On Derivation of Timoshenko Beam Stiffness Equation

Force sensor based on discrete optoelectronic components and compliant frames

“…This allows a simplified formulation of the Timoshenko-like model of the FH, and in particular of its stiffness matrix [26]. With reference to Fig.…”

A Linearized Timoshenko Beam Theory in Finite Displacements

“…In order to derive the stiffness equation, we simply follow an FEM procedure. From (8) and (11), the equation of virtual work for bending of the Timoshenko beam can be expressed as f[EIAAA-Pww+GKA(w+A))dx-(Pzkwk+CkAf]k-i=O, (16) where the distributed force is ignored for simplicity. The simplest but sufficient result can be obtained by assuming the 3rd order polynomial for w and constant for y8).…”

How Much Contribution Does the Shear Deformation Have in a Beam Theory?

“…1), can be a candidate for the physical measure of shear deformation. As G2 remains unit on the cross-section, from (2) and 3, is given by cos $ (X, Y)=(1 + e-Yx)/v'1, sin (X, Y)= y//. (6) Note that E12 in (2) or y in ( 5) is a function of X only; i. e. E,2 is uniform in the cross-section, but that in (6 ) is not.…”

“…assumed; i. e. the displacement field (1), follows from the assumption of the uniform distribution of shear in the cross-section,(2), which violates the boundary condition on the lateral surfaces of a beam where no traction exists unless the distributed load is applied on them. In order to compensate this impropriety, the shear coefficient is introduced in small deformation'.…”