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ATECO TANK TECHNOLOGIES ENGINEERING SERVICE CO.

ALUMINIUM GEODESIC DOME ROOF

DESIGN PHASES

FRAME MODELLING ( GEOMETRICAL MODELLING )

STRUCTURAL ANALYSIS ( FRAME LOADING AND DATAINPUT )

DESIGN CHECK ( RESULTS AND EVALUATION )

REPORTING ( PRINTOUT )

3D MODELLING ( THREE DIMENSIONAL REALISTIC MODELLING )

ASSEMBLY AND SHOP DRAWING

Support Modules

WIND AND SNOW CALCULATION

SEISMIC LOAD CALCULATION

CROSS-SECTION OPRIMISATION

TANK SHELL BUCKLING CALCULATION

JAN. 2014

ATECO TANK – ENGINEERING DEPARTMENT

www.atecotank.com

ATECO TANK GEODESIC DOME ROOF DESIGN PHASES

ATECO DOME FRAME MODELLING

ADFM is intended as a serious design tool for architects, engineers, and designers of geodesic structures including domes. It can also be very useful for others interested in studying the many fascinating aspects of geodesic design. ADFM is NOT a cookbook for building geodesic domes nor does it perform, or confirm, the structural integrity of any design. Our ADFM application is very well suited for structural analysis of geodesic structures with many features included especially for this purpose.

ADFM is a design utility that can generate a wide variety of geodesic and spherical (or ellipsoidal) 3D (wire frame and surface models) for import to CAD or finite element analysis applications and for generating detail design data for the members that make up the structure. In addition to generating its own structures, it can import custom text files of spherical points and element created in other applications to take advantage of the many geometric analysis features in ADFM.

ADFM can produce tables of hubs, struts, and panels grouped into like types with detail geometric information. The like-types of hubs, panels, and/or struts can be highlighted on the structural display. Design drawings of hubs and panels can be output as clean DXF files suitable for import to CAD or structural analysis applications. ADFM is

compatible the structural analysis application as well as with many CAD drawing programs.

ADFM is not only a practical design tool but is an educational tool as well. It supports all major types of geodesic layouts (breakdown methods) for the icosahedron, octahedron, and tetrahedron for both Class I and II with special features for studying single face layouts. ADFM is the only geodesic generator application that supports all three standard breakdown methods for both geodesic class I and II for all the polyhedrons as discussed in the popular geodesic texts.

GENERAL DATA ( Example )

CONFIGURATION

Spheric Zenith Z Radius 46,3303 Rings 10 Sectors 8,0000 Shifted rings 4 Number of nodes 362 HUBS Number of hubs 361 Number of types 26 PANELS

Number of panels 672 Number of types 44 Surface area 2908,0308 Largest panels 5,7495 Smallest panel 3,4054

Largest minimum width 3,0549 Volume 53535,5476 STRUTS Number of struts 1032 Number of types 30 Total length 3334,7579 Longest strut 3,7898 Shortest strut 2,3717 Maximum end-angle 2,34 Minimum end-angle 1,47 DOME METRICS

Dome height 10,0200 Base major radius 28,7760 Base minor radius 0,0000 Spherical radius 46,3303 Base area 2593,9987

STEP-1 FRAME MODELLING

ATECO TANK GEODESIC DOME ROOF DESIGN PHASES

ATECO DOME FRAME STRUCTURAL ANALYSIS

FEA is a powerful 3D FEA program helping structural engineers to meet requirements in modern civil engineering. Intuitive handling, user friendliness

and efficient data input make working with FEA easy.

The FEA program family is based on a modular system. The main program FEA

is used to define structures, materials and loads for planar and spatial structural systems consisting of plates, walls, shells and members. Creating

combined structures as well as modeling solid and contact elements is also

possible.

FEA provides deformations, internal and support forces as well as soil contact stresses. Add-on modules facilitate the data input by creating structures as

well as connections automatically and perform further analyses and designs.

