Loads
Introduction
Normally, a design specification does not prescribe the magnitudes of the loads that are to be used as the basic input to the structural analysis, with the exception of special cases such as crane design specifications. It is the role of the specification to detail the methods and criteria to be used in arriving at satisfactory member and connection sizes for the structural material in question, given the magnitudes of the loads and their effects .The specification therefore reflects the requirements that must be satisfied by the structure in order that it will have a response that allows it to achieve the performance that is needed .Loads, on the other hand, are governed by the type of occupancy of the building, which in turn is dictated by the applicable local, regional, and national laws that are more commonly known at building codes.
The building code loads have traditionally been given as nominal values, determined on the basis of material properties (e.g., dead load) or load surveys (e.g., live load and snow load).To be reasonably certain that the loads are not exceeded in a given structure, the code values have tended to be higher than the loads on a random structure at an arbitrary point in time. This may, if fact, be one of the reasons why excessive gravity loads are rarely the obvious cause of structural failures. Be that at it may, the fact of the matter is that all of the various types of structural loads exhibit random variations that are functions of time, and the manner of variation also depends on the type of load. Rather than dealing with nominal loads that appear to be deterministic a nature, a realistic design procedure should take load variability into account along with that of the strength, in order that adequate structural safety can be achieved through rational means.
Since the random variation of the loads is a function of time as well as a number of other factors, the modeling, strictly speaking, should take this into account by using stochastic analyses to reflect the time and space interdependence. Many studies have dealt with this highly complex phenomenon, especially as it pertains to live load in buildings. In practice, however, the use of time-dependent loads is cumbersome at best, although the relationship must be accounted for in certain cases (i.e., seismic action).For most design situations the code will specify the magnitude of the loads as if they were static. Their time and space variation are covered through the use of the maximum load occurring over a certain reference (return) period, and its statistics. For example, American live load criteria are based on a reference period of 50 years, while Canadian criteria use a 30-year interval.
The geographical location of the structure plays an important role for certain loads. It is particularly applicable to snow, wind and seismic action, the first being of special importance in north-central and north-eastern areas of the United States, the second in high wind coastal and mountain areas, and the last in areas having earthquake fault lines.
Deign for wind effects is complicated by a number of phenomena. Like snow loads and earthquake action, wind loads are given more attention in certain parts of the country. At the same time wind loads are neither static nor uniformly varying, and are heavily influenced by the geometry of the structure as well s the surrounding structures and landscape. To a certain degree this also applies to the magnitude of the snow load. Building codes treat these effects as static phenomena and relate them to the actual conditions through semi empirical equations. This gives the designer a better handle on a difficult problem, but can lead to difficulties when the real structure departs significantly from the bases of the code. For that reason wind loads, and sometimes earthquake and snow loads, are determined on the basis of model test. In particular, wind tunnel testing has become a useful and practical tool in these endeavors.
The loads on the structure are normally assumed to be independent of the type of structure and structural material, with the exception of dead loads. The response of a building, however, will be different for different materials, depending on the type of load. For example, the behavior of a moment-resistant steel frame will be quite unlike that of a braced frame, when subjected to lateral loads, especially those due to an earthquake. On the other hand, the response of these two frames to gravity loads will not be all that different.
The size of a structure (height, floor area) has a significant impact on the magnitudes of most loads. All loads are influenced by the increasing height of a multistory building, for example. Similarly, the greater the floor area that is to be supported by a single member, the smaller will be the probability that the code live load will appear with its full intensity over the entire area. In such cases a live load reduction method is used to arrive at more realistic design data.
Structures can be classified in a variety of ways.The casual observer might first consider classifying structures according to their respective functions: buildings, bridges, ships, aircraft, towers, and so on. This basis for structural classification is in fact fundamental;all structures have some functional reasons for existence.It is the need to fulfill some function that prompts the designer to give life to a structure.Furthermore, it is the need for a safe, serviceable, feasible, and aesthetically pleasing fulfillment of a function that dictates the form, material, and manner of loading of a structure.
