Question

Establish the relationM/I= f/y=E/R with usual notation

Answer 1

Answer:

The material of the beam is stressed within elastic limit and obeys Hooke’s law.

The transverse sections which are plane before bending remains plane after bending.

The material of the beam is perfectly homogenous.

Each layer of the beam is free to expand and contract independently of the layer, above or below it

The value of young’s modulus for the material of beam is same in tension and compression.

Explanation:

M/I = σ/y = E/R

Where, M= bending moment,

 I=Moment of inertia of the area of cross section.

 σ=Bending stress

 y=distance of extreme fibre from the neutral axis

E=Young’s modulus

 R=radius of curvature.

From the bending equation   M/I = σ/y

        Or, M = σI/y = σ Z, where Z is the section modulus

The line of intersection of the neutral layer with any normal cross section of a beam is known as neutral axis of that section.

BEAMS OF UNIFORM STRENGTH

Explanation: