Linear Analysis: Dynamic Analysis of a concrete strucure

Behavior study of a concrete structure, subjected to variable force in relation to time .Given:-E=2.1*104 [MPa]-=0.2-=2500 [kg/m3]-column cross section: 0.4x0.4-beam cross section: 0.3x0.5Perform the study on two stages, distinguished by model and finite element type:A)-The structure created with curves and meshed using BEAM 2D element;B)-The structure created with volumes and meshed using SOLID element.

The case AOrigin of the model is in origin of coordinate system, therefore key point 1 will be (0, 0). The remains points are modeling from bottom to top for each column.From Geo Panel>Status1, toggle flag on for points PT, and for curves CR, then for activation of this modifications, click Auto.Because of the difference in cross section of the model, in the case A the model is performed in two steps:- Step A-1= is modeling only the columns where will be applied the element group, material property and column meshing. - Step A-2= modeling beams and then apply succession of commands from step A-1. The difference between columns and beams is made through cross section.Step A-1 : Columns modeling.

-Defining finite element type from: Propsets > Element Group > Element group: 1 > Element name: BEAM 2D. In the second window, remains default attributes.

-Defining the cross section dimensions from: Propsets > Beam Section > Associated Element group: 1 (this refer to the first type of finite element used in our model) > Real Constant set:1 (this is the first group of constants added to first finite element). In the second window: >Section number (0: user section):1, because one (1) means that we want to use a standard shape available in Cosmosm.

-No. of beam section constants to be entered: Specify how many boundaries have our shape that must be defined. For a rectangular shape is necessary (2) different boundary (height & width).

-Defining material properties. The structure is statically loaded in the field of liner-elastic. This require minimum three constants as follow: Density=DENS; Poisson coefficient=NUXY; Modulus of longitudinal elasticity=EX; to be entered from: > Propsets > Material Property > Material property set:1 (first group of material properties available for finite element 1).

*We give values only for EX and NUXY because our material is considered isotropic.In the study of mechanical properties ofmaterials, "isotropic"means having identical values of a property in all directions. Thisdefinitionis also used in geology and mineralogy. Glass and metals are examples of isotropic materials.

-Meshing the columns: Meshing > Auto_Mesh > Curves.

Define a point which represent X axis, in our case key point 4.

-Now we can start to create beams. This means we create a new Element group (the second).

-Repeat the main three steps to define: Element Group, Material Property + Real Constants and Meshing.

Real constant element 2

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Material property element 2

Now, click Cancel for material properties

It is recommended to check information. Edit > List > Material Props.

In image underneath, the values of material properties has been checked. In this case EX, NUXY and DENS are well entered, but in some cases can be wrong, correction can be made easily navigating to Propsets>Material Prop> choosing the entity, specific attribute and giving it a new value which is overwritten over wrong value. Then check again.

Meshing of element 2Meshing > Automesh > Curves

??????????????????????????????In this case was used point 4, because it is first point in X direction.

After going through steps A-1 & A-2, now the model is ready to be stopped in his moving and loaded.Before to continue with application, bellow is shown the explanation for some terms from strength of materials which will be used in this application.

-Defining supports from LoadsBC > Displacement > Define by Points.

Similar for key point 4 & 7.-Defining loadings as a pressure from LoadsBC >Pressure > Define by Curves

Similar for the next curves: 8, 9, 10, 11 & 12.The sign of pressure magnitude depend on (Pressure direction: 4:Normal, which means vertical on the way of Y axis but in opposite direction).?????

Fusion of nodes: Meshing>Nodes>Merge. Merge means that the program will overwrite NODES with the same coordinates. Compress means to make a new numbering.

Compressing of nodes:

Performing static analysis: Starting with a check of this problem: Analysis>Run Check

Then we can apply some additional default loads: gravity, centrifugal forces, etc.Analysis>Static>Static Analysis OptionsThis window will be left default because we do not take in account the effect of own weight, gravity of another additional effect.

If the Run Check has been proper, then we can go ahead and run static analysis: Analysis>Static>Run Static Analysis.

-Results>Plot>Displacement\Response\Reaction>Load case:1; Component:UY;

Coordinate system 0 (This zero 0 means Cartesian, 1 means cylindrical, 2 means spherical); Click VECTOR PLOT

-LoadsBC/Structural/Pressure/Plot-Edit/Plot/Curves

The extreme displacement along Y axis is: -0.000667 [m]?????.

-Analysis of the frequencies:

Analysis>Frequency\Buckling>Frequency Options

-Analysis>Frequency\Buckling>Run Frequency-Result>List>Natural Frequency

-Dynamic Analysis: Analysis>POST_DYNAMIC>Sel. PD Analysis Type 2: Modal time-history analysis 10; 50; 0; 0.2; 0: Newmark.

- Analysis>POST_DYNAMIC>PD_OUTPUT>Set Print Options

- Analysis>POST_DYNAMIC>PD Curves>Curve Type

- Analysis>POST_DYNAMIC>PD Curves>Define

In the next window PD_CURDEF is filled with information from graphic.

