Simple but genuine problem.

[mrathore]

Sir,
I modeled a very simple cantilever to clarify the doubts regarding local forces and curvatures...

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wipe;
model BasicBuilder -ndm 3 -ndf 6;
source Wsection.tcl

node 1 0 0 0;
node 2 0 43.2 0;

mass 2 5.1784 1e-9 0   0 0 0;

fix 1   1 1 1   1 1 1;

puts "Defining Materials...";
set matTag 1;
set E      29000;
set epsyP  0.002;
uniaxialMaterial ElasticPP $matTag $E $epsyP ;
set nu 0.3;
set Gs [expr $E/2./[expr 1+$nu]];      # FOR TORSIONAL STIFFNESS

puts "Defining Sections...";
# SETTING THE SECTION ID's
# FINAL SECTIONS
# MOMENT RESISTING MEMBERS
set ColExtMom 1;
# FIBER SECTIONS
# MOMENT RESISTING MEMBERS
set ColExtMomF 10;
# TORSIONAL PROPERTIES
set TorsionSec1 101;
#
set matTag 1;
set nfdw 16;
set nftw 2;
set nfbf 16;
set nftf 4;
#-------------------
# W14X257
set d  16.38;
set tw 1.175;
set bf 15.995;
set tf 1.890;
Wsection $ColExtMomF $matTag  $d $bf $tf $tw $nfdw $nftw $nfbf $nftf;
#
set GJ [expr 4690*$Gs];
uniaxialMaterial Elastic $TorsionSec1 $GJ;
section Aggregator $ColExtMom $TorsionSec1 T -section $ColExtMomF;
puts "...Section W14X257 Defined";

geomTransf Linear 1          0       0       1;

set np 10;
element nonlinearBeamColumn  1      1      2   $np          $ColExtMom  1;

puts "Geometry Done";

puts "Defining Recorders...";
file mkdir output;
file mkdir output/modes;
#
recorder Node  -file output/ReactionBase.out   -time -node  1 -dof 1 2 3 4 5 6 reaction;
#
recorder Node  -file output/NodeDisp1st.out    -time -node  2 -dof 1 2 3 4 5 6 disp;
#
recorder Element -file output/LocalForce.out    -time -ele all  localForce;
recorder Element -file output/CurvtrColmi.out   -time -ele all  section 1   deformation;
recorder Element -file output/CurvtrColmj.out   -time -ele all  section $np deformation;
#

constraints Plain;                     
numberer Plain;				
system ProfileSPD;
test NormDispIncr 1e-9 10;
algorithm Newton;

pattern Plain 1 "Linear   -factor 1.0" {
 load 2 100 200 300     0 0 0;
}
puts "Gravity Loading Done";

integrator LoadControl 0.1;
analysis Static;
analyze 10;
puts "Gravity analysis done";

Its output is very interesting

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0.1 -20 10 30 0 1296 432 20 -10 -30 0 7.34029e-014 4.75903e-015 
0.2 -40 20 60 0 2592 864 40 -20 -60 0 -3.33895e-013 -1.08928e-013 
0.3 -60 30 90 0 3888 1296 60 -30 -90 0 1.35708e-012 7.11205e-014 
0.4 -80 40 120 0 5184 1728 80 -40 -120 0 -1.8709e-013 6.96663e-013 
0.5 -100 50 150 0 6480 2160 100 -50 -150 0 1.01602e-012 -9.71097e-013 
0.6 -120 60 180 0 7776 2592 120 -60 -180 0 -7.55524e-013 9.24037e-013 
0.7 -140 70 210 0 9072 3024 140 -70 -210 0 5.18659e-012 6.90056e-013 
0.8 -160 80 240 0 10368 3456 160 -80 -240 0 -1.31511e-012 -3.10884e-013 
0.9 -180 90 270 0 11664 3888 180 -90 -270 0 -2.856e-012 1.48183e-012 
1 -200 100 300 0 12960 4320 200 -100 -300 0 -2.26266e-012 -1.10808e-012 

During transformations, we have already defined local axis with global axis for element 1, why the local force at node 1 in local z direction is +300 (and at node 2 it is -300).

Directions are correct for local x and local y axis.

[fmk]

you need to understand the local coordinate system .. suggest you look at the manual on the geometicTransformation command (the description of the Linear command shows the local axis for 3d case for command given below (yours has local vector flipped in z dirn) .. if you just want a solution to your answer you need to change the geomTransf commmand to

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geomTransf Linear 1 0 0 -1

[mrathore]

Thank you

I was confused in the transformation and was using right handed rule for local axis transformation, while it is the other way.

The statement in manual is very confusing

The y-axis is defined by
taking the cross product of the x-axis and the vecxz vector.

I thought it is localy=vecxz (cross) localx [by right hand rule]

Thanks

[mrathore]

Interestingly the problem is not yet solved.
If I am not wrong then I have made local z axis parallel to +ve global Z axis by following transformation

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geomTransf Linear 1 0 0 -1 

so local y axis is parallel -ve global X axis and local x axis is parallel to +ve global Y axis.

The new output for local forces is

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0.1 -20 -10 -30 0 -1296 -432 20 10 30 0 -7.34029e-014 -4.75903e-015 
0.2 -40 -20 -60 0 -2592 -864 40 20 60 0 7.08075e-013 3.55338e-013 
0.3 -60 -30 -90 0 -3888 -1296 60 30 90 0 -9.82898e-013 -2.41651e-013 
0.4 -80 -40 -120 0 -5184 -1728 80 40 120 0 9.68567e-013 4.25663e-014 
0.5 -100 -50 -150 0 -6480 -2160 100 50 150 0 -2.41338e-012 -5.07097e-013 
0.6 -120 -60 -180 0 -7776 -2592 120 60 180 0 3.48847e-012 1.35023e-012 
0.7 -140 -70 -210 0 -9072 -3024 140 70 210 0 -1.47324e-012 5.14259e-013 
0.8 -160 -80 -240 0 -10368 -3456 160 80 240 0 1.12607e-013 1.11545e-013 
0.9 -180 -90 -270 0 -11664 -3888 180 90 270 0 1.70976e-012 2.08348e-012 
1 -200 -100 -300 0 -12960 -4320 200 100 300 0 -4.28792e-013 -3.10521e-012 

This time local y force is shown -100 (at node1), while it should be +100. Direction of local x and z forces are correct.

[silvia]

the command would make the z parallel to the negatize Z.

[mrathore]

No sir, the command

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geomTransf Linear 1 0 0 -1

will make local z axis parallel to +ve global Z axis. I have cross checked it, and also it is clear from figure in Command Language Manual on page 296 (chapter 25). vecxz is opposit to local z axis in this figure.

Same image it attached herewith.




Last question. If the member is along Y, (with i node 1 at 0,0,0 and j node at 0,1,0... so local x is parallel to +Y) then which one of the following commands should be used to make z parallel to +ve Z.

geomTransf Linear 1 0 0 -1

OR

geomTransf Linear 1 0 0 1

Thanks a lot for your kind help.

[silvia]

please make sure you check the latest manual, you have an old one.
i think i had made a mistake in a figure at some point.
please always use the on-line manual when you have questions, as it is the most updated version.