Eiffel's Tower marks the birth of applied mechanics

Thanks William for your map --- that's a useful technological guide for my July visit to Paris with my students.

I just realized, last year there was this Expo Gustave Eiffel - Paris --- 'expo Gustave Eiffel,
le magicien du fer, se tient à l'Hôtel de Ville, Salle Saint Jean,
jusqu'au 29 août. I guess it is over, what a pity, were you there?  Probably this is because last year t was 120 years anniversary Tour Eiffel, 120 ANS, Gustave Eiffel, 1889 2009, Photo:
Francisco Munoz Espejo 2009

If you prefer a documentary in spanish, see here.  Or here with some nice music. But also here old movies.

There is even a full movie about the history of the tour eiffel..  See here for the first part, and follow the links for the other 5-6 parts.  It's in french...

I am happy to see that Sarkozy is revitalizing Paris with Grand Paris : Les 10 projets architecturaux (hope you don't mind some french..).  

But my students were stimulated by Zhigang's worry that I underestimate them, so they produced a ANSYS input file for the Tour today.  Have a try, we can later discuss optimality of the Tour with various strategies before I actually make the trip in July!

/prep7
et,1,63
mp,ex,1,205000
mp,prxy,1,0.3
! DEFINIZIONE DEI KEYPINTS
k,1,,5
k,2,11.280,5
k,3,17.113,5.284
k,4,23.278,5.585
k,5,29.795,5.903
k,6,36.683,6.239
k,7,43.963,6.594
k,8,51.658,6.969
k,9,59.791,7.365
k,10,68.387,7.784
k,11,77.473,8.227
k,12,87.076,8.696
k,13,97.076,9.245
k,14,107.076,9.999
k,15,117.576,10.790
k,16,128.076,11.786
k,17,138.676,12.880
k,18,149.376,14.303
k,19,160.676,15.806
k,20,165.576,16.925
k,22,185.776,21.583
k,23,196.776,24.365
k,24,207.776,27.415
k,25,218.776,30.919
k,26,225.776,33.697
k,27,236.776,38.673
k,28,247.776,43.578
k,29,258.776,48.519
k,30,269.776,53.459
k,31,269.776
k,32,258.776
k,33,247.776
k,34,236.776
k,35,225.776
k,36,218.776
k,37,207.776
k,38,196.776
k,39,185.776
k,41,165.576
k,42,160.676
k,43,149.376
k,44,138.676
k,45,128.076
k,46,117.576
k,47,107.076
k,48,97.076
k,49,87.076
k,50,77.473
k,51,68.387
k,52,59.791
k,53,51.658
k,54,43.963
k,55,36.683
k,56,29.795
k,57,23.278
k,58,17.113
k,59,11.280
k,60
spline,1,2,3,4,5,6
spline,6,7,8,9,10,11
spline,11,12,13,14,15,16
spline,16,17,18,19,20,22
spline,22,23,24,25,26
spline,26,27,28,29,30
l,30,31
l,31,60
l,60,1
! CREAZIONE AREA
a,1,2,59,60
a,2,3,58,59
a,3,4,57,58
a,4,5,56,57
a,5,6,55,56
a,6,7,54,55
a,7,8,53,54
a,8,9,52,53
a,9,10,51,52
a,10,11,50,51
a,11,12,49,50
a,12,13,48,49
a,13,14,47,48
a,14,15,46,47
a,15,16,45,46
a,16,17,44,45
a,17,18,43,44
a,18,19,42,43
a,19,20,41,42
a,20,22,39,41
a,22,23,38,39
a,23,24,37,38
a,24,25,36,37
a,25,26,35,36
a,26,27,34,35
a,27,28,33,34
a,28,29,32,33
a,29,30,31,32

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878

I am very interested about the study of the Eiffel Tower. In this Ansys input file I introduce the effect of the wind along the right profile of the Tour at a pressure of 300 kg/m2 and weight of the tower. 

