ad validation guide 2012 en

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Advance Design

Validation Guide


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INTRODUCTION

Before being officially released, each version of GRAITEC software, including

Advance Design, undergoes a series of validation tests. This validation is performed in

parallel and in addition to manual testing and beta testing, in order to obtain the

"operational version" status. This document contains a description of the automatictests, highlighting the theoretical background and the results we have obtained using

the current software release.

Usually, a test is made of a reference (independent from the specific software version

tested), a transformation (a calculation or a data processing scenario), a result (given

by the specific software version tested) and a difference usually measured in

percentage as a drift from a set of reference values. Depending on the cases, the

used reference is either a theoretical calculation done manually, a sample taken from

the technical literature, or the result of a previous version considered as good by

experience.

Starting with version 2012, Graitec Advance has made significant steps forward in term ofquality management by extending the scope and automating the testing process.

While in previous versions, the tests were always about the calculation results which

were compared to a reference set, starting with version 2012, tests have been

extended to user interface behavior, import/export procedures, etc.

The next major improvement is the capacity to pass the tests automatically. These

current tests have obviously been passed on the operational version, but they are

actually passed on a daily basis during the development process, which helps improve

the daily quality by solving potential issues, immediately after they have been

introduced in the code.

In the field of structural analysis and design, software users must keep in mind that theresults highly depend on the modeling (especially when dealing with finite elements)

and on the settings of the numerous assumptions and options available in the

software. A software package cannot replace engineers experience and analysis.

Despite all our efforts in term of quality management, we cannot guaranty the correct

behavior and the validity of the results issued by Advance Design in any situation.

With this validation guide, we are providing a set of concrete test cases showing the

behavior of Advance Design in various areas and various conditions. The tests cover

a wide field of expertise: modeling, climatic load generation according to Eurocode 1,

combinations management, meshing, finite element calculation, reinforced concrete

design according to Eurocode 2, steel member design according to Eurocode 3, steel

connection design according to Eurocode 3, timber member design according toEurocode 5, seismic analysis according to Eurocode 8, report generation, import /

export procedures and user interface behavior.

We hope that this guide will highly contribute to the knowledge and the confidence you

are placing in Advance Design.

Manuel LIEDOT

Chief Product Officer


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ADVANCE DESIGN VALIDATION GUIDE

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CONTENTS

1 FINITE ELEMENTS ANALYSIS ..............................................................................................................................17

1.1 Cantilever rectangular plate (01-0001SSLSB_FEM)................................................................................18

1.2 System of two bars with three hinges (01-0002SSLLB_FEM) .................................................................20

1.3 Circular plate under uniform load (01-0003SSLSB_FEM)........................................................................23

1.4 Slender beam with variable section (fixed-free) (01-0004SDLLB_FEM)..................................................26

1.5 Tied (sub-tensioned) beam (01-0005SSLLB_FEM) .................................................................................29

1.6 Thin circular ring fixed in two points (01-0006SDLLB_FEM)....................................................................34

1.7 Thin lozenge-shaped plate fixed on one side (alpha = 0 ) (01-0007SDLSB_FEM)................................38

1.8 Thin lozenge-shaped plate fixed on one side (alpha = 15 ) (01-0008SDLSB_FEM)..............................41



1.11 Vibration mode of a thin piping elbow in plane (case 1) (01-0011SDLLB_FEM) .....................................50



1.14 Thin circular ring hanged on an elastic element (01-0014SDLLB_FEM) .................................................59

1.15 Double fixed beam with a spring at mid span (01-0015SSLLB_FEM) .....................................................63

1.16 Double fixed beam (01-0016SDLLB_FEM) ..............................................................................................66

1.17 Short beam on simple supports (on the neutral axis) (01-0017SDLLB_FEM) .........................................70

1.18 Short beam on simple supports (eccentric) (01-0018SDLLB_FEM) ........................................................74

1.19 Thin square plate fixed on one side (01-0019SDLSB_FEM)....................................................................78

1.20 Rectangular thin plate simply supported on its perimeter (01-0020SDLSB_FEM) ..................................82

1.21 Cantilever beam in Eulerian buckling (01-0021SFLLB_FEM)..................................................................86

1.22 Annular thin plate fixed on a hub (repetitive circular structure) (01-0022SDLSB_FEM) ..........................88

1.23 Bending effects of a symmetrical portal frame (01-0023SDLLB_FEM).................................................... 90

1.24 Slender beam on two fixed supports (01-0024SSLLB_FEM)...................................................................93

1.25 Slender beam on three supports (01-0025SSLLB_FEM).........................................................................97

1.26 Bimetallic: Fixed beams connected to a stiff element (01-0026SSLLB_FEM) .......................................101

1.27 Fixed thin arc in planar bending (01-0027SSLLB_FEM) ........................................................................104

1.28 Fixed thin arc in out of plane bending (01-0028SSLLB_FEM) ...............................................................107

1.29 Double hinged thin arc in planar bending (01-0029SSLLB_FEM)..........................................................109

1.30 Portal frame with lateral connections (01-0030SSLLB_FEM) ................................................................112

1.31 Truss with hinged bars under a punctual load (01-0031SSLLB_FEM) ..................................................115

1.32 Beam on elastic soil, free ends (01-0032SSLLB_FEM) .........................................................................118

1.33 EDF Pylon (01-0033SFLLA_FEM)..........................................................................................................121

1.34 Beam on elastic soil, hinged ends (01-0034SSLLB_FEM).....................................................................125

1.35 Simply supported square plate (01-0036SSLSB_FEM) .........................................................................129

1.36 Caisson beam in torsion (01-0037SSLSB_FEM) ...................................................................................131


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1.37 Thin cylinder under a uniform radial pressure (01-0038SSLSB_FEM) ..................................................134

1.38 Square plate under planar stresses (01-0039SSLSB_FEM)..................................................................136

1.39 Stiffen membrane (01-0040SSLSB_FEM)..............................................................................................139

1.40 Beam on two supports considering the shear force (01-0041SSLLB_FEM)..........................................142

1.41 Thin cylinder under a uniform axial load (01-0042SSLSB_FEM) ...........................................................1441.42 Thin cylinder under a hydrostatic pressure (01-0043SSLSB_FEM).......................................................147

1.43 Thin cylinder under its self weight (01-0044SSLSB_MEF).....................................................................150

1.44 Torus with uniform internal pressure (01-0045SSLSB_FEM).................................................................152

1.45 Spherical shell under internal pressure (01-0046SSLSB_FEM).............................................................154

1.46 Pinch cylindrical shell (01-0048SSLSB_FEM)........................................................................................157

1.47 Spherical shell with holes (01-0049SSLSB_FEM)..................................................................................159

1.48 Spherical dome under a uniform external pressure (01-0050SSLSB_FEM)..........................................162

1.49 Simply supported square plate under a uniform load (01-0051SSLSB_FEM) .......................................165

1.50 Simply supported rectangular plate under a uniform load (01-0052SSLSB_FEM) ................................167

1.51 Simply supported rectangular plate under a uniform load (01-0053SSLSB_FEM) ................................169

1.52 Simply supported rectangular plate loaded with punctual force and moments (01-0054SSLSB_FEM)..171

1.53 Shear plate perpendicular to the medium surface (01-0055SSLSB_FEM)............................................173

1.54 Triangulated system with hinged bars (01-0056SSLLB_FEM)...............................................................175

