Verifikationsbeispiele

Plastic Material Oscillations

This verification example is based on Verification Example 0122. A single-mass system without damping is subjected to an axial loading force. An ideal elastic-plastic material with characteristics is assumed. Determine the time course of the end-point deflection, velocity and acceleration.

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.

Eight-Member Symmetric Shallow Truss Snap-Through

A symmetrical shallow structure is made of eight equal truss members, which are embedded into hinge supports. The structure is loaded by the concentrated force and alternatively by the imposed nodal deformation over the critical limit point when the snap-through occurs. Imposed nodal deformation is used in RFEM 5 and RSTAB 8 to obtain full equilibrium path of the snap-through. The self-weight is neglected in this example. Determine the relationship between the actual loading force and the deflection considering large deformation analysis. Evaluate the load factor at given deflections.

Cable Equilibrium Force

A cable is loaded by means of the uniform load. This causes the deformed shape in the form of the circular segment. Determine the equilibrium force of the cable to obtain the given sag of the cable. The add-on module RF-FORM-FINDING is used for this purpose. Elastic deformations are neglected both in RF-FORM-FINDING and in analytical solution, also self-weight is neglected in this example.

Four-Member Truss Snap-Through

A structure is made of four truss members, which are embedded into hinge supports. The structure is loaded by a concentrated force and alternatively by imposed nodal deformation over the critical limit point, when snap-through occurs. Imposed nodal deformation is used in RFEM 5 and RSTAB 8 to obtain full equilibrium path of the snap-through. The self-weight is neglected in this example. Determine the relationship between the actual loading force and the deflection considering large deformation analysis. Evaluate the load factor at given deflections.

Bourdon Effect

A pipe with the tubular cross-section is loaded by means of internal pressure. The internal pressure causes axial deformation of the pipe, what is called Bourdon effect. Determine the axial deformation of the pipe endpoint.

Catenary

A very stiff cable is suspended between two supports. Determine the equilibrium shape of the cable, the so-called catenary, consider the gravitational acceleration and neglect the stiffness of the cable. Verify the position of the cable at given test points.

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.

Buckling of a Circular Ring

A thin circular ring of rectangular cross-section is exposed to an external pressure. Determine the critical load and corresponding load factor for in-plane buckling.

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.

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