Structural engineering or the statics of building structures is the study of the safety and reliability of supporting structures in the building industry . In structural engineering, the forces and their mutual effects in a building and in each associated component are calculated. The calculation methods of structural engineering are aids in structural planning and, with the teaching of modeling and construction theory, are part of structural theory. Structural engineering uses the means of strength theory , technical mechanics , the statics of rigid bodies and continuum mechanics .
The structural analysis is a collection of computational and graphical methods which serve to infer loads and deformations with their stresses in buildings from the effect of external loads, to understand the load transfer of the structure and thus ultimately to prove its usability (a structure is the model of the load transferring Parts of a structure that can differ fundamentally in terms of stiffness , strength and material).
The loads acting on a structure are divided according to the frequency of their occurrence into permanent (e.g. the dead weight of the structure), variable (e.g. snow, wind, temperature, traffic or fluctuating water levels) and extraordinary effects (e.g. earthquake, fire or the impact of vehicles ). These real loads are i. d. Usually estimated using standards with a certain probability of failure lying on the safe side. One objective of the structural analysis is to find the most unfavorable combination of i. d. As a rule, according to the standard, relevant combinations of these assumed loads must be determined, namely with regard to structural safety (e.g. breakage , plasticity , buckling ) and serviceability (e.g. deformations, crack widths, vibrations).
The problems mainly include quasi-static loads as well as static strength and stability proofs, while the related structural dynamics record the reaction of structures to time-changing loads (such as wind), whereby dynamic loads can be calculated using statics methods. This so-called quasi-static calculation takes into account the dynamic effects with factors that are large enough so that the estimate thus determined is safely on the right side. In normal building construction, vibration verifications in the course of structural analysis are automatically considered to be fulfilled with certain building dimensions depending on the building material (e.g. in the European standard EN 1992 the slenderness limit, which specifies the minimum thickness of a slab depending on a fictitious span and the degree of reinforcement, by one not having to carry out a separate vibration verification).
As a special and specialized sub-area of mechanics , the classical structural analysis makes use of the elasticity theory and Hooke's law , but it can be used in plasticity theory as well as plastic hinge theory.
Limitations and terms
The term statics is used ambiguously and often relates to the theoretical-mathematical-physical side ( statics as a sub-area of technical mechanics ), while structural engineering aims at the application of this statics in construction. The planning of the structure takes place i. d. Usually without structural calculations (usually by the architect). From this, a static model is conventionally defined with the load transfer mechanism which then usually the dimensioning follows, so the setting of dimensions, reinforcement, etc.
The responsible structural engineer or structural engineer - today usually a civil engineer , more rarely an architect - is often referred to colloquially as a structural engineer . The result of his considerations and calculations, the static calculation , is referred to in some contexts as the proof of stability , but mostly also called static in short .
The most important assumption in structural engineering and statics is that the load-bearing system is in equilibrium . An essential aspect of the structural analysis is to model a clearly defined load-bearing system from a complex structure, which can provide the evidence with an economically sensible effort. First the calculated loads are determined. This results in calculated internal forces and deformations in order to carry out a design. The loads acting, which are always in equilibrium in the course of a static assumption, are short-circuited via the load-bearing components.
Structural engineering knows two large groups of structures:
- Frameworks ( bars , beams , columns , frames , arches , trusses )
- Area structures , consisting of plates , disks , shells or membranes .
The actions (or loads) for which a structure must be dimensioned by means of the structural analysis include: a.
- own weight
- Payload (previously also live load )
- Wind load
- Snow load
- Water pressure
- Earth pressure
- Vehicle impact
- Earthquake ; Design criteria (earthquake)
- Ice pressure , ice load
Dynamic loads (e.g. shocks, vibrations, earthquakes) and the resulting deformations (e.g. vibrations, oscillations ) are usually converted into static equivalent loads in building construction and road construction before they are applied to a structure.
The calculation methods in structural engineering can be divided into:
- Drawing procedures ( graphic statics )
- Computational methods ( rigid body statics , elasticity theory , nonlinear bar statics , ...)
