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

An image showing 5 Skylark 250 series blocks of different lengths. They range from XXS to L size.
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

An image showing 5 Skylark 200 series blocks of different lengths. They range from XXXS to S size.

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.

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