过程装备与控制工程专业英民语阅读材料2翻译.docVIP

Reading Material 2 Shear Force And Bending Moment In Beams Let us now consider,as an example ,a cantilever beam acted upon by an inclined load P at its free end [Fig.1.5(a)]. If we cut through the beam at a cross section mn and isolate the left-hand part of the beam as free body [Fig.1.5(b)] ,we see that the action of the removed part of the beam (that is ,the right-hand part) upon the left-hand part must be such as to hold the left-hand part in equilibrium. The distribution of stresses over the cross section mn is not known at this stage in our study ,but we do know that the resultant of these stresses must be such as to equilibrate the load P.It is convenient to resolve the resultant into an axial force N acting normal to the cross section and passing through the centroid of the cross section,a shear force V acting parallel to the cross section, and a bending moment M acting in the plane of the beam. The axial force ,shear force, and bending moment acting a across section of a beam are known as stress resultants. For a statically determinate beam,the stress resultants can be determined from equations of equilibrium. Thus ,for the cantilever beam pictured in Fig.1.5,we may write three equations of statics for the free-body diagram shown in the second part of the figure. From summations of force in the horizontal and vertical directions we find ,respectively, N=P cos V=P sin N=P cos V=P sin And,from a summation of moments about an axis through the centroid of cross section mn ,we obtain: M=Px sin Where x is the distance from the free and to section mn,thus, through the use of a free-body diagram and equations of static equilibrium,we are able to calculate the stress resultants without difficulty. The stresses in the beam due to the axial force N acting alone have been discussed in the text of Unit.2;now we will see how to obtain the stresses associated with bending moment M and the shear force V. The