Buckling Analysis of Plates with Stiffeners Using PLATE-BUCKLING

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Buckling analysis of plates with stiffeners is a unique task for engineers. For this, EN 1993‑1‑5 provides three calculation methods:

  • Effective Cross-Section Method, [1], Chapter 4‑7
  • Reduced Stress Method, [1], Chapter 10
  • Finite Element Methods of Analysis (FEM), [1], Appendix C

PLATE-BUCKLING implements the reduced stress method. The following are some explanations that may become governing during the design of stiffened buckling panels.

Determination of buckling values

There are generally two ways to determine the buckling values of stiffened buckling panels. First, the existing boundary conditions according to [2] and [3] could be used to read them directly from diagrams or, second, to perform an eigenvalue calculation. The eigenvalue calculation determines the critical load factors for the respective available stress. The buckling values are then calculated by means of a retroactive calculation by means of the Ideal buckling stress.

Selecting the governing mode shape

The evaluation of the determined mode shapes is crucial for the design. A buckling analysis should generally be performed on the entire panel and the corresponding buckling figure should represent a global form of failure. The first determined mode shape is decisive for the assessment of whether local single-panel, sub-panel or entire panel buckling is present. In the first mode shape, the following example shows single-panel buckling above and below the longitudinal stiffener.

Figure 01 - Local Buckling

Now it has to be decided whether the corresponding individual fields are to be verified separately or if a higher mode shape is used to search for a global mode shape. In PLATE-BUCKLING, it is possible to determine up to 50 mode shapes. In this example, the mode shape 17 shows global failure of the entire field.

Figure 02 - Global Buckling

Determination of critical plate buckling stresses

Based on the design at the entire field and with the corresponding global eigenmode, the calculation of the critical plate buckling stresses according to [1] , Annex A is performed with the help of the buckling value and the Ideal buckling stress.

Alternatively, analytical formulas for determining the critical plate buckling stress are shown in [1], Annex A. However, the following boundary conditions must be observed for the application:

  • at least three longitudinal stiffeners whose stiffnesses may be smeared and are to be used as an equivalent orthotropic plate
  • a longitudinal stiffness in the pressure area of the buckling panel
  • two longitudinal stiffeners in the pressure area of the buckling panel

The calculation methods for one or two longitudinal stiffeners in the compression area are based on an elastic member. The determined critical buckling stresses result in the critical plate buckling stresses by extrapolation to the compression edge.

Design by means of an example

Basis is the following example:

Figure 03 - Example

As already explained, the first mode shape shows a local buckling shape and would therefore not be governing for the design of the entire panel. In this case, the further design can be selected/decided.

Option 1: Buckling analysis for the single panels above and below the longitudinal stiffener
In a separate design case in PLATE-BUCKLING, the corresponding single panel with its dimensions, boundary conditions, and loads is defined and a buckling analysis is performed on the unstiffened buckling panel.

Figure 04 - Design Local Buckling Panel

Option 2: Buckling analysis for the governing global mode shape on the entire field
PLATE-BUCKLING allows not only the determination of up to 50 mode shapes, but can also perform the corresponding buckling analysis for all. In the present example, the governing eigenmode (17. Buckling figure) for the design on the entire panel.

Figure 05 - Design Global Buckling Panel

At this point, it should be noted that, as an alternative to option 2, the design could be performed using the analytical calculation methods shown in Annex A.2 to determine the critical buckling and plate buckling stresses. Since a clear global mode shape of the entire field could be found here, this is not necessary for this example.

Summary

Manual calculations of stiffened buckling panels are very complex and in many cases not possible without numerical calculations. With the help of PLATE-BUCKLING, these problems can be solved and efficiently processed.

Reference

[1]   DIN EN 1993-1-5, Eurocode 3: Design of steel structures - Part 1–5: Plate-shaped components
[2]  Klöppel, K .; Scheer, J .: Buckling values of stiffened rectangular plates, Volume 1. Berlin: Wilhelm Ernst & Sohn, 1960
[3]  Klöppel, K .; Möller, J .: Buckling values of stiffened rectangular plates, Volume 2. Berlin: Wilhelm Ernst & Sohn, 1968

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