Example : Barrel vault

Building a barrel vault with RV2 constraining the amount of forces in the edges.

1) Create pattern: "From Surface":

• Rectangular or square planar surface:

  • Use the Rhino command: "Rectangular plane: corner to corner".

2) Define boundary conditions:

• Supports:

  • Make continuous linear supports on two opposite sides. (RV2>Define Boundary Conditions>Identify Supports>Select>ByContinuousEdges).

• Openings:

  • No need to assign openings. This step has to be skipped and the openings on the two other sides will be automatically defined by RV2.

    • Explanation: since we have to constrain the forces to be almost 0 along the edges perpendicular to the openings, if we use the sag function (even only 5%), it will try to put some forces in that edges, so we skip this step.

2) Form Diagram: "Create Form Diagram".

3) Constrain force values in the edges of the form diagram:

The structural behaviour of a barrel vault can be approximated by a series of 2D arches put side by side. This means that the forces flow only along the edges parallel to the arches. In the other direction, perpendicular to the arches and parallel to the support lines, forces can be constrained to zero (hmax and hmin equal to 0.00001). In constraining the amount of forces in the edges corresponding to the arches, attention needs to be paid between the edges in the first and last arch, (hmax and hmin equal to 1.0), and the remaining ones in the middle of the vault, (hmax and hmin equal to 2.0). In the form diagram, a tributary area is assigned to each node and the load applied to the node is proportional to the amplitude of that area. The nodes in the first and last arch have a tributary area that is half of the one assigned to the nodes in the middle of the vault. For this reason, the force value in that edges is half (1.0), and the force assigned in the other edges is 2.0.

• Select continuous edges perpendicular to the support, in the arch directions excluding the first and the last (RV2>ModifyFormDiagram>ModifyEdgesAttributes>Continuous):

  • In the pop-up window assign 2.0 as hmax and hmin of the edges.

Repeat the same procedure for the other edges as described below.

• Select the first and last continuous edges perpendicular to the supports (RV2>ModifyFormDiagram>ModifyEdgesAttributes>Continuous):

  • In the pop-up window assign 1.0 as hmax and hmin of the edges.

• Select continuous edges parallel to the support sides (RV2>ModifyFormDiagram>ModifyEdgesAttributes>Continuous):

  • In the pop-up window assign 0.00001 as hmax and hmin of the edges.

4) Force Diagram: "Create Force Diagram".

5) run Horizontal Equilibrium:

• Click on Horizontal Equilibrium>alpha>form100>enter

• If the equilibrium is not found, change the number of iterations to 1000.

6) run Vertical Equilibrium

• Click on Vertical Equilibrium>target_height

  • Input as target height half of the length of the side with an opening and then press enter.

7) Extra: change target height to 1/4 of the length of the side with an opening, and compare the components of the resultant forces with those obtained before.