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2004

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Articles 631 - 660 of 2785

Full-Text Articles in Engineering

Odor, H2S And Nh3 Emissions From Phototrophic And Non-Phototrophic Anaerobic Swine Lagoons, Jason Byler, Dennis D. Schulte, Richard K. Koelsch Aug 2004

Odor, H2S And Nh3 Emissions From Phototrophic And Non-Phototrophic Anaerobic Swine Lagoons, Jason Byler, Dennis D. Schulte, Richard K. Koelsch

Department of Agricultural and Biological Systems Engineering: Presentations and White Papers

Odor, ammonia and hydrogen sulfide emission data were collected from three phototrophic and three non-phototrophic anaerobic swine lagoons in eastern Nebraska from May 27th to June 18th (late spring) and from July 7th to August 13th (summer). The greatest odor, hydrogen sulfide and ammonia emission rates were from non-phototrophic lagoons during late spring (24.5 OU m-2 s-1, 3.2 μg-H2S m-2 s-1, 34.9 kg NH3-N ha-1 d-1, respectively). Non-phototrophic lagoon odor, ammonia and hydrogen sulfide emission rates were much higher in late spring than summer (24.5 vs. 4.8 …


Determination Of Traffic Responsive Plan Selection Factors And Thresholds Using Artificial Neural Networks, Anuj Sharma Aug 2004

Determination Of Traffic Responsive Plan Selection Factors And Thresholds Using Artificial Neural Networks, Anuj Sharma

Department of Civil and Environmental Engineering: Faculty Publications

Traffic congestion has become a menace to civilized society. It degrades air quality, jeopardizes safety and causes delay. Traffic congestion can be alleviated by providing an effective traffic control signal system. Closed-loop traffic control systems are an example of such a system.

Closed-loop traffic control systems can be operated primarily in either of two modes: Time of Day Mode (TOD) or Traffic Responsive Plan Selection Mode (TRPS). TRPS mode, if properly configured, can easily handle time independent variation in traffic volumes. It can also reduce the effect of timing plan aging. Despite these advantages, TRPS mode is not used as …


Willamette River Basin Temperature Tmdl Model: Model Calibration, Chris Berger, Michael Lee Mckillip, Robert Leslie Annear, Sher Jamal Khan, Scott A. Wells Aug 2004

Willamette River Basin Temperature Tmdl Model: Model Calibration, Chris Berger, Michael Lee Mckillip, Robert Leslie Annear, Sher Jamal Khan, Scott A. Wells

Civil and Environmental Engineering Faculty Publications and Presentations

The State of Oregon Department of Environmental Quality (DEQ) is developing a TMDL for temperature in the Willamette River basin shown in Figure 1. The study area included the Willamette River and all major tributaries (except the Tualatin River where a TMDL process was already concluded). A large section of the Columbia River was also modeled to provide adequate boundary representation of tidal flows in the lower Willamette River. The Willamette River below the Oregon City Falls in the Portland metropolitan area has a typical diurnal tidal range of 1 m. The development of a dynamic model of temperature and …


46th Rocky Mountain Conference On Analytical Chemistry Aug 2004

46th Rocky Mountain Conference On Analytical Chemistry

Rocky Mountain Conference on Magnetic Resonance

Final program, abstracts, and information about the 46th annual meeting of the Rocky Mountain Conference on Analytical Chemistry, co-endorsed by the Colorado Section of the American Chemical Society and the Rocky Mountain Section of the Society for Applied Spectroscopy. Held in Denver, Colorado, August 1-5, 2004.


Embrittlement And Localized Corrosion In Alloy Ht-9, Sudheer Sama Aug 2004

Embrittlement And Localized Corrosion In Alloy Ht-9, Sudheer Sama

UNLV Theses, Dissertations, Professional Papers, and Capstones

This investigation is focused on the evaluation of stress corrosion cracking (SCC), hydrogen embrittlement (HE) and localized corrosion susceptibility of Alloy HT -9 in neutral and acidic solutions at 30, 60 and 90°C. Constant-load and slow-strain-rate (SSR) testing techniques were used to evaluate the SCC and HE behavior of this alloy by using smooth and notched tensile specimens. Hydrogen effect on the cracking behavior was evaluated by applying cathodic (negative) potential to the test specimens. Localized corrosion susceptibility was evaluated by cyclic potentiodynamic polarization technique. The results of constant load SCC testing showed a threshold stress at 80% of the …


Neutron Multiplicity Measurements For The Afci Program Quarterly Progress Report June-August 2004, Denis Beller Aug 2004

