Abstract
In a major earthquake the beams in moment resisting frames may develop either reversing or unidirectional plastic hinges. The form of plastic hinge depends upon the ratio of the moments induced by the gravity loading to those induced by the seismic actions. Where this ratio is low the plastic hinges form at the ends of the beams and the sign of the inelastic rotation changes with the direction of sway. These are reversing plastic hinges, and the magnitude of the rotation that they sustained is closely related to the inter-storey displacement. However, when the moment ratio exceeds a certain critical value, unidirectional plastic hinges may form. In this case negative moment plastic hinges develop at the column faces and the positive moment plastic hinges form in the beam spans. As the earthquake progresses the positive and negative inelastic rotations accumulate in their respective zones so that peak values are always sustained at the end of the earthquake. With this type of plastic hinge no simple relationship exists between inter-storey drift and inelastic rotation.
 Several series of time history analyses have been made to assess the relative magnitudes of inelastic rotation that are imposed on the two forms of plastic hinge. It is found that with design level earthquakes typically the unidirectional plastic hinge is required to sustain 21/ 2 to 4 times the rotation imposed on reversing plastic hinges, with the curvature ductilities ranging up to 140. These values are appreciably in excess of the values measured in tests using standard details. This indicates that in structures where unidirectional plastic hinges may form, the design displacement ductility and or the allowable inter-storey drift should be reduced below the maximum values currently permitted in the New Zealand codes. The problems associated with the formation of unidirectional plastic hinges can be avoided by adding positive moment flexural reinforcement in the mid regions of the beams. By this means the potential positive moment plastic hinges can be restricted to the beam ends.
Highlights
With current design practice, moment resisting multi-storey frame structures are generally designed to perform in a ductile manner in a major earthquake
When the seismic induced shear is greater than the shear resulting from the gravity loading, reversing plastic hinges develop as illustrated in Fig. la, with the maximum positive and negative bending moments in the beams occurring at the column faces
Two forms of plastic hinge can form in the beams of ductile frames in a major earthquake
Summary
Moment resisting multi-storey frame structures are generally designed to perform in a ductile manner in a major earthquake. The required level of ductility is achieved by ensuring that a ductile beam sway mechanism forms in preference to a column sway mechanism This results in the majority of plastic hinges forming in the beams and it is the behaviour of these that very largely determines the dynamic performance of the structure. Two different forms of plastic hinge may develop in the beams of a frame subjected to seismic actions Between the two plastic hinges in the beam the member remains elastic and essentially straight With this form of plastic hinge the inelastic rotation that is sustained is closely associated with the inter-storey displacement and as such it can both increase and decrease as the earthquake progresses
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