Internal Force Analysis Due to the Supporting Translation in Statically (Indeterminate) Structures for Different Elastic Modulus

For statically indeterminate structure, the internal force will be changed with the translation of the supports, because the internal force is related to the absolute value of the stiffness EI. When the tension is different with the compression modulus, EI is the function of internal force and is not constant any more that is different from classic mechanics. In the other words, it is a nonlinear problem to calculate the internal force. The expression for neutral axis of the statically indeterminate structure was derived in the paper. The iterative program for nonlinear internal force was compiled. One case study was presented to illustrate the difference between the results using the different modulus theory and the single modulus theory as in classical mechanics. Finally, some reasonable suggestions were made for the different modulus structures.

A Two-Stage Method for an Approximate Calculation of Statically Indeterminate Trusses

The paper presents the principles of a method, which in two simple stages makes possible to carry out the statically calculation of values of forces acting in the fiat static indeterminate trusses. In each stage, it is considered the static determinate truss, scheme of which is obtained after remove the suitable number of members from the basic static indeterminate truss. The both intermediate statically determinate trusses are of the same clear span and they are loaded by forces of half values applied to the corresponding truss nodes. The method applies one of the typical procedures of calculation of the statically determinate trusses and then it is applied in an appropriate way the rule of superposition for obtaining the final values of forces acting in particular members of the basic truss. The values of forces calculated in this way are of a very close approximation to the force values determined in the special and complex ways being considered as the exact calculation methods. The proposed method can be useful mostly but not only for the initial structural design of such systems. The simplicity of the two-stage method justifies an assumption that it can be relatively easy and worthy to adjust to the requirements of the computer aided technology of statically calculation of the complex forms of trusses.

A METHOD OF ADJUSTING BAR-LENGTH OF STATICALLY INDETERMINATE TRUSS FOR INCREASING ITS LOAD CAPACITY

Based on the character of the internal force distribution of the statically indeterminate truss, the elements stresses were changed by adjusting the length of bars to increase load capacity of structure. The efficiency of the method is illustrated by several examples.

Analysis of the Results Obtained from the Application of the Two-Stage Method with Calculations of Some Statically Indeterminate Trusses

The paper presents results of calculations of forces in members of selected types of statically indeterminate trusses carriedout by application of the two-stage method of computations of such structural systems. The method makes possible to do the simple andapproximate calculations of the complex trusses in two stages, in each of which is calculated a statically determinate truss being anappropriate counterpart of the basic form of the statically indeterminate truss structure. Systems of the statically determinate trussesconsidered in the both stages are defined by cancelation of members, number of which is equal to the statically indeterminacy of thebasic truss. In the paper are presented outcomes obtained in the two-stage method applied for two different shapes of trusses and carriedout for various ways of removing of appropriate members from the basic trusses. The results are compared with outcomes gained due toapplication of suitable computer software for computation of the same types of trusses and for the same structural conditions.

Strength weakening effect of high static pre-stressed granite subjected to low-frequency dynamic disturbance under uniaxial compression

This study aimed to elucidate the strength weakening effect of high static pre-stressed rocks subjected to low-frequency disturbances under uniaxial compression.Based on the uniaxial compressive strength(UCS)of granite under static loading,70%,80%,and 90%of UCS were selected as the initial high static pre-stress(σ_(p)),and then the pre-stressed rock specimens were disturbed by sinusoidal stress with amplitudes of 30%,20%,and 10%of UCS under low-frequency frequencies(f)of 1,2,5,and 10 Hz,respectively.The results show that the rockburst failure of pre-stressed granite is caused by low-frequency disturbance,and the failure strength is much lower than UCS.When theσp or f is constant,the specimen strength gradually decreases as the f or σ_(p) increases.The experimental study illustrates the influence mechanism of the strength weakening effect of high static pre-stress rocks under low-frequency dynamic disturbance,that is,high static pre-stress is the premise and leading factor of rock strength weakening,while low-frequency dynamic disturbance induces rock failure and affects the strength weakening degree.

