【摘要】：雙邊箱斷面疊合梁斜拉橋是一種典型的大跨度橋梁形式。與鋼斜拉橋相比具有其剛度大、抗風(fēng)穩(wěn)定性好等特點(diǎn),而且能夠避免正交異性鋼橋面板帶來的疲勞問題。疊合梁斜拉橋的中跨主梁是寬幅疊合梁。對(duì)于寬幅疊合梁的計(jì)算,目前多采用空間實(shí)體有限元建立節(jié)段模型進(jìn)行分析,建模和計(jì)算過程復(fù)雜耗時(shí)。論文采用理論推導(dǎo)和有限元相結(jié)合的方式,研究了寬幅疊合梁第二體系的應(yīng)力和變形的簡化計(jì)算方法。具體而言,論文主要做了以下工作:(1)采用三比擬桿法分析了簡支梁疊合梁和懸臂疊合梁的應(yīng)力簡化計(jì)算問題。首先按照應(yīng)力相等的原則,將疊合梁比擬為只承受軸力的加勁桿和只承受剪力的系板的組合體系。然后根據(jù)加勁桿和系板之間的靜力平衡條件和變形協(xié)調(diào)條件建立微分方程組。接著根據(jù)邊界條件和荷載條件求解出混凝土板的應(yīng)力計(jì)算公式。最后根據(jù)定義得到混凝土翼緣板的有寬度公式。(2)將寬幅疊合梁劃分為三個(gè)體系進(jìn)行簡化分析。第一體系為邊箱梁和混凝土板組成的主梁;第二體系為橫梁和混凝土板組成的疊合梁;第三體系為支承在橫梁上混凝土橋面板。然后對(duì)于第二體系的邊界條件進(jìn)行了簡化分析,得到第二體系在荷載作用下的內(nèi)力計(jì)算公式。提出了第二體系簡化力學(xué)模型中的支點(diǎn)抗彎剛度的簡化計(jì)算方法。最后按照彎矩零點(diǎn)將第二體系解肢為等效簡支梁和等效懸臂梁進(jìn)行分析。(3)采用能量變分法分析了第二體系的撓度簡化計(jì)算問題。首先選擇三次拋物線作為翼緣板合理的縱向翹曲位移模式,選取剪力滯翹曲位移和撓度兩個(gè)廣義位移計(jì)算出結(jié)構(gòu)的總勢能,然后按照最小勢能原理得出控制微分方程和自然邊界條件,接著根據(jù)結(jié)構(gòu)的邊界條件和荷載條件求出待定系數(shù)得到撓度公式,最后把等效懸臂梁長進(jìn)行了修正并考慮剪切變形對(duì)撓度的影響得到改進(jìn)的撓度計(jì)算公式。(4)基于有限元法,采用通用有限元計(jì)算軟件ANSYS,建立寬幅疊合梁的實(shí)體有限元模型。分析了均布荷載和集中荷載作用下第二體系的撓度和應(yīng)力。最后將簡化計(jì)算方法和有限元方法的結(jié)果進(jìn)行對(duì)比,說明了第二體系應(yīng)力和撓度簡化計(jì)算公式的適用性和精度。
[Abstract]:The two-sided box section composite girder cable-stayed bridge is a typical long-span bridge form. Compared with the steel cable-stayed bridge, it has the advantages of high stiffness and good wind stability, and can avoid the fatigue problem caused by orthotropic steel bridge face. The middle span main beam of the composite girder cable-stayed bridge is a wide composite beam. For the calculation of wide-width composite beam, the segmental model is usually established by finite element method, and the modeling and calculation process is complicated and time-consuming. In this paper, the simplified calculation method of stress and deformation of the second system of wide-width composite beam is studied by combining theoretical derivation with finite element method. The main work of this paper is as follows: (1) the simple beam and cantilever superimposed beam are analyzed by using the three-bar analogy method. Firstly, according to the principle of equal stress, the composite beam is compared to a composite system of stiffened bar with only axial force and tie plate with only shear force. Then the differential equations are established according to the static equilibrium conditions and deformation coordination conditions between the stiffener bar and the mooring plate. Then the stress calculation formula of concrete slabs is obtained according to boundary conditions and load conditions. Finally, the width formula of concrete flange slabs is obtained according to the definition. (2) the broad composite beams are divided into three systems for simplified analysis. The first system is composed of side box girder and concrete slab, the second system is a composite beam composed of crossbeam and concrete slab, and the third system is concrete deck slab supported on crossbeam. Then the boundary conditions of the second system are simplified and the formulas for calculating the internal force of the second system under load are obtained. A simplified method for calculating the flexural stiffness of fulcrum in the simplified mechanical model of the second system is presented. Finally, according to the moment zero point, the second system is analyzed as an equivalent simply supported beam and an equivalent cantilever beam. (3) the simplified deflection calculation of the second system is analyzed by using the energy variational method. First, the cubic parabola is chosen as the reasonable longitudinal warping displacement model of the flange plate, and the total potential energy of the structure is calculated by selecting the shear lag warping displacement and the deflection two generalized displacements. Then the governing differential equation and natural boundary conditions are obtained according to the principle of minimum potential energy, and then the deflection formula is obtained according to the boundary conditions and load conditions of the structure. Finally, the equivalent cantilever beam length is modified and the deflection calculation formula is improved considering the effect of shear deformation on deflection. (4) based on the finite element method, the general finite element software ANSYS, is used to calculate the deflection. The solid finite element model of a wide composite beam is established. The deflection and stress of the second system under uniform and concentrated loads are analyzed. Finally, the results of simplified calculation method and finite element method are compared to illustrate the applicability and accuracy of the simplified formula of stress and deflection of the second system.
【學(xué)位授予單位】：西南交通大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：U448.27

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