7.4The Force Ratio

ECSS-E-HB-32-23A, Space Engineering — Threaded Fasteners Handbook

Last Updated 29 Oct 2026

Hover any section to copy its link or text, ask Copilot about it, or bookmark it.

The force ratio $\Phi$ is defined as the ratio of external load to the induced load increment seen by the fastener, and is given by,

\Phi = \frac{\Delta F_{b,A}}{F_{A}} \tag*{[7.4.1]}

For certain joint configurations (such as joint type 2 in Figure 5-1) the external load's effective point of action is at the outer surface of the flanges. This is the situation that is shown in Figure 7-5. For such joints, the force ratio can be shown to depend on the relative stiffnesses (or compliances) of the fastener and the clamped parts,

\Phi = \frac{\Delta F_{b,A}}{F_{A}} = \frac{K_{b}}{K_{c} + K_{b}} = \frac{\delta_{c}}{\delta_{c} + \delta_{b}} \tag{7.4.2}

where $K_{b}$ & $K_{c}$ are the respective stiffnesses of the fastener and clamped parts, and $\mathcal{D}_{b}$ & $\mathcal{D}_{c}$ are the respective compliances of the fastener and clamped parts.

From Figure 7-6 it can be seen that,

F_{A} = \Delta F_{b,A} + \Delta F_{c,A} \tag{7.4.3}

therefore, using Equation [7.4.2],

F_{A} = \Phi F_{A} + \Delta F_{c,A} \tag{7.4.4}

Rearranging, the load reduction felt by the clamped parts due to the external load $F_{A}$ is given by,

\Delta F_{c,A} = (1 - \Phi) F_{A} \tag*{[7.4.5]}

Equations [7.4.2], [7.4.3], [7.4.4] and [7.4.5] are only valid for joints where the point of application of the external load is the outer surface of the flanges. In general, the external load is effectively applied at points located within the flanges. Therefore, the loading plane factor, n, is introduced into equation [7.4.2] resulting in,

\Phi_{n} = n \Phi = n \left( \frac{\delta_{c}}{\delta_{c} + \delta_{b}} \right) \tag{7.4.6}

Methods are presented in the following Sections for calculating the various parameters in Equation [7.4.6].