The modular approach allows you to combine all programs individually

according to your needs. Upgrades at a later time are always possible. FEA offering numerous interfaces represents the perfect tool for a smooth

interaction between CAD and structural analysis in Building Information

Modeling (BIM).

On the following webpages you can get an insight into the possibilities available in FEA. You can also try the free trial version to calculate and design

structures yourself.

Load Cases / Action Types

In the dialog box "Edit Load Cases and Combinations", you can create and

manage load cases as well as generate action, load and result combinations. It is possible to assign different types of actions to the individual load cases in

accordance with the selected standard. If several loads have been assigned

to an action type, they can be effective simultaneously or alternatively (for

example wind from either the left or right).

Individual Setting of Calculation Parameters

All types of members can be calculated according to linear static, second-

order or large deformation analysis. This selection option is available for load

cases as well as load combinations. Further calculation parameters can be

set individually for load cases, load and result combinations, which increases the flexibility regarding calculation method and detailed specifications.

Incremental Load Application

Loads can be applied incrementally. The increment option is especially useful

for calculations according to large deformation analysis. For members you can take into account shear deformations and relate internal forces to the

deformed or undeformed system. Furthermore, FEA is able to perform a post-

critical analysis.

Wind and Snow Load Generation According to Eurocode For modeling frameworks load generators are available to create wind loads

according to EN 1991-1-4 and snow loads according to EN 1991-1-3. The load

cases are generated depending on the roof structure. Another generator

creates coating loads (ice). Recurring load combinations can be stored as

templates.

Easy Structure Check

Members can be extended or divided graphically. The structure check detects

input errors like identical nodes or double members quickly and deletes them.

Intersecting members can be connected automatically during the input. The measure function allows for the determination of lengths and angles for

members and surfaces.

Non-Linearities of Members and Supports

You can specify non-linearities for member end releases (yielding, tearing, slippage etc.) and supports (including friction). Special dialog boxes are

additionally available to determine spring stiffnesses of columns and walls

based on the geometry input.

STEP-2 STRUCTURAL ANALYSIS

ATECO TANK GEODESIC DOME ROOF DESIGN PHASES

ATECO DOME STRUCTURAL ANALYSIS DESIGN CHECK The FEA add-on module ALUMINIUM designs members and sets of members consisting of aluminum for the ultimate and the serviceability limit state according to the standard The data specified in FEA concerning material, loads and load combinations must be entered in accordance with the design concept described in the Eurocode. The FEA material library already contains appropriate materials. Furthermore, FEA allows for an automatic creation of appropriate load combinations in accordance with the Eurocode. It is also possible to generate all combinations manually in FEA. In the add-on module ALUMINIUM you select first the members and sets of members that you want to design. In addition, you determine the load cases, load combinations and result combinations for the design. During the next steps, you can adjust the preset settings for lateral intermediate supports and effective lengths. In case continuous members are used, it is possible to define individual support conditions and eccentricities for each intermediate node of the single members. Then, in the program's background, a special FEA tool determines the critical loads and

moments required for the stability analysis.

Design for tension, compression, bending, shear and combined internal forces

Stability analysis for flexural buckling, torsional buckling and lateral torsional buckling

Automatic determination of critical buckling loads and critical moment for lateral torsional buckling for general load applications and support conditions by means of a special FEA program (eigenvalue analysis) integrated in the module

Option to apply discrete lateral supports for beams

Automatic cross-section classification

Integration of parameters from national annexes for the following countries:

DIN EN 1999-1-1/NA:2010-12 (Germany)

ČSN EN 1999-1-1/NA:2009-02 (Czech Republic)

IS EN 1999-1-1/NA:2010-03 (Ireland)

DK EN 1999-1-1/NA:2007-11 (Denmark)

STN EN 1999-1-1/NA:2011-03 (Slovakia)

CYS EN 1999-1-1/NA:2009-07 (Cyprus)

