土建外文翻譯

1、<p>　　2004年8月1~6號</p><p>　　基于性能的抗震設(shè)計(jì)方法和復(fù)合屈曲約束支撐框架的性能</p><p><b>　　摘要</b></p><p>　　屈曲約束支撐框架的概念相對較為新穎，近年來它的應(yīng)用在美國、日本和臺灣得到增強(qiáng)。然而，對于一般實(shí)踐的詳細(xì)設(shè)計(jì)規(guī)則當(dāng)前還處于發(fā)展階段。從2002年夏開始，密歇根大學(xué)的研究

2、者已經(jīng)開始和臺灣地震工程研究中心的隊(duì)伍展開合作，在設(shè)計(jì)、分析和應(yīng)用模擬動(dòng)力測試方法對這種框架進(jìn)行全方位測試等方面進(jìn)行聯(lián)合研究。</p><p>　　選定的結(jié)構(gòu)是由混凝土灌注的鋼管圓柱、鋼梁和復(fù)合屈曲約束支撐組成的三層三跨的框架。這種框架是應(yīng)用密歇根大學(xué)最近發(fā)展的基于能量的塑性設(shè)計(jì)程序設(shè)計(jì)而成的。這種方法利用了選定的目標(biāo)作業(yè)份額（對這個(gè)框架在50年中2.0%到10%荷載50年設(shè)計(jì)范圍中的2.5%到2%）和總體的屈曲

3、原理。由于在端部連接和支撐的鋼殼之間設(shè)計(jì)空隙的更多精確控制的需要，屈曲約束支撐框架是對這種最新成熟設(shè)計(jì)方法的最好候選者。</p><p>　　這篇文章簡要介紹了由密歇根大學(xué)研究的基于能力原理的設(shè)計(jì)方法和由臺灣地震工程研究中心的科研小組為計(jì)算框架底部剪力的設(shè)計(jì)計(jì)算結(jié)果而采用的基于位移的設(shè)計(jì)程序模式，并對兩種方法對于一次臺灣地震而設(shè)計(jì)的框架無彈性響應(yīng)結(jié)果進(jìn)行了對比。同樣的框架也在美國進(jìn)行了設(shè)計(jì)，并依據(jù)美國的標(biāo)準(zhǔn)在地面

4、運(yùn)動(dòng)下進(jìn)行了分析。由密歇根大學(xué)設(shè)計(jì)的框架對臺灣和美國的地面運(yùn)動(dòng)都基本符合動(dòng)力響應(yīng)。</p><p><b>　　介紹</b></p><p>　　屈曲約束支撐極好的地震反應(yīng)激勵(lì)了臺灣地震工程研究中心的實(shí)驗(yàn)計(jì)劃，也鼓勵(lì)了密歇根大學(xué)的研究者們對分析和設(shè)計(jì)之間結(jié)合的進(jìn)一步研究。在這個(gè)計(jì)劃中，屈曲約束支撐為2003年10月在臺灣地震工程研究中心進(jìn)行模擬動(dòng)力荷載實(shí)驗(yàn)的三層三跨框

5、架提供了最基本的抗力結(jié)構(gòu)。原型建筑的結(jié)構(gòu)布置如圖一a所示，實(shí)驗(yàn)框架的立面如圖一b所示。針對實(shí)驗(yàn)?zāi)康?，假定這些跨中的兩個(gè)能夠抵抗作用在一個(gè)三層建筑原型的全部地震力。地震力作用的框架在圖一a中用粗線表示。</p><p>　　圖一:（a）圓形建筑的平面布置圖 （b）測試框架圖</p><p><b>　　測試框架描述</b></p>&

