And let σ be the longitudinal stress in a filament gℎ at a distance y from the neutral axis.įrom geometry, the length of the neutral axis of the beam ij and that of the filament gℎ, located at a distance y from the neutral axis of the beam, can be computed as follows: Let O be the center and R be the radius of the beam’s curvature, and let ij be the axis of the curved beam. Due to the applied moment M, the fibers above the neutral axis of the beam will elongate, while those below the neutral axis will shorten. To derive the equation of the elastic curve of a beam, first derive the equation of bending.Ĭonsider the portion cdef of the beam shown in Figure 7.1a, subjected to pure moment, M, for the derivation of the equation of bending. The elastic curve of a beam is the axis of a deflected beam, as indicated in Figure 7.1a. Some of the methods used in this chapter include the method of double integration, the method of singularity function, the moment-area method, the unit-load method, the virtual work method, and the energy methods.ħ.2 Derivation of the Equation of the Elastic Curve of a Beam The choice of a particular method is dependent on the nature of the loading and the type of problem being solved. There are several methods of determining the deflection of a beam or frame. To ensure that the possible maximum deflection that could occur under a given loading is within acceptable value, the structural component is usually analyzed for deflection, and the determined maximum deflection value is compared with the specified values in the codes and standards of practice. Most codes and standards provide the maximum allowable deflection for dead loads and superimposed live loads. ![]() Excessive deflection may result in the discomfort of the occupancy of a given structure and can also mar its aesthetics. ![]() The serviceability requirements limit the maximum deflection that is allowed in a structural element subjected to external loading.
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