Drift Limits Research Articles

Drift-Dependent Confinement Requirements for Reinforced Concrete Columns Under Cyclic Loading

This paper examines the influence of transverse reinforcement and axial load on the drift limit of rectangular columns using test results from 184 specimens subjected to cyclic loading. Columns within the set were selected to have shear span-to-depth ratios of at least equal to 2.5 so that truss action would be the main mechanism of shear resistance and the deformation component related to shear would be small compared with that related to flexure. Expressions relating the limiting drift ratio to the axial load ratio and the amount of confining reinforcement were evaluated. Equations indicating the amount of confining reinforcement required to achieve a given limiting drift ratio for reinforced concrete columns in regions of moderate and high seismicity are proposed.

Rehabilitation of a 1985 Steel Moment-Frame Building

A 1985 steel moment frame is seismically upgraded using passive energy dissipation, without adding stiffness to the system. The design and analysis techniques for sizing the Velocity Braces™ and their impact on the demand capacity ratios are reviewed. The structure was built in the San Francisco Bay Area in compliance with the 1985 Uniform Building Code (UBC). The moment frame contains the classic pre-Northridge nonductile moment connection, complete with weld backup bars left attached. Nonlinear time-history analysis procedures were implemented to verify the demand capacity ratios at the critical beam-column connections. Flexural demand capacity ratios of .6 achieve elastic behavior in the design basis earthquake with R=1.0. The response spectra of the time history chosen for design exceed the requirements of the 1997 UBC Zone 4. Torsional response to earthquake excitation is minimized by strategic placement of nonlinear viscous dampers. Nonlinear dampers that reduce the flexural demand on joints and control interstory drift without inelastic excursions of the beam flanges are achieved. Floor spectral accelerations and maximum drift limits are reduced to be consistent with immediate occupancy performance. The damper driver mechanism, being velocity driven, reduces moment frame demands and allows flexibility in configuration.

Background information for some of the proposed earthquake design provisions for the 2005 edition of the National Building Code of Canada

There are many changes proposed for the Earthquake Design Provisions of the 2005 edition of the National Building Code of Canada (NBCC). Among them are requirements for complete load paths, separation of stiff nonstructural elements, and the introduction of definitions of irregular structures and special design requirements associated with these irregularities. A new requirement for direction of loading is introduced, along with requirements for elements common to more than one lateral load resisting system. The effects of displacements are emphasized throughout the document, and revised provisions for drift limits are proposed. Revisions to the importance factor that integrate it into the proposed revised format for Part 4, Structural design, of the NBCC are given. Background information is presented.Key words: load path importance factor, irregular structures, direction of loading, special requirements, drift limits.

Discrete Optimum Design of Steel Frames by Genetic Algorithm

This paper presents genetic based algorithm for the optimum design of multistorey steel frames with sidesway subjected to multiple loading cases. The design method obtains a frame with the least weight by selecting appropriate sections for beams and columns from the British standard for universal beam and column sections. The member grouping is allowed so that the same section can be adopted for each group. The serviceability design constraints include the drift limit of overall height of the frame / 300 and interstorey drift limit of storey height / 300 as specified by BS 5950. The combined strength constraints are considered for beam-columns which are subjected to axial force and bending moments which take into consideration the lateral torsional buckling of frame members. The effective lengths for columns are obtained from the solution of nonlinear equation, which is used to produce Jackson and Moreland nomographs. The use of BS 5950 also necessitates to find out the classification of each universal beam or column section selected for frame members. The design algorithm carries out this process automatically following the steps given in BS 5950 before it computes the design capacities of each frame member. The design examples considered have shown that genetic algorithm provides an efficient tool for the practicing designers in designing tall steel frames.

