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Table of ContentsVersion Info ................................................................................................................................... 1Scope of this book ....................................................................................................................... 3Dynamic loads .............................................................................................................................. 5

Harmonic load ...............................................................................................................................................................5Seismic load ..................................................................................................................................................................5General seismisity ........................................................................................................................................................6

Dynamic load cases ..................................................................................................................... 7Dynamic load cases .....................................................................................................................................................7Defining a new dynamic load case .............................................................................................................................7Defining the harmonic load case ................................................................................................................................7Defining the seismic load case ...................................................................................................................................8Defining the seismic spectrum .................................................................................................................................12

Masses......................................................................................................................................... 15Introduction to masses ..............................................................................................................................................15Mass types ..................................................................................................................................................................15

Point mass..............................................................................................................................................................15Line mass ...............................................................................................................................................................15

Defining a mew mass .................................................................................................................................................16Defining a new point mass in node ........................................................................................................................16Defining a new point mass on a 1D member .........................................................................................................16Defining a new line mass on a 1D member ...........................................................................................................16

Modifying the existing mass .....................................................................................................................................17Editing the existing mass .......................................................................................................................................17Moving the existing mass .......................................................................................................................................17Copying the existing mass .....................................................................................................................................17Deleting the existing mass .....................................................................................................................................17

Mass groups ...............................................................................................................................................................17Introduction to mass groups ...................................................................................................................................17Mass group manager .............................................................................................................................................17Defining a new mass group ....................................................................................................................................17Defining the mass group parameters .....................................................................................................................18

Combinations of mass groups ..................................................................................................................................19Introduction to combinations of mass groups .........................................................................................................19Mass group combination manager .........................................................................................................................19

Calculation .................................................................................................................................. 21Dynamic natural vibration calculation ......................................................................................................................21Dynamic forced harmonic vibration .........................................................................................................................21Dynamic seismic calculation .....................................................................................................................................21Harmonic band analysis ............................................................................................................................................21Non uniform damping in dynamic calculation .........................................................................................................25

Non uniform damping .............................................................................................................................................25Damper setup .........................................................................................................................................................25Defining a new damping group ..............................................................................................................................25Defining a new damper ..........................................................................................................................................26

Results......................................................................................................................................... 29Displaying the natural frequencies ...........................................................................................................................29Evaluating the results for harmonic load .................................................................................................................29


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Version InfoVersion info

Documentation title Dynamics

Version 2009.0

Produced March 2009

Translated N/A

Software covered Scia Engineer

Version 2009.0

Latest Build covered 9.0.108


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Scope of this bookThis manual extends the Reference guide for Scia Engineer. It does not cover basic functions of the program. It focuseson the functionality related to dynamic analysis.


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Dynamic loads

Harmonic loadThere is no need to carry out a special dynamic calculation for a weakly damped structure. The method of expansion into

eigenmodes can be used to determine the final amplitude of deformation line as a linear combination of the eigenmodes(the phase shift between individual eigenmodes can be ignored for weak damping). This type of calculation only requiresthe definition of logarithmic decrement, frequency of excitation impulse in Hz and amplitude of nodal impulses (seeDefining the harmonic load case).

The results may than be reviewed the same way as results of a standard static calculation ( Evaluating the results forharmonic load).

If the phase shift between individual eigenmodes cannot be ignored due to stronger damping, the problem must besolved as a response to a general dynamic load.

Seismic loadDuring earthquake, the subsoil (sub-grade or foundation) bearing a structure moves. The structure tries to follow thismovement. As a result, all masses in the structure begin to move. Subsequently, they subject the structure to inertialforces. Supports can generally move in all directions, but normally only horizontal moves are taken into consideration.

The user may define the direction that s/he considers to be crucial for the structure or s/he may evaluate the effect ofshakes acting in different directions.

Inertial forces arise from the move. It is sufficient to determine these forces and apply them on the structure. Thus, thedynamic calculation is transformed into a static one. But the whole thing is not that simple. We do not know the precisemovement of subsoil and therefore we are not able to determine the seismic forces precisely. But we can apply formulasof a technical standard or employ the frequency spectrum of a real earthquake.

