the impact of comfort assessment criteria on building design...nbr 6118 – 07 and ceo of the...

Title: The Impact of Comfort Assessment Criteria on Building Design

Authors: Ricardo França, Professor, University of São PauloJohann Andrade Ferrareto, Graduate, University of São PauloCarlos Eduardo Nigro Mazzilli, Professor, University of São Paulo

Subject: Wind Engineering

Keywords: Human ComfortWind

Publication Date: 2014

Original Publication: CTBUH 2014 Shanghai Conference Proceedings

Paper Type: 1. Book chapter/Part chapter2. Journal paper3. Conference proceeding4. Unpublished conference paper5. Magazine article6. Unpublished

© Council on Tall Buildings and Urban Habitat / Ricardo França; Johann Andrade Ferrareto; Carlos EduardoNigro Mazzilli

ctbuh.org/papers

http://ctbuh.org/papers

722 | CTBUH 2014 Shanghai Conference

The Impact of Comfort Assessment Criteria on Building Design舒适度评价标准对建筑设计的影响

Johann Andrade Ferrareto Carlos Eduardo Nigro Mazzilli

Johann Andrade Ferrareto, Carlos Eduardo Nigro Mazzilli & Ricardo Leopoldo e Silva França

França & Associados Projetos Estruturais/ Escola Politécnica da Universidade de São Paulo. Rua Doutor Veiga Filho, 207, Apartamento 46. São Paulo, Brazil 01229-001

tel (电话): +55.11.98104.9696 email (电子邮箱): [email protected]

Johann Andrade Ferrareto is a graduate of the Escola Politécnica da Universidade de São Paulo (Civil Engineering) and graduate of the Ecole Spéciale des Travaux Publics du Bâtiment et de l’Industrie (Nuclear Civil Engineering).

琼汉•安德拉德•费哈雷拖 Johann Andrade Ferrareto毕业于圣保罗大学理工学院（土木工程）和巴黎市政工程建筑工业专科学校（核民用工程）。

Carlos Eduardo Nigro Mazzilli is a Professor at the University of São Paulo since 1992. He obtained his PhD from the University of London in 1982 and has been a Visiting Professor in several universities worldwide, including the University of Karlsruhe, Rensselaer Polytechnic Institute, University of Aberdeen and Università Politecnica delle Marche, to name a few.

卡罗丝•艾度阿度•尼各罗•玛子黎 Carlos Eduardo Nigro Mazzilli自1992年担任圣保罗大学教授至今。他于1982年获得了伦敦大学的博士学位，并在世界多所著名高校担任客座教授，其中包括德国卡尔斯鲁厄大学、美国伦斯勒理工学院、英国阿伯丁大学及意大利马尔凯理工大学等。

Ricardo Leopoldo e Silva França is Professor at the University of São Paulo. He has supervised eight MSc and PhD students. He is member of the committee responsible for revising the Brazilian building code NBR 6118 – 07 and CEO of the company França & Associados Projetos Estruturais, a structural design office specializing in tall buildings.

瑞卡尔多•留博多&丝尔瓦•法兰萨 Ricardo Leopoldo e Silva França是圣保罗大学的教授。他督导过8位硕士生和博士生。他是巴西建筑法案NBR6118-07修订责任委员会的成员，也是是法兰萨&合伙人结构项目公司（França & Associados Projetos Estruturais，一家专业设计高层建筑结构的公司）的首席执行官。

Abstract

Comfort performance during wind-induced motions is an important building design consideration. In this paper, a comfort criteria evaluation is carried out. The discussion presented in this article involves comfort evaluation based on the premise that in the future users must be aware of the building motions and trained to cope with it. Alternative approach for human comfort assessment to motion assessing sustained vibration for nausea and task performances. Moreover, through the wind load data gathered from the test of a building in São Paulo at the BLWT of the University of Western Ontario, two dynamic analyses are performed. The first one uses the first three modes of vibration, whilst the second one uses the first six modes, evaluating higher-mode contributions to the building response. This paper investigates the impact of the application of different dynamic analysis criteria to the comfort assessment in the evaluation of a building motion and proposes a new point of view to evaluate user’s comfort.

Keywords: Wind Engineering, Dynamics, Human Comfort

摘要

风致振动对舒适度的影响是建筑设计中一个很重要的因素。本文中涉及到舒适性评估的讨论是建立在未来用户能感知到建筑运动并已接受应对建筑振动的相关训练的前提下的，本文致力于制定一种新的在建筑持续振动时人体舒适度的评估的替代方法，主要评估因素包括持续振动对人体恶心反应和行为能力影响。此外，加拿大西安大略大学的BLWT（边界层风洞）团队运用两类不同的动态分析方法，收集了在圣保罗一栋建筑的风荷载数据，第一类运用了前三种振动模式，而第二类则运用了六种振动模式，以评估高级振动模式下对建筑响应的影响。本文探讨了不同动态分析标准的应用程式在建筑振动舒适度评估中的影响，同时提出了一个评估用户舒适度的新观点。