6、lt;p>　　本框架通過兩個(gè)互相分離的機(jī)構(gòu)來抵抗地震荷載。最基本的抵抗力由框架中主要跨（圖一b）的屈曲約束支撐來提供。這一跨被設(shè)計(jì)為一個(gè)完全的支撐框架，而所有的梁柱連接和支撐與柱間的連接作為最簡單的連接。在每一個(gè)地震作用的框架中，支撐被設(shè)計(jì)為抵抗地震作用力的80%，剩余的20%有外側(cè)的兩跨來抵抗。外側(cè)兩跨作為瞬間框架，同時(shí)外側(cè)梁柱接頭作為瞬間連接。所有柱子都由混凝土灌注鋼管組成。內(nèi)外側(cè)柱子采用不同的型材，隨著建筑物高度的增加尺寸保

7、持不變。梁上采用大法蘭。各層采用不同尺寸的梁，而在同一層上的所有跨都采用相同尺寸的梁。</p><p><b>　　屈曲約束支撐的特性</b></p><p>　　屈曲約束支撐的特色是在混凝土灌注鋼管中插入一個(gè)鋼芯（圖二a）鋼芯和混凝土灌注鋼管由于鋼芯表面的脫膠材料而保持相互分離。灌注的混凝土和鋼管的作用是防止鋼芯屈曲，以至于在大位移撤消后支撐有一個(gè)很好的荷載位移響應(yīng)

8、。脫膠材料能夠保證作用在屈曲支撐上的力僅僅由鋼芯承載，而不會(huì)作用在周圍材料上。在臺灣的地震工程研究中心，各種不同配置的屈曲約束支撐在大周期軸力作用下進(jìn)行試驗(yàn)，從而挑選出最適宜實(shí)驗(yàn)框架的配置（圖二a）一個(gè)挑選出的屈曲約束支撐的配置對應(yīng)的典型荷載位移響應(yīng)如圖二b所示。正如看到的，得到了整個(gè)的滯后線圈和完美的能量擴(kuò)散。然而，要注意的是壓縮的屈服荷載要比拉伸的高出10%左右。這一點(diǎn)要在框架設(shè)計(jì)中進(jìn)行說明。</p><p>

9、;　　圖二：（a）采用的屈曲約束支撐結(jié)構(gòu) （b）屈曲約束支撐的典型荷載位移響應(yīng)</p><p><b>　　設(shè)計(jì)要素</b></p><p>　　為滿足一般的性能要求，依據(jù)不同的設(shè)計(jì)程序設(shè)計(jì)了三個(gè)原型框架來進(jìn)行對比。第一個(gè)框架由臺灣的地震工程研究中心的科研小組設(shè)計(jì)，這個(gè)框架的底部剪力計(jì)算依據(jù)基于位移的多模式抗震設(shè)計(jì)程序，這個(gè)指導(dǎo)方針還在2002年規(guī)定了臺灣的

10、抗震設(shè)計(jì)規(guī)則。這個(gè)框架是根據(jù)彈性方法設(shè)計(jì)的。第二個(gè)框架（密歇根大學(xué)設(shè)計(jì)的第一個(gè)框架）由密歇根大學(xué)的團(tuán)隊(duì)設(shè)計(jì)。他們的底部剪力假定了臺灣地震工程研究中心的結(jié)果，但他們采用了最近形成的塑性設(shè)計(jì)方法。第三個(gè)框架（密歇根大學(xué)的第二個(gè)框架）在計(jì)算底部剪力時(shí)采用了由密歇根大學(xué)研究的基于能量的簡單程序?？蚣艿脑O(shè)計(jì)采用了同密歇根大學(xué)第一個(gè)框架一樣的塑性設(shè)計(jì)方法。</p><p>　　基本設(shè)計(jì)參數(shù)由臺灣地震工程研究中心的科研小組依據(jù)

11、2002年起草的臺灣抗震設(shè)計(jì)規(guī)則選定。每一層的地震作用平均的分配到到兩個(gè)抗震框架上。作用在每層上的地震作用如下，</p><p>　　一層和二層：714千磅 三層564千磅。</p><p>　　為了計(jì)算原型建筑的設(shè)計(jì)底部剪力采用了兩種不同的性能標(biāo)準(zhǔn)，并把其中較大的結(jié)果作為實(shí)驗(yàn)框架的設(shè)計(jì)依據(jù)。根據(jù)第一個(gè)性能標(biāo)準(zhǔn)（保護(hù)準(zhǔn)則），當(dāng)建筑遭受在未來50年超過10%的地震烈度（1

