Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Effects of dead loads on the static analysis of plates

  • Takabatake, Hideo (Department of Architecture, Kanazawa Institute of Technology, Institute of Disaster and Environmental Science)
  • Received : 2011.02.01
  • Accepted : 2012.04.24
  • Published : 2012.06.25
⟨ Previous Next ⟩

Abstract

The collapse of structures due to snow loads on roofs occurs frequently for steel structures and rarely for reinforced concrete structures. Since the most significant difference between these structures is related to their ability to handle dead loads, dead loads are believed to play an important part in the collapse of structures by snow loads. As such, the effect of dead loads on displacements and stress couples produced by live loads is presented for plates with different edge conditions. The governing equation of plates that takes into account the effect of dead loads is formulated by means of Hamilton's principle. The existence and effect of dead loads are proven by numerical calculations based on the Galerkin method. In addition, a closed-form solution for simply supported plates is proposed by solving, in approximate terms, the governing equation that includes the effect of dead loads, and this solution is then examined. The effect of dead loads on static live loads can be explained explicitly by means of this closed-form solution. A method that reflects the effects of dead loads on live loads is presented as an example. The present study investigates an additional factor in lightweight roof structural elements, which should be considered due to their recent development.

Keywords

References

  1. Boscolo, M. and Banerjee, J.R. (2011), "Dynamic stiffness elements and their applications for plates using first order shear deformation theory", Comput. Struct., 89(3-4), 395-410. https://doi.org/10.1016/j.compstruc.2010.11.005
  2. Durmaz, M. and Daloglu, A.T. (2006), "Frequency analysis of ground snow data and production of the snow load map using geographic information system for the Eastern Black Sea region of Turkeys", J. Struct. Eng.-ASCE, 132(7), 1166-1177. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:7(1166)
  3. Fang, X., Hu, C. and Huang, W. (2007), "Dynamic stress concentration of a circular cutout buried in semiinfinite plates subjected to flexural waves", J. Appl. Mech., 74(2), 382-387. https://doi.org/10.1115/1.2198545
  4. Kelly, J.M., Sackman, J.L. and Javid, A. (1991), "The influence of perform on the modes of vibrating beam", Earthq. Eng. Struct. D., 20(12), 1145-1157. https://doi.org/10.1002/eqe.4290201205
  5. Lee, W.M. and Chen, J.T. (2011), "Free Vibration Analysis of a circular pate with multiple circular holes by using indirect BIEM and addition theorem", J. Appl. Mech., 78(1), 011015-1-10. https://doi.org/10.1115/1.4001993
  6. Mostaghel, N., Fu, K.C. and Yu, Q. (1995), "Shifting natural frequencies of plates through performing", Earthq. Eng. Struct. D., 24(3), 411-418. https://doi.org/10.1002/eqe.4290240308
  7. Rao, G.V. and Saheb, K.M. (2008), "Simple formula to study the large amplitude free vibrations of beams and plates", J. Appl. Mech., 75(1), 014505-1-4. https://doi.org/10.1115/1.2755147
  8. Shimpi, R.P., Patel, H.G. and Arya, H. (2007), "New first-order shear deformation plate theories", J. Appl. Mech., 74(3), 523-532. https://doi.org/10.1115/1.2423036
  9. Szilard, R. (1974). Theory and Analysis of Plates, Prentice-Hall, NJ.
  10. Takabatake, H. (1990), "Effects of dead loads in static beams", J. Struct. Eng.-ASCE, 116(4), 1102-1120. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:4(1102)
  11. Takabatake, H. (1991), "Effect of dead loads on natural frequencies on beams", J. Struct. Eng.-ASCE, 117(4), 1039-1052. https://doi.org/10.1061/(ASCE)0733-9445(1991)117:4(1039)
