Earthquake on Five-Story Building

Outline

1 Description 3
2 Finite Element Model 4
2.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Eigenvalue Analysis and Direct Response Analysis 15
3.1 Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4 Modal Response Analysis 41
4.1 Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5 Response Spectrum Analysis 52
5.1 Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Appendix A Additional Information 78

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1 Description
The model of this tutorial represents a five-story building with a cross-section as shown in Figure 1. The dimensions of the cross-section are small in comparison to the length of the building.
Therefore we may assume a plane strain situation. The building is subjected to a base acceleration übase = 1 m/s2 in the horizontal X direction. First we create the model. Then we perform
an eigenvalue analysis, followed by two types of frequency response analyses: direct response (Analysis1 ) and modal response (Analysis2 ). Furthermore, we apply an earthquake spectrum in
a response spectrum analysis (Analysis3 ).

Figure 1: Five-story building [m]

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2 Finite Element Model
Since plane strain conditions can be applied, quadratic, three-noded, infinite shell elements are used to construct the model of the building frame. This is done in the two-dimensional
XY coordinate space.
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Main menu File New [Fig. 2]

Figure 2: New project dialog

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We select the units millimeter and ton.
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Geometry browser Reference system Units [Fig. 3]

Property Panel [Fig. 4]

Figure 3: Geometry browser Figure 4: Property panel - units

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2.1 Geometry
Seven lines are required to build the model. We draw the line for the first floor and it copy it four times to create the other floors and the roof.
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Main menu Geometry Create Add line [Fig. 5]

Main menu Geometry Modify Array copy [Fig. 6] [Fig. 7]

Figure 5: Add first floor Figure 6: Copy wall Figure 7: Both walls

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Next we create the two walls. We draw the line for the left wall and copy it to create the right wall.

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Main menu Geometry Create Add line [Fig. 8]

Main menu Geometry Modify Array copy [Fig. 9] [Fig. 10]

Figure 8: Add left wall Figure 9: Copy wall Figure 10: Model geometry

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2.2 Properties
Material and physical properties are assigned first to the floors and roof. We define an elastic isotropic material named Concrete with Young’s modulus E = 22000 N/mm2 , Poisson’s ratio
ν = 0.2 and mass density ρ = 2.4E − 09 T/mm3 (2400 kg/m3 ).
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Main menu Geometry Assign Shape Properties [Fig. 11]

Shape Properties Material Add material [Fig. 12] Edit material [Fig. 13]

Figure 11: Property assignment floors and roof Figure 12: Add new material Figure 13: Edit material

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As a physical property, the thickness of the floors and roof are specified as Thick with t = 400 mm. The shape of the infinite shell elements are defined as flat.

DianaIE

Shape Properties Geometry Add new geometry [Fig. 14]

Figure 14: Floor and roof thickness Thick

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The same operations are performed for the set of walls. However, since the material properties are the same, we do not need to define a new material. The thickness of the walls are specified
as Thin with t = 150 mm. The shape of the infinite shell elements are defined as flat.
DianaIE

Main menu Geometry Assign Shape Properties [Fig. 15]

Shape Properties Geometry Add new geometry [Fig. 16]

Figure 15: Property assignment walls Figure 16: Wall thickness Thin

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2.3 Boundary Conditions
The bottom end of the vertical lines are clamped, i.e. translations and rotations are restricted.
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Main menu Geometry Assign Add supports [Fig. 17] [Fig. 18]

Figure 17: Attach supports Figure 18: Clamped base

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2.4 Loads
A base excitation with a horizontal acceleration of übase = 1000 mm/s2 in global X direction is applied. Base excitation loads are applied in the direction of the corresponding supports, i.e.
at the bottom end of the vertical lines in this model.
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Main menu Geometry Assign Add global loads [Fig. 19]

