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4. MEMBRANE MODEL

1.1. Preprocessing with surface elements

Start

Start AxisVM by double-clicking the AxisVM icon in the AxisVM folder, found on the Desktop, or in the Start, Programs Menu.

New

Create a new model with the New Icon. In the dialog window that pops up, replace the Model Filename with �Membrane 1�. Select the Design Code. Click Ok.

Objective The objective of the analysis is to determine the internal forces

and reinforcements of the following wall structure.

Assume the wall thickness is 200 mm, the concrete is of C20/25,

and the reinforcement is B500A computed according to Eurocode-2.

The first step is to create the geometry of structure. Coordinate System

In the lower left corner of the graphics area is, in blue color, the coordinate system beginning point marked with a blue X. The coordinate system view can be changed from the Icons Menu

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with the Views Icon. Move the cursor over that icon and the following icon bar is displayed:

The vertical upward direction is taken as the positive Z direction.

It has relevance for the direction of gravitational force. If the view is not already in Z-X plane, switch to it.

Geometry If not already selected, activate the Geometry tab, under which

the Geometry Toolbar is displayed.

Quad/Triangle Division

The geometry of the wall is created with the Quad/Triangle Division Icon. Hold down the left mouse button to display the sub-menu. Click on the first Icon on the left and the following dialog window is displayed:

To create the upper part enter N1=20, N2=8.

Close the dialog window with Ok. Now you have to specify the

corners of the Quad. They can be specified graphically or by entering the coordinates. Lets enter them with coordinates : To enter the first corner, Type in the following sequence of keys :

X=0 Y=0 Z=3, Enter Specify the relative coordinates of the next corners in a similar

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way. Type in the following sequence of keys :

X=12 Y=0 Z=0, Enter X=0 Y=0 Z=3, Enter X=-12 Y=0 Z=0, Enter

Exit from drawing quads by pressing Esc. The following Drawing is displayed:

Quad/Triangle Division

The pillars are created in a similar way. Click the Quad/Triangle Divison Icon. Enter the following values: N1=3, N2=6

Close the dialog window with Ok. Now you have to specify the

corners of the Quad.

Type in the following sequence of keys :

X=0 Y=0 Z=-6, Enter X=1 Y=0 Z=0, Enter

X=0.8 Y=0 Z=3, Enter X=-1.8 Y=0 Z=0, Enter

Exit from drawing quads by pressing Esc.

The following drawing is displayed:

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Mirror

Create the other pillar by mirroring the first one with respect to the center of structure (X=6). Click the Mirror Icon. The Selection Icon Bar is displayed:

Select with a selection window all nodes of the pillar.

The selected elements will be highlighted.

Finish the selection with Ok and the following dialog window

will be displayed:

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Set Mirror: Copy, Nodes to connect: None, Copy: All. Now

you have to specify the mirror plane. First select the middle point of the bottom line of the upper part, then select any point vertically above it.

The following drawing is displayed:

The geometry of the wall has been successfully created. Zoom

Let's zoom to the structure. Move the cursor over the Zoom Icon on the Icons Menu. The Zoom Icon Bar pops up.

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Fit in Window

Click the Fit In Window Icon.

Geometry Check

In the top icon bar, Click the Geometry Check Icon to check for possible duplicate entries. In the dialog window displayed the tolerance for merging the nodes can be specified. If the distance between two nodes is less than the value you enter they respective nodes will be merged. Enter .001.

Click OK and a check summary is displayed when completed.

Elements The next step is to create the finite elements. Activate the

Elements tab.

Surface Elements

Click the Surface Elements Icon. After selecting All elements the following dialog window is displayed:

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Set the type of the element to Membrane(plane stress).

Material Library Import

Click the Material Library Import Icon. The following dialog window is displayed:

Select C25/30 from the Materials list, then accept it with Ok.

Thickness Enter(type) in the Thickness edit box 200 [mm], then close the

dialog window with Ok. The surface elements have been created. Display Options

To view the local coordinate system of the surface elements click on the Display Options Icon on the Icons Menu in the left side. The following dialog window is displayed:

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Check the Surface box in the Local Systems panel.