Usually, horizontal movement of a structure is assumed for seismic load. That means that the earthquake acts in a planehorizontal to XY plane. The direction can be specified by means of coefficient for individual co-ordinate axes.

For example:

earthquake in X-direction set X = 1 and Y = 0

earthquake in Y-direction set X = 0 and Y = 1

earthquake in the axis of the 1st quadrant set X = Y = 0.707 (i.e. sin(45))

On the other hand, it is possible to take account of Z-directions as well. This can be achieved by specifying thecoefficient for Z axis.

Note: We must be careful with the coefficients as earthquake "X=1; Y=0; Z=0.667" is not equal to earthquake"X=1; Y=0; Z=-0.667" nor to earthquake "X=-1; Y=0; Z=0.667".

The seismic calculation runs automatically, which means that both self-weight and input masses are used to generateload for individual eigenmodes.

The evaluation is performed separately for each force and displacement component using generally two availableformulas:

Square root of the sum of squares taking account of the extreme value:

Square root of the sum of squares:

where:

Sdyn component in consideration

Sm the maximum corresponding component for individual eigenmode


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Sj other corresponding components for individual eigenmode

The final force may be both negative and positive. Both possibilities are considered in combinations.

Note: Whatever procedure we apply to the evaluation of quantity X, the result is always positive value. But we

can have also a negative value because in seismicity the vibration is around the equilibrium position. The resultsof seismic calculation are always positive in Scia Engineer. The only exception is with internal forces. Here, theco-ordinate system convention in not used. Instead, the "elasticity" convention (lower and front fibres undertension) is applied. Signs of some shear forces and bending moments may be inverted and "minus" may appearin the results of seismic calculation.

One more fact must be borne in mind. In static analysis we are curious about relations between individual internal forces e.g. extreme axial force and corresponding bending moment. Such relations, however, cannot be determined forresults of seismic calculation because each component is evaluated separately which, as you have surely noticed, is nota linear problem.

When evaluating results of seismic analysis, the one may say "this is the maximal axial force", "this is the maximal axialstress", "this is the maximal vertical displacement". But one cannot calculate stress in a section from the axial force andbending moment even though they appear in the same line of result table. This is the effect of the squares and roots inthe formulas above. Accurate stress can be obtained only in appropriate module for design and checking (steel,concrete, etc. structures).

General seismisityIf a structure is designed for a particular earthquake, we can employ seismicity defined by means of a frequencyspectrum. The following data must be specified:

table of frequencies and accelerations,

coefficients of accelerations,

direction coefficients,

evaluation type.

For more information see chapter Defining the seismic load case.


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Dynamic load cases

Dynamic load casesDynamic load cases cover the following:

response to a harmonic vibration,

response to a seismic load.

A dynamic calculation is carried out for defined dynamic load cases simultaneously with a static calculation. Dynamicload cases can be arbitrarily combined with static load cases. As a result, Scia Engineer provides for a directcombination and evaluation of results for static and dynamic analysis. For example, both static and dynamic wind can beincluded into one selective group and the program automatically determines which one is more unfavourable.

Dynamic load cases can be input only after mass groups and their combinations have been defined. A dynamic loadcase can be input as a standard variable load case; only its type must be set to dynamic. Impulses, usually but notexclusively point impulses in nodes, can then be defined in these load cases.

A load factor can be defined for a dynamic load case. The meaning of the factor is the same as for static load case.Other parameters of a dynamic load case depend on its type.

The meaning of the nodal impulse differs according to the type of dynamic load case. No impulses appear in eigenvalueproblem (free vibration analysis) or in seismic calculation. For harmonic vibration, impulses of exciting forces must be

specified.In case of dynamic wind, impulses from static wind are defined. The impulse size is 1 kN/m2 regardless of the height (i.e.the product of node-corresponding area and shape coefficient). For orthogonal vibration, one must specify the node-corresponding length of cylindrical parts of the structure where vibration can occur.

Defining a new dynamic load case

Note: Prior to the definition of the first load case, at least one mass group combination must have been alreadydefined. In addition, Dynamics must have been selected in the Functionality list of the Project setup dialogue.

A new dynamic load case can be defined in the Load case manager. A dynamic load case is defined like a static loadcase, but its properties are adjusted otherwise.