1.55 A plate (0.01 m thick), fixed on its perimeter, loaded with a uniform pressure (01-0057SSLSB_FEM).177

1.56 A plate (0.01333 m thick), fixed on its perimeter, loaded with a uniform pressure (01-0058SSLSB_FEM)......179

1.57 A plate (0.02 m thick), fixed on its perimeter, loaded with a uniform pressure (01-0059SSLSB_FEM).181

1.58 A plate (0.05 m thick), fixed on its perimeter, loaded with a uniform pressure (01-0060SSLSB_FEM).1831.59 A plate (0.1 m thick), fixed on its perimeter, loaded with a uniform pressure (01-0061SSLSB_FEM)...185

1.60 A plate (0.01 m thick), fixed on its perimeter, loaded with a punctual force (01-0062SSLSB_FEM) .....187

1.61 A plate (0.01333 m thick), fixed on its perimeter, loaded with a punctual force (01-0063SSLSB_FEM).........190



1.64 A plate (0.1 m thick), fixed on its perimeter, loaded with a punctual force (01-0066SSLSB_FEM) .......197

1.65 Vibration mode of a thin piping elbow in space (case 1) (01-0067SDLLB_FEM)...................................199



1.68 Reactions on supports and bending moments on a 2D portal frame (Rafters) (01-0077SSLPB_FEM) ........207

1.69 Reactions on supports and bending moments on a 2D portal frame (Columns) (01-0078SSLPB_FEM) .......209

1.70 Short beam on two hinged supports (01-0084SSLLB_FEM)..................................................................211

1.71 Slender beam of variable rectangular section with fixed-free ends (=5) (01-0085SDLLB_FEM).........213

1.72 Slender beam of variable rectangular section (fixed-fixed) (01-0086SDLLB_FEM)...............................218

1.73 Plane portal frame with hinged supports (01-0089SSLLB_FEM)...........................................................221

1.74 Double fixed beam in Eulerian buckling with a thermal load (01-0091HFLLB_FEM).............................223

1.75 Cantilever beam in Eulerian buckling with thermal load (01-0092HFLLB_FEM)....................................2251.76 A 3D bar structure with elastic support (01-0094SSLLB_FEM)..............................................................227


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1.77 Fixed/free slender beam with centered mass (01-0095SDLLB_FEM) ...................................................234

1.78 Fixed/free slender beam with eccentric mass or inertia (01-0096SDLLB_FEM)....................................239

1.79 Double cross with hinged ends (01-0097SDLLB_FEM) .........................................................................243

1.80 Simple supported beam in free vibration (01-0098SDLLB_FEM) ..........................................................246

1.81 Membrane with hot point (01-0099HSLSB_FEM) ..................................................................................2491.82 Beam on 3 supports with T/C (k = 0) (01-0100SSNLB_FEM)................................................................252

1.83 Beam on 3 supports with T/C (k -> infinite) (01-0101SSNLB_FEM) ......................................................255

1.84 Beam on 3 supports with T/C (k = -10000 N/m) (01-0102SSNLB_FEM)............................................... 258

1.85 Linear system of truss beams (01-0103SSLLB_FEM) ...........................................................................261

1.86 Non linear system of truss beams (01-0104SSNLB_FEM) ....................................................................264

1.87 Study of a mast subjected to an earthquake (02-0112SMLLB_P92) .....................................................268

1.88 Linear element in simple bending - without compressed reinforcement (02-0162SSLLB_B91) ............274

1.89 Design of a Steel Structure according to CM66 (03-0206SSLLG_CM66) .............................................278

1.90 Design of a 2D portal frame (03-0207SSLLG_CM66)............................................................................286

1.91 Design of a concrete floor with an opening (03-0208SSLLG_BAEL91).................................................293

1.92 Verifying displacements for liniar element for vertical seism (TTAD #11756) ........................................301

1.93 Generating planar efforts before and after selecting a saved vue (TTAD #11849)................................301

1.94 Verifying constraints for triangular mesh on planar element (TTAD #11447) ........................................301

1.95 Verifying forces for triangular meshing on planar element (TTAD #11723) ...........................................301

1.96 Verifying stresses in beam with "extend into wall" property (TTAD #11680)..........................................302

1.97 Verifying diagrams after changing the view from standard (top, left,...) to user view (TTAD #11854)...302

1.98 Verifying forces results on concrete linear elements (TTAD #11647) ....................................................3021.99 Generating results for Torsors NZ/Group (TTAD #11633) .....................................................................302

1.100 Verifying Sxx results on beams (TTAD #11599).....................................................................................303

1.101 Verifying the level mass center (TTAD #11573, TTAD #12315) ............................................................303

1.102 Verifying diagrams for Mf Torsors on divided walls (TTAD #11557) ......................................................303

1.103 Verifying results on puctual supports (TTAD #11489)............................................................................303

1.104 Generating a report with torsors / level (TTAD #11421).........................................................................304

1.105 Verifying nonlinear analysis results for frames with semi-rigid joints and rigid joints (TTAD #11495) ...304

1.106 Verifying tension/compression supports on nonlinear analysis (TTAD #11518)....................................304

1.107 Verifying tension/compression supports on nonlinear analysis (TTAD #11518)....................................304

1.108 Verifying the main axes results on a planar element (TTAD #11725)....................................................305

1.109 Verifying the display of the forces results on planar supports (TTAD #11728) ......................................305

1.110 Verifying the internal forces results for a simple supported steel beam.................................................305

1.111 Verifying forces on elastic linear support which is defined in a user workplane (TTAD #11929)........... 305

2 CAD, RENDERING AND VISUALIZATION...........................................................................................................307

2.1 Verifying hide/show elements command (TTAD #11753) ......................................................................308

2.2 System stability during section cut results verification (TTAD #11752)..................................................308

2.3 Verifying the grid text position (TTAD #11704).......................................................................................3082.4 Verifying the grid text position (TTAD #11657).......................................................................................308


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2.5 Generating combinations (TTAD #11721) ..............................................................................................308

2.6 Verifying the coordinates system symbol (TTAD #11611)......................................................................309

2.7 Verifying descriptive actors after creating analysis (TTAD #11589).......................................................309

2.8 Creating a circle (TTAD #11525) ............................................................................................................309

2.9 Creating a camera (TTAD #11526).........................................................................................................3092.10 Verifying the local axes of a section cut (TTAD #11681)........................................................................309

2.11 Verifying the snap points behavior during modeling (TTAD #11458) .....................................................310

2.12 Verifying the representation of elements with HEA cross section (TTAD #11328) ................................310

2.13 Verifying the display of the descriptive model in analysis view (TTAD #11462).....................................310

2.14 Verifying the descriptive model display after post processing results in analysis mode (TTAD #11475)............. 310

2.15 Verifying holes in horizontal planar elements after changing the level height (TTAD #11490)..............310

2.16 Verifying the display of elements with compound cross sections (TTAD #11486).................................311

2.17 Modeling using the tracking snap mode (TTAD #10979) .......................................................................311

