Method for assessing seismic displacement response of buildings

Abstract

To provide a method for accurately assessing a seismic displacement response of buildings in a further short time.SOLUTION: A method includes: calculating a pseudo velocity response spectrum pSV and an energy spectrum VE in a building with a period T and an attenuation constant h; dividing the pseudo velocity response spectrum pSV by an energy spectrum VE to calculate an index F of repetition characteristics of seismic motion; calculating the number of impulses Np from a relation between the index F of the repetition characteristics of the seismic motion and the number of impulses Np; setting an impulse amplitude V using equation (1) from a condition that total input energy input to the building due to the seismic motion matches; selecting the equivalent impulse seismic motion that maximizes an interlayer displacement response when a design seismic motion group is replaced with each equivalent impulse seismic motion; and assessing a seismic displacement response of the building using the equivalent impulse seismic motion.SELECTED DRAWING: None

Description

Technical Field

[0001] The present invention relates to a method for evaluating the seismic displacement response of a building.

Background Art

[0002] In the seismic design of important buildings such as super high-rise buildings and buildings with seismic isolation, it is common to perform seismic response analysis using a plurality of design ground motions. Here, the design ground motions are often selected by the designer from among the ground motions (site waves) that are assumed to occur in the area based on past observation records and current research results. In order to perform a robust design against the uncertainty of ground motion characteristics, it is desirable to perform time history response analysis considering many ground motions and evaluate the response behavior of the building. However, since the analysis takes time depending on the number of ground motions and the length of the duration, there are time constraints in cases where a complex analysis model is handled or when a large number of analyses are repeated for optimal design, and sufficient consideration may not be possible.

[0003] Simplifying the ground motion used in the seismic response analysis of a building is useful for efficiently evaluating the response behavior of the building while considering ground motions with various characteristics. Non-Patent Document 1 proposes a method for evaluating the seismic displacement response of a building by replacing the ground motion with two impulses having the same total input energy.

Prior Art Documents

Non-Patent Documents

[0004]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] This method has been shown to be able to accurately simulate the inter-story displacement response even by replacing it with pulsed ground motion. On the other hand, when this method is applied to general ground motion, the response to two impulses becomes very large compared to the response to ground motion, resulting in the problem of over-design.

[0006] The present invention has been made in view of the above circumstances, and provides a method for accurately evaluating the seismic displacement response of a building in a shorter time.

Means for Solving the Problems

[0007] In order to achieve the above object, the present invention employs the following means. A method for evaluating the seismic displacement response of a building according to the present invention calculates the pseudo-velocity response spectrum p S V and the energy spectrum V E in a building with a period T and a damping constant h, divides the pseudo-velocity response spectrum p S V by the energy spectrum V E to calculate an index F of the repetitive characteristics of ground motion, calculates the number of impulses N p from the relationship between the index F of the repetitive characteristics of ground motion and the number of impulses N p sets the impulse amplitude V using Equation (A) under the condition that the total input energy input to the building by ground motion is the same, selects the equivalent impulse ground motion that maximizes the inter-story displacement response when replacing the design ground motion group with each equivalent impulse ground motion, and evaluates the seismic displacement response of the building using the equivalent impulse ground motion.

[0008]

Equations

Advantages of the Invention

[0009] According to the method for evaluating the seismic time-displacement response of a building according to the present invention, the seismic time-displacement response of the building can be evaluated accurately in a shorter time.

Brief Description of the Drawings

[0010]

Figure 1

Figure 2

Figure 3

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Figure 5

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Figure 8

Figure 9

Modes for Carrying Out the Invention

[0011] A method for evaluating the seismic displacement response of a building according to the first embodiment of the present invention will be described with reference to the drawings. The method for evaluating the seismic displacement response of the building according to this embodiment is a method of replacing the seismic motion with an impulse seismic motion for evaluation. Hereinafter, a method of replacing the seismic motion with an equivalent impulse seismic motion and an example of a design method using the equivalent impulse seismic motion will be described.

[0012] 1. Method of replacing seismic motion with equivalent impulse seismic motion <Overview of impulse seismic motion> FIG. 1 is a conceptual diagram of an analysis using impulse seismic motion. As shown in FIG. 1, the impulse is input as ground motion acceleration, and the impulses after the second one are input in the direction opposite to the previous impulse at the resonance timing of the building. This timing is known to coincide with the timing when the story shear force of the first story of the building becomes zero. When the building is elastic, it approximately coincides with the value of 1 / 2 of the first natural period T 1 of the building (T 0 ≒ T 1 / 2).

[0013] <Repeated characteristics of seismic motion and setting of number of impulses N p > The repeated characteristics are defined using impulse seismic motion composed of a combination of a plurality of impulses. The ground motion acceleration a(t) of the impulse seismic motion is expressed as in Equation (1) with the acceleration amplitude of the impulse being A and the impulse interval being T 0 .

[0014]

Equation

[0015] Here, δ(t) represents the Dirac delta function. Also, N p represents the number of impulses.