UNI EN 1999-1-1/NA:2011-02-25 (Italy)

NBN EN 1999-1-1/NA:2011-03 (Belgium)

NEN-EN 1999-1-1/NA:2011-12 (Netherlands)

BS EN 1999-1-1/NA:2007+A1:2009 (Great Britain)

Serviceability limit state design for characteristic, frequent or quasi-permanent design situation

Automatic cross-section optimization

Variety of cross-sections provided, for example I-sections, C-sections, rectangular hollow sections, square sections, angles with equal and unequal legs, flat steel, round bars

Clearly arranged results tables

Detailed results documentation with references to design equations used and described in the standard

Various options to filter and arrange results, including results listed by member, cross-section, x-location or load cases, load combinations and result combinations

Results table for slenderness of members and governing internal forces

Parts list with weight and volume specifications

Seamless integration in FEA

Metric and imperial units

STEP-3 DESIGN CHECK

ATECO TANK GEODESIC DOME ROOF DESIGN PHASES

ATECO DOME FRAME STRUCTURAL ANALYSIS REPORT

MODEL ( Nodes,Lines;Members,Supports,Cross Sections)

LOAD CASES & COMBINATIONS

LOADS

SUPPORT FORCES

DEFORMATIONS

LOCAL DEFORMATIONS

GLOBAL DEFORMATIONS

INTERNAL FORCES

COEFFIENTS FOR BUCKLING

MEMBER SLENDERNESSES

CROSS-SECTIONS – INTERNAL FORCES

DESIGN OF ALUMINIUM MEMBERS

GENERAL DESIGN DATA

DETAILS

NATIONAL ANENX

MATERIALS

CROSS-SECTIONS

MEMBERS DETAILS & LENGHTS & EFFECTIVE LENGHTS

DESIGN BY LOAD CASES AND COMBINATIONS

DESIGN BY CROSS SECTIONS

DESIGN BY MEMBERS

GOVERNING INTERNAL FORCES BY MEMBERS

MEMBER SLENDERNESSES

PARTS LISTS BY MEMBER

Colored Representation of Internal Forces

The result tables show available positive and negative internal forces highlighted

by colors. Furthermore, the relation to extreme values is indicated. Result tables

of the design modules use color scales to represent respective design ratios. In

this way, you can quickly find out the design locations that are decisive.

Result Diagrams

The result diagrams of members, surfaces and supports can be configured freely:

You can define smooth ranges with average values or, if necessary, display and

hide the distribution of results. This option helps you to evaluate results

specifically. All diagrams can be integrated in the printout report.

Visualization of Results

Results on the rendered model are represented by a number of colors so that

deformations such as the rotation of a member can be detected easily. Colors and

the range of values can be freely defined in the control panel. Computer animation

of deformations, surface stresses as well as internal forces can be set and saved

as a video file.

Detailed Result Tables

The first result table is represented by a summarized overview making up the

balance for the equilibrium of forces in the structural system and the maximum

deformations. In addition, FEA shows you information concerning the calculation

process. All result tables can be filtered by specific criteria such as extreme

values or design locations.

ALUMINIUM MODULE

The first results table shows the maximum design ratios with the corresponding

design for each designed load case, load combination or result combination.

The subsequent tables show all detailed results sorted by specific subjects in

extendable tree menus. Moreover, it is possible to display all intermediate results

for each location along the members. In this way, you can easily retrace how the

individual designs have been carried out by the module.

The complete module data is part of the FEA printout report. The contents for the

report and the extent of the output data can be selected specifically for the

individual designs.

STEP-4 REPORTING

ATECO TANK GEODESIC DOME ROOF DESIGN PHASES

ATECO DOME 3D MODELLING

3D CAD software for mechanical design

3D CAD software offers an easy-to-use set of tools for 3D mechanical design,

documentation, and product simulation. Digital Prototyping with Inventor

helps you design and validate your products before they are built to deliver

better products, reduce development costs, and get to market faster.