/prep7

et,1,3

mp,ex,1,205000

mp,prxy,1,0.3

!DEFINITION OF THE GRAVITY ACCELERATION

g=9.81

acel,,-g

! DEFINITION KEYPOINTS

k,1,5,269.776

k,2,5,258.776

k,3,5.284,247.776

k,4,5.585,236.776

k,5,5.903,225.776

k,6,6.239,218.776

k,7,6.594,207.776

k,8,6.969,196.776

k,9,7.365,185.776

k,10,7.784,165.576

k,11,8.227,160.676

k,12,8.696,149.376

k,13,9.245,138.676

k,14,9.999,128.076

k,15,10.790,117.576

k,16,11.786,107.076

k,17,12.880,97.076

k,18,14.303,87.076

k,19,15.806,77.473

k,20,18.925,68.387

k,21,21.583,59.791

k,22,24.365,51.658

k,23,27.415,43.963

k,24,30.919,36.683

k,25,33.697,29.795

k,26,38.673,23.278

k,27,43.578,17.113

k,28,48.519,11.280

k,29,53.459

k,30,-5,269.776

k,31,-5,258.776

k,32,-5.284,247.776

k,33,-5.585,236.776

k,34,-5.903,225.776

k,35,-6.239,218.776

k,36,-6.594,207.776

k,37,-6.969,196.776

k,38,-7.365,185.776

k,39,-7.784,165.576

k,40,-8.227,160.676

k,41,-8.696,149.376

k,42,-9.245,138.676

k,43,-9.999,128.076

k,44,-10.790,117.576

k,45,-11.786,107.076

k,46,-12.880,97.076

k,47,-14.303,87.076

k,48,-15.806,77.473

k,49,-18.925,68.387

k,50,-21.583,59.791

k,51,-24.365,51.658

k,52,-27.415,43.963

k,53,-30.919,36.683

k,54,-33.697,29.795

k,55,-38.673,23.278

k,56,-43.578,17.113

k,57,-48.519,11.280

k,58,-53.459

!GENERATION OF A SEGMENT SPLINE THROUGH A SERIES OF KEYPOINTS

spline,1,2,3,4,5,6

spline,6,7,8,9,10,11

spline,11,12,13,14,15,16

spline,16,17,18,19,20,21

spline,21,22,23,24,25

spline,25,26,27,28,29

l,29,58

spline,30,31,32,33,34,35

spline,35,36,37,38,39,40

spline,40,41,42,43,44,45

spline,45,46,47,48,49,50

spline,50,51,52,53,54,55

spline,55,56,57,58

l,1,30

! DEFINITION AREAS BY CONNECTING KEYPOINTS

a,1,2,31,30

a,2,3,32,31

a,3,4,33,32

a,4,5,34,33

a,5,6,35,34

a,6,7,36,35

a,7,8,37,36

a,8,9,38,37

a,9,10,39,38

a,10,11,40,39

a,11,12,41,40

a,12,13,42,41

a,13,14,43,42

a,14,15,44,43

a,15,16,45,44

a,16,17,46,45

a,17,18,47,46

a,18,19,48,47

a,19,20,49,48

a,20,21,50,49

a,21,22,51,50

a,22,23,52,51

a,23,24,53,52

a,24,25,54,53

a,25,26,55,54

a,26,27,56,55

a,27,28,57,56

a,28,29,58,57

!vincoli e forze

dl,29,,all

sfl,1,pres,2943

sfl,2,pres,2943

sfl,3,pres,2943

sfl,4,pres,2943

sfl,5,pres,2943

sfl,6,pres,2943

sfl,7,pres,2943

sfl,8,pres,2943

sfl,9,pres,2943

sfl,10,pres,2943

sfl,11,pres,2943

sfl,12,pres,2943

sfl,13,pres,2943

sfl,14,pres,2943

sfl,15,pres,2943

sfl,16,pres,2943

sfl,17,pres,2943

sfl,18,pres,2943

sfl,19,pres,2943

sfl,20,pres,2943

sfl,21,pres,2943

sfl,22,pres,2943

sfl,22,pres,2943

sfl,23,pres,2943

sfl,24,pres,2943

sfl,25,pres,2943

sfl,26,pres,2943

sfl,27,pres,2943

sfl,28,pres,2943

George

 I think this is a good starting point.  However

1) the pressure seems to be orthogonal to the elements, not constant horizontal direction

2) I would prefer to see the definition of the surfaces more "parametric" so that at later stage we can optimize, either in shape optimization (i.e. you change the coordinates of the nodes in the splines), or as a full topological optimization (see here, for example ).  See e.g. these examples

The gallery shows the last 21 computed designs using the
interactive Compliance Design program.

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/

The Matlab code presented in this page is intended for
engineering education. Students and newcomers to the field of topology
optimization can find the code here and download it. The code may be
used in courses in structural optimization where students may be
assigned to do extensions such as multiple load-cases, alternative
mesh-independency schemes, passive areas, etc..

The code is here top.m
(5K, Shift+click to save). This version of the code is optimized
with respect to speed compared to the original version and was released
on May 28th, 2002.

Save the program and start Matlab in the same directory. Run the
program by writing for example:

in the Matlab prompt.

A description of the code can be found in the paper "A 99 line topology
optimization code written in MATLAB" (PDF) (160K) (Structural and
Multidisciplinary Optimization 21(2), 2001, pp. 120-127) by Ole Sigmund.

The
original publication is available on LINK at http://link.springer.de

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878

 More on this can be found here !

Canh V. Le,
PhD in Computational Mechanics
Department of Civil and Structural Engineering

The University of Sheffield

Mappin Street,

Sheffield, S1 3JD, UK.

Phone: GB +44 1142225724
http://sites.google.com/site/canhlewebpage/

Thanks Canh V. Le,

   if you have seen our educational effort here before our trip to Paris, we want to play with Eiffel's tower design.  Do you think the 99 lines program or your LayOpt matlab code,can be adapted for our problem, or at least to something close to it?

Thanks in advance.

mike

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878

 Dear Mike,

I would recommend to use LayOut or DLO since it is in general and has been tested for large-scale performance at our group. The idea behind is that we generate nodes in working domain and make as many as possible connections which can be line (truss) elements (gridlike structures), of course the more elements are used the better solutions can be obtained. In order to reduce computational cost Matthew Gilbert and Andrew Tyas have proposed nodal adaptive to optimize the number of connections. This  procedue has also been extended to plastic limit analysis problems and implemented in a comercial software. Therefore, I believe that you can adapt this technique to your project.

Best,

Canh

Canh V. Le,
PhD in Computational Mechanics
Department of Civil and Structural Engineering

The University of Sheffield

Mappin Street,

Sheffield, S1 3JD, UK.

Phone: GB +44 1142225724
http://sites.google.com/site/canhlewebpage/

I checked the link you provided but it seems to do limit analysis, not truss optimization.

I think in the classical book by Bendsoe, M.P., Sigmund, O. there is an example about Eiffel Tower, and indeed it does suggest we can both use a set of beams, or topological optimization of a continuum --- or a combination of the techniques. But I need to suggest my students something simple, like either in the software ANSYS, or a very well documented simple Matlab routine.

Topology Optimization - Theory, Methods
and Applications

Bendsoe, M.P., Sigmund, O.

2nd ed. 2003. Corr. 2nd printing, 2003,
XIV, 370 p., Hardcover

ISBN: 978-3-540-42992-0

Table of
Contents, Erata

Do you know what to suggest then??

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878

yes, the DLO is for limit analysis, but the procedure is identical to truss optimization. Have you checked this ?

Canh

Canh V. Le,
PhD in Computational Mechanics
Department of Civil and Structural Engineering

The University of Sheffield

Mappin Street,

Sheffield, S1 3JD, UK.

Phone: GB +44 1142225724
http://sites.google.com/site/canhlewebpage/

Dear Cahn

  I am no expert in the field and about Eiffel's tower I only  have a master thesis from a student of Prof. Sacchi Landriani, whom I have been suggested to refer to from the President of the French Academy of Science, my friend Prof. Salencon of Ecole Polytechnique.  But that was not on optimal design.

Prof. Sacchi Landriani incidentally is the author of a nice paper

A
Recollection of Some Results and a Few Remarks on Structural
Optimisation

 Now, I checked briefly the paper you refer to.  It says:-

Abstract:

Computerized layout (or “topology”) optimization
was pioneered almost four decades back. However, despite dramatic
increases in available computer power and the application of
increasingly efficient optimization algorithms, even now only relatively
modest sized problems can be tackled using the traditional “ground
structure” approach. This is because of the need, in general, for the
latter to contain every conceivable member connecting together the nodes
in a problem. A simple, but effective solution method capable of
tackling problems with large numbers of potential members (e.g.
>100,000,000) is presented. Though the method draws on the linear
programming technique of “column generation”, since layout optimization
specific heuristics are employed it is presented as an iterative “member
adding” method. The method requires a ground structure with minimal
connectivity to be used in the first iteration; members are then added
as required in subsequent iterations until the (provably) optimal
solution is found.

Now, the method you suggest seems "the classical sliding block upper
bound method" ( as described by Drucker and Shield, discussed in
Calladine's book and used by, for example, Ian Collins), but using some
sort of
programming method.

 Applying programming methods to
optimal design has a long history. I remember Andrew Palmer working on
the optimal design of electricity pylons using dynamic programming as
they are near serial structures - some time in the
'60. Sounds a bit like the Eifel Tower problem. I'll see if I can find
the reference.

