【正文】 he pressive stress P/A is uniform over the cross section at any point along the length. 對這些短柱以及更細(xì)長的柱，在其屈曲前，在其長度方向上任意點(diǎn)處橫截面上的壓應(yīng)力 P/A都是均勻的。 If the member is more stocky, as the one in , a larger load will be required to bring the member to the point of instability. 如果該構(gòu)件更粗短些，如圖 所示，則需要更大的荷載才能使其屈曲。 Column Theory （柱理論） Consider the long, slender pression member shown in . 考慮如圖 所示的長柱 If the axial load P is slowly applied, it will ultimately reach a value large enough to cause the member to bee unstable and assume the shape indicated by the dashed line. 如果慢慢增加軸向荷載 P，它最終將達(dá)到一個(gè)足夠大的值使該柱變得不穩(wěn)定 (失穩(wěn) )，如圖中虛線所示。 In many instances these members are also called upon to resist bending, and in these cases the member is a beamcolumn. Compression members can also be found in trusses and as ponents of bracing systems. 在許多情況下，它們也需要抵抗彎曲，在此情況下，將它們稱為梁柱。 This cannot always be done if there is a puted bending moment, and situation of this type will be considered in BeamColumns. 但這并非總是可行的，如有計(jì)算出的彎矩存在時(shí)，這種情形將在梁柱 理論 中加以考慮。 This ideal state is never achieved in reality, however, and some eccentricity of the load is inevitable. 然而，現(xiàn)實(shí)中從來都不可能達(dá)到這種理想狀態(tài)，因?yàn)楹奢d的一些偏心是不可避免的。 divert。 inevitable 不可避免的 unavoidable 4. truss 桁架 triangular truss, roof truss, truss bridge 5. bracing brace 支柱，支撐； bracing, 支撐，撐桿 6. slender 細(xì)長，苗條； stout。Lesson 1 Compression Members New Words 1. achieve achievement 2. eccentricity center, 中心 。 eccentric 偏心的； eccentricity 偏心，偏心距 3. inevitable evitable 可避免的 avoidable。 slenderness 7. buckle 壓曲，屈曲； buckling load 8. stocky stout 9. convincingly convince, convincing, convincingly 10. stub 樹樁， 短而粗的東西； stub column 短柱 11. curvature 曲率； curve, curvature 12. detractor detract draw or take away。 belittle， 貶低，誹謗； 13. convince 14. argument dispute, debate, quarrel, reason, 論據(jù)（理由） 15. crookedness crook 鉤狀物， v 彎曲， crooked 彎曲的 16. provision 規(guī)定，條款 Phrases and Expressions 1. pression member 2. bending moment shear force, axial force 3. call upon (on) 要求，請求，需要 4. critical buckling load 臨界屈曲荷載 critical 關(guān)鍵的，臨界的 5. crosssectional area 6. radius of gyration 回轉(zhuǎn)半徑 gyration 7. slenderness ratio 長細(xì)比 8. tangent modulus 切線模量 9. stub column 短柱 10. trialanderror approach 試算法 11. empirical formula 經(jīng)驗(yàn)公式 empirical 經(jīng)驗(yàn)的 12. residual stress 殘余應(yīng)力 residual 13. hotrolled shape 熱軋型鋼 hotrolled bar 14. lower bound 下限 upper bound 上限 16. effective length 計(jì)算長度 2 Definition （定義） Compression members are those structural elements that are subjected only to axial pressive forces: that is, the loads are applied along a longitudinal axis through the centroid of the member cross section, and the stress can be taken as fa=P/A, where fa is considered to be uniform over the entire cross section. 受壓構(gòu)件是僅受軸向壓力作用的構(gòu)件，即：荷載是沿縱軸加在其截面形心上的，其應(yīng)力可表示為 … ，式中，假定 fa在整個(gè)截面上均勻分布。 This will result in bending, but it can usually be regarded as secondary and can be neglected if the theoretical loading condition is closely approximated. 