Figure 19: Define a global load

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2.5 Mesh
The mesh is defined by dividing the horizontal lines into ten equally sized line segments and the vertical lines into fifteen equally sized line segments [Fig. 20] [Fig. 21]. We then generate the
mesh. We shrink the elements and present the node ids to get a better idea of the mesh [Fig. 22].
DianaIE

Main menu Geometry Assign Mesh properties [Fig. 20] [Fig. 21]
Main menu Geometry Generate mesh
Main menu Mesh Mesh Shrunken shading
Main menu Viewer Selection mode Node selection
Graphics window Select all Show ids

Figure 20: Set mesh properties - Figure 21: Set mesh properties - vertical
horizontal lines lines

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 Figure 22: Mesh - shrunken elements and node labels

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3 Eigenvalue Analysis and Direct Response Analysis
We perform a free vibration eigenvalue analysis in order to check the model, followed by a direct frequency response analysis, with which we determine the response of the model to a base
excitation.

3.1 Commands
First we set up the commands for the free vibration eigenvalue analysis.
DianaIE

Main menu Analysis Add analysis [Fig. 23]

Analysis browser Analysis1 Add command Structural eigenvalue [Fig. 24] [Fig. 25]

Figure 23: Analysis browser Figure 24: Add command

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We ask for ten eigenmodes to be determined in the structural eigenvalue analysis. The default output settings will be used for the eigenmodes.
DianaIE

Analysis browser Analysis1 Structural eigenvalue Execute eigenvalue analysis Edit properties [Fig. 25]
Properties - EXECUT Number of eigenfrequencies 10 [Fig. 26]

Figure 25: Analysis browser - Execute eigenvalue analysis Figure 26: Edit properties - Execute eigenvalue analysis

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Next, we define the commands for the structural direct frequency response.
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Analysis browser Analysis1 Add command Structural direct response [Fig. 28] [Fig. 29]

Figure 27: Analysis browser Figure 28: Add command

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A range of excitation frequencies is specified from 0 to 10 Hz in steps of 0.1 Hz for the direct frequency response analysis. This can be input as 0-10(0.1). In a direct frequency response
analysis the complex system of equations needs to be solved for each excitation frequency, because the system is frequency dependent. Therefore, direct response spectrum analyses are
computionally more heavy than modal response analyses, but are needed in case of frequency dependent properties or when there is a considerable amount of damping or discrete dampers in
the model.
DianaIE

Analysis browser Analysis1 Structural direct response Execute frequency response analysis Edit properties [Fig. 29] [Fig. 30]

Figure 29: Analysis browser - Execute frequency response

analysis Figure 30: Edit properties - Execute frequency response analysis

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The last step in defining the analysis commands is specifying the output. We select the displacements, velocities and accelerations.
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Analysis browser Analysis1 Structural direct response Output frequency response analysis Edit properties [Fig. 31]
Properties - Output Result User selection Modify [Fig. 32]

Figure 31: Analysis browser - Output frequency response

analysis Figure 32: Edit properties - Output

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We select the Amplitude/Phase angle represenation for each output item, because, in this manner, the peaks in the displacement amplitudes can be shown and are expected to be in agreement
with the eigenfrequencies found in the eigenvalue analysis.
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Results Selection Add... DISPLA TOTAL TRANSL GLOBAL

< Repeat for VELOCI TOTAL TRANSL GLOBAL and ACCELE TOTAL TRANSL GLOBAL >
Results Selection DISPLA TOTAL TRANSL GLOBAL Properties [Fig. 34]
< Repeat for VELOCI TOTAL TRANSL GLOBAL and ACCELE TOTAL TRANSL GLOBAL >
Main menu Analysis Run selected analysis

Figure 33: Edit properties - Results selection Figure 34: Edit properties - Result item properties

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3.2 Results

After termination of the analysis we assess the results. For an eigenvalue analysis these typically are the eigenfrequencies and the eigenmodes. The Messages dialog displays the eigenfrequenties
and the corresponding relative errors. The small relative errors indicate that all eigenfrequencies could be determined with high accuracy.