12、0/50）時(shí)，最大頂部位移設(shè)定為0.02弧度。根據(jù)第二個(gè)性能標(biāo)準(zhǔn)（預(yù)防準(zhǔn)則），在建筑物遭受2/50的地震作用時(shí)，最大頂部位移設(shè)定為0.025弧度。10/50和2/50這些地震事件會(huì)通過適當(dāng)?shù)囊蛩剡M(jìn)行測量來表示為真實(shí)的地面運(yùn)動(dòng)。這種測量是通過在周期為一秒的SDOF系統(tǒng)中考慮5%的衰減模擬加速度譜線進(jìn)行的。這些測量因素同樣由相同的加速度譜線決定，并與臺灣地震規(guī)則中規(guī)定的在堅(jiān)硬的巖石場地10/50和2/50的地震事件相關(guān)規(guī)則相對應(yīng)。這兩個(gè)測試

13、結(jié)果分別有0.461g和0.622g的地震加速度。</p><p>　　根據(jù)框架的設(shè)計(jì)原則和簡單性能分析，整個(gè)底部剪力將被分配到三個(gè)樓層上。每層上的力將按下面公式進(jìn)行計(jì)算。</p><p><b>　　(1)</b></p><p>　　mi和δi分別表示各層的質(zhì)量和位移，Vd表示總的設(shè)計(jì)底部剪力。各層的地震力的相對值如下：</p>

14、<p>　　一層：0.11 二層：0.365 三層：0.525</p><p><b>　　設(shè)計(jì)底部剪力</b></p><p><b>　　臺灣設(shè)計(jì)方案</b></p><p>　　這一部分將簡單介紹臺灣地震工程研究中心對底部剪力的設(shè)計(jì)，更加詳細(xì)的介紹會(huì)在其他地方看到（文獻(xiàn)1）。</p&

15、gt;<p>　　第一步，將框架理想化為有三個(gè)自由度的MDOF體系。三種模式的模型影響因素以及模型的質(zhì)量和模型各層的位移都將進(jìn)行計(jì)算。對于這個(gè)特殊的框架，由于第二和第三中模式的貢獻(xiàn)率（MCF分別為0.008和0.002）相對于第一模式（MCF=0.99）來說無關(guān)緊要，所以只把第一模式作為實(shí)驗(yàn)?zāi)繕?biāo)。因此，在第一模式下的第三樓層位移將被作為與模型目標(biāo)頂部位移相關(guān)的有效系統(tǒng)位移δeff。</p><p>

16、　　第二步，計(jì)算框架第一模式的延展性。因?yàn)橹慰蚣艹惺芰?0%的地震作用，所以有效系統(tǒng)的屈曲位移根據(jù)支撐點(diǎn)的屈曲位移計(jì)算，再增加25%作為瞬間框架的影響。根據(jù)各層的最大位移，計(jì)算各層的延展性，然后取平均值作為系統(tǒng)的有效延展性。采用這種延展性和有效目標(biāo)位移δeff，系統(tǒng)的有效周期將通過非彈性地面運(yùn)動(dòng)譜線得出。根據(jù)這個(gè)時(shí)間周期，計(jì)算出系統(tǒng)相應(yīng)的有效堅(jiān)硬度Keff。</p><p>　　最后，目標(biāo)位移點(diǎn)的底部剪力通過δ

17、eff和Keff的簡單相乘計(jì)算出。根據(jù)假設(shè)在5%拉力下的線性荷載位移曲線和計(jì)算出的延展度，最終的底部剪力可以簡化為屈服底部剪力。屈服底部剪力作為框架的設(shè)計(jì)底部剪力（Vd）。兩個(gè)性能標(biāo)準(zhǔn)中，第二個(gè)標(biāo)準(zhǔn)的底部剪力起支配作用，等于415千磅。</p><p><b>　　密歇根大學(xué)設(shè)計(jì)方案</b></p><p>　　采用密歇根大學(xué)研究的程序?qū)Φ撞考袅M(jìn)行重新計(jì)算（文獻(xiàn)2,

