Analytical verification example

The system consists of a 0.18 m thick concrete slab measuring 6.0 x 12.0 m. The slab is supported on all four sides so that it cannot move vertically (soft support).The first six natural frequencies and modes of the plate under its own weight are to be determined.SystemL x W = 12 m x 6 mCross-sectiond = 0.18 mModulus of elasticityE = 30 × 103 MPaTransverse contraction ratio= 0.2ElvesG = 25.0 kN/m3

Analytical verification example

For a beam with a square cross-section and hinged supports at both ends, the natural frequencies and natural modes of the first 10 modes are to be determined.Beam lengthL = 4.0 mCross-sectionh = b = 0.3 mModulus of elasticityE = 2.1 × 10⁵ MPaTransverse contraction coefficient= 0.3Weight= 7,850 kg/m³

Standards-based verification example

D1.1Task descriptionHere is the problem from the DBV collection of examples [1], Example 4: Based on a point-supported slab. The slab internal forces and the required longitudinal reinforcement are covered in EvaDAT Example 0036. For this reason, a detailed problem statement and a repeat of the boundary conditions for the FEM analysis are omitted here; please refer to Example 0036 in this regard: In this example, the punching point on the B/2 axis is examined.The punching shear analysis is carried out, on the one hand, using the load calculated manually from the load application areas from [1]…

Analytical verification example

Fig. A1-1The simple plate system outlined above (edge lengths = 1 m, acute angle = 30 degrees) was investigated with a surface load in the z-direction of p = -0.7 \mathrm{kN/m^2} was investigated, taking into account an isotropic material (steel) with a modulus of elasticity of 210*10³ \mathrm{MN/m^2} and a Poisson’s ratio of 0.3. The thickness is 10 mm, and the plate is hinged at all four corners in the vertical direction.The problem is to find the maximum principal stress on the underside of the plate at point m (the centre of the plate).

Analytical verification example

Fig. A1-1gk1 = 10.0 kN/m²qk1 = 7.5 kN/m² OfficeQk2 = 5.0 kN/m snowFor the system shown above, the stability analysis is to be carried out and the support moment at the ultimate limit state above column B is to be determined. The load combination is to be carried out in accordance with the standard, taking into account the partial safety factors and combination factors.

Systemic validation example

E1.1Task descriptionA wall panel in an interior space is subjected to a uniformly distributed load at the top and bottom. The wall has an opening and is supported at both ends by two columns.The internal forces relevant to the design shall be determined in accordance with first-order theory.The following materials are used:C25/30 concreteB500B reinforcing steelE1.2SystemAbb. E1-1: SystemE1.3EffectsConstant exposuregk = 40 kN/mVariable loads (live and dead loads)qk = 20 kN/m

Numerical verification example

Various finite element methods are designed solely for the standard Euler-Bernoulli beam, which does not take shear deformations into account. However, there are also methods for the Mindlin beam or hybrid methods that take shear deformations into account according to Timoshenko’s theory. A beam is fixed at both ends and is loaded in two load cases: with a single load at the centre and at the quarter-point. The solution at the centre (a) is trivial; the problem at hand is the offset load at the quarter-point (b).As this is a statically indeterminate system, the stiffness in case (b) also…

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

The problem of a truss is a fundamental test for geometrically non-linear effects. A slightly over-cambered system comprising two truss members is subjected to a transverse load. There is an initial buckling load and pronounced post-buckling behaviour.In one symmetrical half, one end of an inclined truss member is fixed. At the other end, the node can move freely in the direction of the load.The particular challenge arises in a load-controlled analysis.The parameters are:ParameterE [MPa]H [mm]L [mm]A [mm²]Value500,000252,500100

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.