# Technical mechanics

Sub-areas of technical mechanics
 Technical mechanics Statics dynamics Strength theory kinematics kinetics

The Mechanics is a part of the mechanism . It applies the physical principles to technical systems and mainly deals with the solid bodies that are important in technology. The main goal is to calculate the forces acting in the bodies. Lectures in technical mechanics are an integral part of the mechanical engineering and civil engineering courses . It is also dealt with in other engineering sciences such as electrical engineering , industrial design or industrial and transport engineering , but to a lesser extent.

The area of ​​responsibility of technical mechanics is to provide the theoretical calculation methods, for example for mechanical engineering and structural engineering . The actual dimensioning of the components or supporting structures , the selection of materials and the like is then taken over by application-related disciplines in which technical mechanics is an auxiliary science, for example design theory or operational strength .

Objects of technical mechanics are

• the laws of classical mechanics ,
• mathematical models of the mechanical relationships of physical bodies,
• specific and rational methods of computational analysis of mechanical systems.

The classic division takes place in

• the static , the (mainly with the one-dimensional rods) deals with forces on stationary (non-moving) bodies,
• the strength theory , which deals with deformable bodies (or mainly cross-sections) and integrates material and cross-sectional properties,
• the dynamics with the two sub-areas kinetics and kinematics , which deal with moving bodies.

In physics , on the other hand, mechanics is divided into kinematics and dynamics, which there contain statics and kinetics.

In the theoretical mechanics (also called Analytical Mechanics) it goes against it a matter of axioms such as Newton's laws starting to develop a consistent mathematical theory. In technical mechanics, on the other hand, a methodical structure is chosen that provides the knowledge required for the calculation of machines or structures.

## Sub-areas of technical mechanics

The classification of technical mechanics is not uniform everywhere. In general, the following areas are considered to be sub-areas of engineering.

### Statics

The static is the mechanics of stationary solid. It includes the statics of rigid bodies that do not deform when forces act on them. All forces acting on a resting body are in equilibrium. With this condition, equations for unknown forces can be set up from a number of known forces. In the case of a bridge, for example, the weight forces due to its own weight are known up to structural tolerances, other loads are assumed or calculated, and the forces in the bearings (bridge piers) can be calculated with them. The main aim of the static calculation is to calculate the forces that occur in the components to be designed; in the case of a bridge, for example in the deck. The most important body in statics is the beam , the length of which is much greater than its width and height. Deformable bodies can be calculated with the help of structural engineering . Both in strength theory and in dynamics, the forces determined with the statics are assumed to be known; these areas are therefore based on the statics.

### Strength theory

In principle, strength theory deals with deformable bodies, i.e. bodies that deform but are at rest, as in statics. In elastostatics, a body is assumed to be elastic , which is a common assumption in strength theory. The strength theory also includes plastic and viscous material behavior such as B. when crawling . Strength of materials also deals with the laws of strength and stiffness in order to be able to describe material properties and is therefore closely related to material technology , which, on the other hand, deals with materials and their material-specific properties. The terms mechanical tension (force per cross-sectional area) and elongation (change in length relative to the total length) are of great importance . Assuming Hooke's law , in the one-dimensional case at constant temperature, the strains are directly proportional to the acting mechanical stresses. An important goal of strength theory is the calculation of the necessary cross-sections of components for given forces and materials. It should be ensured that the stresses and deformations that occur are smaller than the permissible ones.

### dynamics

Dynamics deals with movements and stresses that change over time, which lead to accelerations and thus also to movements. The state of rest is also a special case of movement; However, since this is already dealt with in detail in the statics, in this area of ​​technical mechanics motion processes are analyzed with non-zero speeds. An important form of movement are vibrations in structural dynamics and in vibration theory . In technical mechanics, dynamics are usually divided into

• the kinematics , which does not consider forces, but only describes the geometry of the movement of the body,
• the kinetics , which takes into account forces and moments in addition to the kinematics.

In physics, but partly also in technical mechanics, dynamics (Greek for force) is the part of physics that deals with forces and divides them into statics (acceleration equal to zero) and kinetics (acceleration unequal zero).

Dynamics is usually about solid bodies, it also includes hydrodynamics and aerodynamics . These areas are also included in structural dynamics, where z. B. a vibration damping for high-rise buildings is realized with a water basin or in the wind excitation of transmitter masts.

### Special areas

These are sometimes also referred to as "higher technical mechanics".

