# ABS Plate Buckling (2014)

An important aspect in the design of an offshore steel structure is the buckling and ultimate strength behavior of its fundamental structural components. To ensure high technical quality plate buckling check according to ABS 2014 Guide for building and Classing - Floating Production Installations, published July 2014.

Rules for building and classing floating production installations

To add ABS 2014 standard execute

- - from the main menu. Alternatively, use the context menu:- critical buckling stress is multiplied on the utilization factor.

- increases each plate thickness (e.g. 1.1 increase on 10%) and decreases stresses;

- is a proportional linear elastic limit of the structures, which may be taken as 0.6 for steel;

Calculations are performed for each element with converted stresses (into plate direction) or Plate Average Stresses and using Plate dimensions.

- which stress to check.

- average stress among element point of interests.

- minimum midplane stress (Stop + Sbottom / 2), without bending.

- used only together with the plate average option and means that absolute shear is used for plate averaging:

With Absolute Shear option, higher shear stress is used for checking, that makes verification more conservative.

Formulas of ABS Plate Buckling standard use Yield Stress from materials. It is important to set this value for each material. Standard check if all Yield Stress is not equal to zero:

If count > 0 then press to edit Yield Stress:

Plate Buckling Check is calculated on Sections. With the help of Panel Finder tool it is possible to automatically recognize Section and Plates with their dimensions.

By default, all sections are included in the selection but can be changed by pressing . If sections were not recognized, press to run Panel Finder tool.

Check is passed if Ultimate Strength Limit ≤1 and Buckling State Limit ≤1.

### Criteria Plot

Select Load, Parameter, Values to plot, View,and Sections to Plot.

The parameter is set by default to the last one - Buckling State Limit.

should be selected using- can be used for plotting: element values, min plate, max plate and average plate (last 3 variants use one value for the full plate).

- defines the location of a model and displays options. It can be selected from the list of existing, created a new one or modified.

- includes labels with extreme values over plates, display min/max values of the model or show coordinates of sections from Panel Finder.

- gives a possibility to filter elements/node selection based on the result criteria (type): Below, Above, Between, Outside. If the option is set, the absolute result value is compared to the selected criteria.

Use Labels Control to include labels with extreme values over buckling plates.

### Table (Expand/Extreme)

should be selected using- expand - results over sections/plates, extreme - min/max/absolute maximum overall sections only.

- results of the plate buckling are displayed over the plates. This option helps to display results for each plate taking the worst result from all elements of the plate.

If Min, Max, Absolute max is selected, -the worst result is taken from all parameters of the check.

If Related to Last Parameter is selected, - the worst result will be taken only from the last parameter of the check. The rest results for the plate will be taken only from that element which contains the worst result by the selected Search Type. Available for an expand table only.

- displays results over the plates for each section if turned on. Otherwise, displays the results over sections only. Available for an expand table only.

- display what load case cause the highest buckling state limit (short or full title).

- hightlight selected sections/plates;

- display only selected sections/plates;

- press to display selected section/plates with result as labels:

- select element from the model and highlight section/plate which contains it in the table;

Press to export selected plates (using Export Menu);

- display calculation details (stress calculations, all formulas) for single selected plate.

### Flow table (over loads)

A Flow table displays results of the selected section and its plates for multiple loads. For details see in ABS Plate Buckling 2004.

### Calculation approach

For individual loads and loads sets, plate buckling is calculating based on formulas using stresses from the load. For Load Group plate buckling is calculated as an envelope. Load Group items are calculated using formulas and then min/max/abs is found. Load Group contains the worst values for each parameter and gives a possibility to check the highest Ultimate Strength and Buckling State Limits for all items at once.

Ultimate Strength Limit and Buckling State Limit depend on plate results (stresses) and the plate dimensions (length, width, and thickness).

Plate buckling check includes various options for stresses to be checked:

- Element Stress: MidPlane (no bending) or Average;

- Use Plate Average Stress - stress is averaged on the plate using elements area. The calculation is performed on every element but with averaged plate stresses.

- Use Absolute Shear for plate average (Conservative);

Note: for x and y directions only compression (negative) stresses are used in calculations. Positive stress is ignored and set to 0. For shear (xy) direction positive and negative stresses are used.

Stress Conversion. Plate buckling check requires verifying stresses into plate direction (direction of the longest plate edge). Element Sx stress will be translated into plate length direction, element Sy into width direction.

Conversion of stresses is done automatically in the plate buckling check. For average option first stresses are averaged and afterwards translated. For MinMidplane option midplane stresses are translated and then minimum values are taken.

Dimensions. Results depend on the plate dimensions and direction. It is important to understand how the Panel Finder performs recognition. Length is considered to be the longest edge of the plate and width the longest perpendicular to the longest edge:

Plate Thickness. Calculations are performed on every element and thickness is taken directly from each element. It is possible to set thickness manually, in this case, element thickness will be ignored and user-defined thickness will be used.

Example: A plate with 2 properties 0.01 and 0.02 thicknesses. Left picture displays the property labels with property thicknesses and the right one presents plate buckling plot of thickness parameter:

#### Buckling State Limit

The buckling state limit for the plate panels between stiffeners is defined by the following equation:

Where

η - maximum allowable strength utilization factor.(1 / Safety Factor, e.g. Sf = 1.25 then η = 1 / 1.25 = 0.8).

σ_{xmax}/σ_{ymax} - maximum compressive stress in the longitudinal/transverse direction

- edge shear stress

- critical buckling stress for uniaxial compression in the longitudinal/transverse direction.

- critical buckling stress for edge shear.

P_{r} = 0.6 for steel, proportional linear elastic limit of the structures.

σ_{o} = F_{y} - Yield Stress.

*t* - plate (element) thickness, *s* - plate width, *v* - poison ratio = 0.3.

Buckling coefficient k_{s} is calculated:

k_{s} = 4.0*C_{1} - for longitudinal direction;

- for transverse direction

- for shear direction.

Where *s* / *l* - plate width to the length ratio.

The coefficient C_{1} is equal to:

- 1.1 for plate panels between angles or tee stiffeners;
- 1.0 for plate panels between flat bars or bulb plates;
- 1.0 for plate elements, web plate of stiffeners and local plate of corrugated panels.

C_{2} can be defined:

- 1.2 for plate panels between angles or tee stiffeners;
- 1.1 for plate panels between flat bars or bulb plates;
- 1.0 for plate elements and web plates.

#### Ultimate Strength

The ultimate strength limit for plate panels between stiffeners is defined by the following equations:

η - maximum allowable strength utilization factor. (1 / Safety Factor, e.g. Sf = 1.25 then η = 1 / 1.25 = 0.8).

- ultimate strength with respect to uniaxial stress in the longitudinal direction (not less than critical x buckling stress).

- ultimate strength with respect to uniaxial stress in the transverse direction (not less than critical y buckling stress).

- ultimate strength with respect to edge shear (not less than critical shear buckling stress).

- plate length to width ratio.

- Yield Stress.

- coefficient to reflect the interaction between longitudinal and transverse stresses.

- slenderness ratio.