TY - JOUR
T1 - Softening-induced dynamic localization instability
T2 - Seismic damage in frames
AU - Bažant, Zdeněk P.
AU - Jirásek, Milan
PY - 1996/12
Y1 - 1996/12
N2 - This paper analyzes dynamic localization of damage in structures with softening inelastic hinges and studies implications for the seismic response of reinforced concrete or steel frames of buildings or bridges. First, the theory of limit points and bifurcation of the symmetric equilibrium path due to localization of softening damage is reviewed. It is proven that, near the state of static bifurcation or near the static limit point, the primary (symmetric) path of dynamic response or periodic response temporarily develops Liapunov-type dynamic instability such that imperfections representing deviations from the primary path grow exponentially or linearly while damage in the frame localizes into fewer softening hinges. The implication for seismic loading is that the kinetic energy of the structure must be absorbed by fewer hinges, which means faster collapse. The dynamic localizations are demonstrated by exact analytical solutions of torsional rotation of the floor of a symmetric and symmetrically excited frame, and of horizontal shear excitation of a building column. Static bifurcations with localization are also demonstrated for a portal frame, a multibay frame, and a multibay-multistory frame. The widely used simplification of a structure as a single-degree-of-freedom oscillator becomes invalid after the static bifurcation state is passed.
AB - This paper analyzes dynamic localization of damage in structures with softening inelastic hinges and studies implications for the seismic response of reinforced concrete or steel frames of buildings or bridges. First, the theory of limit points and bifurcation of the symmetric equilibrium path due to localization of softening damage is reviewed. It is proven that, near the state of static bifurcation or near the static limit point, the primary (symmetric) path of dynamic response or periodic response temporarily develops Liapunov-type dynamic instability such that imperfections representing deviations from the primary path grow exponentially or linearly while damage in the frame localizes into fewer softening hinges. The implication for seismic loading is that the kinetic energy of the structure must be absorbed by fewer hinges, which means faster collapse. The dynamic localizations are demonstrated by exact analytical solutions of torsional rotation of the floor of a symmetric and symmetrically excited frame, and of horizontal shear excitation of a building column. Static bifurcations with localization are also demonstrated for a portal frame, a multibay frame, and a multibay-multistory frame. The widely used simplification of a structure as a single-degree-of-freedom oscillator becomes invalid after the static bifurcation state is passed.
UR - http://www.scopus.com/inward/record.url?scp=0000719280&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0000719280&partnerID=8YFLogxK
U2 - 10.1061/(ASCE)0733-9399(1996)122:12(1149)
DO - 10.1061/(ASCE)0733-9399(1996)122:12(1149)
M3 - Article
AN - SCOPUS:0000719280
VL - 122
SP - 1149
EP - 1158
JO - Journal of Engineering Mechanics - ASCE
JF - Journal of Engineering Mechanics - ASCE
SN - 0733-9399
IS - 12
ER -