土木工程专业英语上册_翻译苏小卒_同济大学(考试手机专业版)

第一单元

Fundamentally, engineering is an end-product-oriented discipline that is innovative, cost-conscious and mindful of human factors. It is concerned with the creation of new entities, devices or methods of solution: a new process, a new material, an improved power source, a more efficient arrangement of tasks to accomplish a desired goal or a new structure. Engineering is also more often than not concerned with obtaining economical solutions. And, finally, human safety is always a key consideration.

从根本上，工程是一个以最终产品为导向的行业，它具有创新、成本意识，同时也注意到人为因素。 它与创建新的实体、 设备或解决方案有关：新工艺、新材料、一个改进的动力来源、任务的一项更有效地安排，用以完成所需的目标或创建一个新的结构。 工程是也不仅仅关心获得经济的解决方案。最终，人类安全才是一个最重要的考虑因素。

Engineering is concerned with the use of abstract scientific ways of thinking and of defining real world problems. The use of idealizations and development of procedures for establishing bounds within which behavior can be ascertained are part of the process.

工程关心的是，使用抽象的科学方法思考和定义现实世界的问题。理想化的使用和发展建立可以确定行为的边界的程序，是过程的一部分。

Many problems, by their very nature, can’t be fully described—even after the fact, much less at the outset. Yet acceptable engineering solutions to these problems must be found which satisfy the defined needs. Engineering, then, frequently concerns the determination of possible solutions within a context of limited data. Intuition or judgment is a key factor in establishing possible alternative strategies, processes, or solutions. And this, too, is all a part of engineering.

很多的问题，就其本身的性质而言，不能完全被描述 — — 即使这一事实，在其开始之前。然而还必须找到对于这些问题可接受的工程解决方案，来满足预定的需求。直觉或判断是建立可能的替代策略、 流程或解决方案的关键因素。。而这也是工程的一部分。 Civil engineering is one of the most diverse branches of engineering. The civil engineer plans, designs, constructs, and maintains a large variety of structures and facilities for public, commercial and industrial use. These structures include residential, office, and factory buildings; highways, railways, airports, tunnels, bridges, harbors, channels, and pipelines. They also include many other facilities that are a part of the transportation systems of most countries, as well as sewage and waste disposal systems that add to our convenience and safeguard our health. 土木工程是工程的最多样化的分支机构之一。土木工程师计划、设计、施工，和维护大量的结构和公共、商业和工业使用的设施。这些结构包括住宅，办公室和工厂大厦；公路、铁路、机场、隧道、桥梁、港口、渠道和管道。在其他大多数的国家它们还包括运输系统许多其他设施，以及将为我们的生活带来便利的和维护我们的健康污水及废物处理系统。

The term “civil engineer” did not come into use until about 1750, when John Smeaton, the builder of famous Eddystone lighthouse near Plymouth, England, is said to have begun calling himself a “civil engineer” to distinguish himself from the military engineers of his time. However, the profession is as old as civilization.

直到大约1750年，人们才开始使用“土木工程师”这一术语。约翰.斯密顿在英格兰普利茅斯附近，建造了著名的埃迪斯通灯塔的建造师，开始自称为“土木工程师"来将自己与当时的军事工程师区分开。然而，土木工程这个职业却像文明一样古老。

In ancient Egypt the simplest mechanical principles and devices were used to construct many temples and pyramids that are still standing, including the great pyramid at Giza and the temple of Amon-Ra at Karnak. The great pyramid, 481 feet(146.6 meters)high, is made of 2.25 million stone blocks having an average weight of more than 1.5tons (1.4 metric tons). Great numbers of men were used in the construction of such monuments. The Egyptians also made obelisks by cutting huge blocks of stone, some weighing as much as 1000 tons (900 metric tons). Cutting tools of hard bronze were used.

古埃及人用最简单的机械原理和装置建造了许多至今仍矗立的庙宇和金字塔，包括吉萨大金字塔和在卡纳克的Amon-Ra的寺庙。这个大金字塔，481英尺（146.6 米）高，由2250000个石块组成，石块的平均重量超过1.5吨（1.4 吨）。建造如此的纪念性建筑使用了大量的人力。埃及人也作了一些重达1000吨(900吨)的石头的大块切割的方尖塔。硬青铜的切削刀具在其中使用到了。

The Egyptians built causeways and roads for transporting stone from the quarries to the Nile. The large blocks of stone that were erected by the Egyptians were moved by using levers, inclined planes, rollers, and sledges.

为了从采石场向尼罗河运输石材埃及人建造了长堤和道路。由埃及人竖设的大块石头通过使用拉杆、斜平面、滚子和雪橇来移动。 The Egyptians were primarily interested in the know-how of construction; They had very little interest in why-for of use .In contrast, the Greeks made great strides in introducing theory into engineering problems during the 6th to 3rd centuries B.C. They developed an abstract knowledge of lines, angles, surfaces, and solids rather than referring

to specific objects. The geometric base for Greek building construction included figures such as the square, rectangle, and triangle.

埃及人主要对如何建造感兴趣；他们对为什么这么使用没有什么太多的兴趣。相反，在公元前六世纪到公元前三世纪希腊人取得了巨大的进步于工程理论的推广。他们发展了线、角度、面，和实体的抽象的知识，而不是与特定的对象产生联系。 希腊建筑施工的几何基础包括数字如正方形、矩形和三角形。

The Greek architekton was usually the designer, as well as the builder, of architectural and engineering masterpieces. He was an architect and engineer. Craftsmen, masons, and sculptors worked under his supervision. In the classical period of Greece all important buildings were built of limestone or marble; the Parthenon, for example, was built of marble.

希腊建筑师 通常是建筑工程杰作的设计师同时也是建造师。 他既是一个建筑师也是工程师。工匠、石匠和雕塑家在他的监督下工作。在希腊古典时期所有重要建筑物是由石灰

第二单元 土木工程是涉及自然资源的开发、区域性和局部地区的供水、排洪设施、废物处理设施、运输设施、隧道、建筑物、桥梁以及人们所需要的其他结构物的规划、设计和施工的一个工

程领域。具备学历、经验又有国家关于土木工程专业实践要求认证的人员被称为土木工程师

土木工程师职业标准

作为专业人员，土木工程师在履行他们职责的同时，应当遵循以下的原则：

（1）保证公众的安全、健康和福利是极为重要的。

（公众的福利意味着克持续发展的承诺，

即在为子孙后代保护自然资源基础的同时满足当前的需要和工程目标。

（2）称为每一位雇主货委托人的忠实代理货委托人，并且要避免利益冲突。

（3）最大程度的应用他们的知识和技巧来建设所有委托人的工程。

（4）保持终身学习，总是自愿地参与理念于技术信息方面的专业交流。

（5）只能在能力范围内履行职责；其他范围内，工程师可以与有资格的同事、顾问，或者雇

员一起合作来执行任务。

因此，土木工程的工程项目应当被规划、设计和施工以满足下列标准：

（1） 应当满足业主货委托人所指定的用途。

（2）应当在业主货委托人给定的工期内，通过已知的技术和可用的劳动力及设备来建设。

（3）在合理的时间周期里，应当能够经受住自然环境的作用和正常使用。

4）工程竣工时，应是对实现预期用途的最低造价或业主或委托人所花费用达到的最佳效果

进行评定的时机。工程费用不应当超过业主的施工预算，并且当完全投入使用后，其运营、 维护和维修费用不应过度昂贵。

5）工程的设计和施工要满足相关法律要求，符合公认的工程标准，同时，要避免建筑工人、工程操作者以及公众的健康和安全。

6）应当将工程设计成满足可持续发展的要求，即在为子孙后代保藏和保护周围环境质量及自然资源的基础上满足当前工程项目的需要。

7）完全运行时，工程应当有效地利用能源。

8）工程应当尽可能地体现美学的特征

工业 操纵着许多商业交易的工业公司的员工中有它们自己的工程设计师。然而这些工程设计师的角色是多种多样的。一个公司多产，那么车间设施就必须包括车间工程师和普通员工来确保车间的适当维修和运行。在许多工厂里，这些车间工程师也同时为他们的雇主服务于设计部门。例如，如果现在的车间配置了一台新装备，不仅要提供空间，而且必须解决一些工程问题。典型的有：基础是否足够承受这些附加的荷载？是否需要一些新的设施保养服务？现今的能源供应是否足够？进一步的说，可能需要建造一栋新的建筑来容纳这些装备。因此，一个车间工程师的标准的职业行为和责任感常常领导着设计领域。

这个设计是由建设这栋建筑及公共设施的相同的组织或者组织内部的部门来完成的。由于各种各样的因素，在设计公司和建设公司之中同责任部门相比较之下，这种联合服务也有利有弊。

咨询工程师 一个咨询工程师已被定义为一个熟练于运用科学原理来解决工程难题的专业人士。作为专业人员，咨询工程师应该像对他们的顾客一样也对公众负责。除了提供专业的服务，咨询工程师也经营商业交易。咨询工程由一些独资企业，合伙公司，股份有限公司运营着，它们许多都拥有大量专业员工，草图人员，和其他支援人员。不管这些工程师所在机构是什么形式的，客户接收到的终

端产品仍然保留着相同的专业特性，也能满足相同的职业标准。咨询工程师通常都有许多客户，他们必须精选最佳的运营方法来满足客户和他们自己的需求。

建议和咨询 这个阶段仅仅包括了咨询师基于经验和技术知识的抉择。通常，在这个阶段详细的工程设计不是其中的组成部分；但是工程师也许会建议从着手这项工程的价值和相关的技术考虑。或者这个阶段也许仅仅是基于对采取更进一步的研究来决定是否需要对现今的结构进行维修而做的抉择。

计划 基于可行性的报告和其他的信息，如果业主决定继续进行这项建设工程，那么计划阶段就开始了。计划必须从设计中剥离出来考虑。例如，如果一个工厂或复杂建筑结构开始形成，计划方案包括粗略的初步草图和这项拟议工程的总平面图规划。通过这个总平面图的规划，业主可以依据他的可用资金在各个阶段和施工进度中开发这个工程。

设计 这个阶段可以被细分为概要的，初步的，最终的设计。在每个阶段的最后可以和业主进行验收，或者验收应该保持连续性以使业主对一些要求的实施有个形象化的认识以及当需要的时候做必要的增建和改动。完整的设计文件包括详细的设计，详细的说明书和建设合同。然而设计师的角色并不因最终设计的完成而结束。通常，设计师在建设施工招标，签订合同，和执行建设合同中充当着业主代理人的角色。

第三单元

The principal construction materials of earlier times were wood and masonry-brick, stone, or tile, and similar materials. The courses or layers（砖层）were bound together with mortar or bitumen, a tarlike substance, or some other binding agent. The Greeks and Romans sometimes used iron rods or clamps to strengthen their building. The columns of the Parthenon in Athens（雅典的帕台农神庙）, for example, have holes drilled（钻孔） in them for iron bars that have now rusted away（锈蚀殆尽）. The Romans also used a natural cement called pozzolana, made from volcanic ash, that became as hard as stone under water.

早期主要的建筑材料是木材和砌体，如砖、石、瓦以及类似的材料。砖层之间通过砂浆、沥青（一种焦油状的物质）或其他一些粘合剂粘合在一起。希腊人和罗马人有时用铁条或夹子来加固他们的房屋。例如，雅典的帕台农神庙柱子中曾钻孔以便加入铁条，如今都已锈蚀殆尽。罗马人也用称作白榴火山灰的天然水泥，它用火山灰制作，在水中会变得与石头一样坚硬。

Both steel and cement, the two most important construction materials of modern times, were introduced（推广） in the nineteenth century. Steel, basically an alloy of iron （铁合金）and a small amount of carbon, had been made up to that time（到那个时候） by a laborious（繁复的） process that restricted it to such special uses as sword blades（刀刃）. After the invention of the Bessemer process （贝塞麦炼钢法）in 1856, steel was available in large quantities at low prices. The enormous advantage of steel is its tensile strength; that is, it does not lose its strength when it is under a calculated degree (适当的) of tension, a force which, as we have seen, tends to （往往）pull apart many materials. New alloys have further increased the strength of steel and eliminated some of its problems, such as fatigue, which is a tendency for it to weaken as a result of continual changes in stress（连续的应力变化）.