[0016] The index F(T, h) of the repetitive characteristics of ground motion in terms of the period T and the decay constant h is expressed by the ratio of the pseudo-velocity response spectrum p S V (T, h) and the value V E of the energy spectrum at the period T and the decay constant h, with reference to the methods in Document 2 and Document 3 below.

[0017]

Equation

[0018] · Document 2: Hiroshi Akiyama, Haruyuki Kitamura: Correspondence between Energy Spectrum and Velocity Response Spectrum, Transactions of the Architectural Institute of Japan, Structural Series, No. 608, pp. 37 - 43, 2006 · Document 3: Atsuko Kogetsu, Haruyuki Kitamura, Keisuke Yoshie, Toshiaki Sato: Qualitative Evaluation of f-Value of Long-Period Ground Motion for Design Ground Motion, Transactions of the Architectural Institute of Japan, Vol. 77, No. 674, pp. 575 - 584, 2012

[0019] Figure 2 shows the relationships between (a) the number of impulses N 2 , the impulse interval T 0 = 1.5 s, the natural period T = 3 s, and h = 0.02, 0.05, and p S p ; (b) N V and V p ; and (c) N E and F = p S p / V V . The time step in the analysis was set to 0.005 s. E

[0020] As shown in Figure 2, as the number of impulses N p increases, the value of V E increases while the value of p S V converges to a constant value. Therefore, the relationship between the number of impulses N p and the value of F is that the value of F decreases monotonically as the number of impulses N p increases.

[0021] <Method for Setting Impulse Amplitude V of Equivalent Impulse Ground Motion> The variables of impulse ground motion are "impulse interval T 0 ", "impulse amplitude V", and "number of impulses N p ". Among these, since the impulse interval T 0 is always input at the resonance timing of the building, it is a fixed value according to the building model and input level.

[0022] The impulse interval T 0 At the corresponding period (T = 2T 0 ), the impulse ground motion when the total input energy of the ground motion and the impulse ground motion coincides is called the equivalent impulse ground motion. In the method of Non-Patent Document 1, since it is limited to two impulses, the number of impulses N p = 2. At this time, the impulse amplitude V of the equivalent impulse ground motion is defined as in the following formula (3).

[0023]

Equation

[0024] In this embodiment, the number of impulses N p is variable. The velocity v n generated in the single-degree-of-freedom system immediately before inputting the nth impulse (amplitude V) to the single-degree-of-freedom system with mass m and damping constant h is expressed by formula (4).

[0025]

Equation

[0026] Also, the energy E n input by n impulses (amplitude V) is expressed by formula (5) using v n in formula (4).

[0027]

Equation

[0028] Based on the condition that Equation (5) is consistent with the total input energy due to ground motion, the impulse amplitude V of the equivalent impulse ground motion can be set according to the number of impulses N P as appropriate.

[0029] <Relationship between the number of impulses and the maximum inter-story displacement response> With the total input energy constant, when the equivalent impulse ground motion with the number of impulses N p is input into a single-degree-of-freedom system, let the maximum inter-story displacement response be δ Np and, when the equivalent impulse ground motion with the number of impulses N p = 2 is input into a single-degree-of-freedom system, let the maximum inter-story displacement response be δ 2 and the ratio of δ Np be expressed as in Equation (6).

[0030]

Equation

[0031] Figure 3 shows the displacement responses (a) when the number of impulses N p = 2 and (b) when the number of impulses N p = 12 under the condition of constant total input energy.

[0032] Figure 4 shows the relationship between the number of impulses N p and the normalized maximum inter-story displacement response α. From Figure 4, the larger the number of impulses N p , the smaller the normalized maximum inter-story displacement response α. This is due to the fact that the larger the number of impulses N p , the smaller the impulse amplitude V under the condition of constant total input energy. Also, this relationship is independent of the natural period of the single-degree-of-freedom system. In the case of N p = 12 shown in Figure 3(b), α = 0.83, but from the relationship between N p and α, the evaluation of the response value due to the impulse ground motion with N p = 2 in Non-Patent Document 1 pshowed that there is a risk of being excessive for large ground motions.

[0033] 2. Examples of design methods using equivalent impulse ground motions Here, an example of building design considering the variation in the phase characteristics of ground motions is shown. <Target analysis model> Figure 5 is a diagram showing the analysis model. As shown in Figure 5, a 30-story steel frame model is taken as the analysis target. The mass is 1000×10 3 kg for each floor. The stiffness of each floor is set to a trapezoidal distribution such that the stiffness of the 30th floor is 1 / 3 of the stiffness of the 1st floor, and the fundamental natural period is set to 3 seconds. At this time, the stiffness of the 30th floor is 7.17×10 8 N / m, and the stiffness of the 1st floor is 2.15×10 9 N / m. The floor height of each floor is 3.5 m. Also, the damping coefficient of each floor is given by stiffness-proportional damping such that the first damping constant is 0.02. Note that the nonlinearity of each floor is not considered. The above design flow using impulse ground motions is shown in Figure 6.