- Analysis>POST_DYNAMIC>PD_OUTPUT>Set Plot Options

-Display>XY Plot>Activate Preproc

--Display>XY Plot>Plot Curves

-LoadsBC>Structural>Force>Define by curves. Value 1 means the curve 1 defined in previous.

-Analysis>Post Dynamic>Run Post Dynamic-Result > Plot> Displacement/Response/Reaction Vector Plot

-Edit>Plot>Curves

Accelerogram-Dynamic Analysis: Analysis>POST_DYNAMIC>Sel. PD Analysis Type

-Control>Activate>Set Entity>TC:Time Curve

-Analysis>Post_Dynamic>PD_Curves>Curve Type ????? 2 or 1????

-Analysis>Post_Dynamic>PD_Curves>Define

Zero because we need to import a file.

Look in: C\Cosmosm\Vprobs\AdvDynamics >All(*.*)>D15.DAT > Check extension with right click>Properties. Then open.

-Display>XY_Plots>Activate Preproc>

--Display>XY Plot>Plot Curves

-Analysis>Post_Dynamic>PD_Base_Excitation>Base Excitation Factor

Base_cur multiplier Z comp. for SOLID.-Analysis>Post_Dynamic>Run Post DynamicErorr appeared using Curve label 2. Solution?

-Analysis>Post_Dynamic>PD_Curves>Delete. Which curve is deleted?

-Analysis>Post_Dynamic>PD_Curves>Define

-Look in the folder where the model is created for the file with the model name and extension *.CR1

Error which can appear if was used a wrong number for curve label

Good message after loading *.CR1

-Display>XY_Plots>Activate Preproc>

Clear the window using button

-Display>XY_Plots>Plot Curves

Nonexistent information: is an error appeared using a wrong number for curve label and graph number.

Good message after plot curves

A small modification: -Analysis>Post_Dynamic>PD_Base_Excitation>Base Excitation Factor

-Display>XY_Plots>Activate Preproc>

-Display>XY_Plots>Plot Curves

-LoadsBC>Loads Options>Time Parameters

-Analysis>Post_Dynamic>PD Output>Set Print options

-Analysis>Post_Dynamic>PD Output>Set Plot Options

-Analysis>Post_Dynamic>List PD Analysis Options

This is from previous analysis using the variable force according the graph.-Analysis>Post_Dynamic>Select PD Analysis Type

-Analysis> Post_Dynamic>Run Post Dynamic-Results>Plot>Displacement/Response/Reaction

If necessary, is possible to create more windows to show different results simultaneously. Click twice on New win, then on Tile

-Results>Setup>Postproces type>Linear Structural-Results>Plot> Displacement/Response/Reaction>Load case nr. :1Vector plot-Results>Setup>Postproces type>Post Dynamic-Results>Plot> Displacement/Response/Reaction>Time step number: 12Vector plotDo not work????

The Case B-The structure created with volumes and meshed using SOLID element.-Create key points for the base of columns. Coordinates in XY plane: KP1(0, 0); KP2(0, 0.4); KP3(0.4, 0.4); KP4(0.4, 0); KP5(5, 0); KP6(5, 0.4); KP7(5.4, 0.4); KP8(5.4, 0); KP9(10, 0); KP10(10, 0.4); KP11(10.4, 0.4); KP12(10.4, 0);

-Create 3 surfaces using key points: Geometry>Surfaces>Define by 4 Pt. View of the window for third surface.

-Creation of the columns: Before start, switch to isometric view:

Geometry>Volumes>Generation>Extrusion. for volume nr. 1 for volume nr. 2: Similar for volume nr.3.

-Beams creation: It is starting with key points on the face of the column nr. 1.

Coordinates of key points created: KP25(0.4, 0.05, 2.5); KP26(0.4, 0.35, 2.5); KP27(0.4, 0.35, 3); KP28(0.4, 0.05, 3); KP29(0.4, 0.35, 5.5); KP30(0.4, 0.05, 5.5); KP31(0.4, 0.35, 6); KP32(0.4, 0.05, 6);The next step is to create key points on the face of columns nr.2 and nr. 3 to create beams. This step can be solved in two ways. First we can create point by point after a coordinates calculation or the second way is to copy. In this example we will copy.-Create a new coordinate system at the base of column nr.2: Geometry>Coordinate_Systems>3 Points. Before points generation is necessary to go back in initial coordinate system: Control>Activate>Set Entity>CS: Coordinate system>0.-Now we want to copy points: Geometry>Points>Generation>Copy

-As we can see, in the next image has appeared new points from 33 to 40. These points will be used to create surfaces on the face of column nr.2 and then create volumes for beams between column nr.2 and nr.3.

-Now is created a new coordinate system at the base of column nr.3 and then will copy point from the face of column nr. 2 Geometry>Coordinate_Systems>3 Points.