2.18 Moving a linear element along with the support (TTAD #12110)............................................................311

2.19 Turning on/off the "ghost" rendering mode (TTAD #11999) ...................................................................311

2.20 Verifying the "ghost display on selection" function for saved views (TTAD #12054)..............................311

2.21 Verifying the "ghost" display after changing the display colors (TTAD #12064).....................................312

2.22 Verifying the fixed load scale function (TTAD #12183)...........................................................................312

2.23 Verifying the steel connections modeling (TTAD #11698)......................................................................312

2.24 Verifying the dividing of planars elements which contain openings (TTAD #12229)..............................312

2.25 Verifying the program behavior when trying to create lintel (TTAD #12062)..........................................312

2.26 Verifying the display of punctual loads after changing the load case number (TTAD #11958)..............3132.27 Verifying the program behavior when launching the analysis on a model with overlapped loads

(TTAD #11837) .......................................................................................................................................313

2.28 Verifying the display of a beam with haunches (TTAD #12299)............................................................313

2.29 Creating base plate connections for non-vertical columns (TTAD #12170) ...........................................313

2.30 Verifying drawing of joints in y-z plan (TTAD #12453)............................................................................313

2.31 Verifying rotation for steel beam with joint (TTAD #12592) ....................................................................314

2.32 Verifying annotation on selection (TTAD #12700)..................................................................................314

3 CLIMATIC GENERATOR.......................................................................................................................................315

3.1 EC1 NF: generating wind loads on a 3D portal frame with 2 slopes roof (TTAD #11932).....................316

3.2 EC1: wind load generation on a simple 3D structure with horizontal roof ..............................................316

3.3 EC1: wind load generation on a high building with horizontal roof .........................................................316

3.4 EC1: wind load generation on a simple 3D portal frame with 2 slopes roof (TTAD #11602) .................316

3.5 EC1: wind load generation on simple 3D portal frame with 4 slopes roof (TTAD #11604) ....................317

3.6 EC1: wind load generation on building with multispan roofs ..................................................................317

3.7 EC1: wind load generation on a signboard.............................................................................................317

3.8 EC1: generating wind loads on an isolated roof with 2 slopes (TTAD #11695) .....................................317

3.9 EC1: generating wind loads on duopitch multispan roofs with pitch < 5 degrees (TTAD #11852)......... 318

3.10 EC1: generating wind loads on double slope 3D portal frame with a fully opened face (DEV2012 #1.6)...318


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3.11 EC1: generating snow loads on a 2 slopes 3D portal frame with gutter (TTAD #11113).......................318

3.12 EC1: generating snow loads on a 3D portal frame with horizontal roof and gutter (TTAD #11113) ......318

3.13 EC1: snow on a 3D portal frame with horizontal roof and parapet with height reduction (TTAD #11191)... 319

3.14 EC1: generating snow loads on a 3D portal frame with a roof which has a small span (< 5m) and aparapet (TTAD #11735)..........................................................................................................................319

3.15 EC1: generating snow loads on duopitch multispan roofs according to German standards(DIN EN 1991-1-3/NA) (DEV2012 #3.13)...............................................................................................319

3.16 EC1: generating snow loads on monopitch multispan roofs according to German standards(DIN EN 1991-1-3/NA) (DEV2012 #3.13)...............................................................................................319

3.17 EC1: generating snow loads on two close roofs with different heights according to German standards(DIN EN 1991-1-3/NA) (DEV2012 #3.13) ...............................................................................................320

3.18 EC1: generating wind loads on a 55m high structure according to German standards(DIN EN 1991-1-4/NA) (DEV2012 #3.12)...............................................................................................320

3.19 EC1: generating wind loads on double slope 3D portal frame according to Czech standards(CSN EN 1991-1-4) (DEV2012 #3.18) ...................................................................................................320

3.20 EC1: generating snow loads on two close roofs with different heights according to Czech standards(CSN EN 1991-1-3) (DEV2012 #3.18) ...................................................................................................320

3.21 EC1: generating wind loads on a 2 slopes 3D portal frame with 2 fully opened windwalls(TTAD #11937) .......................................................................................................................................321

3.22 EC1: generating snow loads on a 2 slopes 3D portal frame with roof thickness greater than the parapetheight (TTAD #11943) ............................................................................................................................321

3.23 EC1: verifying the snow loads generated on a monopitch frame (TTAD #11302) .................................321

3.24 EC1: generating wind loads on a 2 slopes 3D portal frame using the Romanian national annex(TTAD #11687) .......................................................................................................................................321

3.25 EC1: generating wind loads on a 2 slopes 3D portal frame (TTAD #11699) ........................................322

3.26 EC1: generating snow loads on a 2 slopes 3D portal frame using the Romanian national annex(TTAD #11570) .......................................................................................................................................322

3.27 EC1: generating snow loads on a 2 slopes 3D portal frame using the Romanian national annex(TTAD #11569) .......................................................................................................................................322

3.28 EC1: generating wind loads on a 2 slopes 3D portal frame (TTAD #11531) .........................................322

3.29 NV2009: generating wind loads and snow loads on a simple structure with planar support(TTAD #11380) .......................................................................................................................................323

3.30 Generating the description of climatic loads report according to EC1 Romanian standards(TTAD #11688) .......................................................................................................................................323

3.31 EC1: Verifying the geometry of wind loads on an irregular shed. (TTAD #12233).................................323

3.32 EC1: Verifying the wind loads generated on a building with protruding roof (TTAD #12071, #12278) ..323

3.33 EC1: generating snow loads on a 2 slopes 3D portal frame (NF EN 1991-1-3/NA)(VT : 3.4 - Snow - Example A)................................................................................................................324

3.34 EC1: generating wind loads on a 2 slopes 3D portal frame (NF EN 1991-1-4/NA)(VT : 3.1 - Wind - Example A).................................................................................................................324

3.35 EC1: generating wind loads on a 3D portal frame with one slope roof (NF EN 1991-1-4/NA)(VT : 3.2 - Wind - Example B).................................................................................................................324

3.36 EC1: generating wind loads on a 2 slopes 3D portal frame (NF EN 1991-1-4/NA)(VT : 3.3 - Wind - Example C).................................................................................................................324

3.37 EC1: generating wind loads on a triangular based lattice structure with composed profiles and automaticcalculation of "n" (NF EN 1991-1-4/NA) (TTAD #12276). ......................................................................325


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3.38 EC1: wind loads on a triangular based lattice structure with composed profiles and user imposed n(NF EN 1991-1-4/NA) (TTAD #12276). ..................................................................................................325

3.39 EC1: generating snow loads on a 3 slopes 3D portal frame with parapets (NF EN 1991-1-3/NA)(TTAD #11111) .......................................................................................................................................325

3.40 EC1: Generating snow loads on a 4 slopes shed with gutters. (TTAD #12528) ....................................325

3.41 EC1: Generating snow loads on a 4 slopes shed with gutters. (TTAD #12528) ....................................326

3.42 EC1: Generating snow loads on a single slope with lateral parapets. (TTAD #12606)..........................326

3.43 EC1: generating wind loads on a sqaure based lattice structure with composed profiles and automaticcalculation of "n" (NF EN 1991-1-4/NA) (TTAD #12744)........................................................................326

