4.2 Joves i educació
4.2.3 Anàlisis de la realitat juvenil
Prestress Tendons; Relaxation loss; Elastic Loss; Interpolated/short term Modulus;
User Notes; Stress/Strain calculation Reports; Inverted Neutral Axis for Hogging.
Outline
The pre stressed section defined in Chapter 2 is opened and the slab and edge section are removed from the section definition.
The section represents the mid span section of a 25m long beam which has been cast and stressed and is about to be released from its mould. The concrete strength at this stage is based on grade 32 concrete and the relaxation loss in the tendon force is assumed to be 1.25%. The self weight moment is calculated based upon a weight density of 23.54kN/m3 and applied in the load table.
An SLS stress analysis is carried out assuming that the neutral axis remains horizontal, and the elastic modulus is set to the short term modulus.
The stress results are the stresses in the concrete taking into account the losses in the tendons due to the elastic deformation of the concrete. By temporarily setting the elastic modulus of the concrete to a very high value (say 10000kN/mm2) the resulting stresses are those without elastic deformation losses.
3-44 Procedure
1. Start the program and use the menu item File |Open to open the file “AU Example 2_7.sam” created in Chapter 2 of this manual. If an “Information” form appears containing information about the project template, then click “OK” on this form.
2. Use the menu item Data |Titles to change the Section Title to “Prestressed Section Analysis”, the Sub-title to “Example 3.7” and the Job Number to “3.7”.
Click on “OK” to close the Titles form.
3. Open the Section Definition data form using the menu item Data |Define
Section... Delete the edge detail by clicking in the Library field of the fourth row and using the delete key. Delete the slab section by clicking in the Library field of the second row and using the delete key. Now delete the concrete infill by clicking in the Library field of the second row and using the delete key.
4. Assign Grade 32 concrete to concrete beam component by using the drop down selection of the Property field. Click on the “OK” button to close the Define Section form.
5. To find the cross-sectional area of the beam, use the Data |Analysis Type menu to set the analysis type to “Section Properties”. Use the Calculate
|Analyse menu to open the Calculate Section Properties form.
6. The cross-sectional area is 0.2175m2. The weight density is 23.54kN/m3 and the length of the beam is 25m, therefore an Mx bending moment of 400kNm (i.e 0.2175×23.54×25x25/8) must be applied to the beam.
7. Click on the “OK” button to close the Calculate Section Properties form.
8. Use the Data |Analysis Type menu to set the analysis type to “Bending, Axial and Shear”.
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9. Delete the Structural Steel Material using the Define Material Properties form (if it is still shown on the form).
10. Use the Data |Define Loads |Applied Forces menu to open the Define loads form.
11. Click on the “Insert record” (+) buttons at the top and bottom of the form to add a load case. On the first row of the bottom table, click in the Type column and select “X Moment” from the drop down list. Enter a value of “400kNm” in the Nominal Load column. Set the Perm/Live field to “Perm”. Change the
serviceability
γ
and DLA factors to 1 by clicking in relevant fields and entering a value of “1.0”.12. Click on the “OK” button to close the Define Loads form.
13. The relaxation loss in the tendon force must be accounted for before analysing.
Open the Define Bars and Tendons form using the menu item Data | Define Bars...
14. The tendon forces are 188kN and will be reduced by 1.25% in this example.
Click on the “Edit Tendons” button. Window around the whole section in the graphics window to select all of the tendons. This will open the Edit
Reinforcement sub form. On the sub form set the Edit Option field to “Change force” and enter a value of “186kN” in the Tendon Force field. Click “OK” on the sub form.
15. Click on the “OK” button to close the Define Bars and Tendons form.
16. It is useful to make a note of this in the User Notes form which can be opened up using the menu item Data | Notes... Enter the following text “Tendon forces have been reduced from 188kN to 186kN to represent relaxation losses at transfer.” Then close the form with the “OK” button.
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17. Use the Calculate |Analyse menu to open the Bending, Axial and Shear form.
Click “No” on a form that may appear regarding iterations. Ensure that the Analysis type field is set to “Service Limit State”.
18. Click on the Neutral Axis angle drop down and select “Set angle to” from the list. Click in the corresponding edit box and enter a value of “180°”.
19. By default the elastic modulus used in the calculations will be interpolated between the long and short term values and as the load is totally “Permanent”
the modulus will be equal to the long term value. To force the short term value to be used we use the Set Parameter for: field to “Serviceability Calculations”
and in the displayed sub-form set Elastic Modulus used: to “Short Term”. Close the sub-form with the “OK” button.
20. The results are shown on the graphic display as:
21. Click on the “Results” button to display the Results Viewer.
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22. The maximum stress in the tendons is -1192.939MPa. The minimum stress is -1255.188MPa.
The full stress in the tendon should be the tendon force divided by the tendon area = 186000/143 = 1300.7MPa. The difference in these values is due to elastic deformation losses.
23. Click on the “OK” button to close the Bending, Axial and Shear form.
24. Use the Data |Define Material Properties menu to open the Define Material