Verification Examples

Euler Buckling

A strut with circular cross-section is supported according to four basic cases of Euler buckling and it is subjected to pressure force. Determine the critical load.

Dynamic Force Distribution

A single-mass system with dashpot is subjected to a constant loading force. Determine the spring force, the damping force and the inertial force at given test time. In this verification example, the Kelvin--Voigt dashpot, namely, a spring and a damper element in serial connection, is decomposed into its purely viscous and purely elastic parts, in order to better evaluate the reaction forces.

Thin Rectangular Orthotropic Plate Under Uniform Load

Thin rectangular orthotropic plate is simply supported and loaded by the uniformly distributed pressure. The directions of axis x and y coincide with the principal directions. While neglecting self-weight, determine the maximum deflection of the plate.

Buckling of Beam with Various Cross-Sections

A column is composed of a concrete part - rectangle 100/200 and of a steel part - profile I 200. It is subjected to pressure force. Determine the critical load and corresponding load factor. The theoretical solution is based on the buckling of a simple beam. In this case two regions have to be taken into account due to different moment of inertia and material properties.

Single-Mass Oscillation with Dashpot

A single mass system with dashpot is subjected to the constant loading force. Determine the deflection and the velocity of the dashpot endpoint in given test time.

Curved Beam Without Plane Loading

A quarter-circle beam with a rectangular cross-section is loaded by means of an out-of-plane force. This force causes a bending moment, torsional moment and a transverse force. While neglecting self-weight, determine the total deflection of the curved beam.

Curved Beam with Distributed Loading

A curved beam consists of two beams with a rectangular cross-section. The horizontal beam is loaded by a distributed loading. While neglecting self-weight, determine the maximal stress on the top surface of the horizontal beam.

Thin-Walled Conical Vessel with Hydrostatic Pressure

A thin-walled conical vessel is filled with water. Thus, it is loaded by the hydrostatic pressure. While neglecting self-weight, determine the stresses in surface line and circumferential direction. The analytical solution is based on the theory of thin-walled vessels. This theory was introduced in Verification Example 0084.

Eccentricity Test

Pinned beam with rectangular cross‑section is subjected to distributed loading and shifted vertically by eccentricity. Considering small deformation theory, neglecting self‑weight, and assuming that the beam is made of isotropic elastic material, determine the maximum deflection.

Thin-Walled Spherical Vessel

A thin-walled spherical vessel is loaded by inner pressure. While neglecting self‑weight, determine the von Mises stressand the radial deflection of the vessel.

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