As above, before generation of points is necessary to go back in previous coordinate system: Control>Activate>Set Entity>CS: Coordinate system>3.

Is not very simple and takes time as well as coordinates calculation for each point.-Beams creation: ***We are in the Coordinate system 4. No problem!Geometry>Surfaces>Define by 4 Pt. Geometry>Volumes>Generation>Extrusion.

-Create surfaces 31 and 32 on the face of column nr.2 Geometry>Volumes>Generation>Extrusion.

-Create surfaces 43 and 44 on the face of column nr.3

Geometry>Volumes>Generation>Extrusion.

The model is ready!-Define finite element: Propesets>Element group

-Define Material properties: Propsets>Material Property: ***values to be in [m].

This means 2500 [kg/m3]

This means 2,1104 MPa.

-Meshing>ParamtetricMesh>Volumes: Because columns cross section is deferent from beams, the mesh must be performed separately. To begin with columns. Column mesh***When we are with the arrow of the mouse in the cells of the window, particularly in cells Number of elements on first, second and third curve left click from second by second to find the line of the first volume which become from white to magenta color. -Beams meshing: Meshing>ParamtetricMesh>Volumes>:Clear the screen, then: Edit>Plot>Volumes. Zoom in on volumes 4 and 5 to refresh window and the edges to become white. ***Look closely because first and second curve changes its color almost imperceptible, is observable just a change in texture, instead the color for third curve is well visible.***Mesh step by step each volume from 4 to 9 to identify properly those three curves. The aim is to get a correlation between mesh of the column and beam in two planes XY and XZ.

Clear again the screen and then plot volumes to continue with volume nr. 5.

Above we have correlation in XY plane.Cross section of column on Y axis was divided in 8 elements and on X axis in 4 elements. On the length of the column on Z axis it was divided in 60 elements.The width of beam on Y axis was divided in 6 elements and height on Z axis in 5 elements to get correlation with columns. On the length of the beam on X axis it was divided in 23 elements.

Above we have correlation in XZ plane.Unfortunately some changes are necessary because volumes 8 and 9 was divided in 23 elements on length, but they have not a length of 4.6 as beams between columns, their length is just 2. Now we will delete the mesh for these two volumes and mesh again. In image underneath is visible a difference in density at the right of column 3 where is beam 8 and at the left where is a beam between columns.

Meshing>Parametric_Mesh>Delete Elements on Volume

Meshing>Parametric_Mesh>VolumesBecause after meshing in a lot of elements the program run slowly when it plot them on screen is recommended to clear the screen and edit only volumes.

Now plot elements: Edit>Plot>Elements Now the elements length of beams outside column 3 is ok, 2/10=0.2 is the same with the elements length of the beams between columns 4/23=0.2. The model is upside down in XY plane, and we need it in upright position. Clear the screen/Plot volumes/rotate around X axis until we get XZ plane/Plot elements.

-In this moment our model is in space and it is not supported, so we must to apply supports and to cancel all 6 degree of freedom at the base of the columns (fixed supports). Meaning to fix surface 1, 2 & 3.LoadBC>Structural>Displacement>Define by Surfaces

-Let to load the structure: LoadBC>Structural>Pressure> Define by Surfaces Here was applied the pressure just for one surface.But, knowing value between surface 36 and 48 (12) we have applied the pressure simultaneously. Surfaces [24, 36 & 48] are upper surfaces for inferior beam. Surfaces [30, 42 & 54] are upper surfaces for superior beam and they were loaded simultaneously according image bellow.

And finally our structure is supported and loaded.Prepare the model for analysis: Analysis>Static>Static Analysis Options.Activate stress calculation: Analysis>Static>Activate stress Calc Merge the nodes: Meshing >Nodes>Merge Compress the nodes: Meshing >Nodes>Compress Now run analysis: Analysis>Static>Run Static AnalysisIf all steps was followed the analysis had to run properly and allow us to see results.Results>Plot>Displacement/Response/Reaction. ***Type zero in the cell corresponding to Direction: XComp and YComp.

Edit>Plot>Volumes. Results>Extremes>Displacements/Response/Reaction>UZ: Displacements.Results>List>Displacements/Response/Reaction>Set number-2:Reaction Forces

Analysis>Frequency\Buckling>Frequency Options

-Analysis>Frequency\Buckling>Run Frequency: -Result>List>Natural Frequency

For comparison with frequency of the same structure modeled with beams.

Dynamic Analysis/Curve defined by user: Follow steps shown starting from page 22 until page 27. Graph is ok.In the next images is shown result of the analysis which can be compared with results from the case A, the same structure modeled with beam element.

Dynamic Analysis/Curve created automatically/Accelerogram: Follow steps shown starting from page 28 until page 38.The FREQ graph is ok

The TIME graph is ok

After a correct running of analysis according page 37, results are available to be ploted.-Results>Plot>Displacement/Response/Reaction

Then: Edit>Plot>Volumes