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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

    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.