est référencé par 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.
Accepté le :
Publié le :
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/
[1] Large deflections of an end supported beam subjected to a point load, Int. J. Non-Linear Mech., Volume 32 (1997), pp. 63-72
[2] On the parametric large deflection study of Euler–Bernoulli cantilever beams subjected to combined tip point loading, Int. J. Non-Linear Mech., Volume 49 (2013), pp. 90-99
[3] Large deflections of a beam subject to three-point bending, Int. J. Non-Linear Mech., Volume 69 (2015), pp. 84-92
[4] Large deflections of a simply supported beam subjected to moment at one end, J. Appl. Mech., Volume 51 (1984), pp. 519-525
[5] Large deflection of beams under moment gradient, J. Eng. Mech., Volume 120 (1994), pp. 1848-1860
[6] Elastica of simple variable-arc-length beam subjected to end moment, J. Eng. Mech., Volume 121 (1995), pp. 767-772
[7] Shooting optimization technique for large deflection analysis of structural members, Eng. Struct., Volume 14 (1992), pp. 231-240
[8] A new technique for large deflection analysis of non-prismatic cantilever beams, Mech. Res. Commun., Volume 32 (2005), pp. 692-703
[9] An integral approach for large deflection cantilever beams, Int. J. Non-Linear Mech., Volume 45 (2010), pp. 301-305
[10] Numerical and experimental analysis of large deflections of cantilever beams under a combined load, Phys. Scr. T, Volume 118 (2005), pp. 61-65
[11] Large deflections of cantilever beam subjected to a follower force, J. Sound Vib., Volume 304 (2007), pp. 969-973
[12] Large deflection of constant curvature cantilever beam under follower load, Int. J. Mech. Sci., Volume 52 (2010), pp. 440-445
[13] Large deflections of cantilever beams of nonlinear materials, Compos. Struct., Volume 14 (1981), pp. 357-360
[14] Large deflections of cantilever beams of nonlinear materials of the Ludwick type subjected to an end moment, Int. J. Non-Linear Mech., Volume 17 (1982), pp. 1-6
[15] Large deflections of cantilever beams of nonlinear elastic material under a combined loading, Int. J. Non-Linear Mech., Volume 37 (2002), pp. 439-443
[16] Large deflections of a cantilever beam of nonlinear bimodulus material subjected to an end moment, J. Reinf. Plast. Compos., Volume 24 (2005), pp. 1321-1326
[17] Large deflections of nonlinearly elastic non-prismatic cantilever beams made from materials obeying the generalized Ludwick constitutive law, Meccanica, Volume 44 (2009), pp. 733-739
[18] Large deflections of a non-linear cantilever functionally graded beam, J. Reinf. Plast. Compos., Volume 29 (2010), pp. 1761-1774
[19] Bending of functionally graded cantilever beam with power-law non-linearity subjected to an end force, Int. J. Non-Linear Mech., Volume 44 (2009), pp. 696-703
[20] Large deflection of a non-linear, elastic, asymmetric Ludwick cantilever beam subjected to horizontal force, vertical force and bending torque at the free end, Meccanica, Volume 49 (2014), pp. 1327-1336
[21] A comparison of mechanical properties derived from multiple skeletal sites in mice, J. Biomech., Volume 38 (2005), pp. 467-475
[22] Improving the estimate of the effective elastic modulus derived from three-point bending tests of long bones, Ann. Biomed. Eng., Volume 42 (2014), pp. 1773-1780
[23] Elastic modulus of halloysite nanotubes, Nanotechnology, Volume 24 (2013), p. 105704
[24] Dependence of Young's modulus of nanowires on surface effect, Int. J. Mech. Sci., Volume 81 (2014), pp. 120-125
[25] Effect of scale parameter on the deflection of a nonlocal beam and application to energy release rate of a crack, Z. Angew. Math. Mech., Volume 95 (2015), pp. 1428-1438
[26] Large thermal deflections of Timoshenko beams under transversely non-uniform temperature rise, Mech. Res. Commun., Volume 33 (2006), pp. 84-92
[27] An analytical solution for the large deflection problem of Timoshenko beams under three-point bending, Int. J. Mech. Sci., Volume 78 (2014), pp. 135-139
[28] Effect of horizontal reaction force on the deflection of short simply-supported beams under transverse loading, Int. J. Mech. Sci., Volume 99 (2015), pp. 121-129
[29] Analytical solution for large deflection of Reissner's beam on two supports subjected to central concentrated force, Int. J. Mech. Sci., Volume 107 (2016), pp. 13-20
[30] Mechanics of Materials, PWS Pub. Co., Boston, 1997
[31] An analysis of large deflections in a symmetrical three-point bending of beam, Bull. JSME, Volume 29 (1986), pp. 1988-1995
[32] Flexure testing of plastics, Exp. Mech., Volume 21 (1964), pp. 185-190
