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。然而，對于一般實踐的詳細設(shè)計規(guī)則當前還處于發(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伍展開合作，在設(shè)計、分析和應(yīng)用模擬動力測試方法對這種框架進行全方位測試等方面進行聯(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)計程序設(shè)計而成的。這種方法利用了選定的目標作業(yè)份額（對這個框架在50年中2.0%到10%荷載50年設(shè)計范圍中的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)計方法和由臺灣地震工程研究中心的科研小組為計算框架底部剪力的設(shè)計計算結(jié)果而采用的基于位移的設(shè)計程序模式，并對兩種方法對于一次臺灣地震而設(shè)計的框架無彈性響應(yīng)結(jié)果進行了對比。同樣的框架也在美國進行了設(shè)計，并依據(jù)美國的標準在地面

4、運動下進行了分析。由密歇根大學(xué)設(shè)計的框架對臺灣和美國的地面運動都基本符合動力響應(yīng)。</p><p><b>　　介紹</b></p><p>　　屈曲約束支撐極好的地震反應(yīng)激勵了臺灣地震工程研究中心的實驗計劃，也鼓勵了密歇根大學(xué)的研究者們對分析和設(shè)計之間結(jié)合的進一步研究。在這個計劃中，屈曲約束支撐為2003年10月在臺灣地震工程研究中心進行模擬動力荷載實驗的三層三跨框

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，實驗框架的立面如圖一b所示。針對實驗?zāi)康?，假定這些跨中的兩個能夠抵抗作用在一個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>　　本框架通過兩個互相分離的機構(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)計為一個完全的支撐框架，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。在每一個地震作用的框架中，支撐被設(shè)計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行試驗，從而挑選出最適宜實驗框架的配置（圖二a）一個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，得到了整個的滯后線圈和完美的能量擴散。然而，要注意的是壓縮的屈服荷載要比拉伸的高出10%左右。這一點要在框架設(shè)計中進行說明。</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)計要素</b></p><p>　　為滿足一般的性能要求，依據(jù)不同的設(shè)計程序設(shè)計了三個原型框架來進行對比。第一個框架由臺灣的地震工程研究中心的科研小組設(shè)計，這個框架的底部剪力計算依據(jù)基于位移的多模式抗震設(shè)計程序，這個指導(dǎo)方針還在2002年規(guī)定了臺灣的

10、抗震設(shè)計規(guī)則。這個框架是根據(jù)彈性方法設(shè)計的。第二個框架（密歇根大學(xué)設(shè)計的第一個框架）由密歇根大學(xué)的團隊設(shè)計。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)計方法。第三個框架（密歇根大學(xué)的第二個框架）在計算底部剪力時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)計采用了同密歇根大學(xué)第一個框架一樣的塑性設(shè)計方法。</p><p>　　基本設(shè)計參數(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)計規(guī)則選定。每一層的地震作用平均的分配到到兩個抗震框架上。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>　　為了計算原型建筑的設(shè)計底部剪力采用了兩種不同的性能標準，并把其中較大的結(jié)果作為實驗框架的設(shè)計依據(jù)。根據(jù)第一個性能標準（保護準則），當建筑遭受在未來50年超過10%的地震烈度（1

12、0/50）時，最大頂部位移設(shè)定為0.02弧度。根據(jù)第二個性能標準（預(yù)防準則），在建筑物遭受2/50的地震作用時，最大頂部位移設(shè)定為0.025弧度。10/50和2/50這些地震事件會通過適當?shù)囊蛩剡M行測量來表示為真實的地面運動。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)計原則和簡單性能分析，整個底部剪力將被分配到三個樓層上。每層上的力將按下面公式進行計算。</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)計底部剪力</b></p><p><b>　　臺灣設(shè)計方案</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，更加詳細的介紹會在其他地方看到（文獻1）。</p&

15、gt;<p>　　第一步，將框架理想化為有三個自由度的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行計算。對于這個特殊的框架，由于第二和第三中模式的貢獻率（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驗?zāi)繕?。因此，在第一模式下的第三樓層位移將被作為與模型目標頂部位移相關(guān)的有效系統(tǒng)位移δeff。</p><p>

16、　　第二步，計算框架第一模式的延展性。因為支撐框架承受了80%的地震作用，所以有效系統(tǒng)的屈曲位移根據(jù)支撐點的屈曲位移計算，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位移δeff，系統(tǒng)的有效周期將通過非彈性地面運動譜線得出。根據(jù)這個時間周期，計算出系統(tǒng)相應(yīng)的有效堅硬度Keff。</p><p>　　最后，目標位移點的底部剪力通過δ

17、eff和Keff的簡單相乘計算出。根據(jù)假設(shè)在5%拉力下的線性荷載位移曲線和計算出的延展度，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)計底部剪力（Vd）。兩個性能標準中，第二個標準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)計方案</b></p><p>　　采用密歇根大學(xué)研究的程序?qū)Φ撞考袅M行重新計算（文獻2,

18、3）。其中地震對結(jié)構(gòu)頂點彈性輸入能量的一小部分等于結(jié)構(gòu)達到最大目標位移所需的能量。這個程序的簡單介紹如下。</p><p>　　圖三：倒塌預(yù)防準則的理性框架響應(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。支撐框架的屈服點最大位移可以根據(jù)框架的

19、幾何構(gòu)造計算出。正如前面提到的假定支撐框架在這一點承受未知設(shè)計底部剪力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)計底部剪力的20%。將這兩個雙線性曲線疊加得到整個框架位移荷載的三線性曲線（如圖三所示）。根據(jù)這個曲線計算出框架的延展度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)，這個公式就需要進行改良（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)添加到選定的目標位移中，如圖四a中所示。通過采用這個修正因子，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5）的抗震規(guī)定，三層框架的T 可以估計為0.37秒。用這個周期，可以從臺灣抗震規(guī)則草圖（2002）給定的設(shè)計響應(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)這個能量平衡方程，得到設(shè)計底部剪力Vd.依據(jù)臺灣所采用的方法，由第二準則（在2/50地震作用下有2.5%的位移）計算得到的等于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>&