# Example(sample) input file using multispring element

## Example(sample) input file using multispring element

Hi ALL,

Can someone please send me an example input file which has got multispring element in it ? I am confused with selecting the different parameters for it.

Your help will be much appreciated.

Bidur

Can someone please send me an example input file which has got multispring element in it ? I am confused with selecting the different parameters for it.

Your help will be much appreciated.

Bidur

**bidur**- Posts : 11

Join date : 2010-03-09

## Multispring

The HS is the h in the diagram.

The WGT is the weight of the spring, used to add the weight of the spring to the weight matrix (mass matrix = weight matrix divided by 'g')

The Mult-ispring is like a spring element. The axial and flexural stiffness is given by the longitudinal springs but the unit may also have to carry shear (i.e. at the end of a beam) and so needs a shear stiffness and as it might yield in shear it needs the shear yield actions.

The SL factor is important as part of the shear actions. The moment at the nodes is the moment in the multi-springs plus the shear times lever arm of the shear action about the nodes at the ends. If the SL is at mid-length of the element then the shear affects the moments experience at both ends. The only time the Shear has no effect on the moment is if the member is of zero length. The shear is constant along the member and this (from equilibrium) requires a linear variation of moment. The multi-springs only represent the moment so where is this moment acting?

I may be able to find a data set but it may require a lot of explanation. If I can find a very simple one I will try to post it but it may take several days.

The WGT is the weight of the spring, used to add the weight of the spring to the weight matrix (mass matrix = weight matrix divided by 'g')

The Mult-ispring is like a spring element. The axial and flexural stiffness is given by the longitudinal springs but the unit may also have to carry shear (i.e. at the end of a beam) and so needs a shear stiffness and as it might yield in shear it needs the shear yield actions.

The SL factor is important as part of the shear actions. The moment at the nodes is the moment in the multi-springs plus the shear times lever arm of the shear action about the nodes at the ends. If the SL is at mid-length of the element then the shear affects the moments experience at both ends. The only time the Shear has no effect on the moment is if the member is of zero length. The shear is constant along the member and this (from equilibrium) requires a linear variation of moment. The multi-springs only represent the moment so where is this moment acting?

I may be able to find a data set but it may require a lot of explanation. If I can find a very simple one I will try to post it but it may take several days.

**Athol Carr**- Posts : 115

Join date : 2009-12-09

Location : Christchurch, New Zealand

## Multispring

Dear Athol,

Thank you very much for your kind reply.

Please please send example input file with multispring element . I am keen to get that even it takes some days.

Thank you very much once again.

Regards,

Bidur

Thank you very much for your kind reply.

Please please send example input file with multispring element . I am keen to get that even it takes some days.

Thank you very much once again.

Regards,

Bidur

**bidur**- Posts : 11

Join date : 2010-03-09

## Multispring

Hi Athol,

I am writing just to remind you about the sample input file in case you have forgotten.

I know you have written as "It may take several days."

I am keen to have a look of that.

Thank you very much.

Regards,

Bidur

I am writing just to remind you about the sample input file in case you have forgotten.

I know you have written as "It may take several days."

I am keen to have a look of that.

Thank you very much.

Regards,

Bidur

**bidur**- Posts : 11

Join date : 2010-03-09

## Multispring.

I have found one or data files but would need a fairly complicated description to go with it set out why the parameters are what they are and to describe the structure being modelled. Not sure how to put all of that in a reply.

**Athol Carr**- Posts : 115

Join date : 2009-12-09

Location : Christchurch, New Zealand

## Examples of Multispring.

I have found trying to post papers and data files difficult so am providing the following os help in modelling the multi-spring elements.

The Multi-spring element was developed to model the behaviour of rocking joints as those seen at the ends of the beams in PRESSS type hybrid structures. The common modelling of these joints has been as two springs loacted at the bottom and top surfaces of the beams, a model which is far too stiff, or as some sort of rotational spring which may give a representation of the rocking behaviour but NOT the elongation of the beam that the proper rocking joint exhibits. Where the rotational spring has been used in rocking bridge pier models this elongation effect may not be important but in a framed structure it can have very significant effects.

The difficulties in modelling the multi-spring element is largely that of defining the axial stiffness of the member. Work by Spieth

Spieth,H.A., Carr,A.J., Murahidy,A.G., Arnolds,D., Davies,M. and Mander,J,M.

"Modelling of Post-Tensioned Precast Reinforced Concrete Frame Structures with

Rocking Beam-Column Connection". Proc NZSEE conference, Rotorua, NZ, March 2004.

with detailed non-linear 3D finite element modelling of both armoured and un-armoured rocking joints in concrete beams showed that the best results were in using about of 8 springs in the joint and taking the axial stiffness of the joint as k=AE/H where AE is the axial area and elastic modulus of the beam member in which the joints are

acting and H, an effective length which was found to be around D/4 where D is the depth of the beam member. At 8 springs in the multi-spring the choice of Gauss or Lobartto is not really significant, Gauss is too soft and Lobartto is too stiff. It matters greatly if the number of springs is 2 (a traditional model) or 4.

In Ruaumoko the member can be of zero length if it wishes, but then is unable to show in the plots. The length is arbitrary but should be given a length to let it be shown in the graphics. The operation is at a point given by the parameter SL in the input data.

As part of the axial stiffness of the original beam of length L (AE/L) that has the rocking joints at its ends has been taken by the rocking joints the cross section A that is used by the beam between the two end joints needs to be adjusted to get the same axial stiffness acting between the column intersections. If the lengths chosen for each of the multi-spring rocking joints is P (not to be confused with the H chosen for the stiffness of the multi-spring) then the length of the beam between the joints in the model is Q = L-P-P. The original axial stiffness of the beam was AE/L.