Once the form and material have been determined, a structure may be further classified according to either its form (e.g., an arch, truss, or suspension structure) or the material out of which it is constructed (e.g., steel concrete, or timber). The form and material of a structure in turn dictate its behavior, which in turn dictates the character of the analytical model.Fig. 6.1 illustrates schematically the relationships among the function a structure is to fulfill, the form and material and loading on the structure, the behavior of the structure, and the analytical model of the structure.At this point, we need to discuss some of the aspects of structural behavior indicated in Fig.6.1 and to explain their respective relationships to the form and material of the structure.A structure is linear if its response to loading, say displacement at a point, is directly proportional to the magnitude of the applied load.proportionality does not exist, the structure is said to be nonlinear.Structural nonlinear are of two types:(1) material nonlinear that arise when stress is not proportional to strain, and (2) geometric nonlinear that arise when the configuration of the structure under load is markedly changed from the unloaded configuration. (the presence of cables in a structure often leads to geometric nonlinear because displacements can occur owing to a change in cable sag, which can be shown to be nonlinear related to the force in the cable.)materials, and therefore structures built from them, may be classified as elastic, plastic. Elastic materials rebound to their initial configuration when the load is removed, whereas plastic materials retain a permanent set.The deformations of materials depend on time and therefore load history, whereas the deformations of elastic and plastic materials do not. A structural system is conservative depending on whether or not energy is lost from the system during a cycle of loading and unloading.Energy is generally lost if a system does not recover its initial shape after unloading owing either to plastic behavior of the material or to friction forces within or between parts of the structure.
All these behavioral aspects of the structure will have a significant influence on the nature of the analysis used in studying the structure.In addition, in developing the analytical model it will be necessary to consider whether the structural material is homogeneous or non homogeneous and whether it is an isotropic.(the physical properties of homogeneous materials are the same at each point; those of non homogeneous material are not.The physical properties of isotropic materials are the same in all directions at a point;those of an isotropic materials are not. Or tho tropic material is a special an isotropic material whose properties are different in three principal directions but whose properties in all other direction are dependent on those in the principal directions.) Other aspects of the structure, although important design considerations, will not usually have a significant impact on the analysis technique.These include brittleness, ductility, flammability, texture, color, hardness.
Finally, the nature of the loading, which is dependent on the function of the structure, will also influence the analysis.The only truly static loading on a structure is the dead, or gravity, loading.However, if other load ins are applied gradually enough, they are called quasi-static load ins and may be considered static for analysis purposes.Whether or not the rate of loading is gradual enough depends on whether or not the time it takes to apply the load is longer than the fundamental period of vibration of the structure being analyzed.Loads usually need to be treated as dynamic only if they are periodic in nature or if they are applied very suddenly.Even then, sometimes an “impact factor” is applied to an analysis with a static-loading result to account for the effect of a suddenly applied load.Loads can also be categorized as either external applied forces or internal initial distortions. Thermal loading is an example of an internal initial distortion (or initial strain) loading.
Unfortunately, the picture of structural behavior is generally not so clear as that just painted. That is, materials are not either “linear” or “nonlinear” and “elastic” or “plastic”; instead, their behavior depends on circumstances such as environment and rate of loading.The picture is further clouded in that the type of behavior that must be considered in an analysis may depend on the type of response being investigated. For example, a simpler analytical model may suffice to obtain static displacement and stress results than that which would be required for vibration or buckling results.
To clarify this picture for purposes of a rational presentation of matrix analysis of structures, we will make simplifying assumptions as to the nature of the behavior structures. Thus we will consider only the displacement and stress response due to static loading of linear, elastic, conservative structures.We will further restrict our attention to discrete structures (rigid-and pin-jointed frameworks) as opposed to continuous structures. However, it is important to recognize at the outset that the concepts that will be presented can be extended to the solution of many other classes of structural problems, including those involving dynamic response, material and geometric nonlinear, in elasticity, instability, and continuous systems.Furthermore, the same concepts can be applied to problems from other areas of engineering, such as hydraulics, and heat transfer, as well as to problems outside of engineering altogether.Finally, to conserve space and time, most of our studies will deal with planar structures subjected to planar load ins in the plane of the structure. This approach will retain enough generality that the resulting analysis methods can be readily extended to three-dimensional applications.
