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# Verification Examples

## 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.

## 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.

## 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.

## 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.

## 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.

## Mathematical Pendulum

The mathematical pendulum consists of a zero‑weight rope and a mass point at its end. The pendulum is initially deflected. Determine the angle of the rope at given test time.

## Double Mass Oscillator

A double-mass oscillator consists of two linear springs and masses, which are concentrated at the nodes. The self-weight of the springs is neglected. Determine the natural frequencies of the system.

## Vibrations with Coulomb Friction

A simple oscillator consists of mass *m* (considered only in *x*-direction) and linear spring of stiﬀness *k*. The mass is embedded on a surface with Coulomb friction and is loaded by constant-in-time axial and transversal forces.

## Bending Vibrations with Axial Force

A cantilever of rectangular cross‑section has a mass at its end. Furthermore, it is loaded by an axial force. Calculate the natural frequency of the structure. Neglect the self‑weight of the cantilever and consider the influence of axial force for the stiffness modification.

## Impulse Applied to Simply Supported Beam

A concentrated force is applied for a short period of time at the mid‑span of a simply supported beam. Considering only small deformation theory and assuming that the mass of the beam is concentrated at its mid‑span, determine its maximum deflection.