# Floor blocks

## Introduction

A procedure to calculate WikiHouse floor blocks is provided in this spreadsheet. More details can be found in the tutorial below:

## Design parameters

### 250 series

Span (mm) $$W_j (mm^3)$$ $$W_{L/2} (mm^3)$$ $$I (cm^4)$$ $$k_R (kNm/rad)$$
XXS 3338 1702944 1702944 28765 2295
XS 3938 946080 946080 28765 2295
S 4538 946080 1324512 28765 2295
M 5138 946080 946080 28765 2295
L 5738 1135296 1135296 28765 2295

Where $$W_j$$ is the section modulus at the side dovetail joint, $$W_{L/2}$$ is the section modulus at the mid span, $$I$$ is the effective (recommended) modulus of inertia and $$k_R$$ is the rotational stiffness at the dovetail joint.

### 200 series

Span (mm) $$W_j (mm^3)$$ $$W_{L/2} (mm^3)$$ $$I (cm^4)$$ $$k_R (kNm/rad)$$
XXXS 2700 211896 211896 12692 1713
XXS 3300 211896 353160 12692 1713
XS 3900 211896 494424 12692 1713
S 4500 353160 494424 12692 1713

Where $$W_j$$ is the section modulus at the side dovetail joint, $$W_{L/2}$$ is the section modulus at the mid span, $$I$$ is the effective (recommended) modulus of inertia and $$k_R$$ is the rotational stiffness at the dovetail joint.

## Useful formulae

### Capacity

The moment capacity at the joint $$M_j$$ and the moment capacity and the mid-span $$M_{L/2}$$ can be calculated as:

$$M_j=W_j f_{c,0,d}$$

$$M_{L/2}=W_{L/2} f_{c,0,d}$$

Where $$W_j$$ is the section modulus at the side dovetail joint, $$W_{L/2}$$ is the section modulus at the mid span and $$f_{c,0,d}$$ the compressive stress of the material (parallel to the grain if plywood).

### Deflection

For a distributed load, the deflection in the mid-span can be calculated as:

$$v_{max}=\frac{5qL^4}{384EI}+\frac{qa^2}{2k_r}[L-a]$$

where $$E$$ the elastic modulus of timber, $$I$$ is the modulus of inertia, $$a$$ is the distance between the castellated joint and the support, $$L$$ is the span and $$k_r$$ is the rotational stiffness of the joint.

## How these values\formulae can be used?

These values can be used for design purposes. The formulas were also implemented in a design spreadsheet available here. Please check the worked examples section for more details.

## Where do these values\formulae come from?

These values come from an experimental testing and analytical modelling. Please check the research library (specifically this article) for more details. ### Use it

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