Seismic analysis of MR steel frames based on refined hysteretic models of connections

Evaluation of seismic performance of moment-resisting (MR) steel frames is usually carried out assuming the elastic-perfectly-plastic type of hysteresis model for plastic zones (in particular for beam-to-column connections). This type of model is associated with a conventional available ductility, giving an indication of the maximum deformation beyond which strength degradation is likely to occur. This methodology leads to conservative results and the elastic-perfectly-plastic type of hysteresis model is certainly adequate in obtaining reliable information on deformation when the above ductility limits are not exceeded. However, the safety of the frame at ‘collapse’ remains unknown. The analyses presented in this paper show that safety margins against global collapse of the structure can be predicted only by considering more realistic hysteresis behaviour, i.e. using mathematical models able to take account of strength degradation and pinching phenomena. Moreover, it is shown that the design of conventional steel building systems according to the European seismic code may lead to over-resistant structures, due to the limitation on inter-storey drift angles for non-structural damage control under frequent earthquakes. It is also noticed that this result is inevitable, owing to the indications provided by Eurocode 8 in terms of both prescribed inter-storey drift limits and assumed base shear-force demand under frequent earthquakes.

Loch Lomond Stadial glaciers in the Aran and Arenig Mountains, North Wales, Great Britain

AbstractGeomorphological evidence for four former local glaciers has been mapped in the Aran and Arenig Mountains, North Wales. Former glacial extent was deduced from the distribution and assemblage of end and lateral moraines, hummocky moraine, boulder limits, drift limits and periglacial trimlines. Comparison of infilled lake sediment stratigraphies inside and outside of the former glacier limits suggests a Loch Lomond Stadial (Late Devensian) age of the former glaciers (c. 12.9–11.5 cal. ka BP). This finding is also supported by periglacial–landform contrasts between the land inside and outside of the glacier limits. Reconstruction of the four glaciers illustrates a mean equilibrium line altitude (ELA) of c. 504 m. From the reconstructed ELAs and the combination of precipitation and snowblow input for total accumulation, by analogy with Norwegian glaciers, a mean sea‐level July temperature is calculated at 8.4°C. Copyright © 2002 John Wiley & Sons, Ltd.

Inelastic displacement-based design approach of R/C building structures in seismic regions

A two-level displacement-based design procedure is developed. To obtain the displacement demands, elastic spectra for occasional earthquakes and inelastic spectra for rare earthquakes are used. Minimum global stiffness and strength to be supplied to the structure are based on specified maximum permissible drift limits and on the condition that the structure responds within the elastic range for occasional earthquakes. The performance of the structure may be assessed by an inelastic push-over analysis to the required displacement and the evaluation of damage indices. The approach is applied to the design of a five-story reinforced concrete coupled wall structure located in the most hazardous seismic region of Argentina. The inelastic dynamic response of the structure subjected to real and artificially generated acceleration time histories is also analyzed. Finally, advantages and limitations of the proposed procedure from the conceptual point of view and practical application are discussed.