3.44 NV2009: Verifying wind and snow reports for a protruding roof (TTAD #11318) ...................................326

3.45 NV2009: Generating wind loads on a 2 slopes 3D portal frame at 15 height. (TTAD #12604).............. 326

4 COMBINATIONS....................................................................................................................................................327

4.1 Generating combinations (TTAD #11673) ..............................................................................................328

4.2 Generating combinations for NEWEC8.cbn (TTAD #11431)..................................................................328

4.3 Defining concomitance rules for 2 case families (TTAD #11355)...........................................................328

4.4 Generating load combinations with unfavorable and favorable/unfavorable predominant action(TTAD #11357) .......................................................................................................................................328

4.5 Generating load combinations after changing the load case number (TTAD #11359) ..........................328

4.6 Generating concomitance matrix after adding a new dead load case (TTAD #11361) ..........................329

4.7 Generating the concomitance matrix after switching back the effect for live load (TTAD #11806)........329

4.8 Generating a set of combinations with seismic group of loads (TTAD #11889).....................................329

4.9 Generating a set of combinations with Q group of loads (TTAD #11960) ..............................................329

4.10 Generating a set of combinations with different Q "Base" types (TTAD #11806) ..................................330

4.11 Performing the combinations concomitance standard test no.1 (DEV2010#1.7)...................................331

4.12 Performing the combinations concomitance standard test no.2 (DEV2012 #1.7) ..................................331


4.14 Performing the combinations concomitance standard test no.4 (DEV2012 #1.7).................................332


4.16 Performing the combinations concomitance standard test no.6 (DEV2012 #1.7)..................................333



4.19 Performing the combinations concomitance standard test no.9 (DEV2012 #1.7) ..................................3354.20 Performing the combinations concomitance standard test no.10 (DEV2012 #1.7)................................335

4.21 Verifying combinations for CZ localization (TTAD #12542)....................................................................336

4.22 Verifying the combinations description report (TTAD #11632) ...............................................................336

5 CONCRETE DESIGN.............................................................................................................................................337

5.1 EC2: column design with Nominal Stiffnes method square section (TTAD #11625) ...........................338

5.2 Verifying reinforced concrete results on a structure with 375 load cases combinations (TTAD #11683)..338

5.3 EC2 : calculation of a square column in traction (TTAD #11892)...........................................................338

5.4 Verifying Aty and Atz for a fixed concrete beam (TTAD #11812)...........................................................338

5.5 Verifying the reinforced concrete results on a fixed beam (TTAD #11836)............................................339


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5.6 Verifying the longitudinal reinforcement bars for a filled circular column (TTAD #11678)......................339

5.7 Verifying longitudinal reinforcement for linear element (TTAD #11636).................................................339

5.8 Verifying the longitudinal reinforcement for a fixed linear element (TTAD #11700)...............................340

5.9 Verifying concrete results for planar elements (TTAD #11583)..............................................................340

5.10 Verifying concrete results for linear element (TTAD #11556).................................................................3405.11 Verifying reinforcement for concrete column (TTAD #11635) ................................................................340

5.12 Verifying the minimum transverse reinforcement area results for an articulated beam (TTAD #11342) ...... 341

5.13 Verifying the minimum transverse reinforcement area results for articulated beams (TTAD #11342)... 341

5.14 Verifying the longitudinal reinforcement for a horizontal concrete bar with rectangular cross section...341

5.15 EC2: Verifying the minimum reinforcement area for a simply supported beam .....................................342

5.16 EC2: Verifying the longitudinal reinforcement area of a beam under a linear load ................................342

5.17 EC2: Verifying the longitudinal reinforcement area of a beam under a linear load - inclined stress strainbehavior law............................................................................................................................................342

5.18 EC2: Verifying the longitudinal reinforcement area for a beam subjected to point loads.......................3425.19 EC2: Verifying the longitudinal reinforcement area of a beam uner a linear load - bilinear stress-strain

diagram...................................................................................................................................................343

5.20 Modifying the "Design experts" properties for concrete linear elements (TTAD #12498) ......................343

5.21 EC2: Verifying the transverse reinforcement area for a beam subjected to linear loads .......................343

5.22 EC2: Verifying the longitudinal reinforcement are of a beam under a linear load - horizontal levelbehavior law............................................................................................................................................343

6 GENERAL APPLICATION.....................................................................................................................................345

6.1 Verifying geometry properties of elements with compound cross sections (TTAD #11601).................. 346

6.2 Verifying material properties for C25/30 (TTAD #11617) .......................................................................3466.3 Verifying the synthetic table by type of connection (TTAD #11422).......................................................346

6.4 Importing a cross section from the Advance Steel profiles library (TTAD #11487)................................346

6.5 Creating and updating model views and post-processing views (TTAD #11552) ..................................347

6.6 Verifying mesh, CAD and climatic forces - LPM meeting .......................................................................347

6.7 Creating a new Advance Design file using the "New" command from the "Standard" toolbar(TTAD #12102) .......................................................................................................................................347

6.8 Launching the verification of a model containing steel connections (TTAD #12100).............................347

6.9 Verifying the appearance of the local x orientation legend (TTAD #11737)...........................................348

6.10 Creating system trees using the copy/paste commands (DEV2012 #1.5) .............................................3486.11 Creating system trees using the copy/paste commands (DEV2012 #1.5) .............................................348

6.12 Verifying the objects rename function (TTAD #12162)...........................................................................348

6.13 Generating liquid pressure on horizontal and vertical surfaces (TTAD #10724)....................................349

6.14 Changing the default material (TTAD #11870) .......................................................................................349

6.15 Verifying 2 joined vertical elements with the clipping option enabled (TTAD #12238)...........................349

6.16 Defining the reinforced concrete design assumptions (TTAD #12354) ..................................................349

6.17 Verifying precision for linear and planar concrete cover (TTAD #12525)...............................................350

6.18 Verifying element creation using commas for coordinates (TTAD #11141)...........................................350


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10.12 Verifying signed concomitant linear elements envelopes on Fx report (TTAD #11517) ........................362

10.13 Verifying the global envelope of linear elements forces result (on the start point of super element)(TTAD #12230) .......................................................................................................................................363

10.14 Verifying the global envelope of linear elements forces result (on the end point of super element)(TTAD #12230, #12261) .........................................................................................................................363

10.15 Verifying the global envelope of linear elements displacements (on each 1/4 of mesh element)(TTAD #12230) .......................................................................................................................................363

10.16 Verifying the global envelope of linear elements displacements (on all quarters of super element)(TTAD #12230) .......................................................................................................................................363

10.17 Verifying the global envelope of linear elements displacements (on end points and middle of superelement) (TTAD #12230) ........................................................................................................................364

10.18 Verifying the global envelope of linear elements displacements (on start and end of super element)(TTAD #12230) .......................................................................................................................................364

10.19 Verifying the global envelope of linear elements displacements (on the start point of super element)(TTAD #12230) .......................................................................................................................................364

10.20 Verifying the global envelope of linear elements displacements (on the end point of super element)(TTAD #12230, TTAD #12261) ..............................................................................................................364

