箱形梁剪力滯效應(yīng)分析中的合理翹曲位移模式及其應(yīng)用研究
發(fā)布時(shí)間：2019-05-09 13:18
【摘要】：隨著我國橋梁建設(shè)的蓬勃發(fā)展，在眾多的橋梁截面形式中，箱形截面梁，顧名思義截面形狀猶如“箱子”有其優(yōu)越的截面特性，受到橋梁設(shè)計(jì)師的青睞。而其中大懸臂板、寬體箱梁成為主要的發(fā)展趨勢，由此剪力滯效應(yīng)問題將被重點(diǎn)考慮。在以往的理論研究中，箱形梁剪力滯效應(yīng)的分析方法眾多，各自有其自身的適用條件和優(yōu)缺點(diǎn)，基于最小勢能原理的能量變分法最為經(jīng)典和有效。但是傳統(tǒng)的能量變分法分析剪力滯效應(yīng)還是有一定的不足和缺陷，比如無法滿足軸力自平衡條件，所選取的剪力滯翹曲位移函數(shù)缺乏嚴(yán)密的理論論證，針對不同板寬的翼板沒有合理的修正，，所推導(dǎo)的縱向應(yīng)力計(jì)算式太過于繁瑣復(fù)雜等。本文就這些問題做出較詳細(xì)的理論分析和修正，并建立ansys數(shù)值算例模型驗(yàn)證本文提出的分析方法，具體工作包括以下幾個(gè)方面： 1.歸納出以往文獻(xiàn)中對剪力滯翹曲位移函數(shù)定義的類型，主要有拋物線型和余弦曲線型，給出它們各自的假設(shè)條件和優(yōu)缺點(diǎn)。并從控制剪力滯效應(yīng)的翼板剪切變形規(guī)律出發(fā)，提出定義剪力滯翹曲位移的新方法。 2.以薄壁箱形梁的彎曲計(jì)算理論為基礎(chǔ)，分析各翼板的剪切變形規(guī)律，給出剪力流計(jì)算式，并假定翼板橫向位移對縱向坐標(biāo)的導(dǎo)數(shù)很小可忽略不計(jì)，從理論上證明二次拋物線是較為合理的剪力滯翹曲位移函數(shù)。通過對全截面增加一個(gè)常數(shù)使翹曲應(yīng)力滿足軸力自平衡條件，對懸臂板和底板以不同板寬和水平形心軸不同距離作出修正，定義新的剪力滯翹曲位移函數(shù)。 3.將剪力滯效應(yīng)引起的附加撓度作為剪力滯廣義位移，定義剪力滯廣義力矩作為對應(yīng)剪力滯翹曲應(yīng)力的廣義力。這樣所得到的考慮剪力滯效應(yīng)后的縱向應(yīng)力表達(dá)式和相應(yīng)初等梁理論計(jì)算式形式一致，且物理意義更為明確。 4.以變分法原理建立控制微分方程，并通過邊界條件求解得到簡支箱形梁、懸臂箱形梁作用集中荷載和分布荷載的剪力滯附加撓度表達(dá)式，進(jìn)而與初等梁彎曲理論結(jié)果疊加可得到考慮剪力滯效應(yīng)后的箱形梁縱向應(yīng)力和豎向撓度。 5.通過簡支梁和懸臂梁兩個(gè)計(jì)算算例，依據(jù)本文的理論方法分別求解在選取不同翹曲位移函數(shù)時(shí)的縱向應(yīng)力，并建立ansys數(shù)值模型，驗(yàn)證本文的分析方法和建立的公式是否合理。 6.對一作用對稱集中荷載的預(yù)應(yīng)力混凝土簡支梁算例的計(jì)算表明，實(shí)際的橋梁設(shè)計(jì)中，如若不考慮剪力滯效應(yīng)時(shí)，對豎向撓度的影響可忽略不計(jì)，但縱向應(yīng)力則相差較大，無法忽略。
[Abstract]:With the vigorous development of bridge construction in our country, among many bridge cross section forms, box section beam, as the name implies, has its superior section characteristics and is favored by bridge designers. Among them, large cantilever plate and wide-body box girder become the main development trend, so the shear lag effect will be taken into account. In the previous theoretical research, there are many methods to analyze the shear lag effect of box beams, each of which has its own applicable conditions, advantages and disadvantages, and the energy variation method based on the principle of minimum potential energy is the most classical and effective. However, the traditional energy variation method still has some shortcomings and defects in the analysis of shear lag effect, such as unable to meet the self-balance condition of axial force, and the selected shear lag warping displacement function is lack of rigorous theoretical demonstration. The calculation formula of longitudinal stress is too cumbersome and complex for different width airfoils without reasonable correction. In this paper, the theoretical analysis and correction of these problems are made in detail, and a numerical example of ansys is established to verify the analytical method proposed in this paper. The specific work includes the following aspects: 1. The definition types of shear lag warpage displacement function in previous literatures are summarized, mainly parabola and cosine curves, and their hypotheses, advantages and disadvantages are given. A new method to define the shear lag warping displacement is proposed based on the shear deformation law of the wing plate which controls the shear lag effect. 2. Based on the bending calculation theory of thin-wall box girder, the shear deformation law of each wing plate is analyzed, and the formula for calculating shear flow is given, and it is assumed that the derivative of transverse displacement of wing plate to longitudinal coordinates can be ignored. It is proved theoretically that quadratic parabola is a reasonable function of shear lag warping displacement. A new shear lag warping displacement function is defined by adding a constant to the whole section to make the warpage stress satisfy the self-balancing condition of axial force and modifying the cantilever plate and bottom plate with different width of plate and different distance of horizontal center axis. 3. The additional deflection caused by shear lag effect is regarded as the generalized displacement of shear lag, and the generalized moment of shear lag is defined as the generalized force corresponding to the shear lag warping stress. In this way, the expression of longitudinal stress after considering shear lag effect is in agreement with the corresponding theoretical formula of elementary beam, and the physical meaning is more clear. 4. Based on the principle of variation method, the governing differential equations are established, and the expressions of shear lag additional deflection of simply supported box beams and cantilever box beams acting on concentrated load and distributed load are obtained by solving the boundary conditions. Furthermore, the longitudinal stress and vertical deflection of the box beam with shear lag effect can be obtained by superposition of the results of the bending theory of the primary beam and the results of the bending theory of the primary beam. 5. Based on the calculation examples of simply supported beam and cantilever beam, the longitudinal stress in selecting different warping displacement functions is solved by the theoretical method in this paper, and the ansys numerical model is established to verify the rationality of the analytical method and the formula in this paper. 6. The calculation of a prestressed concrete simply supported beam with symmetric concentrated load shows that if shear lag effect is not considered in the actual bridge design, the influence on vertical deflection can be negligible, but the longitudinal stress is quite different from each other in the actual bridge design, if the shear lag effect is not considered, the influence on the vertical deflection can be negligible, but the longitudinal stress is quite different. You can't ignore it.
