3.3 Differential Temperature

Subjects Covered

• EN1991 Temperature Profile
• Restraining Moments
• Primary differential temperature stresses
• User defined profile

Outline

The composite section shown below has been defined and saved in example 2.6 with a slight modification to include a 200mm by 200mm upstand on the left hand edge constructed with grade C32/40 concrete. The previously defined continuous face on this edge is made non-continuous. A standard temperature gradient, according to EN1991, is applied to the section but it requires modifying it to take account of the upstand, as shown above. It is assumed that the temperature in the upstand will be constant and at the same value as that at the top of the slab. The effect of the reinforcement is to be included in the calculations.

It is required to determine:

• The overall restraining moments and axial forces for both positive and negative cases.
• The unrestrained (self equilibrating) primary stresses at the top and bottom of each of the three components for both positive and negative cases.

Procedure

1. Start the program and use the Home Open button to open the file “My EU Example 2_6.sam” created in example 2.6.
2. Use the menu item File | Titles to change the Sub-title to “Example 3.3 - Differential Temperature” and the Job Number to “3.3”.
3. Click ✓ OK to close the Titles form.

Add Upstand Edge Detail

4. In the Design Section navigation window use the toolbar button to create a new Section element | Parametric Shape.
5. In the Define Section Element form set both the width and depth to “200mm” then and position the Hook point “1” coordinates to (-750,200). The material should be set to grade C32/40 concrete using the drop down list in the Property column.
6. Set the Name field to “Edge Detail” and click ✓ OK to close the form.
7. The left hand edge of the slab is made non-continuous by clicking on the slab element in the navigation window, to get focus, then clicking on the left hand edge of the slab in the graphics window. This will change it from a dashed to a solid line. Click ✓ OK to close the Define Section Element form.
8. Right click anywhere in the Design Section navigation window and select Analyse Section | Differential Temperature.

Apply Temperature Profile

9. In the Differential Temperature Analysis form ensure the Display radio button is set to “Profile” and Ignore Reinforcement is unchecked.

   

10. In the Profile part of the form set Type to be “EN 1991-1-5 Fig 6.2 Non Linear” and the Type of Deck: to “composite decks” and the deck is “Surfaced” with a depth of “0.1m”

    This shows a profile as defined in EN1991-1-5 but the program assumes the top of the section is the top of the upstand. We therefore need to lower this profile so the top of it is aligned to the top of the slab. We also need to add a constant temperature portion from the top of the slab to the top of the upstand.

    

11. To modify this profile we must now change the Type to “User Defined.”

12. In the Heating Differences and Cooling Differences columns of the lower table, change the height and temperature values to those shown below by adding a row after the first row and then starting at the bottom of the list and work your way up with the new values.

    

13. The calculations are done automatically where the fully restrained “Relaxing Moments and Axial Forces” are displayed on the data form. Ensure that the Ignore Reinforcement check box is “unticked." The primary self equilibrating stresses are displayed by changing the Display option to “Stresses”.

    

14. Click on the Detailed Results... button to see all the results including the self equilibrating stresses.

    

15. Close the results viewer and the Differential Temperature Analysis form using the ✓ OK button on the analysis form.

16. Save the data file as “My EU Example 3_3.sam” using the main menu item File | Save As

17. Close the program.

Summary

This example shows how to define a user specific temperature profile on a composite steel/concrete section.

If a beam, made up from this section and temperature profile, was fully constrained along its length then the following forces and moments would be induced along the span:

Temp rise

Temp fall

The self equilibrating Primary Stresses at the top and bottom of each component can be seen in the results shown above.