工程力学专英语翻译.pptx

Translation The concepts of stress and strain can be illustrated in an elementary way by considering the extension of a prismatic bar. As shown in Fig. 1, a prismatic bar is one that has constant cross section throughout its length and a straight axis. 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.; By making an artificial cut (section mm) through the bar at right angles to its axis, we can isolate part of the bar as a free body [see Fig.1(b)]. 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. These forces will be continuously distributed over the part cross section, analogous to the continuous distribution of hydrostatic pressure over a submerged surface. ; The intensity of force, that is, the force per unit area, is called the stress and is commonly denoted by the Greek letter σ. Assuming that the stress has a uniform distribution over the cross section [see Fig.1(b)], we can readily see that its resultant is equal to the intensity σ times the cross-sectional area A of the bar. Furthermore, from the equilibrium of the body shown in Fig.1(b), we can also see that this resultant must be equal in magnitude and opposite in direction to the force P. Hence, we obtain σ = P/A. (1); Eq.(1) can be regarded as the equation for the uniform stress in a prismatic bar. This equation shown that stress has units of force divided by area. When the bar is being stretched by the force P , as shown in the figure, the resulting stress is a tensile stress; if the forces are reversed in direction, causing the bar to be compressed, they are called compressive stress.; A necessary condition for Eq.(1) to be valid is that the stress σ must be uniform over the cross section of the bar. This condition will be rea