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18. Non Non Linear Linear Cable/Truss Cable/Truss Analysis Analysis

When all of the members, elements and support springs are linear except for cable and/or When all of the members, elements and support springs are linear except for cable and/or  preloaded

 preloaded truss truss members, members, then then this this analysis analysis type type may may be be used. used. This This analysis analysis is is based based onon applying th

applying the load e load in steps in steps with equilibrium with equilibrium iterations to coniterations to convergence at vergence at each step. each step. IterationIteration continues at each step until the change in deformations is small before proceeding to the next continues at each step until the change in deformations is small before proceeding to the next step.

step. If not If not converged, then converged, then the solution is the solution is stopped. stopped. The user The user can then select mcan then select more steps orore steps or modify the structure and rerun.

modify the structure and rerun.

Structures can be artificially stabilized during the first few load steps in case the structure is Structures can be artificially stabilized during the first few load steps in case the structure is initially unstable (in the linear, small displacement, static theory sense). The user has control initially unstable (in the linear, small displacement, static theory sense). The user has control of the number of steps, the maximum number of iterations per step, the convergence of the number of steps, the maximum number of iterations per step, the convergence tolerance, the artificial stabilizing stiffness, and the minimum amount of stiffness remaining tolerance, the artificial stabilizing stiffness, and the minimum amount of stiffness remaining after a cable sags.

after a cable sags.

This method assumes small displacement theory for all members/trusses/elements other than This method assumes small displacement theory for all members/trusses/elements other than cables & preloaded trusses.

cables & preloaded trusses. The cables and pThe cables and preloaded trusses can have large displacementreloaded trusses can have large displacement and moderate/large strain.

and moderate/large strain. Pretension is the Pretension is the force necessary to stretch the force necessary to stretch the cable/truss from itscable/truss from its unstressed length to enable it to fit between the two end

unstressed length to enable it to fit between the two end joints. joints. Alternatively, you may enterAlternatively, you may enter the unstressed length for cables.

the unstressed length for cables.

The analysis sequence is as follows:

The analysis sequence is as follows:

•• Compute the unstressed length of the nonlinear members based on joint coordinates,Compute the unstressed length of the nonlinear members based on joint coordinates,  pretension, and temperature.

 pretension, and temperature.

•• Member/Element/Cable stiffness is formed. Cable stiffness is from EA/L and theMember/Element/Cable stiffness is formed. Cable stiffness is from EA/L and the sag formula plus a geometric stiffness based on current tension.

sag formula plus a geometric stiffness based on current tension.

•• Assemble and solve the global matrix with the percentage of the total applied loadAssemble and solve the global matrix with the percentage of the total applied load used for this load step.

used for this load step.

•• Perform equilibrium iterations to adjust the change in directions of the forces in thePerform equilibrium iterations to adjust the change in directions of the forces in the nonlinear cables, so that the

nonlinear cables, so that the structure is structure is in static equilibrium in in static equilibrium in the deformedthe deformed  position.

 position. If If force force changes changes are are too too large large or or convergence convergence criteria criteria not not met met within within 1515 iterations then stop the analysis.

iterations then stop the analysis.

•• Go to step 2 Go to step 2 and repeat with a greater percentage of thand repeat with a greater percentage of the applied load. e applied load. TheThe nonlinear members will have an updated orientation with new tension and sag effects.

nonlinear members will have an updated orientation with new tension and sag effects.

•• After 100% of the applied load has converged then proceed to compute memberAfter 100% of the applied load has converged then proceed to compute member forces, reactions, and static check.

forces, reactions, and static check. Note that the static check Note that the static check is not exactly in is not exactly in balancebalance due to the displacements of the applied static equivalent joint loads.

due to the displacements of the applied static equivalent joint loads.

The load cases in a non linear cable analysis must be separated by the CHANGE command The load cases in a non linear cable analysis must be separated by the CHANGE command and PERFORM CABLE ANALYSIS command. The SET NL command must be provided to and PERFORM CABLE ANALYSIS command. The SET NL command must be provided to specify the total number of primary load cases. There may not be any Multi-linear springs, specify the total number of primary load cases. There may not be any Multi-linear springs, compression only,

compression only, PDelta, NONLINEAR PDelta, NONLINEAR or dynamic or dynamic cases.cases.

   D    D   O    O   N    N   O    O   T    T   D    D   I    I   S    S   T    T   R    R   I    I   B    B   U    U   T    T   E    E  -   -   P    P   r    r   i    i   n    n   t    t   i    i   n    n   g     f   g     f   o   o   r   r   S   S   t   t   u   u     d     d   e   e   n   n   t   t   U   U   s   s   e   e   i   i   s   s   P   P   e   e   r   r   m   m   i   i   t   t   t   t   e   e     d     d    S    S   t    t   u     d   u     d   e   e   n   n   t   t   W   W   i   i   r   r   a   a   H   H   e   e   r   r   u   u   c   c   a   a  :  :     k     k   r   r   a   a    C    C   o    o   m    m   p    p   a    a   n    n   y    y  :  :    P    P   T    T   D    D   i    i   n    n   a    a   m    m   i     k   i     k   a   a   T   T   e   e     k     k   n   n   i   i     k     k   P   P   e   e   r   r   s   s   a   a     d     d   a   a    C     l   C     l   a   a   s   s   s   s   D   D   a   a   t   t   e   e   0   0   9   9   O   O   c   c   t   t   2   2   0   0   1   1   2   2  :  :  -  -  -

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Also for cables and preloaded trusses:

Also for cables and preloaded trusses:

•• Do not use Member Offsets.Do not use Member Offsets.

