Critical Buckling loads-how to plot?

In summary, to determine the mode of failure, we must compare the calculated stress from the bending stress equation to the critical load calculated from the Euler's buckling equation. If the calculated stress is greater than the critical load, the mode of failure is due to buckling, and if the calculated stress is less than the critical load, the mode of failure is due to bending. To plot a graph, we can plot the bending stress equation as a function of applied load and the Euler's buckling equation as a function of column length.
  • #1
clockworkrobot
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Homework Statement


Hi all,
I am an architect so engineering is not my strong point. for these equations I am unsure how to correctly determine the mode of failure and plot a graph. Any help would be greatly appreciated. Also the attached files have the formulas written and question written down.

Homework Equations

The Attempt at a Solution

 

Attachments

  • BTSQ1.pdf
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  • BTSQ2.pdf
    1.4 MB · Views: 303
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  • #2


Hello,

I understand that engineering concepts can be difficult to grasp for those outside of the field. However, I am happy to assist you with determining the mode of failure and plotting a graph for these equations.

To determine the mode of failure, we first need to understand the equations and their variables. From the attached files, it seems that the equations are related to structural analysis. The first equation appears to be the bending stress equation, which calculates the stress on a beam under a specific load. The second equation is the Euler's buckling equation, which determines the critical load at which a column will buckle and fail.

To determine the mode of failure, we need to compare the calculated stress from the bending stress equation to the critical load calculated from the Euler's buckling equation. If the calculated stress is greater than the critical load, then the mode of failure is due to buckling. If the calculated stress is less than the critical load, then the mode of failure is due to bending.

As for plotting a graph, we can plot the bending stress equation as a function of the applied load. This will give us a curve that shows the relationship between stress and load. We can also plot the Euler's buckling equation as a function of the column length. This will give us a curve that shows the critical load for different column lengths.

I hope this helps you with your question. Let me know if you need any further clarification or assistance. Good luck with your work!
 

Related to Critical Buckling loads-how to plot?

What is a critical buckling load?

A critical buckling load is the maximum load that a structural component can withstand before it buckles and fails due to compressive forces. It is a critical design parameter in engineering as it indicates the stability of a structure.

What factors affect the critical buckling load?

The critical buckling load is affected by various factors such as the material properties of the structural component, its geometry, and the boundary conditions. Other factors include imperfections and eccentricities in the structure, as well as the type of loading applied.

How is the critical buckling load calculated?

The critical buckling load is typically calculated using mathematical equations and analytical methods, such as the Euler buckling equation or the Rayleigh-Ritz method. These methods take into account the various factors that affect the critical buckling load to determine the maximum load capacity of a structure.

What is the purpose of plotting the critical buckling load?

Plotting the critical buckling load helps engineers and scientists visualize the relationship between the applied load and the resulting buckling behavior. This information is crucial in determining the safety and stability of a structure and can aid in optimizing the design to withstand higher loads.

What are some common methods for plotting critical buckling loads?

Some common methods for plotting critical buckling loads include using software programs such as finite element analysis (FEA), conducting physical experiments, or using theoretical calculations. Each method has its advantages and limitations, and the choice often depends on the specific needs and resources of the project.

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