Engineering Transactions, 66, 4, pp. 357–373, 2018
10.24423/EngTrans.898.20180809

Analytical Modeling of I-beam as a Sandwich Structure

Krzysztof MAGNUCKI
Institute of Rail Vehicles TABOR
Poland

Jerzy LEWIŃSKI
Institute of Rail Vehicles TABOR
Poland

The paper is devoted to an analytical model of I-beam, with consideration of the shear effect. The model is based on the sandwich beam theory. The field displacements and strains are formulated with consideration of a nonlinear hypothesis of flat cross-section deformation of the beam. The governing differential equations for the I-beam are obtained based on the principle of stationary total potential energy. The shear effect of the beam is illustrated for the threepoint bending case. The analytical solution is compared to FEM numerical calculation. The results of the analysis are presented in Tables and Figures.
Keywords: I-beam; shear deformation; three-point bending; sandwich beam theory
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

Gere J.M., Timoshenko S.P., Mechanics of materials, PWS-KENT Pub. Comp., Boston 1984.

Wang C.M., Reddy J.N., Lee K.H., Shear deformable beams and plates, Elsevier, Amsterdam, Lausanne, New York, Oxford, Tokyo 2000.

Hutchinson J.R., Shear coefficients for Timoshenko beam theory, ASME Journal of Applied Mechanics, 68(1): 87–92, 2001.

Song O., Librescu L., Jeong N-H., Static response of thin-walled composite I-beams loaded at their free-end cross-section: Analytical Solution, Composite Structures, 52(1): 55–65, 2001.

Jung S.N., Lee J-Y., Closed form analysis of thin-walled composite I-Beams considering non-classical effect, Composite Structures, 60(1): 9–17, 2003.

El Fatmi R., Non-uniform warping including the effects of torsion and shear forces, Part I: A general beam theory, International Journal of Solids and Structures, 44(18–19): 5912–5929, 2007.

Romanoff J., Varsta P., Bending response of web-core sandwich plates, Composite Structures, 81(2): 292–302, 2007.

Blaauwendraad J., Shear in structural stability: On the Engesser-Haringx discord, ASME Journal of Applied Mechanics, 77(3): 031005, 2010.

Dong S.B., Alpdogan C., Taciroglu E., Much ado about shear correction factors in Timoshenko beam theory, International Journal of Solids and Structures, 47(13): 1651–1665, 2010.

Shi G., Voyiadjis G.Z., A sixth-order theory of shear deformable beams with variational consistent boundary conditions, ASME Journal of Applied Mechanics, 78(2): 021019, 2010.

Beck A.T., da Silva Jr C.R.A., Timoshenko Versus Euler Beam Theory: Pitfalls of a deterministic approach, Structural Safety, 33(1): 19–25, 2011.

Kim N-I., Shear deformable doubly- and mono-symmetric composite I-beams, International Journal of Mechanical Sciences, 53(1): 31–41, 2011.

Magnucka-Blandzi E., Dynamic stability and static stress state of a sandwich beam with metal foam core using three modified Timoshenko hypothesis, Mechanics of Advanced Materials and Structures, 18(2): 147–158, 2011.

Magnucka-Blandzi E., Mathematical modelling of a rectangular sandwich plate with a metal foam core, Journal of Theoretical and Applied Mechanics, 49(2): 439–455, 2011.

Shi G., Wang X., A constraint on the consistence of transverse shear strain energy in the higher-order shear deformation theories of elastic plates, ASME Journal of Applied Mechanics, 80(4): 044501, 2013.

Li S., Wan Z., Wang X., Homogenized and classical expressions for static bending solutions for functionally graded material Levinson beams, Applied Mathematics and Mechanics – Engl. Ed., 36(7): 895–910, 2015.

Magnucka-Blandzi E., Magnucki K., Wittenbeck L., Mathematical modeling of shearing effect for sandwich beams with sinusoidal corrugated cores, Applied Mathematical Modelling, 39(9): 2796–2808, 2015.

Urbanski A., Analysis of a beam cross-section under coupled actions including transversal shear, International Journal of Solids and Structures, 71: 291–307, 2015.

Magnucki K., Malinowski M., Magnucka-Blandzi E., Lewinski J., Three-point bending of a short beam with symmetrically varying mechanical properties, Composite Structures, 179: 552–557, 2017.

Schulz M., Beam element with a 3D response for shear effects, Journal of Engineering Mechanics, 144(1): 04017149, 2017.




DOI: 10.24423/EngTrans.898.20180809