Non-dimensional pressure–impulse diagrams for blast-loaded reinforced concrete beam columns referred to different failure modes

The pressure–impulse diagram is commonly used to assess the damage level of structural components under explosion. Non-dimensional pressure–impulse diagrams referred to different failure modes was obtained using a new methodology in this article. Nine non-dimensional key parameters were first proposed on basis of the Euler beam theory. Considering the shear failure, an elastic–plastic method to calculate the dynamic response of reinforced concrete beam columns was then proposed for different failure modes. Three failure categories, for example, bending failure, shear failure, and combined shear and bending failure, were considered. The threshold between the three failure modes was determined using non-dimensional pressure–impulse curves. A systematic parametric study was conducted to investigate the effects of different non-dimensional parameters on the dynamic response and the failure modes of reinforced concrete beam column. Parametric study shows that the nine non-dimensional key parameters are sufficient to calculate the dynamic response of reinforced concrete beam columns. Moreover, present study shows that the tangent modulus of direct shear stress–slip relation has a great influence on the failure modes. Beam columns with a smaller tangent modulus are more likely to generate combined shear and bending failure mode.

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.

Elastic Stability of Concrete Beam-Columns

Following the empirical-computational methodology, the contemporary investigations deal with inelastic stability and dynamics of concrete beam-columns. Even under service loads, the concrete structures exhibit physical nonlinearity due to presence of axio-flexural cracks. The objective of the present paper is to analyze the static and dynamic stability of conservative physically nonlinear fully cracked flanged concrete beam–columns. In this paper, using proper reference frames, analytical expressions are developed for the lateral displacement and stiffness of a flanged concrete cantilever under axial compressive and lateral forces. Two critical values of both the axial and lateral loads are identified. For constant lateral force smaller than its first critical value, the concrete beam–columns exhibit brittle buckling mode. Higher lateral forces lesser than the second critical value introduce alternate stable and unstable domains with increase in axial force. The lateral stiffness is predicted to vanish when the axial loads reach the critical values and when the limiting displacement is reached for axial load exceeding its second critical value. The load-space is partitioned into stable and unstable regions. Accessibility of these equilibrium states in the load space has been investigated. Such distinguishing aspects of the predicted behavior of elastic concrete beam–columns are discussed. Their dynamic stability is investigated in second part of the paper.