10.21 Verifying the global envelope of linear elements stresses (on each 1/4 of mesh element)(TTAD #12230) .......................................................................................................................................365

10.22 Verifying the global envelope of linear elements stresses (on all quarters of super element) (TTAD#12230)...................................................................................................................................................365

10.23 Verifying the global envelope of linear elements stresses (on end points and middle of super element)(TTAD #12230) .......................................................................................................................................365

10.24 Verifying the global envelope of linear elements stresses (on start and end of super element)(TTAD #12230) .......................................................................................................................................365

10.25 Verifying the global envelope of linear elements stresses (on the start point of super element)(TTAD #12230) .......................................................................................................................................366

10.26 Verifying the global envelope of linear elements stresses (on the end point of super element)(TTAD #12230, TTAD #12261) ..............................................................................................................366

10.27 Verifying the Min/Max values from the user reports (TTAD# 12231) .....................................................366

10.28 Verifying the shape sheet for a steel beam (TTAD #12455) ..................................................................366

10.29 Verifying the EC2 calculation assumptions report (TTAD #11838) ........................................................366

10.30 Verifying the shape sheet report (TTAD #12353) ...................................................................................367

10.31 Verifying the Max row on the user table report (TTAD #12512) .............................................................367

10.32 Verifying the shape sheet strigs display (TTAD #12622) .......................................................................367

10.33 Verifying the steel shape sheet display (TTAD #12657) ........................................................................367

10.34 Verifying report for modal analysis (TTAD #12718)................................................................................367

11 SEISMIC ANALYSIS..............................................................................................................................................369

11.1 EC8 : Verifying the displacements results of a liniar element according to Czech seismic standards(CSN EN 1998-1) (DEV2012 #3.18).......................................................................................................370

11.2 Verifying the spectrum results for EC8 seism (TTAD #11478)...............................................................370

11.3 Verifying the spectrum results for EC8 seism (TTAD #12472)...............................................................370

12 STEEL DESIGN .....................................................................................................................................................371

12.1 Verifying results on square hollowed beam 275H according to thickness (TTAD #11770)....................37212.2 Verifying shape sheet on S275 beam (TTAD #11731) ...........................................................................372


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1 Finite Elements Analysis


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18

1.1 Cantilever rectangular plate (01-0001SSLSB_FEM)

Test ID: 2433

Test status: Passed

1.1.1 Description

Verifies the vertical displacement on the free extremity of a cantilever rectangular plate fixed on one side. The plate is1 m long, subjected to a uniform planar load.

1.1.2 Background

1.1.2.1 Model description

Reference: Structure Calculation Software Validation Guide, test SSLS 01/89.

Analysis type: linear static.

Element type: planar.

Cantilever rectangular plate Scale =1/401-0001SSLSB_FEM

Units

S.I.

Geometry

Thickness: e = 0.005 m,

Length: l = 1 m,

Width: b = 0.1 m.

Materials properties

Longitudinal elastic modulus: E = 2.1 x 1011

Pa,

Poisson's ratio: = 0.3.


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Boundary conditions

Outer: Fixed at end x = 0,

Inner: None.

Loadings

External: Uniform load p = -1700 Pa on the upper surface, Internal: None.

1.1.2.2 Displacement of the model in the linear elastic range

Reference solution

The reference displacement is calculated for the unsupported end located at x = 1m.

u =bl

4p

8EIz =

0.1 x 14x 1700

8 x 2.1 x 1011

x0.1 x 0.005

3

12

= -9.71 cm

Finite elements modeling

Planar element: plate, imposed mesh,

1100 nodes,

990 surface quadrangles.

Deformed shape

Deformed cantilever rectangular plate Scale =1/4

01-0001SSLSB_FEM

1.1.2.3 Theoretical results

Solver Result name Result description Reference value

CM2 DZ Vertical displacement on the free extremity [cm] -9.71

1.1.3 Calculated results

Result name Result description Value Error

DZ Vertical displacement on the free extremity [cm] -9.58696 cm 1.28%


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Boundary conditions

Outer: Hinged in A and B,

Inner: Hinge on C

Loading

External: Punctual load in C: F = -21 x 10

3

N. Internal: None.

1.2.2.2 Displacement of the model in C

Reference solution

uc= -3 x 10-3

m


Linear element: beam, imposed mesh,

21 nodes,

20 linear elements.

Displacement shape

System of two bars with three hinges Scale =1/33

Displacement in C 0002SSLLB_FEM

1.2.2.3 Bars stresses

Reference solutions

AC bar = 70 MPa

BC bar = 70 MPa



21 nodes,

20 linear elements.


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22

1.2.2.4 Shape of the stress diagram

System of two bars with three hinges Scale =1/34

Bars stresses 0002SSLLB_FEM



CM2 DZ Vertical displacement in point C [cm] -0.30

CM2 Sxx Tensile stress on AC bar [MPa] 70CM2 Sxx Tensile stress on BC bar [MPa] 70



DZ Vertical displacement in point C [cm] -0.299954 cm 0.02%

Sxx Tensile stress on AC bar [MPa] 69.9998 MPa 0.00%

Sxx Tensile stress on BC bar [MPa] 69.9998 MPa 0.00%


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1.3 Circular plate under uniform load (01-0003SSLSB_FEM)

Test ID: 2435

Test status: Passed

1.3.1 Description

On a circular plate of 5 mm thickness and 2 m diameter, an uniform load, perpendicular on the plan of the plate, isapplied. The vertical displacement on the plate center is verified.

1.3.2 Background


Reference: Structure Calculation Software Validation Guide, test SSLS 03/89;

Analysis type: linear static;


Circular plate under uniform load Scale =1/1001-0003SSLSB_FEM

Units

I. S.

Geometry

Circular plate radius: r = 1m,

Circular plate thickness: h = 0.005 m.



Pa,



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Boundary conditions

Outer: Plate fixed on the side (in all points of its perimeter),

For the modeling, we consider only a quarter of the plate and we impose symmetry conditions on some nodes(see the following model; yz plane symmetry condition):translation restrained nodes along x and rotationrestrained nodes along y and z: translation restrained nodes along x and rotation restrained nodes along y andz:

Inner: None.

Loading

External: Uniform loads perpendicular on the plate: pZ= -1000 Pa,

Internal: None.

1.3.2.2 Vertical displacement of the model at the center of the plate

Reference solution

Circular plates form:

u =pr

4

64D

=-1000 x 1

4

64 x 2404

= - 6.50 x 10-3

m

with the plate radius coefficient: D =Eh

3

12(1-2) =

2.1 x 1011

x 0.0053

12(1-0.32)

D = 2404



70 nodes,

58 planar elements.

Circular plate under uniform load Scale =1.5

Meshing 01-0003SSLSB_FEM


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25

Deformed shape

Circular plate under uniform load Scale =1.5

Deformed 01-0003SSLSB_FEM



CM2 DZ Vertical displacement on the plate center [mm] -6.50



DZ Vertical displacement on the plate center [mm] -6.47032 mm 0.46%


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1.4 Slender beam with variable section (fixed-free) (01-0004SDLLB_FEM)

Test ID: 2436

Test status: Passed

1.4.1 Description

Verifies the first eigen mode frequencies for a slender beam with variable section, subjected to its own weight.

