Action on Structures Exposed to Fire— Thermal Elongation

PDF

Action on Structures Exposed to Fire
— Thermal Elongation

This is the 4th verification example from (Ref. 1) which is part of the European Standard EN-1991-1-2:2010-12, Eurocode 1: Actions on structures - Part 1-2: General actions - Actions on structures exposed to fire. It verifies that the calculated elongation matches the expected values.

Model Definition

The modeled geometry is a cube with side length of 100 mm. The temperature in the block is homogeneous and prescribed. The thermal strain function dL (Figure 1) is given in (Ref. 2).

Figure 1: Temperature dependent thermal strain function.

The model is a pure structural mechanics problem. The thermal expansion is calculated according to

with the given thermal strain function dL, the reference temperature Tref = 20°C and the prescribed temperature T (Table 1).

Results and Discussion

The reference and calculated values are given in Table 1 and match exactly. This is expected, because the thermal strain function prescribes the deformation and the deformation is what you compute.

Table 1: Reference and Calculated Elongation.
Temperature (°C)	Reference Elongation	Calculated Elongation
100	0.09984	0.09984
300	0.37184	0.37184
500	0.67584	0.67584
600	0.83984	0.83984
700	1.0118	1.0118
900	1.18000	1.18000

1. DIN EN 1991-1-2/NA, National Annex - Nationally determined parameters - Eurocode 1: Actions on structures - Part 1-2: General actions - Actions on structures exposed to fire

2. DIN EN 1993-1-2 Eurocode 3: Design of steel structures - Part 1-2: General rules - Structural fire design; German version EN 1993-1-2:2005 + AC:2009

Heat_Transfer_Module/Verification_Examples/fire_effects_thermal_elongation

Modeling Instructions

From the menu, choose .

In the window, click

.

1

In the window, click

.

2

In the tree, select .

3

4

5

In the tree, select .

6

Define a parameter for the temperature which is the input for the thermal expansion. A parametric sweep over this temperature will be performed.

Global Definitions

1

In the window, under click .

2

In the window for , locate the section.

3

In the table, enter the following settings:


Name	Expression	Value	Description
T_in	100[degC]	373.15 K	Temperature

1

In the window, under click .

2

In the window for , locate the section.

3

From the list, choose .

1

In the toolbar, click

.

2

In the window for , locate the section.

3

In the text field, type 100.

4

In the text field, type 100.

5

In the text field, type 100.

6

.

Define the material properties for steel.

1

In the window, under right-click and choose .

2

In the window for , type Steel in the text field.

3

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Young’s modulus	E	210000[N/mm^2]	Pa	Basic
Poisson’s ratio	nu	0.3	1	Basic
Density	rho	7850	kg/m³	Basic

4

Click to expand the section. In the tree, select .

5

.

Piecewise 1 (pw1)

1

In the window, expand the node.

2

Right-click and choose .

3

In the window for , type dL in the text field.

4

Locate the section. In the text field, type T.

5

Find the subsection. In the table, enter the following settings:


Start	End	Function
20	750	1.2e-5T+0.4e-8T^2-2.416e-4
750	860	1.1e-2
860	1200	2e-5*T-6.2e-3

6

Locate the section. In the text field, type degC.

7

. Compare with Figure 1.

1

In the window, click .

2

In the window for , locate the section.

3

In the table, enter the following settings:


Property	Variable	Expression	Unit	Size
Thermal strain	dL_iso ; dLii = dL_iso, dLij = 0	dL(T)	1	3x3

The variable T is not known, yet. Add the temperature in the section to define it.

4

Locate the section. Click

.

5

In the dialog box, type temperature in the text field.

6

7

In the tree, select .

8

Solid Mechanics (solid)

1

In the window, under right-click and choose .

2

Select Boundaries 3, 5, and 6 only.

The roller condition ensures that the structure expands in all directions uniformly.

Linear Elastic Material 1

In the window, click .

Thermal Expansion 1

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

From the list, choose .

Define a parameter for the input temperature.

4

Locate the section. From the T list, choose . In the associated text field, type T_in.

In the toolbar, click

.

1

In the window, click .

2

In the window for , locate the section.

3

From the list, choose .

4

.

A very coarse mesh is sufficient. Even just one element would be enough, because the deformation is prescribed and you verify that the calculated deformation gives the same value. This is a basic test to validate that the tested functionality works correctly.

Step 1: Stationary

Set up a parametric sweep over the input temperature.

Parametric Sweep

1

In the toolbar, click

.

2

In the window for , locate the section.

3

4

In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
T_in (Temperature)	100 300 500 600 700 900	degC

5

In the toolbar, click

.

A 3D stress plot is created automatically. Add a new plot group to visualize the displacement field.

Displacement field

1

In the toolbar, click

and choose .

2

In the window for , type Displacement field in the text field.

1

Right-click and choose .

2

In the toolbar, click

.

Surface Average 1

1

In the toolbar, click

and choose .

2

Select Boundary 4 only.

3

In the window for , locate the section.

4

In the table, enter the following settings:


Expression	Unit	Description
w	mm	Displacement field, Z component

5

1

Go to the window.

To compare these results with the reference values, import the data as interpolation function.

Global Definitions

Interpolation 1 (int1)

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

5

Browse to the model’s Application Libraries folder and double-click the file fire_effects_thermal_elongation_dlref.txt.

6

Find the subsection. In the table, enter the following settings:


Function name	Position in file
dl_ref	1

7

Locate the section. In the text field, type degC.

8

Locate the section. Click .

It is not necessary to compute the whole study again. To make the data available for postprocessing, just update the solution.

In the toolbar, click

.

Surface Average 1

1

In the window, under click .

2

In the window for , locate the section.

3

In the table, enter the following settings:


Expression	Unit	Description
w	mm	Displacement field, Z component
dl_ref(T_in)		Interpolation 1

4

In the toolbar, click

and choose .

1

Go to the window.

The computed and reference values match exactly. Compare with Table 1.