# What is the magnitude of deflection in beams and how do we determine it?

When a beam is subjected to a load, it deflects from its original position.  In other words, it bends to a certain extent.  The amount of deflection depends on the beam’s cross-section and its strength.

There are two criteria for a beam: strength and stiffness.  A beam is expected to be ‘strong’ enough to resist shear forces and bending moments.  It should also be ‘stiff’ enough not to deflect beyond the permissible limit.

When loading a beam, the deformation pattern which is also known as the ‘sag’ or ‘curve’ that it makes is termed the Elastic Curve of the beam.

## Checking deflection in structures.

Architects and engineers, as well as some other professionals, use deflection the measure the movement of building beams.  Deflection is important when measuring the weight of a structure as well as how it affects the supporting beams.  A beam is needed to ensure the structure of the floors of a building, and too much movement in them can affect the structural integrity of the building.

Deflection isn’t always visible, making it important to routinely calculate the deflection rates. Overall, this helps professionals maintain the structure and safety of buildings and bridges.

## So, what determines the magnitude of deflection in beams?

There are four variables that we use to determine the magnitude of deflection in beams.  These are:

The higher intensity the load a beam is subjected to the more likely deflection is at the loaded portion of the beam.  So, the greater the applied force, the greater deflection.

### The length of unsupported members

External supports normally provide rigidity to a structure.  However, the unsupported part of the structure will undergo increasing deflection and rotation.

### The material strength

Structural materials have different elastic properties, and this will determine how they deflect when a load is applied.  The greater the strength, the smaller the deflection will be.

### The cross-section size.

Deflection is higher in slender structural members.  We can conclude the geometry of a beam will also affect its deflection.  This fact can be overlooked but it’s important to remember that we could affect the performance of a structural object by altering its geometry alone.

You can watch these excellent videos to find out some more about various structural shapes and their strength and what I-Beam strength is.

## What is the maximum allowable deflection in beams?

There is a maximum allowable deflection for structures, and it’s normally established by building codes and standards.  Limits can vary with the type and purpose of the structure, and the deflection needs to be within this limit.

Codes of Practice will limit deflection by either specifying a maximum span/depth ratio or by fixing the maximum deflection in terms of the span.  For example, a typical limitation of a reinforced concrete beam is the deflection is no more than span/250.  This is a way of controlling deflection of beams, and the resulting effect, such as crack propagation in the structure.

An additional proviso is that the deflection that takes place after construction of any partitions and finishes shouldn’t exceed either span/350 or 20mm, whichever is smaller.

It’s clear the deflections of beams under normal working loads occur within the elastic range of the material of the beam no matter whether elastic or ultimate load theory has been used in their design. Deflections of beams, therefore, are checked using elastic analysis.

The formulae for beam deflection and slope are based on the assumptions that the beam is long, slender, homogenous, has small deflections and linear elastic properties.

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