Stress strain laboratory question

[xzibition8612]

Homework Statement

Establish the constitutive relationship for the cantilever beam material, i.e., provide an empirical formula for the relationship σ_xx=σ_xx(ε_xx) and generate a plot of this relationship. What is the cantilever beam material?

Homework Equations

This is a pure beam bending theory lab, rosette gauge on beam with loads and displacements from a precision micrometer.

The Attempt at a Solution

Not really sure what this question is asking. Also I'm confused about the equation. Wouldn't the stress xx just cancel out and ε_xx=1?? I got a bunch of data on the beam from the rosette gauge, but I don't really get this question. Any help on shedding what its asking would be great. thanks.

 

[Undoubtedly0]

Greetings xzibition8612! The notation $\sigma_{xx}(\epsilon_{xx})$ means "find $\sigma_{xx}$ as a function of $\epsilon_{xx}$". For example, a beam under uniaxial tension might obey $\sigma_{xx}(\epsilon_{xx}) = E\epsilon_{xx}$, where $E$ is the elastic modulus.

 

[xzibition8612]

alright i figured it out using your formula. So this is my result. Now the question is what kind of material follows this graph? Anyone know or where can i find this info? By the way strain is in micro strain, or 10^-6.

thanks

 

[Undoubtedly0]

Given your graph you should be able to find the elastic modulus of the material. Then you may need to consult some tables to see which material has that same elastic modulus.

 

[rezeew]

I would suggest approaching this question by first clarifying any confusion about the equation and the data collected. It is important to fully understand the concepts and variables involved before attempting to establish a constitutive relationship for the cantilever beam material. This relationship is a mathematical representation of how stress (σxx) is related to strain (εxx) for the specific material being studied.

To establish this relationship, you can use the data collected from the rosette gauge on the beam and plot it on a graph, with stress (σxx) on the y-axis and strain (εxx) on the x-axis. This will help to visualize the relationship between the two variables and identify any trends or patterns.

The cantilever beam material refers to the specific material used for the beam in this experiment. It could be any type of material, such as metal, wood, or plastic. The empirical formula for the constitutive relationship will be unique to this specific material and can be used to predict the stress-strain behavior of similar materials.

In summary, the goal of this laboratory question is to establish a mathematical relationship between stress and strain for a specific material, using data collected from the beam. It is important to fully understand the concepts and equations involved before attempting to solve the problem.