# I beams and moments of inertia

• joe tomei
In summary, the shape of an i-beam is considered near optimal due to its moment of inertia. This means that the material is distributed in a way that maximizes its strength without risking buckling. A square-section wooden beam can be used as an example to understand this concept, as the material can be removed from areas with lower stress and added to areas with higher stress. This idea can be further explored using Efunda's resources on moments of inertia for different sections.
joe tomei
I recall that the shape of an i-beam is near optimal because of its moment of inertia. Does any have a reference that shows this, with explanation?

Well, if you think about it, you want to have as much material as possible as far away as possible from the centroidal axis, without a risk of the web buckling.

A structural engineer once told me to imagine a square-section wooden beam, supporting it at both ends, and standing on it. He asked me where the maximum tensile and compressive forces were, and I told him; on the bottom and the top respectively. He then led me to conclude that the beam could be optimised by removing material from the areas where there was not much stress, and putting more material where the stresses were high. Not very scientific, but the reasoning is sound.

Efunda has some nice pages relating to moments of inertia of various sections. If you want to prove this for yourself, just plug in some numbers and see how it affects your second moment of area.

## 1. What is an I beam?

An I beam, also known as an H beam or double-T beam, is a structural beam with an I or H-shaped cross-section. It is commonly used in construction and engineering due to its high strength and stiffness.

## 2. How is the moment of inertia related to I beams?

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. In the case of I beams, it represents the beam's ability to resist bending and torsion. A higher moment of inertia means a stronger and stiffer beam.

## 3. What factors affect the moment of inertia of an I beam?

The moment of inertia of an I beam is affected by its cross-sectional shape, size, and material properties. Generally, a larger and more spread out cross-section will result in a higher moment of inertia.

## 4. How is the moment of inertia calculated for an I beam?

The moment of inertia for a simple I beam can be calculated using the formula I = (b*h^3)/12, where b is the base width of the beam and h is the height of the beam's cross-section. However, for more complex I beams with varying cross-sections, the moment of inertia can be calculated using integration methods.

## 5. Can the moment of inertia be increased for an I beam?

Yes, the moment of inertia can be increased for an I beam by increasing its cross-sectional area, changing its shape to a more spread out one, or using a stronger and stiffer material. This can be done to make the beam more resistant to bending and torsion forces, resulting in a stronger and more stable structure.

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