1.4.2 Background


Reference: Structure Calculation Software Validation Guide, test SDLL 09/89;

Analysis type: modal analysis;

Element type: linear.

Slender beam with variable section (fixed-free) Scale =1/4

01-0004SDLLB_FEM

Units

I. S.

Geometry

Beam length: l = 1 m,

Initial section (in A):

Height: h1 = 0.04 m,

Width: b1 = 0.04 m,

Section: A1 = 1.6 x 10-3 m2,

Flexure moment of inertia relative to z-axis: Iz1= 2.1333 x 10-7

m4,

Final section (in B):

Height: h2= 0.01 m,

Width: b2= 0.01 m,

Section: A2= 10-4m2,

Flexure moment of inertia relative to z-axis: Iz2= 8.3333 x 10-10

m4.


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Longitudinal elastic modulus: E = 2 x 1011

Pa,

Density: 7800 kg/m3.

Boundary conditions

Outer: Fixed in A, Inner: None.

Loading

External: None,

Internal: None.

1.4.2.2 Eigen mode frequencies

Reference solutions

Precise calculation by numerical integration of the differential equation of beams bending (Euler-Bernoulli theories):

2

x2 (EIz2v

x2 ) = -A2v

x2 where Izand A vary with the abscissa.

The result is: fi=1

2i

h2l2

E

12

1 2 3 4 523.289 73.9 165.23 299.7 478.1


Linear element: variable beam, imposed mesh,

31 nodes,

30 linear elements.

Eigen mode shapes


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CM2 Eigen mode Eigen mode 1 frequency [Hz] 54.18







Eigen mode 1 frequency [Hz] 54.01 Hz -0.31%






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1.5 Tied (sub-tensioned) beam (01-0005SSLLB_FEM)

Test ID: 2437

Test status: Passed

1.5.1 Description

Verifies the tension force on a beam reinforced by a system of hinged bars, subjected to a uniform linear load.

1.5.2 Background


Reference: Structure Calculation Software Validation Guide, test SSLL 13/89;

Analysis type: static, thermoelastic (plane problem);


Tied (sub-tensioned) beam Scale =1/37

01-0005SSLLB_FEM

Units

I. S.

Geometry

Length:

AD = FB = a = 2 m,

DF = CE = b = 4 m,

CD = EF = c = 0.6 m,

AC = EB = d = 2.088 m,

Total length: L = 8 m,

AD, DF, FB Beams:

Section: A = 0.01516 m2,

Shear area: Ar= A / 2.5,

Inertia moment: I = 2.174 x 10-4

m4,


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CE Bar:

Section: A1= 4.5 x 10-3

m2,

AC, EB bar:

Section: A2= 4.5 x 10-3

m2,

CD, EF bars:

Section: A3= 3.48 x 10-3

m2.


Isotropic linear elastic material,


Pa,

Shearing module: G = 0.4x E.

Boundary conditions

Outer: Hinged in A, support connection in B (blocked vertical translation),

Inner: Hinged at bar ends: AC, CD, EF, EB.

Loading

External: Uniform linear load p = -50000 N/ml,

Internal: Shortening of the CE tie of = 6.52 x 10-3m (dilatation coefficient: CE= 1 x 10-5

/C and temperature

variation T = -163C).

1.5.2.2 Compression force in CE bar

Reference solution

The solution is established by considering the deformation effects due to the shear force and normal force:

= 1 -43 x

aL

k =AA

r

= 2.5

t =I

A

= (L/c)2x (1+ (A/A1) x (b/L) + 2 x (A/A2) x (d/a)2x (d/L) + 2 x (A/A3) (c/a)

2x (c/L)

= k x [(2Et2) / (GaL)]

= + +

0= 1 (a/L)2x (2 a/L)

0= 6k x (E/G) x (t/L)2x (1 + b/L)

0= 0+0

NCE= - (1/12) x (pL

2

/c) x (0/) + (EI/(Lc2

)) x (/) = 584584 N


Linear element: without meshing,

AD, DF, FB: S beam (considering the shear force deformations),

AC, CD, EF, EB: bar,

CE: beam,

6 nodes.


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Force diagrams


Compression force in CE bar

1.5.2.3 Bending moment at point H

Reference solution

MH= - (1/8) x pL2x [1- (2/3) x (0/)] (EI/(Lc)) x (/p) = 49249.5 N





CE: beam,

6 nodes.


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Shape of the bending moment diagram


Mz bending moment

1.5.2.4 Vertical displacement at point D

Reference solution

The reference displacement vDprovided by AFNOR is determined by averaging the results of several software with

implemented finite elements method.

vD = -0.5428 x 10-3

m





CE: beam,

6 nodes.


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Deformed shape


Deformed


Solver Result name Result description Reference valueCM2 FX Tension force on CE bar [N] 584584



Fx Tension force on CE bar [N] 584580 N 0.00%


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1.6 Thin circular ring fixed in two points (01-0006SDLLB_FEM)

Test ID: 2438

Test status: Passed

1.6.1 Description

Verifies the first eigen modes frequencies for a thin circular ring fixed in two points, subjected to its own weight only.

1.6.2 Background



Analysis type: modal analysis, plane problem;


Thin circular ring fixed in two points Scale =1/2

01-0006SDLLB_FEM

Units

I. S.

Geometry

Average radius of curvature: OA = OB = R = 0.1 m,

Angular spacing between points A and B: 120 ;

Rectangular straight section:

Thickness: h = 0.005 m,

Width: b = 0.010 m,

Section: A = 5 x 10-5

m2,

Flexure moment of inertia relative to the vertical axis: I = 1.042 x 10-10

m4,


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Point coordinates:

O (0 ;0),

A (-0.05 3 ; -0.05),

B (0.05 3 ; -0.05).



Pa

Poisson's ratio: = 0.3,

Density: = 2700 kg/m3.

Boundary conditions

Outer: Fixed at A and B,

Inner: None.

Loading

External: None,

Internal: None.


Reference solutions

The deformation of the fixed ring is calculated from the deformations of the free-free thin ring

Symmetrical mode:

ui= i cos(i)

vi= sin (i)

i=1-i

2

R sin (i)

Antisymmetrical mode: ui= i sin(i)

vi= -cos (i)

i=1-i

2

R cos (i)

From Greens method results:

fj=2

1j

2R

h

12

E

with a support angle of 120.

i 1 2 3 4

Symmetrical mode 4.8497 14.7614 23.6157

Antisymmetrical mode 1.9832 9.3204 11.8490 21.5545


Linear element: beam, without meshing,

32 nodes,

32 linear elements.