- Experimental statics
The computational methods of structural engineering include a .:
- Ritter's cutting method
- Force measurement method
- Path size method
- Deformation process
- Torque compensation method
- Angle of rotation method
- Cross procedure
- Kani method (method according to Kani)
- Tension trapezoidal method
- Finite element method (FEM)
- Finite Difference Method (FDM)
- Boundary Element Method (REM) (= Boundary Element Method BEM)
- Discrete element method (DEM) (= Distinct element method)
For Konrad Zuse , the ease of formalization and the large amount of time required for static calculations were the original motivation for developing programmable computers. Static calculations were about from the beginning to the computer - applications that gradually become static design programs conducted for any purpose. Today, static calculations are almost exclusively made with computer programs. The examined static models are often more complex and demanding. The calculation of flat surface structures such as ceiling panels, elastically bedded panels, wall panels, etc. is now a routine task in practice. With the finite element method i. d. Usually more complicated structures such as membrane and shell structures are examined.
Extended technical bending theory
The technical bending theory has been extended in such a way that the associated state of distortion can be calculated for the general combination of internal forces (N, M y , M z , V z , V y , T) even with non-linear material behavior. It is also an expansion plane that is also warped due to the sliding to be taken into account. In the extended technical bending theory (ETB), analogous to the technical bending theory, the necessary conditions of equilibrium and geometric compatibility with realistic material behavior are met. The application of the ETB makes the separate verifications of bending and shear measurements superfluous.
Theory I., II. Or III. order
Deformed structure with consideration of the equilibrium in the undeformed position
First order theory
In applying the first order theory in the will beam cross section dominant equilibria between loads (forces and moments ) and stress (stress) on non-deformed considered beams. The position of the forces is related to the undeformed rod cross-section, i.e. H. the distortions and rotations must be much smaller than 1; on the other hand, the distortions for the stress calculation are not set to zero, since an undeformed member would be equivalent to an unloaded member based on the generalized Hook's law. This procedure is i. d. R. only permitted if the deformations are so small that they only slightly influence the results of the calculation, or the normative is regulated.
If the change in the internal forces due to the deflection cannot be neglected, the geometry of the deformed structure must be taken into account in the calculation . It is generally also necessary to take into account the unwanted deviations of the structure from the planned geometry (e.g. inclination of columns) and the pre-deformations of the components (e.g. curvature of compression bars ). The size of these imperfections to be considered in civil engineering is suggested in standards.
Second order theory
In the case of the second order theory , i. d. It is generally assumed that the deformations of a component are small . This is the rule in construction, because large rotations lead u. a. to the fact that the usability i. d. R. is no longer given. In the linearized theory of the second order, the assumption of small rotations φ results in the simplifications sin φ = φ and cos φ = 1 of the small-angle approximation (see also P-Delta effect ).
Higher order theories
It is seldom necessary to also record large deformations of a structure, the simplifications of the second-order theory then no longer apply. An example of this is the calculation of rope networks . In this case one speaks of a calculation according to theory III. Order .
Between theories II. And III. There is no clear separation of order, which is why one sometimes only speaks of the first and second order theory.
In some books you can also find a theory of the fourth order , which z. B. the post-dent behavior explained.
