# How are the support spring/link stiffness calculated when using Box Culvert Wizard?

**Question:**

In the wizard option for culvert design, it is required to insert only Modulus of Subgrade Reaction (Lower) and Length of Elastic link. Could you please explain:

1-Automatically, Midas used two point spring type one along the depth of the culvert (fig. a) and the other only 1 point spring in the center of the bottom slab (fig. b);

2-Automatically, Midas considered distributed Elastic Line with a various SDx under the bottom of the slab, and how Midas calculated different SDx for all points (fig. c).

**Answer:**

Let's break the question into 3 parts, based on the provided support stiffness (figures).

1)Point springs Type 1:

As demonstrated in Figure (a) above, the SDx is given very high stiffness along the culvert. This is basically done to stabilize the culvert in the direction of the transverse pressure loads. The culvert is assumed to not move from its position in the longitudinal or lateral direction and hence, very high SDx. Now, this is done along the entire length of the box, because, if this is done at any one node only, then the culvert might exhibit twisting, which won't practically happen. The stiffness value for these springs is equal to 10^7 times the sub-grade modulus of reaction to model extremely rigid behavior.

2)Point springs Type 2:

As demonstrated in Figure (b) above, the SDy is given very high stiffness only near the central node of the culvert. This is done to stabilize the model in the global y direction. This is done at 1 node only because the elastic links will develop tension/compression to stabilize the structure about this node. Hence, this would basically replicate the uplift that might happen in the structure due to the load along y.

3)Elastic link stiffness:

The stiffness for elastic links is calculated based on the sub-grade modulus of reaction and the tributary area of the plates. Consider the image below.

If the sub-grade modulus of reaction is entered as 20000kN/m^3 and the size of the plates is 1m x 1m, then

a) The SDx for the elastic link located at the red circle would be 20000 x 1 x 1 = 20000 kN/m

b) The SDx for the elastic link located at the green circle would be 20000 x 0.5 x 1 = 10000kN/m

c) The SDx for the elastic link located at the orange circle would be 20000 x 0.5 x 0.5 = 5000 kN/m

As demonstrated in Figure (a) above, the SDx is given very high stiffness along the culvert. This is basically done to stabilize the culvert in the direction of the transverse pressure loads. The culvert is assumed to not move from its position in the longitudinal or lateral direction and hence, very high SDx. Now, this is done along the entire length of the box, because, if this is done at any one node only, then the culvert might exhibit twisting, which won't practically happen. The stiffness value for these springs is equal to 10^7 times the sub-grade modulus of reaction to model extremely rigid behavior.

2)Point springs Type 2:

As demonstrated in Figure (b) above, the SDy is given very high stiffness only near the central node of the culvert. This is done to stabilize the model in the global y direction. This is done at 1 node only because the elastic links will develop tension/compression to stabilize the structure about this node. Hence, this would basically replicate the uplift that might happen in the structure due to the load along y.

3)Elastic link stiffness:

The stiffness for elastic links is calculated based on the sub-grade modulus of reaction and the tributary area of the plates. Consider the image below.

If the sub-grade modulus of reaction is entered as 20000kN/m^3 and the size of the plates is 1m x 1m, then

a) The SDx for the elastic link located at the red circle would be 20000 x 1 x 1 = 20000 kN/m

b) The SDx for the elastic link located at the green circle would be 20000 x 0.5 x 1 = 10000kN/m

c) The SDx for the elastic link located at the orange circle would be 20000 x 0.5 x 0.5 = 5000 kN/m

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