Shear Buckling of Isotropic Panels – Post 1

April 14, 2016

Writing the text book has been a good opportunity to go and re-examine the fundamentals of panel buckling analysis.

Shear Buckling of a thin (elastic) panel is a good place to start.

First of all, Terms:

Basic Buckling Equation

General Buckling Terms 2

Why use the term elastic buckling? When you use Young’s Modulus to calculate the buckling allowable no allowance is given for yielding of a ductile material such as aluminum. For relatively stable panels the theory above can give very high buckling allowables, greater than the ultimate strength of the material. This is not realistic and the result from this type of analysis may have to be modified for material non-linearity. We will cover that in a later post.

Where does k come from?

k is related to the panel aspect ratio in the following way. These curves are available in many references, we recommend (NACA-TN-3781, 1957)

Shear Buckling Coefficient

These curves can be accurately approximated by the following expressions:

For a plate simply supported on four edges:

Shear Buckling Plate SS on 4 edges 2

For a plate clamped on four edges:

Shear Buckling Plate Clamped on 4 edges

For a plate clamped on the long edges and simply supported on short edges:

Shear Buckling Plate Clamped on 2 edges

For a plate clamped on the short edges and simply supported on long edges:

Shear Buckling Plate SS on 4 edges

Where r = a/b.

Superimposing these curves over the classic reference for k:

Shear Buckling Approximate K

AA-SM-007-091 Shear Bucking K derivation

How do you assess whether a panel is simply supported (hinged) or clamped for the purpose of analysis? For a first check it is recommended that the panel be considered simply supported. This will give a conservative first estimate of the panel buckling strength.

Our spreadsheet to calculate this first conservative check is linked below.

AA-SM-007-001 Buckling Spreadsheet Link

More to follow on more accurate assessments of panel edge fixity states in post 2, and dealing with calculated buckling allowables above the material elastic limit.

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