关键词：风工程学，动力学，人体舒适度

Comfort Criteria

Current Approach of the Guidelines for Human Comfort Assessment to Motion The compilation of comfort criteria presented in this paper (see Figures 2 and 3) includes the National Building Code of Canada (NBCC), Council of Tall Buildings and Urban Habitat (CTBUH) for residences and offices. It also includes the International Standardization Organization guidelines: ISO10137 (2007) and ISO6897 (1984) adapted for 1-year of recurrence interval with the peak factor proposed by Melbourne and Palmer (1992) (equation 2). The Architectural Institute of Japan Guidelines for the Evaluation of Habitability to Building Vibration (2004) are presented upon in this compilation. Hansen et al. (1973) criteria were adapted for a 1-year recurrence interval (equation 1) and for peak acceleration (equation. 2) using 600s of windstorm peak duration. For the sake of simplicity, only Sarkisian’s (2012) 1-year period of return criteria are presented on the compilation (see Figure 3) since the 10-year period of return criteria was almost the same as the CTBUH criteria. National Brazilian Wind Code (NBR6123 1988) comfort criteria appears

舒适标准

目前人体在建筑振动时舒适度的评估方法

本文中展示的舒适度标准的汇编（见图2和图3）包括加拿大国家建筑规范（NBCC），以及针对住宅和办公室标准的高层建筑和城市住区理事会 (CTBUH) ，还包括国际标准化组织准则： ISO10137 (2007) 和 ISO6897 (1984) 的适用于1年重现期循环间隔的标准，其峰值参数由Melbourne和Palmer（1992）提供（参考公式2）。日本建筑学会（AIJ）建筑振动的宜居评估准则 (2004)也在该汇编中得以呈现。 Hansen et al. (1973) 也使用一年重现期循环间隔标准（见公式1），且其峰值加速度（见公式2）采用600s的暴风高峰期。为简单起见，该汇编只有Sarkisian’s (2012)的1年重现期的标准（见图3），因为10年重现期的标准几乎和CTBUH标准一致。巴西国家风力规范 (NBR6123 1988)的对住宅使用的舒适度标准与加拿大国家建筑规范（NBCC）标准呈现出相同的峰值加速度。

用户投诉的级别是目前在风致振动中人体舒适度的主要指标。Hansen et al. (1973)标准率先跟据6年重现期用户投诉级别（2%）的反馈确立了舒适度加速度值为5mg (1mg代表重力加速度的千分之一)。该加速级别

Ricardo Leopoldo e Silva França

2014年CTBUH上海会议 | 723

with the same value of peak acceleration as NBCC criteria for residences.

The level of users’ complaint is currently the main indicator for human comfort assessment during wind-induced motion. Hansen et al. (1973) first established a comfort acceleration value of 5mg (where 1mg stands for 1/1000th of gravity acceleration) based on a 2% level of users’ complaint for a 6-year period of return. These acceleration levels were gathered from two building surveys after a windstorm and a boundary layer wind tunnel (BLWT) experiment.

Most of the research and guidelines to assess users’ comfort to motion provide either a set of perception level curves (AIJ-GEH 2004, Irwin 1978, ISO6897 1984) or a set of curves correlated to perception to motion (ISO6897 1984, ISO10137 2007). Perception thresholds to motion have been the primary concern of these studies since it is caused by higher levels of acceleration, which can cause users to alarm (Irwin 1978) and consequently object to motion.

Irwin (1978) proposed a frequency dependent rms acceleration curve consistent with the criteria proposed by Hansen et al. (1973). Irwin’s curve was adjusted to a 5-year return period instead of 6 years. Later, ISO6897 (1984) adapted Irwin’s curves to propose a comfort assessment for acceleration rms (see Figure 1).

Melbourne and Palmer (1992) related the response of period of return “R” to the acceleration for return period of 5 years by the following equation:

while ISO6897 (1984) uses a 0.72 factor to convert the 5-year period of return assessment curve into a 1-year period of return curve.

Melbourne and Palmer (1992) also proposed a Peak factor to convert rms acceleration to peak acceleration:

Where n stands for the frequency of oscillation and T stands for the duration of the event in seconds.

AIJ-Guidelines (2004) provides five curves of motion perception where 10%, 30%, 50%, 70% and 90% of people that can perceive the vibration specified on each respective curve. The owner and the designers are to judge suitable peak acceleration levels based on users’ perception (Tamura 2008).

ISO10137 (2007) proposes two evaluation curves for a one-year return period windstorm: one for residences and another for offices. The residence threshold of comfort curve are close to Tamura’s (2003) and AIJ-GEH-2004 90% perception curve, whilst the office threshold of comfort is 1.5 times the residential threshold.

Sarkisian (2012) suggested criteria of perception to motion in tall buildings. Peak accelerations of 5-7mg or 12-15mg for residences with a 1-year or a 10-year period of return wind respectively. For offices, peak accelerations of 10-13mg or 20-25mg with a 1-year or a 10-year period of return wind, in that order.

