# Multiple Continuous Beams

The deflection of Continuous Beams with more than one span.

**Contents**

## Continuous Beams

When a

**Beam**is carried on three or more supports it is said to be**Continuous**. It is possible to use an extension of the Moment-Area method ( See "Bending of Beams Part 3") to obtain a relationship between the Bending Moments at three points (Usually Supports.)A

**beam**is a horizontal structural element that is capable of withstanding load primarily by resisting bending. The bending force induced into the material of the beam as a result of the external loads, own weight, span and external reactions to these loads is called a**bending moment**.##### MISSING IMAGE!

**23287/Multiple-Continous-Beams-108.png** cannot be found in /users/23287/Multiple-Continous-Beams-108.png. Please contact the submission author.

**Elastic Line**of the deflected Beam is shown.

The deflections and are measure relative to the left hand support and are positive upwards. is the slope of the beam over the central support and and are the intercepts for and
Note. This assumes that the slopes everywhere are small.
Note that is a negative intercept.
The above equation can be written as:
If
If the supports are at the same level:
If the Ends are Simply Supported then

## Clapeyron's Equation Or The Equation Of Three Moments

**Span**is the distance between two intermediate supports for a structure, e.g. a beam or a bridge.

Equation (2) is the most general form of The Equation of Three Moments. Equations (3) (4) and (5) are simplifications to meet particular needs. Of these Equation (4) is the form most frequently required.

Example:

[imperial]

##### Example - Example 1

Problem

A Beam Ad 60 ft. long rests on supports at , , and which are at the same level. and The loading is 1 ton/ft. throughout and in addition a concentrated load of 5 tons acts at the mid-point of and a load of 2 tons acts at

**Draw**the Shear Force and Bending Moment diagrams.Workings

Applying

**Equation (3)**to the span The Bending Moment at mid-point of The Bending Moment at the mid-point of To find the reactions at the supports: for for And By difference, From the Shear Force diagram it can be seen that the maximum Bending Moment occurs either at a distance of 13.5 ft. from where: Or at a distance of 10.5 ft. from where: The combined Bending Moment diagram is shown at the bottom of the sketch.