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An important aspect in the design of an offshore steel structure is the buckling and ultimate strength behaviour 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.

Implementation of plate buckling can be found in Part 5A Chapter 3 Section 4 of the following document:

All used formulas from the standard are below the calculation approach chapter.

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. 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.

Warning:

It is possible to turn off automatically conversion of stresses to plate direction (Convert Stress to Plate Direction option). Only in case when stresses are oriented correctly by Femap analysis (by Material direction) and correct plate direction can't be recognized (stiffener is not modeled yet or mesh does not coincide) set option to OFF. Please contact support if extra explanation is required: support@sdcverifier.com

SDC Verifier makes an assumption that plate elements are calculated without any output transformation and default values are used:

- For triangle elements x stress is oriented along the first edge (node1 -> node2 define 1 edge).
- For quad elements x stress is oriented along Diagonal Bisector:

Execute in Femap main menu: Model - Output - Transform... and press Transform Orientation. Check if orientation is set to the default values.

__Dimensions.__ Results depend on the plate dimensions and direction. It is important to understand how Panel Finder perform 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:

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.

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 interaction between longitudinal and transverse stresses.

- slenderness ratio.

To add ABS 2014 standard execute Standard - Plate Buckling ABS 2014 from the main menu. Alternatively, use Standard context menu:

Maximum allowable strength utilization factor - critical buckling stress is multiplied on utilization factor.

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

Pr - is 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.

Stress on Element - which stress to check.

Average - average stress among element point of interests.

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

Use Absolute Shear for Plate Average - 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.

Convert Stress into Plate Direction option allows to turn off automatic stress translation into the plate direction. Almost in all cases it should be ON, see the calculation approach to the explanation when to turn off this option.

Formulas of Plate Buckling ABS 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 it counts > 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 into 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.

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

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

Load should be selected using Single Load Selector;

Values to Plot - can use for plotting: element values, min plate, max plate and average plate (last 3 variants use one value for full plate).

View - defines the location of amodel and display options. It can be selected from the list of existing, created new one or modified.

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

An Expand Table displays the results for each selected section and its plates.

An Extreme table shows only min/max and absolute maximum results among selected sections.

Load should be selected using Single Load Selector;

Define sections to be displayed in the table by pressing .

Search type - 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 plate will be taken only from that element which contains the worst result by the selected Search Type. Available for an expand table only.

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