The calculation results of the structural analysis are used to dimension the supporting structures. These also differ according to the building materials, which therefore require very different design methods:
- Concrete , reinforced concrete , prestressed concrete , masonry ( solid construction )
- Steel and other metals, especially aluminum ( steel construction and general metal construction )
- Concrete with steel ( composite construction )
- Wood ( timber construction )
- Plastic (plastic construction)
- Soil and earth materials ( foundation )
- Constructive glass construction
History of structural engineering
The history of structural engineering is closely related to research and publications u. a. linked by the following authors:
- Archimedes (287–212 BC) Lever law
- Leonardo da Vinci (1452–1519) first vivid reflections on vaulting and beam bending, qualitative statements on load-bearing capacity
- Simon Stevin (1548–1620) Flemish mathematician, physicist and engineer. Parallelogram of forces, statics of solids and liquids; Introduction of the decimal places
- Galileo Galilei (1564–1642) Principles of mechanics, strength theory and the laws of fall
- Edme Mariotte (1620–1684) - Stress distribution - "Axis of equilibrium"
- Robert Hooke (1635–1703) law of proportionality
- Pierre Bullet (1639–1716) first attempt at an earth pressure theory in 1691
- Sir Isaac Newton (1643–1727) founder of classical theoretical physics and thus of exact natural sciences, mathematical foundations of natural sciences, formulation of the three laws of motion, balance of forces, infinitesimal calculus
- Gottfried Wilhelm Leibniz (1646–1716) - Moments of resistance , calculus
- Jakob I Bernoulli (1655–1705) Curvature of the elastic beam, relationship between loading and bending; The cross-sections remain even
- Pierre de Varignon (1654–1722) French mathematician. Composition of forces, law of the parallelogram of forces (Varignon parallelogram), concept of the 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 body theory of the vault 1730
- Thomas Le Seur (1703–1770), French mathematician and physicist; first static report received in 1742 (for the dome of St. Peter's Basilica ), with François Jacquier (1711–1788) and Rugjer Josip Bošković (1711–1787)
- Leonhard Euler (1707–1783) beam theory ; elastic line; Ropes; Buckling rod
- Charles Augustin de Coulomb (1736–1806) Friction, earth pressure theory, arch theory, torsion, strength, stresses, beam bending
- Johann Albert Eytelwein (1764–1848) support forces of the continuous beam, Euler-Eytelwein formula
- Louis Poinsot (1777-1859) couple of forces 1803
- Claude Henri Navier (1785–1836) theory of the suspension bridge 1823; first comprehensive structural analysis, technical bending theory 1826; Investigation of statically indeterminate rod structures
- Jean-Victor Poncelet (1788–1867) pioneer of technical mechanics (1826–1832) and projective geometry (1822), vault theory 1835, earth pressure theory 1840
- Augustin Louis Cauchy (1789–1857) Theory of elasticity, concept of tension
- George Green (1793–1841) Foundation of potential theory for mathematical physics
- Gabriel Lamé (1795–1870) First monograph on elasticity theory 1852
- Barré de Saint-Venant (1797–1886) The principle of St. Venant in strength theory, torsion theory
- Émile Clapeyron (1799–1864) Clapeyron's theorem, three-moment equation on the continuous beam 1857
- William John Macquorn Rankine (1820–1872) Earth pressure theory 1856, further contributions to structural structural questions from 1858
- Karl Culmann (1821–1881) Truss theory 1851; graphic statics 1866
- Gustav Robert Kirchhoff (1824–1887) plate theory
- Federico Luigi Menabrea (1809–1896) Menabrea's theorem on the deformation energy of statically indeterminate systems (Principle of Castigliano and Menabrea)
- Jacques Antoine Charles Bresse (1822–1883) Theory of the elastic arch, core of the cross section
- Johann Wilhelm Schwedler (1823–1894) Truss theory 1851, Schwedler girder, Schwedler dome, three-joint system
- Enrico Betti (1823–1892) Theorem of Betti , 1872
- Georg Rebhann (1824–1892) Stress analysis for simply symmetrical girder cross-sections 1856, earth pressure theory 1870/1871
- August Ritter (1826–1908) Ritter's cutting method for statically determined frameworks 1861
- Luigi Cremona (1830–1903) Drawing determination of the bar forces in statically determined frameworks ("Cremonaplan", 1872)
- James Clerk Maxwell (1831–1879) Principle of virtual forces for trusses 1864, reciprocal figures in truss theory 1864/1867/1870
- Emil Winkler (1835–1888) pioneer of technical elasticity theory, Winkler bedding , method of influence lines ( influence lines ), theory of elastic arches
- Christian Otto Mohr (1835–1918) Mohr-Coulomb's strength hypothesis; Mohr's circle of tension; graphical determination of the bending line, principle of virtual forces for trusses
