Pure bending occurs when a prismatic member possesses a plane of symmetry and experiences couples of equal magnitudes acting within that plane. This type of bending occurs without the influence of direct forces.
For example, pure bending can be observed in the middle portion of a barbell being lifted by a weightlifter. Here, no direct forces are applied to the central part of the barbell. Instead, the weight at each end creates equal and opposite moments, resulting in bending.
When a person climbs a ladder, the ladder's rungs experience pure bending due to the moment generated by the person's weight.
Pure bending analysis is also used to examine beams or prismatic members subjected to transverse loads. In a cantilever beam supporting a concentrated load at its free end, the distribution of normal stresses can be obtained from the couple as if the beam were in pure bending.
It can also be used in studying stresses and deformations in composite members made of more than one material, such as reinforced concrete beams.
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.