20.1: Bending
Pure bending is a fundamental concept in structural mechanics, essential for understanding how materials deform under symmetrical loads without direct forces. Pure bending occurs when prismatic members, such as beams, are subjected to equal and opposite moments that induce bending. The phenomenon is crucial as it allows for predicting stress distributions without the influence of axial or shear forces.
In pure bending, the bending stress in a beam is calculated based on the bending moment and the geometric properties of the beam's cross-section, specifically the moment of inertia and the distance from the neutral axis to the extreme point on the cross-section. This calculation helps determine how much a beam will bend under a given load and ensures it can withstand such stresses without failing.
Practical applications of pure bending are commonly observed in everyday scenarios, such as weightlifting with a barbell, where the weights at the ends create bending in the bar's middle portion without direct forces acting upon the middle part of the bar. Similarly, ladder rungs undergo pure bending when a person climbs, as the climber's weight generates moments across each rung.
Combining different materials, such as concrete and steel, requires an analysis that accounts for their distinct properties in more complex structures like reinforced concrete beams. This composite approach aids in understanding how each material contributes to the overall strength and deformation of the beam under bending.