Figure 35: Messages dialog - Eigenfrequencies

We see that eigenfrequencies are in a range from about 1 to 8 Hz, which is approximately within the frequencies of a typical earthquake spectrum.

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Now the ten eigenmodes are displayed. Note that modes 1, 2, 3, 7, and 10 are dominated by the deformation of the walls, and modes 4, 5, 6, 8, and 9 by the deformation of the floors [Fig. 37
to 46].
DianaIE

Results browser Analysis1 Output eigenvalue analysis Nodal results Displacements DtX Show contours [Fig. 36]
Main menu Results Normalized deformed results

Figure 36: Results browser

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 Figure 37: Eigenmode 1 - 1.04 Hz

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 Figure 38: Eigenmode 2 - 3.12 Hz

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 Figure 39: Eigenmode 3 - 5.12 Hz

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 Figure 40: Eigenmode 4 - 6.13 Hz

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 Figure 41: Eigenmode 5 - 6.48 Hz

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 Figure 42: Eigenmode 6 - 6.79 Hz

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 Figure 43: Eigenmode 7 - 6.90 Hz

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 Figure 44: Eigenmode 8 - 7.05 Hz

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 Figure 45: Eigenmode 9 - 7.19 Hz

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 Figure 46: Eigenmode 10 - 8.17 Hz

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A graph of the horizontal displacement (mm) of node 44 (connection of third floor and left wall) and node 86 (connection of roof and left wall) as a function of the excitation frequency (Hz)
is generated. The location of these nodes in the mesh is shown in Figure 22.
DianaIE

Results browser Analysis1 Output frequency response analysis Nodal results Displacements DCtXA Show table [Fig. 47]

Figure 47: Results browser

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The graphs show a maximum amplitude of 275 mm (node 44) and 350 mm (node 86), at an excitation frequency of approximately 1 Hz which corresponds to the first eigenfrequency. The
other amplitudes also correspond with eigenfrequencies, all of them representing an eigenmode dominated by deformation of the walls: 1, 2, 3, 7, and 10.
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Chart view Node and element selection nodes 44 86 [Fig. 48]

Figure 48: Horizontal displacement response of left wall

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A graph of the vertical displacement (mm) of node 49 (mid node of the third floor) and node 91 (mid node of the roof) as a function of the excitation frequency (Hz) is generated. See the
location of the selected nodes in the mesh in Figure 22.
DianaIE

Results browser Analysis1 Output frequency response analysis Nodal results Displacements DCtYA Show table [Fig. 49]

Figure 49: Results browser

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Both graphs show very small displacements with a maximum amplitude in the order of 10−11 mm at an excitation frequency of approximately 6.8 Hz which presumably corresponds to the
fifth and/or sixth eigenmode, dominated by floor deformation. Please note that the exact results of these graphs may vary on different machines. This is due to the small amplitudes of the
displacements.
DianaIE
Chart view Node and element selection nodes 49 91 [Fig. 50]

Figure 50: Vertical displacement response of third floor and roof

The conclusion of the direct response analysis is that the vertical displacements of the floors are very small compared to the horizontal displacements of the walls. The eigenmodes dominated
by the deformation of the walls are, by far, the most significant ones for the horizontal base acceleration load.

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A graph of the horizontal velocity (mm/s) of node 44 (connection of third floor and left wall) and node 86 (connection of roof and left wall) as a function of the excitation frequency (Hz) is
generated. See the location of the selected nodes in the mesh in Figure 22.
DianaIE

Results browser Analysis1 Output frequency response analysis Nodal results Translational Velocities VtXA Show table [Fig. 51]

Figure 51: Results browser

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 DianaIE
Chart view Node and element selection nodes 44 86 [Fig. 52]

Figure 52: Horizontal velocity response of left wall

Note that peak amplitudes occur at the same frequencies as for the displacements (compare with Figure 48). Compared to the displacements the peaks are relatively higher for higher excitation
frequencies.