Neutron Multiplicity Measurements For The Afci Program Quarterly Progress Report June-August 2004, Denis Beller

Transmutation Sciences Physics (TRP)

The U.S. Advanced Fuel Cycle Initiative (AFCI) is a program to develop economic and environmental methods to reduce the impact of waste from commercial nuclear fuel cycles. One concept for near-complete destruction of waste isotopes from used nuclear fuel is acceleratordriven transmutation. High-power accelerators would be used to produce high-energy charged particles, which then collide with heavy metal targets to create a cascade of neutrons. These neutrons then cause a nuclear chain reaction in subcritical systems. Fission neutrons then transmute fissile waste isotopes as well as other problematic isotopes such as technetium-99 and iodine-129. To design these systems, complex reactor …


Kalman Filtering With Uncertain Noise Covariances, Srikiran Kosanam, Daniel J. Simon Aug 2004

Kalman Filtering With Uncertain Noise Covariances, Srikiran Kosanam, Daniel J. Simon

Electrical and Computer Engineering Faculty Publications

In this paper the robustness of Kalman filtering against uncertainties in process and measurement noise covariances is discussed. It is shown that a standard Kalman filter may not be robust enough if the process and measurement noise covariances are changed. A new filter is proposed which addresses the uncertainties in process and measurement noise covariances and gives better results than the standard Kalman filter. This new filter is used in simulation to estimate the health parameters of an aircraft gas turbine engine.


Environment-Induced Degradations In A Target Structural Material For Transmutation Applications, Ramprashad Prabhakaran Aug 2004

Environment-Induced Degradations In A Target Structural Material For Transmutation Applications, Ramprashad Prabhakaran

UNLV Theses, Dissertations, Professional Papers, and Capstones

This investigation is focused on the evaluation of stress corrosion cracking (SCC) and localized corrosion behavior of Type 422 stainless steel in aqueous environments at ambient and elevated temperature. The results of constant load SCC testing using smooth specimens showed no failure in the neutral solution but a threshold stress of 97 ksi was observed in the 90°C acidic environment. SCC testing by the slow-strain-rate test method indicate that the time-to-failure, true failure stress and ductility parameters were gradually reduced with increasing temperature, showing more pronounced effect in the acidic solution. The application of a controlled cathodic potential showed further …


Percolation Paths Of Three-Dimensions In Sensitized Stainless Steel, Alisa J. Millar Henrie Aug 2004

Percolation Paths Of Three-Dimensions In Sensitized Stainless Steel, Alisa J. Millar Henrie

Faculty Publications

The study of three-dimensional percolation paths through materials is important in its contribution to understanding defect sensitive properties of materials. This work shows the importance of grain boundary character in modeling defect sensitive boundaries. Also presented are trends of percolation of sensitized grain boundaries in 304 stainless steel (304SS). Of particular interest is how open paths form in a three-dimensional model created through serial sectioning. Evidence is presented that triple or quadruple points that contain typically two boundaries with special character that intersect the percolation path break up the path. Some boundaries with no known special qualities; they are not …


High Efficiency 90 Degree Silica Waveguide Bend Using An Air Hole Photonic Crystal Region, J. Cai, S. Kim, Gregory P. Nordin, J. Jiang Aug 2004

High Efficiency 90 Degree Silica Waveguide Bend Using An Air Hole Photonic Crystal Region, J. Cai, S. Kim, Gregory P. Nordin, J. Jiang

Faculty Publications

We propose the hybrid integration of an air hole photonic crystal (PhC) structure with a high (0.75%) single-mode silica waveguide to achieve an ultracompact high efficiency 90 bend for transverse-magnetic polarized light. Diffraction from the periodic boundary between the PhC and silica waveguide regions is shown to seriously degrade the optical efficiency of the bend. A microgenetic algorithm ( GA) combined with a two-dimensional finite-difference time-domain method is used to modify the PhC and its boundary layer to suppress this diffraction which in turn maximizes bend efficiency. The final optimized structure has a 99.4% bend efficiency at a wavelength of …


Microwave Remote Sensing Of The Greenland Ice Sheet: Models And Applications, Ivan S. Ashcraft Jul 2004

Microwave Remote Sensing Of The Greenland Ice Sheet: Models And Applications, Ivan S. Ashcraft

Theses and Dissertations

Spaceborne microwave sensors are powerful tools for monitoring the impacts of global climate change on the Greenland ice sheet. This dissertation focuses on refining methods for applying microwave data in Greenland studies by using new simple theoretical and empirical models to investigate (1) azimuth anisotropies in the data, (2) the microwave signature of the snow surface, (3) detection of snow melt, and (4) classification of snow melt. The results are applicable for identifying geophysical properties of the snow surface and monitoring changes on the ice sheet in relation to melt duration/extent, accumulation, and wind patterns. Azimuth dependence of the normalized …


