Standards-based verification example

Das Verifizierungsbeispiel behandelt die Bemessung einer schlanken Pendelstütze aus Schleuderbeton (s. Zulassung Z-15.13-343 ) nach dem allgemeinen Verfahren gemäß DIN EN 1992-1-1/NA:2011-01 Abschnitt 5.8.6. Zusätzlich zu der geometrischen Nichtlinearität des Systems nach Theorie II. Ordnung sind geeignete Spannungs-Dehnungs-Linien mit Kriechauswirkungen für Beton und Stahl in der Bemessung zu berücksichtigen (s. Beispiele und ). Kriechauswirkungen können gemäß DIN EN 1992-1-1 5.8.6 (3) über den Ansatz einer Formänderung bzw. Vorverformung infolge Kriechens, z.B. mit dem Mehrstufenmodell nach…

Analytical verification example

The two-dimensional frame system is subjected to a point load at A. As the point load increases, the system deforms progressively until stability problems arise. The aim of this example is to calculate the load-deflection behaviour of the system until the buckling point is reached. Deflections are only possible in the XY plane.Material: linearly elastic; modulus of elasticity = 71,740 MPa; coefficient of elasticity = 0.0Support conditions: ux = uy = 0 at B and CLoad: P = 1.0 kN

Analytical verification example

Below, we have calculated the natural frequency of a two-hinged frame. It is 5 m wide, 3 m high and has a strength class of C 30/37. The posts have dimensions b/h = 26/26 cm and the transom has dimensions b/h = 30/30 cm. The density is 2500 kg/m³.The calculations are carried out using the ‘Lanczos method’ and without mass-proportional or stiffness-proportional damping. Furthermore, the quadrilateral elements were generated using the mesh generator and linear spline functions were employed.Both the first symmetric and the first asymmetric natural frequencies are output.

Numerical verification example

A bending moment is applied to the end of the cantilever. When the load is increased to ML/2πEI=1.0, significant displacements and rotations occur in a geometrically non-linear analysis. Deformations are only possible in the XY plane. Deformations at the free end of the cantilever must be determined.Fig. B1-1: SystemMaterial: linearly elastic; modulus of elasticity = 210,000 MPa; Poisson’s ratio = 0.0Conditions: All degrees of freedom fixed at the supportsLoad: ML/2πEI = 1.0

Numerical verification example

Table B1-1: Problem descriptionGeometryL = 10 mMaterialModulus of elasticity: 31,500 MPaTransverse strain ratio: 0.2(reinforced concrete C25/30)Cross-sectionB / H = 1.0 m / 0.3 mSupportElastic support kz = 20 MN/m² with failure upon lifting of the beamLoadFz = 50 kN at x = 2.5 mRequired: Deflection w, bending moment My and base pressure pzz at x = 0.0 m, 2.5 m, 10.0 mVariation in deflection and base pressureFig. B1-1