Seismic Behavior of 3D Steel Moment Frame with Biaxial Columns

Three-dimensional nonlinear dynamic time-history analyses of a three-story steel moment-resisting frame designed according to the Uniform Building Code for Los Angeles seismicity were carried out. Beams in both directions had moment connections to the hollow rectangular columns. Code drift limits, rather than code considerations for bidirectional horizontal shaking, governed the member sizes. It was found that design level shaking caused the structure to exceed story yield drifts in both directions simultaneously and significant column yielding occurred above the base. Shaking in the direction orthogonal to the main shaking direction increased drifts in the main shaking direction by 46 and 64% for the design level and near-fault records, respectively, indicating that 2D analyses would not estimate the 3D response well. Also, maximum horizontal seismic components of axial force in the corner columns and side columns were 4.87 and 5.30 times the code estimations, respectively. It was shown that by increasing the column strength above the present code levels, that drifts during near-fault shaking were significantly decreased. A methodology to encourage strong-column weak-beam behavior, and to more realistically estimate the column axial forces during design level shaking is described. Building structures in seismic zones in the United States have traditionally been designed to resist lateral force with seismic frames. Other frames, referred to as gravity frames, are designed to resist gravity forces only. This design ap- proach, with separate seismic and gravity frames, requires only a few expensive moment connections, the load path is easy to follow, and 2D frame analyses may be used to model 3D frame behavior. However, as a result of the 1994 Northridge earth- quake, fracture occurred at many welded beam-column con- nections in these moment-resisting steel seismic frames (Yang and Popov 1995). The occurrence of fracture was influenced by a large number of factors, including the use of large mem- ber sizes and large welds. The lack of redundancy in these frames (Roeder 1997) and the possibility of yield in gravity columns (Mattheis 1998) are also of concern. An alternative design method in which structures are de- signed as a 3D seismic frame with beams connected to the columns, with moment connections in both directions, has some advantages. It increases the redundancy, no columns are designed to carry gravity force only, and beam and weld sizes are smaller. While many more seismic connections are re- quired, all members contribute to the frame lateral stiffness and strength allowing drift limits to be met with less material volume. However, the possibility of undesirable behavior due to significant column bidirectional loading effects should be considered. A brief summary of considerations for column bi- directional loading effects in 3D steel moment-resisting frames due to bidirectional ground shaking is given herein. The Uniform Building Code (UBC) (ICBO 1997) states that bidirectional orthogonal shaking effects must be considered if a column of a structure forms part of two or more intersecting lateral-force-resisting systems and that ''the requirement that orthogonal effects be considered may be satisfied by designing such elements for 100% of the prescribed design seismic forces in one direction plus 30% of the prescribed design seis- mic forces in the perpendicular direction. The combination re- quiring the greater component strength shall be used for de- sign. Alternatively, the effects of the two orthogonal directions may be combined on a Square Root of the Sum of the Squares (SRSS) basis.'' (ICBO 1997). The SRSS procedure (Clough and Penzien 1993) is based on the assumption that superpo- sition of the actions due to loading in each direction indepen- dently may be combined to obtain the total response. Phase incoherency of response, which may result from ground mo- tions in each direction not being in-phase or from significantly different response periods in each direction, is also assumed. The 30% rule (ICBO 1997) is based on the following con- siderations (Mattheis 1998; Tagawa 2000) following the rea- soning of Clough and Penzien (1993). If the ratio of the re- sponse due to y-direction shaking divided by that due to x-direction shaking of equal magnitude is B, and if the shaking magnitude in the y-direction is a of that in the orthogonal x-direction, then the response due to y-direction shaking, R y, is related to that due to x-direction shaking, Rx ,a s

Measurement of carbon disulfide anion diffusion in a TPC

A Negative Ion Time Projection Chamber was used to measure the field dependence of lateral and longitudinal diffusion for CS 2 anions drifting in mixtures of CS 2 and Ar at 40 Torr . Ion drift velocities and limits on the capture distance for electrons as a function of field and gas mixture are also reported.

Proportioning of Earthquake-Resistant RC Building Structures

A simple and efficient method is presented for proportioning of regular, moderate-rise reinforced concrete building structures. The method differs from conventional procedures in that member sizes are selected based on the demand defined by the displacement spectrum and criteria specified in relation to drift response. The maximum mean drift, or average distortion over the total height, is limited to reduce the expected damage to the structure. A series of analytical reinforced concrete frames are proportioned and tested using a suite of ground motions. Results of the analyses indicated that maximum displacement responses of the proportional frames were within the specified drift limit when a maximum-allowable period criterion was satisfied.

Direct displacement-based seismic design of concrete buildings

A seismic design procedure is developed to enable concrete buildings to be designed to achieve a specified acceptable level of damage under the design earthquake. The acceptable limit is defined as a displacement profile related to limit material strains or code specified drift limits. In this procedure, the elastic properties, including initial stiffness, strength and period, are the end product of the design rather than the starting point. It is shown that the procedure is simple to apply, and results in significant differences from the more conventional force-based procedure. Designs for multi-storey frame and wall buildings are presented, and target displacements are compared with results from inelastic time-history analysis.

Seismic Behavior of Composite RCS Frame Systems

This paper presents the results of an experimental investigation into the seismic performance of a composite moment resisting frame system that consists of reinforced concrete columns (with an embedded steel shape for erection purposes) and composite steel beam-reinforced concrete slab sections. Quasi-static reversed cyclic loading was performed on six two-thirds-scale subassemblage specimens. Various detailing options were evaluated to provide full moment connection in both orthogonal framing directions at the beam-column joints. With appropriate joint detailing, specimens exhibited a desirable beam plastic hinge mechanism with stable hysteretic response. Composite beam sections maintained near full composite behavior beyond code based drift limits with good energy dissipation characteristics and were able to undergo large plastic rotation magnitudes. This framing system may represent a viable alternative for low-to-mid-rise structures in high seismic risk zones.