The procedure for the definition of a dynamic load case

1. Open the Load case manager.

2. Press button [New] to create a new load case.

3. Set Action type to Variable.

4. Set Load type to Dynamic.

5. Select required Specification.

6. Press button [Parameters] to specify required parameters for selected type of dynamic load case.

7. Close the Load case manager.

Each defined dynamic load case, similarly to a static variable load case, must be sorted into a group of variable loads.Identical rules for sorting into groups and for the generation of combinations are applied for both static and dynamicvariable load cases.

IMPORTANT: If the Specification of the load case is set to General dynamics, the program generates a set ofnew load cases. These load cases are used to store the results of the calculation: internal forces, deformation,reactions. Even though these load cases contain these results, it is NOT POSSIBLE to EVALUATE STRESS in1D members (neither standard stress nor stress in steel / concrete code checks). Moreover, if such a load caseis included to a combination of load cases, the stress cannot be evaluated for these combinations neither (thestress in such combinations is set to zero).

Defining the harmonic load caseA general procedure for the definition of a dynamic load case is given in chapter Defining a new dynamic load case.Harmonic load case requires input of the following parameters:

Logarithmic decrement The rate at which the amplitude decays gives us measurement of thedamping in a system. It is known as the logarithmic decrement. This isdefined as the natural logarithm of the ratio of any two successiveamplitudes.

Frequency The frequency of the excitation impulse in Hz.


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Defining the seismic load case

A general procedure for the definition of a dynamic load case is given in chapter Defining a new dynamic load case.Seismic load case parameters

seismic spectrum X If the option is ON, the user can select required spectrum for X-direction. The selection containsall the defined spectra stored in the spectrum database (see Defining the seismic spectrum).Button next to the combo box opens the Spectrum manager and the user may modify theexisting spectrum or add a new one.

For more about the definition of a spectrum see chapter Defining the seismic spectrum.

seismic spectrum Y ditto for Y-direction

seismic spectrum Z ditto for Z-direction

direction X Substitute seismic forces are calculated from masses defined on the structure and from the

acceleration. The values in this and two adjacent fields (for the two other axis-directions) specifythe final direction in which the earthquake acts. Value 1 means full effect along the axis. 0 (zero)stands for no effect along the axis.

direction Y ditto for Y-direction

direction Z ditto for Z-direction

acceleration coefficient All the acceleration values in the spectrum table are multiplied by the given value of accelerationcoefficient.

overturning level This field specifies the height of a point around which the structure may overturn. The height ismeasured from origin of the global co-ordinate system. The final turning moment is related tothis point.

evaluation type There are two basic approaches available for the evaluation of result of seismic calculation. Seebelow.

Evaluation type

sum The result value may be obtained as a square root of the sum of squares of values fromindividual load cases. For more information see chapter Seismic load.

extreme The result may take account of extreme values.

For more information see chapter Seismic load.

CQC Alternatively, an evaluation to CQC (Complete Quadratic Combination) standard may be

applied. This method takes the damping frequency diagram into account.

Button [...] opens the Damping database manager (which is a standards Scia Engineerdatabase manager).

Predominant mode

Signed results If ON, the eigenshape selected in the combo box below is used for the definition of signs ofresult values.

This affects the results on 1D and 2D members.

When the load case is used in a combination, then it is combined once with coefficient 1 andonce with coefficient -1.

Mode shape If the option above is ON, the user may specify the predominant mode = the mode shape which


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determines the sign of the results.

It is possible to select option "Default" or a number from 1 to the total number of selectedeigenshapes.

The "Default" stays for mode shape with biggest mass ratio.

Note:

It is difficult to define the "predominant mode" automatically by the program, because it is a 3Dprogram which computes mass in 3 directions: X, Y and Z.


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Multiple eigenshapes

This feature can be used in the seismic analysis if SRSS is used. Modes are combined together if the precision conditionis met.

Classic SRSS

SRSS with multiple eigen shapes

If precision,

where

mode (i) and (j) are multiple. Then for example

where mode 2 and 3 are multiple.

Unify shapes If ON, the eigenshapes meeting the precision condition are considered multiple.

Precision The procision in the condition for multuiple eigenshapes.

