In this article, there has been studied the bending state of a reinforced concrete beam with a variable cross-sectional height along its length that rests along its entire length on a brick wall. The beam is under the action of arbitrarily located concentrated forces. The study has been performed on the basis of the original inhomogeneous differential equation of the 4th order, taking into account the external load and the bedding coefficients of the elastic foundation. Using the finite difference method, typical resolving finite difference equations have been obtained. A study of the influence of the degree of elasticity of the base, with a change in the value of the bed coefficients and elasticity parameters, was conducted. The results confirm the reliability of theoretical and practical calculations. Given theoretical provisions and applied results can be used in scientific research in the field of mechanics of a deformable solid body, as well as in practical design.
1.
Chithra, J.; Nagarajan, P.;
Sajith, A. (2018). Simplified method for the transverse bending analysis of
twin celled concrete box girder bridges, IOP Conference Series: Materials
Science and Engineering, vol. 330, no. 1, doi:10.1088/1757-899X/330/1/012118
2.
Yayli, M. Ö. (2018). Buckling
analysis of Euler columns embedded in an elastic medium with general elastic
boundary conditions, Mechanics Based Design of Structures and Machines, vol.
46, no. 1, 110–122, doi:10.1080/15397734.2017.1292142
3.
Civalek, Ö.; Uzun, B.; Yaylı,
M. Ö.; Akgöz, B. (2020). Size-dependent transverse and longitudinal vibrations
of embedded carbon and silica carbide nanotubes by nonlocal finite element
method, European Physical Journal Plus, vol. 135, no. 4,
doi:10.1140/EPJP/S13360-020-00385-W
4.
Wstawska, I.; Magnucki, K.;
Kędzia, P. (2022). Stability of three-layered beam on elastic foundation,
Thin-Walled Structures, vol. 175, doi:10.1016/J.TWS.2022.109208
5.
Soltani, M. (2020). Finite
element modeling for buckling analysis of tapered axially functionally graded
timoshenko beam on elastic foundation, Mechanics of Advanced Composite
Structures, vol. 7, no. 2, 203–218, doi:10.22075/MACS.2020.18591.1223
6.
Wang, J.; Xia, G. (2020).
Vibration analysis for a modified Timoshenko beam on Winkler elastic
foundation, Zhendong Yu Chongji/Journal of Vibration and Shock, vol. 39, no. 3,
30–37, doi:10.13465/J.CNKI.JVS.2020.03.005
7.
Wang,
Z. N.; Zhang, Y. H. (2020). Calculation methods of
transverse bending moment of box girder considering the distortional influence,
Jisuan Lixue Xuebao/Chinese Journal of Computational Mechanics, vol. 37, no. 2,
151–158, doi:10.7511/JSLX20190507001
8.
Tan, Z. X.; Liu, X.; Yi, W. J.
(2016). Finite element analysis of RC deep beams with openings and researching
of the design method, Jisuan Lixue Xuebao/Chinese Journal of Computational
Mechanics, vol. 33, no. 3, 313–320, doi:10.7511/JSLX201603006
9.
Banichuk, N.; Barsuk, A.;
Ivanova, S.; Makeev, E.; Neittaanmäki, P.; Tuovinen, T. (2018). Analysis and
optimization against buckling of beams interacting with elastic foundation,
vol. 46, no. 5, 615–633, doi:10.1080/15397734.2017.1377619
10.
Onu, G. (2008). Finite Elements
on Generalized Elastic Foundation in Timoshenko Beam Theory, Journal of
Engineering Mechanics, vol. 134, no. 9, 763–776,
doi:10.1061/(ASCE)0733-9399(2008)134:9(763)
11.
He, F. S.; Zhong, G. L. (2005).
Bending of beams with variable section on bi-parameter elastic foundations,
Xi’an Jianzhu Keji Daxue Xuebao/Journal of Xi’an University of Architecture and
Technology, vol. 37, no. 2, 251–254
12.
Akhazhanov, S.; Omarbekova, N.;
Mergenbekova, A.; Zhunussova, G.; Abdykeshova, D. (2020). Analytical solution
of beams on elastic foundation, International Journal of GEOMATE, vol. 19, no.
73, 193–200, doi:10.21660/2020.73.51487
13.
Rao, S. S. (2019). Vibration of
continuous systems, John Wiley & Sons, Inc., Hoboken, New Jersey.
14.
Schäfer, M. (2006).
Computational engineering - Introduction to numerical methods, Springer Berlin,
Heidelberg.
15.
Appelö,
D.; Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W. (2012). Numerical methods for solid mechanics on overlapping grids: Linear
elasticity, Journal of Computational Physics, vol. 231, no. 18, 6012–6050.
doi:10.1016/j.jcp.2012.04.008
16.
Sorochan, E. A. (1985).
Foundations, Foundations and Underground Structures (in Russian),
Gosstroyizdat, Moscow.
17.
Rausch, E. (1968). Machine
Foundations and Other Dynamically Stressed Building Structures (in German) (2nd
ed.), VDI Verlag, Dusseldorf.
18.
Bosakov, S. V. (2003).
Application of B. N. Zhemochkin’s Method to Analysis of a Bendable Slab on an
Elastic Bed, Soil Mechanics and Foundation Engineering 2003 40:2, vol. 40, no.
2, 48–54, doi:10.1023/A:1024484001627