Alternative Approach for Human Comfort Assessment to Motion According to Lamb et al. (2013), the level of users’ complaint might be a poor indicator to assess human comfort during wind-induced motion. In addition, there are several psychological and physiological effects caused by horizontal motion of the floor such as dizziness,

是对两栋建筑进行风暴和边界层风洞（BLWT）实验后调查得到的。

大部分评估用户对于振动舒适度的研究和准则提供一套感知水平曲线(AIJ-GEH 2004， Irwin 1978， ISO6897 1984)或一套对振动反应感知的相关曲线 (ISO6897 1984， ISO10137 2007)。对于振动感知都是由更高级别的加速度引起的，感知临界值的测量一直是这些研究主要关注的问题，因为超过临界值的振动会引起受试者的抱怨和投诉。

Irwin (1978) 提出了与Hansen et al. (1973)所提标准一致的、建立在均方根加速变化曲线基础上的频率。Irwin变化曲线由6年重现期调整到了5年重现期。之后 ISO6897 (1984) 调整 Irwin变化曲线，提出针对加速度均方根的舒适度评估 (见图1)。

response for return period R years

response for return period 5 years= 0.68+ ln(R)

5

Figure 1. ISO6897 (1984) and Hansen et al. (1973) results图 1. ISO6897 (1984) 和 Hansen et al. (1973) 结果

Peak=√(2×ln (nT))×rms

Figure 2. Peak acceleration criteria, 10-year period of return图2. 峰值加速度标准，10年重现期

Figure 3. Peak acceleration criteria, 1-year period of return图3. 峰值加速度标准，1年重现期


compensatory behaviors, reduction of task performance, difficulty to concentrate, motion sickness and nausea.

Goto (1983) in a study that consisted on a survey of six buildings after a windstorm succeeded in gathering different types and degrees of building responses during wind-induced building motion. The results showed thresholds of perception and physical symptoms. Compensatory behavior, such as stop working and descending to a lower level of the building was observed during the survey.

Jeary et al. (1988) performed a study at an artificially excited building (sinusoidal vibration). The goal was to study the effects of acceleration levels on human task performance. No significant result concerning decrease of task performance was observed. According to the authors, tasks were too simple and the subjects could be able to combat the motion effects by “concentrating harder”. In addition, the vibration did not persist long enough to show any fatigue symptoms on the users. However, seven of the 24 subjects who participated of the experiment claimed to have experienced motion sickness at the highest amplitudes.

Lee (1983) calculated the acceleration of a seventy-eight-meter high building after a windstorm. The calculation used a wind tunnel modelling system and showed good agreement with full-scale data. Peak accelerations for the two modes of vibration during the windstorm peak were 3,9mg for the E-W mode and 5,5mg for the N-S mode.

Resultant peak acceleration can be estimated by simple vectorial addition:

The result needs to be multiplied by a joint action factor “φ” (Boggs, 1997). The joint action factor used for Lee’s (1983) results is 0,7 (see Figure 3).

Denoon (2000) performed an extensive survey of three wind-sensitive structures: Brisbane Airport Control Tower, Sydney Airport Control Tower and Port Operations Control Centre (POCC). The results included a study of motion tolerance thresholds (including perception) in a great range of work conditions, such as temperature of the room, fatigue, concentration and body posture effects on these thresholds. Initially, 39% of the users of Sidney’s Airport Control Tower reported that the motion was disturbing or frightening. After being educated about the building motion and learning that it was not related to unsafety and could not affect the structural integrity of the tower, this group of users showed adaptation to motion effects. These users reported a strong decrease (50%) on the frequency of how often they feel disturbed or frightened due to building motion. In addition, 40% of these users stated that they found the level of motion less disturbing or frightening. Annoyance thresholds raised since annoyance complaints rate dropped 40% with user’s acquaintance to the environment.

Denoon (2000) actually measured a tolerance level either for disturbing, frightening or for nauseating feeling. However, most of the reports of “Disturbing / frightening / nauseating” were of nausea symptoms such as headaches or queasiness leading to an acceleration peak level close to 4mg at a frequency of 0,94Hz for nausea symptoms. Figure 3 shows a compilation of the results from Goto (1983), Lee (1983), Jeary et al. (1988) and Denoon (2000).

Melbourne and Palmer (1992)用以下的公式将“R”年重现期响应和5年重现期期的加速度关联了起来：

而当5年重现期转换成1年重现期时， ISO6897 (1984) 则换用 0.72这个因数。

Melbourne and Palmer (1992)还提出了高峰系数将均方根加速度转换成峰值加速度：

在这里，n代表振动频率，而T代表事件的持续时间（以秒为单位）。

日本建筑学会准则（AIJ-Guidelines） (2004) 提供了五组振动感知曲线，而10%，30%，50%，70%和90%的调查对象能在每一对应的曲线中感知到相应的振动。由所有者和设计者根据用户的感知来判断适当的峰值加速度等级 (Tamura 2008)。