【學(xué)位授予單位】：蘭州交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：U448.213
本文編號：2472798
[Abstract]:With the vigorous development of bridge construction in our country, among many bridge cross section forms, box section beam, as the name implies, has its superior section characteristics and is favored by bridge designers. Among them, large cantilever plate and wide-body box girder become the main development trend, so the shear lag effect will be taken into account. In the previous theoretical research, there are many methods to analyze the shear lag effect of box beams, each of which has its own applicable conditions, advantages and disadvantages, and the energy variation method based on the principle of minimum potential energy is the most classical and effective. However, the traditional energy variation method still has some shortcomings and defects in the analysis of shear lag effect, such as unable to meet the self-balance condition of axial force, and the selected shear lag warping displacement function is lack of rigorous theoretical demonstration. The calculation formula of longitudinal stress is too cumbersome and complex for different width airfoils without reasonable correction. In this paper, the theoretical analysis and correction of these problems are made in detail, and a numerical example of ansys is established to verify the analytical method proposed in this paper. The specific work includes the following aspects: 1. The definition types of shear lag warpage displacement function in previous literatures are summarized, mainly parabola and cosine curves, and their hypotheses, advantages and disadvantages are given. A new method to define the shear lag warping displacement is proposed based on the shear deformation law of the wing plate which controls the shear lag effect. 2. Based on the bending calculation theory of thin-wall box girder, the shear deformation law of each wing plate is analyzed, and the formula for calculating shear flow is given, and it is assumed that the derivative of transverse displacement of wing plate to longitudinal coordinates can be ignored. It is proved theoretically that quadratic parabola is a reasonable function of shear lag warping displacement. A new shear lag warping displacement function is defined by adding a constant to the whole section to make the warpage stress satisfy the self-balancing condition of axial force and modifying the cantilever plate and bottom plate with different width of plate and different distance of horizontal center axis. 3. The additional deflection caused by shear lag effect is regarded as the generalized displacement of shear lag, and the generalized moment of shear lag is defined as the generalized force corresponding to the shear lag warping stress. In this way, the expression of longitudinal stress after considering shear lag effect is in agreement with the corresponding theoretical formula of elementary beam, and the physical meaning is more clear. 4. Based on the principle of variation method, the governing differential equations are established, and the expressions of shear lag additional deflection of simply supported box beams and cantilever box beams acting on concentrated load and distributed load are obtained by solving the boundary conditions. Furthermore, the longitudinal stress and vertical deflection of the box beam with shear lag effect can be obtained by superposition of the results of the bending theory of the primary beam and the results of the bending theory of the primary beam. 5. Based on the calculation examples of simply supported beam and cantilever beam, the longitudinal stress in selecting different warping displacement functions is solved by the theoretical method in this paper, and the ansys numerical model is established to verify the rationality of the analytical method and the formula in this paper. 6. The calculation of a prestressed concrete simply supported beam with symmetric concentrated load shows that if shear lag effect is not considered in the actual bridge design, the influence on vertical deflection can be negligible, but the longitudinal stress is quite different from each other in the actual bridge design, if the shear lag effect is not considered, the influence on the vertical deflection can be negligible, but the longitudinal stress is quite different. You can't ignore it.
【學(xué)位授予單位】：蘭州交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：U448.213
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