# Bending and deflection of composite beam

• Dell
In summary, there are two methods for calculating deflections in homogeneous beams: energy methods and elastic curve equations. However, for a composite beam with two different materials in its cross section, the question arises of which E and I to use in these calculations. The solution is to first determine the neutral axis or centroid of the cross section, which will be skewed towards the material with the higher Young's modulus. Then, the moment of inertia can be calculated for each part of the cross section and added together using the parallel axis theorem. This approach ensures accurate deflection calculations for composite beams.
Dell
my question is regarding calculation of deflection of a composite beam, ie a beam with a cross section made up of 2 separate homogeneous materials.

the methods i know for calculating deflections in homogenous beams are energy methods(catiglianos 2nd) and the elatic curve equations(second integral of the bending moment)

my problem is that in both of these methods(and any other method) i need to use E and I, my question is what E and what I should i use here?
originally i thought i could move over to an equivalen x-section as i would do co calculate stress from bending, expanding one material and then use the E of the other mateerial.
something just doesn't seem right doing that,, (if i used the opposite i would get totally different answers)

I guess you'll have to determine where the neutral axis or centroid is in the cross section, this will be skewed towards the material with the higher young's modulus.

then to determine I, you can determine I for each of the parts of the cross section then use the parallel axis theorem to determine their moment of inertia about the centroid and add them up like any composite material.

## 1. What is a composite beam?

A composite beam is a structural element that is made up of two or more materials with different properties, typically a combination of steel and concrete. This allows for a stronger and more efficient beam than using a single material.

## 2. How does bending affect a composite beam?

Bending refers to the deformation or curvature of a beam under load. In a composite beam, the two materials will have different responses to bending due to their different properties. The steel will resist bending, while the concrete will help to support the load and distribute it evenly.

## 3. What is deflection in a composite beam?

Deflection is the measure of how much a beam bends or deforms under load. In a composite beam, the deflection is affected by the properties of both materials and their ability to resist bending.

## 4. How is the deflection of a composite beam calculated?

The deflection of a composite beam can be calculated using the principles of mechanics and the properties of the materials used. It is important to consider the different properties of each material and how they interact to determine the overall deflection of the beam.

## 5. What are some common factors that can affect the bending and deflection of a composite beam?

Some common factors that can affect the bending and deflection of a composite beam include the properties of the individual materials, the size and shape of the beam, the type and location of the load applied, and any external forces or conditions such as temperature or moisture.

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