# Deflection

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

## Deflection

Deflection ( $$DEF$$ ) is the change in the position of something from zero or from its normal position.

### types of deflection

• angular deflection
• axial deflection
• cyclic deflection
• lateral deflection
• torsional deflection

## Angular Deflection

Angular deflection is when a flex connector is bent on it's centerline.  One end of the hose assembly is deflected or bent with the other end remaining parallel.

### Angular Deflection formula

$$\large{ l= \frac {\pi r \theta}{180} }$$

Where:

$$\large{ C }$$ = connector / coupling

$$\large{ l }$$ = hose length

$$\large{ r }$$ = minimum centerline bend radius for constant flexing

$$\large{ \theta }$$  (Greek symbol theta) = angular deflection

$$\large{ \pi }$$ = Pi

## Axial Deflection

Axial deflection is when a flex connector is compressed or stretched on it's centerline which usually occurs from the change in temperature.

## Cyclic Deflection

Cyclic deflection is the repeated change in temperature or vibration. This may be caused by the starting and stopping of pumps or other equipment.  Over time this may result in the piping system to fail.

## Lateral Deflection

Lateral deflection is when an object (flex connector) is bent off it's centerline and both of it's ends are parallel to each other.

### Lateral Deflection formula

$$\large{ l = \sqrt {6 rd \;+\; d^2} }$$

$$\large{ l_p = \sqrt {l^2 \;-\; d^2} }$$

Where:

$$\large{ C }$$ = connector / coupling

$$\large{ d }$$ = angular deflection

$$\large{ l }$$ = hose length

$$\large{ l_p }$$ = projected hose length

$$\large{ r }$$ = minimum centerline bend radius for constant flexing

$$\large{ d }$$ = offset distance from centerline

### notes

• When the offset motion occures to both sides of the hose centerline: $$2$$ times $$d$$
• The offset distance "$$d$$" for constant flexing should never exceed 25% of the centerline bend radius "$$r$$".
• If the distance "$$l$$" and "$$l_p$$" is significant, take care at installation to avoid stress on the hose and braid at the maximum offset distance.

## Torsional Deflection

Torsional deflection is the twisting of an object around its axis or centerline.  Flex connectors should not be put to this type of stress since the objects they are attached to should be secured from rotation.

Tags: Equations for Force