  12. Takabatake, H. (1991), "Static analyses of elastic plates with voids", Int. J. Solids Struct., 28(2), 179-196. https://doi.org/10.1016/0020-7683(91)90204-S
  13. Takabatake, H. (1991), "Dynamic analyses of elastic plates with voids", Int. J. Solids Struct., 28(7), 879-895. https://doi.org/10.1016/0020-7683(91)90006-2
  14. Takabatake, H. (1992), "Effects of dead loads in dynamic plates", J. Struct. Eng., ASCE, 118(1), 34-51. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:1(34)
  15. Takabatake, H., Imaizumi, T. and Okatomi, K. (1996), "Simplified analysis of rectangular plates with stepped thickness", J. Struct. Eng.-ASCE, 122(7), 839-840.
  16. Takabatake, H., Yanagisawa, N. and Kawano, T. (1996), "A simplified analysis of rectangular cellular plates", Int. J. Solids Struct., 33(14), 2055-2074,. https://doi.org/10.1016/0020-7683(95)00145-X
  17. Takabatake, H., Morimoto, H., Fujiwara, T. and Honma, T. (1996), "Simplified analysis of circular plates including voids", Comput. Struct., 58(2), 263-275. https://doi.org/10.1016/0045-7949(95)00144-6
  18. Takabatake, H., Kajiwara, K. and Takesako, R. (1996), "A simplified analysis of circular cellular plates", Comput. Struct., 61(5), 789-804. https://doi.org/10.1016/0045-7949(96)00106-X
  19. Takabatake, H. (1998), "Dynamic analysis of rectangular plates with stepped thickeness subjected to moving loads including additional mass", J. Sound Vib., 213(5), 829-842. https://doi.org/10.1006/jsvi.1998.1555
  20. Takabatake, H. and Nagareda (1999), "A simplified analysis of elastic plates with edge beam", Comput Struct., 70(5), 129-139. https://doi.org/10.1016/S0045-7949(98)00164-3
  21. Takabatake, H. (2010), "Effects of dead loads on dynamic analyses of beam", Earthq. Struct., 1(4), 411-425. https://doi.org/10.12989/eas.2010.1.4.411
  22. Timoshenko, S. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells, McGraw-Hill Book Company, New York, NY.
  23. Tanveer, M. and Singh, A.V. (2009), "Linear and nonlinear dynamic responses of various shaped laminated composite plates", J. Comput. Nonlinear Dyn., 4(4), 041011-1-13. https://doi.org/10.1115/1.3187177
  24. Volterra, E. and Zachmanoglou, E.C. (1965), Dynamics of Vibrations, Charles, E., Merrill Books, Inc., Columbus, OH.
  25. Washizu, K. (1982), Variational Methods in Elasticity and Plasticity, 3rd Ed., Pergamon Press, New York, NY.
  26. Wu, J.H., Liu, A.Q. and Chen, H.L. (2007), "Exact solutions for free-vibration analysis of rectangular plates using bessel functions", J. Appl. Mech., 74(6), 1247-1251. https://doi.org/10.1115/1.2744043
  27. Yu, O., Mostaghel, N. and Fu, K.C. (1994), "Effect of initial curvature on natural frequency of thin plate on hinge supports", J. Eng. Mech.-ASCE, 120(4), 796-813. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:4(796)
  28. Zhou, S.J. (2002), "Load-induced stiffness matrix of plates", Can. J. Civil. Eng., 29(1), 181-184. https://doi.org/10.1139/l01-064
  29. Zhou, S.J. and Zhu, X. (1996), "Analysis of effect of dead loads on natural frequencies of beam using finiteelement techniques", J. Struct. Eng.-ASCE, 122(5), 512-516. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:5(512)

Cited by

  1. Relaxed Saint-Venant principle for thermoelastic micropolar diffusion vol.51, pp.4, 2014, https://doi.org/10.12989/sem.2014.51.4.651
  2. Effects of dead loads on dynamic analyses of beams subject to moving loads vol.5, pp.5, 2013, https://doi.org/10.12989/eas.2013.5.5.589
  3. Effect of Own Weight on the Static Analysis of a Prestretched Plate-Strip with a Circular Hole in Bending vol.53, pp.2, 2017, https://doi.org/10.1007/s11029-017-9657-9
  4. Effect of microtemperatures for micropolar thermoelastic bodies vol.61, pp.3, 2012, https://doi.org/10.12989/sem.2017.61.3.381
  5. Kendi ağırlığının dairesel delik içeren eğilme altındaki öngerilmeli şerit-plağın dinamik analizine etkisi vol.2018, pp.18, 2018, https://doi.org/10.17341/gazimmfd.460487