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Tải xuống
Chúng tôi muốn để có thể dự đoán độ võng của dầm uốn, bởi vì nhiều ứng dụng có hạn chế về số lượng lệch có thể được dung thứ. Một nhu cầu phổ biến để phân tích độ lệch phát sinh từ vật liệu thử nghiệm, trong đó sự lệch ngang gây ra bởi một tải trọng uốn được đo. Nếu chúng ta biết mối quan hệ dự kiến giữa tải và lệch, chúng ta có thể "sao lưu" tài sản vật chất (cụ thể là mô đun) từ phép đo. . | Beam Displacements David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge MA 02139 November 30 2000 Introduction We want to be able to predict the deflection of beams in bending because many applications have limitations on the amount of deflection that can be tolerated. Another common need for deflection analysis arises from materials testing in which the transverse deflection induced by a bending load is measured. If we know the relation expected between the load and the deflection we can back out the material properties specifically the modulus from the measurement. We will show for instance that the deflection at the midpoint of a beam subjected to three-point bending beam loaded at its center and simply supported at its edges is . PL3 Op - p 48EI where the length L and the moment of inertia I are geometrical parameters. If the ratio of Op to P is measured experimentally the modulus E can be determined. A stiffness measured this way is called the flexural modulus. There are a number of approaches to the beam deflection problem and many texts spend a good deal of print on this subject. The following treatment outlines only a few of the more straightforward methods more with a goal of understanding the general concepts than with developing a lot of facility for doing them manually. In practice design engineers will usually consult handbook tabulations of deflection formulas as needed so even before the computer age many of these methods were a bit academic. Multiple integration In Module 12 we saw how two integrations of the loading function q x produces first the shear function V x and then the moment function M x V y q x dx C1 1 M y V x dx c2 2 where the constants of integration C1 and c2 are evaluated from suitable boundary conditions on V and M. If singularity functions are used the boundary conditions are included explicitly and the integration constants C1 and c2 are identically zero. From Eqn. 6 in .
