ALUMINIUM GEODESIC DOME ROOF DESIGN PHASES

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 DOME FRAME MODELLING ATECO TANK GEODESIC DOME ROOF DESIGN PHASES 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. STEP-1 FRAME MODELLING 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

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, secondorder 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 postcritical 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 STEP-3 DESIGN CHECK 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 quasipermanent 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

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 STEP-4 REPORTING 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.

ATECO DOME 3D MODELLING 3D CAD software for mechanical design ATECO TANK GEODESIC DOME ROOF DESIGN PHASES 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 you design, visualize, and simulate your products before they are built. Digital Prototyping with Inventor helps companies design better products, reduce development costs, and get to market faster. 3D mechanical design software includes CAD productivity and design 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 A y, A z, A u and A v Centroid position y S, z S Second moments of area I y, I z, I yz, I u, I v, I p, I pm Radii of gyration i y, i z, i yz, i u, i v, i p, i pm Inclination of principal axes α Section weight G Section perimeter U Torsional constants J, J St.Venant, J Bredt, J secondary Location of shear center y M, z M Warping constants I ωs, I ωm resp. I ωd for lateral restraint Max/Min section moduli S y, S z, S u, S v, S ωm with locations Section ranges r u, r v, r M,u, r M,v according to DIN 4114 Reduction factor λ M Plastic Section Properties Axial force N pl,d Shear forces V pl,y,d, V pl,z,d, V pl,u,d, V pl,v,d Bending moments M pl,y,d, M pl,z,d, M pl,u,d, M pl,v,d Section moduli Z y, Z z, Z u, Z v Shear areas A pl,y, A pl,z, A pl,u, A pl,v Position of area bisection axes f u, f v Display of the inertia ellipse Statical Moments First moments of area Q u, Q v, Q y, Q z with location of maxima and specification of shear flow Warping coordinates ω M Warping areas Q ωm Cell areas A m Stresses Normal stresses σ x 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 σ eqv 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 α pl 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 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 (2 nd 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. ATECO TANK SHELL BUCKLING ANALYSIS