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878

In addition to this study, I have just realized a different type of model with link8 elements, according to a colleague engineer, who has, recently, implemented a reticular trusses work on Ansys, with elements likes link8. Also, I have to complete this study with a topological analysis.

There is now a problem, in terms of deformation curve, because the postprocessing send me a message with an error about DEGREE of FREEDOM SOLUTION that is "not available"!

According to my colleague there is a constraint problem, but the processor don't give me errors in the /prep7.

Dear Canh V.Le, can you explain me any limitations about this problem, if there are?

Thanks in advance.

 commands list:

/prep7

et,1,8

mp,ex,1,205000

mp,prxy,1,0.3

mp,dens,1,1.2*10**(-3)*7874

r,1,0.001

!DEFINITION OF THE GRAVITY ACCELERATION

g=9.81

acel,,-g

!DEFINITION NODES

n,1,5,269.776

n,2,5,258.776

n,3,5.284,247.776

n,4,5.585,236.776

n,5,5.903,225.776

n,6,6.239,218.776

n,7,6.594,207.776

n,8,6.969,196.776

n,9,7.365,185.776

n,10,7.784,165.576

n,11,8.227,160.676

n,12,8.696,149.376

n,13,9.245,138.676

n,14,9.999,128.076

n,15,10.790,117.576

n,16,11.786,107.076

n,17,12.880,97.076

n,18,14.303,87.076

n,19,15.806,77.473

n,20,18.925,68.387

n,21,21.583,59.791

n,22,24.365,51.658

n,23,27.415,43.963

n,24,30.919,36.683

n,25,33.697,29.795

n,26,38.673,23.278

n,27,43.578,17.113

n,28,48.519,11.280

n,29,53.459

n,30,-5,269.776

n,31,-5,258.776

n,32,-5.284,247.776

n,33,-5.585,236.776

n,34,-5.903,225.776

n,35,-6.239,218.776

n,36,-6.594,207.776

n,37,-6.969,196.776

n,38,-7.365,185.776

n,39,-7.784,165.576

n,40,-8.227,160.676

n,41,-8.696,149.376

n,42,-9.245,138.676

n,43,-9.999,128.076

n,44,-10.790,117.576

n,45,-11.786,107.076

n,46,-12.880,97.076

n,47,-14.303,87.076

n,48,-15.806,77.473

n,49,-18.925,68.387

n,50,-21.583,59.791

n,51,-24.365,51.658

n,52,-27.415,43.963

n,53,-30.919,36.683

n,54,-33.697,29.795

n,55,-38.673,23.278

n,56,-43.578,17.113

n,57,-48.519,11.280

n,58,-53.459

n,59,,269.776

n,60,,258.776

n,61,,247.776

n,62,1,236.776

n,63,1.5,225.776

n,64,2,218.776

n,65,2.5,207.776

n,66,3,196.776

n,67,3.5,185.776

n,68,4,165.576

n,69,4.5,160.676

n,70,5,149.376

n,71,5.5,138.676

n,72,6,128.076

n,73,6,117.576

n,74,6.5,107.076

n,75,6.5,97.076

n,76,7,87.076

n,77,7.5,77.473

n,78,8,68.387

n,79,9,59.791

n,80,11,51.658

n,81,13,43.963

n,82,15,36.683

n,83,17,29.795

n,84,20,23.278

n,85,23,17.113

n,86,26,11.280

n,87,29

n,88,,269.776

n,89,,258.776

n,90,,247.776

n,91,-1,236.776

n,92,-1.5,225.776

n,93,-2,218.776

n,94,-2.5,207.776

n,95,-3,196.776

n,96,-3.5,185.776

n,97,-4,165.576

n,98,-4.5,160.676

n,99,-5,149.376

n,100,-5.5,138.676

n,101,-6,128.076

n,102,-6,117.576

n,103,-6.5,107.076

n,104,-6.5,97.076

n,105,-7,87.076

n,106,-7.5,77.473

n,107,-8,68.387

n,108,-9,59.791

n,109,-11,51.658

n,110,-13,43.963

n,111,-15,36.683

n,112,-17,29.795

n,113,-20,23.278

n,114,-23,17.113

n,115,-26,11.280

n,116,-29

n,117,41.22

n,118,37.26,11.280

n,119,33.29,17.113

n,120,29.34,23.278

n,121,25.35,29.795

n,122,22.95,36.383

n,123,20.21,43.963

n,124,17.68,51.658

n,125,-41.22

n,126,-37.26,11.280

n,127,-33.29,17.113

n,128,-29.34,23.278

n,129,-25.35,29.795

n,130,-22.95,36.383

n,131,-20.21,43.963

n,132,-17.68,51.658

!DEFINITION MONTANTI E CORRENTI

e,87,117

e,117,29

e,86,118

e,118,28

e,85,119

e,119,27

e,84,120

e,120,26

e,83,121

e,121,25

e,82,122

e,122,24

e,81,123

e,123,23

e,80,124

e,124,22

e,116,125

e,125,58

e,115,126

e,126,57

e,114,127

e,127,56

e,113,128

e,128,55

e,112,129

e,129,54

e,111,130

e,130,53

e,110,131

e,131,52

e,109,132

e,132,51

e,79,21

e,78,20

e,77,19

e,76,18

e,75,17

e,74,16

e,73,15

e,72,14

e,71,13

e,70,12

e,69,11

e,68,10

e,67,9

e,66,8

e,65,7

e,64,6

e,63,5

e,62,4

e,61,3

e,60,2

e,59,1

e,108,50

e,107,49

e,106,48

e,105,47

e,104,46

e,103,45

e,102,44

e,101,43

e,100,42

e,99,41

e,98,40

e,97,39

e,96,38

e,95,37

e,94,36

e,93,35

e,92,34

e,91,33

e,90,32

e,89,31

e,88,30

e,1,2

e,2,3

e,3,4

e,4,5

e,5,6

e,6,7

e,7,8

e,8,9

e,9,10

e,10,11

e,11,12

e,12,13

e,13,14

e,14,15

e,15,16

e,16,17

e,17,18

e,18,19

e,19,20

e,20,21

e,21,22

e,22,23

e,23,24

e,24,25

e,25,26

e,26,27

e,27,28

e,28,29

e,30,31

e,31,32

e,32,33

e,33,34