[0034] <Setting of design ground motion group> To consider the variation in the phase characteristics of ground motions, multiple ground motions are targeted. To equalize the magnitudes of the multiple ground motions, 10 types of ground motions fitted to the acceleration response spectrum at the notification level 2 were created. The considered phase characteristics are shown in Figure 7. These ground motions are referred to as the "design ground motion group".

[0035] <Setting of design equivalent impulse ground motion> Using the relationship between the number of impulses N p shown in Figure 4 and α, the ground motion that results in the largest inter-story displacement response when each ground motion in the design ground motion group is replaced with its equivalent impulse ground motion is selected. The number of impulses N p of each ground motion, N p -based α, V at T = 3 s E and α times V EThe values multiplied by are shown in Fig. 8 respectively. From Fig. 8, it can be judged that the response due to the ground motion No. 8 is the largest among the responses due to the equivalent impulse ground motion. The impulse number N of the ground motion No. 8 p is 28. Using Equation (5), the value of the impulse amplitude V is 10.6 cm / s. In this example, since the floor height of each floor is constant, the relationship of α based on the inter-story displacement response can be directly applied.

[0036] <Analysis Results> Fig. 9 shows the maximum inter-story deformation angles when the design ground motion group and the equivalent impulse ground motion are input respectively. Here, the response due to the design ground motion group is shown by a straight line, and the response due to the ground motion No. 8 where the maximum value of the maximum inter-story deformation angle occurs is shown by a two-dot chain line. The maximum inter-story deformation angle of the ground motion No. 8 and the maximum inter-story deformation angle of the equivalent impulse ground motion (one-dot chain line) show a good correspondence. Therefore, it is shown that the maximum displacement response to the equivalent impulse ground motion can accurately evaluate the envelope of the maximum displacement responses to 10 types of ground motions.

[0037] Also, Fig. 9 also shows the maximum inter-story deformation angle (dotted line) of the impulse ground motion (N p = 2) by the method of Non-Patent Document 1. In the past methods, the maximum inter-story deformation angle of the impulse ground motion (N p = 2) is excessive compared to the maximum inter-story deformation angle of the design ground motion group, indicating the effectiveness of the method shown in this embodiment.

[0038] In the method for evaluating the seismic displacement response of the building configured as described above, by inputting the equivalent impulse ground motion that can evaluate the envelope of the maximum displacement responses to a plurality of design ground motions for design, a robust design considering the uncertainties of many ground motions becomes possible.

[0039] Also, compared with the conventional design method that designs using a plurality of design ground motions, since this embodiment designs using one equivalent impulse ground motion, the time required for seismic response analysis can be significantly shortened.

[0040] For example, consider the case where a building is designed using 10 types of design ground motions as in the design example. When using an analysis model that takes 10 minutes for the seismic response analysis of one ground motion, the time required for the seismic response analysis of all ground motions is 100 minutes. Usually, the design is carried out using the maximum displacement response calculated from these analysis results. On the other hand, since the equivalent impulse ground motion can evaluate the maximum displacement response with one wave, the time required for the seismic response analysis is 10 minutes, and the analysis can be performed in 1 / 10 of the time of the normal design method. By shortening the analysis time, it is possible to increase the time allocated to the original design actions such as considering the arrangement of the frame, dampers, etc. and designing the structural members at the initial stage of the design, for example.

[0041] Here, since all the calculations of the V E · p S V and the relational expressions of α are calculated using a single-degree-of-freedom system, the analysis time is about several seconds, and it does not take significantly more time compared to the seismic response analysis of the building's analysis model.

[0042] Note that the various shapes, combinations, etc. of the respective constituent members shown in the above-described embodiments are examples, and can be variously changed based on design requirements and the like without departing from the gist of the present invention.

[0043] There are 17 international goals adopted at the United Nations Summit in September 2015, namely the "Sustainable Development Goals (SDGs)". The method for evaluating the seismic time-displacement response of the building according to the present embodiment can contribute to the achievement of, for example, the goal of "11. Making cities and human settlements inclusive, safe, resilient and sustainable" among these 17 SDG goals.

Claims

【Claim 1】 Pseudo-velocity response spectrum in a building with period T and decay constant h ｐ S Ｖ and energy spectrum V Ｅ are calculated, The pseudo-velocity response spectrum ｐ S Ｖ is divided by the energy spectrum V Ｅ to calculate an index F of the repetitive characteristics of ground motion, The index F of the repeated characteristics of the ground motion and the number of impulses N ｐ Based on the relationship with, the number of impulses N ｐ is calculated, Based on the condition that the total input energy input into the building due to ground motion is the same, the impulse amplitude V is set using Equation (1), when the design ground motion group is replaced with each equivalent impulse ground motion, the equivalent impulse ground motion that maximizes the inter-story displacement response is selected, A method for evaluating the seismic displacement response of a building using the equivalent impulse ground motion. 【Number 1】 Here,[[]] E ｎ : Input energy m: mass V: impulse amplitude v ｎ : The velocity generated in the single-degree-of-freedom system immediately before the n-th impulse is input

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