Tutorial. Spring Foundation

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2 Page i Preface This tutorial provides an example on how to model a spring foundation using BRIGADE/Plus.

3 Page ii Contents 1 OVERVIEW GEOMETRY MATERIAL AND SECTION PROPERTIES STEP DEFINITION INTERACTIONS LOADS MESH RESULT VISUALISATION... 10

4 Page 1 / 11 1 Overview In BRIGADE/Plus the Spring-To-Ground Interaction feature can be used in order to model a spring foundation. This feature enables the user to easily define the interaction between the model and the ground by adding spring stiffness to either a surface or an edge. Spring stiffness is given in terms of stiffness per unit area (or stiffness per unit length in the case of an edge based region). The equivalent nodal spring stiffness are then calculated by using the shape function of the element, in the same way as equivalent nodal loading are calculated for distributed loads. In each node the corresponding spring stiffness will be added by implementing connector elements connected to the ground (CONN3D2). For more information about the spring-to-ground interaction see UM Geometry In this tutorial the use of the Spring-To-Ground Interaction will be demonstrated by modelling a spring foundation to the model shown in Figure 1. It is a model of a V- shaped bridge column situated on a foundation slab. Figure 1 FE model of the bridge column and spring foundation.

5 Page 2 / 11 3 Material and section properties The materials and sections are defined in the Property Module. The bridge column and spring foundation are modelled with a linear concrete material. The concrete properties are listed in the Table 1 below. Table 1 Concrete Properties Symbol Value Unit Description ρ 2500 E 34 υ 0.2 Kg/m 3 Density GPa Young modulus / Poisson s ratio The column and slab section are 0.75m and 0.8m respectively. The rendered shell thickness of both sections are displayed in Figure 2. Figure 2 Model with rendered shell thickness.

6 Page 3 / 11 4 Step definition Two General, Static steps are defined in order to carry out this tutorial. These steps correspond to dead weight and arbitrary lateral forces acting on the structure. 5 Interactions A kinematic coupling constraint is created between a reference point (RP) and the two column heads, see Figure 3. The RP is aligned between and directly in line with both heads and is used for applying external loads. Figure 3 Kinematic coupling between column and reference point. The core of this this tutorial is the modelling of a spring-to-ground interaction. Follow the steps outlined below to define the spring foundation. 1. Create a CSYS for the spring foundation. From the main menu select Tools Datum. Select 3 Points in the Method List.

7 Page 4 / Name the coordinate system SlabCSYS and choose Rectangular. Press Continue. 3. Select the midpoint of the slab as origin. The middle point of the edge in the global positive X-axis as a point on the X-axis and any point on the slab to be in the XY-Plane. Figure 4 SlabCSYS highlighted in red. 4. From the main menu in the Interaction module, select Spring-To-Ground Interaction Create. 5. Name the interaction Spring_Foundation and press OK.

8 Page 5 / The interaction now appears in the Spring-To-Ground Interaction Manager. Press Edit to proceed. 7. In the Spring-To-Ground Interaction press Create Set to select Host region for the interaction. 8. Give the name Spring_bed and select Faces. Press Continue. 9. Select the foundation slab in the viewport and press Done in the prompt area.

9 Page 6 / 11 Figure 5 The foundation slab selected as host region. 10. Select SlabCSYS as Reference CSYS for stiffness definitions and activate U1, U2 and U3. The spring stiffness in this tutorial is defined as 80 MN/m/m 2 in all stiffness directions. The Spring-To-Ground Interaction dialogue should be defined as shown below.

10 Page 7 / 11 6 Loads In this tutorial the model is subjected to a gravity load and an external dead weight load from the overhead bridge deck. Also, two lateral forces with direction in each principal axis of the horizontal plane are applied at the RP. The load definitions are given in the table below. Table 2 Load definitions. Load Value Unit Direction Global CSYS Region DW_Gravity 9.81 m/s 2 Negative Y Whole Model DW_External 3.75 MN Negative Y RP LateralForces MN Positive X, Z RP The external dead weight and lateral forces are displayed in Figure 6 and Figure 7 below. Figure 6 External dead weight load shown in viewport. Figure 7 Lateral forces shown in viewport. Both the gravity load and the external dead weight load is calculated in the DW step and propagated in LateralForces step where the lateral forces also are calculated, see the Load Manager below.

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12 Page 9 / 11 7 Mesh Both the slab and the column are modelled with 4-node shell elements with reduced integration denoted S4R in BRIGADE/Plus. Note: Not all element types are supported for spring-to-ground interaction, see UM for more information on this topic. Figure 8 displays the generated mesh. Figure 8 Generated mesh of the FE-model. Information about the created mesh is displayed in Table 3. Table 3 Mesh Parameters Mean size of the elements 0.1 m 0.1 m Number of elements Number of nodes Number of degrees of freedom

13 Page 10 / 11 8 Result Visualisation The vertical displacement U2 due to dead weight and lateral forces is displayed in the contour plot below. Figure 9 Vertical displacement U2.

14 Page 11 / 11 The total displacement is displayed in Figure 10 with a deformation scale factor of 100. Figure 10 Total displacement U, Magnitude.