Buckling Failure of Metallic Structure

Buckling failure is another form of compression failure. When structural engineers talk about buckling they are normally referring to Euler Johnson column buckling failure or plate buckling failure. I will cover both of these in this post.

Plate buckling refer to failure of thin sheets, which can occur under shear or compression loading. The allowable buckling stress is calculated using the following equation:



Where

v = poisson ratio

b = width of plate

t = thickness of plate

E = Youngs modulus

k = constant function of plate width and length.


The constant k above can be found in many text books such as bruhn, flabel, niu ... Note that the derivation of this constant is quite extensive.

Note that the derivation of this constant is quite extensive and not the intent of this website. The figure below shows some of the k values for a flat plate under compression.



Column buckling is very similar to plate buckling in terms of mathematical equations. The critical column buckling stress is calculated as follow:




Where L is the length of the column.

Note that the above equation is commonly referred to as the Euler Johnson equation.



Disclaimer: The content on this site is provided as general information only and should not be taken as engineering advice. All site content, including advertisements, shall not be construed as a recommendation to specifically analyze a stress problem. The ideas expressed on this site are solely the opinions of the author(s) and do not necessarily represent the opinions of sponsors or firms affiliated with the author(s). Any action that you take as a result of information, analysis, or advertisement on this site is ultimately your responsibility. Consult professional adviser before making any engineering decisions. 

Crippling Failure Part 2

One of the most common equation for crippling is shown below:

Fcc = (Ce*(Fcy*Ec)^0.5)/(b'/t)^3/4

Where
Fcc = Allowable crippling stress
Fcy = yield compression stress allowable
Ec = elastic modulus of material in compression
Ce = material boundary coefficient
b'/t = equivalent width over thickness ratio

Reference: Practical Stress Analysis for Design Engineers, Jean-Claude Flabel

As mentioned in the part 1 post of crippling failure, you can observed from the crippling allowable equation that it is not a function of length but only a function of material properties and width/thickness ratio whereas buckling is a function of length. This is an important distinction between crippling and buckling. For clarity the Euler column buckling equation is shown below:

Pcr-buckling = (Pi^2*E*I)/L^2

Where
Pcr = Critical buckling load
E = Elastic modulus of material in compression
I = moment of inertia about the failure axis of the column
L = column length

The above buckling equation is based on a pinned-pinned type boundary column. As shown the buckling is a function of column length.

Example Problem:

Assuming a flange with a width of 1.2 in and a thickness of 0.1in thick. The crippling allowable stress can be calculated:

Ce = 0.317 (1 edge free aluminum - Ref Flabel)
Fcy = 34 ksi (2024-T3 ref MMPDS)
Ec = 11.0 x 10^6

Fcc = 0.295*SQRT(34000*11*10^6)/(1.2/0.1)^(3/4) = 27.9ksi

Disclaimer: The content on this site is provided as general information only and should not be taken as engineering advice. All site content, including advertisements, shall not be construed as a recommendation to specifically analyze a stress problem. The ideas expressed on this site are solely the opinions of the author(s) and do not necessarily represent the opinions of sponsors or firms affiliated with the author(s). Any action that you take as a result of information, analysis, or advertisement on this site is ultimately your responsibility. Consult professional adviser before making any engineering decisions. 

Crippling Failure Part 1

Crippling is a phenomenon that occurs in a member that is under compression with sufficiently short length to prevent instability. Unstable members under compression tend to buckle as shown in figure below.

I will go over buckling some other time, but the key point to remember here is that a long member doesn't have the lateral stability for crippling to occur because the long member will fail under buckling before crippling. Stability in aircraft are generally provided by web and skin members. As compression force increases, these mating members will tend to hold the stability of the main load carrying part. Hence allowing the part to reach crippling. For example look at the sketch below. 

In the first sketch the compression load is evenly distributed across the entire section of the plate. As the compression load is increase the plate will buckle and it won’t be efficient is carrying load. As I like to say “ the load is not stupid”, if the plate can no longer carry load it will try to look for an alternative path. As you can see in Sketch 2, the load runs to the stiffer side supported by the I beams. Failure of this structure will occur when the supported sides reaches compression yield strength of the material. This yield strength can be think of as the crippling strength.

Using the same thinking, an L angle can have it’s flanges buckle as the compression load increases. As the compression load further increase the load will “run” to the stiffer corner of the L-angle. Further increase in load will cause the L-angle to fail  under what we call crippling. This brings us to another key point about crippling, the crippling allowable is a function of the structures geometry. Generally, the more corner a section has, the higher the crippling allowable. For example an U-section will have an higher L-section crippling allowable as I will prove later on in another post. This post was just intended to give you an overview of what crippling is and I hope it did the job. If you have any comments, questions or correction please leave me a comment. Stay tuned for the hardcore calculations on crippling soon.  

Disclaimer: The content on this site is provided as general information only and should not be taken as engineering advice. All site content, including advertisements, shall not be construed as a recommendation to specifically analyze a stress problem. The ideas expressed on this site are solely the opinions of the author(s) and do not necessarily represent the opinions of sponsors or firms affiliated with the author(s). Any action that you take as a result of information, analysis, or advertisement on this site is ultimately your responsibility. Consult professional adviser before making any engineering decisions.