e,34,35

e,35,36

e,36,37

e,37,38

e,38,39

e,39,40

e,40,41

e,41,42

e,42,43

e,43,44

e,44,45

e,45,46

e,46,47

e,47,48

e,48,49

e,49,50

e,50,51

e,51,52

e,52,53

e,53,54

e,54,55

e,55,56

e,56,57

e,57,58

e,59,60

e,60,61

e,61,62

e,62,63

e,63,64

e,64,65

e,65,66

e,66,67

e,67,68

e,68,69

e,69,70

e,70,71

e,71,72

e,72,73

e,73,74

e,74,75

e,75,76

e,76,77

e,77,78

e,78,79

e,79,80

e,80,81

e,81,82

e,82,83

e,83,84

e,84,85

e,85,86

e,86,87

e,88,89

e,89,90

e,90,91

e,91,92

e,92,93

e,93,94

e,94,95

e,95,96

e,96,97

e,97,98

e,98,99

e,99,100

e,100,101

e,101,102

e,102,103

e,103,104

e,104,105

e,105,106

e,106,107

e,107,108

e,108,109

e,109,110

e,110,111

e,111,112

e,112,113

e,113,114

e,114,115

e,115,116

e,117,118

e,118,119

e,119,120

e,120,121

e,121,122

e,122,123

e,123,124

e,125,126

e,126,127

e,127,128

e,128,129

e,129,130

e,130,131

e,131,132

!DEFINITION TRAVERSI DESTRA

e,59,2

e,60,1

e,60,3

e,61,2

e,61,4

e,62,3

e,62,5

e,63,4

e,63,6

e,64,5

e,64,7

e,65,6

e,65,8

e,66,7

e,66,9

e,67,8

e,67,10

e,68,9

e,68,11

e,69,10

e,69,12

e,70,11

e,70,13

e,71,12

e,71,14

e,72,13

e,72,15

e,73,14

e,73,16

e,74,15

e,74,17

e,75,16

e,75,18

e,76,17

e,76,19

e,77,18

e,77,20

e,78,19

e,78,21

e,79,20

e,79,22

e,80,21

e,80,123

e,81,124

e,124,23

e,123,22

e,81,122

e,82,123

e,123,24

e,122,23

e,82,121

e,83,122

e,122,25

e,121,24

e,83,120

e,84,121

e,121,26

e,120,25

e,84,119

e,85,120

e,120,27

e,119,26

e,85,118

e,86,119

e,119,28

e,118,27

e,86,117

e,87,118

e,118,29

e,117,28

!DEFINITION TRAVERSI SINISTRA

e,30,89

e,31,88

e,31,90

e,32,89

e,32,91

e,33,90

e,33,92

e,34,91

e,34,93

e,35,92

e,35,94

e,36,93

e,36,95

e,37,94

e,37,96

e,38,95

e,38,97

e,39,96

e,39,98

e,40,97

e,40,99

e,41,98

e,41,100

e,42,99

e,42,101

e,43,100

e,43,102

e,44,101

e,44,103

e,45,102

e,45,104

e,46,103

e,47,104

e,46,105

e,48,105

e,47,106

e,48,107

e,49,106

e,50,107

e,49,108

e,50,109

e,51,108

e,51,131

e,52,132

e,132,110

e,131,109

e,52,130

e,53,131

e,131,111

e,130,110

e,53,129

e,54,130

e,130,112

e,129,111

e,54,128

e,55,129

e,129,113

e,128,112

e,55,127

e,56,128

e,128,114

e,127,113

e,56,126

e,57,127

e,127,115

e,126,114

e,57,125

e,58,126

e,126,116

e,125,115

!DEFINITION PIANI INTERMEDI

e,80,109

e,79,108

e,109,79

e,108,80

e,102,73

e,103,74

e,102,74

e,103,73

!DEFINITION VINCOLI INCASTRO

d,58,all

d,125,all

d,116,all

d,87,all

d,117,all

d,29,all

!DEFINITION FORZE VENTO

f,28,fx,-1188089

f,27,fx,-2335859

f,26,fx,-2822043

f,25,fx,-2886642

f,24,fx,-1938554

f,23,fx,-1691636

f,22,fx,-1505786

f,21,fx,-1107157

f,20,fx,-1040645

f,19,fx,-1022987

f,18,fx,-783132

f,17,fx,-716620

f,16,fx,-689986

f,15,fx,-456253

f,14,fx,-433503

f,13,fx,-413138

f,12,fx,-386180

f,11,fx,-360076

f,10,fx,-352571

f,9,fx,-303599

f,8,fx,-247212

f,7,fx,-233850

f,6,fx,-221254

f,5,fx,-209335

f,4,fx,-198063

f,3,fx,-187410

f,2,fx,-177286

f,1,fx,-249301

!SOLVING

finish

/solu

solve

finish

/post1

pldisp,1

/title,toureiffel

/filename,toureiffel

/prep7

et,1,95

mp,ex,1,205000

mp,prxy,1,0.3

! DEFINITION KEYPOINTS

k,1,5,269.776,5

k,2,5,258.776,5

k,3,5.284,247.776,5.284

k,4,5.585,236.776,5.585

k,5,5.903,225.776,5.903

k,6,6.239,218.776,6.239

k,7,6.594,207.776,6.594

k,8,6.969,196.776,6.969

k,9,7.365,185.776,7.365

k,10,7.784,165.576,7.784

k,11,8.227,160.676,8.227

k,12,8.696,149.376,8.696

k,13,9.245,138.676,9.245

k,14,9.999,128.076,9.999

k,15,10.790,117.576,10.790

k,16,11.786,107.076,11.786

k,17,12.880,97.076,12.880

k,18,14.303,87.076,14.303

k,19,16.306,77.473,16.306

k,20,18.925,68.387,18.925

k,21,21.583,59.791,21.583

k,22,24.365,51.658,24.365

k,23,27.415,43.963,27.415

k,24,30.919,36.683,30.919

k,25,34.697,29.795,34.697

k,26,38.673,23.278,38.673

k,27,43.578,17.113,43.578

k,28,48.519,11.280,48.519

k,29,57.459,0,57.459

k,30,-5,269.776,5

k,31,-5,258.776,5

k,32,-5.284,247.776,5.284

k,33,-5.585,236.776,5.585

k,34,-5.903,225.776,5.903

k,35,-6.239,218.776,6.239

k,36,-6.594,207.776,6.594

k,37,-6.969,196.776,6.969

k,38,-7.365,185.776,7.365

k,39,-7.784,165.576,7.784

k,40,-8.227,160.676,8.227

k,41,-8.696,149.376,8.696

k,42,-9.245,138.676,9.245

k,43,-9.999,128.076,9.999

k,44,-10.790,117.576,10.790

k,45,-11.786,107.076,11.786

k,46,-12.880,97.076,12.880

k,47,-14.303,87.076,14.303

