# 3.1: Equilibrium of Structures

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Engineering structures must remain in equilibrium both externally and internally when subjected to a system of forces. The equilibrium requirements for structures in two and three dimensions are stated below.

3.1.1 Equilibrium in Two Dimensions

For a structure subjected to a system of forces and couples which are lying in the xy plane to remain at rest, it must satisfy the following three equilibrium conditions: $\sum F_{x}=0 ; \sum F_{y}=0 ; \sum M_{z}=0$

The above three conditions are commonly referred to as the equations of equilibrium for planar structures. $$\Sigma F_{X}$$ and $$\Sigma F_{Y}$$ are the summation of the $$x$$ and $$y$$ components of all the forces acting on the structure, and $$\Sigma M_{Z}$$ is the summation of the couple moments and the moments of all the forces about an axis $$z$$, perpendicular to the plane xy of the action of the forces.

3.1.2 Equilibrium in Three Dimensions

A structure in three dimensions, that is, in a space, must satisfy the following six requirements to remain in equilibrium when acted upon by external forces: $\begin{array}{l} \sum F_{x}=0 ; \sum F_{y}=0 ; \sum F_{z}=0 \\ \sum M_{x}=0 ; \sum M_{y}=0 ; \sum M_{z}=0 \end{array}$

This page titled 3.1: Equilibrium of Structures is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by René Alderliesten (TU Delft Open) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.