中文译文：
荷载
简介
通常除特殊情况设计规程外，如：起重机设计规程，一般设计规程并不规定荷载的大小，尽管它是作为结构分析所输入的基本变量。设计规程的作用就是对于给定的荷载值及其效应，详细说明用设计材料能得到满意构件及其连接尺寸的方法和准则。 因此，规程反映了结构必须满足的各种要求，从而使其具有这样一种结构反应，它能使其达到所要求的性能。另一方面，荷载取决于建筑物的使用类型，这反过来取决于相应的地区，地方和国家法规，即常说的建筑规范。
建筑规范的荷载传统上都是作为标准值给出，它们是根据材料特性确定（如恒载）或荷载调查所确定（如活荷载及雪荷载）。为了适当地确保作用在任一结构上的荷载不超过规范值，后者往往都要比任一时刻作用任一结构上的荷载值大些。事实上，这可能就是过大的重力荷载大都不会导致结构破坏的原因所在。尽管可能如此，实际上结构上的各种荷载都具有随时间而变化的随机变化特性，且这种变化也取决于荷载类型。不是去处理看上去具有定值特征的标准荷载，现实的设计方法应同时考虑荷载和强度的变异性，以便以合理的手段得到足够的结构安全度。
由于荷载的随机变化是时间以及许多因素的函数，严格地讲，通过采用随机分析方法以反映时间与空间的相互影响，应使建模对此加以考虑。许多研究工作都涉及了这一高度复杂的现象，特别是当其属于活荷载时。然而，实践中采用时间相关荷载至少半是麻烦的，尽管在一些情况下必须考虑其相关性（即在有地震作用时）。 对于大多数设计，规范将规定荷载的大小，就象它们是静载似的。通过采用出现在某一参照期（重现周期）内的最大荷载及其统计特性，将它们的时间和空间的变异加以考虑。例如，美国活荷载准则基于50年重现周期，而加拿大准则是30年。
结构的地理位置对某些荷载起很重要的作用。特别是对于雪、风和地震作用更是如此。第一种荷载对美国中北部和东北部地区非常重要，第二种对具有大风的沿海地区和山岭地区特别重要，第三种对具有地震断裂带的地区则特别重要。
由于数个现象使风作用效果的设计复杂化。类似于雪荷载和地震作用，在本国的一些地区，对风荷载更加重视。同时，风载不但非静态，而且也非均匀变化，同时还受结构几何形式和周围结构物及地形的影响。建筑规范将这些作用作为静力荷载并用半经验公式将其与实际情况相联系。这使设计者能更好地处理复杂问题，但当实际结构与设计规范出入太大时，便导致了一些困难。为此，风荷载、有时地震荷载和雪荷载都要用模型试验来确定。特别是风洞试验，它已经成为这些努力中一个有用且实用工具。
除恒载外，通常都假定结构上的荷载与结构类型及其材料无关。然而，一建筑物的反应将随其建材的不同而不同，这取决于荷载的类型。例如，在侧向荷载作用下，特别是当其由地震所引起时，抗弯钢框架的工作性能将全然不同于有支撑框架的性能。
一个结构物的大小（如其高度，楼层面积）对大多数荷载的量值影响很大。 例如，所有的荷载都受多层建筑高度增加的影响。与这类似，单个构件所支承的楼层面积越大，整个楼层上满载规范规定的活荷载的可能性将越小。在此情况下，将采用活荷载折减法以得到更真实的设计值。
能用各种方法对结构进行分类。 不认真的观察者首先考虑的是根据其相应功能进行分类，如建筑物、桥梁、飞机、塔楼等等。事实上这种结构分类的根据是基本的。 所有结构物都因其某些功能而存在。正是由于要使它们完成某些功能要求才促使设计者终生致力于结构设计。此外，也正是对某一功能的安全的、适用的、可行的、和美学上满意的实现决定了一个结构的形式、所用材料和加载方式。一旦结构的形状和建筑材料确定之后，可将结构再按其形式分类（如拱、桁架或悬挂结构）或按其所用材料分类（如钢结构、混凝土结构或木结构）。