Essentially, the area of ​​technical mechanics can be narrowed down to the determination of stresses, deformations, strengths and stiffnesses of solid bodies as well as the movements of solid bodies . The rest position, an important borderline case of a movement, is determined in technical mechanics with the help of statics. In addition to classical technical mechanics, which strives for a closed mathematical description in differential equations , the development of numerical methods is becoming increasingly important. Thermodynamics (e.g. heat transport or cycle processes in engines and turbines) and fluid mechanics (hydraulics, fluid mechanics) are usually not considered components of technical mechanics, but rather as independent sub-areas of engineering.

Other special sub-areas of technical mechanics are position calculations and control of the satellites and ballistics .

## History of technical mechanics

For most people it is out of your own intuition given out to solve elementary problems of statics and dynamics, without being aware of the actual background. A very typical example of this assumption is the girder in statics , about whose load-bearing capacity one can make quite precise information from mere observation.

Formally, technical mechanics was already practiced by Archimedes , but analytically usable findings have only been handed down from the first half of the 17th century. The mathematicians of that time were inspired by the descriptive laws of mechanics to their new knowledge, at the same time they discovered a number of new knowledge and mathematical laws of technical mechanics. In the centuries that followed, their theories were introduced into engineering and made practicable, while more theoretical insights followed. At the same time, the practitioners calculated the ballistic flight of a cannonball and, on the other hand, tried to minimize the effect of this cannonball on the walls of a fortress through a clever choice of the external dimensions of the fortress.

Illustration of a beam loaded by an external load in Galileo's Discorsi

The Greek Archimedes was the first mathematician to study mechanical problems in depth. He discovered the laws of hydrostatics as they are still valid today. Simon Stevin designed the parallelogram of forces using the Stevin thought experiment named after him . Johannes Kepler described the movements of the planets and moons with mathematical tools. The Kepler laws discovered in this process are still used today to calculate the orbit of artificial satellites and space probes .

In the early modern era, Galileo Galilei has the merit of having put the emerging science of technical mechanics on a formal mathematical basis. The second day of his Discorsi is essentially concerned with the discussion of strength problems . Isaac Newton , who wrote the history of science with the invention of infinitesimal calculus based on mechanical observations, had the same effect . Christiaan Huygens already provided practical results of his research in the form of the pendulum clock and more precise knowledge of astronomy . In the 18th century, the members of the Bernoulli family , along with further theoretical knowledge, prepared the ground for technical mechanics that are still valid today, which forms the basis for many technical disciplines. Leonhard Euler named the theories on buckling , beam bending and understanding modern turbines . During the same period, Charles Augustin de Coulomb established the fundamentals of the theory of friction , which provided a better understanding of how the machines that were invented at the same time worked . In the 19th century, Karl Culmann , August Ritter , Giuseppe Cremona and Carlo Alberto Castigliano developed technical mechanics that were also more tailored to practical needs . In the absence of powerful computing machines, their solutions to mechanical problems were essentially based on exact geometric drawings . Another important name from the end of the 19th and beginning of the 20th century in the field of technical mechanics is Christian Otto Mohr , who carried out the research on Mohr's circle and who taught at the Technical University of Dresden at the same time as Ludwig Burmester , the inventor of the stencils of the same name .

In the 20th century was built for the needs of aviation and space flight , the aerodynamics by Nikolai Jegorowitsch Zhukovsky , Ludwig Prandtl and Theodore von Kármán . At the same time, John Argyris and other mathematicians developed the finite element method . The building construction , which flourished in the thirties, used iterative methods for the static calculation, as published by Gaspar Kani or Hardy Cross . All of these methods use numerics as an essential approach.

Many of the people mentioned have also made great contributions in other areas (e.g. in hydromechanics , optics, electrical engineering). On the other hand, technical mechanics gave names to a whole class of mathematical objects: The tensors were named after the stress tensor that was introduced in connection with the theory of elasticity .