這將導(dǎo)致彎曲，但通常認(rèn)為它是次要的，如果理論工況是足夠近似的，就可將其忽略。 The most mon type of pression member occurring in buildings and bridges is the column, a vertical member whose primary function is to support vertical loads. 在建筑物和橋梁中最常見的受壓構(gòu)件就是柱，其主要功能就是支承豎向荷載。受壓構(gòu)件也存在于桁架和支撐系統(tǒng)中。 The member is said to have buckled, and the corresponding load is called the critical buckling load. 這時(shí)認(rèn)為構(gòu)件已經(jīng)屈曲，相應(yīng)的荷載稱為臨界屈曲荷載。 For extremely stocky members, failure may be by pressive yielding rather than buckling. 對特別粗短的構(gòu)件，破壞可能是由受壓屈服引起而非由屈曲引起。 As we shall see, the load at which buckling occurs is a function of slenderness, and for very slender members this load could be quite small. 我們將會(huì)看到，屈曲發(fā)生時(shí)的荷載是 長細(xì)程度 的函數(shù)，非常細(xì)長的構(gòu)件的屈曲荷載將會(huì)很低。 For to be valid, the member must be elastic, and its ends must be free to rotate but not translate laterally. This end condition is satisfied by hinges or pins. 要使方程 成立，構(gòu)件必須是彈性的，且其兩端必須能自由轉(zhuǎn)動(dòng)，但不能側(cè)向移動(dòng)。 The critical load is sometimes referred to as the Euler load or the Euler buckling load. The validity of has been demonstrated convincingly by numerous tests. 因此有時(shí)將臨界荷載稱為歐拉荷載或歐拉臨界荷載。 It will be convenient to rewrite as follows: 方程 可方便地寫為 2222222)/( rL EALE A rL EIP cr ??? ??? () where A is the crosssectional area and r is the radius of gyration with respect to the axis of buckling. The ratio L/r is the slenderness ratio and is the measure of a pression member?s slenderness, with large values corresponding to slender members. 式中 A 為截面面積， r 為關(guān)于屈曲軸的回轉(zhuǎn)半徑， L/r 為長細(xì)比，它是對受壓構(gòu)件細(xì)長程度的一種度量，該值越大，構(gòu)件越細(xì)長。 Since buckling will take place as soon as the load reaches the value by , the column will bee unstable about the principle axis corresponding to the largest slenderness ratio. This usually means the axis with the smaller moment of inertia. 由于一旦荷載達(dá)到式 之值，柱將在與最大長細(xì)比對應(yīng)的主軸方向變得不穩(wěn)定 （失穩(wěn)） ，通常該軸是慣性矩較小的軸。 Early researchers soon found that Euler?s equation did not give reliable results for stocky, or less slender, pression members. 早期的研究者很快發(fā)現(xiàn)對短柱或不太細(xì)長的受壓構(gòu)件，歐拉公式并不能給出可靠的結(jié)果， This is because of the small slenderness ratio for members of this type, which results in a large buckling stress (from ). 這是因?yàn)檫@種構(gòu)件的長細(xì)比較小，從而產(chǎn)生較高的屈曲應(yīng)力。 4 This difficulty was initially resolved by Friedrich Engesser, who proposed in 1889 the use of a variable tangent modulus Et in . 這一困難最初由 Friedrich Engesser 所克服，他在 1889年將可變的切線模量用于方程 . For a material with a stressstrain curve like the one in , E is not a constant for stress greater than the proportional limit Fpl. The tangent modulus Et is defined as the slope of the tangent to the stressstrain curve for values of f between Fpl and Fy. 對于如圖 所示的應(yīng)力應(yīng)變曲線 (的材料 )，當(dāng)應(yīng)力超過比例極限時(shí)， E 并非常數(shù)，當(dāng)應(yīng)力處于 Fpl和 Fy之間時(shí)，將切線模量定義為應(yīng)力應(yīng)變曲線的切線的斜率， If the pressive stress at buckling, Pcr/A, is in this region, it can be shown that 如果屈曲 時(shí)的壓應(yīng)力在此范圍時(shí)，可以證明 22L IEP tcr ??