Regional geochemical reconnaissance of the Cordillera Occidental of Ecuador: economic and environmental applications

A regional geochemical reconnaissance survey of the Cordillera Occidental of Ecuador was initiated in 1995 as a sub-component of a wider Mining Development and Environmental Control Technical Assistance Project (PRODEMINCA) in Ecuador. The 36,000 km 2 survey area encompasses oceanic and continental-margin volcano-sedimentary terranes with known occurrences of porphyry-style Cu-Mo, exhalative massive sulphide, epithermal Au and mesothermal polymetallic mineralisation. A survey sample medium of <177 μm stream sediments was selected following an orientation study in the vicinity of known porphyry Cu mineralisation. In the 2–4°S sector of the Cordillera Occidental for which data are presented, 4850 drainage samples were collected at an average density of 1 per 2.57 km 2. All were analysed for 36 major and trace elements (Au, Ag, Cu, Pb, Zn, Mo, Ni, Co, Cd, Bi, As, Sb, Fe, Hg, Mn, Te, Ba, Cr, V, Sn, W, La, Al, Mg, Ca, Na, K, Sr, Y, Ga, Li, Nb, Sc, Ta, Ti, Zr). A stringent quality-control procedure included the systematic analysis of certified reference samples, field duplicates and replicates, data for which were used to calculate analytical precision, temporal drift and practical detection limits. Results for this part of the cordillera highlight the contrasting lithogeochemical signatures of the ocean-floor basalt terrane (Pallatanga Unit), the island-arc terrane of the Macuchi Unit, the continental volcanics of the Saraguro Group and the acid and intermediate lavas extruded from the Late Miocene to the Quaternary. Regional geochemical images for Au and associated pathfinder elements are dominated by anomalies relating to known mines and prospects. New exploration targets, often inconspicuous at the regional scale, have however been identified through the normalisation of data for individual lithological units against their respective geochemical backgrounds. In addition to mineral exploration, the drainage geochemical dataset for the Cordillera Occidental provides an unparalleled environmental baseline against which the impacts of future anthropogenic activities (including mining) may be assessed. A basis for the formulation of pragmatic sediment quality criteria and for the identification of natural geochemical hazards is also provided.

Stability of Solutions of Parabolic PDEs with Random Drift and Viscosity Limit

Let u α be the solution of the Ito stochastic parabolic Cauchy problem $\partial u/\partial t-L_\a u = \xi \cdot \nabla u, u\v_{t=0} = f$ , where ξ is a space—time noise. We prove that u α depends continuously on α , when the coefficients in L α converge to those in L 0 . This result is used to study the diffusion limit for the Cauchy problem in the Stratonovich sense: when the coefficients of L α tend to 0 the corresponding solutions u α converge to the solution u 0 of the degenerate Cauchy problem $\partial u_0/ \partial t =\xi\circ \nabla u_0, u_0\v_{t=0} = f$ . These results are based on a criterion for the existence of strong limits in the space of Hida distributions (S) * . As a by-product it is proved that weak solutions of the above Cauchy problem are in fact strong solutions.

A proposed strategy for seismic design of steel buildings

The conceptual basis of the seismic design procedure in the National Building Code of Canada is reviewed. The design earthquake is specified only for the ultimate limit states at which the performance of both ordinary and important buildings is evaluated by an elastic static analysis in all zones. Criteria for checking the serviceability limit states, which apply to moderate earthquakes that may occur relatively frequently in the life of the building, are not specified explicitly. It is suggested that the current design approach could be improved by adopting a design strategy that addresses as well the serviceability limit states and associated evaluation criteria and gives methods for design and analysis as a function of the seismic zone and the importance of the structure. An earthquake with a return period of 1 in 50 years is proposed tentatively for the serviceability limit states with appropriate drift limits. The proposed serviceability limit states are shown to govern the design of buildings for values of the force modification factor greater, on average, than 3.Key words: analyses, earthquake, seismic design, serviceability limit state, steel, ultimate limit state.