k,48,-16.306,77.473,16.306

k,49,-18.925,68.387,18.925

k,50,-21.583,59.791,21.583

k,51,-24.365,51.658,24.365

k,52,-27.415,43.963,27.415

k,53,-30.919,36.683,30.919

k,54,-34.697,29.795,34.697

k,55,-38.673,23.278,38.673

k,56,-43.578,17.113,43.578

k,57,-48.519,11.280,48.519

k,58,-57.459,0,57.459

!GENERATION OF A SEGMENT !SPLINE THROUGH A ERIES OF KEYPOINTS

spline,1,2,3,4,5,6

spline,6,7,8,9,10,11

spline,11,12,13,14,15,16

spline,16,17,18,19,20,21

spline,21,22,23,24,25

spline,25,26,27,28,29

spline,30,31,32,33,34,35

spline,35,36,37,38,39,40

spline,40,41,42,43,44,45

spline,45,46,47,48,49,50

spline,50,51,52,53,54,55

spline,55,56,57,58

! DEFINIZIONE SPESSORE DELLA GAMBA dx

k,59,0.001,269.776,5

k,60,0.001,269.776,0

k,61,5,269.776,0

a,1,59,60,61

vdrag,1,,,,,,1,2,3,4,5,6

vdrag,31,,,,,,7,8,9,10,11,12

vdrag,61,,,,,,13,14,15,16,17,18

vdrag,91,,,,,,19,20,21,22,23,24

vdrag,121,,,,,,25,26,27,28

! DEFINIZIONE SPESSORE DELLA GAMBA sx

k,174,-5,269.776,0

k,175,-0.001,269.776,0

k,176,-0.001,269.776,5

a,30,174,175,176

vdrag,142,,,,,,29,30,31,32,33,34

vdrag,172,,,,,,35,36,37,38,39,40

vdrag,202,,,,,,41,42,43,44,45,46

vdrag,232,,,,,,47,48,49,50,51,52

vdrag,262,,,,,,53,54,55,56

vsymm,z,1,56,1,,0,0

! DEFINIZIONE DEL PIANO 1

a,21,370,486,50

a,24,382,498,53

a,24,21,50,53

a,24,382,370,21

a,382,370,486,498

a,498,486,50,53

va,565,566,567,568,569,570

! DEFINIZIONE DEL PIANO 2

a,15,346,462,44

a,17,354,470,46

a,17,15,44,46

a,17,354,346,15

a,354,346,462,470

a,470,462,44,46

va,571,572,573,574,575,576

!DEFINIZIONE AREA SUPERIORE

a,1,30,405,289

!DEFINIZIONE VOLUME SUPERIORE

k,521,5,270.776,5

k,522,-5,270.776,5

k,523,-5,270.776,-5

k,524,5,270.776,-5

a,521,522,523,524

a,1,30,522,521

a,30,522,523,405

a,523,524,289,405

a,1,521,524,289

va,565,566,567,568,569,570

!DEFINIZIONE VINCOLI

da,141,all

da,282,all

da,423,all

da,564,all

!DEFINIZIONE DELLA MESH

ESIZE,10,0,

MSHAPE,1,3D

MSHKEY,0

FLST,5,114,6,ORDE,2

FITEM,5,1

FITEM,5,-114

CM,_Y,VOLU

VSEL, , , ,P51X

CM,_Y1,VOLU

CHKMSH,'VOLU'

CMSEL,S,_Y

VMESH,_Y1

CMDELE,_Y

CMDELE,_Y1

CMDELE,_Y2

!DEFINIZIONE VINCOLI AREE

da,572,all

da,566,all

!DEFINIZIONE CARICHI PRIMA GAMBA

f,2413,fx,124651

f,2523,fx,88643

f,2623,fx,93705

f,2723,fx,99032

f,2814,fx,104668

f,2880,fx,110627.5

f,2980,fx,116925.5

f,3080,fx,123606

f,3186,fx,151800

f,3290,fx,176285.5

f,3356,fx,180038

f,3456,fx,193090

f,3556,fx,206569

f,3656,fx,216752

f,3756,fx,228126.5

f,3856,fx,344993

f,3956,fx,358310.5

f,4056,fx,391566

f,4153,fx,511493.5

f,4243,fx,520322.5

f,4343,fx,553578.5

f,4353,fx,752893

f,4358,fx,845818

f,4467,fx,969277

f,4523,fx,1443321

f,4579,fx,1411021.5

f,4635,fx,1167929.5

f,4700,fx,594044.5

!DEFINIZIONE CARICHI SECONDA GAMBA

f,7195,fx,124651

f,7305,fx,88643

f,7405,fx,93705

f,7505,fx,99032

f,7592,fx,104668

f,7663,fx,110627.5

f,7762,fx,116925.5

f,7862,fx,123606

f,7968,fx,151800

f,7969,fx,176285.5

f,8138,fx,180038

f,8238,fx,193090

f,8338,fx,206569

f,8438,fx,216752

f,8538,fx,228126.5

f,8638,fx,344993

f,8782,fx,358310.5

f,8739,fx,391566

f,8839,fx,511493.5

f,9025,fx,520322.5

f,9035,fx,553578.5

f,9134,fx,752893

f,9139,fx,845818

f,9249,fx,969277

f,9305,fx,1443321

f,9361,fx,1411021.5

f,9417,fx,1167929.5

f,9483,fx,594044.5

I'm going to check for a middle sectional area, because the sistem's response was really unsatisfactory, in fact the gravity effect was excessive..

However, I'm going to post  you the new command list with some important corrections, so that you can check it.

I think the  wind forces are the most probably, checking some bibliographic informations, there are about 300 Kg/m2, for variable loads on the profile of the tower.

Thanks to the availability, I'll ask you later!! 

R.C.

Dear,

I have just made some corrections on my 2D model, on real costants values and density value of Skeletal elements.

Finally, I have had some results, particularly: maximum deflection (at node 1) = 0.497997 [m]

*if we consider that it's a 2D model, with application of "3D" wind effects on nodes,  the response is largely probable. In fact, some effective data of the tower (also wikipedia..), are in the order of 0.12 [m] for the maximum deflection atop, in case of variable conditions of wind.

Below there is the commands list and the graphical response.

Thanks for your cooperation.