A New Method For Melt Detection On Antarctic Ice-Shelves And Scatterometer Calibration Verification, Lukas Brad Kunz Jul 2004

A New Method For Melt Detection On Antarctic Ice-Shelves And Scatterometer Calibration Verification, Lukas Brad Kunz

Theses and Dissertations

Ku-band dual-polarization radar backscatter measurements from the SeaWinds on QuikScat scatterometer and microwave radiometer measurements from the Special Sensor Microwave/Imager (SSM/I) are used to determine periods of surface melt and freeze in the Antarctic ice-shelves. The normalized radar backscatter (sigma-0) and backscatter polarization ratio (PR) are used in the maximum likelihood estimation of the ice-state. This method is used to infer the daily ice-surface conditions for 25 selected study points located on the Ronne, Ross, Larsen, Fimbul, Amery, and Shackleton Ice-shelves. The temporal and spatial variations of the radar response are also observed for various neighborhood sizes surrounding each given …


Improving Electromagnetic Bias Estimates, Floyd W. Millet Jul 2004

Improving Electromagnetic Bias Estimates, Floyd W. Millet

Theses and Dissertations

The electromagnetic (EM) bias is the largest source of error in the TOPEX/Poseidon and Jason-1 satellite sea surface height (SSH) estimates. Due to incomplete understanding of the physical processes which cause the bias, current operational models are based on empirical relationships between the bias wind speed and significant wave height. These models reduce RMS estimation errors of the EM bias to approximately 4 cm.

To improve EM bias estimation the correlation between the bias and RMS long wave slope is studies using data from tower-based experiments in the Gulf of Mexico and Bass Straight, Australia. Models based on significant wave …


Fully Compliant Tensural Bistable Mechanisms (Ftbm) With On-Chip Thermal Actuation, Daniel L. Wilcox Jul 2004

Fully Compliant Tensural Bistable Mechanisms (Ftbm) With On-Chip Thermal Actuation, Daniel L. Wilcox

Theses and Dissertations

The Fully compliant Tensural Bistable Mechanism (FTBM) class is introduced. The class consists of fully compliant linear bistable mechanisms that achieve much of their displacement and bistable behavior through tension loading of compliant segments. Multiple topologies of designs arising from the FTBM class were designed using a finite element analysis (FEA) model with optimization. In a coupled design approach, thermal actuators were optimized to the force and displacement requirements of the bistable mech-anisms, and selected FTBM devices were combined in switching systems with the result-ing Thermomechanical In-plane Microactuators (TIMs) and Amplified Thermomechanical In-plane Microactuators (ATIMs). Successful on-chip actuation was demonstrated. …


Transport Logistics Planning With Service-Level Constraints, Hoong Chuin Lau, K. M. Ng, Xintao Wu Jul 2004

Transport Logistics Planning With Service-Level Constraints, Hoong Chuin Lau, K. M. Ng, Xintao Wu

Research Collection School Of Computing and Information Systems

In this paper, we study a logistics problem arising in military transport planning. A military organization operates a large fleet of vehicles in a depot to serve the requests of various operational units. Each request has a fixed start and end time, and is served by a prescribed number of vehicles. We address the following two problems: (1) how many vehicles are at least needed to meet a given service level of requests; and (2) suppose we allow each request to shift its start time by a constant duration, call all the requests be met? A Niche genetic algorithm, together …


Reactor Physics Studies For The Afci Race Project: Reactor-Accelerator Coupling Experiments Project, Denis Beller Jul 2004

Reactor Physics Studies For The Afci Race Project: Reactor-Accelerator Coupling Experiments Project, Denis Beller

Transmutation Sciences Physics (TRP)

In the RACE Project of the U.S. Advanced Fuel Cycle Initiative (AFCI), a series of accelerator driven subcritical systems (ADSS) experiments will be conducted at the Idaho State University’s Idaho Accelerator Center (ISU-IAC), at the University of Texas (UT) at Austin, and at the Texas A&M University. In these experiments we will use electron accelerators to induce bremsstrahlung photon-neutron reactions in heavy-metal targets; this source of about 1012 to 1013 n/s will then initiate fission reactions in the subcritical systems. These systems will include a compact, transportable assembly at ISU and TRIGA reactors at UT-Austin and Texas A&M. …


A Review Of Hot Water Draw Profiles Used In Performance Analysis Of Residential Domestic Hot Water Systems, Florida Solar Energy Center, Philip W. Fairey Jul 2004

A Review Of Hot Water Draw Profiles Used In Performance Analysis Of Residential Domestic Hot Water Systems, Florida Solar Energy Center, Philip W. Fairey

FSEC Energy Research Center®

As a result of efforts on the part of various organizations to improve the specifications for performance-based analysis of energy use in residences, the literature on residential hot water use has been reviewed, specifically as it relates to typical hot water use draw profiles. A number of daily hot water use draw profiles have been identified and reviewed.


