Analytical solution for fixed-end beam subjected to uniform load. (English) Zbl 1144.74345
A bi-harmonic stress function is constructed in this work. Ariy stress function methodology is used to obtain a set of analytical solutions for both ends fixed beams subjected to uniform load. The treatment for fixed-end boundary conditions is the same as that presented by S. P. Timoshenko and J. N. Goodier [Theory of elasticity. 3rd ed. Engineering Societies Monographs. International Student Edition. New York etc.: McGraw-Hill Book Comp.; Tokyo: Kogakusha Company, Ltd. XXIV (1970; Zbl 0266.73008)]. The solutions for propped cantilever beams and cantilever beams are also presented. All of the analytical plane-stress solutions can be obtained for a uniformly loaded isotropic beam with rectangular cross section under different types of classical boundary conditions.
MSC:
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |
Citations:
Zbl 0266.73008References:
| [1] | Ahmed, S.R., Idris, B.M., Uddin, M.W., 1996. Numerical solution of both ends fixed deep beams.Computer & Structures,61(1): 21-29. · Zbl 0900.73929 · doi:10.1016/0045-7949(96)00029-6 |
| [2] | Gere, J.M., Timoshenko, S.P., 1984. Mechanics of Materials. PWS-KENT Publishing Company, Boston. |
| [3] | Jiang, A.M., Ding, H.J., 2005. The analytical solutions for orthotropic cantilever beams (I): Subjected to surfaceforces.Journal of Zhejinag University SCIENCE,6A(2): 126-131. · Zbl 1161.74421 · doi:10.1631/jzus.2005.A0126 |
| [4] | Lekhnitskii, S.G., 1968. Anisotropic Plate. Gordon and Breach, New York. |
| [5] | Timoshenko, S.P., Goodier, J.N., 1970. Theory of Elasticity, 3rd Edition. McGraw Hill, New York. · Zbl 0266.73008 |
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