Standards-based verification example

This verification example deals with the design of a slender pendulum support made of centrifugally cast concrete (see approval Z-15.13-343 [1]) in accordance with the general procedure set out in DIN EN 1992-1-1/NA:2013-04, Section 5.8.6. In addition to the geometric non-linearity of the system according to second-order theory, suitable stress-strain curves incorporating creep effects for concrete and steel must be taken into account in the design (see examples [2, S. 29-35] and [3]).Creep effects may be modelled in accordance with DIN EN 1992-1-1 5.8.6 (3) by assuming a change in shape or…

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