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petrasvestartas authored and gitbook-bot committed Jan 29, 2025
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32 changes: 13 additions & 19 deletions gitbook/examples/historical-typologies/barrel-vault.md
Original file line number Diff line number Diff line change
@@ -1,20 +1,10 @@
# Barrel Vault

<figure><img src="../../.gitbook/assets/barrel_0.png" alt=""><figcaption></figcaption></figure>
<figure><img src="../../.gitbook/assets/barrel_8.png" alt=""><figcaption></figcaption></figure>

In this tutorial, we will explore the basic features of RhinoVAULT to determine the equilibrium shape of a barrel vault with two boundary supports. To form-find the barrel vault, we will adjust the form diagram parameters for the allowable internal horizontal force limits: [**hmax**](../../manual/7.-modify-diagrams/supports.md) (upper limit) and [**hmin**](../../manual/7.-modify-diagrams/supports.md) (lower limit).

A barrel vault is unique because its edges orthogonal to the arches carry almost no load (e.g., **1e-5**), while the edges along the arches share the same internal horizontal force (e.g., **2**). The exception occurs at the boundary, where half of the horizontal force is used (e.g., **1**) for the small tributary area. Due to this special force distribution, the force diagram collapses into a single line.\
\
Table of Contents:

1. [Create Pattern](barrel-vault.md#create-pattern)
2. [Identify Supports](barrel-vault.md#identify-supports)
3. [Form Diagram](barrel-vault.md#form-diagram)
4. [Modify Form Diagram](barrel-vault.md#modify-form-diagram)
5. [Force Diagram](barrel-vault.md#force-diagram)
6. [Horizontal Equilibrium](barrel-vault.md#horizontal-equilibrium)
7. [Vertical Equilibrium](barrel-vault.md#vertical-equilibrium)
A barrel vault is unique because its edges orthogonal to the arches carry almost no load (e.g., **1e-5**), while the edges along the arches share the same internal horizontal force (e.g., **2**). The exception occurs at the boundary, where half of the horizontal force is used (e.g., **1**) for the small tributary area. Due to this special force distribution, the force diagram collapses into a single line.

## Create Pattern

Expand All @@ -26,7 +16,7 @@ Create a pattern from a mesh. You can start with the attached Rhino file or a se

{% file src="../../.gitbook/assets/rhinovault_barrel_0.json" %}

<figure><img src="../../.gitbook/assets/barrel_1.png" alt=""><figcaption></figcaption></figure>
<figure><img src="../../.gitbook/assets/barrel_0 (1).png" alt=""><figcaption></figcaption></figure>



Expand All @@ -38,7 +28,7 @@ Manually set the boundary points on the top and bottom edges of the mesh.

{% file src="../../.gitbook/assets/rhinovault_barrel_1.json" %}

<figure><img src="../../.gitbook/assets/barrel_2.png" alt=""><figcaption></figcaption></figure>
<figure><img src="../../.gitbook/assets/barrel_1 (1).png" alt=""><figcaption></figcaption></figure>

## Form Diagram

Expand All @@ -48,7 +38,7 @@ The mesh geometry is converted into a line preview, marked with green lines.

{% file src="../../.gitbook/assets/rhinovault_barrel_2.json" %}

<figure><img src="../../.gitbook/assets/barrel_3.png" alt=""><figcaption></figcaption></figure>
<figure><img src="../../.gitbook/assets/barrel_2 (1).png" alt=""><figcaption></figcaption></figure>

## Modify Form Diagram

Expand All @@ -57,7 +47,11 @@ Set the horizontal edge constraints (h\_min and h\_max) to: a) 0.00001, b) verti

{% file src="../../.gitbook/assets/rhinovault_barrel_3.json" %}

<figure><img src="../../.gitbook/assets/barrel_4.png" alt=""><figcaption></figcaption></figure>
<figure><img src="../../.gitbook/assets/barrel_3 (1).png" alt=""><figcaption></figcaption></figure>

<figure><img src="../../.gitbook/assets/barrel_4 (1).png" alt=""><figcaption></figcaption></figure>

<figure><img src="../../.gitbook/assets/barrel_5 (1).png" alt=""><figcaption></figcaption></figure>

## Force Diagram

Expand All @@ -67,7 +61,7 @@ On the right side, the force diagram is created with TextDots marking the angle

{% file src="../../.gitbook/assets/rhinovault_barrel_4.json" %}

<figure><img src="../../.gitbook/assets/barrel_5.png" alt=""><figcaption><p>.</p></figcaption></figure>
<figure><img src="../../.gitbook/assets/barrel_6 (1).png" alt=""><figcaption><p>.</p></figcaption></figure>

## Horizontal Equilibrium

Expand All @@ -77,7 +71,7 @@ Set the iteration to 1000 to reach the horizontal equilibrium. Since horizontal

{% file src="../../.gitbook/assets/rhinovault_barrel_5.json" %}

<figure><img src="../../.gitbook/assets/barrel_6.png" alt=""><figcaption></figcaption></figure>
<figure><img src="../../.gitbook/assets/barrel_7 (1).png" alt=""><figcaption></figcaption></figure>

## Vertical Equilibrium

Expand All @@ -87,4 +81,4 @@ The final geometry is computed by running the vertical equilibrium command, keep

{% file src="../../.gitbook/assets/rhinovault_barrel_6.json" %}

<figure><img src="../../.gitbook/assets/barrel_7.png" alt=""><figcaption></figcaption></figure>
<figure><img src="../../.gitbook/assets/Artboard 10.png" alt=""><figcaption></figcaption></figure>

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