P-delta effect

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The P-Delta effect , also called the P-Δ effect , is a group of phenomena that occur in structural calculations in structural engineering . It consists of the additional bending moments that result from calculations according to the theory of the second order , because the nodes of the structure move relative to one another under the load . This member end shift is usually identified with the symbol . The name P-Delta effect comes from the fact that the moments in this group of effects depend on the load and the member end displacement .

In some structures that require the calculation according to the second order theory, no P-Delta effect occurs, as for example in the second to fourth Euler buckling cases .

Cause and limits

Since the internal forces on the deformed system are calculated in the calculation according to the second-order theory , eccentricities that arise when the system is loaded must also be taken into account.

  • Concerning pressurized subsystems these eccentricities act stiffness -reducing .
  • In the case of a tensile rod , a calculation results according to the theory II. Order in the case of pure normal force loads generally more economic results, since a pulling force in combination with an eccentricity results in a restoring moment that a stiffening (d. E. Stiffness enhancing ) effect on the overall system has.

The standards stipulate whether or from when a calculation according to the second order theory is necessary.

  • The second order theory must be taken into account for steel structures with a normal compressive force in the longitudinal axis of the member that is greater than 10% of the ideal buckling load .
  • In the case of concrete structures, calculations must be based on the theory of the second order, provided that a pressure-loaded component exceeds a certain slenderness limit.
  • In timber construction , calculations are based on the first order theory, but the permissible strength value is reduced for slender bars subjected to compression.

However, according to current standards, the calculation with the P-Delta effect is not permissible for structures in steel construction, concrete construction and timber construction, which must be calculated according to the second order theory.

literature

  • MR Lindeburg, M. Baradar: Seismic Design of Building Structures. A Professional's Introduction to Earthquake Forces and Design Details. 8th edition, Professional Publications, Inc. Belmont, CA 2001.
  • P. Comino: What is P-Delta Analysis? SkyCiv Engineering, Sydney, Australia 2016.

Individual evidence

  1. ↑ C. Adam, J.-P. Spieß: Simplified determination of the global collapse capacity of frame structures at risk of stability under the influence of earthquakes . In: DA-CH 2007 conference of the Austrian Society for Earthquake Engineering and Structural Dynamics . Vienna 2007 ( oge.or.at [PDF]).
  2. ^ BJ Davidson, RJ Fenwick, BT Chung: P-delta effects in multi-storey structural design . In: Earth Quake Engineering, Tenth World Conference . Rotterdam 1992, ISBN 90-5410-060-5 ( iitk.ac.in [PDF]).
  3. ^ Bernhard Pichler, Josef Eberhardsteiner : Structural Analysis VO - LVA-Nr . 202.065 . Ed .: E202 Institute for Mechanics of Materials and Structures - Faculty of Civil Engineering, TU Vienna . SS 2017 edition. TU Verlag, Vienna 2017, ISBN 978-3-903024-41-0 , 24.1.1 Definition of the stability risk, p. 445 ( tuverlag.at ). Structural Analysis VO - LVA-Nr. 202.065 ( Memento of the original from March 13, 2016 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.  @1@ 2Template: Webachiv / IABot / shop.tuverlag.at
  4. ↑ H. Bruckner et al. a .: Entry of stability risk in the Beuth building dictionary . Ed .: Klaus-Jürgen Schneider, Rüdiger Wormuth. April 2016.
  5. ↑ Jan Höffgen: Fundamentals of steel construction formula collection. May 2, 2014, accessed March 25, 2018 .
  6. ↑ CEN European Committee for Standardization: EN 1992-1-1: 2015-03-01 Eurocode 2: Design and construction of reinforced and prestressed concrete structures - Part 1-1: General design rules and rules for building construction; EN 1992-1-1: 2004 / A1: 2014 . 2014, 5.8.3.1 (1), p. 69 .
  7. ↑ a b CEN European Committee for Standardization: EN 1995-1-1: 2015-03-01 Eurocode 5: Dimensioning and construction of wooden structures - Part 1-1: General - General rules and regulations for building construction; EN 1995-1-1: 2004 + AC: 2006 + A1: 2008 . December 2010, 6.3.2 Flexural buckling of compression rods, p. 45-46 .
  8. ↑ CEN European Committee for Standardization: EN 1992-1-1: 2015-03-01 Eurocode 2: Design and construction of reinforced and prestressed concrete structures - Part 1-1: General design rules and rules for building construction; EN 1992-1-1: 2004 / A1: 2014 . 2014, 5.8.3.1 (1), p. 69 .