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Topic Introduction

The term statics is derived from the Greek word statikos, which translated to English means “to bring to a standstill”, to linger and to rest. Today, statics is understood to be the study of the equilibrium of forces. Statics plays a fundamental role both in physics, engineering, civil engineering and electrical engineering.

The classification of statics as a branch of physics (mechanics) can be illustrated by the classification according to the type of description of the motion:

- Kinematics: (Geometric) description of motion without consideration of forces.
- Dynamics: Description of motion and its change under acting forces.
- Kinetics: Description of the forces in a motion.
- Statics: Description of the forces in a system at rest (or uniform motion)

Statics is therefore used whenever technical structures are subject to the effect of forces. Such forces are, for example, weight forces, natural forces (water, earthquake, wind), mechanical forces (steam force, explosion hazard) and muscle forces. In addition to these forces acting from the outside, there are also so-called internal forces. The statics of a structure result from the relationship between the internal forces. These always occur in pairs, e.g. as tensile or compressive forces in the components of a suspension structure.

It therefore need no further explanation that houses, bridges, towers, cranes, masts or other structures have to be constructed in such a way that they do not collapse under their own load or under external loads (live load). In all building projects, therefore, all conceivable forces that can ever occur on a structure must be considered. While statics, as the study of the equilibrium of internal and external forces, endeavours to describe material-independent laws, the designer can use strength theory to assess whether the components or building materials used will withstand the stresses they are intended to withstand. [1]

The term statics is used ambiguously and often refers to the theoretical-mathematical-physical side (statics as a branch of engineering mechanics), while structural analysis aims at the application of this statics in civil engineering. Structural analysis or the statics of building structures is the study of the safety and reliability of load-bearing structures in the building industry. In structural analysis, the forces and their mutual effects in a structure and in each associated component are calculated. [2]

Historie

The complex history of structural analysis is closely linked to the research and publications of very many scholars and scientists, so that only authors who directly affect the thematic content and technical terms of the statics learning kits are listed here.

- Archimedes (287–212 BC) Lever principle
- Leonardo da Vinci (1452–1519) Initial illustrative considerations on vaulting action and beam deflection, qualitative statements on load-bearing capacity
- Simon Stevin (1548–1620) Flemish mathematician, physicist and engineer. Parallelogram of forces, statics of solids and fluids; introduction of decimal places
- Galileo Galilei (1564–1642) Principles of mechanics, strength theory and laws of gravitation
- Edme Mariotte (1620–1684) – Tension distribution – “Axis of balance”
- Robert Hooke (1635–1703) Proportionality law
- Sir Isaac Newton (1643–1727) Founder of classical theoretical physics and thus of the exact natural sciences, mathematical foundations of the natural sciences, formulation of the three laws of motion, equilibrium of forces, infinitesimal calculus
- Gottfried Wilhelm Leibniz (1646–1716) – Section modulus, infinitesimal calculus
- Jakob I Bernoulli (1655–1705) Curvature of the elastic beam, relationship between load and bending; keeping the cross-sections flat
- Pierre de Varignon (1654–1722) French mathematician. Composition of forces, law of the parallelogram of forces (Varignon parallelogram), concept of moment of force, rope polygon
- Antoine Parent (1666–1716) – Triangular distribution of tensile stress
- Jakob Leupold (1674–1727) – Deflection and load-bearing capacity
- Pierre Couplet Rigid bodies – Theory of the vault 1730
- Thomas Le Seur (1703–1770) French mathematician and physicist; first preserved static report 1742 (for the dome of St. Peter’s Basilica), with François
- Jacquier (1711–1788) and Rugjer Josip Bošković (1711–1787)
- Louis Poinsot (1777–1859) Forces couple 1803
- Claude Henri Navier (1785–1836) Theory of the suspension bridge 1823; first comprehensive structural analysis, technical bending theory 1826; investigation of statically indeterminate beams
- Karl Culmann (1821–1881) Truss theory 1851; graphical statics 1866
- August Ritter (1826–1908) Ritter's method of dissection for statically determined trusses 1861
- Luigi Cremona (1830–1903) Graphical determination of forces of the members in statically determined trusses (“Cremona diagram”)

Since many dangers can emanate from unstable buildings, structural engineering has also been the subject of legislation and jurisprudence for several thousand years. Already in the early cultures of Mesopotamia, there were special penal regulations for builders whose buildings killed people by collapsing, for example in the Codex Hammurapi, a collection of laws by King Hammurapis of Babylon (* 1810 BC; † 1750 BC).

Static regulations in the narrower sense, which prescribe a certain quality, are historically younger. In 27 AD, for example, a wooden amphitheatre built too cheaply collapsed in Fidenae north of Rome, causing thousands of deaths according to the description of the Roman historian Publius Cornelius Tacitus (* c. 58 AD; † c. 120). [3] As a result, the Senate of Rome issued static regulations.

Curriculum requirements

The Statics Class Set for primary level and STEM Statics for secondary level can only be understood as an introduction to selected static facts. The level of demand is deliberately aligned with the current curriculum requirements of the respective target group and the task sheets are formulated in a skills-oriented way. The objective is to control, reflect and evaluate your own thinking when solving problems and thus build up new knowledge. Working alone or in teams, pupils build simple and more sophisticated models. Process-related skills are promoted by the solving of problems, in-depth research and suggestions for creative changes to the models.

The primary learning objective at primary level is static-constructive building and to sharpen the children’s view of the static and constructive facts that surround them.

Other topics and learning objectives of the primary level covered by the Class Set Statics include:

- Stability and strength in engineering structures
- Discovering correlations between load-bearing capacity and the connections of construction elements
- Experimental construction of buildings, load-bearing structures
- Functional features of load-bearing structures
- Trusses
- Getting to know the system of beam and support
- Recognising the skeleton construction method in various structures in their environment
- Understanding compression and tensile forces, the system of triangular bracing
- Transferring features of a stable construction to a movable one
- Stability/balance
- Two-sided lever arm
- Learning specialist terms

At secondary level, in addition to the implementation of static principles using models as examples, STEM Statics covers, among other things:

- The application of physical ways of thinking and working
- Basic laws of statics
- The two-dimensional determination of tensile and compressive forces
- Forces in equilibrium of stationary bodies
- Hooke’s law
- Force components, inclined plane, equilibrium, torque, lever principle, centre of gravity, types of equilibrium
- Learning specialist terms

Fun with construction and tinkering are just as important elements as the playful development of relevant technical terms using a variety of tasks and their solution examples.

- Hörner, Kaufmann, Statische Probleme bei Brücken, Türmen und Masten, fischertechnik Schulprogramm, ISBN 978-3141680089 (Static problems with bridges, towers and masts, fischertechnik school series)
- https://de.wikipedia.org/wiki/Baustatik#Abgrenzungen_und_Begriffe
- Tacitus, C., Annalen, Buch 4, Kap. 62/63, Reclams Universalbibliothek, 2013. Philip Reclam Jun.,Stuttgart. S 247 f147

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