18、3）。其中地震對結(jié)構(gòu)頂點(diǎn)彈性輸入能量的一小部分等于結(jié)構(gòu)達(dá)到最大目標(biāo)位移所需的能量。這個(gè)程序的簡單介紹如下。</p><p>　　圖三：倒塌預(yù)防準(zhǔn)則的理性框架響應(yīng)</p><p>　　首先，用理性的三線性曲線來模擬最大底部剪力和位移的關(guān)系，如圖三所示。這個(gè)三線性曲線是分別根據(jù)支撐框架的最大底部剪力剖面圖和瞬間框架得到的。這些剖面圖是理性的彈塑性響應(yīng)曲線。支撐框架的屈服點(diǎn)最大位移可以根據(jù)框架的

19、幾何構(gòu)造計(jì)算出。正如前面提到的假定支撐框架在這一點(diǎn)承受未知設(shè)計(jì)底部剪力Vd的80%。根據(jù)過去的分析結(jié)果，瞬間框架的最大屈服位移假定為2%，承受剩余設(shè)計(jì)底部剪力的20%。將這兩個(gè)雙線性曲線疊加得到整個(gè)框架位移荷載的三線性曲線（如圖三所示）。根據(jù)這個(gè)曲線計(jì)算出框架的延展度μ。</p><p>　　第二部，根據(jù)彈性SDOF系統(tǒng)，利用Housner給出的公式計(jì)算出最大輸入能量，公式如下所示：</p><

20、;p><b>　?。?）</b></p><p>　　M和Sv分別表示總質(zhì)量和模擬線譜速率。然而，對于非彈性系統(tǒng)，這個(gè)公式就需要進(jìn)行改良（如圖四a所示）。因此，在公式（2）中添加修正因子γ將理性彈塑性系統(tǒng)添加到選定的目標(biāo)位移中，如圖四a中所示。通過采用這個(gè)修正因子，并將Sv轉(zhuǎn)化為線譜加速度Ceg，模型所需能量Em可表示為下式所示，</p><p><b&g

21、t;　?。?）</b></p><p>　　W和T分別表示系統(tǒng)的質(zhì)量和基本周期，Ce表示最大的聯(lián)合底部剪力。根據(jù)IBC2000（文獻(xiàn)5）的抗震規(guī)定，三層框架的T 可以估計(jì)為0.37秒。用這個(gè)周期，可以從臺灣抗震規(guī)則草圖（2002）給定的設(shè)計(jì)響應(yīng)譜線得到Ce。γ可以根據(jù)Leelataviwat提出的γ-μ-T關(guān)系（如圖四b所示）得到。</p><p>　　圖四：（a）彈性、非彈性

22、能量的輸入 （b）周期能量修正因素</p><p>　　改良的輸入能量Em等于作用在框架上的地震作用,如圖四a所示的位移。為這個(gè)目的，假定了雙線性荷載位移關(guān)系圖（如圖四a所示）和隨框架高度線性分配的樓層位移。如上所述，可以得到各層的地震力分配。根據(jù)這個(gè)能量平衡方程，得到設(shè)計(jì)底部剪力Vd.依據(jù)臺灣所采用的方法，由第二準(zhǔn)則（在2/50地震作用下有2.5%的位移）計(jì)算得到的等于340千磅，需要注

23、意它比臺灣采用的方法得到的計(jì)算結(jié)果小。</p><p>　　13th World Conference on Earthquake Engineering</p><p>　　Vancouver, B.C., Canada</p><p>　　August 1-6, 2004</p><p>　　Paper No. 497</p>

24、<p>　　PERFORMANCE-BASED SEISMIC DESIGN AND BEHAVIOR OF A</p><p>　　COMPOSITE BUCKLING RESTRAINED BRACED FRAME</p><p>　　Prabuddha DASGUPTA1, Subhash C. GOEL2, Gustavo PARRA-MONTESINOS3, and