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A graph of the horizontal accelerations (mm/s2 ) of node 44 (connection of third floor and left wall) and node 86 (connection of roof and left wall) as a function of the excitation frequency
(Hz) is generated. See the location of the selected nodes in the mesh in Figure 22.
DianaIE

Results browser Analysis1 Output frequency response analysis Nodal results Translational Accelerations AtXA Show table [Fig. 53]

Figure 53: Results browser

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 DianaIE
Chart view Node and element selection nodes 44 86 [Fig. 54]

Figure 54: Horizontal acceleration response of left wall

Again, note that peak amplitudes occur at the same frequencies as for the displacements [Fig. 48]. Compared to the displacements and velocities, the peaks are relatively higher for higher
excitation frequencies.

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4 Modal Response Analysis
For comparison with the direct response analysis, as performed in the previous section, we will now determine the response of the model to a base excitation via a modal response analysis.
Compared to the direct response analysis, modal response analysis has the advantage of not requiring to set up the element matrices for the complex system for each excitation frequency;
they are only set up once. The disadvantage is that a modal response analysis requires the preliminary determination of eigenvalues and eigenmodes and is therefore limited to modal damping
and cannot be used for models with a considerable amount of damping or discrete dampers. Frequency dependent properties cannot be taken into account in a modal respose analysis.

4.1 Commands
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Main menu Analysis Add analysis [Fig. 55]

Analysis browser Analysis2 Add command Structural modal response [Fig. 56] [Fig. 57]

Figure 55: Analysis browser Figure 56: Add command Figure 57: Analysis browser

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We toggle off the output of the eigenvalue analysis and ask for ten eigenmodes to be determined.
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Analysis browser Analysis2 Structural modal response Eigenvalue analysis Output eigenvalue analysis Toggle off [Fig. 58]
Analysis browser Analysis2 Structural modal response Eigenvalue analysis Execute eigenvalue analysis Edit properties [Fig. 59]
Properties - EXECUT Number of eigenfrequencies 10 [Fig. 60]

Figure 58: Analysis browser - Output eigenvalue analysis Figure 59: Analysis browser - Execute eigenvalue analysis Figure 60: Edit properties - Execute eigenvalue analysis

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We assign a damping coefficient of 0.011 , specify a range of excitation frequencies from 0 to 10 Hz in steps of 0.1 Hz, which can be input again as 0-10(0.1), and ask to return the eigenmodes
that are dominated by deformation of the walls, i.e. eigenmode 1, 2, 3, 7 and 10, because from the direct frequency analysis we know that the floors will not show large deformations due to
the horizontal earthquake.
DianaIE

Analysis browser Analysis2 Structural modal response Frequency response analysis Execute frequency response analysis Edit properties [Fig. 61] [Fig. 62]

Figure 62: Edit properties - Execute frequency

Figure 61: Analysis tree - Execute frequency response analysis response analysis

1
Modal damping is required if any excitation frequency is equal to an eigenfrequency. The real damping factor of the structure is often not known. Normally, values are chosen between 0 and 10% of the critical damping
factor. Because we do not want to overestimate the damping we choose for 1% of the critical damping.

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The last step in defining the analysis commands is specifying the output: we select the displacements, velocities and accelerations.
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Analysis browser Analysis2 Structural modal response Frequency response analysis Output frequency response analysis Edit properties [Fig. 63] [Fig. 64]

Figure 64: Edit properties - Output

Figure 63: Analysis tree - Output frequency response analysis frequency response analysis

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We select the Amplitude/Phase angle represenation for each output item, because, in this manner, the peaks in the displacement amplitudes can be shown and are expected to be in agreement
with the eigenfrequencies found in the eigenvalue analysis, similar to the direct frequency response analysis.
DianaIE

Results Selection Add... DISPLA TOTAL TRANSL GLOBAL [Fig. 65]