Mass in analysis

Participation mass only When you consider only participation mass, i.e. you dont take all modes in the analysis, youmake some error. You say something like "not all mass is included in the analysis". This "error"can be corrected by the two following options.

Missing mass in modes The program recalculates the missing mass in modes that has been already computed (e.g. thenumber of modes selected by the user).

Residual mode "Residual mode" method install the missing mass as "weight" (e.g. standard load case). Theresult of this load case is handled as an "extra mode".

A few note concerning options Missing mass in modes and Residual mode

The two methods (Missing mass in modes and Residual mode) are intended for bigger models, where it is difficult tocompute the minimal required modes. French norm say, for example, that you need all modes until 33hz. Then you lookat the participation ratio.

You never obtain good results if you compute only two modes and take the rest in missing mass or residual modes.Thats not the purpose.

The selection affects the results 1d, 2d

Redistribute missing mass to the known modes

This means to smooth the missing mass to the known modes and compute modal deformations and then the modalforces.

Afterwards its summed depending the selected rule SRSS, CQC, MAX

We proposed assign "missing mass" to known eigenmode. Let us suppose that we have determined k eigenmodes,where


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kis direction

is effective mass

Missing mass can now be written as

Ratio between effective mass and missing mass is

Now we can write these formulas

Then

Missing mass is installed as an extra mode which is computed as an equivalent static load case

Missing mass is computed in each node as the difference between total mass and effective mass

kis direction

i is node

j is mode

is effective mass, direction k, node i

Missing mass can now be written as

A static load case of weight in computed, which is handled as a "real" mode.

For each direction k, selected in "General seismic load" interface, the amplitude of static load is computed as:


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is acceleration of "cut off" frequency in direction k (i.e. last calculated frequency),

missing mass in direction k, node i .

Afterwards the extra mode is summed depending on the selected rule SRSS, CQC, MAX.

Remark: For CQC we do not assume correlation with the other modes (i.e. absolute value is added).

Remark 1:

The direction of the static equivalent loads is the same as the direction selected by user in the spectrum direction.

Remark 2:

If the user installs seismic load in 2 or 3 global directions, then the static equivalent mass in the residual mode iscomputed in the global 2 or 3 installed directions with respect to the directions defined in the input.

Remark 3:

The program doesnt check the level of the cut off frequency. This part is the responsibility of the user.


Defining the seismic spectrumA new seismic spectrum can be defined in the Seismic spectra manager. It can also be used for editing of an earlierinput spectrum. The manager is analogous to other Scia Engineer database managers.

Pressing button [New] in the manager opens the dialogue for input of a new seismic spectrum. The dialogue consists ofthe following controls. The set of the control covered by the first table below can be used to define an arbitrary user-define spectrum.

The controls described in the second table below provide for the input of seismic spectrums for national codes.

General seismic spectrum

graphical window shows the frequency-acceleration diagram of the defined spectrum

table contains the values of frequencies and corresponding accelerations

name is used for identification of the spectrum

control buttons enable the user to confirm or abort the input values

National seismic spectrum

In addition to the controls described in the previous table, the definition of the seismic spectrums for a particular nationalcode offers the following items (when the seismic spectrum is defined according to a particular national code, the tablewith the input values is disabled).

Type of drawing Frequency the horizontal axis shows the frequency

Period - the horizontal axis shows time

Type of input Input for this option, the input table is accessible and the user can inputall the values manually

"Particular national standard" for this option, the values are takenautomatically from the selected national seismic code. The spectra areavailable for the following countries:

India

Czech Republic

Slovakia

Austria

France


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Germany

Eurocode

Italy

Suisse

Max frequency This item limits the spectrum.

Step This item defines the "density" with which the spectrum is defined.

Code This button opens a separate dialogue that enables the user to specifyother parameters contained in the currently selected national code.

The operation of the dialogue is quite straightforward and similar to other curve defining dialogues in Scia Engineer (e.g.see chapter Advanced input data > Initial deformations > Initial deformation curve).


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Masses

Introduction to massesMasses represent a kind of load that is used with dynamic analysis. The mass then models the effect of some real load.

