（選自書籍）土木工程外文翻譯--梁的撓度（原文）

1、 551 9.1 Introduction different functions defining the elastic curve in the various por- tions of the beam. In the case of the beam and loading of Fig. 9.2, for example, two differential equations are required, one for

2、 the portion of beam AD and the other for the portion DB. The first equation yields the functions u1 and y1, and the second the func- tions u2 and y2. Altogether, four constants of integration must be determined; two

3、will be obtained by writing that the deflection is zero at A and B, and the other two by expressing that the portions of beam AD and DB have the same slope and the same deflection at D.You will observe in Sec. 9.4 tha

4、t in the case of a beam support- ing a distributed load w(x), the elastic curve can be obtained directly from w(x) through four successive integrations. The constants intro- duced in this process will be determined from

5、 the boundary values of V, M, u, and y.In Sec. 9.5, we will discuss statically indeterminate beams where the reactions at the supports involve four or more unknowns. The three equilibrium equations must be supplemente

6、d with equa- tions obtained from the boundary conditions imposed by the supports.The method described earlier for the determination of the elastic curve when several functions are required to represent the bending mome

7、nt M can be quite laborious, since it requires match- ing slopes and deflections at every transition point. You will see in Sec. 9.6 that the use of singularity functions (previously discussed in Sec. 5.5) considerably

8、 simplifies the determination of u and y at any point of the beam.The next part of the chapter (Secs. 9.7 and 9.8) is devoted to the method of superposition, which consists of determining sepa- rately, and then adding,

9、 the slope and deflection caused by the vari- ous loads applied to a beam. This procedure can be facilitated by the use of the table in Appendix D, which gives the slopes and deflections of beams for various loadings a

10、nd types of support.In Sec. 9.9, certain geometric properties of the elastic curve will be used to determine the deflection and slope of a beam at a given point. Instead of expressing the bending moment as a function

11、M(x) and integrating this function analytically, the diagram represent- ing the variation of MyEI over the length of the beam will be drawn and two moment-area theorems will be derived. The first moment- area theorem wi

12、ll enable us to calculate the angle between the tan- gents to the beam at two points; the second moment-area theorem will be used to calculate the vertical distance from a point on the beam to a tangent at a second poi

13、nt.The moment-area theorems will be used in Sec. 9.10 to deter- mine the slope and deflection at selected points of cantilever beams and beams with symmetric loadings. In Sec. 9.11 you will find that in many cases the

14、areas and moments of areas defined by the MyEI diagram may be more easily determined if you draw the bending- moment diagram by parts. As you study the moment-area method, you will observe that this method is particula

15、rly effective in the case of beams of variable cross section.B ADy[x ? 0, y1 ? 0]? ?xx ? L, 1 ? 21 4 [[ x ? L, y1 ? y21 4 [[x ? L, y2 ? 0 [[PFig. 9.2 Situation where two sets of equations are required.bee80288_ch09_5

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