Characteristics of Statically Indeterminate Symmetric Flexure Structures

Statically indeterminate symmetric(SIS)flexure structures are symmetric structures with“clamped-clamped”boundary conditions.The static indeterminacy and topological symmetry significantly attenuate the parasitic motions associated with statically determinate flexure structures.Hence,SIS flexure structures feature decoupled linear and angular motions,improved motion accuracy,high stiffness,and high stability.Although SIS flexure structures have been more frequently utilized as prismatic joints,they can also be utilized as revolute joints.This study systematically investigates the characteristics of SIS flexure structures.Based on the unified compliance models of a single flexure hinge,analytical compliance models of two fundamental types of SIS flexure structures are established.In 1-degree-of-freedom or planar applications,multiple SIS-based structures can also be integrated into various configurations to transmit linear or angular motions.Corresponding stiffness models are also established.The characteristics and possible applications of the SIS flexure structures are computationally investigated through case studies.Ultimately,several SIS prototypes are manufactured,and the modeling accuracy of the established stiffness models is experimentally verified.

转轮式反应容器支撑辊子强度计算与结构改进设计

一种超静定结构转轮式反应容器采用8个辊子支撑。本文提出了一种辊子强度计算方法,为支撑系统优化提供理论依据。首先根据极限支撑情况将超静定结构简化为静定结构计算支反力;再针对超静定结构,建立静力平衡方程和变形协调方程求解辊子支反力,进而根据弯曲和接触理论确定辊子最大弯曲应力和接触应力;并通过有限元计算通过实验得到部分工况下辊子的最大弯曲应力。将实验结果和有限元结果与理论计算结果进行对比,并针对辊子出现的应力集中现象,提出结构改进方案。结果对比表明所提出的应力计算方法和结构改进方案可行。

多头电脑刺绣机超静定梁机架的设计

多头刺绣机机架为大跨距横梁结构,机头为偏心凸轮机构,在高速工况下常激发出强烈振动,影响刺绣产品的质量和产量。为了解决多头刺绣机横梁的振动问题,通过多体动力学分析和有限元分析,提出了多头电脑刺绣机超静定横梁机架的概念。通过机头两侧配置半圆柱形平衡块,降低机头运行的惯性力,减小内部激励;采用超静定梁的设计理念,对横梁的约束进行加强,降低横梁的振幅,改善振动周期。与目前市场上多个机架减振方案对比,文章提出的超静定梁的振动幅值具有明显优势,横梁振动周期发生明显变化,摆脱了机头运行带来的周期性冲击影响,从而大幅度减少由于刺绣机机头高速运转而导致的大跨距横梁振动问题,有利于提高刺绣机高速运转下的工艺精度。

空间任意汇交杆系的变形协调几何方程组及其组合学释义

将平面汇交杆系的变形协调问题拓展到空间任意汇交杆系的情形,运用微分解析法,通过对空间任意4根汇交杆的求解,直观地得到了空间任意n根汇交杆系变形协调几何方程组的一般形式,解决了空间汇交杆系的超静定问题。结论中所有下标的顺序符合组合学中字典序数排列,因此可以用计算机编程去求解超静定空间汇交杆系的变形协调方程。

Reaction Forces on a Fixed Ladder in Static Equilibrium: Analysis and Definitive Experimental Test of the Ladder Problem

The development of a theoretical model to predict the four equilibrium forces of reaction on a simple ladder of non-adjustable length leaning against a wall has long remained an unresolved matter. The difficulty is that the problem is statically indeterminate and therefore requires complementary information to obtain a unique solution. This paper reports 1) a comprehensive theoretical analysis of the three fundamental models based on treating the ladder as a single Euler-Bernoulli beam, and 2) a detailed experimental investigation of the forces of reaction as a function of applied load and location of load. In contrast to previous untested proposals that the solution to the ladder problem lay in the axial constraint on compression or the transverse constraint on flexure, the experimental outcome of the present work showed unambiguously that 1) the ladder could be modeled the best by a pinned support at the base (on the ground) and a roller support at the top (at the wall), and 2) the only complementary relation needed to resolve the static indeterminacy is the force of friction at the wall. Measurements were also made on the impact loading of a ladder by rapid ascent and descent of a climber. The results obtained were consistent with a simple dynamical model of the ladder as a linear elastic medium subject to a pulse perturbation. The solution to the ladder problem herein presented provides a basis for theoretical extension to other types of ladders. Of particular importance, given that accidents involving ladders in the workplace comprise a significant fraction of all industrial accidents, the theoretical relations reported here can help determine whether a collapsed structure, against which a ladder was applied, met regulatory safety limits or not.

