假定公式

By using the mathematical method of curve integrals,it derives the mathematical formula to calculate the cross-section ductile coefficient of RC ring section member.

从钢筋混凝土正截面承载力计算时的基本假定出发，建立了环形截面上各种应力图形的函数表达式，利用曲线积分的数学方法，推导出计算钢筋混凝土环形截面构件截面延性系数的数学公式。

The main objective of this dissertation was to develop methodologies with capability of engineering application for simulating flow in fractured rock using discontinuum models. The study work includes three parts. In the first part, numerical methodology of three-dimensional discrete fracture network model casing on hybrid BEM-channel was presented, and the technique for improve the model's computing efficiency was also studied. Firstly in this part, computer simulation methodology based on the Baechermodel for generating network of discrete fractures was presented, which includes the follow details: probability distributions of fracture density,orientation, trace length, size, and aperture and estimation of their statistical parameters; stochastic models of fracture network; Monte-Carlo's simulation method; numerical simulation procedure and technicality.

给出了离散裂隙网络模型所依据的基本假定；发展了基于Baecher模型的离散裂隙网络计算机随机生成技术：详细地推导了单裂隙渗流和多裂隙相交网络渗流的边界单元法公式，发展了离散裂隙网络中稳态渗流的边界元数值技术，并且讨论了相关的具体数值技术细节，如角点的处理方法，单元的自动剖分等：描述了混合边界元—管流模拟方法及其数值实现；研究了裂隙网络的简化方法，并针对裂隙网络边界元法的特点提出了一种改进的分块三角分解法。

In the Culmann analysis method, the assumption that the soil failure is in the mode of sliding along a plane is adopted; however only one force equilibrium equation along some special direction is utilized to derive the computation formula of earth pressure.

在Culmann分析方法中，沿用了Coulomb土压力理论关于平面滑动破坏的假定，而在推导土压力计算公式的过程中，仅利用了滑动体沿某一特定方向的一个力的平衡方程。

Based on wave propagating in three directions of elastic foundation, vibrating displacement could be assumed to be in three forms along three directions. Hooke's law and theory of waves were adopted to deduce the formula of coupled viscous boundary. The coupled viscous boundary could be applied in finite element method.

根据波在地基的3个方向都可以进行传播的特点，假定了地基中质点沿3个方向的振动表达式，通过胡克定律和波动理论，推导了弹性地基中三维动力问题的耦合粘性边界的公式。

Given the incompressibility of water, a relation between specific elastic storage, compressibility modulus and deformation modulus was inferred by applying current related formulas.

主要完成了如下工作：(1)在假定水不可压缩的情况下，利用已有的相关公式推导了单位弹性释水系数与土层压缩模量、变形模量之间的关系。

It is assumed that potential sliding surface of the soil in the back of the retaining wall is composed of logarithmic spiral arc and line.

假定挡土墙后土体潜在滑裂面由对数螺线滑动面和平面组合而成，根据挡土墙后土体薄层单元的平衡条件推导出粘性土层主动土压力的计算公式。

According to the plane cross section assumption, configuration of a rod is expressed as a history of the cross section with arc coordinate. A special solution which stands for equilibrium in straight line state is obtained from differential equilibrium equation. Linear perturbation equation is derived and its general solution is obtained in which the integral constants are determined by constrained conditions at two ends of the rod. The condition of existence of non zero solution of the integral constants gives to the Greenhill formula of exact elastic rod model, which shows that the boundary of stable area is a closed curve and of symmetry, and inference of shearable and extensible to stability of the rod is depend on three factors: difference between flexibility of shear and extension of a section of the rod, bending stiffness and the length of the rod.

基于平面截面假定，弹性杆的位形表达为截面的弧坐标历程，根据平衡微分方程得到了两端受力螺旋作用时的直线平衡特解，导出了线性化扰动方程及其通解，积分常数根据两端铰支时的边界条件确定，并根据其存在非零解的条件得到弹性直杆精确模型的Greenhill公式，表明稳定域为一对称的封闭区域，拉/压和剪切对稳定性的影响取决于：拉/压柔度与剪切柔度之差，抗弯刚度和杆长这三个因素