25、 K. C. TSAI4</p><p><b>　　SUMMARY</b></p><p>　　The concept of Buckling Restrained Braced Frames is relatively new and recently their use has increased</p><p>　　in the U.S

26、., Japan and Taiwan. However, detailed design provisions for common practice are currently</p><p>　　under development. Since the summer of 2002, researchers at the University of Michigan (UM) have</p>

27、<p>　　been working cooperatively in a joint study with research team at the National Center for Research on</p><p>　　Earthquake Engineering (NCREE), Taiwan, involving design, analysis and full scale te

28、sting of such a</p><p>　　frame by pseudo-dynamic method.</p><p>　　The selected structure is a three story, three bay frame consisting of concrete-filled-tube (CFT) columns,</p><p>　

29、　steel beams, and composite buckling restrained braces. The frame was designed using an Energy-Based</p><p>　　Plastic Design procedure recently developed by co-author Goel at UM. The method utilized selected

30、</p><p>　　target drifts (2.0% for 10% in 50 year and 2.5% for 2% in 50 year design spectra for this frame) and</p><p>　　global yield mechanism. Because of the need for more precise control of de

31、sign clearances between the</p><p>　　end connections and steel casing of the braces, buckling restrained braced frames are excellent candidates</p><p>　　for application of this newly developed d

32、esign methodology.</p><p>　　The paper briefly presents the energy-based approach developed at UM as well as a modal displacementbased</p><p>　　design procedure adopted by the research team at NC

33、REE for calculation of design base shear for</p><p>　　the frame. Results from inelastic response analyses of frames deigned by the two methods for a Taiwan</p><p>　　earthquake are compared. The

34、same frame was also designed for a U.S. location and analyzed under</p><p>　　ground motions scaled for U.S. standards. The frames designed by the UM approach exhibited</p><p>　　satisfactory dyna

35、mic responses for both Taiwan and U.S. ground motions.</p><p>　　INTRODUCTION</p><p>　　Excellent seismic behavior of buckling restrained braces (BRBs) (Tsai [1]) encouraged an experimental</p&

36、gt;<p>　　program at the National Center for Research on Earthquake Engineering (NCREE), Taiwan, in</p><p>　　conjunction with analysis and design studies by researchers in the U.S. at the University of

37、 Michigan. In</p><p>　　1 Ph.D. Candidate, University of Michigan, Ann Arbor, MI</p><p>　　2 Professor, University of Michigan, Ann Arbor, MI</p><p>　　3 Assistant Professor, Universit

38、y of Michigan, Ann Arbor, MI</p><p>　　4 Professor, National Taiwan University, Taiwan</p><p>　　this program, the BRBs provide the primary seismic resistance mechanism to a 3-story 3-bay frame,&l

39、t;/p><p>　　tested under pseudo-dynamic loading at NCREE in October 2003. General layout of the prototype</p><p>　　building is shown in Figure 1a, while a view of the test frame is shown in Figure 1

40、b. For design purpose,</p><p>　　two of such frames were assumed to resist the total seismic force for a 3-story prototype building. The</p><p>　　seismic frames are indicated by thick lines in Fi

41、gure 1a.</p><p>　　DESCRIPTION OF TEST FRAME</p><p>　　The frame was designed to resist the seismic loading through two separate mechanisms. The primary</p><p>　　resistance is provide

42、d by buckling restrained braces in the central bay of the frame (Figure 1b). This bay</p><p>　　is designed to act as a purely braced frame with all beam-to-column and brace-to-column connections</p>&

43、lt;p>　　made as simple (pinned) connections. The braces are designed to resist 80% of the total seismic force for</p><p>　　each seismic frame, while 20% of the load is resisted by the two external bays, de

44、signed as moment</p><p>　　frames with moment connections at the joints of exterior beams and columns. All columns are made of</p><p>　　concrete filled tubes. Different sections are chosen for in

45、terior and exterior columns, while keeping the</p><p>　　same size along the building height. Wide flange sections are used for beams. Different beam sizes are</p><p>　　used at different floors,

