If a beam is undergone with simple bending, beam deforms under action of bending moment. If this bending moment is constant and does not affect by any shear force, n beam is in state of simple bending.

The beam being subjected to pure bending, re will be only bending moment and no shear force it results in formation of an arc of circle with some radius known as radius of curvature.

It is one of most important assumptions made in ory of simple bending that is modulus of elasticity that is Young?s modulus [E] is same in both tension and compression for material and stress in a beam do not exceed elastic limit.

The above-mentioned equation is absolutely correct.
E/R = M/I = f/y is a bending equation. It is also known as flexure equation (or) equation for ory of simple bending.
Where,
E stands for Young?s modulus or modulus of elasticity.
R stands for radius of curvature.
M stands for bending moment
I stand for moment of inertia
f stands for bending stress
y stands for neutral axis.

Shearing stress is defined as resistance offered by internal stress to shear force. Shearing stress in a beam is maximum at a neutral axis.

Neutral axis is defined as a line of intersection of neutral plane or neutral layer on a cross section at neutral axis of that section. At NA, bending stress or bending strain is zero. The first moment of area of a beam section about neutral axis is also zero. The layer of neutral axis neir contracts nor extends.

From flexural equation, we have 1/R is called as ?curvature of beam?.
1 / R = M / EI
Hence curvature of beam is directly proportional to bending moment and inversely proportional to flexural rigidity (EI).

The product of young?s modulus (E) of material and moment of inertia (I) of beam section about its neutral axis is called flexural rigidity.
Units for E are N/m²
Units for I are m⁴
Their product is Nm².

The ratio of moment of inertia to distance to extreme fibre is called modulus of section or section modulus. It is generally denoted by letter Z. Section modulus is expressed in m³
Z = I/y
= m⁴/ m
= m³.

Axial rigidity is a product of young?s modulus (E) and cross-sectional area (A) of that section. Axial rigidity per unit length is known as axial stiffness si units of axial stiffness are Newton per metre (N/m).