Combining with the National Natural Science Foundation ofChina(No.50478032), following researches were done in this thesis: 1 The variation regularity of the ultimate anti-bending capacity of therectangular-sectioned beam with different corrosion has been obtained through thequalitative analysis of 48 beams (32 corroded beams and 12 comparing beams) withaccelerated corrosion; 2 The conclusion has been obtained that the strain of corroded steel bar andconcrete no longer fit in with the assumption of plane section through the analysis ofthe strain data, the strain relation of steel bar and concrete in the mid-span section ofvariously corroded beams at ultimate has been obtained. Through the building of newgeometric relation, the expression of the height of compressive area in the corrodedbeam with rectangular section has been deduced, and the formula with corrosion rateas the main variable for the anti-bending capacity of the corroded concrete beam hasbeen suggested and verified by experiment.; 3 The influence of steel bar corrosion and the concrete regression to the flexureductility coefficient of the corroded structure component has been analyzed. Based onthe relation of steel bar and concrete at yield and ultimate, the expression for theflexure at yield and ultimate of corroded reinforced concrete beam, and the model forthe calculation of the flexure ductility has been built.

本文结合国家自然科学基金项目(50478032)"既有钢筋混凝土桥梁时变可靠度研究"，主要进行了以下研究工作： 1通过对48根快速锈蚀钢筋混凝土矩形截面梁(32根锈蚀梁和12根对比试验梁)数据的定性分析，得到了不同锈蚀率下，锈蚀钢筋混凝土矩形截面梁极限抗弯承载力的变化规律； 2通过对应变数据的分析，论证了锈蚀构件钢筋和混凝土的应变不再符合平截面假定的结论，并通过回归分析得出了不同锈蚀率的螺纹钢筋梁和光圆钢筋梁在极限弯矩作用下，跨中截面处钢筋应变和钢筋处混凝土应变的关系，通过构造新的几何关系，得出了锈蚀钢筋混凝土矩形截面梁计算受压区高度的表达式，既而得出了以锈蚀率为主要变量的锈蚀钢筋混凝土矩形截面梁的正截面抗弯计算建议公式，并通过试验数据加以验证； 3分析了钢筋锈蚀和混凝土劣化对锈蚀构件曲率延性系数的影响，结合钢筋屈服和极限弯矩两种状态下钢筋和混凝土的应变关系，分别得到了锈蚀钢筋混凝土矩形截面梁屈服曲率和极限曲率的计算表达式；既而推导出曲率延性系数的计算模型。

Therefore,a series studies of ice-pier vibration are performed from different aspects in this paper.The main work of this his thesis is summarized as follows:(1) Ice response spectra is proposed based on the idea of a seismic response spectra analysis of str .. uctures.Firstly,ice response spectra on the basis of power spectra density function is established;Secondly,based on the assumption of quadratic parabolic interpolation method,the nonlinear interpolation analysis method of ice response spectra is studied from both theoretical and practical points of view,and the successive computation formulas including ice displacement,velocity and acceleration response spectrum are deduced by Duhamel integral.Furthermore,to analyze the effectivity and applicability of the method, the real temporal curves of ice pressure are used to be studied.The results show that the presented method is more convenient and accurate to study the structural response induced by ice force,also it can be effectively applied in the design of ice resistance.

鉴于此，本文针对冰激桥墩结构振动问题从不同方面展开了一系列与之相关的研究，主要研究内容如下：(1)根据结构抗震反应分析思想提出了冰振反应谱，首先建立了基于功率谱密度函数的冰振反应谱；其次借鉴地震反应谱内插法的思想从理论和实际观点出发，假定在等距离微小时间间隔内冰荷载按二次抛物线规律变化，由Duhamel积分推导出冰振位移、速度以及加速度反应谱的一系列连锁公式，建立了基于非线性内插法的冰振反应谱，并利用实际冰压力时程曲线进行了冰振反应谱数值分析，为以后冰激结构振动的研究提供一种方便、简捷、精确的分析方法，也能够将其有效地应用到结构的抗冰计算中。

How to easily and reasonably determine the value of principal stress in the direction of plane strain is the key point.

基于弹塑性理论及土的试验规律，在平面应变的简单加载条件下，假定主应力之间的关系为双线性函数，并利用一维固结和破坏时的主应力状态，确定双线性函数的系数，得到平面应变方向上主应力计算公式的一个较合理形式，为应力状态和材料性质的函数。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。