Wrench Equivalent Force Systems

Concurrent, coplanar, and parallel force systems can always be reduced to an equivalent Force system consisting of a single force only.

• In these special cases we cna always reduce the external forces and moments to a single resultant force ${\overrightarrow{F}}_R$ and a resultant moment ${\overrightarrow{M}}_R$ where ${\overrightarrow{F}}_R\perp {\overrightarrow{M}}_R$.
• ${\overrightarrow{F}}_R$ and ${\overrightarrow{M}}_R$ at point can be further reduced to a single force at point $B$ located a distance $d$ away from point $A$ where $d=\frac{M_R}{F_R}$.

More generla force systems cannot be simplified to this extent.

Examples: