Advanced stress and stability analysis: worked examples by V.I. Feodosiev, Sergey A. Voronov, Sergey V. Yaresko

By V.I. Feodosiev, Sergey A. Voronov, Sergey V. Yaresko

This booklet is a suite of difficulties for complex scholars within the quarter of power of fabrics. It attracts the reader´s awareness additionally to difficulties which are frequently missed and solutions questions which are a ways past a coaching path and require extra basic figuring out. All difficulties are supplied with certain options to permit the reader to both know about the problem-solving technique or simply to envision his/her personal method of answer. The examine and academic paintings of V.I. Feodosiev used to be conducted within the Bauman Moscow country technical collage the place he held the path on energy of fabrics for fifty years. Deep perception into engineering difficulties, clearness of techniques and magnificence of ideas observed via pedagogical expertise are the most gains of his style.

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130 Fig. 131 140. Let us imagine a rod with narrow rectangular cross-section clamped at its lower end (Fig. 131). If load P is central then its critical value is known to be equal to ¼ 2E J=(4l 2 ): What will be the change in this result if the point of load application is displaced along axis z by the value a from the cross-section centroid? 54 4. Stability Part I. Problems 141. A column with plane ends is compressed between two slabs (Fig. 132a). Two main equilibrium de‡ection curves are possible under buckling: the …rst one shown in Fig.

Problems 25 57. A beam of length 5l (Fig. 54) is under action of load P . The dependence of load application point de‡ection f on load P has apiece-wise linear character. Its form is de…ned by restraints on beam de‡ection due to four equally spaced supports placed under the beam with the same clearance. Fig. 54 Analyze how will the sti¤ness c = dP change as the force P increases. df 58. A ‡at spring of constant cross-section (Fig. 55) under bending is laying on a rigid mould having a pro…le speci…ed by the function y = y(x).

Thus we obtain that the strip is loaded by two equal opposite forces P subjected to its end. Is this state of equilibrium stable? Fig. 126 52 4. Stability Part I. Problems 136. A column clamped at its lower end is loaded on the upper end by two equal and opposite moments created by four weights P (Fig. 127): Fig. 127 Investigate the system’s stability. 137. The following question arises in connection with the previous problem: Would the critical moment value depend on the forces arms orientation with respect to the principal axes of the column cross-section?

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