力学专业英语.pdf

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1、Lessen1 Stress and strain The concepts of stress and strain can be illustrated in an elementary way bu 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 assum

2、ed 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

3、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.The intensity of force

4、,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 body shown in Fig.1(b),

5、we can also see that this resultant must be equal in magnitude and opposite in direction to the force P.Hence,we obtain.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 b

6、y 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.A necessary condition for Eq.(1)to be valid is that the stress must be uniform over the cross section of the bar

7、.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 cent

8、roid of the 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.The total elongation of a bar carrying an axial force will be denoted by the Greek

9、letter see Fig.1(a),and the elongation per unit length,or strain,is then determined by the equation.where I 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

10、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 compression strain,which means that adjacent cross sections of the bar move closer to one another.When a material exhibits a linear relationship

11、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

12、E is a constant of proportionality known as the modulus of elasticity for the material.Note that E has the same units as stress.The modulus of elasticity if 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.