46、while keeping the same size in all the bays at each floor.</p><p><b>　　4@23 ft</b></p><p><b>　　6@ft</b></p><p><b>　　3@23 ft</b></p><p&

47、gt;<b>　　(a) (b)</b></p><p>　　Figure 1: (a) Layout of the prototype building, (b) View of the test frame</p><p>　　BUCKLING RESTRAINED BRACE PROPERTIES</p><p>　　Buckling r

48、estrained braces are typically made by encasing a steel core member in a concrete filled steel</p><p>　　tube (Figure 2a). The steel core is kept separated from the concrete filled tube by a layer of unbondin

49、g</p><p>　　material applied on the surface of the steel core. The role of concrete encasing and steel tube is to prevent</p><p>　　buckling of the steel core, so that a well formed load-displacem

50、ent response of the brace is achieved</p><p>　　under large displacement reversals. The unbonding material ensures that the force coming into the BRB is</p><p>　　carried by the core only, without

51、 engaging the encasing material. Different configurations of BRBs were</p><p>　　tested at NCREE under large reversed cyclic axial loading and an optimum configuration was selected for</p><p>　　u

52、se in the test frame (Tsai [1]) (Figure 2a). A typical load-displacement response obtained from the</p><p>　　selected BRB configuration is shown in Figure 2b. As can be seen, full hysteretic loops and excell

53、ent</p><p>　　energy dissipation were achieved. However, it is to be noted that the yield load reached in compression</p><p>　　was about 10% higher than that reached in tension. This needs to be

54、accounted for while designing the</p><p><b>　　frame.</b></p><p>　　Seismic frame</p><p><b>　　3@13 ft</b></p><p><b>　　BRBs</b></p&g

55、t;<p><b>　　4@23 ft</b></p><p>　　6@23 ft 3@23 ft</p><p><b>　　(a) (b)</b></p><p>　　Figure 2: (a) Configuration of the BRB adopted, and (b) Typical load-

56、displacement behavior of a BRB</p><p>　　(From Tsai [1])</p><p>　　DESIGN CONSIDERATIONS</p><p>　　A comparative study is presented on the behavior of three prototype frames designed t

57、o meet common</p><p>　　performance criteria through different design procedures. The first frame was designed by the research</p><p>　　team at NCREE. For this frame, calculation of base shear wa

58、s done following a multi-modal</p><p>　　displacement-based seismic design (DSD) procedure and the guidelines stipulated in the 2002 Draft</p><p>　　Taiwan Seismic Design Code. Design of that fram

59、e was done by elastic method. The second frame was</p><p>　　designed by the team at University of Michigan. In this case, same base shear as calculated by the</p><p>　　NCREE team was assumed. Ho

60、wever, a plastic design procedure, recently developed by Goel, was</p><p>　　adopted to design the frame (UM Frame 1). The third frame (UM Frame 2) was designed for a base shear</p><p>　　calculat

61、ed by following a simple energy-based procedure developed at UM (Leelataviwat [2], Lee [3]).</p><p>　　Frame design was done by the plastic design method as used for UM Frame 1.</p><p>　　The basi

62、c design parameters were selected by the research team at NCREE following the 2002 Draft</p><p>　　Taiwan Seismic Design code. Total seismic weight of each floor was divided equally between the two</p>

63、<p>　　seismic frames. The seismic weights applied on each frame were as follows,</p><p>　　1st and 2nd Floor: 714 kips, and 3rd Floor: 564 kips</p><p>　　In order to calculate the design bas

64、e shear for the prototype building, two performance criteria were</p><p>　　considered and the one that resulted in higher design base shear was chosen for the design of the test</p><p>　　frame.

