在以鋼筋混凝土構築形式之公眾建築物與校舍中，承受垂直載重的物件以柱子為主，其餘則為承重牆。就柱子而言，除為通風與照明而開窗所造成的短柱外，幾乎多為長柱，一旦柱桿件破壞，建築物整體的安全與穩定性將遭受無可彌補的災損。
一般長柱多發生撓曲破壞的型態，而大多的文獻是用統計方式估算其在試驗過程中所發生的極限位移，或探討主筋挫曲的原因與預防對策，但是針對主筋挫曲後之位移與強度，則因為考慮到試驗的安全與困難度，而鮮少有人能在極限位移之外再討論殘餘強度與其挫曲後的位移，故試驗資料付之闕如，無法在文獻中搜尋到相關結果。
在台灣傳統校舍中，因空間需求多半常以磚牆做為教室與教室之間的隔間材料，而現行的分析多半都忽略不計磚牆的面外力強度，但是國家地震工程研究中心(下稱國震中心) 在其校舍建築物耐震能力之現地側推試驗中，發現在現地試驗中承受垂直承載力的撓曲柱桿件開始破壞後，建築物在隔間磚牆的面外方向存有部分殘餘強度因而延緩了倒塌，故可利用磚牆補強的方式，藉以提高校舍結構物在面外方向的耐震能力。如此，在延緩倒塌與增加耐震能力的雙重機制下，可增加民眾於地震中存活下來的機率。
在本文中，筆者利用了華盛頓大學維護的柱子資料庫，嘗試建立主筋挫曲後位移與強度的模型，並定義柱桿件的強度衰減方法，為柱桿件建議了一個三折線的載重位移曲線，其中的關鍵點分別為最大階段點、主筋挫曲階段點、主筋挫曲後階段點與殘餘階段點。在構架內填磚牆的部分，本文以五個足尺比例之試體，試圖建立補強與未補強的構架殘餘強度之曲線模型，其中補強的工法，本文在不改變現有門窗的配置下，而僅以黏貼碳纖維貼片(CFRP)於教室隔間的磚牆上，藉此提高其面外之抗震能力。
根據上述的柱桿件模型分析發現以下現象：一、混凝土保護層的剝落與主筋的挫曲為柱桿件破壞前的指標；二、當柱桿件強度進入塑性鉸後期，可將鋼筋的降伏強度提高1.25倍做為計算的基準，與試驗的挫曲強度與挫曲後強度有相當程度的吻合。而在構架內填磚牆的殘餘強度模型部分，有以下的現象：一、構架含磚牆試驗的殘餘強度是清楚呈現，且分析與試驗結果相近；二、將補強與未補強的構架相比，補強者之側向強度和殘餘強度皆會提升；三、柱桿件的垂直承載力在破壞後會轉移至磚牆上，磚牆便扮演另一個傳力機制，即磚牆和拉力鋼筋所形成的力偶將支撐構架，而不致立即的倒塌。
將筆者建議的柱桿件曲線模型與資料庫試驗比對，曲線走勢與試驗相符，故建議之模型屬合理假設。而為更進一步驗證本研究模型之預測結果可否實際應用在其他試驗場資料上，特試用國震中心於不同年度所完成的四座單柱試體來分析，結果顯示，本建議模型均能合理評估並符合試驗結果。在應用於工程界的部分，則採用國震中心之二層樓三跨之單面教室構架的試驗並做側推分析，其中撓曲桿件之塑性鉸利用本文的模型模擬，其結果也與試驗的破壞趨勢相仿。而在構架內填磚牆的殘餘強度曲線模型部分，本建議模型與試驗的載重位移具良好相關性。

Reinforced concrete (RC) columns are the most important elements in public and school buildings for bearing vertical loads. Generally, columns are slender and can be formed to meet ventilation and lighting requirements. Once columns fail, the loss in overall building safety and stability induces irreparable damage.
Flexural failure usually occurs in slender columns; a great deal of discussion in the literature is about ultimate displacement, as calculated with the statistical method. However, there has been little discussion on post-bar buckling displacement and residual strength for flexural failure modes because test-related information is not available for investigation; most tests aim to investigate the reasons for buckling and its prevention. Laboratory safety and test difficulty are the main concerns, so few studies have focused on the residual strength and bar buckling displacement after ultimate displacement.
In old Taiwanese school buildings, brick walls are widely used as partition structures for larger space requirements, but the strength of the brick walls due to the out-of-plane direction is ignored in most cases. The National Center for Research on Earthquake Engineering (NCREE) investigated the residual strength in-situ pushover test for the seismic capacity of school buildings out-of-plane. Rather than attempting to change existing doors and windows, it seems more convenient to retrofit the confined brick walls between classrooms with carbon fiber reinforced plastic to improve their out-of-plane seismic capacities. The residual strength is derived from the fact that the infilled brick wall takes over the axial load from the columns and delays their axial failure.
In this study, the University of Washington database of columns was used to propose a formula for the post-bar buckling displacement and residual strength as well as a trilinear curve model for the load displacement at four points: the maximum state point, the bar buckling state point, post-bar buckling state point, and residual state point. For the RC frames infilled with brick walls, a residual strength model for brick walls is proposed; tests were conducted on five full-scale specimens.
Analysis based on the proposed model yielded the following results: (1) Fail indicators for the cover spalled with bar buckling. (2) Reinforcement of the yield strength increased 1.25 times over that calculated when the column strength was at the plastic hinge, and satisfied the test results of strength for the BB and PB states. (3) The residual strength of frames infilled with brick walls, however, was clearly observed. (4) The retrofitted specimens exhibited improved structural performance compared to non-retrofitted specimens in terms of both the maximum strength and residual strength. (5) This residual strength can prevent frames from immediate collapse.
For comparison, the analysis results were assumed to show a similar trend to the test results; this assumption is proved reasonable. To further validate this proposed model as being able to efficiently predict other laboratory experiments and practical application in field tests, research on four single-column specimens constructed at the NCREE was adopted to analyze the results. The proposed model was found to effectively and reasonably predict the test results. For practical engineering applications, a single frame of a classroom test containing the second floor with three spans by the NCREE was performed by pushover analysis. The setting of plastic hinges employed the proposed model of this study to simulate flexural failure. The results showed that the analysis results had a similar trend to the results of the collapse test.. For the model of the RC frames infilled with brick walls, the proposed analytical model predicted the out-of-plane load–displacement relationship of the frames with flexural failure.

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