# STRENGTH ANALYSIS OF OVERHEAD TRAVELING CRANE WITH USE OF FINITE ELEMENT METHOD

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3 Strength analysis of overhead traveling crane 21 Table 2 Material data used in calculations for structural steel S235 Poisson's ratio ν 0,3 [-] Young's modulus E [MPa] Density ρ 7.86e-9 [ton/mm 3 ] Kirchhoff s modulus G [MPa] The units in Table 2 result from the adoption force in [N] and length in [mm] as the basis for the calculations. In order to support the structure shafts of wheel axles located on both buffer beams were modeled. These axes are modeled as MPC BEAM type elements. This has provided an opportunity to establish boundary conditions [1, 2]. MPC type BEAM element is modeled as rigid beam between two nodes, thereby limiting the displacements and rotations between them (Fig. 3). Fig. 3. Support of the buffer beam Rys. 3. Podparcie czołownicy The FEM model is shown in Fig. 4 where the location of supports is specified (1-4). In place of the support No.4 six degrees of freedom are taken away, at the supports No. 1, 2 only two degrees of freedom are taken away: translations in the y-axis (the direction of cranes movement), and the z-axis (in the direction perpendicular to the xy plane), while at the No. 3 three degrees of freedom are taken away (translations in the x, y and z directions). Fig. 4. Boundary conditions Rys. 4. Warunki brzegowe Supports of the buffer beam were moved from points on the axis of the wheels shaft to the buffer beam structure by a RIGID - DISTRIBUTING COUPLING element type (Fig. 3).

6 24 T. Haniszewski Reduced stress value for the unloaded construction in the middle of the cranes span was σ = 58[MPa], and for the construction loaded with gravitational force induced by the mass of the load 5000[kg] was σ = 164,4[MPa] (Fig. 7). Fig. 8. Reduced stress by Huber-Mises-Hencky theory stress concentrations in the girder Rys. 8. Naprężenia zredukowane wg teorii Hubera-Misesa-Hencky ego koncentracje naprężeń w dźwigarze Fig. 9. Reduced stress by Huber-Mises-Hencky theory stress concentrations in the girder Rys. 9. Naprężenia zredukowane wg teorii Hubera-Misesa-Hencky ego koncentracje naprężeń w dźwigarze The analysis indicate that the maximum reduced stresses σ = 164 [MPa] occurs in the corners of the membranes (Fig. 8) and in extreme girder cross-sections σ = 146 [MPa] (Fig. 9). 5. NATURAL FREQUENCY DETERMINATION Each elastic system with linear characteristics has "n" degrees of freedom and "n" natural frequencies of oscillations. These are frequencies with which the system vibrates after the unbalance [4]. Each natural frequency corresponds to a certain form of vibration. Forced oscillations of any mechanical system are the result of the external variable force after natural vibrations damping. If the frequency coincides with one of the natural frequencies of the structure, there would occur a resonance phenomenon. The increase in the amplitude of vibration at resonance, leads to large displacements and strains, and thus to the dynamic loading of structural elements [6]. Calculation of natural vibration frequencies with a modal analysis, allows to avoid the phenomenon of resonance. In the case of the crane the significant impact on the structure will have all drives, which should be configured or designed to prevent formation of vibrations at a frequency close to the natural frequency of vibration of the structure, on which they are located.

8 26 T. Haniszewski POKL /08 ". Numerical calculations were carried out in the Abaqus system, shared under the grant number: MNiSW/IBM_BC_HS21/PŚląska/021/2010. Bibliography 1. Gąska, D. & Pypno, C. Strength and elastic stability of cranes in aspect of new and old design standards. Mechanika Vol. 17(3). P Haniszewski, T. & Gąska, D. & Matyja, T. Modeling assumptions influence on stress and strain state in 450 t cranes hoisting winch construction. Transport Problems Volume 6. Issue 1. P Jakubowicz, A. & Orłoś, Z. Wytrzymałość materiałów. Warszawa: WNT [In Polish: Jakubowicz, A. & Orłoś, Z. Strength of materials. Warsaw: WNT.] 4. Kruszewski, J. & Sawiak, S. & Wittbrodt, W. Metoda sztywnych elementów skończonych w dynamice konstrukcji. Warszawa: WNT [In Polish: Kruszewski, J. & Sawiak, S. & Wittbrodt, W. Rigid finite element method in the dynamics of the structure. Warsaw: WNT.] 5. Niezgodziński, M.E. & Niezgodziński, T. Zadania z wytrzymałości materiałów. Warszawa: WNT [In Polish: Niezgodziński, M.E. & Niezgodziński, T. Tasks of the strength of materials. Warsaw: WNT.] 6. Parszewski, Z. Drgania i dynamika maszyn. Warszawa: WNT [In Polish: Parszewski, Z. Vibrations and dynamics of machines. Warsaw: WNT.] 7. Piątkiewicz, A. & Sobolski, R. Dźwignice. Warszawa: WNT [In Polish: Piątkiewicz, A. & Sobolski, R. Cranes. Warsaw: WNT.] 8. Reymer, B. (red.) Mały poradnik mechanika. Tom 1. Warszawa: WNT [In Polish: Reymen, B. (ed.) Small tutorial of mechanic. Volume 1. Warsaw: WNT.] 9. Сладковский, А. & Ханишевский, Т. & Матыя, Т. Динамика мостового крана. Часть 1. Определение характеристик мостового крана. Вісник Східноукраїнського національного університету No. 10 (152) ч.1. P [In Russian: Sładkowski, A. & Haniszewski, T. & Matyja, T. The dynamics of the bridge crane. Part 1. Determination of characteristics of the bridge crane. Journal of East-Ukrainian National University.] 10. Cyfronet AGH, 5. Available at: Research work carried out under a grant BK-355/RT-3/2011 Received ; accepted in revised form

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