Elastic Stability of Concrete Beam-Columns

In the first part of this paper, elastostatic stability of cracked conservative flanged concrete beam-columns has been analyzed. Using the derived expression for the lateral stiffness under constant axial force, their elastodynamic stability is investigated in this second part. As expected, the instantaneous values of the stiffness and the damping coefficients of the lumped-mass underdamped SDOF nonlinear structures are found to depend upon the vibration amplitude. The natural frequency has been found to vanish at the two critical axial loads defined in the first part. For axial load exceeding the second critical value, the concrete beam-columns in the second equilibrium state are shown to exhibit loss of dynamic stability by divergence. Depending upon the initial conditions, the phase plane has been partitioned into dynamically stable and unstable regions. Under harmonic excitations, the nonlinear dynamical systems exhibit subharmonic resonances and jump phenomena. Loss of dynamic stability has been predicted for some ranges of damping ratio as well as of peak sinusoidal force and forcing frequency. Sensitivity of dynamic stability to the initial conditions and the sense of the peak sinusoidal force have also been predicted. The theoretical significance and the methodology adopted in this paper are also discussed.