- Study on bending characteristics of CNT-reinforced metal Timoshenko composite porous beam exposed to transverse patch loading, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science (2025) | DOI:10.1177/09544062251325160
- Reliability-based design optimization of screw shaft for continuous high-pressure hydrothermal co-liquefaction process, Chemical Industry and Chemical Engineering Quarterly, Volume 30 (2024) no. 4, p. 335 | DOI:10.2298/ciceq231124004v
- An Analytical Model for Nonlinear-Elastic Compliant Mechanisms With Tension–Compression Asymmetry, Journal of Mechanisms and Robotics, Volume 16 (2024) no. 12 | DOI:10.1115/1.4065025
- Analysis of Steel Beams for Different Loadings Using MIF, Proceedings of the Indian Structural Steel Conference 2020 (Vol. 1), Volume 318 (2024), p. 777 | DOI:10.1007/978-981-19-9390-9_63
- Micromechanical modeling and experimental study of the flexural properties of impregnated woven textile-reinforced concrete, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, Volume 238 (2024) no. 9, p. 1791 | DOI:10.1177/14644207241233719
- Experimental and analytical study of flexural creep of impregnated woven fabric-reinforced concrete, Composite Structures, Volume 321 (2023), p. 117192 | DOI:10.1016/j.compstruct.2023.117192
- Continuous deformation analysis and contact force estimation for pneumatic bending actuators interacting with environment, Comptes Rendus. Mécanique, Volume 351 (2023) no. G1, p. 43 | DOI:10.5802/crmeca.167
- A Numerical Study on the Large Displacement in Functionally Graded Beam under Thermal Effect, Journal of Materials and Mechatronics: A, Volume 4 (2023) no. 2, p. 492 | DOI:10.55546/jmm.1363808
- A Method for Comparison of Large Deflection in Beams, International Journal of Applied Mechanics and Engineering, Volume 27 (2022) no. 4, p. 179 | DOI:10.2478/ijame-2022-0058
- Influence of face grain angle, size, and moisture content on the edgewise bending strength and stiffness of birch plywood, Materials Design, Volume 223 (2022), p. 111227 | DOI:10.1016/j.matdes.2022.111227
- Correction factors to strength of thin silicon die in three- and four-point bending tests due to nonlinear effects, Microelectronics Reliability, Volume 128 (2022), p. 114424 | DOI:10.1016/j.microrel.2021.114424
- Simultaneous measurement of elastic constants from dynamic mechanical analysis with digital image correlation, Polymer, Volume 242 (2022), p. 124562 | DOI:10.1016/j.polymer.2022.124562
- Investigation of the effect of three-point bending testing parameters on the behavior of 3D printed sand, The International Journal of Advanced Manufacturing Technology, Volume 121 (2022) no. 1-2, p. 1415 | DOI:10.1007/s00170-022-09418-3
- Explicit analysis of large transformation of a Timoshenko beam: post-buckling solution, bifurcation, and catastrophes, Acta Mechanica, Volume 232 (2021) no. 9, p. 3565 | DOI:10.1007/s00707-021-02993-8
- Case study of GFRP as a sheet-pile wall for stream bank protection in Taiwan, Case Studies in Construction Materials, Volume 15 (2021), p. e00602 | DOI:10.1016/j.cscm.2021.e00602
- Contact-electrification-activated artificial afferents at femtojoule energy, Nature Communications, Volume 12 (2021) no. 1 | DOI:10.1038/s41467-021-21890-1
- Bending Response of a Book with Internal Friction, Physical Review Letters, Volume 126 (2021) no. 21 | DOI:10.1103/physrevlett.126.218004
- 3D small strain large deflection beam shape sensing including poisson effect, Engineering Structures, Volume 209 (2020), p. 109948 | DOI:10.1016/j.engstruct.2019.109948
- Bending, buckling and free vibration of an axially loaded timoshenko beam with transition parameter: Direction of axial force, International Journal of Mechanical Sciences, Volume 176 (2020), p. 105545 | DOI:10.1016/j.ijmecsci.2020.105545
- Large-deflection analysis of prismatic and tapered beam-columns using the Differential Transform Method, Structures, Volume 28 (2020), p. 923 | DOI:10.1016/j.istruc.2020.09.034
- Evaluation of Three-Point Bending Strength of Thin Silicon Die With a Consideration of Geometric Nonlinearity, IEEE Transactions on Device and Materials Reliability, Volume 19 (2019) no. 4, p. 615 | DOI:10.1109/tdmr.2019.2937988
- Nonclassical axisymmetric bending of circular Mindlin plates with radial force, Meccanica, Volume 54 (2019) no. 10, p. 1623 | DOI:10.1007/s11012-019-01038-8
- Effect of radial reaction force on the bending of circular plates resting on a ring support, International Journal of Mechanical Sciences, Volume 119 (2016), p. 197 | DOI:10.1016/j.ijmecsci.2016.10.014
Cité par 23 documents. Sources : Crossref
Commentaires - Politique