static analysis of 3d structure -...

EXAMPLE 3

Static analysis of 3D structure

Perform the analysis of the 3D structure presented in the following figure for

vertical and simplified earthquake actions.

Input data:

Consideration of diaphragm function of each floor.

Uniform distributed loading on beams:

Permanent actions g=15kN/m

Variable actions q=10kN/m.

Consideration of cracked cross-sections during the analysis.

Column cross-sections:40x60 (cm)

Beam cross-sections:

EXAMPLE 4: Static analysis of 3D structure 38

Frame in X-X direction

Frame in Y-Y direction

3.1 Model Geometry

In this case it is quite convenient for the user to select the 3D model from the

SAP model library. From FileNew Model from Template and selection of the

appropriate icon (Figure 3.1) the new model can be introduced very quickly.

Figure 3.1. Selection of existing model

In the window of Figure 3.2 the details of the model geometry are filled in the

appropriate fields. These are the storey number the span (beam openings) number

as well as their dimensions in each direction.


Figure 3.2. Details of model geometry

The result can be seen in Figure 3.3.

Figure 3.3. Initial appearance of the model in SAP 2000

In the left window of the figure above we can see the structural model in 3

dimensions whereas in the right window the model appears in the X-Y plane at

altitude Z=12m. From the respective toolbar (Figure 3.4) the user can make the


selection of the desired 2D or 3D view of the model. It is recommended to have the

3D view in the left window and a plane view in the right window.

Figure 3.4. Toolbar for 2D or 3D view selection

Thus by clicking the xz icon of the previous figure (when the right window is

activated) we can see in Figure 3.5 the plane X-Z view at Y=-2m. The user can be

informed of the y-level from the window title (X-Z Plane @ Y=2). Simultaneously a

discontinuous line of light blue color appears at the 3D view window, that specifies

the location of the plane view. Changing of the Y level can take place using the up-

down arrows of Figure 3.5.

Figure 3.5. 3D and 2D views of the model. Changing levels

In order to apply the correct supports we can work as follows. First in a x-Y view

of the right window we can move to tha base (Z=0) and select all the base joints

(Figure 3.6). Then from AssignJointRestraints replace all supports with full

fixities (restrain all degrees of freedom).


Figure 3.6. Full fixities assignment at the base joints

3.2 Materials

The determination of materials takes place from

DefineMaterials

We choose Add New Material in order to create a new material using the material

properties given with the problem data (Figure 3.7).

Figure 3.7. Define new material properties


3.3 Cross-sections

Cross-section determination for linear elements (Frame elements - beams,

columns) takes place from DefineFrame Sections. Columns are rectangular and

can be defined as presented in Figure 3.8 choosing the Add Rectangular option. In

this example the large dimension is given in the t3 (Depth) field. As explained in the

previous example the modification factors for resistance in flexural and shear forces

are taken equal to 0.5 of their initial value because of cracking (Figure 3.9).

Figure 3.8. Column cross-sections

Figure 3.9. Geometric characteristics of the column section and modification factors

In the same way the beam cross-sections are also introduced (Figure 3.10) using

the same modification factors.


Figure 3.10. Geometry of beams

After defining the new sectiona they should be assigned to the related elements.

A “clever” way to assign quickly the cross-sections is described below.

Before assigning any section the existing elements belong to the FSEC1 cross-

section type. The most convenient way to make the assignment is to select first all

beam elements by using the right window in X-Y plane view. With the arrows we

can easily move levels (from Z=3m to Z=12m) and select all horizontal elements.

Then from AssignFrameSections assign the beam section to all selected

elements.

Now all horizontal elements are assigned the beam section whereas all vertical

elements are still FSEC1. SAP2000 gives the option to select all elements that

belong to the same section. Thus, with left window activated, using

SelectSelectSection (Figure 3.11) we choose all the FSEC1 elements and then

from AssignFrameSections we define the correct section of COL type.

Figure 3.11. Select all vertical elements using their initial section type

The model now looks like Figure 3.12.


Figure 3.12. 3D view of the structure

From set elements show extrusions (left window activated) we can view a

3D-visualization of the elements dimensions. This way is convenient to easily detect

any geometry errors or section assignment errors.

Figure 3.13. 3D visualization of cross-section dimensions


3.4 Loads

For this example we need to create 4 separate Static Load Cases.