作为现代两种最重要的建筑材料，钢材与水泥在十九世纪得到了推广。直到那个时候，钢材才通过繁复的过程制造出来，基本上是铁合金，并含有少量的碳，因而被限制在一些特殊的用途如刀刃。在1856年发明了贝塞麦炼钢法后，钢材才得以大量低价获得。钢材巨大的优势即是它的抗拉强度，也就是当它在适当的拉力下不会失去强度，正如我们所看到的，该力往往能够将很多材料拉开。新的合金进一步提高了钢材的强度，并消除了一些缺点，如疲劳，即在连续的应力变化下导致强度减弱的趋势。

Modern cement, called Portland cement, was invented in 1824. It is a mixture of limestone（石灰石） and clay, which is heated and then ground into a powder（磨成粉末）. It is mixed at or near the construction site （施工现场）with sand, aggregate (small stones, crushed rock, or gravel), and water to make concrete. Different proportions of the ingredients （配料）produce concrete with different strength and weight. Concrete is very versatile; it can be poured, pumped, or even sprayed into （喷射成）all kinds of shapes. And whereas steel has great tensile strength, concrete has great strength under compression. Thus, the two substances complement each other（互补）.

现代水泥发明于1824年，称为波特兰水泥。它是石灰石和粘土的混合物，加热后磨成粉末。在或靠近施工现场，将水泥与砂、骨料（小石头、压碎的岩石或砾石）、水混合而制成混凝土。不同比例的配料会制造出不同强度和重量的混凝土。混凝土的用途很多，可以浇筑、泵送甚至喷射成各种形状。混凝土具有很大的抗压强度，而钢材具有很大的抗拉强度。这样，两种材料可以互补。 They also complement each other in another way: they have almost the same rate of contraction and expansion. They therefore can work together in situations where（在 情况下） both compression and tension are factors（主要因素）. Steel rods（钢筋） are embedded in（埋入）concrete to make reinforced concrete in concrete beams or structures where tension will develop（出现）. Concrete and steel also form such a strong bond - the force that unites（粘合） them - that the steel cannot slip（滑移） with the concrete. Still（还有） another advantage is that steel does not rust in concrete. Acid

（酸） corrodes steel, whereas concrete has an alkaline chemical reaction, the opposite of acid.

它们也以另外一种方式互补：它们几乎有相同的收缩率和膨胀率。因此，它们在拉、压为主要因素时能共同工作。在出现拉力的混凝土梁或结构中，将钢筋埋入混凝土而成钢筋混凝土。混凝土与钢筋形成如此强大的结合力——这个力将它们粘合在一起——以致于钢筋在混凝土中不会滑移。还有另一个优势是钢筋在混凝土中不会锈蚀。酸能腐蚀钢筋，而混凝土会发生碱性的化学反应，与酸相反。

The adoption of structural steel and reinforced concrete caused major changes in traditional construction practices（施工作业）. It was no longer necessary to use thick walls of stone or brick for multistory buildings, and it became much simpler to build fire-resistant floors（防火地面）. Both these changes served to（有利于） reduce the cost of construction. It also became possible to erect（建造）buildings with greater heights and longer spans.

结构钢与钢筋混凝土的采用使传统的施工作业发生了明显的变化。对多层建筑，再也没必要采用厚的石墙或砖墙，且施工防火地面变为容易得多。这些变化有利于降低建筑的成本。它也使建造高度更高和跨度更大的建筑物成为可能。

Since the weight of modern structures is carried（承受） by the steel or concrete frame, the walls do not support the building. They have become curtain walls, which keep out the weather and let in light. In the earlier steel or concrete frame building, the curtain walls were generally made of masonry; they had the solid look of bearing walls（承重墙）. Today, however, curtain walls are often made of lightweight materials such as glass, aluminum, or plastic, in various combinations.

由于现代结构的重量由钢或混凝土框架承受，墙体不再支承建筑物。它们成为幕墙，将日晒风吹雨打阻挡在外，而让光线进入。在较早的钢或混凝土框架建筑中，幕墙一般由砌体构成；它们具有承重墙的结实外观。但是今天，幕墙通常由轻质材料组成，如玻璃、铝或塑料，并形成不同的组合。

Another advance in steel construction（结构） is the method of fastening together（连在一起） the beams. For many years the standard method was riveting. A rivet is a bolt with a head that looks like a blunt screw（圆头螺丝钉） without threads（螺纹）. It is heated, placed in holes through the pieces of steel（钢构件）, and a second head is formed at the other end by hammering（锤击）it to hold it in place（固定就位）. Riveting has now largely been replaced by welding, the joining together of pieces of steel by melting（熔化） a steel material between them under high heat.

钢结构中的另一个进步是梁的连接方式。在很多年里，连接的标准方式是铆接。铆钉是个有头的螺栓，看上去象个没有螺纹的圆头螺丝钉。铆钉加热后穿过钢构件之间的孔洞，并通过锤击另一端而形成第二个铆钉头，从而将其固定就位。如今铆接已大量地被焊接所替代，钢构件间的连接通过在高热下熔化它们之间的钢材料（即焊条）进行。

Prestressed concrete is an improved form of reinforcement（加强方法）. Steel rods are bent into the shapes to give them the necessary degree of tensile strength. They are then used to prestress （对..预加应力）concrete, usually by one of two different methods. The first is to leave channels in a concrete beam that correspond to（相应于） the shapes of the steel rods. When the rods are run through the channels, they are then bonded to the concrete by filling the channels with grout, a thin mortar or binding agent. In the other (and more common) method, the prestressed steel rods are placed in the lower part of a form（模板） that corresponds to the shape of the finished structure（成品结构）, and the concrete is poured around them. Prestressed concrete uses less steel and less concrete. Because it is so economical, it is a highly desirable（非常理想） material.

预应力混凝土是加强法的改进形式。将钢筋弯成一定的形状以使它们具有必要的抗拉强度，然后用该钢筋对混凝土施加预应力，通常可采用两种不同方法中的任何一种。第一种方法是在混凝土梁中按钢筋的形状留下孔道，当钢筋穿过孔道后，通过在孔道内灌注薄砂浆（一种稀薄的砂浆或粘合剂）将钢筋与混凝土粘结在一起。另一种（更常用的）方法是将预应力钢筋置于按成品结构的形状设置的模板的较低部位，然后将混凝土倒入（模板）而包围着钢筋。预应力混凝土使用了较少的钢筋和混凝土，由于它是如此的经济，因此是一种非常理想的材料。

Prestressed concrete has made it possible to develop（建造） buildings with unusual shapes, like some of the modern sports arenas, with large space unbroken by any obstructing supports（阻碍的支撑物）. The uses for this relatively new structural method are constantly being developed（不断地扩大）.

预应力混凝土使建造独特形状的建筑物成为可能，象一些现代的运动场，它具有不受任何支撑物阻挡视线的大空间。这种较新的结构方法的使用正在不断地被扩大。

The current tendency is to develop（采用） lighter materials, aluminum, for example, weighs much less than steel but has many of the same properties. Aluminum beams have already been used for bridge construction and for the framework of a few buildings.

目前的趋势是采用较轻的材料。例如，铝的重量比钢轻得多，但具有很多相同的性能。铝材梁已经用于桥梁建筑和一些

建筑的框架。

Lightweight concretes, another example, are now rapidly developing（发展） throughout the world. They are used for their thermal insulation(绝热性). The three types are illustrated below（举例说明如下）: (a) Concretes made with lightweight aggregates; (b) Aerated concretes (US gas concretes) foamed（起泡） by whisking（搅拌）or by some chemical process during casting; (c) No-fines concretes.

另一个例子是轻质混凝土，如今已在全世界快速地发展，因它们的绝热性而被采用，其三种类型举例说明如下：(a)轻质骨料制成的混凝土；(b)通过浇筑时搅拌或一些化学方法起泡而成的加气混凝土（US加气混凝土）；(c)无细骨料混凝土。

All three types are used for their insulating properties（绝热性）, mainly in housing, where they give high（非常） comfort in cold climates and a low cost of cooling（降温成本）in hot climates. In housing, the relative weakness of lightweight concrete walls is unimportant, but it matters（有重大关系） in roof slabs, floor slabs and beams.

这三种类型的混凝土都是由于它们的绝热性而被使用，主要用于房屋，使其在寒冷的气候中非常舒服，在炎热的气候中降温的成本不高。在房屋中，墙采用较薄弱的轻质混凝土不重要，但是屋面板、楼面板和梁（采用轻质混凝土）则有重大关系。

In some locations, some lightweight aggregates cost little more than（几乎等于） the best dense（致密） aggregates and a large number of （大量） floor slabs have therefore been built of lightweight aggregate concrete purely for its weight saving, with no thought of（没考虑） its insulation value.

在某些地区，一些轻质骨料的费用几乎等于最致密的骨料，因此大量的楼面板采用轻骨料混凝土制作纯粹是节约重量，而没考虑它的绝热价值。

The lightweight aggregate reduces the floor dead load（恒载） by about 20 per cent resulting in（导致）considerable savings in the floor（楼盖结构） steel in every floor and the roof, as well as in the column steel and (less) in the foundations. One London contractor（承包商）prefers to use lightweight aggregate because it gives him the same weight reduction in the floor slab as the use of hollow tiles, with simpler organization and therefore higher speed and profit. The insulation value of the lightweight aggregate is only important in the roof insulation, which is greatly improved（改进）.

轻质骨料使楼面的恒载减少了约20%，因而大量的节约了每层楼面以及屋面的楼盖结构中的钢材和柱子与基础中（较少）的钢材使用量。一位伦敦的承包商宁愿使用轻质骨料，因为这使楼面板上减少的重量与用空心砖相同，且组织更简单，因而速度和利润更高。轻质骨料的绝热价值只在屋面绝热时显得重要，它已被大大地改进了。

4 Mechanics of Materials deals with（研究）the response of various bodies, usually called members（构件）, to applied forces（施加力）. In Mechanics of Engineering Materials the members have shapes that either exist in actual structures or are being considered for their suitability（根据其需要）as parts of proposed（拟建的）engineering structures. The materials in the members have properties that are characteristic of commonly used（常用的）engineering materials such as steel, aluminum, concrete, and wood.

材料力学用以研究不同物体（通常称为构件）对施加力的响应。在工程材料力学中，构件的形状可以是实际结构中存在的，也可以根据其需要而进行考虑（设计），作为拟建工程结构的部件。构件中材料的性能即是常用的工程材料如钢材、铝材、混凝土和木材的特性。

As you can see already from the variety of materials, forces, and shapes mentioned, Mechanics of Engineering Materials is of interest to（对..有价值）all fields of engineering. The engineer uses the principles of Mechanics of Materials to determine if the material properties and the dimensions of a member are adequate to（足以）ensure that it can carry its loads safely and without excessive distortion. In general（通常）, then, we are interested in both the safe load that a member can carry and the associated（相关的）deformation. Engineering design would be a simple process if the designer could take into consideration（考虑）the loads and the mechanical properties of the materials, manipulate（利用）an equation, and arrive at（得到）suitable dimensions.

Design is seldom that simple. Usually（通常）, on the basis of（根据）experience, the designer selects a trial（试算） member and then does an analysis to see if that member meets the specified requirements. Frequently（常常）, it does not and then a new trial member is selected and the analysis repeated. This design cycle（设计周期） continues until a satisfactory solution is obtained. The number of cycles（循环次数） required to find an acceptable design diminishes as the designer gains experience.

