Pure bending:
Pure bending of a beam refers to the condition of a beam loaded under a constant bending moment and shear force on it is zero. So in solid mechanics pure bending means the bending of a beam under the effect of a constant bending moment only. When considering of pure bending we assume no shear force or transverse force acts on it.
But in real cases when a beam is loaded under a certain load, pure bending is not possible in the whole length of the beam. Instead we can consider a portion of the length where bending moment is constant and shear force is zero.
\(\frac{dM}{dx}\) = Shear force = 0
or, \(\frac{dM}{dx}\) = 0
So, bending moment (M) = Constant
Assumptions made in theory of pure bending:
- The material of the beam is homogeneous and isotropic.
- The beam is loaded within the elastic limit. All the permissible stresses are within elastic limit.
- Initially the beam is straight and bends into a circular arc when subjected to pure bending.
- Young’s modulus in both tension and compression are same.( when a section is under pure bending its top layers are in compression and bottom layers are in tension.
- All transverse sections remain plan even after bending. (if its not pure bending the sections will be curved due to shear stresses)
- The cross section of the beam is symetrical about the plane of loading.
