Dowel & Bolt Connection Design

1. The Yield Limit Equations (Automated)

The NDS requires you to check six different failure modes, ranging from wood crushing (Mode I) to fastener bending (Mode IV).

Our calculator runs the full matrix:

• Mode $I_m$, $I_s$: Bearing failure in main or side member.
• Mode $II$: Rigid rotation (common in single shear).
• Mode $III_m$, $III_s$: Fastener yielding with wood crushing.
• Mode $IV$: Double plastic hinge formation (Fastener failure).
• Result: The tool finds the governing mode ($Z$) and applies all adjustment factors ($Z’$).

2. Combined Actions (Moment + Shear)

The NDS provides little guidance on how to calculate the force on a bolt in a moment connection.

Our module uses a Rational Analysis (Elastic Method). It resolves the Moment, Shear, and Axial forces into a vector resultant ($R$) for every bolt. It then checks this resultant against the bolt’s capacity at that specific angle to grain ($Z’_{\theta}$), ensuring safety for the “worst-case” fastener in the group.

3. Group Action ($C_g$)

In a long row of bolts, the leading bolts take more load.

The calculator applies the Group Action Factor ($C_g$) formula (NDS Eq. 11.3-1) based on the stiffness of the members ($A_m E_m$) and the fastener ($RE$). This prevents the dangerous over-estimation of capacity in large truss connections.

Adjusted Design Value ($Z’$):

$$Z’ = Z \cdot C_D \cdot C_M \cdot C_t \cdot C_g \cdot C_{\Delta}$$

The tool automates the modification factors:

• $C_D$ (Load Duration): Adjusts for Wind (1.6), Snow (1.15), or Live (1.0).
• $C_g$ (Group Action): Dynamically calculated based on the number of fasteners ($n$) in a row.
• $C_{\Delta}$ (Geometry): Reduces capacity if end distance is less than optimum (e.g., $< 7D$).

Hankinson’s Formula:

For bolts loaded at an angle to grain ($\theta$):

$$Z’_{\theta} = \frac{Z’_{\parallel} \cdot Z’_{\perp}}{Z’_{\parallel} \sin^2 \theta + Z’_{\perp} \cos^2 \theta}$$

The visual engine calculates the exact force vector angle for every bolt in a moment group and applies Hankinson’s formula individually.