正如你已经从提到的各种各样的材料、力和形状所看到的，工程材料力学对所有的工程领域都有价值。工程师利用材料力学的原理来确定是否该材料的性能和构件尺寸足以保证它能安全地承受荷载且没有过多的变形。通常，我们关心的是构件能承受的安全荷载及其相应的变形。如果设计者能通过考虑荷载和材料的力学性能，并利用公式得到合适的构件尺寸，那么工程设计将是一个简单的过程。

然而设计很少那么简单。通常，根据经验，设计者选择一个试算构件，然后进行分析，看它是否满足规定的要求。它常常不会满足要求，则再选择一个新的试算构件，再进行分析。这样的设计不断重复，直至得到一个满意的结果。当设计师拥有一定的经验后，为得到一个可接受的设计所需要的循环次数会减少。

Design of Axially Loaded Members 轴向力构件的设计

To give you some insight into （使..有一些了解）the design cycle, an extremely simple member will be dealt with first. That member is a prismatic bar with a force, P, acting along its longitudinal axis in the direction（纵轴向）such that it tends to elongate the bar. Such a force is referred to as（称为）an axial tensile load（轴向拉力）, and we can readily imagine it trying to（努力..）pull the fibers apart and to cause failure on a transverse plane（横向平面）. It is safe to assume that all fibers of the bar, in regions remote from（远离）the point of application of the load, are being pulled apart with the same load intensity（荷载强度）. With this assumption, the load intensity or stress is uniform on a transverse plane and is given by

when P is in（以..为单位）Newtons and A is in square metres, stress, ,is in Newtons per square metre (N/m2), which is by definition（根据定义）Pascals (Pa).

为了使你对设计周期有一些了解，首先研究一个非常简单的构件。构件是个棱形的杆件，其上沿着它的纵轴向作用一个力P，这样往往使杆件在该方向上伸长。这样的力称为轴向拉力，我们能容易地想象它在努力地将纤维拉开，导致横向平面的破坏。安全地假定杆件的所有纤维在远离荷载施加点的区域以相同的荷载强度被拉开。在此假定下，荷载强度或应力在横向平面上是均匀的，为 当P的单位为牛顿、A的单位为平方米时，应力σ的单位为牛顿每平方米（N/m2），根据定义为帕斯卡（Pa）。

For a given axial load and given dimensions, the stress can be calculated from (4-1) and compared with（与..相比）the stress that can be safely carried by the material. The safe stress, known as（称为）the design stress or allowable stress（许用应力）, is determined by tests performed on material made to（按照） the same specifications as the part being considered.

A safety factor（安全系数）, frequently imposed by a legally established code（法规）, is applied to the strength, as determined by tests, to give the allowable stress. The allowable stress, a , is given by

where f is the stress at which the material fails (failure to be defined later) and n is the safety factor.

对已知的轴向力和（构件）尺寸，可根据公式（4-1）计算出应力，并与材料能安全承受的应力作比较。安全应力，称为设计应力或许用应力，它是通过对材料的试验来确定的，该（试验）材料按照与所考虑（验算）的杆件相同的规范制作。根据法规规定，通常对试验所确定的强度考虑安全系数后得到许用应力。许用应力 a 为

这里， f 为材料失效（失效在下文有定义）时的应力，而n为安全系数。

Before approving（核准）trial dimensions, the designer makes certain（确信）that the design is safe by determining that the inequality（不等式）

is satisfied. The inequality is usually more convenient in the form

不等式常常以更合适的形式出现，即

在核准试算的尺寸之前，设计者通过确定不等式成立而确信设计的安全，即

It might at first（起先）seem that the designer would always dimension（选定..的尺寸）the cross section（横截面） so that the stress would exactly equal the allowable stress. However, it may be very costly to produce parts that have nonstandard sizes, so it is usually more economical to waste some material by selecting the next（接近的）larger standard size above that required by the allowable stress. Departure from（背离）standard sizes is justified（合理的） in cases where the penalty（不利后果）for excess weight is very severe, as in aircraft（航天器）or space-ship（宇宙飞船）design.

起先似乎设计者总是在选定横截面的尺寸，以使应力恰好等于许用应力。但是，生产非标准尺寸部件的成本可能很高，因此，通常人们会选择比按许用应力要求的尺寸大一些的标准尺寸部件，这样尽管浪费了一些材料，但总体上更经济。但不选择标准尺寸的做法在诸如航天器和宇宙飞船的设计中证明是合理的，因为多余重量产生的不利后果是很严重的。

Design of Beams 梁的设计

Up to this point（至此）we have looked at（考虑）the beam problem as a problem in analysis; that is（即）, for a given set of loads, span, and cross section we have been calculating the stress. The more commonly encountered problem is to select a standard section, or design a member, for a given span and loads without exceeding a certain allowable stress. Under some conditions the allowable stress may be dependent upon the dimensions and shape of the cross section, in which case the selection of the member becomes more difficult. For the present（暂时）we will take the allowable stress as though（似乎）it depends only on the strength of the material and the safety factor.

至此，我们已经考虑了梁的问题而进行了（问题）分析，即对给定的一组荷载、跨度和横截面，我们已经计算了应力。更常遇到的问题是在不超过某个许用应力下对一个给定的跨度和荷载选择一个（构件的）标准截面，或设计一个构件。在某些条件下，许用应力可

能依赖于横截面的尺寸和形状，这种情况下的构件选择会变得比较困难。暂时我们将采用许用应力法，似乎它只取决于材料的强度和安全系数。

A trial member will be acceptable（合格）when the stress is equal to, or less than, the allowable stress, that is, if For design purposes this inequality is more useful in the form

In the usual design process the maximum bending moment is taken from（取自于）the bending moment diagram（弯矩图） and the allowable stress is determined (quite frequently in accordance with（根据）the rules of some legally constituted code) from standard strength tests in combination with（与..结合）a safety factor. The right-hand side of (4-6) is then known, and it remains（仍然是） to select or design a member that will satisfy the inequality. When a standard section is to be used, the tables（表格）could be searched until a member is found such that the combination of I and c satisfies (4-6). This takes more time than is really necessary, since the tables also provide the value of I/c for each member under the heading（标题）S, the section modulus（截面模量）.

当试算构件的应力等于或小于许用应力时，也就是说，如果

在通常的设计过程中，最大的弯距从弯距图上取得，而许用应力通过标准强度试验并考虑安全系数后确定（往往是根据一些法规的规则）。这样，已知式（4-6）右手边的值，则仍然是选择或设计构件以满足该不等式。当使用标准截面时可以查找表格，直至找到的构件其I和c值的组合能满足式（4-6）。这样花费的时间比实际需要的多，因为表格中在截面模量S的标题下也提供了每一个构件的I/c的值。

试算构件即为合格。根据设计的需要，（上述）不等式以下列形式出现更有用，即

That is, the section modulus is defined as（定义为）

To select a member, the S column（列） is consulted（查阅） and any member that satisfies (4-8) could be used. The members with very high values of S will obviously be understressed（应力不足的）and wasteful of material. The best design, if there are no other constraints, will be that which satisfies (4-8) with the minimum amount of material.

With tabulated values of S available it is much more convenient to use (4-6) in the form

The smallest acceptable S does not necessarily coincide with（符合）the most economical member. To select the lightest and most economical standard section, the listed values of mass should be examined to find the lightest member with an acceptable S. The problem becomes much more complex if built-up（组合）member is being designed because its cost will depend upon the combined costs of web plate, angles and cover plates as well as fabrication（装配）costs so that the lightest member is not necessarily the most economical.

截面模量定义为

为选择构件而查阅S这一列，则任何满足式（4-8）的构件都可采用。显而易见，对S值很高的构件，其应力是不足的，并浪费了材料。如果没有其他的限制，最好的设计将是以最少的材料满足式（4-8）。能接受的最小的S值不必是最经济的构件。为了选择最轻和最经济的标准截面，应检查列出的质量值，以找到能接受的S值下的最轻构件。如果在设计一个组合构件时，则问题变得复杂得多，因为它的费用将依赖于腹板、角钢和盖板的费用以及装配的费用，因此，最轻的构件未必是最经济的构件。

根据表格中得到的值S，将式（4-6）以下列形式使用要方便得多，即

Deflections Due to Bending 弯曲挠度

The main purpose of this chapter（本节） was to develop（提出）the flexure（屈曲）formulas, and to provide some experience in applying them. Statically indeterminate（超静定）cases were encountered and some insight（认识） gained as to（就..）the difficulty and importance of this category of problem.

本节的主要目的是提出屈曲公式，并在运用公式时提供一些经验。当遇到超静定的情况时，就此类问题的难点和重点获得一些认识。

Superposition（叠加法）was presented（提出） as the preferred（优先的）method for solving certain problems. However, becoming familiar with（熟悉）superposition was more important than finding solutions to the problems（问题的答案） because superposition has application in many areas of stress analysis and will be used frequently in our future studies. 为解决某些问题，叠加法作为优先的方法被提出。但是，熟悉叠加法远比找到问题的答案重要，因为叠加法已经用于应力分析的很多领域，而且，在我们今后的研究中还会经常使用。

Moment-area（弯距图面积法）was found to be a convenient method for solving various problems. It is a method that becomes quite complicated and requires further development（展开） when more advanced structures are encountered. At the present stage it is sufficient for you to be acquainted with（了解）the fundamentals（基本原理）of the method. Deflection of long-radius（长半径） curved beams was introduced（引入）to illustrate the power of the principles underlying（构成..的基础）the moment-area method and so that you would appreciate（知道）the differences between straight and curved beams.

为解决不同的问题，发现弯距图面积法是一种很便利的方法。但当遇到更先进的结构时，此法会变得非常复杂，需要进一步地展开。对你来说在目前阶段了解此法的基本原理已经足够了。引入长半径曲梁的挠度来举例说明构成弯距图面积法基础的原理的功效，使你能知道直梁与曲梁之间的区别。

This chapter afforded an opportunity to become familiar with singularity functions （奇异函数）, and you have seen that certain problems can be greatly simplified by their use. It must be appreciated（意识到）that merely an introduction to the topic has been given; there is much more to learned by those who have a special interest. To illustrate a serious limitation（缺陷） at our present stage, we can express distributed loads （分布荷载） that are variable and are intermittent, but we cannot write a load function for concentrated loads. If we had taken the next step and dealt with the concentrated load, we would have encountered the source of the expression（表达式）“singularity function”, but having regard for（考虑）the scope of this book we have stopped short of（达不到）that step.

本节使你熟悉了奇异函数，并发现通过利用它们能大大地简化某些问题。但必须意识到仅仅是介绍了题目，对那些有特殊兴趣的人还有很多要学。我们可以表示变化的、间断的分布荷载，但不能写出集中荷载的荷载函数，说明了在我们目前阶段（该函数）还存在着严重的缺陷。如果我们进入下一步去研究集中荷载，便会遇到奇异函数表达式的来源，但是考虑到本书的范围，我们不再进入那一步。 Failure Theories 失效理论

In the design of a member subjected to a uniaxial（单轴的） load, the stress was compared with the stress to cause failure in test specimens（试件）that had also been subjected to uniaxial load. This is the simplest of all design problems; the method is quite adequate（合适的）, since the nature（性能）of the loads and the stresses in the test and in the part being designed are identical. However, we soon encounter cases where the member being designed is not so simple and the stresses are not uniaxial; consider, for example, the stresses in the web of a beam or in a pressure vessel（压力容器）. In these cases we know that the stress is two-dimensional（两向的）or biaxial and it may, in other cases, be three-dimensional, or triaxial.

For a structure having biaxial or triaxial stresses, how should we check the safety of the design? The most obvious way would be to conduct tests（进行） in which specimens are stressed（受力）to failure in the same multiaxial（多轴的）manner as in the structure; the allowable multiaxial stress then be determined by the application of an adequate safety factor. However, this would require a group of tests for every new set of multiaxial stresses that occurred in design. Such tests are difficult to perform, and the cost of performing them in the required numbers would be prohibitive. Consequently, we need a theory by which the results of the standard uniaxial test can be used to predict（预测）the failure of a part made of the same material when the stresses are multiaxial. In other words（换句话说）, we need a failure theory. 在设计承受轴向力的构件时，将其应力与导致同样承受轴向力的试验样本（试件）失效的应力相比。这是所有设计问题中最简单的；该法是非常合适的，因为试验和设计中的荷载和应力性质是完全相同的。但是，不久我们便会遇到正在设计的构件不是那么简单，其应力也不是单轴向的；例如，考虑梁的腹板应力或压力容器中的应力。在这些情况下，我们知道其应力是两向的或两轴的，而在其他情况下可能是三向或三轴的。对一个有着两轴或三轴应力的结构，我们应该如何检查它的设计安全性？最显然的办法是进行试验，即试件以与结构相同的多轴受力方式失效；然后运用适当的安全系数确定许用的多轴应力。但是，对设计中出现的每组新的多轴应力都将需要一组试验。这样的试验很难进行，而且以需要的数量进行试验的费用也是禁止的。因此，我们需要一个理论，根据它可以通过利用标准单轴试验的结果来预测同样材料制作的构件在承受多轴应力时的失效。换句话说，我们需要一个失效理论。

To illustrate the need for a failure theory, let us consider a cylindrical pressure vessel. To avoid unnecessary complications, we will consider that all welds（焊缝）are 100% efficient and that the walls（容器壁）are thin. Under internal pressure the main stresses（主应力） are circumferential and longitudinal, and it was implied（认为）in an earlier case that only the circumferential stress, because it is larger than the longitudinal stress, needs to be considered in judging the adequacy of the design. In this approach we tacitly（默认）assumed that the maximum stress could be treated as（看作为）a uniaxial stress and that it alone determined the safety of the design. The longitudinal stress was not considered although it may, without our knowledge（在我们的知识之外）, have had an influence on strength. It happens that our approach in this case is acceptable, but, in a biaxial state of stress, the second stress is not always inconsequential（不重要）and an understanding of failure theory is necessary in order to avoid making some serious errors.

