【正文】 ource of the expression（表達(dá)式）“singularity function”, but having regard for（考慮）the scope of this book we have stopped short of（達(dá)不到）that step. 本節(jié)使你熟悉了奇異函數(shù)，并發(fā)現(xiàn)通過利用它們能大大地簡化某些問題。但必須意識到僅僅是介紹了題目，對那些有特殊興趣的人還有很多要學(xué)。我們可以表示變化的、間斷的分布荷載，但不能寫出集中荷載的荷載函數(shù)，說明了在我們目前階段（該函數(shù)）還存在著嚴(yán)重的缺陷。如果我們進(jìn)入下一步去研究集中荷載，便會(huì)遇到奇異函數(shù)表達(dá)式的來源，但是考慮到本書的范圍，我們不再進(jìn)入那一步。 In the design of a member subjected to a uniaxial（單軸的） load, the stress was pared with the stress to cause failure in test specimens（試件）that had also been subjected to uniaxial load. This is the simplest of all design problems。 the method is quite adequate（合適的）, 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（壓力容器）. In these cases we know that the stress is twodimensional（兩向的）or biaxial and it may, in other cases, be threedimensional, 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（進(jìn)行） in which specimens are stressed（受力）to failure in the same multiaxial（多軸的）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（預(yù)測）the failure of a part made of the same material when the stresses are multiaxial. In other words（換句話說）, we need a failure theory. 在設(shè)計(jì)承受軸向力的構(gòu)件時(shí)，將其應(yīng)力與導(dǎo)致同樣承受軸向力的試驗(yàn)樣本（試件）失效的應(yīng)力相比。這是所有設(shè)計(jì)問題中最簡單的；該法是非常合適的，因?yàn)樵囼?yàn)和設(shè)計(jì)中的荷載和應(yīng)力性質(zhì)是完全相同的。但是，不久我們便會(huì)遇到正在設(shè)計(jì)的構(gòu)件不是那么簡單，其應(yīng)力也不是單軸向的；例如，考慮梁的腹板應(yīng)力或壓力容器中的應(yīng)力。在這些情況下，我們知道其應(yīng)力是兩向的或兩軸的，而在其他情況下可能是三向或三軸的。對一個(gè)有著兩軸或三軸應(yīng)力的結(jié)構(gòu)，我們應(yīng)該如何檢查它的設(shè)計(jì)安全性？最顯然的辦法是進(jìn)行試驗(yàn)，即試件以與結(jié)構(gòu)相同的多軸受力方式失效；然后運(yùn)用適當(dāng)?shù)陌踩禂?shù)確定許用的多軸應(yīng)力。但是，對設(shè)計(jì)中出現(xiàn)的每組新的多軸應(yīng)力都將需要一組試驗(yàn)。這樣的試驗(yàn)很難進(jìn)行，而且以需要的數(shù)量進(jìn)行試驗(yàn)的費(fèi)用也是禁止的。因此，我們需要一個(gè)理論，根據(jù)它可以通過利用標(biāo)準(zhǔn)單軸試驗(yàn)的結(jié)果來預(yù)測同樣材料制作的構(gòu)件在承受多軸應(yīng)力時(shí)的失效。換句話說，我們需要一個(gè)失效理論。 To illustrate the need for a failure theory, let us consider a cylindrical pressure vessel. To avoid unnecessary plications, we will consider that all welds（焊縫）are 100% efficient and that the walls（容器壁）are thin. Under internal pressure the main stresses（主應(yīng)力） are circumferential and longitudinal, and it was implied（認(rèn)為）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（默認(rèn)）assumed that the maximum stress could be treated as（看作為）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（在我們的知識之外）, 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. 為了舉例說明需要一個(gè)失效理論，讓我們考慮一個(gè)圓柱形的壓力容器。為避免不必要的復(fù)雜，我們認(rèn)為焊縫完全有效，容器壁是薄的。在內(nèi)部壓力下，主應(yīng)力是環(huán)向和縱向的，由于環(huán)向應(yīng)力比縱向應(yīng)力大，因此，在一個(gè)較早的例子中認(rèn)為只有環(huán)向應(yīng)力需要在判斷設(shè)計(jì)的適用性時(shí)加以考慮。在這個(gè)方法中，我們默認(rèn)地假定最大的應(yīng)力（即環(huán)向應(yīng)力）可看作為單軸應(yīng)力，并由它單獨(dú)地確定設(shè)計(jì)的安全性。盡管在我們的知識以外，縱向應(yīng)力可能會(huì)對強(qiáng)度有影響，但不被考慮。正巧，在這種情況下我們的方法能被接受，但是，在兩軸應(yīng)力狀態(tài)下，第二種應(yīng)力不總是不重要的，為了避免造成一些嚴(yán)重的錯(cuò)誤，對失效理論的理解是必要的。 Unfortunately, as we will discover, no single theory（單一理論） 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 plex for everyday use and that most designers prefer（更喜歡）a simpler theory that introduces（產(chǎn)生）a small but safeside（安全的）error. 很不幸，正如我們將發(fā)現(xiàn)的，沒有找到一個(gè)單一的理論能運(yùn)用于所有的狀況，例如，滿足延性材料的理論，脆性材料不能接受。我們也將發(fā)現(xiàn)每天在使用一個(gè)最好的理論太復(fù)雜了，多數(shù)設(shè)計(jì)者更喜歡用一個(gè)會(huì)產(chǎn)生小而安全的錯(cuò)誤但較簡單的理論。 In developing（提出）the various failure theories, we cannot avoid threedimensional effects, but we will treat（討論）only those cases in which one of the stresses is zero, thus avoiding plications 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（工程實(shí)踐） most problems are reduced to（簡化為）the biaxial stress state for design. When shear stresses（剪應(yīng)力）occur along with（與..一起）normal stresses（正應(yīng)力）, the principal stresses（主應(yīng)力）are determined. Thus, for practical（實(shí)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（為了便于..）designating （稱呼）those principal stresses we will use numerical subscripts（數(shù)字下標(biāo)）。 s1 and s2 being the nonzero stresses and s3 being zero. 在提出不同的失效理論時(shí)，我們不能避免三向的影響，但我們將只討論其中某一個(gè)應(yīng)力為零的情況，因而避免了復(fù)雜性，因它往往使理論的重要部分模糊不清。這不是個(gè)嚴(yán)重的缺陷，因?yàn)樵诠こ虒?shí)踐中，多數(shù)問題在設(shè)計(jì)時(shí)被簡化為兩軸應(yīng)力狀態(tài)。當(dāng)剪應(yīng)力與正應(yīng)力一起存在時(shí)，主應(yīng)力便被確定。這樣，為了實(shí)用的目的，我們需要考慮承受兩個(gè)非零正應(yīng)力而第三個(gè)正應(yīng)力為零的材料的失效。為了便于稱呼那些主應(yīng)力，我們采用數(shù)字下標(biāo)： s1和s2作為非零應(yīng)力，而s3為零。 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（分為）two or more parts. However, it has already been pointed out that in most applications a member would be unserviceable（不再適用）due to excessive distortion long before（早在）it actually ruptured（斷裂）. Consequently, we will relate failure to yielding and consider that a material has failed when it will no longer return to（恢復(fù)）its original（最初的）shape upon（一旦）release of the loads. In a simple tensile test（拉伸試驗(yàn)）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, sy , in either tension or pression. 在我們定義了失效后才能對其進(jìn)行討論。我們可能會(huì)下一個(gè)明顯的定義，即當(dāng)材料分成兩部分或更多時(shí)失