The drift approximation solves the Poisson, Nernst-Planck, and continuum equations in the limit of large external voltages

Nearly linear current-voltage curves are frequently found in biological ion channels. Using the drift limit of the substantially non-linear Poisson-Nernst-Planck equations, we explain such behavior of diffusion-controlled charge transport systems. Starting from Gauss' law, drift, and continuity equations we derive a simple analytical current-voltage relation, which accounts for this deviation from linearity. As shown previously, the drift limit of the Nernst-Planck equation applies if the total electric current is dominated by the electric field, and integral contributions from concentration gradients are small. The simple analytical form of the drift current-voltage relations makes it an ideal tool to analyze experiment current-voltage curves. We also solved the complete Poisson-Nernst-Planck equations numerically, and determined current-voltage curves over a wide range of voltages, concentrations, and Debye lengths. The simulation fully supports the analytical estimate that the current-voltage curves of simple charge transport systems are dominated by the drift mechanism. Even those relations containing the most extensive approximations remained qualitatively within the correct order of magnitude.

Brief comments on elastic flexibility of reinforced concrete frames and significance to seismic design

It is shown, from analysis of typical reinforced concrete beam sections, that current design practice, which assumes beam stiffness is independent of reinforcement ratio but equal to a constant fraction of gross section stiffness is inappropriate. The analyses indicate that effective beam yield curvature can be considered constant, when non-dimensionalized by beam depth and yield strain, indicating that beam stiffness is proportional to strength. Based on this observation, a simple expression for yield drift of frames is proposed and is calibrated by comparing with results of a large number of beam/column subassemblage experiments. Good agreement is obtained. It is pointed out that current estimates of frame stiffness are generally too high. A consequence is that simple calculations show that the vast majority of frame buildings will be unable to achieve code design ductility levels before exceeding code drift limitations.

The seismic behaviour of steel moment-resisting frames with stiffening braces

The present paper deals with the seismic behaviour of steel structures which are designed in the attempt of exploiting the dual characteristics of moment resisting frames (MRFs) and concentrically braced frames (CBFs) as lateral force resisting systems. Three prototype frames are studied within the context of Eurocode 8 (EC8) provisions; these are MRFs which are traditionally designed, against ultimate seismic actions (ULS), without checking serviceability limit state rules (SLS-interstory drift limits). To fulfill these requirements concentrical braces are inserted in the frames, which are not considered in the collapse resistance of the structural system. The non-linear behaviour of these systems under ultimate seismic environment is studied and compared to the one of the unbraced MRFs. The influence of second order effects is also investigated.

Aspects of drift and ductility capacity of rectangular cantilever structural walls

Moment-curvature analyses of cantilever shear walls are used to show that yield curvature, serviceability curvature, and ultimate (damage-control) curvature are insensitive to variations of axial load ratio, longitudinal reinforcement ratio, and distribution of longitudinal reinforcement. The results are used to determine available displacement ductility factors for walls of different aspect ratios and drift limits. It is shown that drift capacity will generally exceed code levels of permissible drift, and that code drift limits will normally restrict, sometimes severely, the design displacement ductility factor.

Analytical characterization of a planar magnetron radio frequency glow-discharge source

The analytical characteristics of a radio frequency (rf) planar magnetron glow-discharge source were determined with a high-resolution echelle spectrometer. Two sample configurations (both with flat-cathode geometry) were studied. Smaller samples were mounted on a 5 cm square copper plate, whereas samples of diameter 2.6 cm or greater were placed directly upon the pressure seal. The source was optimized for maximum signal. At all pressures (0.05–0.6 Torr) and power levels (10–100 W) studied here, the precision was detector-readout-noise-limited. The analyte-emission drift, short-term precision, and detection limits for the source were measured. Warm-up time was around 5–7 min (with a conducting cathode), after which the rsd of the signal was 0.29%. The relative signal drift was 10% over a 5 min interval during this warm-up time. Detection limits for elements in conducting matrices ranged from 0.04 to 3 ppm, roughly an order of magnitude better than for elements in insulating matrices. The shape of the sputtering track was measured in order to determine the viability of the source for depth profiling. © 1997 Elsevier Science B.V.