为了举例说明需要一个失效理论，让我们考虑一个圆柱形的压力容器。为避免不必要的复杂，我们认为焊缝完全有效，容器壁是薄的。在内部压力下，主应力是环向和纵向的，由于环向应力比纵向应力大，因此，在一个较早的例子中认为只有环向应力需要在判断设计的适用性时加以考虑。在这个方法中，我们默认地假定最大的应力（即环向应力）可看作为单轴应力，并由它单独地确定设计的安全性。尽管在我们的知识以外，纵向应力可能会对强度有影响，但不被考虑。正巧，在这种情况下我们的方法能被接受，但是，在两轴应力状态下，第二种应力不总是不重要的，为了避免造成一些严重的错误，对失效理论的理解是必要的。

Unfortunately, as we will discover, no single theory（单一理论） will be found to apply in all cases; for example, theories that are satisfactory for ductile materials are not acceptable for brittle materials. We will also find that one of the best theories is too complex for everyday use and that most designers prefer（更喜欢）a simpler theory that introduces（产生）a small but safeside（安全的）error.

很不幸，正如我们将发现的，没有找到一个单一的理论能运用于所有的状况，例如，满足延性材料的理论，脆性材料不能接受。我们也将发现每天在使用一个最好的理论太复杂了，多数设计者更喜欢用一个会产生小而安全的错误但较简单的理论。

In developing（提出）the various failure theories, we cannot avoid three-dimensional effects, but we will treat（讨论）only those cases in which one of the stresses is zero, thus avoiding complications that would tend to obscure（使..模糊不清）the important part of the theories. This is not a serious limitation, since in engineering practice（工程实践） most problems are reduced to（简化为）the biaxial stress state for design. When shear stresses（剪应力）occur along with（与..一起）normal stresses（正应力）, the principal stresses（主应力）are determined. Thus, for practical（实用的）purposes, we need to consider failure in a material subjected to two nonzero（非零）normal stresses while the third normal stress is zero. For ease in（为了便于..）designating （称呼）those principal stresses we will use numerical subscripts（数字下标）; 1 and 2 being the nonzero stresses and 3 being zero.

在提出不同的失效理论时，我们不能避免三向的影响，但我们将只讨论其中某一个应力为零的情况，因而避免了复杂性，因它往往使理论的重要部分模糊不清。这不是个严重的缺陷，因为在工程实践中，多数问题在设计时被简化为两轴应力状态。当剪应力与正应力一起存在时，主应力便被确定。这样，为了实用的目的，我们需要考虑承受两个非零正应力而第三个正应力为零的材料的失效。为了便于称呼那些主应力，我们采用数字下标： 1和 2作为非零应力，而 3为零。

We cannot discuss failure theory until we have defined failure. We might take the obvious definition that a material has failed when it has broken into（分为）two or more parts. However, it has already been pointed out that in most applications a member would be unserviceable（不再适用）due to excessive distortion long before（早在）it actually ruptured（断裂）. Consequently, we will relate failure to yielding and consider that a material has failed when it will no longer return to（恢复）its original（最初的）shape upon（一旦）release of the loads. In a simple tensile test（拉伸试验）we would then say that a ductile material has failed when the material begins to yield. Then for uniaxial stress, failure occurs when the stress reaches the yield stress, y , in either tension or compression.

在我们定义了失效后才能对其进行讨论。我们可能会下一个明显的定义，即当材料分成两部分或更多时失效。但是，在多数应用中已经被指出，一个构件早在它实际断裂之前由于过分的变形而不再适用。因此，我们将失效与屈服联系起来，并认为一旦荷载解除而材料不再恢复到其最初的形状时即为失效。在一个简单的拉伸试验中，我们可以说当延性材料开始屈服时即已失效。对单轴应力而言，当应力达到屈服应力 y（不管拉或压）时即为失效。

Brittle materials fail by a different mechanism and will be discussed after the theories for ductile materials have been presented（介绍）.

脆性材料由于不同的机理而失效，这将在介绍延性材料的理论之后进行讨论。

Unit 5 第五单元

A structure consists of（由..组成）a series of connected parts used to support loads. Notable（显著的） examples include buildings, bridges, towers, tanks, and dams. The process（过程）of creating any of these structures requires planning（规划）, analysis, design, and construction（施工）. Structural analysis consists of （包括）a variety of mathematical procedures（数学程序）for determining such quantities as the member forces and various structural displacements（位移） as a structure responds to its loads. Estimating realistic loads for the structure considering（根据）its use and location is often a part of structural analysis.

结构由一系列相连的用以支撑荷载的构件组成。显著的例子包括建筑、桥梁、塔、水箱和大坝等。建造这些结构中的任何一个的过程需要规划、分析、设计和建造。结构分析包括各种各样的数学程序以确定诸如当一个结构对荷载有响应时构件的力和不同结构位移的大小。根据结构的使用和位置来估计它的实际荷载经常是结构分析的一部分。

Only two assumptions are made regarding（关于）the materials used in the structures of this chapter. First, the material has a linear stress-strain relationship（线性的应力-应变关系）. Second, there is no difference in the material behavior when stressed in tension vis-a-vis（与..相比）compression. The frames and trusses studied are plane structural systems（平面结构体系）. It will be assumed that there is adequate bracing perpendicular to（垂直于）the plane so that no member will fail due to an elastic instability（弹性失稳）. The very important consideration regarding such instability will be left for the specific（具体的）design course.

All structures are assumed to undergo only small deformations as they are loaded. As a consequence（因此）we assume no

change in the position or direction of a force as a result of （由于）structural deflections（变位）. Finally, since linear elastic materials and small displacement are assumed, the principle of superposition will apply in all cases. Thus the displacements or internal forces that arise from two different forces systems applied one at a time（一次一个）may be added algebraically（几何相加）to determine the structure’s response when both system(s) are applied simultaneously. 关于本章结构中所用的材料只作了两点假设。首先，材料具有线性的应力应变关系。其次，材料的性能在受拉和受压时没有区别。研究的框架和桁架是平面结构体系。假定垂直于平面的方向有足够的支撑，因而构件不会因为弹性失稳而失效。一个非常重要的关于这种失稳的考虑留待具体的设计过程。假定所有的结构在它们加荷时只经历小的变形。因此，我们假定当结构变位时荷载的位置与方向不变。最后，因为假定了线弹性材料和小位移，叠加原理将适用于所有的情况。这样当两种不同的力系同时施加时，可以由不同的力系一次施加一个引起的位移或内力几何相加来确定结构的响应。

In the real sense（真正意义上）an exact analysis of a structure can never be carried out since estimates always have to be made of the loadings and the strength of the materials composing（构成）the structure. Furthermore, points of application（作用点）for the loadings must also be estimated. It is important, therefore, that the structural engineers develop（形成）the ability to model（模拟）or idealize（使..理想化）a structure so that he or she can perform a practical force analysis of the members.

Structural members are joined together in various ways depending on the intent（意图）of the designer. The two types of joints most often specified（规定的）are the pin connection and the fixed joint（节点）. A pin-connected joint allows some freedom for slight（轻微）rotation, whereas the fixed joint allows no relative rotation between the connected members. In reality, however, all connections exhibit（显现）some stiffness toward joint rotations, owing to friction（摩擦）and material behavior. When selecting a particular model for each support（支座）or joint, the engineer must be aware of how the assumptions will affect the actual performance（运行）of the member and whether the assumptions are reasonable for the structural design. In reality, all structural supports actually exert（产生）distributed surface loads（面荷载）on their contacting members.

The resultants（合力） of these load distributions are often idealized as the concentrated forces（集中力）and moments, since the surface area （表面积）over which the distributed load acts is considerably smaller than the total surface area of the connecting members. The ability to reduce an actual structure to（将..简化为）an idealized form can only be gained by experience. In engineering practice, if it becomes doubtful（不明确）as to how to model a structure or transfer the loads to the members, it is best to consider several idealized structures and loadings and then design the actual structure so that it can resist（抵抗）the loadings in all the idealized models.

结构构件根据设计者的意图采用不同的方式连在一起。最常规定的两种节点是铰接节点和固定节点。铰接节点允许有一些轻微的转动自由，而固定节点不允许相连的构件有相对的转动。但是，事实上由于摩擦和材料的特性使所有的连接对节点的转动显现出一些刚度。当为每一个支座或节点选择一个特定的模型时，工程师必须知道该假设将如何影响构件的实际运行，以及该假设是否对结构的设计是合理的。实际上，所有的结构支座在它们接触的构件上产生分布的面荷载。这些荷载分布的合力常常理想化为集中力和弯矩，因为分布荷载作用的表面面积比相连的构件的总的表面面积小很多。将一个实际的结构简化成一种理想的形式的能力只有通过经验才能获得。在工程实践中，如果就怎样模拟一个结构或将荷载传递给构件变得难以确定时，最好考虑几个理想的结构和荷载，然后设计实际的结构，使它在所有理想的模型中都能抵抗荷载。

It may be recalled（回想）from statics that a structure or one of its members is in equilibrium（处于平衡） when it maintains a balance of force and moment. When all the forces in a structure can be determined strictly from these equations, the structure is referred to as statically determinate（静定的）. Structures having more unknown forces than available equilibrium equations（平衡方程）are called statically indeterminate. As a general rule, a structure can be identified as（确定）being either statically determinate or statically indeterminate by drawing free-body diagrams（隔离体图）of all its members, or selective parts of its members, and then comparing the total number of unknown reactive force and moment components（分量）with the total number of available equilibrium equations.

从静力学可以回想起当一个结构或它的一个构件维持力和弯矩的平衡时即处于平衡状态。当一个结构中所有的力能严格地根据这些方程式来确定，该结构称为静定的。如果结构上未知的力比能得到的平衡方程多时称为超静定结构。作为一般的规律，一个结构可以通过画出所有构件或经选择的部分构件的隔离体图，然后比较未知的反力和弯矩的分量总数目与可用的平衡方程总数目是否相等来确定其是静定结构还是超静定结构。 真正意义上对一个结构准确的分析是永远也不可能进行的，因为总是不得不估计荷载和构成结构的材料的强度。而且，必须估计荷载的作用点。因此，结构工程师有能力模拟一个结构或使其理想化很重要，这样，他或她能对构件进行实际的力的分析。

In particular, if a structure is statically indeterminate, the additional equations（附加方程）needed to solve for（求解）the unknown reactions（反力）are obtained by relating the applied loads and reactions to the displacement or slope（转角）at different points on the structure. These equations, which are referred to as compatibility equations（相容性方程或协调方程）, must be equal in number to the degree of indeterminacy（不确定次数）of the structure. Compatibility equations involve（涉及）the geometric and physical properties of the structure.

特别地，如果一个结构是超静定的，可以通过建立作用力和反力与结构不同点上的位移或转角的关系来得到用以求解未知反力所需的附加方程。这些称为相容性方程的方程式在数量上必须等于结构的不确定次数。相容性方程涉及结构的几何和物理性能。 There are two fundamental methods of analysis for trusses: the method of joints and the method of sections. Both start with（从..着手）a free-body diagram of the truss as a whole（基本上）, from which the equilibrium equations are written and solved for the support reactions（支座反力）.