3D CAD software products offer a comprehensive, flexible set of software for 3D mechanical design, product simulation, tooling creation, engineer to order,

and design communication. Inventor takes you beyond 3D to Digital

Prototyping by enabling you to produce an accurate 3D model that can help

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Prototyping with Inventor helps companies design better products, reduce

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communication tools that can help you reduce errors, communicate more

effectively, and deliver more innovative product designs faster. The Inventor

model is an accurate 3D digital prototype that can validate the form, fit, and

function of a design as you work and unites direct modeling and parametric workflows so you always have the right tool for the job.

3D CAD software can help you design, visualize, and simulate a more complete

digital representation of your end product. It includes all of the core 3D

mechanical design, CAD productivity, and design communication functionality

of Autodesk Inventor plus extended capabilities for:

Features

Engineering design productivity

Digital Prototyping Easy-to-use 3D mechanical design

Large assembly design

Sheet metal design

Rules-based design/automation

Catalog/purchased/standard part library Frame and weldment design

Plastic parts design

Mold, and tool and die

Electrical systems design/tube and pipe runs

Visualization

Real-time design visualization

Simulation and design validation

Validate performance with simulation and FEA Point cloud tools

Select material by environmental/cost impact

Assembly collision and interference detection

Check for manufacturability

Draft analysis

CAD file conversion and compatibility

Review/mark up DWG™, DWF™, and PDF files

Mobile and online sharing of 3D designs

BIM interoperability

Native translators

CAD rendering and design documentation

Professional drafting and documentation tools

Native support for DWG files

Automatic drawing view creation BOM generation

International standards support

STEP-5 3D MODELLING

ATECO TANK GEODESIC DOME ROOF DESIGN PHASES

ATECO DOME ASSEMBLY DRAWINGS (TYPICAL LIST )

GENERAL ARRENGEMENT DRAWINGS.

BEAM PLAN ASSEMBLY DRAWING.

NODE PLAN ASSEMBLY DRAWINGS.

SHEET PLAN ASSEMBLY DRAWINGS.

FULL STRUCTURE ASSEMBLY DRAWING.

1 SEGMENT STRUCTURE ASSEMBLY DRAWING.

OUTWARD STRUCTURE ASSEMBLY DRAWING

INWARD STRUCTURE ASSEMBLY DRAWING

DOME LIFTING POINT TYPICAL ARRANGEMENT

LIFTING PLAN

LIFTING JOINT ARRANGEMENT DRAWING

ANCHOR BOLT ARRANGEMENT DRAWING

BATTEN-SKIN INSTALLATION DRAWING

BATTEN-SKIN PANEL AND NODE INSTALLATION PLAN

TYPICAL NODE CONNECTION INSTALLATION DETAIL

FIXED SUPPORT INSTALLATION DETAIL

SLIDING SUPPORT INSTALLATION DETAIL

CENTRE/FREE VENT DETAIL

CENTRE/FREE VENT INSTALLATION DETAIL

TRI-ANGULAR SKYLIGHT INSTALLATION DETAIL

NODE INSTALLATION DETAILS

HUB COVER INSTALLATION DETAILS

CENTER SAFETY LINE INSTALLATION DETAIL,

LIFTING LUG DETAIL

GAUGE PIPE BOOT DETAILS

GAUGE PIPE BOOT INSTALLATION DRAWING

HUB CONNECTION ASSEMBLY DETAILS

MANHOLE COVER INSTALLATION DETAIL

GAUGE HATCH COVER INSTALLATION DETAIL

NOZZLE CONNECTION DETAILS

FIRE FIGHTING SYSTEM INSTALLATION DETAILS

PLATFORM AND WALKWAY INSTALLATION DETAILS

TYPICAL BEAM AND SECTIONAL DETAIL DRAWINGS

STEP-6 ASSEMBLY – SHOP DRAWING

ATECO TANK GEODESIC DOME ROOF DESIGN PHASES

ATECO DOME STRUT CROSS SECTION OPTIMISATION

Section Properties of Thin-Walled Sections, Elastic and Plastic Design

SPO can be run independently. This program calculates the cross-section properties for thin-walled sections of any shape and determines their stresses. There exists an interface to SAS and FEA: SPO sections are also accessible in the framework and FEA programs, and vice versa it is possible to import the internal forces from SAS and FEA into SPO. The sections can be defined graphically, in tables or by importing a DXF file. Features

