單對稱I型懸臂梁側向扭轉挫屈強度分析

Strength Analysis for Singly-symmetric Overhanging I-beams

劉育欣(Yu-Xin Liu)

指導教授 ： 徐暐亭

朝陽科技大學/理工學院/營建工程系/碩士(2017年)

摘要

常見之鋼梁斷面如雙對稱I-型斷面與單對稱I-型斷面，雙對稱斷面設計與分析較為簡單，但以材料用量的考量經濟性卻不佳，而單對稱斷面其斷面特性為增加受壓面積以提供較佳之抗彎矩能力及穩定性，為此可減少材料用量提高經濟性。單對稱I型鋼梁的各種性質之計算與分析過程繁瑣，尤其進行扭轉分析時，必須同時考慮扭曲應力與翹曲應力，其彈性強度相關參數包含翹曲常數Cw、單對稱係數βx、扭轉常數J，以及剪力中心距離等牽涉到複雜積分運算，因此工程師易忽略相關的計算，而採用較保守的設計致使提高設計成本。
本研究整理單對稱梁之理論彈性與非彈性、AISC 1999規範、AISC 2005規範、AISC 2010規範及AISC 2015規範之公式來源與差異性，並且提供例題說明及分析。最後針對單對稱斷面單側翼板變化對彎矩強度的影響分析，提出斷面效益最佳的單對稱I型斷面，將繁雜之規範公式整理並繪製流程表以利縮短計算時間，利用Excel VBA程式之撰寫，能快速且正確求得彎矩強度，消除業界工程師分析與設計時所面臨的障礙，提升設計品質與效率。
本研究提供設計單對稱I型懸臂鋼梁斷面彎矩計算之相關數值，提出如為使單對稱斷面彎矩強度提升建議以增加受壓側翼板斷面最為有利，以材料之經濟性考量建議以縮減受拉側翼板斷面對彎矩強度影響較低，但無論受壓或受拉側翼板增加或縮減，應避免Iyc / Iy ≤ 0.23之極端設計導致彎矩強度驟降，作為業界設計之參考，提高其設計的經濟性及全理性。
關鍵字：單對稱Ｉ型鋼梁、拉力構件、側向扭轉挫屈、受壓側及受拉側斷
面變化

關鍵字

單對稱Ｉ型鋼梁 ； 拉力構件 ； 側向扭轉挫屈 ； 受壓側及受拉側斷面變化

並列摘要

Common cross-section of steel beams such as double and singly-symmetric cross-section, double symmetric I-beams design and analysis is relatively simple, but the amount of material consumption is not economical, and singly-symmetric I-beams characteristics to increase the compression area to provide better resistance to bending moment and stability. However, the theoretical elastic moment calculation for singly-symmetric I-beams is not an easy and the difficulty comes from some of the evaluation of torsion properties including the warping constant (Cw) and coefficient of monosymmetry (Bx), the torsion constant (J), so engineers are easy to ignore the relevant calculations, and the use of more conservative design to improve design costs.
This study has explored major fundamental equations regarding to the flexural design of steel beam based on the AISC specification (1999, 2005, 2010, 2015). Finally, aiming at the analysis of the influence of the uniaxial flang changes on the bending moment strength of I-beams, the singly-symmetric I-beams with the best cross-section efficiency is put forward. Use Excel VBA quickly and correctly determines the strength of the bending moment, and improving design quality and efficie.
This study provides the relevant value for calculating the bending moment calculation of singly-symmetric overhanging steel I-beams. Regardless of the compression or tension flang to increase or decrease, should avoid Iyc / Iy ≤ 0.23 extreme design led to sudden drop in bending strength, as the industry design The reference to improve the design of its economy and the whole rational.
Keywords:Singly-symmetric I-beam, Tension members, Lateral torsion buckling, Compression and tension side of the cross-section changes.

並列關鍵字

Singly-symmetric I-beam ； Tension members ； Lateral torsion buckling ； Compression and tension side of the cross-section changes

參考文獻

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