R.Carrieri

/prep7

et,1,8

mp,ex,1,160000*10**(6)

mp,prxy,1,0.3

mp,dens,1,7874

r,1,0.2











!DEFINITION OF THE GRAVITY ACCELERATION

g=9.81

acel,,g





!DEFINITION NODES

n,1,5,269.776

n,2,5,258.776

n,3,5.284,247.776

n,4,5.585,236.776

n,5,5.903,225.776

n,6,6.239,218.776

n,7,6.594,207.776

n,8,6.969,196.776

n,9,7.365,185.776

n,10,7.784,165.576

n,11,8.227,160.676

n,12,8.696,149.376

n,13,9.245,138.676

n,14,9.999,128.076

n,15,10.790,117.576

n,16,11.786,107.076

n,17,12.880,97.076

n,18,14.303,87.076

n,19,15.806,77.473

n,20,18.925,68.387

n,21,21.583,59.791

n,22,24.365,51.658

n,23,27.415,43.963

n,24,30.919,36.683

n,25,33.697,29.795

n,26,38.673,23.278

n,27,43.578,17.113

n,28,48.519,11.280

n,29,53.459

n,30,-5,269.776

n,31,-5,258.776

n,32,-5.284,247.776

n,33,-5.585,236.776

n,34,-5.903,225.776

n,35,-6.239,218.776

n,36,-6.594,207.776

n,37,-6.969,196.776

n,38,-7.365,185.776

n,39,-7.784,165.576

n,40,-8.227,160.676

n,41,-8.696,149.376

n,42,-9.245,138.676

n,43,-9.999,128.076

n,44,-10.790,117.576

n,45,-11.786,107.076

n,46,-12.880,97.076

n,47,-14.303,87.076

n,48,-15.806,77.473

n,49,-18.925,68.387

n,50,-21.583,59.791

n,51,-24.365,51.658

n,52,-27.415,43.963

n,53,-30.919,36.683

n,54,-33.697,29.795

n,55,-38.673,23.278

n,56,-43.578,17.113

n,57,-48.519,11.280

n,58,-53.459



n,59,,269.776

n,60,,258.776

n,61,,247.776

n,62,1,236.776

n,63,1.5,225.776

n,64,2,218.776

n,65,2.5,207.776

n,66,3,196.776

n,67,3.5,185.776

n,68,4,165.576

n,69,4.5,160.676

n,70,5,149.376

n,71,5.5,138.676

n,72,6,128.076

n,73,6,117.576

n,74,6.5,107.076

n,75,6.5,97.076

n,76,7,87.076

n,77,7.5,77.473

n,78,8,68.387

n,79,9,59.791

n,80,11,51.658

n,81,13,43.963

n,82,15,36.683

n,83,17,29.795

n,84,20,23.278

n,85,23,17.113

n,86,26,11.280

n,87,29

n,88,,269.776

n,89,,258.776

n,90,,247.776

n,91,-1,236.776

n,92,-1.5,225.776

n,93,-2,218.776

n,94,-2.5,207.776

n,95,-3,196.776

n,96,-3.5,185.776

n,97,-4,165.576

n,98,-4.5,160.676

n,99,-5,149.376

n,100,-5.5,138.676

n,101,-6,128.076

n,102,-6,117.576

n,103,-6.5,107.076

n,104,-6.5,97.076

n,105,-7,87.076

n,106,-7.5,77.473

n,107,-8,68.387

n,108,-9,59.791

n,109,-11,51.658

n,110,-13,43.963

n,111,-15,36.683

n,112,-17,29.795

n,113,-20,23.278

n,114,-23,17.113

n,115,-26,11.280

n,116,-29

n,117,41.22

n,118,37.26,11.280

n,119,33.29,17.113

n,120,29.34,23.278

n,121,25.35,29.795

n,122,22.95,36.383

n,123,20.21,43.963

n,124,17.68,51.658

n,125,-41.22

n,126,-37.26,11.280

n,127,-33.29,17.113

n,128,-29.34,23.278

n,129,-25.35,29.795

n,130,-22.95,36.383

n,131,-20.21,43.963

n,132,-17.68,51.658







!DEFINITION MONTANTI E CORRENTI

e,87,117

e,117,29

e,86,118

e,118,28

e,85,119

e,119,27

e,84,120

e,120,26

e,83,121

e,121,25

e,82,122

e,122,24

e,81,123

e,123,23

e,80,124

e,124,22

e,116,125

e,125,58

e,115,126

e,126,57

e,114,127

e,127,56

e,113,128

e,128,55

e,112,129

e,129,54

e,111,130

e,130,53

e,110,131

e,131,52

e,109,132

e,132,51

e,79,21

e,78,20

e,77,19

e,76,18

e,75,17

e,74,16

e,73,15

e,72,14

e,71,13

e,70,12

e,69,11

e,68,10

e,67,9

e,66,8

e,65,7

e,64,6

e,34,5

e,33,4

e,32,3

e,31,2

e,30,1

e,108,50

e,107,49

e,106,48

e,105,47

e,104,46

e,103,45

e,102,44

e,101,43

e,100,42

e,99,41

e,98,40

e,97,39

e,96,38

e,95,37

e,94,36

e,93,35

e,75,104

e,74,103

e,73,102

e,72,101

e,71,100

e,70,99

e,69,98

e,68,97

e,67,96

e,66,95

e,65,94

e,64,93





e,1,2

e,2,3

e,3,4

e,4,5

e,5,6

e,6,7

e,7,8

e,8,9

e,9,10

e,10,11

e,11,12

e,12,13

e,13,14

e,14,15

e,15,16

e,16,17

e,17,18

e,18,19

e,19,20

e,20,21

e,21,22

e,22,23

e,23,24

e,24,25

e,25,26

e,26,27

e,27,28

e,28,29

e,30,31

e,31,32

e,32,33

e,33,34

e,34,35

e,35,36

e,36,37

e,37,38

e,38,39

e,39,40

e,40,41

e,41,42

e,42,43

e,43,44

e,44,45

e,45,46

e,46,47

e,47,48

e,48,49

e,49,50

e,50,51

e,51,52

e,52,53

e,53,54

e,54,55

e,55,56

e,56,57

e,57,58

e,59,60

e,60,61

e,61,62

e,62,63

e,63,64

e,64,65

e,65,66

e,66,67

e,67,68

e,68,69

e,69,70

e,70,71

e,71,72

e,72,73

e,73,74

e,74,75

e,75,76

e,76,77

e,77,78

e,78,79

e,79,80

e,80,81

e,81,82

e,82,83

e,83,84

e,84,85

e,85,86

e,86,87

e,88,89

e,89,90

e,90,91

e,91,92

e,92,93

e,93,94

e,94,95

e,95,96

e,96,97

e,97,98

e,98,99

e,99,100

e,100,101

e,101,102

e,102,103

e,103,104

e,104,105

e,105,106

e,106,107

e,107,108

e,108,109

e,109,110

e,110,111

e,111,112

e,112,113

e,113,114

e,114,115

e,115,116

e,117,118

e,118,119

e,119,120

e,120,121

e,121,122

e,122,123

e,123,124

e,125,126

e,126,127

e,127,128

e,128,129

e,129,130

e,130,131

e,131,132





!DEFINITION TRAVERSI DESTRA

e,59,2

e,60,1

e,60,3

e,61,2

e,61,4

e,62,3

e,62,5

e,63,4

e,63,6

e,64,5

e,64,7

e,65,6

e,65,8

e,66,7

e,66,9

e,67,8

e,67,10

e,68,9

e,68,11

e,69,10

e,69,12

e,70,11

e,70,13

e,71,12

e,71,14

e,72,13

e,72,15

e,73,14

