ES 3

• Bending is a major concept in the design of many machine and structural components such as beams.
• Members that are subjected to equal and opposite couples acting in the same longitudinal planes are said to be in pure bending, where the members are assumed to possess a plane of symmetry and the couples to be acting in that plane.
• The internal forces in any cross section of a symmetric member in pure bending are equivalent to a couple.
• The moment M of that couple is referred to as the bending moment in the section. The bending moment is positive when the member is bent, when the concavity of the beam faces upward. Otherwise, it is negative.
• From statics, a couple consists of two equal and opposite forces. The sum of the components of these forces in any direction is therefore equal to zero.
• The moment of the couple is the same about any axis perpendicular to its plane, and is zero about any axis contained in that plane.
• A prismatic member subjected to equal and opposite couples M and M' acting in the plane of symmetry will bend under the action of these couples but will remain symmetric with respect to that plane.
• The only nonzero stress component exerted on any element is the normal component.
• Any point of a slender member in pure bending is in a state of uniaxial stress.
• The neutral surface intersects the plane of symmetry along an

  arc of circle and it intersects a transverse section along a straight line called the neutral axis of the section.
• Torsion refers to the twisting of a structural member when it is loaded by couples that produce rotation about its longitudinal axis. The moment of the couple is equal to the product of one of the forces and the

  perpendicular distance between the lines of action of the forces.
• The equation may be called the equation of compatibility, since the stresses expressed by it are compatible with the elastic deformations.