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Strength of Materials: Axial Loading

Axial loading occurs when an object is loaded so that the force is normal to the axis that is fixed, as seen in the figure. Taking statics into consideration the force at the wall should be equal to the force that is applied to the part.

Axial Loading Diagram

To calculate the stress caused by axial loading equation 1 would be used, and to calculate the deflection caused by loading equation 2 would be used.

Axial Stress (1)

Typically the stress on a part under axial loading is constant when the cross-sectional area is constant. However, at the fixed point it can be seen that the stress can vary. This is known as Saint Venant's Principle, and can only be seen through Finite Element Analysis. Saint Venant's principle happens for any type of loading situation.

Axial Loading Diagram

Deflection Equation Axial Loading (2)

In addition to a calculating deflection and stress the stiffness of the part can be calculated by using equation 3. Stiffness is used to relate the deflection to the force required to deflect the object. Also, it could be used to calculate the natural frequencies of the part. Plus, if the force and deflection aren't known, stiffness can be used to predict how strong that part is.

Stiffness Equation Axial Loading (3)

Multiple Loading

In some cases there could be multiple axial loads placed on an object, in that case the load on each section would need to be determined by using statics, as can be seen in the following figure.

Multiple Axial Loading Problem

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