Timber Stud Wall Design

1. Buckling & Slenderness ($\lambda$)

A wall stud is a slender column. Its capacity is governed by how easily it buckles under load.

The calculator determines the Slenderness Ratio ($\lambda$) for both axes:

• Y-axis (Major): Typically the depth of the stud (e.g., 140mm).
• Z-axis (Minor): The width (e.g., 38mm). Crucial: The tool allows you to specify “Sheathing Restraint” (e.g., OSB/Plasterboard) which effectively prevents minor axis buckling, massively increasing capacity.

2. Combined Axial + Bending

External walls are rarely just columns; they are also beams resisting wind.

Eurocode 5 Clause 6.3.2 requires a non-linear interaction check:

$$\left(\frac{\sigma_{c,0,d}}{k_c \cdot f_{c,0,d}}\right) + \left(\frac{\sigma_{m,y,d}}{f_{m,y,d}}\right) \le 1.0$$

Our tool runs this check for both buckling axes, ensuring the stud doesn’t snap or buckle under the “perfect storm” of heavy snow and high wind.

3. Noggins & Restraints

The effective length ($L_{eff}$) of a stud can be reduced by introducing horizontal noggins (blocking).

You can toggle “Noggins at Mid-height” in the calculator to reduce the buckling length ($L_{cr}$) and optimize your timber section size.

Instability Factor ($k_c$):

$$k_c = \frac{1}{k + \sqrt{k^2 – \lambda_{rel}^2}}$$

This factor reduces the compressive strength of the timber based on its slenderness and straightness ($\beta_c$). The tool applies $\beta_c = 0.2$ for solid timber as per standard Eurocode rules.

Deflection Limits:

• Instantaneous ($w_{inst}$): Checked against $L/300$ (or user defined limits) to prevent cracking of brittle finishes like render or brick slips.
• Final ($w_{fin}$): Includes creep effects ($k_{def}$), though for wind loads (Short Term), creep is less critical than for floor joists.

Bearing Check:

$$f_{c,90,d} = \frac{k_{c,90} \cdot k_{mod} \cdot f_{c,90,k}}{\gamma_M}$$

The tool checks if the stud will crush the timber wall plate (sole plate), applying the $k_{c,90}$ enhancement factor (typically 1.25 or 1.5) if the stud is spaced sufficiently apart.