Mathematical Modeling
Vol. 5 (2021), Issue 4, pg(s) 120-123

THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

Consistent Presentation of the Beam Deflection Theory Including Shear Correction

  • 1 Institute of Mechanics - Bulgarian Academy of Sciences

Abstract

This article explains a mathematically consistent approach for solving the equations of Timoshenko’s beam theory for statically loaded beams. Theoretic sections 3.4 – 3.5 give a good description of the shear deformation and the primary approach for calculating deflections of beams under bending, taking into account both causes for deflection: bending moment and shear force. Values for the shear correction factor are discussed in section 4. This work was started to check the validity of an equation for deflection of a symmetrically loaded short rectangular beam with span/height ratio = 3 under four-point bending with upper-span/span ratio = 1/3. The exact solution is not presented here, but we can confirm that the presented theory, when applied for the mentioned loading scheme, leads to thi s equation using a shear correction factor k = 5/6.

Keywords

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