Volume 42 Issue 6
Jun.  2021
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WANG Dan, WANG Jian. Analysis of Deformation and Bearing Capacity of Flexible Beams Under Gravitational Loads[J]. Applied Mathematics and Mechanics, 2021, 42(6): 611-622. doi: 10.21656/1000-0887.410169
Citation: WANG Dan, WANG Jian. Analysis of Deformation and Bearing Capacity of Flexible Beams Under Gravitational Loads[J]. Applied Mathematics and Mechanics, 2021, 42(6): 611-622. doi: 10.21656/1000-0887.410169

Analysis of Deformation and Bearing Capacity of Flexible Beams Under Gravitational Loads

doi: 10.21656/1000-0887.410169
Funds:

The National Natural Science Foundation of China(11902151)

  • Received Date: 2020-06-11
  • Rev Recd Date: 2020-11-09
  • The large deformation of flexible structure can decrease the load. The relation between the large deformation of the flexible beam and the gravitational load was studied. Based on the experiments, the distribution mode for the gravitational load was built. With the large deflection constitutive model for Timoshenko beams, the governing equation for the large-deformation beam under the gravitational load was derived. Two dimensionless parameters were defined, i.e. the Cauchy number and the deformation coefficient. Through numerical calculation of the governing equation, the quantitative relation between the Cauchy number and the deformation coefficient was discussed. The theoretical results are compared with the experimental data to confirm the reliability of the theoretical model. The model was used to analyze the snow load data in previous literatures to verify the applicability in reality. The research indicates that, the proposed method applies to the design of deflection and bearing capacity of flexible beams in engineering systems, as well as the prediction of the lodging resistance of vegetations in sand storm or snow storm.
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