strange results with a CABLE

jeanpierreaubry

i run this simple test case and it gives strange results

a cable runs across two fixed points and is loaded with a middle load

the problem may be solved by static equilibrium equations
(we have to solve an implicit equation, the solution is explained in Roark Formula for stress and strain table 12)

solving the problem with code_aster rises the following discrepancy

traction in cable (T) = horizontal reaction (DX)

while it should be

traction in cable = sqrt (horizontal reaction² = vertical reaction²)

thus whatever the load (hence the slope of the cable) is!!!

reaction DX and DZ are correct

and the problem solves correctly with a distributed load

jacob

Well, obviously it does into take into account large rotations.

jeanpierreaubry

jacob

Well, obviously it does into take into account large rotations.

it looks like it!
but why not with a nodal load?
and yes with a distributed load?

jacob

Do you mean FORCE_POUTRE?

Still, it seems there is some difference

jeanpierreaubry

jacob
you are right
either with FORCE_POUTRE or FORCE_NODALE on 20 nodes along the length
the equilibrium is not strictly verified although not as bad as a middle load
and the results are slightly different from Roark formula (that derive from an analytic approach)

what are the calculation parameters of the attached pic

jacob

url=https://code-aster.org/forum/assets/files/2026-08-26/1787733989-910425-org.7z

weird that the tensile force is the same if I use green-lagrange deformations.

jacob

maybe reactions are wrong, not SIEF?

jeanpierreaubry

jacob
from an engineer point of view the discrepancy may become an issue with large displacement
whatever oit is i have some critics about you file
E=200000 is too much the apparent modulus of a cable depends on its build, number of strands and for steel is more likely around 150000 N/mm2
SECTION=78.54 is lot huge for a length of 1OO

in my examples
l=1000, E=80000, SECTION=(pi/422,), middle load FZ=-50000.0,
code_aster gives
reactions
NOEUD X Y Z DX DZ
N1 0.000E+00 0.000E+00 -1.000E+00 1.931E-14 -2.909E+02
traction in cable
LA VALEUR MAXIMALE DE N EST 4.282E+04 EN 2 MAILLE(S) : M6
LA VALEUR MINIMALE DE N EST 4.282E+04 EN 2 MAILLE(S) : M12
displacement
NOEUD X Y Z DX DZ
N1 0.000E+00 0.000E+00 -1.000E+00 1.931E-14 -2.909E+02

i thinks reactions are ok SIEF is not

jeanpierreaubry

my mistake
CHAMP AUX NOEUDS DE NOM SYMBOLIQUE REAC_NODA
NUMERO D'ORDRE: 20 INST: 1.000E+00
NOEUD X Y Z DX DZ
N4 -5.100E+02 0.000E+00 0.000E+00 -4.282E+04 2.500E+04
N5 5.100E+02 0.000E+00 0.000E+00 4.282E+04 2.500E+04

jacob

I am getting a different force for the displacement

jeanpierreaubry

jacob
concerning the pic with analytical
i agree with what you show on the left hand side
i do not understand what is on the right hand side

jacob

I just tried, if the strain is computed differently.

But if you notice, the stress is quite unrealistic.

For normal values the axial and horizontal force is almost the same. GROT_GDEP considers small deformation so there is probably some assumption to linerize some nonlinear terms.

jeanpierreaubry

of course some values i use in my calculation gives unrealistic stress, this was just for testing

it remains that code aster result
traction in cable (T) = horizontal reaction (DX)
is wrong

i recently made a calculation on a cable setup 130 m long, for a funambulist, circling on the right an old XIV century building
i had to asses the forces the building

the deflection was small enough that the wrong result is not very troublesome, but that made me wonder

jacob

Like I said, it's not wrong, just linerized small angle sin(phi) = phi , cos(phi) = 1