Combined Continua and Lumped Parameter Modeling for Nonlinear Response of Structural Frames to Impulsive Ground Shock

The response of a beam-column frame to impulsive ground shock, such as those induced by an underground explosion, has characteristics of both impact and natural earthquake responses. The critical effects may be governed by the dynamic response of individual elements as continuous mass systems, while to a certain extent the global vibration (as of lumped-mass systems) may also be involved. To incorporate both dynamic features, the present study proposes a combined continua and lumped parameter (CCLP) model, which consists of the basic beam-column element with distributed stiffness and mass, along with concentrated mass-springs at element ends to form the reduced dynamic system. To take into account of the shear deformation and rotary inertia which become important in the impulsive response, the governing equations are formulated based on the Timoshenko beam theory. The nonlinearities are described through three mechanisms, namely the distributed nonlinear flexural and diagonal shear behavior, and the direct sliding shear at the member ends. A generic restoring force model is adopted to describe the hysteretic behavior. Comparison with a scaled model test demonstrates that the CCLP model is capable of representing the primary dynamic features in a frame structure under impulsive ground shock. Extended parametric studies indicate that, with increase of the ground shock frequency, the failure tends to become shear dominant. For ground shocks of frequency at $20–30\mathrm{Hz}$ and above, the failure in a reinforced concrete column will require a peak ground velocity (PGV) on the order of $3\mathrm{m}∕\mathrm{s}$ , whereas failure in a beam would occur at PGV of about $1.5\mathrm{m}∕\mathrm{s}$ .