- Maurice Lévy (1838–1910) Graphic statics, earth pressure theory, plate theory
- Hermann Zimmermann (1845–1935) Zimmermann dome, theory of the space frame, buckling theory
- Carlo Alberto Castigliano (1847–1884) Theorems of Castigliano , based on the analysis of statically indeterminate systems
- Rudolf Bredt (1842–1900) Bredt's formulas in strength theory
- Jakob Johann von Weyrauch (1845–1917) coined the term influence line (influence line) in 1873, earth pressure theory, technical elasticity theory
- Friedrich Engesser (1848–1931) Earth pressure theory, buckling theory, additional deformation energy
- Heinrich Müller-Breslau (1851–1925) Theory of statically indeterminate elastic rod structures (force quantity method), in particular the principle of virtual forces for rod structures and the systematic application of the sets of energy, earth pressure theory
- Joseph Melan (1853–1941) Theory of Arch and Suspension Bridges (Second Order Theory) 1888
- August Föppl (1854–1924) theory of the space framework, torsion theory
- Robert Land (1857–1899) Kinematic Carrier Theory 1887/1888, Inertia Circle 1892
- Vito Volterra (1860–1940) Integral equation methods of elasticity theory
- Augustus Edward Hough Love (1863–1940) theoretical continuum mechanics; Textbook on elasticity theory
- Hans-Detlef Krey (1866–1928) Earth pressure theory
- Asger Skovgaard Ostenfeld (1866–1931) Displacement size method (displacement size method or deformation method) 1921/1926
- Maksymilian Tytus Huber (1872–1950) Strength Hypothesis 1904, Theory of the Orthotropic Plate (1915–1926)
- Robert Maillart (1872–1940) thrust center 1924
- Hans Jacob Reissner (1874–1967) Dynamics of the framework 1899/1903, container and shell theory, earth pressure theory
- Theodore von Kármán (1881–1963) discoverer of the vortex-excited transverse oscillation, buckling theory, theory of thin shells
- Stepan Prokofievich Timoshenko (1878–1972) pioneer of modern strength theory
- Kurt Beyer (1881–1952) solving systems of linear equations
- Hardy Cross (1885–1959) Cross method, a method for the iterative calculation of statically indeterminate rod structures, 1930
- Georg Prange (1885–1941) Generalized variation principle for elastic and plastic structures 1916
- Hermann Maier-Leibnitz (1885–1962) Experimental load-bearing theory, steel composite theory
- Franz Dischinger (1887–1953) theory of reinforced concrete shells, theory of concrete creeping
- Harold Malcolm Westergaard (1888–1950) theory of the concrete roadway, historiographer of structural engineering
- Richard V. Southwell (1888-1970) relaxation method 1935/1940
- Gábor von Kazinczy (1889–1964) pioneer of the load bearing method
- Lloyd H. Donnell (1895–1997) Buckling theory of thin shells
- Alexander Hrennikoff (1896–1984) Preparatory work for FEM, 1941
- Aleksei A. Gvozdev (1897–1986) Displacement size method (path size method or deformation method) 1927 and ultimate load method 1936
- Hans Ebner (1900–1977) preliminary work on FEM, 1937 (shear field theory)
- Herbert Wagner (1900–1982) Theory of Warping Torsion, Wagner Hypothesis 1929
- Kurt Klöppel (1901–1985) made pioneering contributions to steel construction science
- William Prager (1903–1980) Framework Dynamics 1933, pioneer of plasticity theory
- Robert Kappus (1904–1973) Theory of torsional buckling 1937
- Vasily Zacharovich Vlasov (1906–1958) Theory of the elastic rod shell 1940
- Raymond D. Mindlin (1906–1987) soil mechanics, plate theory
- Hellmut Homberg (1909–1990) Theory of the carrier grid 1949
- Gaspar Kani (1910–1968) Kani method 1949
- Kurt Hirschfeld (1902–1994) Structural engineering textbook 1958
- John Argyris (1913–2004) matrix statics, co-founder of the finite element method
- Eric Reissner (1913–1996) plate theory
- Li Guohao (1913–2005) Theory of the suspension bridge
- Warner T. Koiter (1914–1997) Stability Theory
- Wolfgang Zerna (1916–2005) Tensorial formulation of the shell bending theory
- Clifford Truesdell (1919–2000) pioneer of rational mechanics
- Olgierd Cecil Zienkiewicz (1921–2009) pioneer of the finite element method; first textbook of the FEM
- Kyūichirō Washizu (1921–1981) Generalized variation principle for elastic and plastic structures 1955
- Bruce Irons (1924–1983) made important contributions to FEM
- Haichang Hu (1928–2011) Generalized variation principle for elastic and plastic structures 1955
History of statics law
In view of the dangers posed by unstable buildings, structural engineering has also been the subject of legislation and case law for several thousand years. Even in the early cultures of Mesopotamia there were special penalties for builders whose buildings collapsed and killed people, for example in the Codex Hammurapi , a legal collection of the King Hammurapis of Babylon (* 1810 BC; † 1750 BC).