•• Do not include the end joints in Master/Slave command.Do not include the end joints in Master/Slave command.

•• Do not connect to inclined support joints.Do not connect to inclined support joints.

•• Y direction must be up.Y direction must be up.

•• Do not impose displacements.Do not impose displacements.

•• Do not use Support springs in the model.Do not use Support springs in the model.

•• Applied loads do not change global directions due to displacements.Applied loads do not change global directions due to displacements.

•• Do not apply Prestress load, Fixed end load.Do not apply Prestress load, Fixed end load.

•• Do not use Load Combination command to combine cable analysis results.Do not use Load Combination command to combine cable analysis results.

Use a primary case with Repeat Load instead.

Use a primary case with Repeat Load instead.

Syntax Syntax

Steps

Steps = = Number Number of load of load steps. The steps. The applied applied loads loads will will be be applied applied gradually gradually in in thisthis many steps.

many steps. Each step will Each step will be iterated to convergence. be iterated to convergence. Default is 145.Default is 145.

The f1 value, if entered, should be in the range 5 to 145.

The f1 value, if entered, should be in the range 5 to 145.

Eq-iterations =

Eq-iterations = Maximum Maximum number of number of iterations permitted in iterations permitted in each load step. each load step. Default is 1Default is 15.5.

Should

Should be in be in the range the range of of 10 10 to 30.to 30.

Eq-tolerance

Eq-tolerance = = The The convergence convergence tolerance tolerance for for the the above above iterations. iterations. Default Default is is 0.0005.0.0005.

Sag

Sag minimum minimum = = Cables (noCables (not trusses) t trusses) may may sag whsag when tension en tension is low. is low. This This is accounted is accounted for for byby reducing the

reducing the E E value. value. Sag Sag minimum minimum may bmay be between e between 1.0 (no 1.0 (no sag Esag E reduction) and

reduction) and 0.0 (full 0.0 (full sag E sag E reduction). reduction). Default is 1.0Default is 1.0. . If f4 If f4 is entered, itis entered, it should be in

should be in the range 0.7 to the range 0.7 to 1.0 for a relatively simple process. 1.0 for a relatively simple process. As soonAs soon as SAGMIN becomes less than 0.95 the possibility exists that a converged as SAGMIN becomes less than 0.95 the possibility exists that a converged solution will not be achieved without increasing the steps or the

solution will not be achieved without increasing the steps or the  pretension loads.

 pretension loads. The The Eq iterations may need to be 30 or more. Eq iterations may need to be 30 or more. The EqThe Eq tolerance may need to be greater or smaller.

tolerance may need to be greater or smaller.

Stability stiffness = A stiffness matrix value, f5, that is added to the global matrix at each Stability stiffness = A stiffness matrix value, f5, that is added to the global matrix at each

translational

translational direction for jodirection for joints connected to ints connected to cables and ncables and nonlinearonlinear trusses

trusses

for the

for the first f6 first f6 load steps. load steps. The amThe amount addount added linearly ed linearly decreases withdecreases with

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Default is 0.

Default is 0. For f6 use a For f6 use a max value of 1max value of 145.45.

K small stiffness

K small stiffness = A stiffness matrix value, f7, = A stiffness matrix value, f7, that is added to the that is added to the global matrix at eachglobal matrix at each translational direction for joints connected to cables and nonlinear trusses translational direction for joints connected to cables and nonlinear trusses for every

for every load step. load step. If entered, If entered, use 0.0 use 0.0 to 1.0to 1.0. . Default is Default is 0.0. 0.0. ThisThis  parameter alters the stiffness

 parameter alters the stiffness of the of the structure.structure.

Frequently Asked question Frequently Asked question But would

But would like to knolike to know how w how to to arrive at the values arrive at the values for all these parameters for all these parameters ??

Answer : Answer :

There is no direct way to find

There is no direct way to find the values of the pthe values of the parameters. arameters. If the default values fail, then If the default values fail, then trytry sagmin 0.5 first.

sagmin 0.5 first. If that doesn't work I If that doesn't work I try 0.7, then try 0.7, then 0.8. 0.8. If any value woIf any value works then reduce itrks then reduce it halfway to last one that failed.

halfway to last one that failed.

If 0.8 doesn't work, then try S

If 0.8 doesn't work, then try STABL 0.1 14TABL 0.1 145. 5. Then keep increasing the 0.1 value unThen keep increasing the 0.1 value until ittil it works.

works. If this fails at about 95% to 100%, then try KSMAIf this fails at about 95% to 100%, then try KSMALL of about 0.1 LL of about 0.1 times the lasttimes the last STABL value that you used.

STABL value that you used.

If it is allowed try increasing the tension in the MEMBER CABLE command.

If it is allowed try increasing the tension in the MEMBER CABLE command.

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