The real load is idealised and introduced in the form of a material point, i.e. mass.To some extent, the masses are analogous to loads and mass groups are analogous to load cases.

Mass types

Point mass

Point mass represents a mass concentrated into a single point. It may be considered as analogous to point load. Pointmass may be positioned into a node or into an intermediate point of a 1D member.

point mass in a node point mass on a 1D member

Line mass

Line mass represents a mass concentrated into a line. It may be considered as analogous to line load.


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Defining a mew mass

Defining a new point mass in node

The procedure for the definition of a new point mass in a node

1. Open tree menu function Dynamics > Masses > Mass in node.

2. Specify the parameters of the mass:

a. weight,

b. mass moments of inertia.3. Confirm the settings with [OK] button.

4. Select nodes where the mass should act.

5. Close the function.

Defining a new point mass on a 1D member

The procedure for the definition of a new point mass on a 1D member

1. Open tree menu function Dynamics > Masses > Mass on beam.


a. weight,

b. position of the mass on a 1D member,

c. number of repetitions.

3. Confirm the settings with [OK] button.

4. Select 1D members where the mass should act.


Defining a new line mass on a 1D member

The procedure for the definition of a new line mass on a 1D member

1. Open tree menu function Dynamics > Masses > Line mass on beam.


a. type of the mass distribution (uniform or trapezoidal),

b. weight,


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c. position on a 1D member.

3. Confirm the settings with [OK] button.

4. Select 1D members where the mass should act.


Modifying the existing mass

Editing the existing mass

Mass is a standard Scia Engineers entity. Therefore, it can be modified in the same way as other entity types. Whatsmore, similarly to e.g. supports or loads, it belongs to Additional dataof the Scia Engineer project. The procedure for themodification of mass is therefore identical to the procedure for the modification of model data (e.g. supports, etc.).

Moving the existing mass

Mass is a standard Scia Engineers entity. Therefore, it can be modified in the same way as other entity types. Whatsmore, similarly to e.g. supports or loads, it belongs to Additional dataof the Scia Engineer project. The procedure for

move of mass is therefore identical to the procedure for move of model data (see chapter Model data > Modifying theexisting model data > Moving the model data).

Copying the existing mass

Mass is a normal Scia Engineers entity. Therefore, it can be modified in the same way as other entity types. Whatsmore, similarly to e.g. supports or loads, it belongs to Additional dataof the Scia Engineer project. The procedure forcopying of mass is therefore identical to the procedure for copying of model data (see chapter Model data > Modifyingthe existing model data > Copying the model data).

Deleting the existing massMass is a normal Scia Engineers entity. Therefore, it can be modified in the same way as other entity types. Whatsmore, similarly to e.g. supports or loads, it belongs to Additional dataof the Scia Engineer project. The procedure forremoval of mass is therefore identical to the procedure for removal of model data (see chapter Model data > Modifyingthe existing model data > Deleting the model data).

Mass groups

Introduction to mass groups

Mass groups are analogous to load cases. Individual masses may be combined in mass groups and later combinationsof these mass groups may be created.

Mass group manager

The Mass group manager is a standard Scia Engineer manager. It provides for basic operations with mass groups.

The Mass group manager can be opened:

using tree menu function Dynamics > Mass group.

Defining a new mass group

The procedure for the definition of a new mass group

1. Open the Mass group manager.

2. Click button [New].


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3. A new mass group is created.

4. Click button [Edit] to open the editing dialogue.

5. Input the required values for individual mass group parameters.

6. Confirm with button [OK].

7. If required, repeat steps 2 to 6.

8. Close the Mass group manager.

Defining the mass group parameters

In the editing dialogue, parameters of a particular mass group may be edited.

Load case Here, the user may select a load case that should be used for anautomatic generation of masses.

Create masses from loadcase

This button tells the program to generate masses from all load defined inthe load case specified above.

A few notes concerning the generation of masses from load case

Mass from self-weight is created EVERY TIME and is NOT displayed.

Masses from other load cases are generated on pressing button [Create masses from load case] from the load caseadjusted in the dialogue.

They are created only once! (If the button is pressed again for the same load case, nothing happens).

On the other hand, it is possible to add masses from different load cases. Or more precisely, masses are addedaccording to the following criterion: if a mass has been already created from a force in a node, no other mass (created)from a force is added to this particular node, even though the force is (created) from another load case.

