Verification Examples

Center of Gravity

VE 0081

16 October 2017

RFEM Member Plate Solid

Determine the y-position of the center of gravity for the given bodies, namely semicircle, half-disc, hemispherical shell and half-ball.

A bimetallic strip is composed of the invar and copper. The left end of the bimetallic strip is fxed, and the right end is free, loaded by temperature difference. While neglecting self-weight, determine the deflection of the bimetallic strip (free end).

A double‑mass system consists of two shafts and two masses represented by the corresponding moments of inertia, concentrated in given distance as nodal masses. The left shaft is fixed, and the right mass is free. Neglecting the self‑weight of the shafts, determine the torsional natural frequencies of the system.

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.

A steel rod between two rigid supports with a gap is loaded by a temperature difference. While neglecting self‑weight, determine the total deformation of the rod and its internal axial force.

A truss structure consists of three rods - one steel and two copper joined by a rigid member. The structure is loaded by a concentrated force and by a temperature difference. While neglecting self‑weight, determine the total deflection of the structure.

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.

A concentrated force is suddenly applied at the mid‑span of a simply supported beam at given time. Considering only small deformation theory, determine the maximum deflection of the beam.

A rectangular steel plate of dimensions is simply supported at its edges. Determine the natural frequencies of the rectangular plate.

A circular steel plate is clamped around its circumference. Determine the natural frequencies of the circular plate.

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