The Role of Friction in the Static Equilibrium of a Fixed Ladder: Theoretical Analysis and Experimental Test

In a recent publication the author derived and experimentally tested several theoretical models, distinguished by different boundary conditions at the contacts with horizontal and vertical supports, that predicted the forces of reaction on a fixed (i.e. inextensible) ladder. This problem is statically indeterminate since there are 4 forces of reaction and only 3 equations of static equilibrium. The model that predicted the empirical reactions correctly used a law of static friction to complement the equations of static equilibrium. The present paper examines in greater theoretical and experimental detail the role of friction in accounting for the forces of reaction on a fixed ladder. The reported measurements confirm that forces parallel and normal to the support at the top of the ladder are linearly proportional with a constant coefficient of friction irrespective of the magnitude or location of the load, as assumed in the theoretical model. However, measurements of forces parallel and normal to the support at the base of the ladder are linearly proportional with coefficients that depend sensitively on the location (although not the magnitude) of the load. This paper accounts quantitatively for the different effects of friction at the top and base of the ladder under conditions of usual use whereby friction at the vertical support alone is insufficient to keep the ladder from sliding. A theoretical model is also proposed for the unusual circumstance in which friction at the vertical support can keep the ladder from sliding.

Examples of Application of Principle of Superposition in the Design of Structural Systems and in Static Analyses

The paper presents general description of combined structural system and initial analysis of an innovative system proposed as the main support structure for tall or heavy loaded buildings located on subsoil of very small load-carrying ability or in earthquake areas. Moreover there is presented also an innovative two-stage method of the approximate calculation of the statically indeterminate trusses. Both are invented by the author by application of the principles of the superposition method.

基于力等价结构的复杂超静定结构求解新方法研究

超静定结构内力计算是结构力学课程学习的重点和难点,当超静定次数较多时,采用传统方法计算时难度极大且不易理解。本文总结提出了力等价结构思想,力等价结构与原结构在内力、变形上完全等价,基于该思想提出了复杂超静定结构内力计算的新方法,并将其应用到位移法、混合法求解多次超静定的复杂结构算例中。通过与传统方法对比,验证了所提力等价结构思想的可行性。所提方法可大大降低复杂超静定结构基本未知量的数目,简化计算过程,提高求解效率。

大跨度悬索桥桥塔横梁施工优化方法研究

在大跨度悬索桥桥塔横梁施工过程中,为保证横梁不出现受拉开裂现象,往往在横梁中布置大量预应力钢束进行分批张拉。为研究浇筑法、落架时机、预应力张拉方案不同对混凝土横梁及支架受力的影响,采用ABAQUS软件建立伶仃洋大桥桥塔横梁有限元模型,通过计算得到9种施工方案中桥塔横梁及支架在施工全过程中的受力状态,并提出受力合理、安全经济的3层浇筑施工方案。经分析发现,由横梁与塔柱组成的超静定结构,在自重及预应力荷载施加作用下,对应结构体系会因施工方案不同发生变化,从而使结构施工完成阶段内力状态与施工过程有关。采用分层浇筑法时,结构最不利受力状态可能发生在施工过程中,因此应防止施工过程中出现过大应力,导致横梁开裂或压碎。

静不定复合材料夹芯梁弹性屈曲载荷的近似解

利用能量法得到静不定夹芯梁剪切刚度表达式,构造静不定夹芯梁的挠度函数,进而得到静不定复合材料夹芯梁的弹性屈曲载荷近似解。相关试验证明了静不定夹芯梁剪切刚度表达式的计算精度的可靠性及实际工程的适用性。算例分析表明,静不定复合材料夹芯梁弹性屈曲载荷的计算应考虑剪切刚度的影响,否则会产生很大的计算误差。