有两种分析桁架的基本方法：节点法和截面法。两种方法基本上都从桁架的隔离体图着手，根据它可以写出平衡方程并求解支座反力。

The method of joints: After the support reactions have been found, a joint is selected that has no more than（不超过）two members connecting for which the axial forces are unknown. The free-body diagram of that joint is drawn, the forces are summed（合计）in two directions, and each sum is equated to（等于）zero. When drawing the free-body diagram, it is a good idea to assume that the unknown forces are tensions and to show（表示）them so on the free-body diagram by their exerting a pull on（对..施加拉力）the joint. When this is assumed, the resulting sign（符号）of the unknowns when evaluated（计算）will match（符合）the conventional（习惯的）+ for tension and – for compression. Once a joint has been analyzed, its members become knowns, and adjacent joints（相邻节点）, which might have had three or more unknowns, can then be solved since some of these unknowns have become knowns. This process（过程）continues from joint to joint, each time selecting a joint whose number of unknown members does not exceed 2.

节点法：求出支座反力后，选择一个节点其上连接着轴向力未知的构件不超过两根。画出节点的隔离体图，将力在两个方向上进行合计，每个方向（力）的合计等于零。当画出隔离体图时，有个好主意是假定未知力是拉力，并在隔离体图上通过对该节点施加一个拉力来表示。这样假定后，未知力计算结果的符号将与习惯的正为拉力负为压力相符。一旦一个节点已经被分析，其上的构件成为已知构件，相邻的节点可能曾经有三个或更多的未知力，但因为其中的一些已经成为已知，因此也能求出。这个过程从一个节点到另一个节点连续进行，每次选择的节点其上未知构件（力）的数量不超过两根。

Almost all truss systems are configured（装配）so that analysis using the method of joints must begin at one end and proceed（继续）joint by joint toward the other end. If it is necessary to evaluate the forces carried by a member located（位于）some distance from the ends, the method of joints requires the calculation of the forces in many members before the desired one is reached. The method of sections provides a means（方法）for a direct calculation in these cases. After the support reactions have been calculated the truss is cut through（切开）(analytically分析上) so that one part of the truss is completely severed from the rest. When this is done, no more than three unknown members should be cut. If possible（如果可能）the cut（切口）should pass through the member or members whose internal forces are to be found. A free-body diagram of the part of the truss on one side of（在..一边）this section is drawn, and the internal forces are found through the equilibrium equations. Since the system of forces（力系）on the free-body diagram is a plane non-concurrent（非共点）force system, three equilibrium equations may be written and solved for the three unknowns.

几乎所有的桁架体系是装配的，因此采用节点法进行的分析必须从一个端点开始，并一个节点连着一个节点地朝另一个端点继续进行。如果有必要计算位于端部一定距离的构件上的力，节点法需要在到达这根要求（计算）的构件之前计算很多构件中的力。在这些情况下截面法提供了一个直接计算的方法。当求出支座反力后，桁架（在分析上）被切开，从而一部分桁架同其余部分完全分离。当这样切开时，应该切出不超过三个构件的力是未知的。如果可能，切口应穿过将要求解内力的构件。画出在截面一边的桁架部分的隔离体图，并通过平衡方程式求解内力。由于隔离体图上的力系是平面非共点的，因而可以写出三个平衡方程式并求出三个未知力。

Influence lines（影响线）have important application for（应用）the design of structures that resist large live loads（活荷载）. An influence line represents（代表）the variation of either the reaction, shear, moment, or deflection at a specific （特定的）point in a member as concentrated force moves over the member. Once this line is constructed（作图）, one can tell at a glance（一眼便知）where a live load should be placed on the structure so that it creates（引起）the greatest influence at the specified point. Furthermore, the magnitude（大小）of the associated （相关的）reaction, shear, moment, or deflection at the point can then be calculated from the ordinates（纵坐标）of the influence-line diagram. For these reasons（因此）, influence lines play an important part in the design of bridges, industrial crane rails（吊车轨道）, conveyors, and other structures where loads move across their span（全长）. Although the procedure（步骤）

for constructing an influence line is rather basic（基本的）, one should clearly be aware of the difference between constructing an influence line and constructing a shear or moment diagram. Influence lines represent the effect of a moving load only at a specified point on a member, whereas shear and moment diagrams represent the effect of fixed loads at all points along the axis of the member.

影响线在设计抵抗大量活荷载的结构时有着重要的应用。一根影响线代表着当集中力在构件上移动时构件上一个特定点的反力、剪力、弯矩或挠度的变化。一旦画出这根线，任何人一眼便知活荷载应该置于结构的哪个位置才能对这个特定的点引起最大的影响。而且，这点上相关的反力、剪力、弯矩或挠度可从影响线图的纵坐标上计算出来。因此，影响线在桥梁、工业吊车轨道、输送机和其它有荷载在整个结构长度上移动的结构设计中扮演着重要的角色。虽然画出一条影响线的步骤是相当基本的，但任何人应该清楚地意识到画一条影响线与画一条剪力或弯矩图的区别。影响线只代表着移动荷载对构件上特定点的影响，而剪力和弯矩图代表固定荷载对沿着构件轴线的所有点的影响。

Deflections of structures can occur from various sources（原因）, such as loads, temperature, fabrication errors, or settlement. In design, deflections must be limited in order to prevent cracking of attached（附属的） brittle materials such as concrete or plaster (石膏) . Furthermore, a structure must not vibrate or deflect（变位）severely in order to “appear” safe for its occupants（居住者）. More important, though（然而）, deflections at specified points in a structure must be computed if one is to analyze statically indeterminate structures. We often determine the elastic deflections of a structure using both geometrical and energy methods. Also, the methods of double integration（双重积分）are used. The geometrical methods include the moment-area theorems（弯矩图面积定理）and the conjugate-beam method（共轭梁法）, and the energy methods to be considered are based on virtual work（虚功）and Castigliano’s theorem（卡氏最小功定理）. Each of these methods has particular advantages or disadvantages.

结构的挠度可以因不同的原因而发生，如荷载、温度、制造错误或沉降。设计中，挠度必须加以限制以阻止附属的脆性材料如混凝土或石膏的开裂。而且，为了向居住者显示安全性，结构不能严重地振动或变位。而更重要的是如果有人要分析超静定结构，必须计算出结构中规定点的挠度。我们通常采用几何法和能量法来确定结构的弹性挠度。也采用双重积分法。几何法包括弯矩图面积定理和共轭梁法，而考虑的能量法是基于虚功定理和卡式最小功定理。每一种方法都有其特别的优缺点。

We can determine the equation of the elastic curve by integration of equation d2v / dx2 = M / EI. Solution of this equation requires two successive（连续的）integrations to obtain the deflection v of the elastic curve. For each integration, it is necessary to introduce（引入）a “constant of integration”（积分常数）, and then solve for the constants to obtain a unique solution（唯一解）for a particular（特定的）problem. It should be realized that the method of double integration is suitable only for elastic deflections（变位）such that the beam’s slope is very small. Furthermore, the method considers only deflections due to bending.

我们可以通过对方程d2v / dx2 = M / EI的积分来确定弹性曲线的方程。该方程的求解需要两个连续的积分，以获得弹性曲线的挠度v。对每次积分，有必要引入积分常数，求出该常数以获得一个特定问题的唯一解。应该了解到双重积分法只适合于弹性变位，因而梁的转角是非常小的。而且，该法只考虑了由于弯曲引起的挠度。

The initial ideas（最初的概念）for the two moment-area theorems were developed（提出）by Otto Mohr and later stated formally（正式确定）by Charles E. Greene in 1872. These theorems provide a semi-graphical （半图解）technique for determining the slope of the elastic curve and its deflection due to bending. They are particularly advantageous（有利）when used to solve problems involving beams especially those subjected to a series of concentrated loadings or having segments（段）with different moment of inertia（惯性矩）. Theorem 1: The change in slope（转角变化）between any two points on the elastic curve equals the area of the M / EI diagram between these two points. Theorem 2: The deviation（偏差）of the tangent（正切）at point B on the elastic curve with respect to（相对于）the tangent at point A equals the “moment” of the M / EI diagram between the two points A and B computed about point A (the point on the elastic curve), where（这里）the deviation tA/B is to be determined.

最初的关于两个弯矩图面积定理的概念是由Otto Mohr提出，后来由Charles E. Greene在1872年正式加以确定。这些定理为确定弹性曲线由于弯曲引起的转角和挠度提供了半图解的方法。当用以解决包括梁在内的问题，特别是那些承受一组集中加载的梁或有着不同惯性矩的梁段时，它们（指弯矩图面积定理）是特别得有利。定理1：弹性曲线上任何两点之间转角的变化等于这两点之间的M / EI图的面积。定理2：弹性曲线上B点的正切相对于A点的正切的偏差等于点A与点B之间的M / EI图对A点（该点在弹性曲线上）的矩，这里偏差tA/B将被确定。

The conjugate-beam method was first presented（提出）by Otto Mohr in 1860. Essentially（本质上）, it requires the same amount of computation（计算量）as the moment-area theorems to determine a beam’s slope or deflection; however, this method relies only on the principles of statics and hence its application will be more familiar（常见）. The basis for the method

comes from（来自于）the similarity（相似性）between both dV/dx = - and d2M/dx2 = - , which relate a beam’s internal shear and moment to its applied loading, and d /dx = M/EI and d2y/dx2 = M/EI, which relate the slope and deflection of its elastic curve to the internal moment.

共轭梁法首先在1860年由Otto Mohr提出。本质上说，它与弯矩图面积定理一样在确定梁的转角或挠度上需要相同的计算量；但是这种方法只依赖于静力学的原理，因此，它的应用更常见。该法的基础来自于dV/dx=- 和d2M/dx2=- 之间的相似性，它将梁的内部剪力和弯矩与它施加的荷载联系起来，而d /dx = M/EI和d2y/dx2 = M/EI将弹性曲线的转角和挠度与内部弯矩联系起来。

Note that the shear V compares with（与..对应）the slope , the moment M compares with the displacement y and the intensity of the external load compares with the area under the M/EI diagram. To make use of this comparison we will consider a beam having the same length as the real beam, but referred to here as the “conjugate beam”.

注意剪力V与转角 相对应，弯矩M与位移y相对应，而外力的强度 与M/EI图下的面积相对应。为了利用这些对应，我们将考虑一根与实际梁一样长的梁。但是这里称为共轭梁。

In general, though（然而）, remember that if the real support allows a slope, the conjugate support must develop（产生）a shear; and if the real support allows a displacement, the conjugate support must develop a moment, note that the conjugate beam is “loaded” with the M/EI diagram, in order to conform to（与..一致）the load on the real beam. We can therefore state（陈述）two theorems related to the conjugate beam, namely（即）, Theorem 1: The slope at a point in the real beam is equal to the shear at the corresponding point（相应点）in conjugate beam. Theorem 2: The displacement of a point in the real beam is equal to the moment at the corresponding point in the conjugate beam.

然而通常要记住如果实际的支座允许一个转角，共轭的支座必须产生一个剪力；如果实际的支座允许一个位移，共轭的支座必须产生一个弯矩，注意共轭梁用M/EI图来加荷，以便与实际梁上的荷载一致。因此，我们可以陈述与共轭梁相关的两种定理，即，定理1：实际梁上某一点的转角等于共轭梁上相应点的剪力。定理2：实际梁上某一点的位移等于共轭梁上相应点的弯矩。

For more complicated loadings or for structures such as trusses and frame, it is suggested（建议）that energy methods be used for the computation. All energy methods are based on the conservation of energy principle（能量守恒原则）, which states（规定）that the work（功）done by all the external forces acting on a structure, Ue, is transformed into（转化为）internal work or strain energy（应变能）UI, which is developed（形成）when the structure deforms（变形）.

对于较复杂的荷载或结构如桁架和框架，建议应该采用能量法来计算。所有的能量法是基于能量守恒原则，它规定了作用在结构上的所有外力作的功Ue转化成内部功或结构变形时形成的应变能UI 。

The principle of virtual work was developed by John Bernoulli in 1717 and is sometimes referred to as the unit-load method（单位荷载法）. It provides a general means（一般方法）of obtaining the displacement and slope at a point on a structure, be it（无论是）a beam, frame, or truss. Before developing the principle of virtual work, it is necessary to make some general statements（一般规定）regarding the principle of work and energy.

