Transcription of Stresses: Beams in Bending - MIT OpenCourseWare
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Stresses: Beams in Bending - MIT OpenCourseWare
9 Stresses: Beams in Bending The organization of this chapter mimics that of the last chapter on torsion of cir-cular shafts but the story about stresses in Beams is longer, covers more territory, and is a bit more complex. In torsion of a circular shaft, the action was all shear; contiguous cross sections sheared over one another in their rotation about the axis of the shaft. Here, the major stresses induced due to Bending are normal stresses of tension and compression. But the state of stress within the beam includes shear stresses due to the shear force in addition to the major normal stresses due to Bending although the former are generally of smaller order when compared to the latter. Still, in some contexts shear components of stress must be considered if failure is to be avoided. Our study of the deflections of a shaft in torsion produced a relationship between the applied torque and the angular rotation of one end of the shaft about its longitudinal axis relative to the other end of the shaft.
mation of the beam. 9.1 Compatibility of Deformation We consider first the deformations and displacements of a beam in pure bending. Pure bending is said to take place over a finite portion of a span when the bending moment is a constant over that portion. Alternatively, a portion of a
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