Research Article
Several Stress Resultant and Deflection Formulas for Euler-Bernoulli Beams under Concentrated and Generalized Power/Sinusoidal Distributed Loads
Abstract
In the
present paper, the transfer matrix method based on the Euler-Bernoulli beam
theory is exploited to originally achieve some exact analytical formulas for
classically supported beams under both the concentrated and generalized power/sinusoidal
distributed loads. A general solution
procedure is also presented to consider different loads and boundary
conditions. Those closed-form formulas can be used in a variety of engineering
applications as well as benchmark solutions.
References
- Young, W.C., Budynas, R.G., Roark’s Formulas for Stress and Strain, Seventh Edition, McGraw-Hill, New York, ISBN 0-07-072542-X, 2002.
- Köktürk, U., Makina Mühendisinin El Kitabı Cilt 1, Nobel Akademik Yayıncılık, ISBN 975927101X, 2005. (in Turkish)
- Miller ve Kirişler, (08.06.2018), http://www.guven-kutay.ch/ozet-konular/06a_miller_kirisler.pdf, 2018. (in Turkish)
- İnan M., The Method of Initial Values and the Carry-Over Matrix in Elastomechanics, ODTÜ Publication, Ankara, No: 20, 1968.
- Arici, M., Granata, M.F., Analysis of curved incrementally launched box concrete bridges using the Transfer Matrix Method, Bridge Structures, 3(3-4),165-181, 2007.
- Arici, M., Granata, M.F., Generalized curved beam on elastic foundation solved by Transfer Matrix Method, Structural Engineering & Mechanics, 40(2), 279-295, 2011.
- Reddy, J.N., Pang, S.D., Nonlocal continuum theories of beams for the analysis of carbon nanotubes, J. Appl. Phys. 103, 023511, 2008.
- Civalek, Ö., Demir, Ç., Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory, Applied Mathematical Modelling, 35, 2053–2067, 2011.
- Tuna, M., Kirca, M., Exact solution of Eringen’s nonlocal integral model for bending of Euler–Bernoulli and Timoshenko beams, Int J Eng Sci, 105, 80–92, 2016.
- Peddieson, J., Buchanan, G.R., McNitt, R.P., Application of nonlocal continuum models to nanotechnology, Int. J. Eng. Sci., 41, 305–312, 2003.
- Karamanli, A., Elastostatic deformation analysis of thick isotropic beams by using different beam theories and a meshless method, International Journal of Engineering Technologies, 2(3), 83-93, 2016.
- Aydoğdu, M., A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration, Physica E, 41, 1651–1655, 2009.
Year 2018,
, 35 - 63, 15.08.2018
Abstract
References
- Young, W.C., Budynas, R.G., Roark’s Formulas for Stress and Strain, Seventh Edition, McGraw-Hill, New York, ISBN 0-07-072542-X, 2002.
- Köktürk, U., Makina Mühendisinin El Kitabı Cilt 1, Nobel Akademik Yayıncılık, ISBN 975927101X, 2005. (in Turkish)
- Miller ve Kirişler, (08.06.2018), http://www.guven-kutay.ch/ozet-konular/06a_miller_kirisler.pdf, 2018. (in Turkish)
- İnan M., The Method of Initial Values and the Carry-Over Matrix in Elastomechanics, ODTÜ Publication, Ankara, No: 20, 1968.
- Arici, M., Granata, M.F., Analysis of curved incrementally launched box concrete bridges using the Transfer Matrix Method, Bridge Structures, 3(3-4),165-181, 2007.
- Arici, M., Granata, M.F., Generalized curved beam on elastic foundation solved by Transfer Matrix Method, Structural Engineering & Mechanics, 40(2), 279-295, 2011.
- Reddy, J.N., Pang, S.D., Nonlocal continuum theories of beams for the analysis of carbon nanotubes, J. Appl. Phys. 103, 023511, 2008.
- Civalek, Ö., Demir, Ç., Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory, Applied Mathematical Modelling, 35, 2053–2067, 2011.
- Tuna, M., Kirca, M., Exact solution of Eringen’s nonlocal integral model for bending of Euler–Bernoulli and Timoshenko beams, Int J Eng Sci, 105, 80–92, 2016.
- Peddieson, J., Buchanan, G.R., McNitt, R.P., Application of nonlocal continuum models to nanotechnology, Int. J. Eng. Sci., 41, 305–312, 2003.
- Karamanli, A., Elastostatic deformation analysis of thick isotropic beams by using different beam theories and a meshless method, International Journal of Engineering Technologies, 2(3), 83-93, 2016.
- Aydoğdu, M., A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration, Physica E, 41, 1651–1655, 2009.
There are 12 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | August 15, 2018 |
| Acceptance Date | June 8, 2018 |
| Published in Issue | Year 2018 |