# Deflection of cantilever beam having two Young's modulas

In summary, the formula for a cantilever beam with two different Young's Modulas and moments of inertia is:
what is the formula for the cantilever beam having two different young's modulas and moment of inertia, when a point load is acting on the free end.

i have been trying but unable to get the formula. if the formula i can validate my project work and complete it

what is the formula for the cantilever beam having two different young's modulas and moment of inertia, when a point load is acting on the free end.

i have been trying but unable to get the formula. if the formula i can validate my project work and complete it
I'm afraid this description of the beam and the materials composing it is a little vague.

Are we talking something like a leaf spring, with two different materials lapped together? Is one portion of the length of the beam one material, and the rest of the beam composed of another material?

You should try to be as specific as possible about the construction of your beam. Pictures always help.

Each material has only one Young's Modulus value. If there are two involved, then there must be two materials and the geometry of the two becomes significant.

SteamKing said:
I'm afraid this description of the beam and the materials composing it is a little vague.

Are we talking something like a leaf spring, with two different materials lapped together? Is one portion of the length of the beam one material, and the rest of the beam composed of another material?

You should try to be as specific as possible about the construction of your beam. Pictures always help.
Yes, your right one length one material and rest of the length will be another material...

I derived the formula using basic govering equation yesterday and verified it with MATLAB program for cantilever beam. Both the results are correct, it is used for having two different materials and moment of inertia for a cantilever beam.

OldEngr63 said:
Each material has only one Young's Modulus value. If there are two involved, then there must be two materials and the geometry of the two becomes significant.
yes sir, i have posted formula. i hope it is correct and useful.

## 1. What is a cantilever beam?

A cantilever beam is a type of structural element that is supported at only one end, with the other end projecting freely into space. It is commonly used in construction and engineering to provide support for structures such as bridges, balconies, and shelves.

## 2. How does a cantilever beam behave under load?

When a load is applied to a cantilever beam, it experiences both bending and shear stresses. The bending stress causes the beam to deflect, or bend, while the shear stress causes it to twist. The magnitude of these stresses depends on the type and magnitude of the load, as well as the material properties of the beam.

## 3. What is Young's modulus?

Young's modulus, also known as the modulus of elasticity, is a measure of the stiffness of a material. It describes the relationship between stress and strain in a material under tension or compression. The higher the Young's modulus, the stiffer the material is.

## 4. How do two different Young's moduli affect the deflection of a cantilever beam?

The deflection of a cantilever beam is directly proportional to the Young's modulus of the material. Therefore, if a cantilever beam is made of two different materials with different Young's moduli, the deflection will be greater in the material with the lower modulus and less in the material with the higher modulus.

## 5. What are the factors that affect the deflection of a cantilever beam with two Young's moduli?

The deflection of a cantilever beam with two Young's moduli is affected by several factors, including the type and magnitude of the load, the geometry of the beam, and the material properties of the two materials. Other factors such as temperature, humidity, and aging of the materials can also have an impact on the deflection. Additionally, the method of support and the boundary conditions of the beam can also affect its deflection.

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