Modeling of the cross-section via elements, sections, arcs and point elements

Expandable library of material properties, yield strengths and limit stresses

Section properties of open, closed or non-connected cross-sections

Ideal section properties for sections featuring different materials

Stress analysis, inclusive of design for primary and secondary torsion

Check for (c/t) ratios of compression parts

Effective cross-section according to

DIN 18800-2:1990-11

EN 1993-1-5:2006

Classification according to EN 1993-1-1:2005

Interface with MS Excel to import and export tables

Printout report with option to print short form Cross-Section Properties

Cross-sectional area A

Shear areas Ay, Az, Au and Av

Centroid position yS, zS

Second moments of area Iy, Iz, Iyz, Iu, Iv, Ip, IpM

Radii of gyration iy, iz, iyz, iu, iv, ip, ipM

Inclination of principal axes α

Section weight G

Section perimeter U

Torsional constants J, JSt.Venant, JBredt, Jsecondary

Location of shear center yM, zM

Warping constants IωS, IωM resp. IωD for lateral restraint

Max/Min section moduli Sy, Sz, Su, Sv, SωM with locations

Section ranges ru, rv, rM,u, rM,v according to DIN 4114

Reduction factor λM

Plastic Section Properties

Axial force Npl,d

Shear forces Vpl,y,d, Vpl,z,d, Vpl,u,d, Vpl,v,d

Bending moments Mpl,y,d, Mpl,z,d, Mpl,u,d, Mpl,v,d

Section moduli Zy, Zz, Zu, Zv

Shear areas Apl,y, Apl,z, Apl,u, Apl,v

Position of area bisection axes fu, fv

Display of the inertia ellipse Statical Moments

First moments of area Qu, Qv, Qy, Qz with location of maxima and specification of shear flow

Warping coordinates ωM

Warping areas QωM

Cell areas Am Stresses

Normal stresses σx due to axial force, bending moments and warping bimoment

Shear stresses τ due to shear forces as well as primary and secondary torsional

moments

Equivalent stresses σeqv with customizable factor for shear stresses

Stress ratios, related to limit stresses

Stresses for element edges or center lines Shear Wall Sections

Section properties of non-connected cross-sections.

Shear wall shear forces due to bending and torsion Plastic Analysis

Plastic capacity design with determination of the enlargement factor αpl

Check of the (c/t) ratios following the design methods el-el, el-pl or pl-pl according to DIN 18800

CROSS-SECTION OPTIMISATION

ATECO TANK GEODESIC DOME ROOF WIND LOAD CALCULATION

ATECO DOME WIND LOAD CALCULATION

MecaWind is a cost effective program used by Engineers and

designers to perform Wind calculations per ASCE 7-05 and ASCE 7-

10. The program is simple to use, and offers a professional looking

output with all necessary wind calculations. The user also has a great

deal of conrol at their fingertips to customize their output to suite

their needs.

The base version of the software is Wind, and it offers the most cost

effective option of performing wind calculations. Wind Pro offers the

same calculations, with the added benefit of being able to graphically

see all Main Wind Force Resisting System (MWFRS) pressures on each

surface. Seeing the pressures graphically gives the user a real

advantage at being able to visualize what is physically

occuring. Figure 3 shows a typical MWFRS graphic. The user can turn

on/off different surfaces, change colors or rotate and manipulate the

graphic just as you could in any 3D modeling package. In addition you

can toggle between Wind Direction, +/- Internal Building Pressures

and Minimum wind pressures with ease.

