Lesson 1土木工程专业英语

1、Lesson 1 Stress and Strain The concepts of stress and strain can be illustrated in an elementary way by considering the extension of a prismatic bar（see Fig.1-1a）.应力和应变的概念可以通过考虑等截面杆延伸的基本方法来说明（参见图1-1a）。A prismatic bar is one that has constant cross section throughout its length and a straight axis.等截

2、面杆沿整个长度和直线轴线方向具有恒定的截面。In this illustration the bar is assumed to be loaded at its ends by axial forces P that produce a uniform stretching, or tension, of the bar.此图中，假定杆两端施加轴向力P，在轴向力P的作用下（沿杆长）产生均匀拉伸或（在杆截面）产生均匀拉力。By making an artificial cut (section m-m) through the bar at right angles to its axis,

3、we can isolate part of the bar as a free body (see Fig.1-1b).垂直于轴线做一个截面（截面m-m），取杆其中一部分作为隔离体（如图1-1b）。At the left-hand end the tensile force P is applied, and at the other end there are forces representing the action of the removed portion of the bar upon the part that remains.在杆左端作用拉力P，在杆另一端移动部分对保留部分

4、存在力的作用。These forces will be continuously distributed over the cross section, analogous to the continuous distribution of hydrostatic pressure over a submerged surface.这些力连续分布在杆整个横截面上，类似于浸没面上液体静压力的连续分布。The intensity of force, that is , the force per unit area, is called the stress and is commonly den

5、oted by the Greek letter .力的集度，即单位面积上的力叫应力，通常用希腊字母表示。Assuming that the stress has a uniform distribution over the cross section (see Fig.1-1b), we can readily see that its resultant is equal to the intensity times the cross-sectional area A of the bar.假定应力沿横截面均匀分布（如图1-1b），我们很容易得到截面上的合力等于强度乘以杆截面积A。Fu

6、rthermore, from the equilibrium of the body shown in Fig.1b, we can also see that this resultant must be equal in magnitude and opposite in direction to the force P. Hence, we obtainPAPA此外，从图Fig.1b中由力的平衡我们也可以看出截面上合力必须与力P大小相等方向相反，我们得到方程（1）Eq. (1) can be regarded as the equation for the uniform stress

7、 in a prismatic bar.方程（1）即为等截面杆均匀应力方程。This equation shows that stress has units of force divided by areafor example, pounds per square inch (psi) or kips per square inch (ksi) .此方程表示应力为单位面积上所受的力（例如磅每平方英寸或千磅每平方英寸）。When the bar is being stretched by the force P, as shown in the figure, the resulting s

8、tress is a tensile stress; if the forces are reversed in direction, causing the bar to be compressed, they are called compressive stresses.当杆在力P的作用下被拉伸，如图中所示，则应力是拉应力；如果力的方向相反，使杆受压，则被称为压应力。A necessary condition for Eq.(1) to be valid is that the stress must be uniform over the cross section of the ba

9、r.方程(1)有效的必要条件是杆横截面上的应力必须均匀的。This condition will be realized if the axial force P acts through the centroid of the cross section, as can be demonstrated by statics.用静力学可以说明，假设轴力P作用在截面形心，那么这个条件就可以满足。When the load P does not act at the centroid, bending of the bar will result, and a more complicated a

10、nalysis is necessary.如果荷载P不是作用在形心，杆中将产生弯矩，那就有必要进行更复杂的分析。However, here, it is assumed that all axial forces are applied at the centroid of the cross section unless specifically stated to the contrary.然而，在这里，除非特别说明，假定所有的轴向力都作用在横截面的形心。Also, unless stated otherwise, it is generally assumed that the weig

11、ht of the object itself is neglected, as was done when discussing the bar in Fig.1-1.同样，除非另有说明，通常假定物体的自重忽略不计，如图1-1中就忽略了杆的自重。The total elongation of a bar carrying an axial force will be denoted by the Greek letter (see Fig.1-1a), and the elongation per unit length, or strain, is then determined by t

12、he equation.L轴力引起的总延伸量用希腊字母表示（见图Fig.1-1a ），单位长度的延伸率或应变用公式（1-2）来表示。Where L is the total length of the bar. Note that the strain is a non-dimensional quantity.式中L表示杆总长。 应变是无量纲量。It can be obtained accurately from Eq.(2) as long as the strain is uniform throughout the length of the bar.只要应变沿杆长是均匀的就可以从公式1-2精确得到应变。If the bar is in tension, the strain is a tensile strain, representing an elongation or stretching of the material;假设杆受