e,73,16

e,74,15

e,74,17

e,75,16

e,75,18

e,76,17

e,76,19

e,77,18

e,77,20

e,78,19

e,78,21

e,79,20

e,79,22

e,80,21

e,80,123

e,81,124

e,124,23

e,123,22

e,81,122

e,82,123

e,123,24

e,122,23

e,82,121

e,83,122

e,122,25

e,121,24

e,83,120

e,84,121

e,121,26

e,120,25

e,84,119

e,85,120

e,120,27

e,119,26

e,85,118

e,86,119

e,119,28

e,118,27

e,86,117

e,87,118

e,118,29

e,117,28





!DEFINITION TRAVERSI SINISTRA

e,30,89

e,31,88

e,31,90

e,32,89

e,32,91

e,33,90

e,33,92

e,34,91

e,34,93

e,35,92

e,35,94

e,36,93

e,36,95

e,37,94

e,37,96

e,38,95

e,38,97

e,39,96

e,39,98

e,40,97

e,40,99

e,41,98

e,41,100

e,42,99

e,42,101

e,43,100

e,43,102

e,44,101

e,44,103

e,45,102

e,45,104

e,46,103

e,47,104

e,46,105

e,48,105

e,47,106

e,48,107

e,49,106

e,50,107

e,49,108

e,50,109

e,51,108

e,51,131

e,52,132

e,132,110

e,131,109

e,52,130

e,53,131

e,131,111

e,130,110

e,53,129

e,54,130

e,130,112

e,129,111

e,54,128

e,55,129

e,129,113

e,128,112

e,55,127

e,56,128

e,128,114

e,127,113

e,56,126

e,57,127

e,127,115

e,126,114

e,57,125

e,58,126

e,126,116

e,125,115







!DEFINITION TRAVERSI INTERMEDI

e,75,103

e,104,74

e,74,102

e,103,73

e,73,101

e,102,72

e,72,100

e,101,71

e,71,99

e,100,70

e,70,98

e,99,69

e,69,97

e,98,68

e,68,96

e,97,67

e,67,95

e,96,66

e,66,94

e,95,65

e,65,93

e,94,64

e,64,92

e,93,63

e,63,91

e,92,62

e,91,61

e,62,90







!DEFINITION PIANI INTERMEDI

e,80,109

e,79,108

e,109,79

e,108,80









!DEFINITION VINCOLI INCASTRO

d,58,all

d,125,all

d,116,all

d,87,all

d,117,all

d,29,all









!DEFINITION FORZE VENTO

f,28,fx,-1188089

f,27,fx,-2335859

f,26,fx,-2822043

f,25,fx,-2886642

f,24,fx,-1938554

f,23,fx,-1691636

f,22,fx,-1505786

f,21,fx,-1107157

f,20,fx,-1040645

f,19,fx,-1022987

f,18,fx,-783132

f,17,fx,-716620

f,16,fx,-689986

f,15,fx,-456253

f,14,fx,-433503

f,13,fx,-413138

f,12,fx,-386180

f,11,fx,-360076

f,10,fx,-352571

f,9,fx,-303599

f,8,fx,-247212

f,7,fx,-233850

f,6,fx,-221254

f,5,fx,-209335

f,4,fx,-198063

f,3,fx,-187410

f,2,fx,-177286

f,1,fx,-249301





!SOLVING

finish

/solu

solve

finish

/post1

pldisp,1





!TABLE STAMP

prnsol,u,x

prnsol,u,y





!GRAPHIC STAMP

plnsol,u,x,1

 PRINT U    NODAL SOLUTION PER NODE

 

  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           

 

  LOAD STEP=     1  SUBSTEP=     1                                            

   TIME=    1.0000      LOAD CASE=   0                                        

 

  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 

 

    NODE      UX   

       1 -0.49500   

       2 -0.45798   

       3 -0.42301   

       4 -0.38814   

       5 -0.35434   

       6 -0.33278   

       7 -0.30060   

       8 -0.26939   

       9 -0.23933   

      10 -0.18576   

      11 -0.17397   

      12 -0.14805   

      13 -0.12518   

      14 -0.10419   

      15 -0.85099E-01

      16 -0.67968E-01

      17 -0.53902E-01

      18 -0.41771E-01

      19 -0.31425E-01

      20 -0.23178E-01

      21 -0.17140E-01

      22 -0.14451E-01

      23 -0.13003E-01

      24 -0.11607E-01

      25 -0.99823E-02

      26 -0.74985E-02

      27 -0.47286E-02

      28 -0.28243E-02

      29   0.0000   

      30 -0.49496   

      31 -0.45796   

      32 -0.42301   

      33 -0.38816   

      34 -0.35445   

      35 -0.33300   

      36 -0.30084   

      37 -0.26971   

 

  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           

 

  LOAD STEP=     1  SUBSTEP=     1                                            

   TIME=    1.0000      LOAD CASE=   0                                        

 

  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 

 

    NODE      UX   

      38 -0.23967   

      39 -0.18600   

      40 -0.17466   

      41 -0.14868   

      42 -0.12587   

      43 -0.10510   

      44 -0.86174E-01

      45 -0.69357E-01

      46 -0.54329E-01

      47 -0.39489E-01

      48 -0.27699E-01

      49 -0.21554E-01

      50 -0.16607E-01

      51 -0.12329E-01

      52 -0.70391E-02

      53 -0.38390E-02

      54 -0.14326E-02

      55 -0.15978E-02

      56 -0.24363E-02

      57 -0.31831E-02

      58   0.0000   

      59 -0.49379   

      60 -0.45902   

      61 -0.42287   

      62 -0.38772   

      63 -0.35341   

      64 -0.33280   

      65 -0.30057   

      66 -0.26935   

      67 -0.23928   

      68 -0.18571   

      69 -0.17391   

      70 -0.14798   

      71 -0.12511   

      72 -0.10410   

      73 -0.84994E-01

      74 -0.67758E-01

 

  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           

 

  LOAD STEP=     1  SUBSTEP=     1                                            

   TIME=    1.0000      LOAD CASE=   0                                        

 

  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 

 

