instability zero stiffness.docx

7/29/2019 Instability zero stiffness.docx

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If there are instability messages, does it mean my analysisresults may be unsatisfactory?

There are many situations where instabilities are unimportant and the STAAD approach of adding a weakspring is an ideal solution to the problem. For example, sometimes an engineer will release the MX

torsion in a single beam or at the ends of a series of members such that technically the members are

unstable in torsion. If there is no torque applied, this singularity can safely be "fixed" by STAAD with a

weak torsional spring.

Similarly a column that is at a pinned support will sometimes be connected to members that all have

releases such that they cannot transmit moments that cause torsion in the column. This column will be

unstable in torsion but can be safely "fixed" by STAAD with a weak torsional spring.

Sometimes however, a section of a structure has members that are overly released to the point where

that section can rotate with respect to the rest of the structure. In this case, if STAAD adds a weak spring,

there may be large displacements because there are loads in the section that are in the direction of the

extremely weak spring. Another way of saying it is, an applied load acts along an unstable degree of

freedom, and causes excessive displacements at that degree of freedom.

If there are instability messages, are there any simplechecks to verify whether my analysis results aresatisfactory?

There are 2 important checks that should be carried out if instability messages are present.

a) A static equilibrium check. This check will tell us whether all the applied loading flowed through the

model into the supports. A satisfactory result would require that the applied loading be in equilibrium with

the support reactions.

b) The joint displacement check. This check will tell us whether the displacements in the model are within

reasonable limits. If a load passes through a corresponding unstable degree of freedom, the structure will

undergo excessive deflections at that degree of freedom.

One may use the PRINT STATICS CHECK option in conjunction with the PERFORM ANALYSIS

command to obtain a report of both the results mentioned in the above checks. The STAAD output file will

contain a report similar to the following, for every primary load case that has been solved for :

***TOTAL APPLIED LOAD ( KG METE ) SUMMARY (LOADING 1 )

SUMMATION FORCE-X = 0.00

SUMMATION FORCE-Y = -817.84


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SUMMATION FORCE-Z = 0.00

SUMMATION OF MOMENTS AROUND THE ORIGIN-

MX= 291.23 MY= 0.00 MZ= -3598.50

***TOTAL REACTION LOAD( KG METE ) SUMMARY (LOADING 1 )

SUMMATION FORCE-X = 0.00

SUMMATION FORCE-Y = 817.84

SUMMATION FORCE-Z = 0.00

SUMMATION OF MOMENTS AROUND THE ORIGIN-

MX= -291.23 MY= 0.00 MZ= 3598.50

MAXIMUM DISPLACEMENTS ( CM /RADIANS) (LOADING 1)

MAXIMUMS AT NODE

X = 1.00499E-04 25

Y = -3.18980E-01 12

Z = 1.18670E-02 23

RX= 1.52966E-04 5

RY= 1.22373E-04 23

RZ= 1.07535E-03 8

Go through these numbers to ensure that

i) The "TOTAL APPLIED LOAD" values and "TOTAL REACTION LOAD" values are equal and opposite.

ii) The "MAXIMUM DISPLACEMENTS" are within reasonable limits.

What does a zero stiffness warning message in theSTAAD output file mean?

The procedure used by STAAD in calculating displacements and forces in a structure is the stiffness

method. One of the steps involved in this method is the assembly of the global stiffness matrix. During

this process, STAAD verifies that no active degree of freedom (d.o.f) has a zero value, because a zero

value could be a potential cause of instability in the model along that d.o.f. It means that the structural

conditions which exist at that node and degree of freedom result in the structure having no ability to resist

a load acting along that d.o.f.

A warning message is printed in the STAAD output file highlighting the node number and the d.o.f at

which the zero stiffness condition exists.


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Examples of cases which give rise to these conditions :

Consider a frame structure where some of the members are defined to be trusses. On this model, if a joint

exists where the only structural components connected at that node are truss members, there is no

rotational stiffness at that node along any of the global d.o.f. If the structure is defined as STAAD PLANE,

it will result in a warning along the MZ d.o.f at that node. If it were declared as STAAD SPACE, there will

be at least 3 warnings, one for each of MX, MY and MZ, and perhaps additional warnings for the

translational d.o.f.

These warnings can also appear when other structural conditions such as member releases and element

releases deprive the structure of stiffness at the associated nodes along the global translational or

rotational directions. A tower held down by cables, defined as a PLANE or SPACE frame, where cable

members are pinned supported at their base will also generate these warnings for the rotational d.o.f. at

the supported nodes of the cables.

Solid elements have no rotational stiffness at their nodes. So, at all nodes where you have only solids,these zero stiffness warning messages will appear.

These are warnings and not errors because :

The reason why these conditions are reported as warnings and not errors is due to the fact that they may

not necessarily be detrimental to the proper transfer of loads from the structure to the supports. If no load

acts at and along the d.o.f where the stiffness is zero, that point may not be a trouble-spot.

What is the usefulness of these messages :

A zero stiffness message can be a tool for investigating the cause of instabilit ies in the model. An

instability is a condition where a load applied on the structure is not able to make its way into the supports

because no paths exist for the load to flow through, and may result in a lack of equilibrium between the

applied load and the support reaction. A zero stiffness message can tell us whether any of those d.o.f are

obstacles to the flow of the load.

instability zero stiffness.docx

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