The mass remains unchanged after any modification or removal of the originan force. If the mass is supoosed tocorrespond to the modified force, it is necessary to remove the mass and create it once more.

The mass is generated ONLY from vertical force component horizontal forces would create no mass at all.

Conversion formula used: m * g = F (default value is g = 9.81).

The display of masses in controlled by a separate view parameter (pop-up menu function Set view parameters/all) andis independent on the displayed load case.

Masses are also displayed (by default setting) in the service Masses. Therefore is probably the best approach togenerate masses from withing this servise.

The calculation module concentrates masses into nodes, therefore finer mesh is requierd. For example, part of the massin a node with support "will disappear" (produces no response). If the mesh is fine enough, this arrangement has nonegative influence on the accuracy of results. However, apparent irregularities may appear if coarse mesh is used andthe user wants to compare the results of this rough calculation with manually obtained values.

Example

Below there are two pictures. The first one with line loads defined. The other one then demonstrates the massesgenerated automatically from that load.


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Combinations of mass groups

Introduction to combinations of mass groups

Mass groups defined in the project can be combined in mass group combinations. The combinations then can be usedfor evaluation of results.

Mass group combination manager

The Mass group combination manager is a standard Scia Engineer manager. It provides for basic operations withcombinations of mass groups.

The Mass group combination manager can be opened:

using tree menu function Dynamics > Combination of mass group.


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Calculation

Dynamic natural vibration calculationIn addition to general parameters controlling the calculation, the dynamic calculation enables the user to define additional

options.

Number of eigenvalues Here the user specifies how many eigen frequencies should be calculated.

Calculation for selected mass combinations

If general option Advanced solver option is ON, the user may specify which mass combinations will be calculated.Otherwise, all non-calculated are always calculated.

Note: The dynamic calculation can be carried out for mass combinations only.

Dynamic forced harmonic vibration

The principles of how Scia Engineer deals with a structure subject to a harmonic load are given in chapters: Loads > Load types > Dynamic loads > Harmonic load

Loads > Load cases > Dynamic load cases > Defining the harmonic load case

Results > Evaluating the results for harmonic load

And the core of dynamic calculations is laid down in:

Loads > Load cases > Dynamic load cases > Dynamic load cases

Loads > Load cases > Dynamic load cases > Defining a new dynamic load case

Dynamic seismic calculationThe principles of how Scia Engineer deals with a structure subject to a harmonic load are given in chapters:

Loads > Load types > Dynamic loads > Seismic load

Loads > Load cases > Dynamic load cases > Defining the seismic load case

And the core of dynamic calculations is laid down in:

Loads > Load cases > Dynamic load cases > Dynamic load cases

Loads > Load cases > Dynamic load cases > Defining a new dynamic load case

Harmonic band analysisHarmonic Band Analysis = Harmonic analysis performed as a multiple analysis on a range of frequencies.

Description

This calculation represents a new way of dealing with the calculations in harmonic analysis. Multiple analyses on a rangeof frequencies are carried out. The harmonic analysis is possible for a range of frequencies controlled by the user. In thestandard harmonic analysis, the forces and the frequency are defined. In this type (Harmonic Band Analysis) of analysis,the frequency of the harmonic force varied over a range and the harmonic analysis is performed for multiple values inthat range.

To fit the needs of this type of calculation, a new load case type named "Harmonic Band Analysis" has been introducedinto Scia Engineer. the properties of this load case are similar to the standard harmonic load case. But, instead of thefrequency, there are 5 new parameters: A, n1, n2, C, N (explained below). The input of loads is the same as for thestandard harmonic load cases.

Scia Engineer generates a set of extra load cases:

1. one set of main F frequencies (their number is n=n2-n1+1) and

2. nsets of secondary frequencies (each of them with 2Nitems).

The secondary load cases are the standard Scia Engineer harmonic load cases and have standard results.

The results of the main load cases are calculated by RMS (root mean square) method from the appropriate set of thesecondary load cases.

Scia Engineer generates the following result classes:


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1. one with all main load cases and

2. nwith the sets of the secondary load cases.