65、In the first performance criterion (Life Safety), maximum roof drift was set at 0.02 radian when the</p><p>　　building is subjected to an earthquake that has a 10% probability of exceedance in 50 years (10/5

66、0). In the</p><p>　　second performance criterion (Collapse Prevention), maximum roof drift was set at 0.025 radian for a</p><p>　　2/50 seismic event. A real ground motion time history was scaled

67、 by appropriate factors to represent the</p><p>　　10/50 and 2/50 events. Scaling was done by considering the 5% damped Pseudo Spectral Acceleration</p><p>　　(PSA) of a SDOF system with period T=

68、1 sec. The scaling factors were determined by equating this</p><p>　　spectral acceleration to the corresponding values prescribed in the draft Taiwan seismic code for 10/50</p><p>　　and 2/50 eve

69、nts at a hard rock site. The two resulting time histories have PGA values of 0.461g and</p><p>　　0.622g, respectively.</p><p>　　For the purpose of frame design and for performing the push-over a

70、nalysis, the total base shear needs to</p><p>　　be distributed over the three floor levels. The force at i-th floor was calculated by using the following</p><p><b>　　equation:</b><

71、;/p><p><b>　　N d</b></p><p><b>　　i</b></p><p><b>　　i i</b></p><p><b>　　i i</b></p><p><b>　　i V</b>

72、</p><p><b>　　m</b></p><p><b>　　m</b></p><p><b>　　F</b></p><p><b>　　Σ?</b></p><p><b>　　?</b><

73、/p><p><b>　　1</b></p><p><b>　　?</b></p><p><b>　　?</b></p><p><b>　　, (1)</b></p><p>　　where i i m and ??are the

74、 mass and target displacement, respectively, of the i-th floor, and d V is the total</p><p>　　design base shear. The relative floor forces obtained are as follows:</p><p>　　1st Floor: 0.11, 2nd

75、Floor: 0.365, and 3rd Floor: 0.525</p><p>　　DESIGN BASE SHEAR</p><p>　　Taiwan Design</p><p>　　A brief description of the NCREE procedure to arrive at the design base shear is presen

76、ted in this section.</p><p>　　A detailed description of this procedure can be found elsewhere (Tsai [1]).</p><p>　　In the first step, the frame was idealized as a MDOF system with three degrees

77、of freedom. Modal</p><p>　　Contribution Factors (MCF) for the three modes, as well as their modal masses and modal story drifts,</p><p>　　were then computed. Since, for this particular frame, th

78、e contributions from the 2nd and 3rd modes (MCF =</p><p>　　0.008 and 0.002, respectively) were insignificant compared to the contribution from the 1st mode (MCF =</p><p>　　0.99) (Tsai [1]), only

79、 the 1st mode was considered for design purposes. Thus, the three floor</p><p>　　displacements of the 1st mode were used to obtain an effective system displacement eff ??associated with</p><p>　

80、　the modal target roof drift.</p><p>　　In the next step, the ductility demand for the 1st mode of the frame was computed. Because 80% of the</p><p>　　seismic force was to be carried by the brace

81、d frame, yield drift of the effective system was computed</p><p>　　based on the drift at the point of brace yielding and increased by 25% to account for the contribution from</p><p>　　the moment

82、 frame. From the target maximum story drifts, ductility demand for each story was calculated</p><p>　　and a simple average was taken as the effective ductility demand for the system. Using this ductility<

83、/p><p>　　demand, and from the effective target displacement eff ??, the effective time period of the system was</p><p>　　obtained from the inelastic displacement spectrum of the ground motion consi

84、dered. Corresponding</p><p>　　effective stiffness eff K value of the system was computed from this time period.</p><p>　　Finally, the base shear required at the point of target drift was compute

85、d by simply multiplying eff K</p><p>　　by eff ??. This ultimate base shear was reduced to the yield base shear by assuming a bi-linear loaddisplacement</p><p>　　curve with a strain hardening of

86、5% and the ductility demand as computed earlier. This</p><p>　　yield base shear served as the design base shear (Vd) of the frame. Of the two performance criteria, the</p><p>　　base shear comput

87、ed from the second criterion governed and was equal to 415 kips.</p><p><b>　　UM Design</b></p><p>　　The base shear was re-calculated by using a procedure developed at UM (Leelataviwa

88、t [2], Lee [3]),</p><p>　　where a fraction of the peak elastic input energy of an earthquake to a structure is equated to the energy</p><p>　　needed by the structure in getting pushed up to the