< Repeat for VELOCI TOTAL TRANSL GLOBAL and ACCELE TOTAL TRANSL GLOBAL >
Results Selection DISPLA TOTAL TRANSL GLOBAL Properties [Fig. 66]
< Repeat for VELOCI TOTAL TRANSL GLOBAL and ACCELE TOTAL TRANSL GLOBAL >
Main menu Analysis Run selected analysis

Figure 65: Edit properties - Results Selection Figure 66: Edit properties - Result Item Properties

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4.2 Results
We plot graphs of the frequency response for displacements, velocities and accelerations of the nodes at the junction of the left wall with the third floor and the left wall with the roof. A
graph of the horizontal displacement (mm) of node 44 (connection of third floor and left wall) and node 86 (connection of roof and left wall) as a function of the excitation frequency (Hz) is
generated first. See the location of the selected nodes in the mesh in Figure 22.
DianaIE

Results browser Analysis2 Output frequency response analysis Nodal results Displacements DCtXA Show table [Fig. 67]
Results browser Case Excitation 1, Frequency 0.0000 [Fig. 67]

Figure 67: Results browser

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The maximum amplitudes near 1 Hz for the modal response analysis with 1% modal damping [Fig. 68] are considerably larger than those obtained via direct response analysis without damping
[Fig. 48]. This may appear strange, but for the direct frequency response analysis there is an asymptote at the eigenfrequencies leading to very sharp spikes in the response in a small frequency
range aroung these eigenfrequencies. While in the modal response analysis with modal damping, there are no longer asymptotes at the eigenfrequencies, i.e. the amplitudes are limited to
a certain value, but the peak is spread over a larger frequency range around these eigenfrequencies. Since we execute at discrete excitation frequencies, we may observe, that we see larger
amplitudes for the modal frequency response with damping than for the direct frequency response without damping at specific excitation frequencies as can be seen in this specific tutorial.

Figure 68: Horizontal displacement response of left wall

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A graph of the horizontal velocity (mm/s) of node 44 and node 86 as a function of the excitation frequency (Hz) is generated. See the location of the selected nodes in the mesh in Figure 22.
DianaIE

Results browser Analysis2 Output frequency response analysis Nodal results Translational Velocities VtXA Show table [Fig. 69]
Results browser Case Excitation 1, Frequency 0.0000 [Fig. 69]

Figure 69: Results browser

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The maximum amplitudes of the velocities [Fig. 70] are also a bit lower than those obtained via direct response analysis [Fig. 52], except for the peaks at around 1 (Hz) who reach a value of
approximately 7200 and 9500 (mm/s).

Figure 70: Horizontal velocity response of left wall

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A graph of the horizontal accelerations (mm/s2 ) of node 44 and node 86 as a function of the excitation frequency (Hz) is generated.
DianaIE

Results browser Analysis2 Output frequency response analysis Nodal results Translational Accelerations AtXA Show table [Fig. 71]
Results browser Case Excitation 1, Frequency 0.0000 [Fig. 71]

Figure 71: Results browser

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The maximum amplitudes of the accelerations [Fig. 72] are considerably lower than those obtained via direct response analysis [Fig. 54] except for the peak near 1 Hz. Apparently, modal
damping and/or floor modes affect the acceleration more than the displacement and the velocity. Only for the peak near 1 Hz we see a higher acceleration due to the larger frequency range
around the peak of the damped first eigenfrequency for the modal frequency response with 1% modal damping as explained earlier.

