MOMENT AREA METHOD - introduction

MOMENT AREA METHOD

Introduction

1.     Whenever a structure subjected to external load, due to action of external load on the structure, beyond elastic limit the structure will deform with an eccentric distance with reference to its initial position.

2.     The deformation values are most important to be known in order to design a structure.

3.     The deformation in a structure should be within the range and if its values are large then it causes crack and damage to the structure.

4.     The most important factor on which deflection of a structure depends on bending moment and flexural stiffness.

5.     Analysis of deflection is required to solve the statically indeterminate structure.

Moment area method

1.     Moment area method is one of the important and easy ways to determine slope and deflection in various structural elements.

2.     In this method area of M/EI diagram is used compute slope and defection in a structure.

3.     There are two important theorems used to determine the slope and deflection f a structure.

4.     1^st theorem of moment area is used to determine slope of the deformed structure.

5.     2^nd theorem of moment area is used to determine value of deflection for a deformed structure with respect to its initial position.

6.     Moment area method is basically depend on classical beam theory to analyse the deflected shape of the beam

Classical beam theory

·  This theory is used to determine the deformation of the structure subjected to transverse load.

·        It is also called as Euler –Bernoulli theory.

·        Assumptions in this theory for analyzing a structure.

1.     Plane sections remains plane even after loading: Consider the large span of beam subjected to external loading .If the small portion of the beam is sectioned; then the flat portion of the sectioned beam remains flat even after action of loading (deformation).This assumption is applied for bending of beams only for transverse loads which is symmetric in nature but not for the torsional force. This assumption is also valid for the sections perpendicular to the neutral axis remains perpendicular to the neutral axis even after loading.

2.     The deformations are small compared to length of the beam.

3.     The material of the structure is elastic.

4.     The cross section of the beam remains constant throughout.

5.     The material of the beam should be homogeneous and isotropic.

6.     The length of the beam is should be greater than its cross sectional dimensions.

Under these Assumptions the relation between deflection and bending moment is given by the equation

d² y(x)/dx² = M(x)/EI

Where y = deflection in mm

 x = span to determine deflection

M = Bending moment

E = young’s modulus

I = moment of inertia of cross section of the beam.

Also watch explanation on Youtube channel,