89、maximum target displacement. The procedure is</p><p>　　briefly described below.</p><p>　　In the first step, the base shear-roof displacement profile of the frame was modeled by an idealized tril

90、inear</p><p>　　curve, as shown in Figure 3. This tri-linear curve was obtained by considering the base shear-roof</p><p>　　displacement profiles of the braced frame and the moment frame separate

91、ly. Both of these profiles were</p><p>　　idealized by elastic-perfectly plastic responses. Roof drift of the braced frame at yield point can be easily</p><p>　　calculated from the geometry of th

92、e frame. As mentioned earlier, the base shear carried by the braced</p><p>　　frame at this point was assumed as 80% of the total design base shear Vd, which is an unknown at this</p><p>　　stage.

93、 Based on past analysis results, roof drift of the moment frame at yield was assumed as 2%, carrying</p><p>　　the remaining 20% of the total base shear. These two bi-linear curves were superimposed to obtain

94、 the trilinear</p><p>　　load-displacement curve of the whole frame (Figure 3). This tri-linear curve was further simplified</p><p>　　to a bi-linear curve (Figure 3) by equating the areas under t

95、he two curves. The design ductility</p><p>　　demand??for the frame was calculated from this curve.</p><p><b>　　0</b></p><p><b>　　0.2</b></p><p>

96、<b>　　0.4</b></p><p><b>　　0.6</b></p><p><b>　　0.8</b></p><p><b>　　1</b></p><p><b>　　1.2</b></p><p&

97、gt;　　0 0.5 1 1.5 2 2.5 3</p><p>　　Roof Drift (%)</p><p>　　Base Shear/Vd</p><p>　　Figure 3: Idealized frame responses for Collapse Prevention criterion</p><p>　　In the n

98、ext step, the peak input energy was calculated by considering an elastic SDOF system and by</p><p>　　using the equation given by Housner [4], as shown below,</p><p><b>　　2</b></p&

99、gt;<p><b>　　2</b></p><p><b>　　1</b></p><p>　　E ??MSv , (2)</p><p>　　where M and Sv are the total mass and the pseudo spectral velocity of the system,

100、respectively. However,</p><p>　　for an inelastic system, this equation needs to be modified (Figure 4a). Thus, a modification factor??was</p><p>　　applied to Eqn. (2) to estimate the energy need

101、ed to push the idealized elastic-perfectly plastic system to</p><p>　　the selected target displacement, as shown in Figure 4a. Applying this modification factor and converting</p><p>　　Sv to spe

102、ctral acceleration C g e , the modified required energy, m E , can be re-written as,</p><p><b>　　2</b></p><p><b>　　2 2</b></p><p><b>　　1</b></

103、p><p><b>　　??</b></p><p><b>　　?</b></p><p><b>　　??</b></p><p><b>　　? ??m e C</b></p><p><b>　　T</b>

104、</p><p><b>　　E Wg</b></p><p><b>　　?</b></p><p><b>　　??, (3)</b></p><p>　　where W and T are the total weight and the fundamental peri

105、od of the system, respectively. e C is the</p><p>　　maximum base shear coefficient. Following the seismic provisions of IBC 2000 [5], the value of T for the</p><p>　　3-story frame was estimated

106、as 0.37 sec. Using this period, e C was obtained from the design response</p><p>　　spectra given in the Draft Taiwan Seismic Code (2002) for the two considered hazard levels. The value of</p><p>

107、;　　??was obtained from the ????????T relationship (Figure 4b) proposed by Leelataviwat [2].</p><p>　　The modified input energy, m E is then equated to the total work done by the seismic forces applied to the

108、</p><p>　　frame as it is pushed to the target drift as shown in Figure 4a. For this purpose, a bi-linear loaddisplacement</p><p>　　behavior (Figure 4a) and a linear distribution of the floor dis

109、placements along the height of</p><p>　　the frame were assumed. A distribution of floor forces, as mentioned earlier, was also assumed. From this</p><p>　　Idealized tri-linear curve</p>&