Input Parameters: Detailed Wind Load Design (Method 2) per ASCE 7-05

Basic Wind Speed(V) = 122,00 mph Structure Type = BUILDING

Structural Category = III Exposure Category = C

Natural Frequency = N/A Flexible Structure = No

Importance Factor = 1,15 Kd Directional Factor = 0,85

Alpha = 9,50 Zg = 900,00 ft

At = 0,11 Bt = 1,00

Am = 0,15 Bm = 0,65

Cc = 0,20 l = 500,00 ft

Epsilon = 0,20 Zmin = 15,00 ft

f: Dome Height = 20,00 ft hD: Cylinder Base Height= 45,00 ft

D: Cylinder Base Dia = 100,00 ft

Gust Factor Calculations

Gust Factor Category I Rigid Structures - Simplified Method

Gust1: For Rigid Structures (Nat. Freq.>1 Hz) use 0.85 = 0,85

Gust Factor Category II Rigid Structures - Complete Analysis

Zm: 0.6*Ht = 33,00 ft

lzm: Cc*(33/Zm)^0.167 = 0,20

Lzm: l*(Zm/33)^Epsilon = 500,00 ft

Q: (1/(1+0.63*((D+Ht)/Lzm)^0.63))^0.5 = 0,88

Gust2: 0.925*((1+1.7*lzm*3.4*Q)/(1+1.7*3.4*lzm)) = 0,86

Gust Factor Summary

Not a Flexible Structure use the Lessor of Gust1 or Gust2 = 0,85

Figure 6-5 Internal Pressure Coefficients for Buildings, GCpi

GCPi : Internal Pressure Coefficient = +/-0,18

Base Cylinder Wind Pressures per Figure 6-21:

h: Height of Cylinder = 45,00 ft

D: Outer Diameter of Cylinder = 100,00 ft

h/D: h / D = 0,5

Cf: Force Coeff for Moderately Smooth Round - Figure 6-21 = 0,500

Kz: Velocity pressure Coefficient @ Top of Cylinder = 1,070

Kzt: Topographic Factor = 1,000

Kd: Directionality Factor = 0,950

G: Gust Factor = 0,850

qz: Velocity Pressure: 0.00256*Kz*Kzt*Kd*V^2 = 39,84 psf

P: Wind Pressure Acting on Cylinder: qz*G*Cf = 16,93 psf

External Pressure Coefficients for Domed Roof, Cp per Figure 6-7

D-Diameter of cylinder structure = 100,00 ft

f-Height of Dome = 20,00 ft

hD-Height of cylinder base = 45,00 ft

f/D = 0,20

hD/D = 0,45

Point Cp Wind Press (-GCpi) Wind Press (+GCpi)

psf psf

------ ---------- ------------------ ------------------

A -0,906 -24,532 -39,495

B -1,016 -28,430 -43,393

C -0,450 -8,417 -23,380

Load Case A - Linear Interpolation between pt A & B and B & C

Line # X Wind Press (-GCpi) Wind Press (+GCpi)

ft psf psf

------ ---------- ------------------ ------------------

0 ,000 -24,532 -39,495

1 12,500 -25,506 -40,469

2 25,000 -26,481 -41,444

3 37,500 -27,456 -42,419

4 50,000 -28,430 -43,393

5 62,500 -23,427 -38,390

6 75,000 -18,423 -33,387 7 87,500 -13,420 -28,383

8 100,000 -8,417 -23,380

Note: D/8 = 12,5 ft

Notes - Case A

Load Case B - Const value of A <= 25 Deg, linear interpolation on remainder

Line # X Wind Press (-GCpi) Wind Press (+GCpi)

ft psf psf

------ ---------- ------------------ ------------------

0 ,000 -24,532 -39,495

1 18,606 -24,532 -39,495

2 34,303 -26,481 -41,444

3 50,000 -28,430 -43,393

4 62,500 -23,427 -38,390

5 75,000 -18,423 -33,387

6 87,500 -13,420 -28,383

7 100,000 -8,417 -23,380

Notes - Case B

ATECO TANK SHELL BUCKLING ANALYSIS

ATECO DOME WIND LOAD CALCULATION

Plate Buckling Analysis for Plates with or Without Stiffeners The ATECO program PLATE-BUCKLING is used to perform plate buckling

analyses for rectangular plates according to the following standards:

