How Can Strain Be Calculated from Force Displacement Data in a Cantilever Beam?

In summary: L^2/(6*displacement), and assuming that strain is equal to y/R (as found online), he would have an expression for the curvature of L^2/(6*displacement). This doesn't seem correct to me though.
  • #1
nomority
4
0
Hi everyone. I feel there should be a simple answer to this but I can't seem to find anything on this.

So I have a simple cantilever beam, supported at one side and loaded at the free end. I have the force displacement data and can easily calculate the stress.

However, for the strain I do not want to use Hookes Law, but instead calculate the strain from the force displacement data. Any hints?

Thanks!
 
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  • #2
nomority said:
Hi everyone. I feel there should be a simple answer to this but I can't seem to find anything on this.

So I have a simple cantilever beam, supported at one side and loaded at the free end. I have the force displacement data and can easily calculate the stress.

However, for the strain I do not want to use Hookes Law, but instead calculate the strain from the force displacement data. Any hints?

Thanks!
The strain varies through the cross section of the beam. It is equal to the distance from the neutral axis times the curvature. So if you know the curvature at any location, you know the strain variation through the thickness. The strain is positive on the outside of the bend, and negative on the inside of the bend. Of course, it also varies with distance along the beam.

Chet
 
  • #3
Apologies, I should have stated I am looking for the maximum strain.

I have got the full force-displacement data of a bend experiment. I know the geometry of the beam (triangular cross section) so can calculate the maximum stress at any time as (M*y)/I, which for the triangular cross-section is equal to (24*Force*Length)/(width*thickness^2).

In a code I have access to it states that the maximum strain at any time would be equal to (2*displacement*thickness)/(Length^2), but I can't figure out why this would be the case.
 
  • #4
nomority said:
Apologies, I should have stated I am looking for the maximum strain.

I have got the full force-displacement data of a bend experiment. I know the geometry of the beam (triangular cross section) so can calculate the maximum stress at any time as (M*y)/I, which for the triangular cross-section is equal to (24*Force*Length)/(width*thickness^2).

In a code I have access to it states that the maximum strain at any time would be equal to (2*displacement*thickness)/(Length^2), but I can't figure out why this would be the case.

Where does the maximum curvature occur, and, in terms of the displacement , what is that curvature?

Chet
 
  • #5
Thanks for your reply. Maximum curvature is at the fixed end. However, I can't measure the curvature to any degree of accuracy, as such for the sake of this problem it is not available.
 
  • #6
What I meant was, analytically , what is the curvature in terms of the displacement ?
 
  • #7
I'm not sure how I could describe the curvature in terms of the parameters I have.

If I was to reverse engineer the equation for strain I have

(2*displacement*thickness)/(Length^2)
, and assume that strain is equal to y/R (as found online), I would have an expression for the curvature of L^2/(6*displacement). This doesn't seem correct to me though.
 
  • #8
If you know the maximum stress, you can get the maximum strain using Young's modulus and Hooke's law.

The stresses and strains in the beam are statically determinate. They only depend on the applied loads, not on the displacement of the beam.
 
  • #9
nomority said:
I'm not sure how I could describe the curvature in terms of the parameters I have.

If I was to reverse engineer the equation for strain I have


, and assume that strain is equal to y/R (as found online), I would have an expression for the curvature of L^2/(6*displacement). This doesn't seem correct to me though.
Step 1: Express the bending moment M at the built-in end in terms of the load F.
Step 2: What is your equation for the displacement in terms of the load F.
Step 3: Combine these relationships to get the bending moment in terms of the displacement.
Step 4: Determine the curvature from the bending moment
Step 5: Determine the curvature as a function of the displacement
Step 6: Determine the strain from the curvature

chet
 

1. What is meant by strain in a cantilever beam?

Strain in a cantilever beam refers to the deformation or change in length that occurs in the beam when a load is applied to it. It is a measure of the amount of stress that the beam experiences due to the applied load.

2. How is strain calculated in a cantilever beam?

Strain in a cantilever beam is calculated by dividing the change in length of the beam by its original length. This is also known as the engineering strain and is typically expressed as a decimal or percentage.

3. What factors affect strain in a cantilever beam?

The primary factors that affect strain in a cantilever beam are the magnitude and direction of the applied load, the length and dimensions of the beam, and the type of material the beam is made of. The stiffness of the beam and any external supports or restraints can also impact strain.

4. How does strain impact the strength of a cantilever beam?

Strain is directly related to the stress that a beam experiences, and therefore, it can also impact the strength of the beam. Too much strain can cause the beam to fail, while some amount of strain is necessary for the beam to be able to support a load without breaking.

5. What are some methods for reducing strain in a cantilever beam?

To reduce strain in a cantilever beam, the load can be spread out over a larger area, the beam can be made thicker or with a stronger material, or additional supports can be added. The beam can also be designed with a different shape or with reinforcement to better distribute the load and reduce strain.

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