Second order theory

The articles Theory II. Order and Structural Analysis # Theory_I., _ II._or_III._Order overlap thematically. Help me to better differentiate or merge the articles (→  instructions ) . To do this, take part in the relevant redundancy discussion . Please remove this module only after the redundancy has been completely processed and do not forget to include the relevant entry on the redundancy discussion page{{ Done | 1 = ~~~~}}to mark. Acky69 ( discussion ) 13:53, Aug 24, 2018 (CEST)

The four Euler cases in one experiment

The second order theory , also called the deformation theory, is a theory in structural engineering in which the equilibrium is determined on the deformed system. Thus, the internal forces are dependent on the load and the deflection .

In the building industry, bars and slabs subjected to pressure must be checked for stability risks (usually kinking) and, if necessary, verified according to the second-order theory. In steel construction, in (steel) concrete construction as well as in wood construction, according to current standards, bars that are at risk of stability must be verified for buckling.

To describe buckling, one has to calculate according to the theory of the second order, in which the bending stiffness depends on the normal force . If the stiffness drops to zero, neglecting non-linear stiffening effects, a stability failure occurs in imperfect systems , e.g. B. Buckling.

Stability failure, apart from kinks, which can only be solved with the second order theory:

• Bending torsion problems , torsional torsional buckling , tilting
• Bumps .

In the second-order theory, imperfections , so-called pre-deformations, can be taken into account; this is required, for example, in steel construction standards for calculations according to the second-order theory.

Theory I., II. And III. order

Breakdown problem

A clear distinction can be made between the first and second order theories, since the first order theory does not take into account any eccentricities due to deflections.

On the other hand, one cannot distinguish so clearly between the theories of the second and higher order, since they are based on different assumptions:

• In the second-order theory, it is typically assumed that the cross-sectional rotation angle is much smaller than one and that the small-angle approximation therefore applies.
• if this linearization is no longer permissible, it is often referred to as theory III. Order denotes; this is often the case with rope nets and breakdown problems.

literature

• Petersen, Christian: Proof of stability (buckling - tilting - buckling) . In: Steel construction. Basics of the calculation and structural training of steel structures, 4th edition Wiesbaden: Springer-Fachmedien 2013, pp. 289–435, ISBN 978-3-528-38837-9 .
• Kurrer, Karl-Eugen: Theory II. Order . In: History of structural engineering. In search of balance . Berlin: Ernst & Sohn 2016, pp. 114–121, ISBN 978-3-433-03134-6 .

Individual evidence

1. ↑ Yoshio Namita: The theory of the second order of crooked bars and their application to the tilting problem of the arch support . In: Transactions of the Japan Society of Civil Engineers . tape 1968 , no. 155 . Japan Society of Civil Engineers, 1968, pp. 32-41 .
2. ↑ ^{a b} Karlheinz Roik, Jürgen Carl, Joachim Lindner: Bending torsion problems of straight thin-walled bars . 1972.
3. ↑ Dieter Kraus, K.-H. Ehret: Calculation of reinforced concrete and prestressed concrete girders at risk of tipping according to the second order theory. In: Concrete and reinforced concrete construction . tape 87 , no. 5 . Wiley Online Library, 1992, pp. 113-118 .
4. ↑ U. Quast: Load verification for reinforced concrete columns according to the theory of the second order with the help of a simplified moment-curvature relationship . In: Concrete and reinforced concrete construction . tape 65 , no. 11 , 1970.