

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 for estimating a natural period of a low-rise steel-framed building 10 is provided, the method involving estimating the natural period T of the low-rise building 10 using the following estimation formula (A).SELECTED DRAWING: Figure 1

Description

Technical Field

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

Background Art

[0002] In buildings (or structures), there are always minute vibrations caused by so-called environmental vibrations such as the minute vibrations of the earth itself, traffic vibrations caused by the running of vehicles including railways, vibrations during the operation of factory equipment, and vibrations caused by wind loads. During an earthquake, vibrations with a larger amplitude than the minute vibrations generally occur according to the scale of the seismic motion. In the construction of buildings, it is important to consider not only the examination of building vibrations during an earthquake but also the presence or absence of building damage and the impact on the living environment at the above-mentioned minute vibration level. At that time, it is necessary to calculate the (horizontal) fundamental natural period (or natural period) of the building. Since the ground on which the building is erected is likely to vibrate at the natural period of the ground due to this environmental vibration, if a design can be made to shift the natural period of the ground and the natural period of the building, it is possible to avoid the resonance of the minute vibrations of the building caused by environmental vibrations and to reduce the minute vibrations as much as possible.

[0003] By the way, regarding mid-rise buildings, super high-rise buildings, etc., the natural period of the building at the minute vibration level is generally almost equal to the natural period calculated by structural calculation. In this structural calculation, first, a two-dimensional model or a three-dimensional model for mid-rise buildings, etc. is created in a computer, and various static loads and dynamic loads are applied to this analysis model to verify the structural stability of the analysis model. The analysis model used for such structural calculation is formed by connecting columns and beams, which are structural frameworks (these are called structural members or primary members that make up the structural framework), as beam members having rigidity and weight. That is, for example, in the design of mid-rise buildings or super high-rise buildings of 6 floors or more, since the analysis results are generally dominated by the structural framework, secondary members such as outer walls, partition walls (including boundary walls), and intermediate columns (members other than primary members, non-structural members, etc.) are generally not included in the analysis model.

[0004] However, in low-rise buildings such as those with five stories or less (e.g., typical detached houses or low-rise apartment buildings), the influence of secondary members other than the structural frame on the overall rigidity of the building becomes significant. Depending on the building specifications, the rigidity of the building may be dominated by the secondary members, and in some cases, the rigidity of the structural frame can be ignored, as identified by the inventors.

[0005] The Building Standards Act stipulates an estimation formula for the primary natural period (Ministry of Land, Infrastructure, Transport and Tourism Notification No. 597 of 2007). This estimation formula uses the height of the building and the structural specifications of the building (steel frame, reinforced concrete, etc.) as variables. Specifically, the natural period is given as T=h(0.02+0.01α), where h is the height of the building and α is 1 for steel frame and 0 for reinforced concrete. In addition, there are other primary approximation formulas, such as T=0.0202h, proposed by the Architectural Institute of Japan (AIJ).

[0006] These estimation formulas are applied uniformly to buildings ranging from low-rise to high-rise. However, according to the inventors, while they show approximate validity in estimating the natural period of high-rise buildings where vibrations are significant during major earthquakes, there is room for improvement in estimating the natural period of low-rise buildings where vibrations are significant during normal microtremors.

[0007] Regarding methods for estimating (predicting) the natural frequency (reciprocal of the natural period) of such low-rise buildings, a prediction method has been proposed in which the natural frequency Va of the building's frame during an earthquake is calculated based on the results of structural calculations for the building, a correction coefficient C is calculated based on the building's external shape and the amount of openings on the first floor of the building, and the natural frequency Vb of the building during small vibrations is calculated based on the natural frequency Va of the building's frame during an earthquake and the correction coefficient C (see, for example, Patent Document 1). [Prior art documents] [Patent Documents]

[0008] [Patent Document 1] Japanese Patent Publication No. 2004-27679 [Overview of the Initiative] [Problems that the invention aims to solve]

[0009] However, the method for predicting the natural frequency of a building described in Patent Document 1 is a prediction method that relies on structural calculations, and therefore requires time and effort to predict the natural frequency.

