What are the assumpions made in the theory of pure bending?

What are the assumpions made in the theory of pure bending?

The theory of pure bending relies on several key assumptions: the material is homogeneous and isotropic, the beam is initially straight, plane sections remain plane after bending, and the material obeys Hooke's law within the elastic limit. 

Here's a more detailed breakdown of the assumptions:

Homogeneous and Isotropic Material:

The material of the beam is assumed to be uniform throughout (homogeneous) and have the same properties in all directions (isotropic). 

Initial Straightness:

The beam is considered to be initially straight before any bending occurs. 

Plane Sections Remain Plane:

Transverse sections of the beam that are plane before bending remain plane after bending. 

Material Obeying Hooke's Law:

The material is assumed to behave elastically and obey Hooke's law, meaning stress is directly proportional to strain within the elastic limit. 

Modulus of Elasticity is the Same in Tension and Compression:

The material's Young's modulus (a measure of stiffness) is assumed to be the same whether the material is under tensile or compressive stress. 

Large Radius of Curvature:

The radius of curvature of the bent beam is assumed to be large compared to the dimensions of the cross-section. 

No Shear Forces:

The theory of pure bending specifically deals with situations where bending moments are present, but shear forces are negligible. 

Symmetrical Cross-section:

The beam's cross-section is typically assumed to be symmetrical about the plane of bending. 

Independent Expansion/Contraction:

Each layer of the beam is assumed to be free to expand or contract independently of the layers above or below it.