Figure 72: Horizontal acceleration response of left wall

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5 Response Spectrum Analysis
In this last section we demonstrate a response spectrum analysis of the frame. As is done for the modal response analysis, we only consider the eigenmodes dominated by deformation of
the walls. Before the analysis commands are specified, an addition needs to be made to the model: a typical earthquake spectrum is applied which in Diana relates frequencies to load
amplification factors for the base excitation load.
DianaIE

Geometry browser Loads Cases AcceleratedBase Edit frequency dependency [Fig. 73] [Fig. 74]

Figure 73: Geometry browser Figure 74: Edit frequency dependency factors

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5.1 Commands
We add a new analysis.
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Main menu Analysis Add analysis [Fig. 75]

Analysis browser Analysis3 Add command Structural response spectrum [Fig. 76]
Analysis browser Analysis3 Structural response spectrum Rename Structural response spectrum ABS [Fig. 77]
Analysis browser Analysis3 Add command Structural response spectrum [Fig. 76]
Analysis browser Analysis3 Structural response spectrum Rename Structural response spectrum SRSS [Fig. 77]

Figure 75: Analysis browser Figure 76: Add command Figure 77: Analysis browser

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We ask for ten eigenmodes to be determined.
DianaIE

Analysis browser Analysis3 Structural response spectrum Eigenvalue analysis Execute eigenvalue analysis Edit properties [Fig. 78]
Properties - EXECUT Number of eigenfrequencies 10 [Fig. 79]

Figure 78: Analysis browser - Execute eigenvalue analysis Figure 79: Edit properties - Execute eigenvalue analysis

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For the output of the eigenvalue analysis, we specify the eigenmodes that are dominated by deformation of the walls, i.e. eigenmode 1, 2, 3, 7 and 10.
DianaIE

Analysis browser Analysis3 Structural response spectrum Eigenvalue analysis Output eigenvalue analysis Edit properties [Fig. 80]
Properties - Output Modes 1-3 7 10 [Fig. 81]

Figure 80: Analysis browser - Output eigenvalue analysis Figure 81: Edit properties - Output

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For the output of the response spectrum analysis, we select the displacements, residual forces and the Cauchy total stresses. The maximum modal quantity values are superposed according
to the absolute rule, that is the sum of absolute maximum values obtained for each eigenmode.

DianaIE

Analysis browser Analysis3 Structural response spectrum Response spectrum analysis Structural response spectrum ABS Edit properties [Fig. 82] [Fig. 83]
Properties - Output Result User selection Modify [Fig. 83]
Results Selection Add... DISPLA TOTAL TRANSL GLOBAL [Fig. 84]
< Repeat for FORCE RESIDU TRANSL GLOBAL and STRESS TOTAL CAUCHY VONMIS >

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 Figure 82: Analysis browser - Output response Figure 83: Edit properties -
spectrum analysis Ouptut Figure 84: Edit properties - Results selection

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Next to the absolute superposition, we also want to get the same results items where the maximum modal quantity vales are superposed according to the Square Root of the Summed Squares
(SRSS). These results will be defined in another output block.

DianaIE

Analysis browser Analysis3 Structural response spectrum Response spectrum analysis Structural response spectrum SRSS Edit properties [Fig. 85] [Fig. 86]
Properties - Output Result User selection Modify [Fig. 83]
Results Selection Add... DISPLA TOTAL TRANSL GLOBAL [Fig. 84]
Results Selection Add... FORCE RESIDU TRANSL GLOBAL [Fig. 84]
Results Selection Add... STRESS TOTAL CAUCHY VONMIS [Fig. 84]
Main menu Analysis Run selected analysis

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 Figure 85: Analysis browser - Output response Figure 86: Edit properties -
spectrum analysis Output Figure 87: Edit properties - Results selection

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5.2 Results
Eigenmodes 1, 2, 3, 7, and 10 are presented in Figure 89 to Figure 93.
DianaIE

Results browser Analysis3 Output eigenvalue analysis Nodal results Displacements DtX Show contours [Fig. 88]
Results browser Case Mode 1, Eigen frequency 1.0438 Hz [Fig. 88]
Main menu Results Normalized deformed results

Figure 88: Results browser

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 Figure 89: Displacement response individual modes - Eigenmode 1 - 1.04 Hz