[0010] This invention has been made in view of the above problems, and aims to provide a method for estimating the natural period of a low-rise building that can estimate the natural period of a low-rise building simply and with high accuracy without requiring structural calculations. [Means for solving the problem]

[0011] To achieve the above objective, one aspect of the method for estimating the natural period of a low-rise building according to the present invention is: A method for estimating the natural period of a low-rise building constructed of steel frame, The natural period T of the aforementioned low-rise building is estimated using the following estimation formula (A).

[0012]

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[0013] According to this embodiment, by setting only the height and a portion of the external dimensions of a low-rise steel-frame building, the natural frequency of a low-rise steel-frame building can be estimated with high accuracy, replacing the estimation formula for the primary natural frequency stipulated in the Building Standards Act, which is conventionally applied and has been deemed valid for estimating the natural frequency of high-rise buildings. Here, since the primary natural frequency of a building is the reciprocal of the primary natural frequency, the primary natural frequency of a building is similarly determined by only the height and a portion of the external dimensions of the building.

[0014] The inventors focused on the fact that secondary members have a significant influence on low-rise buildings, as described above, and that the additional stiffness due to the exterior walls has a particularly large influence. Therefore, in addition to the height of the low-rise building, they expressed the elements of the exterior walls in terms of the building length in the natural vibration direction, and by setting these two variables, they aimed to estimate the natural period of a low-rise steel-frame building with high accuracy and simplicity. Here, regarding the "building length in the natural vibration direction," if there are multiple building lengths along the natural vibration direction of the low-rise building, the longest building length is applied.

[0015] The above estimation formula (A) has demonstrated that the natural period (or natural frequency) of a low-rise steel-frame building can be estimated with high accuracy. Thus, according to the low-rise building natural period estimation method of this embodiment, the natural period of a low-rise steel-frame building can be estimated with high accuracy without requiring any structural calculations of the building using a computer.

[0016] Furthermore, the method for estimating the natural period of a low-rise building according to this embodiment enables the rapid and simple estimation of the natural period of a low-rise building at an even earlier stage in the design process, for example, when only a rough sketch is available. If the natural period of the low-rise building can be estimated at this stage, and the natural period (or natural frequency) of the ground on which the low-rise building will be constructed is identified, for example, 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 carried out in a way that prevents the two from matching (preventing resonance). In other words, this method is clearly different from the time-consuming methods of past estimation and prediction methods, which involve determining the design of the low-rise building, modeling it in a computer, performing structural calculations, comparing the natural period based on the calculation results with the natural period of the ground, and if the natural periods of the two match, revising the design of the low-rise building and performing structural calculations again to confirm the natural period.

[0017] Furthermore, another aspect of the method for estimating the natural period of a low-rise building according to the present invention is: A method for estimating the natural period of a low-rise building constructed of steel frame, The natural period: T of the low-rise building is estimated using the following estimation formula (B).

[0018]

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[0019] According to this aspect, even by the estimation formula (B) in which the building length in the direction orthogonal to the natural vibration direction in the horizontal plane is used as a variable instead of the building length in the natural vibration direction in the estimation formula (A), the natural period of the low-rise building made of steel frame can be estimated with high accuracy. Here, regarding the "building length in the direction orthogonal to the natural vibration direction in the horizontal plane", when there are a plurality of building lengths along the direction orthogonal to the natural vibration direction of the low-rise building in the horizontal plane, the longest building length is applied.

Advantages of the Invention

[0020] As can be understood from the above description, according to the method for estimating the natural period of the low-rise building of the present invention, it is possible to estimate the natural period of the low-rise building simply and with high accuracy without requiring structural calculations.

