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Now you know how to find a Second Moment of Area you may be wondering what you can do with it and the key lies in beam theory. This is covered in more depth here but the important part here is the following equation:
Which can then be integrated twice to give:
Where F is the force applied, δ is the maximum amount the beam is deflected form its original position and C1 is a geometrical constant.
Once you have the second of these equations the Second Moment of Area can be used, along with other known constants of the material and the force being applied, to find the amount that a beam will be deflected. This could also be taken with a maximum known deflection and force to be experienced to determine what material properties are needed.
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