## literature

• István Szabó : Introduction to Engineering Mechanics. 8th revised edition 1975, reprint 2003 ISBN 3-540-44248-0 .
• István Szabó: Higher Technical Mechanics. 5th edition. Springer, Berlin 1985, ISBN 3-540-67653-8 (first 1956).
• RC Hibbeler: Technical Mechanics 1 - Statics. 10th, revised edition. Pearson Studium, Munich 2005, 8th, revised edition 1975, reprint. 2003 ISBN 3-8273-7101-5 .
• RC Hibbeler: Technical Mechanics 2 - Strength of Materials . 5th, revised and expanded edition. Pearson Studium, Munich 2005, ISBN 3-8273-7134-1 .
• RC Hibbeler: Technical Mechanics 3 - Dynamics. 10th, revised and expanded edition. Pearson Studium, Munich 2006, ISBN 3-8273-7135-X .
• Gross / Hauger / Schröder / Wall: Technical Mechanics 1 - Statics. 11th, edited edition Springer, Berlin 2011, ISBN 978-3642138058 .
• Gross / Hauger / Schröder / Wall: Technical Mechanics 2 - Elastostatics. 11th, edited edition Springer, Berlin 2011, ISBN 978-3642199837 .
• Gross / Hauger / Schröder / Wall: Technical Mechanics 3 - Kinetics. 12th, edited edition Springer, Berlin 2012, ISBN 978-3642295287 .
• Gross / Hauger / Wriggers: Technical Mechanics 4 - Hydromechanics, Elements of Higher Mechanics, Numerical Methods. 8th edition Springer, Berlin 2011, ISBN 978-3642168277 .
• István Szabó: History of mechanical principles and their main applications. Birkhäuser Verlag, ISBN 3-7643-1735-3 .
• R. Mahnken: Textbook of technical mechanics - statics. 1st edition Springer, Berlin 2012, ISBN 978-3-642-21710-4 .
• R. Mahnken: Textbook of Technical Mechanics - Dynamics. 2nd edition Springer, Berlin 2012, ISBN 978-3-642-19837-3 .
• R. Mahnken: Textbook of Technical Mechanics - Elastostatics. 1st edition Springer, Berlin 2015, ISBN 978-3-662-44797-0 .
• Wriggers / Nackenhorst / Beuermann / Spiess / Löhnert: Compact technical mechanics. 2nd edition, Teubner-Verlag, Stuttgart, 2006, ISBN 978-3-8351-0087-9 .
• Helga Dankert, Jürgen Dankert: Technical mechanics, statics, strength theory, kinematics / kinetics. 4. corr. u. additional edition, Teubner-Verlag, 2006, ISBN 3-8351-0006-8 .
• Herbert Balke : Introduction to Technical Mechanics . Springer-Vieweg, Berlin
• Heinz Parkus: Mechanics of Solid Bodies. 2nd edition, Springer-Verlag, 2009, ISBN 978-3211807774 .

## Individual evidence

1. Hartmann: Technical Mechanics. Wiley, 2015, p. 1.
2. Bruno Assmann: Technical Mechanics - Volume 1: Statics. Oldenbourg, 11th edition, 1989, p. 13.
3. a b Ulrich Gabbert , Ingo Raecke: Technical mechanics for industrial engineers. Hanser, 4th edition, 2008, p. 5.
4. Peter Hagedorn: Technical Mechanics - Volume 1: Statics. Verlag Harry Deutsch, 1993, p. 3 f.
5. Hartmann: Technical Mechanics. Wiley, 2015, p. XI, 1.
6. Horst Herr: Technical mechanics - statics, dynamics, strength theory. 2008, foreword, p. 2.
7. Peter Hagedorn: Technical Mechanics - Volume 1: Statics. Verlag Harry Deutsch, 1993, foreword.
8. ^ Mahnken: Textbook of technical mechanics. Dynamics. Springer, 2nd edition, 2012, p. 3.
9. ^ Günther Holzmann, Heinz Meyer, Georg Schumpich: Technical Mechanics. Statics. 12th edition, p. 2.
10. Peter Hagedorn: Technical Mechanics - Volume 1: Statics. Verlag Harry Deutsch, 1993, p. 4.
11. ^ Rolf Mahnken: Textbook of technical mechanics. Statics: Basics and Applications. Springer Verlag, 2011, Google Books.
12. Herbert Mang , Günter Hofstetter: Strength theory. Springer, Vienna, New York 2004, ISBN 3-211-21208-6 .
13. Horst Herr: Technical mechanics - statics, dynamics, strength theory. 2008, foreword, pp. 2–4.
14. Ulrich Gabbert , Ingo Raecke: Technical mechanics for industrial engineers. Hanser, 4th edition, 2008, p. 213.
15. a b c d Günter Holzmann, Heinz Meyer, Georg Schumpich: Technical Mechanics. Statics. 12th edition.
16. ^ HG Hahn: Technical Mechanics. Hanser, 2nd edition, 1990, p. 1.
17. 100 years of Zeunerbau. ( Memento from May 31, 2011 in the Internet Archive ). PDF with picture by Otto Mohr and representation of the Mohr circle.
18. Karl-Eugen Kurrer : The first technical and scientific basic disciplines: structural engineering and technical mechanics . In: History of structural engineering. In search of balance . 2nd, greatly expanded edition. Ernst & Sohn , Berlin 2016, ISBN 978-3-433-03134-6 , pp. 144–197.