The satisfactory performance of a structure frequently is determined by the amount of deformation or distortion that can be permitted. A deflection of a few thousandths of an inch might make a boring machine useless, whereas the boom on a dragline might deflect several inches without impairing its usefulness. It is often necessary to relate the loads on a structure, or on a member in a structure, to the deflection the loads will produce. Such information can be obtained by plotting diagrams showing loads and deflections for each member and type of loading in a structure, but such diagrams will vary with the dimensions of the members, and it would be necessary to draw new diagrams each time the dimensions were varied. A more useful diagram is one showing the relation between the stress and strain.Such diagrams are called stress-strain diagrams ( see Fig. 3.1).

結(jié)構(gòu)正常的工作性能通?？梢杂稍试S的變形量或扭曲量來確定。鏜床如果產(chǎn)生了千分之幾英寸的撓度就不能正常工作，而挖掘機(jī)的懸臂即使產(chǎn)生幾英寸的撓度也不妨礙其使用。經(jīng)常需要建立結(jié)構(gòu)或每個(gè)結(jié)構(gòu)構(gòu)件上載荷與由于載荷作用所產(chǎn)生的撓度之間的關(guān)系。這種數(shù)據(jù)可通過畫出表示結(jié)構(gòu)中的每一個(gè)構(gòu)件所承受的荷載及其撓度以及載荷種類的圖而得到，但這種圖將隨構(gòu)件的尺寸而變化，而且每當(dāng)尺寸發(fā)生變化時(shí)就要畫出新的圖。更有用的圖是表示應(yīng)力與應(yīng)變關(guān)系的圖。這樣的圖稱為應(yīng)力－應(yīng)變圖。

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Figure 3.1 Stress-strain curve for a typical low-carbon steel in tension

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Data for stress-strain diagrams are usually obtained by applying an axial load to a test specimen and measuring the load and deformation simultaneously. A testing machine is used to strain the specimen and to measure the load required to produce the strain. The stress is obtained by dividing the load by the initial cross-sectional area of the specimen. The area will change somewhat during the loading, and the stress obtained using the initial area is obviously not the exact stress occurring at higher loads. It is the stress most commonly used, however, in designing structures. The stress obtained by dividing the load by the actual area is frequently called the true stress and is useful in explaining the fundamental behavior of materials. Strains are usually relatively small in materials used in engineering structures, often less than 0.001, and their accurate determination requires special measuring equipment.

應(yīng)力－應(yīng)變圖的數(shù)據(jù)通常由在試件上加軸向載荷，并通過同時(shí)測(cè)量載荷和變形而得到。試驗(yàn)機(jī)用來使試件產(chǎn)生應(yīng)變，并測(cè)量產(chǎn)生應(yīng)變時(shí)所施加的載荷。把載荷除以試件原有的橫截面面積就得到應(yīng)力。在加載時(shí)橫截面面積會(huì)有些變化，在載荷較大時(shí)用原有的橫截面面積算得的應(yīng)力顯然不是精確的應(yīng)力。然而，在結(jié)構(gòu)設(shè)計(jì)中，這是最常采用的應(yīng)力。用載荷除以實(shí)際的橫截面面積而求得的應(yīng)力，通常稱之為真實(shí)應(yīng)力，在解釋材料的基本性能時(shí)應(yīng)用真實(shí)應(yīng)力。工程結(jié)構(gòu)中材料的應(yīng)變通常是很小的，一般小于 0.001,需要采用專門的測(cè)量?jī)x器才能進(jìn)行精確測(cè)量。

True strain, like true stress, is computed on the basis of the actual length of the test specimen during the test and is used primarily to study the fundamental properties of materials. The difference between nominal stress and strain, computed from initial dimensions of the specimen, and true stress and strain is negligible for stresses usually encountered in engineering structures, but sometimes the difference becomes important with larger stresses and strains.

真實(shí)應(yīng)變同真實(shí)應(yīng)力一樣，是在試驗(yàn)中試件實(shí)際長(zhǎng)度的基礎(chǔ)上計(jì)算得來的，主要是用來研究材料的基本性質(zhì)。對(duì)于工程結(jié)構(gòu)中通常承受的應(yīng)力來說，用試件原來尺寸算得的名義應(yīng)力和應(yīng)變與真實(shí)應(yīng)力和應(yīng)變之間的差別可以忽略不計(jì)，但是對(duì)于較大的應(yīng)力和應(yīng)變，有時(shí)這種差別是重要的。

The initial portion of the stress-strain diagram for most materials used in engineering structures is a straight line. The stress-strain diagrams for some materials, such as gray cast iron and concrete, show a slight curve even at very small stresses, but it is common practice to draw a straight line to average the data for the first part of the diagram and neglect the curvature. The maximum stress for which stress and strain are proportional is called the proportional limit.

在工程結(jié)構(gòu)中使用的大多數(shù)材料的應(yīng)力－應(yīng)變圖的初始部分是直線。有些材料，如灰鑄鐵和混凝土的應(yīng)力－應(yīng)變圖，即使在很小的應(yīng)力下也表現(xiàn)為微李的曲線，但在實(shí)際中通常把圖的開始部分按平均值畫成直線，略去其曲率。應(yīng)力與應(yīng)變成比例的最大應(yīng)力，稱為比例極限。

The action is said to be elastic if the strain resulting from loading?disappears when the load is removed.?The elastic limit is the?maximum stress for which the material acts elastically.