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 Figure 90: Displacement response individual modes - Eigenmode 2 - 3.12 Hz

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 Figure 91: Displacement response individual modes - Eigenmode 3 - 5.12 Hz

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 Figure 92: Displacement response individual modes - Eigenmode 7 - 6.90 Hz

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 Figure 93: Displacement response individual modes - Eigenmode 10 - 8.17 Hz

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We select the superposed modal displacements, starting with superposition type ‘ABS’ [Fig. 95]. The absolute maximum of the displacements are the sum of the maximum displacements of
all contributing modes separately.
DianaIE

Results browser Case Superposition type ABS [Fig. 94]

Results browser Analysis3 Superposition type ABS Nodal results Displacements DtXH Show contours [Fig. 94]

Figure 94: Results browser

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 Figure 95: Displacement response superposed modes - ABS rule

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In general it is not likely that all modes reach their maximum at the same moment. A more realistic approach to calculate the maximum displacements is using the SRSS rule which takes the
Square Root of the Summed Squares [Fig. 97]. Therefore, lower amplitudes are obtained with the SRSS superposition compared to the absolute superposition.
DianaIE

Results browser Case Superposition type SRSS [Fig. 96]

Results browser Analysis3 Superposition type SRSS Nodal results Displacements DtXH Show contours [Fig. 96]

Figure 96: Results browser

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 Figure 97: Displacement response superposed modes - SRSS rule

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We select the superposed modal forces, starting with superposition type ‘ABS’ [Fig. 99]. The absolute maximum of the forces are the sum of the maximum forces of all contributing modes
separately. This absolute maximum is calculated by the ABS rule.
DianaIE

Results browser Case Superposition type ABS [Fig. 98]

Results browser Analysis3 Output response spectrum analysis Nodal results Residual Forces FRXH Show contours [Fig. 98]

Figure 98: Results browser

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 Figure 99: Force response - ABS rule

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In general it is not likely that all modes reach their maximum at the same moment. A more realistic approach to calculate the maximum forces acting on the structure is using the SRSS rule
which takes the Square Root of the Summed Squares [Fig. 101]. Therefore, lower amplitudes are obtained with the SRSS superposition compared to the absolute superposition.
DianaIE

Results browser Case Superposition type SRSS [Fig. 100]

Results browser Analysis3 Output response spectrum analysis Nodal results Residual Forces FRXH Show contours [Fig. 100]

Figure 100: Results browser

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 Figure 101: Force response - SRSS rule

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We select the equivalent (i.e. Von Mises) stresses in order to get an estimation of the damage inflicted by the earthquake on our building. Starting with superposition type ‘ABS’ [Fig. 103].
DianaIE

Results browser Case Superposition type ABS [Fig. 102]

Results browser Analysis3 Output response spectrum analysis Element results Cauchy Total Stresses SeqH Show contours [Fig. 102]

Figure 102: Results browser

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 Figure 103: Equivalent stress response - ABS rule

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In general it is not likely that all modes reach their maximum at the same moment. A more realistic approach to calculate the equivalent stresses is using the SRSS rule which takes the Square
Root of the Summed Squares [Fig. 105]. Therefore, lower amplitudes are obtained with the SRSS superposition compared to the absolute superposition.
DianaIE

Results browser Case Superposition type SRSS [Fig. 104]

Results browser Analysis3 Output response spectrum analysis Element results Cauchy Total Stresses SeqH Show contours [Fig. 104]

Figure 104: Results browser

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 Figure 105: Equivalent stress response - SRSS rule

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Appendix A Additional Information

Folder: Tutorials/FiveStoryBuilding

Number of elements ≈ 80

Keywords:
analys: dynami respon spectr.
constr: suppor.
elemen: cl9pe pstrai shell.
load: base freque.
materi: elasti isotro.
option: direct units.
post: binary ndiana.
pre: dianai.
result: cauchy displa force reacti residu stress total vonmis.

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