Output of results

Alphanumerical output

All the results of the main and secondary load cases are presented in the standard Scia Engineer way in result tablesusing the generated results classes.

Graphical output

The results of the main frequencies or results of the bands around the main frequency can be presented also graphicallyin the form of a diagram. For that purpose a new tool has been integrated into Scia Engineer.

Refresh after modifications of the structure and changes in other input values

When the user changes parameters n1, n2or N, all the generated load cases and all the generated result classes aredeleted and all the document items with band analysis load cases are not valid any more. If any other project data arechanged, all generated items remain in the project and their content is updated after next calculation.

(Little) Theoretical background

The user defines constants A, n1, n2, C, N.

The default values are: A = 2, n1 = 6, n2= 30, C= 3, N= 10.

From these data, a geometric series are generated using the following formula

where nvaries from n1 to n2with a step of 1.

The result is a series of so-called main frequencies F. The default set is: 4,00; 5,04; 6,35; 8,00; 10,08; etc. Around eachof these values, an interval Fi- - Fi+ is defined:

The interval [Fi- - F] is now divided into Nsteps to generate the secondary frequencies "f".

For each value of "f" a harmonic analysis is carried out. The displacement or inner force in a specified node in a givendirection is calculated, giving Nresult values. The same is done for the interval [F Fi+]. From these 2Nvalues, one

value is calculated using RMS (root mean square) and assigned to the main frequency F.Combination with other load cases

The results of this analysis can not be combined with other static and dynamic analyses.

Input of the load case for the Harmonic Band Analysis

The input of the load case for the Harmonic Band Analysis requires similar prerequisites as other dynamic load cases.

Procedure do define a new load case for the Harmonic Band Analysis

1. In the Project setup dialogue, on tab Functionality, select Dynamics and Harmonic band analysis.

2. In the Dynamics branch of the tree menu define at least one Mass group and at least one Combination of massgroups.

3. Then you may open the Load case manager and input a new load case for the Harmonic Band Analysis.

4. Select the following options and define the appropriate parameters:

a. Action type = variableb. Load group = as required in the particular project

c. Load type = dynamic

d. Specification = Harmonic band analysis

e. Parameters = as required in the particular project

f. Master load case = none or as required in the particular project

g. Mass combi = as required in the particular project

5. When ready, close the Load case manager.

Note: Before the calculation is performed, the load case manager shows just this (these) input load case(cases). All the automatically generated load cases, generated according to the description provided above, areadded to the Load case manager only after the calculation has been carried out.

Example

The list of load cases after performed Harmonic Band Analysis may look like


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This picture shows an extract of the list of load cases. It contains one main frequency (BA1-F1) and eight secondaryfrequencies (BA1-4, BA1-3, BA1-2, BA1-1, BA1+1, BA1+2, BA1+3, BA1+4).

Performing the Harmonic Band Analysis

In order to start the Harmonic Band Analysis, the linear static calculation must be run.Note: Similarly to other dynamic calculations, attention must be paid the size of the finite elements. This is truealso in simple structures with a few 1D members only. The analysis may require a certain number of finiteelements in order to calculate the total number of required bands.

Display of results of Harmonic Band Analysis

There is a special display mode for the results of the Harmonic Band Analysis. This mode is available in the followingfunctions of service Results:

Beams > Internal forces,

2D members > deformation of nodes,

2D members > Internal forces.

In this mode a new item (parameter) appears in the property window. This item is called Text output and can be set totwo options: (i) Texts or (ii) Graph.

The Text option displays the results in a standard way, i.e. using the diagram in the graphical window andalphanumerical table in the Preview window.

The Graph option draws a special diagram in the Preview window. For this option one more item is added to theproperty window: Selection tool. This tool accessible through the three-dot button allows you to select the 1Dmembers or slabs and nodes for which the diagram is to be displayed.

The later will be demonstrated on a few examples.

Example 1 - Setup for graphical result at main frequencies at a selected mesh node:

Function: Deformation of nodesType of load: Class

Class: Main

Text output: Graph

Selection tool: S1, node no. 1.

Example 2 - Setup for graphical result at a selected band for a selected mesh node:

Function: Deformation of nodes

Type of load: Class

Class: Sec3


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Text output: Graph

Selection tool: S1, node no. 1.

