本研究探討一線彈性完美塑性材料所構成之梁，梁之不同斷面包括矩形、圓形、菱形及工字形等常見幾何形狀，分別考慮三種不同梁之邊界束制條件：簡支梁、固定端梁與懸臂梁，藉由塑性變形理論分析計算此三種基本量承受外載集中力下之撓曲變位行為，另外，使用ABAQUS有限元素分析軟體驗證理論推導結果之正確性。理論推導與數值分析結果皆可發現，若將基本梁上之外載集中力及撓度，分別進行第一次正規化處理，可消除梁不同邊界束制條件之影響，使得此三種基本梁正規化外載集中力與撓度之關係重合於同一曲線，然而，不同斷面形狀基本第一次正規化外載集中力與撓度之關係曲線並未重合。若將上述各斷面形狀基本梁之關係曲線進行第二次正規化處理，將使得不同斷面基本梁第二次正規化外載集中力與撓度之關係曲線近乎重合。為進一步評估第二次正規化關係曲線之應用範圍，將使用此第二次正規化關係曲線計算分析其他斷面基本梁之完美彈塑性撓曲行為，本研究以箱型斷面基本梁為例，將預估之關係曲線函數與理論推導結果互相比較驗證，確認本研究所建立基本梁外載集中力與撓度關係曲線函數之適用性。

The bending deflections of some basic beams with various cross-sectional shapes, made from elasto-perfectly plastic solid material and subjected to a concentrated force, were derived theoretically by using plastic deformation theory and conjugate beam method. The spreading of the plastic zones of the beams from initial yielding to fully plasticity was analyzed and their corresponding elasto-plastic deflections were calculated. Furthermore, the resulting theoretical results were verified numerically by using a finite element analysis software ABAQUS. It is found that if the applied external concentrated forces and the corresponding bending deflections are both normalized simultaneously, the effects of boundary condition and cross-sectional shape of the beams can be eliminated. Moreover, if the force-deflection curves of the basic beams are normalized again by their initial yielding values, the resulting relation curves of the beams with different cross-sectional shapes coincide. As a result of those, a normalized simple relation can be used to predict the elasto-plastic behavior of some basic beams with arbitrary cross-sectional shape. In this study, basic beams with box-shaped cross-sections were considered to demonstrate how to obtain their force-deflection curves directly from the normalized simple relation. Also, the predicted elasto-perfectly plastic curves of the beams with box-shaped cross-sections were compared with theoretical and numerical results to verify the validity and accuracy of the normalized simple relation.

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