虚功原理在1717年由John Bernoulli提出，有时称为单位荷载法。它提供了获得结构上某一点的位移和转角的一般的方法，不管该结构是梁、框架还是桁架。在提出虚功原理之前，关于功和能量的原理有必要作些一般规定。

If we take（取）a deformable（可变形）structure of any shape or size and apply a series of external loads P to it, it will cause internal loads u at points throughout the structure. It is necessary that the external and internal loads be related by the equation of equilibrium. As a consequence of（通过）these loadings, external displacement will occur at the P loads and internal displacement will occur at each point of internal load u.

如果我们取一个任何形状或尺寸的可变形结构，并对它施加一组外力P，它将导致整个结构上的点产生内力u。有必要通过平衡方程将内外力联系起来。通过这些荷载，外部的位移 发生在荷载P作用处，而内部位移 发生在内力u所处的每个点。

In general, these displacements do not have to be elastic, and they may not be related to（与..有关）the loads; however, the external and internal displacements must be related by the compatibility of the displacements. In other words, if the external displacements are known, the corresponding internal displacements are uniquely defined（唯一确定）. In general, then, the principle of work and energy states（表述）:

P = u （5-1）

Work of External Loads = Work of Internal Loads

一般来说，这些位移不必是弹性的，它们可能与荷载无关。但是外部位移与内部位移必须通过位移协调联系起来。换句话说，如果已知外部位移，则相应的内部位移可惟一的确定。通常，功和能量原理表述为

P = u （5-1）

外力功=内力功

Based on this concept, we will now develop（提出）the principle of virtual work so that it can be used to determine the displacement of a point on a structure. To do this, we will consider the structure (or body) to be of arbitrary（任意）shape as shown in Fig. 5-1-(b). Suppose it is necessary to determine the displacement of point A on the body caused by the “real loads” P1, P2, and P3. It is to be understood that these loads cause no movement of the supports; in general, however, they can strain(使..产生应变) the material beyond the elastic limit.

基于这个概念，现在我们将提出虚功原理，以便用以确定结构上某一点的位移。为此，我们考虑图5-1-(b)显示的具有任意形状的结构或物体。假定有必要确定由实际荷载P1、P2 和 P3 引起的A点的位移。可以被理解为这些荷载不引起支座的移动；但是一般而言，它们能使材料的应变超过弹性极限。

Since no external load acts on the body at A and in the direction of , the displacement can be determined by first placing on the body a “virtual” load such that this force P’ acts in the same direction as , Fig.5-1-(a). For convenience（方便起见）, which will be apparent（显而易见）later, we will choose P’ to have a “unit” magnitude（单位值）, that is P’ = 1. The term “virtual” is used to describe the load, since it is imaginary（想象的）and does not actually exist as part of the real loading. The unit load (P’) does, however, create an internal virtual load u in a representative（典型的）element or fiber of the body, as shown in Fig.5-1-(a).

由于没有外力作用在物体的A点以及 的方向上，则位移 可以通过在物体上先设置一个虚力，即如图5-1-(a)中作用一个与方向 相同的力P’来确定。为了方便起见（后面会显而易见），我们选择P’有一个单位值，即P’=1。用术语“虚”来描述荷载，因为它是想象的，非实际存在的真实荷载的部分。但是，单位荷载P’在物体的典型单元或纤维中产生了一个内部虚力u，如图5-1-(a)所示。

Here it is required that P’ and u be related by the equation of equilibrium. As a result of（通过）these loadings, the body and the element will each undergo a virtual displacement due to the load P’, although we will not be concerned with（关心）its magnitude. Once the virtual loadings are applied and then the body is subjected to the real loads P1, P2, and P3, Fig.5-1-(b), point A is displaced an amount , causing the element to deform dL.

这里要求P’和u通过平衡方程联系起来。通过这些（虚）荷载，物体和单元各自由于荷载P’而经历一个虚位移，尽管我们不会关心它的数值。一旦施加虚荷载，然后物体承受图5-1-(b)中的实际荷载P1、P2和P3，则点A产生位移值 ，导致单元发生变形dL。

As a result（因此）, the external virtual force P’ and internal virtual load u “ride along” by（乘上） and dL, respectively（分别地）, and therefore perform external virtual work of 1 on the body and internal virtual work of u dL on the element. Realizing that the external virtual work is equal to the internal virtual work done on all the elements of the body, we can write the virtual work equation as

1 = u dL （5-2）

因此，外部虚力P’和内部虚力u分别与 和dL“乘在一起”，因此在物体上形成外部虚功，在单元上形成内部虚功。了解到外部虚功等于对物体所有单元作的内部虚功，我们可以写出虚功方程

1 = u dL （5-2）

Where P’=1=external virtual unit load acting in the

direction of

u = internal virtual load acting on the element in = external displacement caused by the real loads dL = internal deformation of the element caused the direction of dL

by the real loads

By choosing P’ = 1, it can be seen that the solution for follows directly, since = u dL .

这里，P’等于1，也等于作用在 方向上的外部虚单位力；

u等于以dL方向作用在单元上的内部虚力； 等于真实荷载引起的外部位移； dL等于真实荷载引起的单元的内部变形。

可以看到通过选择P’=1能直接得到解，因为 = u dL 。

In a similar manner, if the rotational displacement（转动位移）or slope（转角）of the tangent at a point on a structure is to be determined, a virtual couple moment（力偶矩）M’ having a “unit” magnitude is applied at the point. As a consequence（因此）, this couple moment cause a virtual load in one of the element of the body. Assuming that the real loads deform

（使..变形）the element at amount dL, the rotation can be found from the virtual-work equation 1 = u dL . This method for applying the principle of virtual work is often referred to as the method of virtual forces（虚力法）, since a virtual force is applied resulting in the calculation of a real displacement. The equation of virtual work in this case represents a compatibility requirement for the structure.

以相似的方法，如果要确定结构上某一点切线的转动位移或转角，可在该点上施加一个虚的单位力偶矩M’。因此，力偶矩在物体的某一单元中形成一个虚力。假定实际的力使单元的变形值为dL，则转角 可从虚功方程1 = u dL中得到。运用虚功原理的方法通常称为虚力法，因为施加虚力能计算出实际的位移。在这种情况下虚功方程代表着对结构的协调要求。

Although not important here, realize（意识）that we can also apply the principle of virtual work as a method of virtual displacements（虚位移）. In this case virtual displacements are imposed on（强加于）the structure, while the structure is subjected to real loadings. This method can be used to determine a force on or in a structure, so that the equation of virtual work is then expressed as an equilibrium requirement.

了解到我们也能运用虚功原理形成虚位移法，尽管在这儿不太重要。这种情况下，虚位移强加于结构，而结构承受实际的荷载。该法能用以确定结构上或结构中的力，因此虚功方程表示为平衡要求。

In 1879 Alberto Castigliano, an Italian railroad engineer, published a book in which he outline（概述）a method for determining the deflection or slope at a point in a structure, be it a truss, beam, or frame. This method, which is referred to as Castigliano’s second theorem（卡氏第二定理）, or the method of least work（最小功法）, applies only to structures that have constant temperature（恒温）, unyielding（不易弯曲）supports, and linear elastic material response.

1879年Alberto Castigliano，一个意大利的铁路工程师，出版了一本书，书中他概述了确定结构（无论是桁架、梁或框架）中某一点的挠度或转角的方法。这种称为卡氏第二定理或最小功法的方法仅应用于具有恒温、支座不易弯曲和材料线弹性响应的结构中。

If the displacement of a point is to be determined, the theorem states（表明）that it is equal to the first partial derivative（一阶偏导数）of the strain energy in the structure with respect to （关于）a force acting at a point and in the direction of displacement. In a similar manner, the slope at a point in a structure is equal to the first partial derivative of the strain energy in the structure with respect to a couple moment acting at the point and in the direction of rotation. 如果要确定某一点的位移，该定理表明位移等于结构中的应变能对于作用在该点并沿该位移方向的力的一阶偏导数。以相似的方式，结构上某一点的转角等于结构中的应变能对于作用在该点并沿该转角方向的力偶的一阶偏导数。

The derivation（推导）of the theorem requires that only conservative forces（保守力）be considered for the analysis. These forces do work that is independent of（与..无关）the path and therefore create no energy loss（能量损失）. Since forces causing a linear elastic response are conservative, the theorem is restricted to linear elastic behavior of the material. This is unlike the method of virtual force, which applies to both elastic and inelastic behavior.

定理的推导要求分析时只考虑保守力。这些力作功与路径无关，因此不造成能量的损失。由于引起线弹性响应的力是保守的，因此该定理（在运用时）被限制在材料的线弹性状态。它不象虚力法可以运用于弹性和非弹性状态。

When analyzing any indeterminate structure, it is necessary to satisfy equilibrium, compatibility, and force-displacement requirements for the structure. Equilibrium is satisfied when the reactive forces hold the structure at rest（保持结构静止）, and compatibility is satisfied when the various segments（部分）of the structure fit together（配合在一起）without intentional（故意的）breaks or overlaps（断裂或重叠）. The force displacement requirements depend upon the way the material responds, which in this chapter we have assumed linear-elastic response. In general there are two different ways to satisfy these requirements when analyzing a statically indeterminate structure: the force or flexibility method（柔度法）, and the stiffness or displacement method.

当分析任何不确定的结构时，有必要满足结构的平衡、协调和力-位移要求。当反力保持结构的静止时满足平衡（要求），当结构中不同的部分配合在一起而没有故意地断开或重叠时满足协调（要求）。力-位移要求依赖于材料响应的途径，在本篇我们已经假定为线弹性响应。当分析一个超静定结构时，一般有两种不同的方法来满足这些要求：力法或柔度法以及刚度法或位移法。

The force method was originally（最初地）developed by James Clerk Maxwell in 1864 and later refined（提炼）by Otto Mohr and Heinrich Muller-Breslau. This method was one of the first available（最早采用）for the analysis of statically indeterminate structures. As suggested（提示）by the name, the force method consists of writing equations that satisfy the compatibility and force-displacement requirements for the structure and involve（涉及）redundant forces（冗余力）as the unknowns. The coefficients（系数）of these unknowns are called flexibility coefficients. Since compatibility forms（形成）the basis for this method, it has sometimes been referred to as the compatibility method or the method of consistent displacements（位移协调法）. The redundant forces are determined by satisfying the equilibrium requirements for the structure.

The fundamental principles（基本原理）involved in （涉及）applying this method are easy to understand and develop（阐述）.

力法最初由James Clerk Maxwell 在1864提出，后由Otto Mohr和Heinrich Muller-Breslau加以提炼。该法是最早可采用的分析超静定结构的方法之一。正如其名称所提示的，力法包括写出满足结构协调要求和力-位移要求的方程以及涉及未知冗余力的方程。这些未知力的系数称为柔度系数。由于协调性形成了这个方法的基础，它有时被称为协调法或位移协调法。通过满足结构的平衡要求来确定冗余力。涉及该法运用的基本原理是很容易理解和阐述的。

When Marxwell developed the force method of analysis, he also published（发表）a theorem that relates（使..互相关联） the flexibility coefficients of any two points on an elastic structure – be it a truss, a beam, or a frame. This theorem is referred to as the theorem of reciprocal displacements（位移互等定理）and may be stated as follows（陈述如下）: The displacement of a point B on a structure due to a unit load acting at point A is equal to the displacement of point A when the unit load is acting at point B, that is fBA = fAB. The theorem also applies for reciprocal rotations（转角互等）. Furthermore, using a unit force and unit couple moment, applied at separate（分开的）points on the structure, we may also state: The rotation in radians（以弧度为单位）at point B on a structure due to a unit load acting at point A is equal to the displacement at point A when a unit couple moment is acting at point B.

当Marxwell提出力法分析时，他也发表了使弹性结构上任意两点的柔度系数相关的定理-无论是桁架、梁或框架。该定理称为位移互等定理，可以陈述如下：由作用在结构上A点的单位力引起B点的位移等于当单位力作用在B点时引起的A点的位移，即fBA = fAB。该定理也适用于转角互等。而且，将单位力和单位力偶矩施加在结构上不同的点，我们也可以陈述为：由作用在结构上A点的单位力引起B点的转角（单位为弧度）等于当单位力偶矩作用在B点时引起的A点的位移。

The displacement / stiffness method of analysis is based on first writing force-displacement relations（关系式）for the members and then satisfying the equilibrium requirements for the structure. In this case the unknowns（未知量）in the equations are displacements and their coefficients are called stiffness coefficients. Once the displacements are obtained, the forces are determined from the compatibility and force-displacement equations.

