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Stresses: Beams in Bending

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.

The extensional strain of the longitudinal elements of the beam is the most important strain component in pure bending. The shear strain γ we have shown xy to be zero; right angles formed by the intersection of cross sectional planes with longitudinal elements remain right angles. This too is an important result. Symme-

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