is referenced by Reply to “Comments on ‘Large deflection and rotation of Timoshenko beams with frictional end supports under three-point bending’ ” [C. R. Mecanique 345 (2017), doi:10.1016/j.crme.2017.01.004]

Three-point bending of a beam is studied based on the Timoshenko beam theory. Large deflection and large rotation of a beam resting on simple supports with friction are calculated for a concentrated force acting at the midspan. Using the Lagrangian kinematic relations, a system of non-linear differential equations are obtained for a prismatic shear-deformable Timoshenko beam. Exact solutions for the deflection, horizontal displacement, and rotation of cross-section are derived analytically. Two deflections of small and large scale exist under three-point bending. The solutions corresponding to linearized model coincide with the well-known solutions to the classical Timoshenko beams. Numerical calculations are carried out to show the effect of the important parameters such as shear rigidity of the beam and the coefficient of friction at the contact position between the beam and supports on the deflection. The load–deflection curves are graphically presented. A comparison of large deflections and large rotations with their classical counterparts and with experimental data is made. The obtained results are useful in safety design of linear and non-linear beams subject to three-point bending.

Accepted:

Published online:

Dao-Kui Li ^{1};
Xian-Fang Li ^{2}

@article{CRMECA_2016__344_8_556_0, author = {Dao-Kui Li and Xian-Fang Li}, title = {Large deflection and rotation of {Timoshenko} beams with frictional end supports under three-point bending}, journal = {Comptes Rendus. M\'ecanique}, pages = {556--568}, publisher = {Elsevier}, volume = {344}, number = {8}, year = {2016}, doi = {10.1016/j.crme.2016.01.007}, language = {en}, }

TY - JOUR AU - Dao-Kui Li AU - Xian-Fang Li TI - Large deflection and rotation of Timoshenko beams with frictional end supports under three-point bending JO - Comptes Rendus. Mécanique PY - 2016 SP - 556 EP - 568 VL - 344 IS - 8 PB - Elsevier DO - 10.1016/j.crme.2016.01.007 LA - en ID - CRMECA_2016__344_8_556_0 ER -

Dao-Kui Li; Xian-Fang Li. Large deflection and rotation of Timoshenko beams with frictional end supports under three-point bending. Comptes Rendus. Mécanique, Volume 344 (2016) no. 8, pp. 556-568. doi : 10.1016/j.crme.2016.01.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.01.007/

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