Static regulations in the narrower sense that specify a certain quality are historically more recent. In the year 27 AD e.g. B. In Fidenae, north of Rome, an under- built wooden amphitheater collapsed, killing thousands. The Senate of Rome then issued static regulations.
Typical today's regulation
Every structural system must be stable and durable as a whole and in its individual parts as well as on its own. The stability of other structures and the load-bearing capacity of the subsoil of the neighboring property must not be endangered.
As a rule, however, it is then stipulated that further regulations can be issued on the construction. The quoted LBO stipulates in § 87:
The responsible ministry can issue statutory ordinances on ... 2. the necessary applications, notifications, evidence and certificates.
In § 5 of the relevant state ordinance on construction documents and the structural examination it then states:
(1) To prove the stability, the necessary calculations with a representation of the entire static system as well as the necessary construction drawings must be submitted. Drawings and calculations must match and have the same position information. (2) The static calculations must prove the stability of the planned structures and their parts. The nature of the subsoil and its load-bearing capacity must be specified. ...
There are, in turn, a large number of technical rules relating to the individual components of the structural analysis. In Germany z. There are, for example, a large number of binding DIN standards . With just a few paragraphs, hundreds of standards with thousands of individual stipulations become binding, which ideally make the technical state of the art of building binding.
The OIB guideline states in 2.1.1:
Structures are to be planned and manufactured in such a way that they have sufficient load-bearing capacity, usability and durability to absorb the effects to which the structure is exposed and to dissipate them into the ground.
These proofs of stability, which are required in practically all modern building regulations, are often created by a special group of engineers, the structural engineers , or structural engineers for short, who also monitor the construction work, such as compliance with the steel reinforcement specified by them in concrete construction .
- B. Hartung: On the mechanics of the reinforced concrete beam . Dissertation . TH Darmstadt, 1985, D 17.
- B. Hartung, A. Krebs: Extension of the technical bending theory part 1. In: Concrete and reinforced concrete construction. Volume 99, Issue 5, 2004.
- A. Krebs, J. Schnell, B. Hartung: Extension of the technical bending theory part 2. In: Concrete and reinforced concrete construction. Volume 99, Issue 7, 2004.
- A. Krebs, B. Hartung: For a realistic description of the load-bearing and deformation behavior of reinforced concrete and prestressed concrete girders with the ETB. In: civil engineer. Volume 82, Issue 10, 2007.
- Karl-Eugen Kurrer : History of Structural Analysis. In search of balance. 2nd, greatly expanded edition. Ernst & Sohn, Berlin 2016, ISBN 978-3-433-03134-6 .
- Karl-Eugen Kurrer: The History of the Theory of Structures. From Arch Analysis to Computational Mechanics . Ernst & Sohn, Berlin 2008, ISBN 978-3-433-01838-5 .
- Karl-Eugen Kurrer: The History of the Theory of Structures. Searching for Equilibrium . 2nd, greatly expanded edition. Ernst & Sohn, Berlin 2018, ISBN 978-3-433-03229-9 .
- K.-J. Schneider: Construction tables for engineers. 19th edition. Werner Verlag, Cologne 2008, ISBN 978-3-8041-5242-7 .
- K.-J. Schneider: Construction tables for architects. 18th edition. Werner Verlag, Cologne 2008, ISBN 978-3-8041-5237-3 .
- Wilfried Wapenhans, Jens Richter: The first statics of the world 260 years ago. (pdf)
- Theodor Kissel: mass leader. In: The Rheinpfalz on Sunday . May 31, 2009, p. 20.
- Example: http://www.mauerwerk.fd-bau.de/html/statikmw/s_vorsch.htm
- OIB guideline 1 Mechanical strength and stability. (PDF) Austrian Institute for Structural Engineering , April 2019, accessed on June 20, 2019 .
- Learn statics
- KI-SMILE - visualizations on the topic of statics and effects
- EasyStatics - computer program from the ETH Zurich for the calculation of flat bar structures.
- Eurocode statics online - online calculation of simple timber structures according to Eurocode 5.
- Beam dimensioning online - online calculation of a single-span timber beam according to Eurocode 5.
- Civil engineering aids online - online calculation - general level framework