# What is the deflection of a structure and what determines its magnitude?

If you’ve read our previous articles on how to determine forces on a joint or structure,  you’ll know that there are many different calculations used in civil engineering.  Now we’re going to change direction slightly and take a look at deflection and what it is.

## What is deflection?

When a beam or cantilever is subjected to loading, it deflects from its initial position.  The amount of deflection depends on the beam’s cross-section and its strength.

Let’s have a look at two criteria for a beam: strength and stiffness.  The beam is expected to be ‘strong’ enough to resist shear forces and bending moments.  However, it should also be ‘stiff enough not to deflect beyond the permissible limit.

During the process of subjecting a beam to loading, the deformation pattern (we say ‘sag’ or ‘curve’) the deflected beam makes with the original neutral axis is termed the Elastic Curve of the beam. The angle of the elastic curve is known as the slope (in radians).

## How do we check deflection in structures?

Architects and engineers use deflection to measure the movement of beams in a building. Other professionals who work with structural engineering, including researchers or building designers, may also work with deflection. Deflection is important for measuring the weight of a structure and how it affects the supporting beams. A beam is necessary to ensure the structure of building floors, and too much movement can affect the overall structural integrity of the building.

Deflection isn’t always visible, so it’s important to routinely calculate the deflection rates to help professionals maintain the structure and safety of buildings and bridges.

## What determines the magnitude of deflection in beams?

The four variables that determine the magnitude of deflection in beams are:

The higher the intensity of loading a beam is subjected to, the greater the tendency for deflection to occur at the loaded portion of the beam. In other words, the greater the applied force, the greater the deflection.

ii. The length of unsupported members:

External supports generally provide rigidity to a structure. However, as we move away from the supports, the unsupported portion of the structure undergoes increasing deflection and rotation.

iii. The material strength [specifically the Young’s Modulus (E)]:

Structural materials have different elastic properties (accounted for in Young’s Modulus, E) and this also determines how they deflect under an applied load. The greater the strength and hence the greater the Young’s Modulus, the smaller the deflection will be.

iv. The cross-section size (specifically the Moment of Inertia (I))

Deflection is higher in slender structural members, and this property is accounted for in the Moment of Inertia, I.  Therefore, we can conclude that the geometry of a beam also affects its deflection. This is an often-overlooked fact, but it is important to remember that we can affect the performance of a structural member by altering its geometry alone.

## Maximum Allowable Deflection in Beams

It is important to note that there is a maximum allowable deflection for structures, and that this value is usually established by building codes and standards. Generally, the limits vary with the type of structure and the purpose of the structure.

Codes of Practice limit deflections of beams either by specifying maximum span/depth

ratios or by fixing the maximum deflection in terms of the span. This is a way of controlling deflection of beams, and the resulting effect, such as crack propagation in the structure.

We’re going to continue with more articles on deflection in structures, so keep an eye out for more in this series.

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