位移法或刚度法的分析是基于最初写出的构件的力-位移关系式，并且要满足结构的平衡要求。在这种情况下，方程式中的未知量是位移，而它们的系数称为刚度系数。一旦求得位移，就可从协调方程和力-位移方程中确定力。

Early in the 20th century slope deflection（转角位移法）was the most popular（流行的）method in use for analyzing statically indeterminate frames. It was developed by Professor G.A. Maney and began its reign of popularity（开始盛行）almost immediately after its publication（发表）in 1915. Fifteen years later the moment distribution method（弯矩分配法）was introduced and there began a period of spirited professional competition （激烈的专业竞争）over the merits（优势）of the two methods, with moment distribution eventually emerging as the “winner”, primarily because of its speed and simplicity. But the competition has not ended. Today, although moment distribution continues as（依然作为）the more popular method, there remain many contemporary（同时代的）engineers who prefer slope deflection.

早在20世纪，转角位移法是用以分析超静定框架最流行的方法。它由G.A. Maney教授提出，并在1915年发表后几乎迅速开始盛行。15年后弯矩分配法被采用，并在一段时期内开始了对两种方法的优势展开的激烈的专业竞争，弯矩分配法最终以胜者出现，主要是由于它的速度和简单。但是竞争没有结束。今天，尽管弯矩分配法依然作为较流行的方法，仍有很多同时代的工程师较喜欢用转角位移法。

They contend（辩解）that in performing a slope deflection analysis the engineer can acquire a better “intuitive feel”（直觉）for the structure than the use of any other method. More significant（重要的）, though, slope deflection has gained renewed（重新）importance（重要地位）with the advent（到来）of the computer, serving as（作为）the central method（重要方法） used for structural analysis software. Slope deflection focuses on（着重于）individual members, their loads, and certain conditions at their ends.

他们辩解在进行转角位移分析时能比在使用任何其它的方法中获得对结构更好的直觉。然而更重要的是，转角位移法由于计算机的到来已经重新获得了重要地位，作为用于结构分析软件的重要方法。转角位移法着重于单个构件、作用于它们的荷载和端部的某些条件。

In using this method, simultaneous equations（联立方程）are written and solved that have displacements, rather than forces or moments, as unknowns. It employs a simple sign convention（符号约定）: all variables（变量）related to a member are positive（正的）if they are clockwise（顺时针的）. The complete slope deflection equations for MAB and MBA are the superpositions of four parts: A, B, , and loads. Thus

MAB = 4EI/L A +2EI/L B -6EI/L2 +FEMAB （5-3） MBA = 2EI/L A +4EI/L B -6EI/L2 +FEMBA （5-4）

在采用该法时，写出联立方程并求解位移的未知量，而不是力或弯矩作为未知量。它采用了简单的符号约定：所有与构件有关的变量如果是顺时针则为正。对MAB和MBA ,完整的转角位移方程为四个部分的叠加： A, B , 和荷载。因此

MAB = 4EI/L A +2EI/L B -6EI/L2 +FEMAB （5-3）

MBA = 2EI/L A +4EI/L B -6EI/L2 +FEMBA （5-4）

Where MAB and MBA are clockwise end moments

Aand B are clockwise end rotations is a relative linear displacement of ends A and

B that matches（符合）a clockwise rotation

of AB

FEM is referred to as fixed end moment. A和 B为顺时针的端部转角； 是端部A相对于B的线位移，符合 AB的 FEM 称为固定端弯矩。 这里， MAB和MBA为顺时针的端部弯矩； 顺时针转动；

Analysis by slope deflection begins with use of above equations to write separate expressions for the end moments at each end of each member. Equilibrium is then imposed（利用）using moment equilibrium at joints rotated an unknown and transverse force equilibrium on members with an unknown . A system of equations（方程组）is produced that has the end displacements as unknowns. When solved simultaneously（联立求解）, the resulting displacements（得到的位移）are substituted in（代入）the slope deflection equations, giving the end moments.

转角位移法的分析从采用上述方程分别写出每个构件在每一端的端部弯矩表达式着手。然后利用平衡，即采用节点转动未知量 时的弯矩平衡和构件有未知量 时的横向力平衡。形成以端部位移为未知量的方程组。当联立求解时，将求解得到的位移代入转角位移方程，得到端部弯矩。

The method of analyzing beams and frames using moment distribution was developed by Hardy Cross, a professor of civil engineering at the University of Illinois. At the time this method was first published（公布）in 1932, it attracted immediate attention, and it has been recognized as one of the most notable（显著的） advances in structural analysis during the twentieth century. Moment distribution is a method of successive approximations（逐次近似计算法）that may be carried out （实现）any desired degree of accuracy（精度）. Essentially（本质上）, the method begins by（首先）assuming each joint of structure is fixed. Then, by unlocking and locking（解开与锁住）each joint in succession（连续地）, the internal moments at the joints are “distributed”（分配）and balanced until the joints have rotated to their final or nearly final positions. 采用弯矩分配法分析梁和框架的方法由Illinois大学的土木工程教授Hardy Cross提出。该法于1932年首次公布时便立刻受到了注意，并被承认是20世纪结构分析中最显著的进步之一。弯矩分配法是一种逐次近似计算法，可以实现任何需要的精度。本质上来说，该法首先假定结构的每一个节点是固定的。然后连续地解开和锁住每个节点，节点的内部弯矩被分配和平衡，直到节点转至它们最终的或几乎最终的位置。

It will be found that this process of calculation is both repetitive（重复的）and easy to apply. Before explaining the techniques of moment distribution, however, certain definitions and concepts must be presented（介绍）. Clockwise moments that act on the member are considered positive, whereas counterclockwise（反时针的）moments are negative. The moments at the “walls”（墙壁）or fixed joints of a loaded member are called fixed-end moments（固端弯矩）. The member stiffness factor at A can be defined as the amount of moment M required to rotate the end A of the beam A=1 rad. If several members are fixed-connected to a joint, then by the principle of superposition, the total stiffness factor at the joint is the sum of the member stiffness factors at the joint, that is, KT= K.

发现该计算过程是重复的且容易运用。但是在解释弯矩分配法的技术之前，必须介绍某些定义和概念。作用在构件上的顺时针弯矩为正，而逆时针弯矩为负。“墙”上的弯矩或负荷构件上固定节点的弯矩称为固端弯矩。构件在A点的刚度系数可定义为使梁端A转动值 A=1弧度所需要的弯矩M的值。如果一些构件与一个节点固接，则根据叠加原理，该节点处总的刚度系数为该节点处的构件刚度系数的总和，即KT= K 。

This value represents the amount of moment needed to rotate the joint through an angle of 1 rad. If a moment M is applied to a fixed-connected joint, the connecting members will each supply a portion of（一部分）the resisting moment necessary to satisfy moment equilibrium at the joint. That fraction of（部分） the total resisting moment supplied by the member is called the distribution factor (DF)（分配系数）. The carry-over factor（传递系数）represents the fraction of M that

is “carried over” from the pin to the far end.

这个值代表了使该节点转动1弧度的角度所需要的弯矩数量。如果将弯矩M施加于固定连接节点，则相连的构件各自提供一部分满足节点弯矩平衡必需的抵抗弯矩。在总的抵抗弯矩中由单个构件提供的部分称为分配系数（DF）。传递系数代表着弯矩从铰传递至远端的部分。

Unit 7 第七单元

Reinforced Concrete Structures

Concrete and reinforced concrete are used as building materials in every country. In many, including the United States and Canada, reinforced concrete is a dominant（主要的） structural material in engineered construction（建造的建筑物）. The universal（通用的）nature of reinforced concrete construction stems from（归因于）the wide availability of reinforcing bars（钢筋）and the constituents（组成部分）of concrete, gravel,sand, and cement, the relatively simple skills required in concrete construction（施工）, and the economy（经济性）of reinforced concrete compared to other form of construction. Concrete and reinforced concrete are used in bridges, buildings of all sorts（各种各样）, underground structures, water tanks, television towers, offshore oil exploration and production structures（近海石油开采和生产结构）, dams, and even in ships.

混凝土与钢筋混凝土作为建筑材料在每个国家被使用着。在很多国家，包括美国和加拿大，钢筋混凝土是建造的建筑物中主要的结构材料。钢筋混凝土建筑物通用的特性归因于能大量得到钢筋和混凝土的组分（即碎石、砂和水泥），混凝土施工需要相对简单的技术，以及与其他形式的建筑相比钢筋混凝土的经济性。混凝土与钢筋混凝土用于桥梁、各种房屋、地下结构、水箱、电视塔、近海石油开采和生产结构、大坝甚至船舶。

Mechanics of Reinforced Concrete

钢筋混凝土的力学

Concrete is strong in compression but weak in tension. As a result, cracks develop（形成）whenever（每当）loads, or restrained shrinkage（收缩限制）or temperature changes, give rise to（导致）tensile stresses in excess of（超过）the tensile strength of the concrete. In the plain concrete（素混凝土）beam, the moments due to applied loads are resisted by an internal tension-compression couple（拉压力偶）involving tension in the concrete. Such a beam fails very suddenly and completely when the first crack forms. In a reinforced concrete beam, steel bars（钢筋）are embedded in the concrete in such a way that the tension forces needed for moment equilibrium after the concrete cracks can be developed in the bars.

混凝土受压强、受拉弱。因此，每当受荷、收缩受阻或温度变化引起的拉应力超过混凝土的抗拉强度时，便会发生开裂。在素混凝土梁中，因外力引起的力矩由内部的拉-压形成的力偶来抵抗，此力偶中包含了混凝土的拉力。当第一条裂缝形成时，此梁会突然、完全地失效。在钢筋混凝土梁中，钢筋埋置在混凝土内的方式应能使混凝土开裂后在钢筋中产生平衡力矩所需的拉力。

The construction（施工）of a reinforced concrete member involves building a form or mold（模具）in the shape of the member being built. The form must be strong enough to support the weight and hydrostatic pressure（静水压力）of the wet concrete, and any forces applied to it by workers, concrete buggies（料车）, wind, and so on. The reinforcement（钢筋）is placed in this form and held in place（固定就位）during the concreting（用混凝土浇筑）operation. After the concrete has hardened, the forms are removed（拆除）.

钢筋混凝土构件的施工包括以在建构件的形状搭建模板或模具。模板必须足够强劲以支承湿混凝土的重量和静水压力，以及任何由工人、混凝土料车、风等施加给它的力。钢筋置于模板中，并在混凝土浇筑过程中固定就位。当混凝土硬化后便拆除模板。 The choice of whether a structure should be built of concrete, steel, masonry, or timber（木材）depends on the availability（可得性）of materials and on a number of（许多）value decisions（价值判断）.

一个结构选择由混凝土、钢材、砌体还是木材建造取决于材料的可得性和许多价值判断。

Factors Affecting Choice of Concrete For a Structure

影响一个结构选择混凝土的因素

Economy Frequently, the foremost（最重要的）consideration is the overall cost（总费用）of the structure. This is, of course, a function of the costs（费用函数）of the materials and the labor necessary to erect them. Frequently, however, the overall cost is affected as much or more by the overall construction time（总的建造时间）since the contractor and owner must allocate（分配）money（资金）to carry out the construction and will not receive a return on this investment （收回投资）until the building is ready for occupancy（居住）. As a result, financial savings（财务的节约）due to rapid

construction may more than offset（足以抵消）increased material costs. Any measures designer can take to standardize the design and forming（加工）will generally pay off（使人得益）in reduced overall costs.

经济性 最重要的考虑常常是该结构的总费用。当然，这是一个建造结构而必需的材料和劳动力费用的函数。但是，总费用经常同样地或更多地受总的建造时间的影响，因为承包商和业主必须分配资金来进行建造，并直到建筑物可以使用才能收回投资。因快速施工而使财务的节约可足以抵消增加的材料费用。设计者为使设计和加工标准化所采取的任何措施通常都将在降低的总费用中得益。 In many cases the long-term economy（长期的经济性）of the structure may be more important than the first cost. As a result, maintenance（维护）and durability（耐久性）are important considerations.