ISO10137 (2007)提出了用于1年重现期针对风暴测量的两种评估曲线：一种是针对住宅，另一种是针对办公室。住宅的舒适度曲线测量接近于Tamura’s (2003) 和AIJ-GEH-2004 90% 的感知变化曲线，然而办公室的舒适度测量是住宅的1.5倍。

Sarkisian (2012) 提出了高层建筑振动感知的标准。如文中所述，对于住宅来讲，一个1年重现期的峰值加速度为 5-7mg 或一个10年重现期的峰值加速度为12-15mg。对于办公室来讲，一个1年重现期的峰值加速度为10-13mg，或一个10年重现期的峰值加速度为 20-25mg。

人体在减值振动时的舒适度评估的替代方法根据Lamb et al. (2013)，风致振动中，用户投诉的级别可能不能完整地评估人体舒适度。此外，楼层的晃动还会产生一些生理和心理影响，例如晕眩、代偿行为、行为能力下降、难以集中注意力、恶心呕吐。

Goto (1983)中有一项包括六栋建筑在风暴后的调查的研究报告，成功地收集了在风作用下建筑振动的不同类型和不同程度，结果显示了人体心理和生理症状的临界值。调查过程中观察到人在该环境下产生的代偿行为，如：停止工作和降低所在楼层。

Jeary et al. (1988)进行了一项人为模拟建筑振动（正弦振动）的研究。目的是为了研究加速度的不同级别对人类行为能力产生的影响。该研究中未出现明显的行为能力下降的结果。据作者描述，由于任务过于简单，受试者可以通过“更加集中注意力”来克服建筑振动产生的影响。此外，振动没有持续足够长的时间，以致于受试者并没有表现出疲劳的症状。然而，24位参加该项试验的受试者中仍有7位声称在最高振幅的时候有晕眩的感觉。

Lee (1983) 计算出了一栋78米高的建筑在风暴后的加速度。该计算方法采用了风洞模拟系统，并且该计算方法与全尺寸数据高度吻合。在风暴高峰时，E-W模型的高峰振动加速度为3.9mg，而N-S模型为5.5mg。

合成峰值加速度可以通过以下简单的矢量加法来估算：

结果需乘以一个联合作用系数。该联合作用系数在Lee’s（1983）的结果中为0.7（见图3）。

Denoon (2000)针对三栋风敏感建筑进行了扩展调查：布里斯本机场控制塔，悉尼机场控制塔和港口作业控制中心(POCC)。调查包括一项不同试验条件（如室内温度、疲劳程度、专注度和身体姿

x _Resultant=φ×√((x _(N-S) )^2+(x _(E-W) )^2 )

x _Resultant=φ×√((x _(N-S) )^2+(x _(E-W) )^2 )

𝑅𝑅5 年重现期响应

= 0.68 +𝑙𝑙 𝑛𝑛 𝑅𝑅

5 年重现期响应

Peak=√(2×ln (nT))×rms


Frequency Dependence and Comfort Thresholds Burton et al. (2006) performed a landmark experiment on 10 subjects in a shaking room to study uni-axial fore-aft and lateral biodynamic responses. The 10 human subjects aged between 22 and 32 years old, with a mean age of 27 and included men and women. The test consisted in watching a video on a 430mm screen placed at a distance of 1,25m in front of the person while the room would undergo the motion. The acceleration was measured by triaxial accelerometers weighing 50g each. Two accelerometers were used on each subject: one was placed between the shoulder blades, while the other was placed on the top of the head. The rms of the acceleration was used to evaluate body and head motions. The results showed that the acceleration of the head increases as the frequency of oscillation increases, for both fore-aft and lateral motions. It is also the most significant magnification factor observed, where values vary within the range [2; 4] at the lowest (0,15Hz) and at the highest (1,00Hz) frequency of oscillation respectively.

Burton et al. (2006) also concluded that vestibular system is the primary indicator of the body to motion perception and its frequency dependence is the same as for the head. In addition, for accelerations at frequencies greater than 0,50Hz, para-spinal muscles become stiffer and increase the damping effects towards body motions. Decrease of the magnification factors is to be expected for frequencies above 1Hz.

Assuming a constant comfort threshold for the head acceleration, the acceleration value for a certain level of comfort/discomfort at 1Hz should be half of that for the value for 0,15Hz, since the magnification factor for 1Hz is twice as large the factor for 0,15Hz (4 and 2, respectively). For the ongoing analysis, it will be considered a set of log-log straight lines with the angular coefficient “m” consistent with the magnification factors found on Burton et al. (2006) studies. The angular coefficient “m” is calculated by:

These lines stop at 1Hz frequency, since the range of frequencies tested does not go any further. Yet, a change of behavior in the magnification factor is expected above 1Hz, as previously stated by Burton et al. (2006).

Picking up the exact line that passes through Goto’s (1983) lower motion sickness threshold (see Figure 4, lower nausea threshold), it can be observed that Denoon’s (2000) nausea threshold is very close to this line. The line was drawn with a constant acceleration value between 1Hz and 2Hz, the same behavior of ISO10137 (2007), to fit with the results from Jeary et al. (1988).