Brief Description of the Drawings

[0021] [Figure 1] It is a perspective view of an example of a low-rise building to which the natural period estimation method according to the embodiment is applied. [Figure 2] It is a perspective view of another example of a low-rise building to which the natural period estimation method according to the embodiment is applied. [Figure 3A] It is a graph showing the correlation between the estimated natural period and the measured natural period by the estimation formula (announcement formula) of the natural period defined in the Building Standards Law. [Figure 3B] It is a graph showing the correlation between the estimated natural period and the measured natural period by the estimation formula (proposed formula) of the natural period by AIJ. [Figure 4A] It is a graph showing the correlation between the estimated natural period and the measured natural period when α = 0.02 in the estimation formula (A). [Figure 4B]This graph shows the correlation between the estimated natural period and the measured natural period when α = 0.025 in estimation formula (A). [Figure 4C] This graph shows the correlation between the estimated natural period and the measured natural period when α = 0.035 in estimation formula (A). [Figure 5A] This graph shows the correlation between the estimated natural period and the measured natural period when α = 0.02 in estimation formula (B). [Figure 5B] This graph shows the correlation between the estimated natural period and the measured natural period when α = 0.025 in estimation formula (B). [Figure 5C] This graph shows the correlation between the estimated natural period and the measured natural period when α = 0.035 in estimation formula (B). [Modes for carrying out the invention]

[0022] The method for estimating the natural period of a low-rise building according to the embodiment will be described below with reference to the attached drawings. In this specification and drawings, substantially identical components may be denoted by the same reference numerals to avoid redundant explanations.

[0023] [Method for estimating natural period according to an embodiment] First, the natural period estimation method according to the embodiment will be described with reference to Figures 1 to 3. Here, both Figures 1 and 2 are perspective views of an example of a low-rise building to which the natural period estimation method according to the embodiment is applied. Figure 3 is a graph showing the natural period estimation formula (official formula) stipulated in the Building Standards Act and the natural period estimation formula (proposed formula) by AIJ, plotted against the measured natural period of the low-rise building.

[0024] The natural period estimation method according to this embodiment is applicable to estimating the natural period of low-rise buildings with steel frames and five stories or less, but does not preclude its application to mid-to-high-rise buildings with six stories or more. However, as will be explained below, the accuracy of the natural period estimated when applied to low-rise buildings is very high, so it is preferable to apply the natural period estimation method according to this embodiment to low-rise buildings. Figures 1 and 2 both illustrate a three-story low-rise building as an example of a low-rise building with steel frames and five stories or less to which the natural period estimation method according to this embodiment is applied. Here, Figures 1 and 2 are diagrams to explain the general proportions of the low-rise building, and illustrations of doors, windows, roofs, balconies, etc. are omitted.

[0025] The low-rise steel-frame building 10 shown in Figure 1 is a three-story building with a rectangular shape in plan view and a height of H. On the other hand, the low-rise steel-frame building 20 shown in Figure 2 is a three-story building with an L-shape in plan view and a height of H. In both figures, in the plan view of low-rise buildings 10 and 20, the length along one side of the building is the building length in the direction of natural vibration: Wp, and the length of the other side of the building perpendicular to this in the horizontal plane is the building length in the direction perpendicular to the direction of natural vibration in the horizontal plane: Wo. In the illustrated examples, the settings of Wp and Wo may be reversed. Here, two representative low-rise buildings with typical plan view shapes are illustrated, but buildings with other plan view shapes, such as a U-shape, can also be subject to the estimation formula.

[0026] Here, referring to Figures 3A and 3B, we will consider the correlation between the estimated natural period and the measured natural period using the official formula and the AIJ proposed formula. Figure 3A is a graph showing the correlation between the estimated natural period and the measured natural period using the natural period estimation formula (official formula) stipulated in the Building Standards Act, and Figure 3B is a graph showing the correlation between the estimated natural period and the measured natural period using the natural period estimation formula (proposed formula) by AIJ. The measured values ​​are the natural periods of low-rise steel-frame buildings, mainly including low-rise buildings 10 and 20 with rectangular or L-shaped plan views. In Figures 3A and 3B, the graph in the 45-degree direction (Y=X graph) indicates a 100% correlation, and the error range is shown based on the dots around it (results of estimated and measured values). The coefficient of determination calculated for both the official formula and the AIJ proposed formula is 0.433, and the correlation coefficient is 0.658.

[0027] Figure 3A shows that the estimated natural period calculated using the official formula has an error dispersion of approximately -50% to +30% relative to the measured natural period. On the other hand, Figure 3B shows that the estimated natural period calculated using the AIJ-proposed formula has an error dispersion of significantly more than -30% to +50% relative to the measured natural period.

