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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.
Closely coiled helical spring is loaded by a compression force. The spring has a middle diameter D, the wire diameter d, and it consists of i turns. The total length of the spring is L. Determine the total deflection of the spring for the member model and one‑turn deflection for the solid model.
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 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 rectangular steel plate of dimensions is simply supported at its edges. Determine the natural frequencies of the rectangular plate.
A cantilever with circular cross‑section is loaded by a concentrated bending force and torque. The aim of this verification example is to compare the reduced stress according to the von Mises and Tresca theories.
A composite plate, consisting of three glass layers, one foil layer and the inner space with the dry air is fully fixed and loaded with the variable temperature. Neglecting it's self-weight, determine plate's maximum deflection.
A timber beam, reinforced by two steel plates at its ends, is loaded by the pressure. Wood fibres are parallel to the upper loaded side of the beam. The plastic surface is described according to the Tsai-Wu plasticity theory.
Four columns are fixed at the bottom and connected by the rigid block at the top. Block is loaded by the pressure and modeled by an elastic material with high modulus of elasticity. Outer columns are modeled by linear elastic material and inner columns by a stress-strain diagram with the decaying dependence. Assuming only small deformations theory and neglecting structure's self-weight, determine its maximum deflection.