3d Analysis Of Hybrid Photonic Crystal/Conventional Waveguide 90° Bend, J. Cai, S. Kim, Gregory P. Nordin, J. Jiang Jul 2004

3d Analysis Of Hybrid Photonic Crystal/Conventional Waveguide 90° Bend, J. Cai, S. Kim, Gregory P. Nordin, J. Jiang

Faculty Publications

We present a three-dimensional (3D) analysis of a hybrid photonic crystal conventional waveguide 90° bend proposed previously [Opt. Express 10, 1334 (2002)] as an ultracompact component for large-scale planar lightwave circuit integration. Both rigorous 3D finite-difference time-domain modeling and a simple perfect mirror model analysis were carried out for different Si post heights in the photonic crystal region. Results show that the bend efficiency increases rapidly with Si post height. For a post height of 6.5 µm, this structure yields a bend efficiency of 97.3% at a wavelength of 1.55 µm for 90° bends in 2 µm X 2 µm …


Cavity Enhancement Of The Magneto-Optic Kerr Effect For Optical Studies Of Magnetic Nanostructures, Aaron R. Hawkins, N. Qureshi, Holger Schmidt Jul 2004

Cavity Enhancement Of The Magneto-Optic Kerr Effect For Optical Studies Of Magnetic Nanostructures, Aaron R. Hawkins, N. Qureshi, Holger Schmidt

Faculty Publications

We present a study of cavity enhancement of the magneto-optic Kerr effect using dielectric multilayers in order to facilitate optical studies of individual single-domain nanomagnets. We develop a transfer matrix theory to analyze Kerr rotation from an arbitrary number of possibly lossy dielectric layers. The combination of one lossless and one thin metallic layer is found to be most favorable for studying individual nanomagnets, providing the best tradeoff between signal enhancement and spatial resolution. Accounting for the microscopic surface structure, we find good agreement between theory and experiment. Using this technique, we demonstrate Kerr enhancements by a factor of more …


Discovering Transcriptional Regulatory Rules From Gene Expression And Tf-Dna Binding Data By Decision Tree Learning, Jianhua Ruan, Weixiong Zhang Jul 2004

Discovering Transcriptional Regulatory Rules From Gene Expression And Tf-Dna Binding Data By Decision Tree Learning, Jianhua Ruan, Weixiong Zhang

All Computer Science and Engineering Research

Background: One of the most promising but challenging task in the post-genomic era is to reconstruct the transcriptional regulatory networks. The goal is to reveal, for each gene that responds to a certain biological event, which transcription factors affect its transcription, and how several transcription factors coordinate to accomplish specific regulations. Results: Here we propose a supervised machine learning approach to address these questions. We build decision trees to associate the expression level of a gene with the transcription factor binding data of its promoter. From the decision trees, we extract regulatory rules that specify how the binding of a …


Investigation Into The Ultrasonic Setting Of Glass Ionomer Cements : Part Ii Setting Times And Compressive Strengths, E. Twomey, Mark R. Towler, C. M. Crowley, J. Doyle, S. Hampshire Jul 2004

Investigation Into The Ultrasonic Setting Of Glass Ionomer Cements : Part Ii Setting Times And Compressive Strengths, E. Twomey, Mark R. Towler, C. M. Crowley, J. Doyle, S. Hampshire

Chemical and Biochemical Engineering Faculty Research & Creative Works

The ultrasonic setting of glass ionomer cements (GIC) was discussed. It was observed that the ultrasonic setting resulted in improvements of compressive strength. An increase in the PAA molecular weight from PAA50 to PAA200 resulted in an increase in the strength, but with a further increase in the PAA molecular weight to PAA450, there was a reduction in the strength. Results show that the strength of the ultrasonically set materials after 1 day were close to the values for the 7 days chemically set samples.


