Much ado about shear correction factors in Timoshenko beam theory

• DOI: 10.1016/j.ijsolstr.2010.02.018
• Publication Date: 2010-03-02T09:47:41Z
• Authors: S.B. Dong; C. Alpdogan; E. Taciroglu
• Keywords: Saint-Venant solutions; Materials Science(all); 0203 mechanical engineering; Mechanics of Materials; Semi-analytic finite elements; Mechanical Engineering; Modelling and Simulation; Applied Mathematics; 02 engineering and technology; Condensed Matter Physics; 0210 nano-technology; Timoshenko beam; Shear correction factors

AbstractMany shear correction factors have appeared since the inception of Timoshenko beam theory in 1921. While rational bases for them have been offered, there continues to be some reluctance to their full acceptance because the explanations are not totally convincing and their efficacies have not been comprehensively evaluated over a range of application. Herein, three-dimensional static and dynamic information and results for a beam of general (both symmetric and non-symmetric) cross-section are brought to bear on these issues. Only homogeneous, isotropic beams are considered. Semi-analytical finite element (SAFE) computer codes provide static and dynamic response data for our purposes. Greater clarification of issues relating to the bases for shear correction factors can be seen. Also, comparisons of numerical results with Timoshenko beam data will show the effectiveness of these factors beyond the range of application of elementary (Bernoulli–Euler) theory.An issue concerning principal shear axes arose in the definition of shear correction factors for non-symmetric cross-sections. In this method, expressions for the shear energies of two transverse forces applied on the cross-section by beam and three-dimensional elasticity theories are equated to determine the shear correction factors. This led to the necessity for principal shear axes. We will argue against this concept and show that when two forces are applied simultaneously to a cross-section, it leads to an inconsistency. Only one force should be used at a time, and two sets of calculations are needed to establish the shear correction factors for a non-symmetrical cross-section.