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Eigen mode shapes


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37

1.6.2.3 Theoretic results


CM2 Eigen mode Eigen mode 1 frequency - 1 antisymmetric 1 [Hz] 235.3

CM2 Eigen mode Eigen mode 2 frequency - 2 symmetric 1 [Hz] 575.3




CM2 Eigen mode Eigen mode 6 frequency - 6 antisymmetric 4 [Hz] 2557




Eigen mode 1 frequency - 1 antisymmetric 1 [Hz] 236.32 Hz 0.43%Eigen mode 2 frequency - 2 symmetric 1 [Hz] 578.52 Hz 0.56%

Eigen mode 3 frequency - 3 antisymmetric 2 [Hz] 1112.54 Hz 0.61%


Eigen mode 5 frequency - 5 symmetric 2 [Hz] 1760 Hz 0.51%


Eigen mode 7 frequency - 7 symmetric 3 [Hz] 2777.43 Hz -0.87%


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1.7 Thin lozenge-shaped plate fixed on one side (alpha = 0 ) (01-0007SDLSB_FEM)

Test ID: 2439

Test status: Passed

1.7.1 Description

Verifies the eigen modes frequencies for a 10 mm thick lozenge-shaped plate fixed on one side, subjected to its ownweight only.

1.7.2 Background


Reference: Structure Calculation Software Validation Guide, test SDLS 02/89;



Thin lozenge-shaped plate fixed on one side Scale =1/1001-0007SDLSB_FEM

Units

I. S.

Geometry

Thickness: t = 0.01 m,

Side: a = 1 m,

= 0

Points coordinates:

A ( 0 ; 0 ; 0 )

B ( a ; 0 ; 0 )

C ( 0 ; a ; 0 )

D ( a ; a ; 0 )


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Test ID: 2440

Test status: Passed

1.8.1 Description


1.8.2 Background






Units

I. S.

Geometry


Side: a = 1 m,

= 15

Points coordinates:

A ( 0 ; 0 ; 0 )

B ( a ; 0 ; 0 )

C ( 0.259a ; 0.966a ; 0 ) D ( 1.259a ; 0.966a ; 0 )


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Pa,



Boundary conditions

Outer: AB side fixed,

Inner: None.

Loading

External: None,

Internal: None.

1.8.2.2 Eigen modes frequencies function by angle

Reference solution

M. V. Barton formula for a lozenge of side "a" leads to the frequencies:

fj= 2a2

1i

2

)1(12

Et2

2

where i = 1,2, or i

2= g().

= 151

2 3.6012

2 8.872M. V. Barton noted the sensitivity of the result relative to the mode and the angle. He acknowledged that the ivalues were determined with a limited development of an insufficient order, which led to consider a reference valuethat is based on an experimental result, verified by an average of seven software that use the finite elementscalculation method.



961 nodes,


Eigen mode shapes


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Test ID: 2441

Test status: Passed

1.9.1 Description


1.9.2 Background






Units

I. S.

Geometry


Side: a = 1 m,

= 30

Points coordinates:

A ( 0 ; 0 ; 0 )

B ( a ; 0 ; 0 )

C ( 0.5a ;32

a ; 0 )

D ( 1.5a ;32

a ; 0 )


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Pa,



Boundary conditions


Inner: None.

Loading

External: None,

Internal: None.

1.9.2.2 Eigen mode frequencies relative to the angle

Reference solution


fj= 2a2

1i

2

)1(12

Et2

2

where i = 1,2, or i

2= g().

= 301

2 3.9612

2 10.19

M. V. Barton noted the sensitivity of the result relative to the mode and the angle. He acknowledged that the ivalues were determined with a limited development of an insufficient order, which led to consider a reference valuethat is based on an experimental result, verified by an average of seven software that use the finite elementscalculation method.



961 nodes,


Eigen mode shapes


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Test ID: 2442

Test status: Passed

1.10.1 Description


1.10.2 Background






Units

I. S.

Geometry


Side: a = 1 m,

= 45

Points coordinates:

A ( 0 ; 0 ; 0 )

B ( a ; 0 ; 0 )

C (2

2a ;

2

2a ; 0 )

D (2

22+a ;

2

2a ; 0 )


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Pa,



Boundary conditions


Inner: None.

Loading

External: None,

Internal: None.

1.10.2.2 Eigen mode frequencies relative to the angle

Reference solution


fj= 2a2

1i

2

)1(12

Et2

2

where i = 1,2, or i

2= g().

= 451

2 4.45022

2 10.56

M. V. Barton noted the sensitivity of the result relative to the mode and the angle. He acknowledged that the ivalues were determined with a limited development of an insufficient order, which led to consider a reference valuethat is based on an experimental result, verified by an average of seven software that use the finite elementscalculation method.



961 nodes,


Eigen mode shapes


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Eigen mode 1 frequency [Hz] 11.28 Hz 1.41%

Eigen mode 2 frequency [Hz] 28.08 Hz 6.02%


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1.11 Vibration mode of a thin piping elbow in plane (case 1) (01-0011SDLLB_FEM)

Test ID: 2443

Test status: Passed

1.11.1 Description

Verifies the vibration modes of a thin piping elbow (1 m radius) with fixed ends and subjected to its self weight only.

1.11.2 Background



Analysis type: modal analysis (plane problem);


Vibration mode of a thin piping elbow in plane Scale = 1/7

Case 1 01-0011SDLLB_FEM

Units

I. S.

Geometry

Average radius of curvature: OA = R = 1 m,

Straight circular hollow section:

Outer diameter: de= 0.020 m,

Inner diameter: di= 0.016 m,

Section: A = 1.131 x 10-4

m2,

Flexure moment of inertia relative to the y-axis: Iy= 4.637 x 10

-9

m

4

, Flexure moment of inertia relative to z-axis: Iz= 4.637 x 10

-9m

4,

Polar inertia: Ip= 9.274 x 10-9

m4.


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Points coordinates (in m):

O ( 0 ; 0 ; 0 )

A ( 0 ; R ; 0 )

B ( R ; 0 ; 0 )



Pa,



Boundary conditions

Outer: Fixed at points A and B ,

Inner: None.

Loading

External: None,

Internal: None.


Reference solution

The Rayleigh method applied to a thin curved beam is used to determine parameters such as:

in plane bending:

fj=2

2

i

R2

A

EIz

where i = 1,2,


Linear element: beam,

11 nodes,

10 linear elements.

Eigen mode shapes


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CM2 Eigen mode Eigen mode frequency in plane 1 [Hz] 119




Eigen mode frequency in plane 1 [Hz] 120.09 Hz 0.91%



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Test ID: 2444

Test status: Passed

1.12.1 Description

Verifies the vibration modes of a thin piping elbow (1 m radius) extended by two straight elements of length L,subjected to its self weight only.

1.12.2 Background





Vibration mode of a thin piping elbow Scale = 1/11Case 2 01-0012SDLLB_FEM

Units

I. S.

Geometry


L = 0.6 m,


Outer diameter de= 0.020 m,

Inner diameter di= 0.016 m,

Section: A = 1.131 x 10-4

m2,

Flexure moment of inertia relative to the y-axis: Iy= 4.637 x 10

-9

m

4

, Flexure moment of inertia relative to z-axis: Iz= 4.637 x 10

-9m

4,


m4.


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Points coordinates (in m):

O ( 0 ; 0 ; 0 )

A ( 0 ; R ; 0 )

B ( R ; 0 ; 0 )

C ( -L ; R ; 0 )

D ( R ; -L ; 0 )



Pa,



Boundary conditions

Outer:

Fixed at points C and D

At A: translation restraint along y and z,

At B: translation restraint along x and z,

Inner: None.