The tree members are in series so the flexibilities of the three members need to be equated with the original flexibility. Let Aa be the axial area required in the central beam so that the flexibility between the column intersections is maintained then

L/(A*E) = H/(A*E)+H/(A*E)+P/(Aa*E)

as everything else is defined the Aa can be computed.

The multi-spring, on its own, is not a stable member it would need gravity (as a column base) or pre-stress (as a beam) to make it work if the "bi-linear with gap" (IHYST=5) hysteresis model is chosen. The pre-stress is usually modelled as a spring member between beam-column joints and the prestress action MUST affect the structure.

The shear stiffness must be supplied (to represent the shear keys of other shear resistingmechanism across the rocking joint orof the shear l-nk is Rigid(!) then this could be achieved by slaving the shear displacements at the noedes at the two ends of the multi-spring.

Obviously, axial slaving is not possible with these models, it would stop the multi-spring element working. There is another aspect that will need consideration.One has now coupled the axial and flexural effects in the structure. This means that the time-step required will be much-much smaller than is normally used in frame structure analyses. One required a time step that is about a 1/4 of the shortest mode period that matters in your analysis if the hysteretic models are able to track their hysteresis loops, some experience say 0.1 of that period. The axial displacements

play an important part in the rocking behaviour of the joint and the axial stiffness of the beams at a floor is often very high giving very high local periods of free vibration. It will also be important to have a relatively correct horizontal mass at the nodes at the ends of the beams with the rocking joints. Even mass should be applied at the joint between the multi-spring and the adjoining beam.

The Multi-spring element was developed to model the behaviour of rocking joints as those seen at the ends of the beams in PRESSS type hybrid structures. The common modelling of these joints has been as two springs loacted at the bottom and top surfaces of the beams, a model which is far too stiff, or as some sort of rotational spring which may give a representation of the rocking behaviour but NOT the elongation of the beam that the proper rocking joint exhibits. Where the rotational spring has been used in rocking bridge pier models this elongation effect may not be important but in a framed structure it can have very significant effects.

The difficulties in modelling the multi-spring element is largely that of defining the axial stiffness of the member. Work by Spieth

Spieth,H.A., Carr,A.J., Murahidy,A.G., Arnolds,D., Davies,M. and Mander,J,M.

"Modelling of Post-Tensioned Precast Reinforced Concrete Frame Structures with

Rocking Beam-Column Connection". Proc NZSEE conference, Rotorua, NZ, March 2004.

with detailed non-linear 3D finite element modelling of both armoured and un-armoured rocking joints in concrete beams showed that the best results were in using about of 8 springs in the joint and taking the axial stiffness of the joint as k=AE/H where AE is the axial area and elastic modulus of the beam member in which the joints are

acting and H, an effective length which was found to be around D/4 where D is the depth of the beam member. At 8 springs in the multi-spring the choice of Gauss or Lobartto is not really significant, Gauss is too soft and Lobartto is too stiff. It matters greatly if the number of springs is 2 (a traditional model) or 4.

In Ruaumoko the member can be of zero length if it wishes, but then is unable to show in the plots. The length is arbitrary but should be given a length to let it be shown in the graphics. The operation is at a point given by the parameter SL in the input data.

As part of the axial stiffness of the original beam of length L (AE/L) that has the rocking joints at its ends has been taken by the rocking joints the cross section A that is used by the beam between the two end joints needs to be adjusted to get the same axial stiffness acting between the column intersections. If the lengths chosen for each of the multi-spring rocking joints is P (not to be confused with the H chosen for the stiffness of the multi-spring) then the length of the beam between the joints in the model is Q = L-P-P. The original axial stiffness of the beam was AE/L.

The tree members are in series so the flexibilities of the three members need to be equated with the original flexibility. Let Aa be the axial area required in the central beam so that the flexibility between the column intersections is maintained then

L/(A*E) = H/(A*E)+H/(A*E)+P/(Aa*E)

as everything else is defined the Aa can be computed.

The multi-spring, on its own, is not a stable member it would need gravity (as a column base) or pre-stress (as a beam) to make it work if the "bi-linear with gap" (IHYST=5) hysteresis model is chosen. The pre-stress is usually modelled as a spring member between beam-column joints and the prestress action MUST affect the structure.

The shear stiffness must be supplied (to represent the shear keys of other shear resistingmechanism across the rocking joint orof the shear l-nk is Rigid(!) then this could be achieved by slaving the shear displacements at the noedes at the two ends of the multi-spring.

Obviously, axial slaving is not possible with these models, it would stop the multi-spring element working. There is another aspect that will need consideration.One has now coupled the axial and flexural effects in the structure. This means that the time-step required will be much-much smaller than is normally used in frame structure analyses. One required a time step that is about a 1/4 of the shortest mode period that matters in your analysis if the hysteretic models are able to track their hysteresis loops, some experience say 0.1 of that period. The axial displacements

play an important part in the rocking behaviour of the joint and the axial stiffness of the beams at a floor is often very high giving very high local periods of free vibration. It will also be important to have a relatively correct horizontal mass at the nodes at the ends of the beams with the rocking joints. Even mass should be applied at the joint between the multi-spring and the adjoining beam.

**Athol Carr**- Posts : 115

Join date : 2009-12-09

Location : Christchurch, New Zealand

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