本文選題：細長柱 + 解析法��； 參考：《昆明理工大學(xué)》2014年博士論文

【摘要】：鋼筋混凝土柱的二階彈塑性問題涉及到材料和幾何雙重非線性的耦合作用。采用有限元方法需要耗費大量時間建模,效率較低。通過對現(xiàn)有的數(shù)值方法和簡化方法的分析,以理論推導(dǎo)方式,在截面上,采用由應(yīng)變求內(nèi)力的逆算方法來確定截面承載力和彎矩-曲率關(guān)系。這一計算過程完整地利用了鋼筋和混凝土的本構(gòu)關(guān)系而沒有進行簡化,同時解析的算法沒有迭代和收斂帶來的誤差,因而是精確解。在桿件上,采用三種具有不同精度的方法來分析和計算鋼筋混凝土柱的二階彈塑性性能,進而提供了三種水平的設(shè)計工具。 為了驗證這些計算方法,利用計算結(jié)果繪制了大量的曲線,通過曲線族變化規(guī)律的合理性和曲線間的邏輯關(guān)系來判斷,通過與已有方法、現(xiàn)行規(guī)范方法和已有試驗結(jié)果的對比等方式來判斷。 (1)參考歐洲規(guī)范2,得到適用于我國的極限狀態(tài)截面所有可能的應(yīng)變分布,這些應(yīng)變與極限軸力-彎矩是一一對應(yīng)關(guān)系,因而無需迭代可直接由這些應(yīng)變計算截面承載力,給出了鋼筋混凝土矩形和圓形截面的計算過程,得到截面的軸力-彎矩相關(guān)關(guān)系,可用于截面強度驗算和短柱的配筋設(shè)計。 (2)通過引入一些中間計算參數(shù),推導(dǎo)了一種新的適用范圍較廣的鋼截面的彎矩-曲率關(guān)系的解析算法,給出了矩形和工字形截面的解析表達式,得到了軸力不變的彎矩-曲率關(guān)系曲線、軸力-彎矩相關(guān)曲線和曲率不變的軸力-彎矩曲線,這些曲線反映了截面的延性性能以及彎矩-曲率-軸力三個變量相互依存和變化的全貌。結(jié)果表明：軸力對彎矩-曲率關(guān)系的影響是很大的,軸力的存在或增加使得截面較早、較快地進入塑性階段,從而使得彎矩承載力降低,軸力的這一影響在不同的截面形式下表現(xiàn)也是不同的,工字形截面比矩形受到的影響更為不利。 (3)基于鋼截面的相同的計算思路,推導(dǎo)了鋼筋混凝土矩形截面彎矩-曲率關(guān)系的解析算法,可計算用于延性分析的屈服曲率和延性系數(shù),同樣得到三個變量的關(guān)系曲線。結(jié)果表明：通常情況下鋼筋混凝土截面與鋼截面類似,軸力的存在是不利的,軸力使得彎矩承載能力降低,然而在小縱向壓力情況下,軸力的存在是有利的,隨著軸壓力的增加,彎矩承載力略有提高。在大軸力作用下,截面的延性顯著變差。曲率越大,軸力-彎矩值越接近截面極限承載力。 (4)基于截面彎矩-曲率關(guān)系的解析算法,推導(dǎo)了鋼筋混凝土細長柱配筋設(shè)計和強度驗算的三種方法。一是數(shù)值方法的改進Newmark法,很少的簡化使這一方法具有很高的精度。二是基于正弦變形曲線假設(shè)的圖解分析和計算方法,能在彎矩-曲率二維圖形上直觀地表示出材料非線性和幾何非線性的相互作用,因較少的簡化和解析的計算過程而具有較高的精度和很高的計算效率。三是基于拋物線曲率分布假設(shè)和簡化的極限曲率模型的圖算法,簡化較多,但能夠推導(dǎo)出直接用于手算設(shè)計的諾模圖,僅需計算3個基本變量和在圖形中做4條輔助線,就可進行細長柱的配筋設(shè)計和強度驗算,實現(xiàn)了鋼筋混凝土柱二階彈塑性的簡單計算。 (5)鋼筋混凝土柱二階彈塑性分析結(jié)果表明：對于雙側(cè)配筋的鋼筋混凝土矩形柱子,可以近似地認為柱子極限承載力等于截面極限承載力。這一假設(shè)只有極少數(shù)情況下不成立,即長細比非常大,并且一階偏心矩非常小。鋼筋和混凝土應(yīng)變的限制條件,使得截面極限狀態(tài)的切線剛度遠大于0,因而在軸力較大時,長細比在很大范圍內(nèi)變化都可能出現(xiàn)柱子的強度破壞。
[Abstract]:The reinforced concrete columns of two order elastic-plastic problem involves coupling of both geometric and material nonlinearity. Using the finite element method requires a lot of time modeling, low efficiency. Through the analysis of existing numerical methods and the simplified method, with theoretical derivation, in cross section, inverse calculation method to determine the relationship between force and the Moment Curvature section bearing for internal force by using strain. The calculation process of full use of the constitutive relation between steel and concrete without simplification, while parsing algorithm without error iteration and convergence brought about, so it is an exact solution. In the bar, using three methods with different accuracy analysis and the two order elastic-plastic performance calculation of reinforced concrete columns, and provides a design tool for three levels.
In order to verify these calculation methods, a large number of curves were drawn by using the results of calculation. It was judged by the rationality of curve family variation and the logical relationship between curves.
(1) refer to the European standard 2, get the limit state cross section applies to our country all possible strain distribution, the ultimate strain and axial force bending moment is one-to-one correspondence, so without iteration section bearing capacity calculation directly from these strains, the calculation process of reinforced concrete rectangular and circular cross-section are obtained axis force - section moment correlation, can be used for reinforcement design section strength calculation and the short column.