结构的形式和建材反过来决定了结构的性能，其性能进而又分析模型的特点。图中形象地说明了结构的功能、形式、建筑材料、荷载、结构性能、分析模型储因素之间的关系。图中所示结构性能的一些方面，并我解释一下它们各自与结构的形式和建筑材料的关系。如果一结构对其加载的响应，譬如某点的位移与所施加的荷载大小成正比，则此结构就是线性的。如果此比例不存在，则该结构就是非线性的。结构非线笥分为两类(1)材料非线性，此时材料的应力与应变不呈比例；(2)几何非线性，此时在荷载作用下其形状与未加载前发生了很大变化。(例如结构中索的存在往往会引起几何非线性，因为索的下垂会产生位移，可以证明，这种位移与索中的内力并不成线性关系)， 因此，结构所采用的建筑材料可能被分类为弹性、塑性或粘弹性。(位置，状态). 当卸除荷载后，弹性材料能回弹以其初始外形，但塑性材料会有一永久变形，粘弹性材料的变形与时间有关，因而与加载历史有关，但弹性和塑性材料的变形却与时间无关。一个结构体系是非保守的或保守的，取决于经过一次加载和卸载该体系中有无能量损失。如果卸载后体系并未回到其初始形状，通常都有能量损失，这是要么是由材料非线性引起，要么是由结构内部或其构件之间存在摩擦力。
结构的所有这些性能都将对研究结构时的分析方法起到很大的影响。 而且，在建立分析模型时，必须考虑结构材料是否均质、是否各向同性，还是正交各向异性。 均质材料的物理性能在各点都相同的，但非均质材料并非如此。各向同性材料的物理性能在各个方向都是相同，但各向异性材料却并非如此。正交各向异性材料是一种特殊的各向异性材料，它在其三个主轴方向的特性不同，但在所有其它方向上的特性则取决于其三个主轴方向的特性。 结构的其它方面，尽管也是设计中要考虑的主要因素，通常将对分析方法影响不大。 这些因素包括脆性、延性、可燃性、质地、颜色、硬度和可加工性。
最后讨论一下加载特点，它取决于结构的功能，也会影响结构的分析。结构上真正的静力荷载是恒载，即重力荷载。然而，如果其它荷载施加的足够缓慢，就将其称为伪静力加载，从而分析时可认为是静力的。 加载是否足够缓慢取决于加载持续时间是否大于所分析结构的基本周期。通常只有当荷载是周期性的或当共是突然施加的，才将其作为动力荷载处理。 即使在此情况下，有时在分析中采用一个所谓的“动力系数”来考虑突然施加荷载的效应，分析结果仍以静态加载形式结出。 荷载还可分为外力或内部初始变形。 热负荷就是内部初始变形（如初始应变）加载的典型例子。
不幸的是，通常对结构性能的描述并不象上述如此清楚。也就是说，材料并不是“线性”或“非线性”；也不是“弹性”或“塑性”，其性能取决于环境因素，如外界情况和加载速率。 由于分析中所必须考虑的结构性能类型可能取决于要研究的结构响应的类型，这就使这种描述变得更加含糊不清。 例如，比较简单的分析模型可能足以得到静态的位移和应力结果，但需要更复杂的模型以得到振动或曲屈分析结果。
为了阐明这一问题以讲解清楚结构矩阵分析方法，我们将对结构特性作一些简化假定。 因此，我们将讨论线弹性保守结构因静力加载所引起的位移和应力。我们将进一步将注意力集中到离散杆系结构（刚结和铰结框架结构）而非连续结构。然而，重要的是要在开始就认识到我们将要介绍的概念可推广到许多其它结构问题，其中包括动力响应、材料及几何非纯属、非弹性、失稳和连续结构体系。而且，同样的概念也可应用于其它工程领域的问题，如土工学、水力学、热传导以及甚至是工程领域之外的问题。 最后，为了节省时间和篇幅，我们研究的大多数问题将涉及平面内受平面力作用的平面结构。这一方法将保持足够的普遍性，从而使所得到的分析方法能容易地推广到三维空间问题。