Bending of a beam under uniform bending moment

When a beam is subjected to a uniform bending moment throughout its length, it undergoes bending in the form of a circular arc. This is because the bending moment produces a curvature in the beam, and the curvature of a circular arc is the most natural and uniform form of curvature.

Explanation

When a beam is subjected to a uniform bending moment, the beam experiences a moment of force that varies linearly along its length. This moment of force produces a curvature in the beam, which is proportional to the moment of force and the flexural rigidity of the beam. The flexural rigidity of a beam depends on its geometry and material properties, and it determines the resistance of the beam to bending.

When the bending moment is uniform along the length of the beam, the curvature of the beam is also uniform. In this case, the beam bends in the form of a circular arc, with the center of curvature located at the midpoint of the beam. The radius of curvature of the arc is proportional to the bending moment and the flexural rigidity of the beam.

The circular arc is the most natural and uniform form of curvature for a beam under uniform bending moment, because it minimizes the bending stresses and strains in the beam. The circular arc distributes the bending stresses and strains evenly along the length of the beam, and it ensures that the beam undergoes pure bending without any axial or shear deformation.

Conclusion

In summary, a beam of constant section that is subjected throughout its length to a uniform bending moment will bend in the form of a circular arc. This bending is the most natural and uniform form of bending for a beam under uniform bending moment, and it ensures that the beam undergoes pure bending without any axial or shear deformation.