The assessed peak acceleration for Lee’s (1983) survey results is 4,09mg for a frequency of 0,68Hz, bellow the lower nausea threshold (see Figure 4). It is important to state that no episodes of nausea or sickness motion were noted during Lee’s (1983) survey.

Angular coefficients neighboring the value -0,365 appear on ISO6897 (1986) and on ISO10137 (2007) standards, -0,32 and -0,45 respectively, which might indicate similar behavior between perception and nausea thresholds in the range of frequencies between 0,15Hz and 1Hz. However, nausea and motion sickness thresholds are clearly higher than perception thresholds.

The “motion sickness lower threshold” is above Tamura’s (2003) 30% perception threshold (see Figure 5). At the same time as “Limit of

势）对人体振动耐受临界值（包括感知）产生的不同影响的研究。刚开始，悉尼机场控制中心有39%的受试者反映振动令人不安或恐惧。但在在接受了建筑振动的相关知识普后，他们意识后这种建筑振动不会影响建筑结构完整性，也不会有安全隐患，这组受试者显示出了对振动影响的适应性和自我调节性。这些受试者因振动产生焦虑恐惧的频率产生了大幅度的下降（50%）。此外，40%的受试者声称他们找到了产生相对较少焦虑恐惧的振动级别。因为受试者对环境的适应性得到了提高，所以负面情绪投诉率下降了40%，同时产生焦虑恐惧的临界值也上升了。

Denoon (2000)测试过对于焦虑、恐惧或恶心的耐受级别。研究报告中“焦虑/恐惧/恶心”大多数都是由于接近于在0.94Hz频率的4mg峰值加速度水平产生的恶心症状，如头痛或反胃。图3显示了Goto (1983)， Lee (1983)， Jeary et al. (1988) 和Denoon (2000)的结果汇编。

频率相关性和舒适度临界值 Burton et al. (2006)进行了一次具有里程碑意义的试验：通过10个受试者在振动的房间里的反应来研究单向轴前后振动和横向振动时的生物动态响应。这10位受试者（包括男性和女性）的年龄段从22岁到32岁，平均年龄为27岁。该测试中，在受试者正观看前方1.25米的430毫米的屏幕上的录像时，房间开始振动。由三个各重50克的三轴加速度计测量房间振动加速度。每位受试者使用两个三轴加速度计：一个放在肩胛骨之间，而另一个则放在头顶上。所测加速度均方根分别用来评估身体和头部的振动。结果显示：当振动频率增大，头部的加速度也增大，包括前后振动和横向振动。这也是观察到的最重要的倍率系数，当振动频率在最低（0.15赫兹）和最高（1.00赫兹）之间变动时，该倍率系数的变化区间为 [2; 4]。

Figure 4. Motion sickness and perception field data图4. 晕眩和感知区域数据

Figure 5. Comparison: motion sickness vs. perception图5. 比较：晕眩 vs. 感知

ln(2⁄4)ln(1⁄0,15) =-0,37

m=


Burton et al. (2006)也得出过结论：前庭系统是人体对振动感知的主要指标，它的频率指标和头部的频率指标一致。此外，当加速度的频率超过0.50赫兹时，脊旁肌肉变得僵硬，同时对身体振动的阻尼效应增强。当加速度频率超过1赫兹的时候，倍率系数有望降低。

假设振动时，头部加速度的舒适度临界值为恒定，那么当振动频率为1赫兹时，舒适/不舒适度的相应水平的加速度值应为振动频率为0.15赫兹时加速度值的一半，因为1赫兹时的倍率系数是0.15赫兹时倍率系数的两倍（分别为4和2）。该项分析中，这将被认为是带有角系数“m”的一组双对数直线，与 Burton et al. (2006)对于倍率系数的研究一致。该角系数计算方式如下：

由于受测试中的频率范围的制约，这组双对数直线最高仅限于振动频率为1赫兹。然而，如之前 Burton et al. (2006)所述，振动频率高于1赫兹所对应的倍率系数有望变化。

让我们选取一条穿过Goto’s (1983) 晕眩反应较低临界值（见图4，恶心反应较低临界值）的线，可以观察到Denoon’s (2000)恶心反应临界值非常接近这条线。这条线显示1赫兹到2赫兹区间内的加速度值是恒定的，与 ISO10137 (2007)一致，符合 Jeary et al. (1988)的结果。

Lee’s (1983) 调查结果中，在振动为0.68赫兹的条件下，峰值加速度评估值为4.09mg，低于恶心反应较低临界值（见图4）。值得指出的是在Lee’s (1983) 调查中，没有提到恶心或晕眩反应的发生。

在ISO6897 (1986) 和 ISO10137 (2007)中出现了接近-0.365的角系数值，分别为-0.32和-0.45，这可能表明在振动频率区间为0.15赫兹到1赫兹时，感知临界值和恶心反应临界值是很相似的。尽管如此，恶心反应临界值和晕眩反应临界值还是要明显高于感知临界值的。

“晕眩反应较低临界值”高于Tamura’s (2003) 30%感知临界值（见图5）同时，峰值加速度为40mg时的“生理和行为能力极限” (Goto 1983) 远远高于NBCC较高的舒适度临界值（办公室）和 AIJ-GEH-2004 H-90曲线（见图5）。.

