# Bending moment definition equation Calculation and diagram

Bending moment definition equation Calculation and diagram, hi guys in this article we know about bending moment definition equation Calculation and diagram. As we know bending moment and shearing forces are very important factor to be considered during the designing of any structural component like Beem.

There are two types of Forces acting on in first one is transverse load acting perpendicular on beam and second one is shearing process which is acting along axial direction of beam. When transverse load is applied over structural member like Beam it will be band.

## What is definition of bending moment

A bending moment is the reaction induced in a structural member when an external force or transverse load or moment is applied to the member causing the member to bend.The most common or simplest structural member subjected to bending moments is the beam.

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### Types of bending moment

When transverse load is acting perpendicular to neutral axis of structural members is known as bending. Bending in structural member is 2 types sagging and hogging

1) Sagging

2) Hogging

### What do you mean by sagging bending moment

1) Sagging:- If we have simply supported beam a structure member which is supported at both end by column when load is applied on beam it will experience positive bending moment and bend in concave face structure in downward direction like Cup shaped.

in concave face there is three layer middle one is known as neutral axis, below middle layer there is a tension layer and upper of neutral layer is known as compression layer. For simply supported beam top fiber is compression zone and bottom fibre is tension zone.

Note:- top compression zone is taken as positive sign and bottom compression zone is taken as negative sign.So sagging is positive bending moment.

### What do you mean by hogging bending moment

2) Hogging:- negative bending moment hogging is found in cantilever beam which supported only one end by supporting member that is column and second end is free.

when load is applied on cantilever beam it will experience negative bending moment and bend in convex structure in upward direction. top of convex face is in maximum tension and below face in maximum compression.

there is a neutral layer between maximum tension layer and maximum compression layer. And hogging is negative bending moment because of bottom compression zone.

### What is bending moment diagram

Bending moment at a section of beam is defined as algeberic sum of moment of all the transverse load or forces acting on one side of the section.

For example following figure which shows the the bending moment diagram of simply supported beam suppose F1 F2 F3 and F4 are the applied load on the beam and RA and RB are the support reaction. X-X is the section of point of equilibrium between two half. LA is distance between section X-X and supporting member RA left side and LB is distance between section X-X and supporting member RB right side

And X is distance between two supporting chamber and X1 is distance between cross section x-x and F1left side , X2 is distance between cross section x-x and F2 left side, X3 is distance between cross section x-x and F3 right side, X4 is distance between cross section x-x and F4 right side.

Based on sign convention we can write equation for the bending moment at cross section x-x

1) left of section x-x

Mx = RA×LA _ F1X1 _ F2X2

2) right of section x-x

Mx = RB×LB _ F3X3 _ F4X4

Equation is known as bending moment equation

### Sign convention of bending moment

1) sagging is results of developing tension in the bottom and compression in the top fibre of The Beam have positive bending moment, and it is represented by (+ BM)

2) Hogging is result of developing tension in top and compression in the bottom fibre of the beam that is negative bending moment and it is represented by( _ BM)