Loading

External: None,

Internal: None.


Reference solution

The Rayleigh method applied to a thin curved beam is used to determine parameters such as:

in plane bending:

fj=2

2i

R2

A

EIz

where i = 1,2,



23 nodes,

22 linear elements.


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Eigen mode shapes










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Test ID: 2445

Test status: Passed

1.13.1 Description

Verifies the vibration modes of a thin piping elbow (1 m radius) extended by two straight elements of length L,subjected to its self weight only.

1.13.2 Background





Vibration mode of a thin piping elbow Scale = 1/12Case 3 01-0013SDLLB_FEM

Units

I. S.

Geometry



Outer diameter: de= 0.020 m,

Inner diameter: di= 0.016 m,

Section: A = 1.131 x 10-4

m2,

Flexure moment of inertia relative to the y-axis: Iy= 4.637 x 10-9

m4,

Flexure moment of inertia relative to z-axis: Iz= 4.637 x 10-9m4,


m4.


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58

Eigen mode shapes



CM2 Eigen mode Eigen mode frequency in plane 1 [Hz] 25.300

CM2 Eigen mode Eigen mode frequency in plane 2 [Hz] 27.000



Eigen mode frequency in plane 1 [Hz] 24.96 Hz -1.36%

Eigen mode frequency in plane 2 [Hz] 26.71 Hz -1.09%


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1.14 Thin circular ring hanged on an elastic element (01-0014SDLLB_FEM)

Test ID: 2446

Test status: Passed

1.14.1 Description

Verifies the first eigen modes frequencies of a circular ring hanged on an elastic element, subjected to its self weightonly.

1.14.2 Background



Analysis type: modal analysis, plane problem;


Thin circular ring hang from an elastic element Scale = 1/101-0014SDLLB_FEM

Units

I. S.

Geometry

Average radius of curvature: OB = R = 0.1 m,

Length of elastic element: AB = 0.0275 m ;


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Straight rectangular section:

Ring


Width: b = 0.010 m,


m2,

Flexure moment of relative to the vertical axis: I = 1.042 x 10-10m4,

Elastic element


Width: b = 0.010 m,


m2,

Flexure moment of inertia relative to the vertical axis: I = 2.25 x 10-11

m4,

Points coordinates:

O ( 0 ; 0 ),

A ( 0 ; -0.0725 ),

B ( 0 ; -0.1 ).



Pa,



Boundary conditions

Outer: Fixed in A,

Inner: None.

Loading

External: None, Internal: None.


Reference solutions

The reference solution was established from experimental results of a mass manufactured aluminum ring.



43 nodes,

43 linear elements.


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Eigen mode shapes



CM2 Eigen mode Eigen mode 1 Asymmetrical frequency [Hz] 28.80

CM2 Eigen mode Eigen mode 2 Symmetrical frequency [Hz] 189.30



CM2 Eigen mode Eigen mode 5 Symmetrical frequency [Hz] 682.00



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Eigen mode 1 Asymmetrical frequency [Hz] 28.81 Hz 0.03%

Eigen mode 2 Symmetrical frequency [Hz] 189.69 Hz 0.21%



Eigen mode 5 Symmetrical frequency [Hz] 683.9 Hz 0.28%



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1.15 Double fixed beam with a spring at mid span (01-0015SSLLB_FEM)

Test ID: 2447

Test status: Passed

1.15.1 Description

Verifies the vertical displacement on the middle of a beam consisting of four elements of length "l", having identicalcharacteristics. A punctual load of -10000 N is applied.

1.15.2 Background


Reference: internal GRAITEC test;

Analysis type: linear static;


Units

I. S.

Geometry

l = 1 m

S = 0.01 m2

I = 0.0001 m4



Pa,


Boundary conditions

Outer:

Fixed at ends x = 0 and x = 4 m,

Elastic support with k= EI/lrigidity

Inner: None.

Loading

External: Punctual load P = -10000 N at x = 2m,

Internal: None.


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Reference solution

The reference vertical displacement v3, is calculated at the middle of the beam at x = 2 m.

Rigidity matrix of a plane beam:

[ ]

=

llll

llll

ll

lll

llll

ll

EIEIEIEI

EIEIEIEI

EIEIEIEI

EIEIEIEI

460

260

6120

6120

00l

ES00

ES

260

460

6120

6120

00ES

-00ES

K

22

2323

22

2323

e

Given the symmetry / X and load of the structure, it is unnecessary to consider the degrees of freedom associatedwith normal work (u2, u3, u4).

The same symmetry allows the deduction of:

v2= v4

2= -4

3= 0

( )( )( )( )( )( )65

4

3

2

1

0

0

0

0

0

4626

612612

2680

26

6120

24612

2680

26

6120

124612

2680

26

6120

24612

2646

612612

5

5

1

1

5

5

4

4

3

3

2

2

1

1

22

22

22

22

22

22

22

22

22

22

=

+

M

R

P

M

R

v

v

v

v

v

EI

llll

llll

lllll

lllll

lllll

llllll

lllll

lllll

llll

llll

33

333

333

333

33


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65

The elementary rigidity matrix of the spring in its local axis system, [ ])(

)(

11

11

6

3

5U

UEIk

=l

, must be expressed in

the global axis system by means of the rotation matrix (90 rotation):

[ ]

( )( )( )( )( )( )6

6

6

3

3

3

5

000000

010010

000000

000000

010010

000000

v

u

v

u

EIK

=l

344332 4

30

826vvllll

==++

34433233 2024612

vvvv ==+lll

y)unnecessar(usually026826

244423222 vvvv ==+++ lllll

(3) ( )

m1011905.03

612124612 03

2

3

34243332223

=+

==

++

EIl

Pv

EI

Pvvv

llllll



6 nodes,

4 linear elements + 1 spring,

Deformed shape

Double fixed beam with a spring at mid span

Deformed

Note: the displacement is expressed here in m

1.15.2.3 Theoretical resultsSolver Result name Result description Reference value

CM2 Dz Vertical displacement on the middle of the beam [mm] -0.11905



Dz Vertical displacement on the middle of the beam [mm] -0.119048 mm 0.00%


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66

1.16 Double fixed beam (01-0016SDLLB_FEM)

Test ID: 2448

Test status: Passed

1.16.1 Description

Verifies the eigen modes frequencies and the vertical displacement on the middle of a beam consisting of eightelements of length "l", having identical characteristics. A punctual load of -50000 N is applied.

1.16.2 Background


Reference: internal GRAITEC test (beams theory);

Analysis type: static linear, modal analysis;


Units

I. S.

Geometry

Length: l = 16 m,

Axial section: S=0.06 m2

Inertia I = 0.0001 m4



N/m2,


Density: = 7850 kg/m3

Boundary conditions

Outer: Fixed at both ends x = 0 and x = 8 m,

Inner: None.

Loading

External: Punctual load P = -50000 N at x = 4m,

Internal: None.


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67


Reference solution

The reference vertical displacement v5, is calculated at the middle of the beam at x = 2 m.

m05079.00001.0111.2192

1650000

192

33

5

=

==

EEI

Plv



9 nodes,

8 elements.

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