这些结果证实了恶心反应/行为能力临界值远高于感知临界值。因此，这可能会得出一个保守的结论，并导致更大的建筑材料消耗。因该结果显示出受过训练的人不容易感受到振动引起的恐惧，所以一种替代方法可以用来评估受试者的舒适度。通过采用更高的振动临界值，可以得到一个更开放的结果，也有望降低建筑材料的损耗。

案例分析

建筑描述该案例研究的对象是坐落在巴西圣保罗市的一座高180米的有51层楼的建筑。该建筑是低层为购物中心、中/高层为办公区域的综合性多功能建筑。办公区域楼层尺寸：面积为50米x46米，高4.3米。该建筑的一阶固有频率和振动类型为：

• 第一模式： 0.183赫兹 – 轻摇，Y轴.

• 第二模式： 0.190 赫兹 – 轻摇，X轴.

• 第三模式： 0.270赫兹 – 摇摆， Z轴.

• 第四模式： 0.530赫兹 – 摇摆， Z轴.

• 第五模式： 0.603赫兹 – 轻摇， Y轴.

• 第六模式： 0.663 赫兹 – 轻摇， X轴.

physiological task performance” of 40mg peak acceleration (Goto 1983) is far above from NBCC upper threshold for comfort (offices) and from AIJ-GEH-2004 H-90 curve (see Figure 5).

These results confirm that nausea/task performance thresholds are much higher than perception thresholds. Therefore, it might lead to conservative results and greater structural material consumption. Since it was shown that trained personnel is less susceptible to fear of motion, an alternative approach could be used to evaluate user’s comfort. Adopting higher thresholds for motion, less conservative results can be achieved and consequently lower material consumption can be expected.

Case Study

Building Description The building studied is a 51-story high with a total of 180m from the ground level at the city of São Paulo, in Brazil. An office tower on the mid/top levels and a shopping mall on the lower levels compose it. The floor dimensions at the office tower floors are 50mx46m with a 4,30m story height. The building’s first natural frequencies and type of vibration are:

• First mode: 0,183Hz – Sway, Y-axis.

• Second mode: 0,190 Hz – Sway, X-axis.

• Third mode: 0,270 – Torsion, Z-axis.

• Fourth mode: 0,530 – Torsion , Z-axis.

• Fifth mode: 0,603 – Sway, Y-axis.

• Sixth mode: 0,663 Hz – Sway, X-axis.

The building was modeled as a lumped mass system for the dynamic analysis. The modal shapes and modal displacements overview of the building are shown in Figure 6.

A boundary layer wind tunnel test was made for this building using High Frequency Pressure Integration technique (HFPI) at the University of Western Ontario, providing acceleration levels of the top occupied floor of the building using three modes of vibration on the dynamic analysis. A second dynamic analysis took place on this paper, providing acceleration levels on the top occupied floor using higher modes of vibration (4, 5 and 6 modes, respectively). The time-history wind load data used for this subsequent dynamic analysis was the same one used by the first 3-mode analysis (provided by the HFPI method).

Dynamic Analysis Framework Accelerations, velocities and displacements were calculated by time history integration of a modal system with six degrees of freedom. Mass matrix was calculated as for a lumped mass system with the mass of each floor concentrated around a reference axis. Each modal mass “M*n” is given by (Chen and Kareem 2005):

where “Mji” stands for the element at the line “j” and column “i” of the structure lumped mass matrix. “Φni” is the element of the eigenvector of the mode “n” for the degree-of-freedom “i”. Likewise, “Φnj” corresponds to the nth mode and to the degree of freedom “j”.

The time-history “{P(t)}” was transformed in modal time histories “Pn(t)” through the following operation for each time step (Chen and Kareem 2005):

ln(2⁄4)ln(1⁄0,15) =-0,37

m=


where “Pi(t)” stands for the horizontal force or torsion moment of the ith degree of freedom of the vector representing the wind loads at each time step.

Once known the natural frequencies, modal time histories and modal masses, a 1% damping ratio (Wu, Liu and Li 2007, Tamura 2007) was used to complete the dynamic analysis.

The modal equation resulting from the framework proposed was:

where, ¨qn(t), ̇qn(t) and qn(t) stand respectively for the acceleration, velocity and displacement of the nth generalized coordinate. The nth natural frequency (Hz) is denoted “fn”.

The numerical integration was performed using a 4th order Runge-Kutta method for each of the six degrees of freedom.

