金陵科技学院工管Stress-and-Strain.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,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.,Fig.1 Prismatic bar in tension,Lesson 1:Stress and Strain,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 cross section,analogous to the continuous distribution of,hydrostatic pressure,over a submerged surface.,Fig.1 Prismatic bar in tension,Lessen 1:Stress and Strain,The intensity of force,that is,the force,per unit area,is called the stress and is commonly denoted by the Greek letter.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,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,Lessen 1:Stress and Strain,Eq,.(1)can be regarded as the equation for the,uniform stress,in a prismatic bar.This equation shows 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 stresses,.,Lessen 1:Stress and Strain,A,necessary condition,for,Eq,.(1)to be valid is that the stress must be uniform over the cross section of the bar.This condition will be,realized,if the axial force P acts through the,centroid,of the cross section.When the load P does not act at the,centroid,bending of the bar will result,and a more complicated analysis is necessary.At present,however,it is assumed that all axial forces are applied at the,centroid,of cross section,unless specifically stated to the contrary,.Also,unless stated otherwise,it is generally assumed that the weight of the object itself is neglected,as was done when discussing the bar in Fig.1.,Lessen 1:Stress and Strain,The total elongation of a bar,carrying,an axial force will be denoted by the Greek letter see Fig.1(a),and the elongation per unit length,or strain,is then determined by the equation.,Where L is the total length of the bar.Note that the strain is a,non-dimensional quantity,.It can be obtained accurately from,Eq,.(2)as long as the strain is uniform throughout the length of the bar.If the bar is in tension,the strain is a tensile strain,representing an elongation or stretching of the material;if the bar is in compression,the strain is a compressive strain,which means that adjacent cross sections of the bar move closer to one another.,Lessen 1:Stress and Strain,7.,When a material exhibits a,linear relationship,between stress and strain,it is said to be,linear elastic,.This is an extremely important property of many solid materials,including most metals,plastics,wood,concrete,and ceramics.The linear relationship between stress and strain for a bar in tension can be expressed by the simple equation,in which E is,a constant of proportionality,known as the modulus of elasticity for the material.,Lessen 1:Stress and Strain,8.,Note that E has the same units as stress.The modulus of elasticity is sometimes called Youngs modulus,after the English scientist Thomas Young(1773-1829)who studied the elastic behavior of bars.For most materials the modulus of elasticity in compression is the same as in tension.,Lessen 1:Stress and Strain,Lessen 1:New Words and Expressions,Lessen 1:New Words and Expressions,Lessen 1:New Words and Expressions,Lessen 1:New Words and Expressions,Lessen 1:Practice,Rod,Bar,Truss,Beam,Axial force,Shearing force,Bending moment,Consentrated,force(load),Distributed force(load),Uniform distributed force(load),Fixed end,Pin support,Roller support,