ABSTRACT
In 1920, Hencky (1920) proposed that in buckling of beams, the continuum structure may be replaced by a structural model comprising rigid segments connected by frictionless hinges with elastic rotational springs that are capable of resisting elastic deformation. In the literature, this structural model has now been referred to as a Hencky “bar chain”. When Salvadori (1951) published a paper showing how one can compute the buckling loads of beams and plates using the finite difference method, Silverman (1951) promptly wrote a discussion note on Salvadori’s paper. Silverman pointed out the interesting analogy between the first order central finite difference formulation and the physical Hencky’s bar chain model if one sets the segmental bar length to be the same and the internal rotational spring constant to be equal to EI/a where EI is the beam flexural rigidity and a is the length of the rigid segment. When it comes to an elastically restrained end, the rotational spring constant and lateral springs constant have to be calibrated to make the central finite difference formulation analogous to the Hencky bar-chain model. This paper investigates the expressions for the end spring restraints of the Hencky bar-chain model with the aid of the central finite difference beam model for beam buckling and vibration.