- G for permanent actions

- Q for variable actions

- EX for earthquake forces in X direction

- EY for earthquake forces in Y direction

Figure 3.14. Load cases definition

Then the appropriate load combinations according to EC-8 are defined. These

are:

- GRAV: Gravitational 1.35G+1.50Q

- EARTHQX: G+0.3Q+EX+0.3EY

- EARTHQY: G+0.3Q+EY+0.3EX

In the previous earthquake combinations we must notice that according to the

code we do not add the maximum values of EX and EY directions of the earthquake

forces. The code suggests that when the full power of the earthquake hits the

structure in X-direction, then we can accept that the simultaneous Y-direction is up

to 30% of its maximum value. Moreover, as explained in Example 2, the

simultaneous vertical loading is assumed not to exceed G+0.3Q at the moment of

the earthquake.

Load combinations are defined according to Figure 3.15.


Figure 3.15. Load combinations

The seismic actions in common structures can be applied in the geometrical

centre of each floor. It is obvious though that in this location there are no joints in

the model. So these additional nodes should be defined and connected somehow to

the other joints at each floor.


In order to make the creation of the new joints easier we define some additional

Grid Lines from Draw Edit Grid inserting value 0 in X and Y direction.

Figure 3.16. Introduction of new joints at (0,0)

After defining the new grid lines the Figure 3.17 appears..

Figure 3.17. Appearance of the new grid lines

After moving to the first floor (Z=3) of the X-Y view we can insert a new joint

using the command DrawAdd Special Joint and then clicking once at the centre of

the floor. After creating the new joint it is essential we press Escape button to avoid

accidental drawing of other joints. Right-clicking the joint can verify if the

coordinates are correct.


Figure 3.18. Drawing new joint

Now if we move to an X-Z view in the right window and using the arrows go to

Y=0 we can see the joined that was previously drawn.

We can create joints at the remaining floors by selecting the joint and go to

EditCopy. Then again from EditPaste we provide the required information for the

new joint to be created. Here we want to copy the joint from Z=3 to Z=6, Z=9 and

Z=12. In Figure 3.19 we are supposed to provide the height difference value

between the copied and the paste location. Thus the Delta Z value should be equal

to 3m, 6m and 9m.

Figure 3.19. Copy to new joints

After drawing all the new joints we specify the loads applied on them. We first

make sure that in the right window the X-Z plane is visible at level Y=0. We choose

the joint of the first floor and assign first the horizontal load in X-direction using

AssignJoint Static LoadsForces and inserting 100kN in the “Force Global X” field


for EX load case (Figure 3.20). We follow the same procedure for the remaining

floors and for direction Y.

Figure 3.20. Assign earthquake forces to joints

In order to assign the vertical forces we select the beam elements from

SelectSelectFrame Sections and then using AssignFrame Static LoadsPoint

and Uniform fill the appropriate value for G loading. Q loading is assigned the same

way.

3.5 Introduction of diaphragm constraint

The new joints where the earthquake loading was applied are not connected in

some way with any other structural element. However these new joints along with

the other floor joints are part of the storey and should move accordingly (diaphragm

movement). This assumption arises from the large in-plane stiffness of the floor

that won’t allow any in-plane deformations (change of lengths etc).

In order to introduce this characteristic to the program we can use the

diaphragm constraint option.

In each floor separately all the joints are selected and from AssignJoint

Constraints a diaphragm is defined around Ζ constraint axis (Figure 3.21 and Figure

3.22). ATTENTION must be paid not to include one joint to more than one

diaphragms.


Figure 3.21. Diaphragm definition at floor level

Figure 3.22. Diaphragm definition at floor level

After defining the diaphragms, the nodes at the centre of each floor are

“connected” to the rest of the floor and they move along it. This way the earthquake

load applied on the joints is transferred to the structure.

3.6 Analysis

After finishing the input data

introduction and select 3D analysis

from AnalyzeSet Options we are

ready to run the analysis.

Figure 3.23. 3D analysis of the model


3.7 Results

Indicatively we can see the bending moments diagram of the corner column for the

GRAV load combination:

a) for the frame of X direction (moment Μ33 - Figure 3.24)

b) for the frame of Y direction (moment Μ22 - Figure 3.25)

Figure 3.24. Moment of the corner column (bending of X-direction frame - Μ33)

Figure 3.25. Moment of the corner column (bending of Y-direction frame – Μ22)

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