Strain on different parts of a cantilever

In summary: A is the cross-sectional area of the cantilever at each gauge location.Now, you have also mentioned that you need to repeat this process with the cantilever twisted to various angles. In this case, we can use the equation τ = Gθ/L, where τ is the shear stress, G is the shear modulus, θ is the angle of twist, and L is the length of the cantilever. This equation will help us find the shear stress at each point on the cantilever when it is twisted at different angles.To summarize, in order to find the theoretical strains at all of the given points on the cantilever, you will need to use the
  • #1
franks1no
1
0
Hey physics forums people, this is my first post ever and I am not sure if this is the right sub forum, but w.e, let's try this out anyways

Homework Statement


K so the problem is I've got a weight hanging on the shear centre of a cantilever and there are strain gauges all over it
It is an L shaped cantilever with a weight being hung off of the corner of the L.
If you look at the cantilever from the side, all of the gauges are on the same part of the plane...sort of like this

(FIXED) -------GAUGES----------------------(Free)
----------D1 ------------- D2

so they are all at the same distance from the free end, just different parts of the...cross section. yea.

so the lab asks me to find the theoretical strains at all of the given points on the cantilever

i know

D1
D2
The location of all of the gauges
The force applied to the end (weight x g)
The dimensions of the cross section
Young's ModulusYeah.

the kicker with this one too is that i have to repeat it with the cantilever twisted to various angles as well...pretty rockin

Homework Equations



NO IDEA...if you guys could help me out with this, that would rock.
like i know the general strain equations, but how would they change with the different angles to get to the gauges...like would i a^2 + b^2 = c^2?
and there would be different answers because some parts are in tension and others are compression

The Attempt at a Solution



Derp
Yeah any help would rock a looot
thanks guys
 
Last edited:
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  • #2


Hello and welcome to the forum! I am glad to see that you are taking the initiative to seek help with your problem. This forum is a great place to get assistance with any physics problems you may encounter.

From what I understand, you are trying to find the theoretical strains at different points on an L-shaped cantilever with a weight hanging off the corner. You have mentioned that you know the dimensions of the cross section, the location of the gauges, the force applied to the end, and the Young's Modulus. These are all important pieces of information that will help us find a solution to your problem.

To start off, we need to understand what strain is. Strain is a measure of how much an object is deformed from its original shape due to an applied force. It is usually represented as a percentage or a decimal value. In your case, we are dealing with a cantilever that is being strained due to the weight hanging off of it.

To find the theoretical strains at the given points on the cantilever, we first need to understand the concept of stress and strain. Stress is the force per unit area that is applied to an object, while strain is the resulting deformation or change in shape of the object. These two concepts are related by a material property known as Young's Modulus, which you have mentioned you know.

Now, let's look at the equation for strain: ε = ΔL/L, where ε is the strain, ΔL is the change in length, and L is the original length. In your case, the change in length will be caused by the weight hanging off of the cantilever. We can use this equation to find the strain at each of the gauges on the cantilever.

To find the theoretical strain at D1 and D2, we can use the equation ε = σ/E, where σ is the stress and E is Young's Modulus. We can find the stress at D1 and D2 by using the equation σ = F/A, where F is the force applied to the end (weight x g) and A is the cross-sectional area of the cantilever.

To find the strain at the location of all the gauges, we can use the equation ε = σ/E, where σ is the stress at each gauge and E is Young's Modulus. To find the stress at each gauge, we can use the equation σ = F/A, where F is the
 

1. What is a cantilever and how does it experience strain?

A cantilever is a long, narrow beam that is supported at only one end. It experiences strain, or deformation, when a force is applied to it, causing it to bend or deflect.

2. What are the different parts of a cantilever and how do they contribute to strain?

The different parts of a cantilever include the fixed end, the free end, and the body. The fixed end is where the cantilever is attached or supported, and it experiences the least amount of strain. The free end is where the force is applied, and it experiences the most strain. The body of the cantilever experiences strain in between the fixed and free ends.

3. How does the shape of a cantilever affect the distribution of strain?

The shape of a cantilever, specifically its length and thickness, affects the distribution of strain. A longer and thinner cantilever will experience more strain than a shorter and thicker cantilever, as the force is spread out over a larger area.

4. What is the relationship between the amount of strain and the applied force on a cantilever?

The amount of strain on a cantilever is directly proportional to the applied force. This means that the greater the force applied, the more the cantilever will bend or deflect, and the higher the strain will be.

5. How does the material of a cantilever affect its ability to withstand strain?

The material of a cantilever plays a crucial role in its ability to withstand strain. Materials with higher tensile strength, such as steel, can withstand greater amounts of strain before reaching their breaking point, while materials with lower tensile strength, such as wood, will experience strain at lower forces.

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