Force Systems

The Theory of Structures is the basic discipline for the sizing and verification of the structural safety of all Engineering Buildings. It consists of two primary parts: the Theory of elasticity and the Theory of structures. To these we must add a mention of a third section: the Stability of equilibrium, which is such a frequent, dangerous and complex phenomenon that it requires even a brief mention of anticipation. They are largely Mathematical Theories that simulate, in a practically perfect way, the behavior of solid bodies under the hypothesis of linear elasticity and small deformations, a fully satisfactory hypothesis on a technical level.

In this treatise, which reflects the numerous courses in Constructions Science held by Aldo Maceri at the “La Sapienza” and “Roma Tre” Universities of Rome, great emphasis is given to the displacement method, on which the automatic calculation of structures is based , and ample space is also given to traditional structural calculation methods (congruence, principle of virtual works, graphic methods), which are still very important for a full understanding of the problem.

In composing this treatise, Aldo Maceri has had the constant commitment to achieve maximum clarity and has sacrificed more than one brilliant discussion to it. He carried out the discussion in a classical way, but in the light of the modern Mathematical Theory of Elasticity and with more accentuated emphasis on the connections with Thermodynamics. The exhibition is constantly accompanied by numerous examples of calculations, of varying complexity, all carried out in full and in detail. To read this treatise, the classical notions of Mathematical Analysis and Physics taught in university Engineering courses are sufficient as prerequisites.

In chapter 1 (Force Systems) the definitions of are given, in the three-dimensional case, of

• force
• moment of a force with respect to a point
• moment of a force with respect to a straight line
• system of forces
• resultant of a system of forces
• resultant moment of a system of forces with respect to a point
• resultant moment of a system of forces with respect to a straight line
• central axis of a system of forces
• coplanar force systems
• systems of parallel forces

and, in the two-dimensional case, of

• force
• moment of a force with respect to a point
• system of forces
• resultant of a system of forces
• resultant moment of a system of forces with respect to a point
• central axis of a system of forces
• coplanar force systems
• systems of parallel forces
• center of a system of forces
• funicular polygon

accompanying everything with numerous calculation examples of varying complexity. To complete, in both cases the effect of changing the reference is detailed.