Accept the change with Ok. If the Mesh, Node, Surface Center is switched on among the

Graphics Symbols, it is visible that the program uses 9-node membrane elements. These 9 nodes are the corners, middpoints and center point of surface element. If you move the cursor on the surface center symbol (a filled square), a hint window is displayed with the property of the surface element: its tag, material, thickness, mass and references, as shown in the next drawing:

The red line shows the x axis of the local coordinate system, the yellow one the y axis and the green one the z axis.

Line Support To create the supports click on the Line Support Icon and

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select the bottom lines of the pillars with a selection box.

Finish the selection with Ok. The following dialog window is

displayed:

To create a pinned support use the following settings:

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Nodal DOF

Click the Nodal DOF Icon, select all nodes with the All command and accept the selection. In the dialog window scroll to Membrane in Plane X-Z and apply it.

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1.2. Preprocessing with domains

Start

Start AxisVM by double-clicking the AxisVM icon in the AxisVM folder, found on the Deskto, or in the Start, Programs Menu.

New

Create a new model with the New Icon. In the dialog window that pops up, replace the Model Filename with �Membrane-2�.

Objective The objective of the analysis is to determine the internal forces

and reinforcements of the following wall structure:

Assume that the wall thickness is 200 mm, the concrete is of

C25/30, and the reinforcement is B500A, computed according to Eurocode-2.

The first step is to create the geometry of structure. Coordinate System

In the lower left corner of the graphics area is the global coordinate system symbol. The positive direction is marked by

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the corresponding capital letter (X, Y, Z). The default coordinate system of a new model is the X-Z coordinate system. It is important to note that unless changed the gravity acts along the �Z direction. In a new model, the global coordinate default location of the cursor is the bottom left corner of the graphic area, and is preset to X=0, Y=0, Z=0. The location of the cursor is defined as a relative coordinate. You can change to the relative coordinate values by pressing the �d� labeled button on the left of the Coordinate Window. (Hint: In the right column of the coordinate window you can specify points in cylindrical or spherical coordinate systems). The origin of the relative coordinate system is marked by a thick blue X.

Geometry If not already selected, activate the Geometry tab. The

Geometry Toolbar is displayed:

Line

Press down the left mouse button while the mouse is on the Line Icon. (Note: Icons default display is to the last icon selection) The following icon sub-menu is displayed:

Note: When the a line type is chosen, the Relative coordinate

system automatically changes to the local system (�d� prefix) Polygon

Select the Polygon icon, which is the second from left. When the Polygon is chosen, the Relative coordinate system automatically changes to the local system (�d� prefix) The polygon coordinates for the frame model can be drawn with the mouse, or by typing in their numerical values.

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Set the first point (node) of the polygon by typing in these entries:

X=0 Y=0 Z=3 Finish specifying the first line point by pressing Enter.

To enter the remaining nodes of the polygon membrane model,

enter the following sequence of values: X=1 Y=0 Z=0, Enter

X=0.8 Y=0 Z=3, Enter X=8.4 Y=0 Z=0, Enter X=0.8 Y=0 Z=-3, Enter

X=1 Y=0 Z=0, Enter X=0 Y=0 Z=6, Enter

X=-12 Y=0 Z=0, Enter X=0 Y=0 Z=-6, Enter

Exit from the command by clicking Esc twice. Translate

Click the Translate Icon. Select the top horizontal line and finish the selection with Ok. Choose Incremental from the Method panel, N=1, Nodes to Connect: None, then close the dialog window with Ok. Now you must specify the translation vector. Click any empty place in the Graphics Area, then type in the following sequence:

X=0 Y=0 Z= -0.75, Enter The following drawing results:

Elements The next step is to create the finite elements. Click the

Elements tab.

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Domain

Click the Domain Icon, then select All. Accept the selection with Ok and the following dialog window is displayed:

Set the type of the element to Membrane (plane stress).

Material Library Import

Click the Material Library Import Icon and the following dialog window is displayed:

Thickness Enter(Type in) 200 [mm] as the thickness of wall

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, then close the dialog window with Ok.

