In regions, described as plastic hinge zones, in beams and columns, tensile yielding of the reinforcement through flexural action can occur in severe earthquakes. Where the beams and columns are lightly loaded, axially, member elongation can occur. Test results show that axial extensions of the order of several percent of the member depth may be expected. This deformation, which is ignored in current design practice, can have a major influence on the distribution of forces in a structure and its ability to survive without collapse. This paper describes the way in which elongation develops in plastic hinge zones together with the form of load deflection characteristics associated with the development of different types of plastic hinge zone.
The results of several thousands of inelastic time history analyses, which have been made on single degree of freedom structures to assess P-delta effects induced in earthquakes, are reviewed. The principal factors influencing P-delta actions are shown to be the ductility, the duration of the severe ground motion, the level of damping and the period of the structure. A method of designing for P-delta effects for single degree of freedom structures is presented. A limited number of analyses of multi-storey frames and walls indicate that the approach may be used for multi-storey structures. This paper gives background information on the P-delta method of analysis given in an appendix to the commentary of the proposed loading code.
Major changes have occurred over the last six decades in New Zealand design codes for seismic resistance of structures. This paper describes the changes in the required design strengths, stiffness levels and capacity design provisions with particular reference to buildings where the lateral force resistance is provided by reinforced concrete moment resisting frames. It is shown that simple comparisons of response spectra and limiting inter-storey drifts can give misleading conclusions regarding relative strength and stiffness requirements unless allowance is made for many other interacting factors. To illustrate this, minimum design requirements defined in codes (or standards) over the last six decades are compared with the corresponding 2009 design requirements for regular buildings in which the lateral force resistance is provided by moment resisting frames. The approach that is described can be applied to other forms of structure. The paper is intended to provide background information for engineers planning to assess the need for seismic retrofit of existing buildings and to show the different factors which should to be considered in assessing existing structures against current design criteria.
Continuous recordings of the instantaneous frequency of the strongest received signal component of WWV‐20 (4000 km distant) were made for a period of 30 days in the spring of 1960 at Palo Alto, California. On normal days regular morning and evening frequency shifts, amounting to roughly 1 part in 107, were observed. The received frequency was higher than normal in the morning and lower than normal at night. On magnetically disturbed days, the maximum observed frequency shifts probably amounted to 3 parts in 107, a figure frequently cited by others [Essen, 1935; Booth and Gregory, 1948; Jackson, 1952; Lincoln, 1960]. On days when only the one‐hop mode could propagate over the path, the observed frequency shifts were considerably smaller than when the two‐hop mode was present. This circumstance may be of practical interest. On many days short‐enduring upward frequency shifts amounting to as much as 3 cps, 1.5 parts in 107, were observed. The upward portion of these shifts typically took place in 1 to several minutes; they were followed by small downward shifts lasting several times as long. It is tentatively suggested that these shifts are caused by entry into the ionosphere of the downward‐moving clouds of ionization first identified on ionograms by Wells, Watts, and George [1946] and subsequently studied by Bibl [1952]. During magnetically disturbed days, occasional periods were found during which changes in the instantaneous frequency of WWV‐20 seemed to correlate reasonably well with changes in the earth's total magnetic field as measured at Palo Alto.
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.
To study the behaviour of multistorey building frames under gravity and severe earthquake conditions a reinforced concrete portal frame was constructed. The beam was subjected to constant vertical loads while a cyclic lateral load was applied to the unit. Negative moment plastic hinges formed at the column faces while the positive moment hinges were located in the span. The rotations generated by each inelastic displacement accumulated. This placed high rotational demands on the plastic hinges, which reduced the overall ductile behaviour compared with that observed in typical beam-column sub-assembly tests. The high rotations caused the beam to grow in length.
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