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