超静定桁架的定性分析

定性结构力学好似进入瓶颈期,为推动定性结构力学的发展,针对超静定桁架进行了定性分析示例,从荷载、支座移动、制造误差、温度改变等四个方面展开分析,以变形趋势作为基本思路,把拉压杆的判断、各点位移的分析以及是否为主要受力构件等作为超静定桁架定性分析的主要指标。

4X框架木箱结构内力计算方法研究

目的以重型包装运输用木质框架结构为研究对象,解决木质框架结构内力求解困难的问题。方法利用解析法,以4X框架结构为例,分别以经验简化静定桁架与无简化超静定桁架进行求解;基于ANSYS软件建立经验简化静定桁架、无简化超静定桁架、梁模型、梁杆组合模型及实体模型,并进行对比分析。结果有限元求解结果与解析法结果具有高度的一致性;经验简化静定桁架的最大轴力超过无简化超静定桁架的最大轴力15%;梁模型、梁杆组合模型及实体模型的计算结果与无简化超静定桁架的计算结果一致。结论经验法对框架结构的简化往往会导致比较大的误差,可能导致过包装设计或欠包装设计。梁杆组合模型和实体模型建模过程比较复杂,选用梁单元对木箱用框架结构进行数值计算分析,不仅计算精度高,分析处理快捷,而且对复杂工况具有较好的适应性。

超静定钢桁架桥预拱度设计的温度假载优化法

为使超静定钢桁架桥在成桥后达到目标线形,需要确定桁架杆件在制造阶段的无应力长度。对于超静定钢桁架桥,若采用常规温度法确定杆件的无应力长度时,可能会使拼装后的结构产生较大的杆件次内力。为此,提出了温度假载杆件的选取原则,在此基础上建立了基于拼装次内力最小化的温度假载优化法,通过假载杆件的温度荷载和桥面节点位移及冗余支座反力的关系,求解一组既满足预拱度,冗余支座次内力又较小的杆件假载温度组合。以南通市深南路大桥三跨连续钢桁梁为例验证该方法的适用性,计算发现该方法可在满足设计预拱度逼近目标预拱度的基础上,控制杆件拼装次内力满足了安装要求。该方法可为超静定钢桁架桥的预拱度设计提供参考。

Experimental and parametrical investigation of pre-stressed ultrahigh-performance fiberreinforced concrete railway sleepers

In this study,ultrahigh-performance fiber-reinforced concrete(UHPFRC)used in a type B70 concrete sleeper is investigated experimentally and parametrically.The main parameters investigated are the steel fiber volume fractions(0%,0.5%,1%,and 1.5%).Under European standards,35 UHPFRC sleepers are subjected to static bending tests at the center and rail seat sections,and the screw on the fastening system is pulled out.The first cracking load,failure load,failure mode,crack propagation,load–deflection curve,load–crack width,and failure load from these tests are measured and compared with those of a control sleeper manufactured using normal concrete C50.The accuracy of the parametric study is verified experimentally.Subsequently,the results of the study are applied to UHPFRC sleepers with different concrete volumes to investigate the effects of the properties of UHPFRC on their performance.Experimental and parametric study results show that the behavior of UHPFRC sleepers improves significantly when the amount of steel fiber in the mix is increased.Sleepers manufactured using UHPFRC with a steel fiber volume fraction of 1%and a concrete volume less than 25%that of standard sleeper B70 can be used under the same loads and requirements,which contributes positively to the cost and surrounding environment.

独塔非对称自锚式悬索桥合理约束体系研究

自锚式悬索桥通过主缆与加劲梁锚固结合的方式,形成闭合传力路径。主缆的水平分力通过锚固区逐渐传递到主跨加劲梁,竖向分力则主要通过边跨自重平衡。在静力情况下,主梁为超静定体系;在动力情况下,通常为全飘浮或者半飘浮体系来达到减隔震目的。这样就会造成主梁约束转变的情况,这个问题在独塔非对称自锚式悬索桥中尤为凸显。以太原市通达街跨汾河的四跨独塔非对称自锚式悬索桥为背景工程,建立全桥有限元模型,分析了全桥在静力及动力情况下不同约束体系对全桥受力的影响,为今后同类型结构设计提供依据。