(2) calculated by introducing some parameters, deduces the algorithm of relation between moment steel section of a wide scope of the curvature of the analytical expressions of rectangular and I-shaped cross section are given, the axial force and moment invariant curvature curves of axial force, axial force and bending moment curve the bending moment and curvature invariant curve, the curve reflects the section ductility and Moment Curvature and axial force of three variables are interdependent and change the whole picture. The results show that the influence of axial force on the moment curvature relationship is great, the axial force of the existence or increase the cross section earlier, fast access to plastic stage, so as to reduce the bearing capacity of the bending moment, axial force effect in different section forms under the influence is also different, the I-shaped cross section is more unfavorable than the rectangle.
(3) steel section of the same computational thinking based on the deduced analytic algorithm of relation between moment of reinforced concrete rectangular cross section curvature ductility analysis, can be used to calculate the yield curvature and ductility coefficient, also get the relation curve of three variables. The results showed that: under normal circumstances the reinforced concrete section and steel section, axial force there is a disadvantage, the axial force bending moment bearing capacity decreased, but in the case of small vertical pressure, axial force is favorable, with the increase of axial pressure, bearing capacity increases slightly. In the role of large axial force bending moment, section ductility significantly worse. The greater curvature, axial force bending moment the value of bearing capacity is close to the ultimate.
(4) parsing algorithm based on the moment curvature relationship of the section, we derive three kinds of methods of reinforced concrete slender column reinforcement design and strength calculation. The improved Newmark method is a numerical method, a few simplified so that this method has high precision. The two is a graphic sine curve hypothesis analysis and calculation method based on the energy is clearly shown that the interaction of material nonlinear and geometry nonlinear Moment Curvature in two-dimensional graphics, and has high because of less calculation process is simplified and the analytical accuracy and high computation efficiency. Three is the graph algorithm, limit curvature model curvature distribution hypothesis and simplification based on simplified more but can be deduced directly for hand design nomograms, only needs to calculate the 3 basic variables and 4 auxiliary line in the graph, can be carried out on slender column reinforcement design and strength calculation of the steel. Simple calculation of two order elastic-plastic properties of reinforced concrete columns.
(5) reinforced concrete columns of two order elastic-plastic analysis results show that the rectangular reinforced concrete columns were reinforced, can be similar to that of the bearing force is equal to the column section bearing capacity limit. This hypothesis was not only a very few cases, the slenderness ratio is very large, and a very small eccentric moment order restrictive conditions. Strain of steel and concrete, the sectional tangent stiffness limit state is far larger than 0, so in the larger axial force, slenderness ratio in a wide range of changes are likely to destroy pillars of strength.

【學(xué)位授予單位】：昆明理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TU375.3

【參考文獻】

相關(guān)期刊論文 前10條

1 耿旭陽;周東華;陳旭;姚凱程;王月s，

本文編號：1737419