Note that for a band, beside the deformation curve also the RMS is drawn.

Example 3 - Setup for envelope graphical result at main band frequencies, all nodes selected:


Type of load: Class

Class: Main

Text output: Graph

Selection tool: all members, (by default all nodes are selected)

Extreme: Global

Example 4 - Setup for graphical result at the main band frequencies for all nodes displayed in the same diagram:


Type of load: Class

Class: Main

Text output: Graph

Selection tool: all members, (by default all nodes are selected)

Extreme: no


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Non uniform damping in dynamic calculation

Non uniform damping

This type of calculation is a dynamic calculation that takes into account non-uniform damping on members and supports.

There is a possibility to input a damping value on each 1D and 2D member. It can be (i) relative damping, (ii) logarithmicdecrement or (iii) Rayleigh damping. Moreover, a damper can be input in direction X, Y, Z of a nodal flexible support.

If a dynamic calculation (seismic + harmonic) is carried out and the load case has "Damping group" defined, then SciaEngineer takes into account the non-uniform damping of the members and supports. The modal relative damping foreach direction (i.e. the damping percentage for each mode and each direction) is calculated automatically for each loadcase.

All 1D and all 2D members must have the damping value assigned before the calculation starts or the default value isused. The input of damping in supports is possible only in the GCS directions.

Damper setup

The damper setup provides for the input of global defaults.

Base value logarithmic decrement Default value of logarithmic decrement.

Alpha factor for supports Factor for supports.

Must be >0; default 1.

Maximal modal damping Is used to limit the calculated damping.

Default 30%.

Defining a new damping group

Procedure to define a new damping group

1. In the Project setup dialogue > tab Functionality options Dynamics and Non proportional damping must beselected.

2. Open service Dynamics.

3. Start function Damping group.

4. The Damping group manager is opened on the screen.

5. Click button [New].

6. A new damping group is added to the list of defined groups.

7. If necessary, change the name and/or other group parameters.


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Damping group parameters

Name Specifies the name of the group.

Description Provides a short description of the group.

Type of default damping Global default

The default values are taken from the Damper setup.

Material default

The default values are taken from material properties.

Defining a new damper

A damper can be defined in a support, on a beam membe, on a slab.

Procedure to define a new damper

1. Open service Dynamics.

2. Start function Dampers.

3. If no damping has been defined so far, the Damping groups manager is opened on the screen. Define at least onedamping group.

4. The Dampers branch is opened in the tree menu bar.

5. Select and start the function corresponding to the required type of damper:

a. 1D damping,

b. 2D damping,

c. Node damping.

6. Fill in the parameters.

7. Select the appropriate 1D member/slab/support where the damper is to be installed.

8. End the function.

1D damping

Name Specifies the name of the damper.

Type Select the type of the damping parameter.

Logarithmic decrement

Relative damping

Rayleigh damping

Value

Alpha / Beta

Specifies the value of the parameter selected in the item above.

Note: The Rayleigh damping requires the definition of two parameters. Theremaining two types need just one value.

2D damping


Type Select the type of the damping parameter.

Logarithmic decrement

Relative damping

Rayleigh damping

Value

Alpha / Beta

Specifies the value of the parameter selected in the item above.

Note: The Rayleigh damping requires the definition of two parameters. Theremaining two types need just one value.


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Node damping


Damping X

Damping Y

Damping Z

Defines the damping in individual directions of the global coordinate system.


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Results

Displaying the natural frequenciesThe calculated eigenfrequencies (natural frequencies) may be displayed in summarised form in a preview table.

The procedure to display the table with eigenfrequencies

1. If it is not the case, perform dynamic calculation of the project.

2. Open service Results.

3. Double click function Eigen frequencies

Evaluating the results for harmonic loadOnce the calculation has been finished, the user may review the results the same way s/he is accustomed to doing forstatic calculations.

In addition to standard result quantities, some additional result can be found in the calculation report. These are:

omega, period, frequency,

participation coefficients: wx, i/wx,tot, wy, i/wy,tot, wz, i/wz,tot.The above-mentioned values are stated for every calculated eigenmode.

dynamics enu

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