The duration of the numerical integration was 10 minutes, during the worst windstorm responses (Melbourne and Palmer 1992). The final time history acceleration with respect to the reference axis was assessed by:

该建筑作为动态分析的集中系统的模型。图6显示了该建筑的模型外形和模型位移概况。

通过采用加拿大西安大略大学的高频高压集成技术（HFPI）对该栋建筑进行了边界层风洞测试，测试运用了三种振动模式进行的动态分析，从而提供了该建筑最高使用层的加速度级别。第二类动态分析出现在本论文中，采用了高级别的振动模式（分别为第4、5和6模式）提供了该建筑最高使用层的加速度级别。后一个动态分析所用的时程风荷载数据和前三个模式分析（由HFPI方法提供）是一样的。

动态分析框架加速度、速度和位移都是由一种模式系统的时程集成法运算的，该时程集成法包含有自由度的六种级别。质量矩阵被用于计算汇聚在基准轴上的大量的每层楼的集中质量系统数据。每个模式质量 “M*n” 是这样运算得出的 (Chen and Kareem 2005)：

在这里， “Mji” 代表集总质量矩阵中“j”行和“i”列的元素。 “Φni” 代表自由度“i”中第“n”个模式的特征向量元素。同样的， “Φnj”代表“f”自由度中第“n”个模式的特征向量元素。

时程 “{P(t)}”每一计算步骤通过以下公式被转化成模型时程 “Pn(t)” (Chen and Kareem 2005)：

在这里， “Pi(t)” 代表每一计算步骤中代表风荷载向量的第“i”自由度的横向力量或摇摆时间。

一旦得到固有频率、模型时程和模型质量的值，那么一个1%的阻尼因数(Wu， Liu and Li 2007， Tamura 2007) 被采用来完成该动态分析。

从以上动态分析框架得出的模型运算方程式为：

在这里¨qn(t), ̇qn(t) and qn(t)分别代表第n广义坐标的加速度、速度和位移。 “fn”代表第n固有频率（赫兹）。

可以采用四阶龙格-库塔法运算自由度的六级别的数值积分。

在最差的风暴响应中，数值积分的持续时间为10分钟(Melbourne

Figure 6. Building’s modal shapes and modal displacements图6.建筑的模式外观和模式位移

Figure 7. Time-history resultant acceleration at the corner of the top occupied floor, 1-year and 10-year period of return图7. 最高使用楼层角落的合成加速度，1年和10年重现期


where “ax,m(t), ay,m(t) and aθ,m(t)” correspond to the contribution of each of the three degrees of freedom to the overall horizontal acceleration (translational x, translational y and torsional, respectively) truncating at the mth mode of vibration. “Φx,n,l”, “Φy,n,l” and “Φθ,n,l” stand for the position on the eigenvector of the nth mode and degree of freedom “x”, “y” or “θ” at the last occupied floor “l”. The distance from the most distant point on the last occupied floor to the axis of reference is termed .

The absolute value for the final acceleration was assessed by equations 4, 5 and 6 combined:

The absolute value for the torsional contribution to the motion is reasonable, since one cannot know the exact location of the user at the building floor during the windstorm. Therefore, it is assumed that the acceleration due to the building torsion has the same direction than the resultant acceleration at the reference axis, justifying the sum of absolute values to assess the final acceleration.

Results The building accelerations at the corner of the top occupied floor were calculated to 1-year and 10-year period of return, truncating both in the 3rd, 4th, 5th and 6th modes of vibration. Time-history resultant accelerations for three modes and for six modes responses both for 1-year and for 10-year period of return are given in Figure 7.

The results (see Table 1) showed an increase of approximately 10% on the assessed peak resultant acceleration. This result shows consistency with previous research (Huang and Chen 2007, Rosa et al. 2012). Still, Huang and Cheng’s (2007) results measured the contribution of the higher modal contribution compared with the response of the fundamental mode. Rosa et al. (2012) revealed that higher modal contribution (4th, 5th and 6th modes) could be significant for the building acceleration. Usually, only the first three or four modes of vibration (including, at least, one torsional mode and two sway modes, one for each direction) are required to perform a BLWT dynamic analysis for comfort assessment. Different situations and design complications, however, still might require higher modal contribution analysis. This paper analyses the contribution of each modal response after the first two sway modes (1st and 2nd mode) and the first torsional mode (3rd mode).

and Palmer 1992)。关于基准轴的最终时程加速度的运算方程式如下：

在这里，”ax,m(t), ay,m(t) and aθ,m(t)” 代表整体横向加速度在振动的第m模式的截断面中对应自由度的三个级别（分别是平移X、平移Y和扭摆度θ）。 “Φx,n,l”, “Φy,n,l” and “Φθ,n,l”代表第n模式的特征向量和在上述最高使用楼层“f”的自由度级别。“d”代表从上述使用楼层最远点到基准轴的距离。

最终加速度的绝对值是由公式4、公式5和公式6联合运算得出：

该绝对值代表振动中的摇摆影响是合理的，因为风暴中受试者在楼层中的具体位置是不能被定位的。因此，我们可以假设合成加速度和因建筑摆动引起的加速度在基准轴上有相同的方向，这样一来，他们的绝对值总数等同于最终需要评估的加速度。

结果结果采用该建筑最高使用层边角加速度基于1年重现期和10年重现期的计算值，横截面选用振动的第3模式、第4模式、第5模式和第6模式，由此计算出的1年重现期和10年重现期对应的三种模式和六种模式的合成加速度结果，请参考图7。

