Statical analysis of elastically and continuously supported helicoidal structures by the transfer and stiffness matrix methods

The behaviour of single and/or continuous and elastically supported helicoidal structures made of elastic and isotropic materials is studied by the stiffness matrix approach based on the transfer matrix method. The Timoshenko beam theory is extended for the case of spatial bars of helicoidal axes taking into account the effect of axial deformations. The compatibility conditions, constitutive relations, and equilibrium equations in terms of resultant forces and moments are combined to yield a system of twelve first-order differential equations. This system is then solved by the transfer matrix method. The element transfer matrix used in the solution is computed by an efficient algorithm upto any desired accuracy. The helicoidal element stiffness matrix and load vector determined by considering the full effects of axial and shear deformations together with continuous elastic supports are exact. The developed procedure coded in Fortran-77 is employed for the solution of any helicoidal spatial systems and planar bars as well. For helicoidal staircases, the significance of both axial and shear deformations and eccentricities existing in wide and shallow sections are also investigated. The results of the herein developed procedure as applied to some typical examples presented in literature compare favourably with those of the latter. © 1993