[0028] Thus, since neither the generally applied notification formula nor the AIJ proposed formula can be said to estimate the natural period of low-rise buildings (low-rise steel-frame buildings) with high accuracy, the inventors focused on the fact that secondary members have a large influence on the natural period of low-rise buildings, and in particular the influence of the additional stiffness due to the exterior walls, and decided to verify the influence of the planar shape and planar dimensions defined by the exterior walls.

[0029] Both the official format and the AIJ proposed format determine the period solely by the height of the building. However, in practice, it is generally known that the natural period of a building is proportional to the square root of the building's mass and inversely proportional to the square root of its stiffness, as shown in equation (C) below.

[0030]

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[0031] Here, we will verify equation (C) using the low-rise building 10 shown in Figure 1 as an example. If the mass is the value obtained by multiplying the volume of the building by the coefficient p, then M = p × Wp × Wo × H. Also, if the stiffness is the shear stiffness of the building, then this shear stiffness, including the coefficient q, becomes K = q × Wp × Wo × 1 / H. By substituting these into equation (C), the following estimation equation (D) is derived.

[0032]

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[0033] Estimation formula (D) is determined solely by the height of the building, and the official formula and the AIJ proposed formula are derived from the value of α.

[0034] Here, in the process of deriving estimation formula (D), it is assumed that the shear stiffness of the building is uniform. However, actual buildings do not have uniform stiffness in their cross-section, and especially in low-rise buildings, as mentioned above, the effect of additional stiffness due to the exterior walls is large. Therefore, when examining the natural period in the natural vibration direction, the shear stiffness is set to K = q' × Wo × 1 / H, and when examining the natural period in the direction perpendicular to the natural vibration direction on the horizontal plane, the shear stiffness is set to K = q' × Wp × 1 / H. By expanding these equations, the following estimation formulas (A) and (B) can be derived.

[0035]

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[0036]

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[0037] According to the present inventors, although the second coefficients β and γ differ slightly between estimation formula (A), which uses the building length in the natural vibration direction as a variable, and estimation formula (B), which uses the building length in a direction perpendicular to the natural vibration direction on the horizontal plane as a variable, the first variable α can be defined within a similar range in both formulas, and both can estimate the natural period of a low-rise building with high accuracy.

[0038] Both estimation formulas (A) and (B) do not use only height H as a variable, as in the official notification formula and the AIJ proposed formula, but rather use the unidirectional lengths Wh and Wo of the low-rise building as variables in addition to height H. It can be seen that the variables Wh and Wo, which are the unidirectional lengths of the low-rise building, are correction elements in the official notification formula and the AIJ proposed formula. Furthermore, as mentioned above, the unidirectional lengths Wh and Wo of the building are part of the length of the exterior wall, which is a secondary member that affects the natural period of the low-rise building, and can be said to be suitable elements for correcting the estimation formula for the natural period of the low-rise building.

[0039] Furthermore, regardless of whether estimation formula (A) or (B) is applied, the natural period of a low-rise building can be easily and quickly estimated by setting two elements: the height of the low-rise building: H, and the building length in the direction of natural vibration: Wp, or the building length in a direction perpendicular to the direction of natural vibration on the horizontal plane: Wo. Therefore, if the natural period of the ground has already been determined, the general shape of the low-rise building can be set in an early stage of design that does not resonate with the natural period of the ground.

[0040] As detailed below, the results of verification by the inventors have demonstrated that by applying estimation formulas (A) and (B), the natural period of low-rise steel-frame buildings can be determined with higher accuracy than the natural period calculated based on the conventionally applied notification formula and AIJ proposed formula.

