2.1. Force, Moment of a Force, Distributed Actions#
2.1.1. Concentrated Force#
A (concentrated) force is a vector quantity with physical dimensions,
which can be measured using a dynamometer, and whose effect can alter the equilibrium or motion conditions of a physical system.
In addition to the typical information of a vector quantity - magnitude, direction, and sense - contained in the force vector \(\vec{F}\), it is often necessary to know the point of application or the line of application of the force.
2.1.2. Moment of a Concentrated Force#
The moment of a force \(\vec{F}\) applied at point \(P\), or with a line of application passing through \(P\), relative to point \(H\) is defined as the vector product,
2.1.3. System of Forces, Resultant of Actions, and Equivalent Loads#
Given a system of \(N\) forces \(\left\{ \vec{F}_n \right\}_{n=1:N}\), applied at points \(P_n\), we define:
resultant of the system of forces: the sum of the forces,
\[\vec{R} = \sum_{n=1}^{N} \vec{F}_n \ ,\]resultant of the moments with respect to a point \(H\): the sum of the moments
\[\vec{M}_H = \sum_{n=1}^{N} (P_n - H) \times \vec{F}_n \ ,\]an equivalent load: a system of forces that has the same resultant of forces and moments; for a system of forces, an equivalent load can be defined as a single force, the resultant of the forces \(\vec{R}\) applied at point \(Q\) derived from the equivalence of moments
\[\begin{split}\begin{aligned} \vec{R} & = \sum_{n=1}^{N} \vec{F}_n \\ (Q - H) \times \vec{R} & = \sum_{n=1}^{N} (P_n - H) \times \vec{F}_n \\ \end{aligned}\end{split}\]
2.1.4. Couple of Forces#
A couple of forces is an equivalent load to two forces of equal magnitude and opposite sense, \(\vec{F}_2 = - \vec{F}_1\), applied at two points \(P_1\), \(P_2\) not aligned along the line of application of the forces to have non-zero effects.
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The resultant of the forces is zero,
while the resultant of the moments does not depend on the moment pole,
2.1.5. Force Fields#
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2.1.6. Distributed Actions#
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