    NODE      UX   

      75 -0.53651E-01

      76 -0.41634E-01

      77 -0.31346E-01

      78 -0.23221E-01

      79 -0.16489E-01

      80 -0.13231E-01

      81 -0.12666E-01

      82 -0.11416E-01

      83 -0.98516E-02

      84 -0.79083E-02

      85 -0.56977E-02

      86 -0.33031E-02

      87   0.0000   

      88 -0.49375   

      89 -0.45838   

      90 -0.42194   

      91 -0.38717   

      92 -0.35337   

      93 -0.33287   

      94 -0.30067   

      95 -0.26950   

      96 -0.23947   

      97 -0.18574   

      98 -0.17423   

      99 -0.14832   

     100 -0.12546   

     101 -0.10457   

     102 -0.85420E-01

     103 -0.68415E-01

     104 -0.53290E-01

     105 -0.37900E-01

     106 -0.26323E-01

     107 -0.19186E-01

     108 -0.15388E-01

     109 -0.10819E-01

     110 -0.61528E-02

     111 -0.17645E-02

 

  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           

 

  LOAD STEP=     1  SUBSTEP=     1                                            

   TIME=    1.0000      LOAD CASE=   0                                        

 

  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 

 

    NODE      UX   

     112  0.74992E-03

     113  0.17771E-02

     114  0.14893E-02

     115  0.15448E-03

     116   0.0000   

     117   0.0000   

     118 -0.25826E-02

     119 -0.50654E-02

     120 -0.76238E-02

     121 -0.98263E-02

     122 -0.11397E-01

     123 -0.12654E-01

     124 -0.14089E-01

     125   0.0000   

     126 -0.16234E-02

     127 -0.46720E-03

     128  0.36049E-03

     129 -0.27889E-03

     130 -0.24641E-02

     131 -0.63204E-02

     132 -0.11099E-01



 MAXIMUM ABSOLUTE VALUES

 NODE          1

 VALUE  -0.49500   

 

PRINT U    NODAL SOLUTION PER NODE

 

  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           

 

  LOAD STEP=     1  SUBSTEP=     1                                            

   TIME=    1.0000      LOAD CASE=   0                                        

 

  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 

 

    NODE      UY   

       1 -0.22811E-01

       2 -0.22820E-01

       3 -0.21866E-01

       4 -0.21061E-01

       5 -0.20354E-01

       6 -0.19546E-01

       7 -0.18708E-01

       8 -0.17851E-01

       9 -0.17043E-01

      10 -0.16525E-01

      11 -0.15695E-01

      12 -0.15069E-01

      13 -0.14347E-01

      14 -0.13357E-01

      15 -0.12532E-01

      16 -0.11727E-01

      17 -0.11068E-01

      18 -0.10208E-01

      19 -0.94365E-02

      20 -0.77106E-02

      21 -0.72632E-02

      22 -0.77046E-02

      23 -0.74401E-02

      24 -0.64173E-02

      25 -0.51261E-02

      26 -0.25582E-02

      27 -0.27902E-03

      28  0.56114E-03

      29   0.0000   

      30 -0.54916E-01

      31 -0.54737E-01

      32 -0.55282E-01

      33 -0.55553E-01

      34 -0.55739E-01

      35 -0.56095E-01

      36 -0.56169E-01

      37 -0.56073E-01

 

  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           

 

  LOAD STEP=     1  SUBSTEP=     1                                            

   TIME=    1.0000      LOAD CASE=   0                                        

 

  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 

 

    NODE      UY   

      38 -0.55790E-01

      39 -0.53846E-01

      40 -0.53743E-01

      41 -0.52592E-01

      42 -0.51331E-01

      43 -0.50125E-01

      44 -0.48477E-01

      45 -0.46644E-01

      46 -0.44685E-01

      47 -0.42277E-01

      48 -0.38627E-01

      49 -0.34488E-01

      50 -0.30413E-01

      51 -0.26416E-01

      52 -0.23993E-01

      53 -0.21257E-01

      54 -0.17865E-01

      55 -0.12247E-01

      56 -0.69210E-02

      57 -0.25752E-02

      58   0.0000   

      59 -0.39097E-01

      60 -0.39035E-01

      61 -0.38661E-01

      62 -0.35293E-01

      63 -0.33658E-01

      64 -0.32112E-01

      65 -0.30392E-01

      66 -0.28794E-01

      67 -0.27237E-01

      68 -0.25783E-01

      69 -0.24450E-01

      70 -0.23139E-01

      71 -0.21947E-01

      72 -0.20826E-01

      73 -0.20654E-01

      74 -0.19565E-01

 

  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           

 

  LOAD STEP=     1  SUBSTEP=     1                                            

   TIME=    1.0000      LOAD CASE=   0                                        

 

  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 

 

    NODE      UY   

      75 -0.19408E-01

      76 -0.18450E-01

      77 -0.17416E-01

      78 -0.16152E-01

      79 -0.14210E-01

      80 -0.12373E-01

      81 -0.11337E-01

      82 -0.10624E-01

      83 -0.10022E-01

      84 -0.88356E-02

      85 -0.69752E-02

      86 -0.42506E-02

      87   0.0000   

      88 -0.38471E-01

      89 -0.38410E-01

      90 -0.38403E-01

      91 -0.41432E-01

      92 -0.42577E-01

      93 -0.43636E-01

      94 -0.44578E-01

      95 -0.45230E-01

      96 -0.45629E-01

      97 -0.45079E-01

      98 -0.45261E-01

      99 -0.44708E-01

     100 -0.43959E-01

     101 -0.42893E-01

     102 -0.40641E-01

     103 -0.38819E-01

     104 -0.35800E-01

     105 -0.33239E-01

     106 -0.31016E-01

     107 -0.28228E-01

     108 -0.24488E-01

     109 -0.21157E-01

     110 -0.18622E-01

     111 -0.17771E-01

 

  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           

 

  LOAD STEP=     1  SUBSTEP=     1                                            

   TIME=    1.0000      LOAD CASE=   0                                        

 

  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 

 

    NODE      UY   

     112 -0.16618E-01

     113 -0.14742E-01

     114 -0.11371E-01

     115 -0.64371E-02

     116   0.0000   

     117   0.0000   

     118 -0.13447E-02

     119 -0.37708E-02

     120 -0.60390E-02

     121 -0.77530E-02

     122 -0.86270E-02

     123 -0.93988E-02

     124 -0.99885E-02

     125   0.0000   

     126 -0.40912E-02

     127 -0.96613E-02

     128 -0.14650E-01

     129 -0.17879E-01

     130 -0.20105E-01

     131 -0.21397E-01

     132 -0.20392E-01



 MAXIMUM ABSOLUTE VALUES

 NODE         36

 VALUE  -0.56169E-01

 

Interesting Cauchy and Lame stayed on Paris outskirts  maybe for their undisturbed researches?...

Using an ANSYS model for same height and load bearing functionality (as a visitors' monument) with self weight,wind and earthquake resistance etc., can one optimize/redesign for another structural configuration using only a fraction of weight of steel originally used? What such lighter re-designs have been made so far?