由加載所產(chǎn)生的應(yīng)變?cè)谛冻d荷后消失的現(xiàn)象，稱為彈性。材料產(chǎn)生彈性作用時(shí)所對(duì)應(yīng)的最大應(yīng)力，稱為彈性極限。

When the stress exceeds the elastic limit (or proportional limit for practical purposes) , it is found that a portion of the deformation remains after the load is removed. The deformation remaining after an applied load is removed is called plastic deformation. Plastic deformation independent of the time duration of the applied load is known as slip. Creep is plastic deformation that continues to increase under a constant stress. In many instances creep continues until fracture occurs; however, in other instances the rate of creep decreases and approaches zero as a limit. Some materials are much more susceptible to creep than are others, but most materials used in engineering exhibit creep at elevated temperatures. The total strain is thus made up of elastic strain, possibly combined with plastic strain that results from slip, creep, or both. When the load is removed, the elastic portion of the strain is recovered, but the plastic part (slip and creep) remains as permanent set.

可以發(fā)現(xiàn)當(dāng)應(yīng)力超過彈性極限（或?qū)嶋H上的比例極限）時(shí)，在載荷卸除后仍會(huì)保留部分變形。這種載荷卸除后仍然存在的變形，稱為塑性變形。與加載持續(xù)時(shí)間無(wú)關(guān)的塑性變形，稱為滑移。蠕變是在恒定應(yīng)力下繼續(xù)增長(zhǎng)的塑性變形。在許多情況下，蠕變持續(xù)作用直至斷裂；然而，在另一些情況下，蠕變率減小并趨近于為零的極限。某些材料對(duì)蠕變比另外一些材料要敏感得多，但是大部分工程材料在高溫下呈現(xiàn)蠕交現(xiàn)象。因此，總應(yīng)變是由彈性應(yīng)變以及可能出現(xiàn)的塑性應(yīng)變組成的，而塑性應(yīng)變是由滑移，蠕變或者兩者共同組成的。當(dāng)載荷卸除時(shí)，應(yīng)變的彈性部分消失，但塑性部分（滑移和蠕變）保留下來，成為永久性應(yīng)變。

A precise value for the proportional limit is difficult to obtain, particularly when the transition of the stress-strain diagram from a straight line to a curve is gradual. For this reason, other measures of stress that can be used as a practical elastic limit are required. The yield point and the yield strength for a specified offset are frequently used for this purpose.

要想得到比例極限的精確值，特別在應(yīng)力－應(yīng)變圖是由直線漸漸過渡成曲線的情況下是很困難的。因此，需要另外的度量方法來確定可以用作實(shí)際彈性極限的應(yīng)力。某一特定變形的屈服點(diǎn)和屈服強(qiáng)度常常用于這一目的。

The yield point is the stress at which there is an appreciable increase in strain with no increase in stress, with the limitation that, if straining is continued, the stress will again increase.

屈服點(diǎn)就是應(yīng)力不增加而應(yīng)變明顯增加時(shí)的應(yīng)力，而且有這樣的限制，即如果應(yīng)變繼續(xù)增加，應(yīng)力將再增加。

The yield strength is defined as the stress that will induce a specified permanent set, usually 0.05 to 0.3 percent, which is?equivalent to a strain of 0. 0005?to 0.003. The yield strength is?particularly useful for materials with no yield point.?

屈服強(qiáng)度被定義為產(chǎn)生某一特定永久變形的應(yīng)力，其永久變形通常為0.05% ~0.3%，等于應(yīng)變?yōu)?0.0005~0.003。屈服強(qiáng)度對(duì)于沒有屈服點(diǎn)的材料特別有用。

The maximum stress, based on the original area, developed in a material before rupture is called the ultimate strength of the material, and the term may be modified as the ultimate tensile, compressive, or shearing strength?of the material.?Ductile materials undergo?considerable plastic tensile or shearing deformation before rupture.

When the ultimate strength of a ductile material is reached, the cross-sectional area of the test specimen starts to decrease or neck down, and the resultant load that can be carried by the specimen decreases.?Thus, the stress based on the original area decreases beyond the ultimate strength of the material, although the true stress continues to increase until rupture.

按照材料在斷裂前，原來的面積求得的最大應(yīng)力，稱為材料的極限強(qiáng)度，這一名詞可以被改稱為材料的極限拉伸強(qiáng)度，極限壓縮強(qiáng)度或極限剪切強(qiáng)度。延性材料在斷裂前能承受相當(dāng)大的塑性拉伸變形 或剪切變形。當(dāng)延性材料達(dá)到極限強(qiáng)度時(shí)，試件橫截面開始變小或產(chǎn)生頸縮，試件所能承受的總載荷減小。因此，材料達(dá)到極限強(qiáng)度以后，雖然實(shí)際應(yīng)力繼續(xù)增大直至斷裂，但是按原來截面算的的應(yīng)力卻是在減少。