EN 1993-1-5:2006

DIN 18800-3:1990-11 You can apply horizontal or vertical stiffeners to the plates (for example flat

plates, angles, T-stiffeners, trapezoidal stiffeners, C-sections). Loading on the

plate boundaries can be applied in several ways. It is also possible to import

them from FEA.

The plate buckling design in PLATE-BUCKLING always takes into account the total buckling panel because in this way stiffeners that may be available are

considered in the 3D FE model. Thus, designs for single (c/t) parts or buckling

panel sections are omitted.

The following national annexes (NAs) are available for the design according to

Eurocode 3:

o DIN EN1993-1-5/NA:2010-12 (Germany)

o CSN EN1993-1-5/NA:2008-07 (Czech Republic)

o UNI EN1993-1-5/NA:2011-02 (Italy)

o NBN EN 1993-1-5/NA:2011-03 (Belgium) In addition to the NAs listed above, you can specify user-defined NAs with your

own factors.

Import of all relevant internal forces from FEA by selecting numbers of

members and buckling panels with determination of governing boundary

stresses

Summary of stresses in load cases with determination of governing load

Separate materials can be set for stiffener and plate

Import of stiffeners from comprehensive library (flat plate and bulb flat steel,

angle, T-, C- and trapezoidal stiffener)

Determination of effective widths according to EN 1993-1-5 (table 4.1 or 4.2) or DIN 18800 part 3 eq. (4)

Optional calculation of critical local buckling stresses by analytical formulas

of annexes A.1, A.2, A.3 of EC 3 or by means of FEA calculation

Designs (stress, deformation, torsional buckling) of longitudinal and

transverse stiffeners

Option to consider buckling effects according to DIN 18800, part 3, eq. (13)

Photo-realistic representation (3D rendering) of buckling panel including

stiffeners, stress conditions and buckling modes with animation

Documentation of all input and output data in printout report prepared for

test engineer

Analysis Analyses are carried out successively by eigenvalue calculation of the ideal

buckling values for the individual stress conditions as well as of the buckling value

for the simultaneous effectiveness of all stress components.

The performance of the buckling analysis is based on the method of reduced

stresses, comparing the acting stresses with a limit stress condition reduced

from the yield condition of von Mises for each buckling panel. The basis for the

design is a single global slenderness ratio determined on the basis of the entire stress field. Thus, an analysis of single loading and the subsequent merging via

interaction criterion is omitted.

To determine the plate buckling behavior which is similar to the behavior of a

buckling member, PLATE-BUCKLING calculates the eigenvalues of the ideal panel

buckling values with freely assumed longitudinal edges. Then, slenderness ratios

and reduction factors are determined according to EN 1993-1-5, Chapter 4 or

Annex B, or DIN 18800, part 3, Table 1. Finally, the analysis is performed in accordance with EN 1993-1-5, Chapter 10, or DIN 18800, part 3, Eq. (9), (10) or (14).

The buckling panel is discretized in finite quadrilateral or, if necessary, triangular

elements. Each node of an element has six degrees of freedom.

The bending component of the triangular element is based on the LYNN-DHILLON

element (2nd Conf. Matrix Meth. JAPAN – USA, Tokyo) according to the bending

theory described by Mindlin. The membrane component, however, is based on the BERGAN-FELIPPA element. The quadrilateral elements consist of four triangular

elements and the inner node is eliminated.