[0041] Furthermore, by storing the above estimation formulas (A) and (B) in a computer and running a program that causes the computer to execute estimation formulas (A) and (B), it becomes possible to quickly calculate the natural period of a low-rise steel-frame building. Although not shown in the diagram, this computer has a CPU (Central Processing Unit), RAM (Random Access Memory), ROM (Read Only Memory), HDD (Hard Disk Drive), NVRAM (Non-Volatile RAM), input devices, display devices, etc., and these parts are connected by a bus so that they can communicate with each other. ROM stores various programs and data used by those programs. RAM is used as a memory area for loading programs and as a work area for loaded programs. The CPU realizes various functions by processing the programs loaded into RAM. HDD stores programs and various data used by those programs. NVRAM stores various setting information.

[0042] For example, when a designer inputs various conditions for a low-rise building (building height: H, building length in the natural vibration direction: Wp, or building length in the direction perpendicular to the natural vibration direction on the horizontal plane: Wo) into the input device, estimation formulas (A) and (B) stored in ROM are read into RAM. Based on these input conditions, the CPU reads estimation formulas (A) and (B) into RAM, and the calculation using the estimation formulas is performed to calculate the natural period of the target low-rise steel-frame building.

[0043] [Experiments and results verifying the accuracy of estimation formulas (A) and (B)] The inventors applied the estimation formulas (A) and (B) described above to numerous existing low-rise buildings to calculate their natural periods, and also measured the natural periods of these existing low-rise buildings. They then conducted an experiment to verify the correlation between these estimated natural periods and the measured natural periods. In this experiment, all the buildings examined were steel-framed and low-rise buildings ranging from three to five stories in height. The shapes of the buildings examined were generally those of low-rise buildings 10 and 20 shown in Figures 1 and 2.

[0044] Figures 4A to 4C are graphs showing the correlation between the estimated natural period using estimation formula (A) and the measured natural period, respectively, for α = 0.02, 0.025, and 0.035. On the other hand, Figures 5A to 5C are graphs showing the correlation between the estimated natural period using estimation formula (B) and the measured natural period, respectively, for α = 0.02, 0.025, and 0.035. As already explained, in Figures 4 and 5, the graph at a 45-degree angle (Y=X graph) indicates a 100% correlation, and the dots around it (results of estimated and measured values) indicate the error range. The coefficients of determination calculated for estimation formulas (A) and (B) are 0.610 and 0.497, respectively, and the correlation coefficients are 0.781 and 0.705, respectively.

[0045] From Figures 4A to 4C, it has been determined that when α = 0.02, the error is concentrated around +30%, when α = 0.035, the error is concentrated around -30%, and when α = 0.025, the error is concentrated around ±10%.

[0046] Therefore, all of these have a small error range compared to the estimated natural period using the official formula and the AIJ proposed formula shown in Figures 3A and 3B, and the error is minimized around α = 0.025. For this reason, the range of α in estimation formula (A) is set to the range of 0.02 to 0.035.

[0047] On the other hand, as can be seen from Figures 5A to 5C, when α = 0.02, the error is concentrated around +30%, when α = 0.035, the error is concentrated around -30%, and when α = 0.025, the error is concentrated around ±10%.

[0048] Therefore, in both cases, the error range is small compared to the estimated natural period using the official formula and the AIJ proposed formula shown in Figures 3A and 3B, and the error is minimized around α = 0.025. Thus, in estimation formula (B), similar to estimation formula (A), the range of α is set to the range of 0.02 to 0.035.

[0049] The results of this experiment demonstrate that, in estimating the natural period of low-rise steel-framed buildings, applying estimation formula (A) or (B) can achieve high accuracy and rapid estimation of the natural period.

[0050] Furthermore, other embodiments may be used in which other components are combined with the configurations listed in the above embodiments, and the present invention is not limited in any way to the configurations shown herein. In this regard, modifications can be made without departing from the spirit of the present invention, and can be appropriately determined according to the application form. [Explanation of Symbols]

[0051] 10,20: Low-rise buildings

Claims

1. A method for estimating the natural period of a low-rise building constructed of steel frame, A method for estimating the natural period of a low-rise building, characterized by estimating the natural period T of the low-rise building using the following estimation formula (A). [Math 1]

2. A method for estimating the natural period of a low-rise building constructed of steel frame, A method for estimating the natural period of a low-rise building, characterized by estimating the natural period T of the low-rise building using the following estimation formula (B). [Math 2]

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