结果（表1）显示出所评估的高峰合成加速度增加了大概10%。该结果与以前的研究结果 (Huang and Chen 2007， Rosa et al. 2012)一致。而且，Huang and Cheng(2007)的结论展现了高端模型结论对比基础模型结论的作用。Rosa et al. (2012)揭示了高级别模式（第4、5和6模式）可能对建筑加速度的影响是巨大的。通常，只需前三个或前四个振动模式（至少包括一个摇摆模式和两个轻摇模式，每个方向一个模式）来对舒适度评估进行边界层风洞测试的动态分析。但是在复杂的设计和其他不同的情况下，还是需要有高级别的模式分析。本文对前两个轻摇模式（第1和第2模式）和前一个摇摆模式（第3模式）之后的每个模式响应影响都做了分析。

水平分量ax， ay 和 aθ 分别代表10年重现期中高级别模式作用引起的 4.0%， 4.5% and13.1% 的增幅。在前三个模式的高峰段，由于高级别模式的负面叠加，“x”方向上的一年峰值加速度产生了显著的下降; 另一方面，均方根上升了3.0%。然而在摇摆的影响下，合成加速度出现了10%的提高。

Figure 8. Case study comfort assessment, 1-year period of return (peak)图8. 案例研究舒适度评估，1年重现期（高峰）

Figure 9. Case study comfort assessment, 10-year period of return (peak)图9. . 案例研究舒适度评估，10年重现期（高峰）


Horizontal components ax, ay and aθ presented, respectively, 4,0%, 4,5% and 13,1% of increase due to higher modal contribution for 10-year return period. One-year peak acceleration for the “x” direction showed a significant decrease due to negative superposition of the higher modes on the peak of the first three modes; rms on the other hand increased 3,0%. Still, resultant acceleration showed increase of 10%, mostly due to torsional contribution.

The assessed 1-year period of return resultant accelerations were compared with the available current normative documents (see Figures 8 and 9). One-year peak accelerations are acceptable for CTBUH and ISO10137 (2007) criteria, whilst 1-year rms resultant acceleration (3,99mg) is above ISO6897 (1984) curve adapted for 1-year period of return (see Figure 10). Ten-year peak acceleration levels were in agreement with NBCC and with CTBUH criteria, but they were far above the comfort threshold specified by NBR6123 (1988). This building’s structural costs could be greatly reduced by raising the comfort threshold based on the point of view presented in this study, since it points toward greater thresholds when it comes to nausea/motion sickness and task performance criteria.

Conclusions

Higher modal contributions presented substantial increase on the assessed resultant peak acceleration. In this study, torsional modes have showed the greatest contribution on these results.

Comfort assessment through level of perception/complaint can lead to conservative results, which leads to greater structural material consumption and consequently greater costs. Hence, normative documents around the world are not consistent with each other. To increase the building stiffening to allow normative conformity with certain codes might lead to prohibitive structural costs.

An alternative approach that might provide less conservative results is the comfort evaluation through motion sickness, compensatory behaviors and task performance reduction (this approach need trained users, i.e., users educated about the building motion). However, further investigation on these elements are needed to achieve practical results and criteria.

本文评估的1年重现期的合成加速度与目前可用文件的相关规范对照（见图8和图9）。一年峰值加速度是可以被CTBUH和ISO10137 (2007) 标准接受的，而一年均方根加速度（3.99mg）是高于ISO6897 (1984)曲线中采用的1年重现期数据的（见图10）。10年期峰值加速度级别与NBCC和CTBUH标准一致，但是它们远远高于 NBR6123 (1988)所规定的舒适度临界值标准。据本文的观点，提高舒适度临界值，可以让该建筑结构成本得到大幅度的下降，因为当涉及到恶心/晕眩和行为能力标准时，需要更大的临界值。

结论

高级别模式作用让被评估的合成峰值加速度产生了大幅的提高。在本研究中，摇摆模式对研究结果有更大的影响。

通过感知/投诉级别产生的舒适度评估会得出保守的结果，这会导致更大的建筑结构材料的消耗，从而成本也会更大。因此，世界各地的规范性文件也千差万别。为了在某些要求上达到标准而增强建筑的坚固性，可能会导致巨额的建筑结构成本。

而替代方法可能会产生相对开放的结果，它通过晕眩、代偿行为和行为能力下降（这种方法需要经过训练后的受试者，如受试者培训学习过建筑的振动）的影响而做出舒适度的评价。但是这些理论需要进一步的研究后才能取得实效和实用标准。

Figure 10. Case study comfort assessment, 1-year period of return (rms)图10. 案例研究舒适度评估，1年重现期（均方根）

Table 1. Higher modal contribution analysis表 1.高级别模式作用分析


References (参考书目): Boggs, D. (1997) Acceleration Indexes for Human Comfort in Tall Buildings – Peak or Rms? CTBUH Monograph Chapter 13: Motion Perception Tolerance and Mitigation.

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