在很多情况下，结构长期的经济性可能比初始费用更重要。因此，维护和耐久性是重要的考虑因素。

Suitability of Material for Architectural and Structural Function A reinforced concrete system frequently allows the designer to combine the architectural and structural functions（功能）. Concrete has the advantage that it is placed in a plastic condition（塑性状态）and is given the desired shape and texture（密度）by means of the forms and the finishing techniques（加工技术）. This allows such elements（构件）as flat plates or other types of slabs to serve as load-bearing elements while providing the finished floor and ceiling surface（楼面和顶棚面）. Similarly, reinforced concrete walls can provide architecturally attractive surfaces in addition to having the ability to resist gravity, wind, or seismic loads. Finally, the choice of size or shape is governed（决定）by the designer and not by the availability of standard manufactured members.

材料对建筑和结构功能的适应性 钢筋混凝土系统常常允许设计者将建筑和结构的功能结合起来。混凝土的优势是能以塑性的状态放置，并通过模板和加工技术给出需要的形状和密度。当楼面和顶棚面完成时，允许这些构件诸如平面板或其他类型的板充当受力构件。类似地，钢筋混凝土墙除了能抵抗重力、风或地震荷载外，还能提供建筑上吸引人的外观。最后，尺寸和形状的选择由设计者来决定，而不是由标准制造构件的可得性来决定。

Fire Resistance The structure in a building must withstand the effects of a fire and remain standing（直立）while the building is evacuated（撤空）and the fire is extinguished（熄灭）. A concrete building inherently（固有地）has a 1- to 3-hour fire rating（耐火等级）without special fireproofing （防火）or other details（说明）. Structural steel or timber（钢结构或木结构） buildings must be fireproofed to attain similar fire ratings.

抗火性 当房屋被撤空、火被熄灭时，建筑中的结构必须经得起火的影响，并仍能保持直立。混凝土房屋在没有采取特殊的防火措施或其他说明的情况下本来就有1-3小时的耐火等级。钢结构或木结构的房屋必须采取防火措施，以得到相似的耐火等级。

Rigidity The occupants of a building may be disturbed （干扰）if their building oscillates（摇动）in the wind or the floors vibrate as people walk by（走过）. Due to the greater stiffness and mass（刚度和质量）of a concrete structure, vibrations are seldom a problem.

刚性 如果房屋在风中摇动，或者人们走过时底板振动，则房屋的居住者可能会被干扰。由于混凝土结构具有较大的刚度和质量，振动很少成为问题。

Low Maintenance Concrete members inherently require less maintenance than do structural steel or timber members （结构钢构件或结构木构件）. This is particularly true（尤其正确）if dense, air-entrained concrete has been used for surfaces exposed to the atmosphere, and if care has been taken in the design to provide adequate drainage off and away （使水排出） from the structure.

低维护性 混凝土构件比结构钢构件或结构木构件需要的维护本来就少。特别是当暴露在空气中的表面混凝土采用密实的加气混凝土，并在设计中小心地让水分充分地排出结构时更是如此。

Availability of Materials Sand, gravel, cement, and concrete mixing facilities（搅拌设施） are very widely available, and reinforcing steel（钢筋）can be transported to most job sites（施工现场）more easily than can structural steel（结构钢）. As a result, reinforced concrete is frequently used in remote areas.

材料的可得性 砂、碎石（砾石）、水泥以及混凝土的搅拌设施可以非常广泛的得到，且钢筋比结构钢更容易地运至多数施工现场。因此，钢筋混凝土经常用在偏远的区域。

On the other hand, there are a number of factors that may cause one to select a material other than (..除外，不是..）reinforced concrete. These include：

另一方面，有许多因素可能导致一个人选择的材料不是钢筋混凝土。这包括：

Low Tensile Strength As stated（叙述）earlier, the tensile strength of concrete is much lower than its compressive strength (about 1/10), and hence concrete is subject to（易遭受）cracking. In structural uses this is overcome by using reinforcement to carry tensile forces and limit crack widths（宽度）to within acceptable values. Unless care is taken in design and construction, however, these cracks may be unsightly（难看）or may allow（使..能）penetration（渗透）of water.

低的抗拉强度 正如前面所述的，混凝土的抗拉强度比它的抗压强度要低得多（约1/10），因而混凝土易遭受开裂。在结构使用中，通过采用钢筋承受拉力，并限制裂缝宽度在可接受的数值内来克服这一点。但是，除非在设计与施工中小心谨慎，否则这些裂缝可能会难看或使水渗透。

Forms and Shoring The construction of a cast-in-place structure（现浇结构）involves（涉及）three steps（步骤）not encountered in the construction of steel or timber structures. These are (a) the construction of the forms, (b) the removal（拆除）of these forms, and (c) propping or shoring（支撑）the new concrete to support its weight until its strength is adequate. Each of these steps involves（包含）labor（人工）and/or materials which are not necessary with other forms of construction（建筑形式）.

模板和支撑 现浇结构的施工涉及到三个步骤在钢结构或木结构的施工中不会遇到。它们是(a)模板的施工；(b)模板的拆除；(c)支撑新浇混凝土，支撑其重量直至混凝土达到足够的强度。每一步都包括其他建筑形式中不必要的人工和/或材料。

Relatively Low Strength Per Unit of Weight or Volume The compressive strength of concrete is roughly 5% to 10% that of steel, while its unit density is roughly 30% that of steel. As a result, a concrete structure requires a larger volume and a greater weight of material than does a comparable（类似的） steel structure. As a result, long-span structures（大跨结构）are often built from steel.

相对低的单位重量或单位体积的强度 混凝土的抗压强度大约是钢材的5%-10%，而它的单位密度约是钢材的30%。因此，混凝土结构与类似的钢结构相比需要较大的材料体积和较重的材料重量。因此，大跨结构常常由钢材制造。

Time-dependent volume changes Both concrete and steel undergo approximately the same amount of thermal expansion and contraction. Because there is less mass of steel to be heated or cooled（变热或变冷）, and because steel is a better conductor（导体）than concrete, a steel structure is generally affected by temperature changes to a greater extent （程度）than is a concrete structure. On the other hand, concrete undergoes drying shrinkage（干缩）, which, if restrained, may cause deflections or cracking. Furthermore, deflections will tend to increase with time（随时间）, possibly doubling（双倍）, due to creep（徐变）of the concrete under sustained loads（持续荷载）.

体积随时间变化 混凝土与钢筋都经过了大约相同量的热膨胀和收缩。因为变热或变冷的钢材质量较少，且钢材与混凝土相比是一种较好的导体，因此，钢结构通常受温度变化的影响程度比混凝土结构要大。另一方面，混凝土经历了干缩，如果受到约束，干缩可能会引起挠度或开裂。而且，挠度往往会随着时间增加，其值由于混凝土在持续荷载作用下的徐变而可能会是两倍。

The first set of building regulations（建筑规范）for reinforced concrete were drafted（起草）under the leadership of（在..的领导下） Professor Morsch of the University of Stuttgart and were issued（发布）in Prussia in 1904. Design regulations were issued in Britain, France, Austria, and Switzerland between 1907and 1909.

在Stuttgart（斯图加特）大学Morsch教授的领导下起草了第一套钢筋混凝土的建筑规范，并于1904年在Prussia（普

建筑规范 鲁士）发布。1907-1909年在英国、法国、奥地利和瑞士发布了设计规范。 Building Codes

The American Railway Engineering Association（协会） appointed（任命）a Committee on Masonry（砌体委员会）in 1890. In 1903 this committee presented（提出）specifications for Portland cement concrete. Between 1908 and 1910 a series of committee reports led to the Standard Building Regulations for the Use of Reinforced Concrete published（发表）in 1910 by the National（国家的）Association of Cement Users（用户）which subsequently（随后）became the American Concrete Institute（协会）.

美国的铁路工程协会在1890年任命了一个砌体委员会。该委员会在1903年提出了波特兰水泥混凝土的规范。1908-1910间，一些列的委员会报告使国家水泥用户协会在1910年发表了钢筋混凝土使用的标准建筑规范，其随后成为美国混凝土协会。

A Joint Committee（联合委员会）on Concrete and Reinforced Concrete was established in 1904 by the American Society of Civil Engineers（土木工程师协会）, American Society for Testing and Materials, the American Railway Engineering Association, and the Association of American Portland Cement Manufactures. This group was later joined by（加入）the American Concrete Institute. Between 1904 and 1910 the Joint Committee carried out research. A preliminary （初步的）report issued in 1913 lists the more important papers and books on reinforced concrete published（发表）between 1898 and 1911. The final report of this committee was published in 1916. The history of reinforced concrete building codes in the United States was reviewed（回顾）in 1954 by Kerekes and Reid.

水泥与钢筋混凝土的联合委员会于1904年建立，包括美国土木工程师协会、美国测试和材料协会、美国铁路工程协会和美国波特兰水泥制造协会。该团体中后来又加入了美国混凝土协会。在1904-1910年间，联合委员会进行了研究。在1913年发布的初步报告中列出了在1898-1911年间发表的关于钢筋混凝土的较重要的文件和书籍。该委员会最后的报告发表于1916。Kerekes and Reid在1954对钢筋混凝土建筑规范在美国的发展历史作了回顾。

The design and construction of buildings is regulated（控制）by municipal bylaws（市政细则）called building codes. These exist to protect（用以保护）the public health and safety. Each city and town is free to（允许）write（编制）or adopt its own building code, and in that city or town, only that particular code has legal status（合法地位）. Because of the complexity of building code writing, cities in the United States generally base their building codes on one of three model（典型）codes: the Uniform（统一）Building Code, the Standard Building Code, or the Basic Building Code. These codes cover（包括） such things as use and occupancy requirements, fire requirements, heating and ventilating（供热和通风） requirements, and structural design.

建筑的设计和施工是由称为建筑规范的市政细则来控制的。这些规范是用以保护公众的健康和安全。每个城市和城镇允许编制或采用其自己的建筑规范，并且在那个城市或城镇只有那个特定的规范才有合法的地位。由于建筑规范编制的复杂性，美国的城市通常将它们的建筑规范以三个典型规范中的一个为基础，即统一建筑规范、标准建筑规范或基本建筑规范。这些规范包括诸如使用和居住的要求，防火要求、供热和通风要求以及结构的设计。

The definitive（最终的）design specification for reinforced concrete buildings in North America（北美）is the Building Code Requirements for Reinforced Concrete (ACI-318-95), which is explained in a Commentary（说明）.

在北美，钢筋混凝土建筑最终的设计规范是钢筋混凝土建筑规范要求（ACI-318-95），并通过说明（对该规范要求）加以解释。

This code, generally referred to as （指..） the ACI Code, has been incorporated（体现）in most building codes in the United States and serves as the basis for comparable codes in Canada, New Zealand, Australia, and parts of Latin America. The ACI Code has legal status only if（只要）adopted in a local（当地的）building code.

该规范通常称为ACI规范，它已经在美国的大多数建筑规范中被体现，并作为加拿大、新西兰、澳大利亚和部分拉丁美洲国家类似规范的基础。ACI规范只要在当地的建筑规范中被使用便拥有合法的地位。

The rules for the design of concrete highway bridges（公路桥） are specified in the Standard Specifications for Highway Bridges, American Association of State Highway and Transportation Officials（美国国家公路和运输官方协会）, Washington,

D.C.（哥伦比亚华盛顿特区）.

混凝土公路桥的设计规则在哥伦比亚华盛顿特区的美国国家公路和运输官方协会对公路桥的标准规范中作了规定。 Each nation or group of（一群）nations in Europe has its own building code for reinforced concrete. The CEB-FIP Model Code for Concrete Structures is intended to（用来）serve as the basis for future attempts to unify（统一）European codes. This code and the ACI Code are similar in many ways.

在欧洲每个国家或一群国家都有自己的钢筋混凝土建筑规范。混凝土结构的典型规范CEB-FIP被用来作为将来尝试统一欧洲规范的基础。该规范在很多方面与ACI规范是相似的。

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