The following drawing results:

It is easy to observe the symbol of the domain - a blue line on the inner contour of the domain. Moving the cursor over it a hint window is displayed with the properties of the domain:

Domain Meshing

Click the Domain Meshing Icon. Select the domain with the All command (the asterisk) and finish the selection with Ok. The following dialog window is displayed:

Type in 0.75 [m] for the average mesh element size. After

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closing this dialog window with Ok the automatic mesh generation is started. The progress of mesh generation is shown in a window.

After the mesh generation is completed, the following drawing is displayed:

If you move the cursor on the surface center symbol (a filled

square), a hint window is displayed with the property of the surface element : it's tag, material, thickness, mass and references as shown in the next drawing.

Line Support

The next step is to specify the supports. Click the Line support Icon. Select the bottom lines with a selection box.

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Accept the selection with Ok. The following dialog window is displayed:

To create pinned support set the dialog window as shown below:

Close the dialog window with Ok, and the following drawing is

displayed:

Nodal DOF

The next (optional) step is to set the nodal degrees of freedom. Click the Nodal DOF Icon. Select all nodes with the All command, finish the selection with Ok, and in the dialog window select Membrane in plane X-Z.

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The finite elements have now been created. The next step is to apply the loads. Load Click the Loads tab.

Surface Edge Load

Assume a 50kN/m vertical distributed load. Click on the Surface Edge Load Icon, then select the line you have created with the translate command (the second black line from top):

Finish the selection with Ok, and enter(type) in: py 50 [kn/m]:

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Press Ok and the load is applied.

The following drawing is displayed:

Static The next step is the analysis and postprocessing. Click the

Static tab.

Linear Static Analysis

Click the Linear Static Analysis Icon. The model will be saved with it's current name (which is Membrane 2 in this case).

A Model Save Dialog will appear if you haven�t already

assigned a name for the model. Accept save and a Save dialog window appears, where you can specify the model filename and path.

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Calculation During the calculation the following window is visible:

Click the Details button to view the details of calculation:

The topmost label shows the current computation step, and the bar below it shows its progress. The second bar shows the global progress of computation. The estimated memory requirement shows the estimated virtual memory needed. If the virtual memory of the computer is set to a lower value than the needed value, an error message is displayed. When the computation has finished, the progress bars will disappear.

Postprocessor Close the window with Ok. By default the postprocessor will

start with the ez displacement, the display mode will be isoline. You will see the vertical displacements.

Display Options

For a clearer view, switch off the display of Loads. Click the Display Options Icon, and uncheck the Load box.

Fit in Window

Click on the Fit in Window Icon.

The following drawing results:

Click the Result Component combo box (the one showing

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ez[mm] and select nx from Surface Internal Forces.

Min/Max Value

To find the location of maximum internal force. Click the Min, Max Value Icon. The following dialog window is displayed:

Here you can select the component you are interested in. Accept

nx by clicking Ok. A dialog window will show the value and location of the negative maximum.

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Click Ok and another window is displayed showing the location

and value of positive maximum. The color regions are delimited by the values in the Color

Legend Window. You can change the number of colors by dragging the handle beside the level number edit box or entering a new value.

Color Legend Setup Window

To find the ranges with a normal force larger than -100 kN/m, Click on the values in the Color Legend Window. In the Color Legend Setup dialog window check Auto Interpolate, then click on the bottom value in the left column, and replace �331.62 with -100.

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Close the dialog window with OK, and the new ranges will be applied.

The following drawing results:

The regions with a normal force greater then -100 are hatched.

Isoline View the internal forces in Isoline display mode. Click the

Display Mode combo box (the one which displays Isosurface 2D) and select Isoline from the list.

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The isoline drawing is shown below:

View the internal forces of the supports. Select rz from Line Support Internal Forces in the Result Component combo box.

Result Display Parameters

Click the Result Display Parameters Icon, and the following dialog window is displayed. Check the Lines box in the Write Values To panel and set the Display Mode to Diagram

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Close the dialog window with Ok and the values of support forces is displayed on the screen:

R.C. Design The next step is to calculate the reinforcement. Click the R.C.

Design tab:

Click on the Reinforcement Parameters Icon, and select all surface elements with the All command. Complete the selection with OK, and the following dialog window is displayed:

Close the dialog window with OK and the axb diagram is

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displayed:

The area of reinforcement in the x direction is the sum of the axt and axb values.