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研究生:張雲妃
研究生(外文):Chaung, Yhei-Fei
論文名稱:雙軸彎曲鋼筋混凝土柱之直接分析法
論文名稱(外文):Direct Analysis for Reinforced Concrete Columns Subject to Biaxial Bending
指導教授:許茂雄許茂雄引用關係
指導教授(外文):Maw-Shyong Sheu
學位類別:碩士
校院名稱:國立成功大學
系所名稱:建築(工程)學系
學門:建築及都市規劃學門
學類:建築學類
論文種類:學術論文
論文出版年:1998
畢業學年度:86
語文別:中文
論文頁數:1
中文關鍵詞:鋼筋混凝土柱雙軸彎曲剛度
外文關鍵詞:Reinforced Concrete ColumnBiaxial bendingstiffness
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摘要 在已知軸
力和雙向彎矩作用下,雙軸彎曲柱斷面常以斷面上混 凝土最大壓應變、
中性軸方向及位置為三個未知數,而這三個 未知數照理可以利用柱斷面
F=0、Mx=0及My=0所穫得的 三條非線性聯立方程式求解之。因為
要建立這三條聯立方程式 相當困難與複雜,且囿於計算工具,所以過去
研究者常避重就 輕,例如:假定中性軸方向、假定混凝土等值應力塊與
規範相 等、或假定材料的應力─應變為線性關係、或假定柱斷面以等
值彈簧替代之;這些假定雖簡化過程,卻無法真實描述雙軸彎 曲柱的行
為。有鑑於此,本文目的在直接、忠實、完整地建立 三元非線性聯立方
程式,以電腦程式迅速、精確求得斷面上混 凝土最大壓應變、中性軸方
向及位置,以便後續探討雙軸彎曲 鋼筋混凝土柱之行為。
本文假定斷面受彎前後平面仍保持平面,混凝土應力─應變曲 線採用
Kent及Part修正式並考慮箍筋之圍束效應,鋼筋應力─ 應變曲線分彈性
、屈服平台、應變硬化三階段,直接積分雙軸 彎曲柱斷面的合力與合彎
矩,推導適用於任何外力作用下之三 元高次非線性聯立方程式,並修正
Newton-Raphson Method解 出三個未知數:斷面上混凝土最大壓應變、
中性軸方向及位置。同時,本文亦修正ACI規範之有效撓曲剛度(EcIeff)
公式,使之 可預測單軸或雙軸彎曲柱之變形,包括桿件於極限點後破壞
解 壓的階段。
為驗證本文提出的直接分析法及柱剛度計算之正確性,分析國 內外40支
試驗柱之極限載重與11支試驗柱之載重─位移全程 曲線,分析結果與
試驗結果比較,證實均屬合理。此外,本文 亦討論雙軸彎曲柱斷面之載
重等高線圖及中性軸方向,並提出 壓力破壞時中性軸方向之公式。
關鍵詞:鋼筋混凝土柱;雙軸彎矩;柱剛度;破壞面;載重等 高線;中
性軸方向
The cross sections of reinforced concrete column with axial load
and biaxial bending often have three unknowns : (1) maximum
concrete compressive stress ,(2) the inclination and (3) depth
of neutral axis. Theoretically,they can be obtained with three
simultaneous nonlinear equations of (F=0 ,(Mx=0, and (My=88饗
ecause it is difficult and complex to derive these three
equations and the poor of numerical methods and computing tools,
many reseachers usually made some simplifying assumptions in
attempt to overme these difficulties, but the results can not
reflect the actual behavior of biaxially loaded column. For
example, the inclination of neutral axis was proposed, material
stress-strain relationship was assumed to be linear, equivalent
compressive stress block of concrete was estimated as ACI Code,
or adopting equivalent springs to represent cross section of
columns.Therefore, the aim of this paper is to directly, really,
and completely derive three simultaneous nonlinear equations,
and use computer program carry out fastly and exactly. At the
same time, this method can be adopted to study about the
behavior of biaxially loaded column later.
This analysis is based on the assumption that plane section
remains plan before and after bending, and utilizes the modified
Kent and Park stress-strain curve for concrete and a complete
idealized stress-strain curve for steel to integrate directly
resultant force and moment of biaxially loaded reinforced
concrete column section. Based on those, three simultaneous
nonlinear equations is derived and solved by modified the
Newton-Raphson method to obtain maximum concrete compressive
stress in the cross sectio the inclination and depth of neutral
axis. Besides, this paper modifies the equation of effective
flexural rigidity presented by ACI Code, and use it to find the
load-deformation curves of biaxially or uniaxially loaded
columns, including the failure and unloading step of member.
In order to verify the directly analytical method and stiffness
equation of column presented by this paper, this research
analyzes 40 experimental specimens of ultimate loads and 11
experimental specimens of P-△ curve for columns. By comparing
test and theoretical values, it is evident that results show an
excellent agreement. Besides, this paper investigates load-
contour diagrams and neutral axis angle of biaxially loaded RC
columns, and presents an equation to determine neutral axis
angle at compressive ilure.
Keyword : RC column , biaxially bending, column stiffness,
failure surface, load-contour curve, the neutral axis angle.
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