Effect Of Chromium-Gold And Titanium-Titanium Nitride-Platinum-Gold Metallization On Wire/Ribbon Bondability, Jianbiao Pan, Robert M. Pafchek, Frank F. Judd, Jason Baxter Jul 2004

Effect Of Chromium-Gold And Titanium-Titanium Nitride-Platinum-Gold Metallization On Wire/Ribbon Bondability, Jianbiao Pan, Robert M. Pafchek, Frank F. Judd, Jason Baxter

Industrial and Manufacturing Engineering

Gold metallization on wafer substrates for wire/ribbon bond applications require good bond strength to the substrate without weakening the wire/ribbon. This paper compares the ribbon bondability of Cr/Au and Ti/TiN/Pt/Au metallization systems. Both chromium and titanium are used to promote adhesion between substrates and sputtered gold films. Both can diffuse the gold surface after annealing and degrade the wire/ribbon bondability. Restoring bondability by ceric ammonium nitrate (CAN) etch was investigated. Experiments were conducted to investigate the effect of Cr/Au and Ti/TiN/Pt/Au, annealing, and CAN etch processes on 25.4 times; 254 μm (1 × 10 mil) ribbon bonding. All bonds were …


2004 Directory Of Indiana State, County, City And Town Officials Responsible For Road And Street Work, Indiana Ltap Jul 2004

2004 Directory Of Indiana State, County, City And Town Officials Responsible For Road And Street Work, Indiana Ltap

Indiana Local Technical Assistance Program (LTAP) Directory

Contact information for agency officials and employees responsible for Indiana’s local road infrastructure.


Unitary Space-Time Transmit Diversity For Multiple Antenna Self-Interference Suppression, Adam Lane Anderson Jul 2004

Unitary Space-Time Transmit Diversity For Multiple Antenna Self-Interference Suppression, Adam Lane Anderson

Theses and Dissertations

A common practice for government defense agencies and commercial aeronautical companies is to use dual antennas on test flight air vehicles in order to overcome occlusion issues during high-speed telemetric maneuvers. The dual antennas, though never being masked at the same time, unfortunately lead to a drastic increase in nulls in the signal pattern. The result of this interference pattern can be compared to the effect of fading in a multiple-input multiple-output (MIMO) multi-path scattering environment. Confidence in this comparison leads to the use of unitary space-time MIMO codes to overcome the signal self-interference. The possibility and performance of several …


Bubble Column Apparatus For Separating Wax From Catalyst Slurry, James K. Neathery, Burtron H. Davis Jul 2004

Bubble Column Apparatus For Separating Wax From Catalyst Slurry, James K. Neathery, Burtron H. Davis

Center for Applied Energy Research Faculty Patents

Novel methods and devices for production of liquid hydrocarbon products from gaseous reactants are disclosed. In one aspect, a method for separating a liquid hydrocarbon, typically a wax, from a catalyst containing slurry is provided, comprising passing the slurry through at least one downcomer extending from an overhead separation chamber and discharging into the bottom of a slurry bubble column reactor. The downcomer includes a cross-flow filtration element for separating a substantially particle-free liquid hydrocarbon for downstream processing. In another aspect, a method for promoting plug-flow movement in a recirculating slurry bubble column reactor is provided, comprising discharging the recirculating …


Field-Controlled Domain-Wall Resistance In Magnetic Nanojunctions, John D. Burton, Arti Kashyap, Mikhail Ye. Zhuravlev, Ralph Skomski, Evgeny Y. Tsymbal, Sitaram Jaswal, O.N. Mryasov, R.W. Chantrell Jul 2004

Field-Controlled Domain-Wall Resistance In Magnetic Nanojunctions, John D. Burton, Arti Kashyap, Mikhail Ye. Zhuravlev, Ralph Skomski, Evgeny Y. Tsymbal, Sitaram Jaswal, O.N. Mryasov, R.W. Chantrell

Materials Research Science and Engineering Center: Faculty Publications

The electrical resistance of a constrained domain wall in a nanojunction is investigated using micromagnetic modeling and ballistic conductance calculations. The nanojunction represents two ferromagnetic electrodes connected by a ferromagnetic wire of 10 nm in length and of a few nanometers in cross section. We find that the anisotropy of the electrodes favors a localization of the domain wall within the constriction (wire) revealing a positive domain-wall resistance. An applied magnetic field moves the domain wall toward one of the electrodes and reduces its width. This compression of the domain wall leads to a sizeable enhancement of the domain-wall resistance.


Field-Programmable Analog Arrays: A Floating-Gate Approach, Tyson S. Hall Jul 2004

Field-Programmable Analog Arrays: A Floating-Gate Approach, Tyson S. Hall

Faculty Works

Field-programmable analog arrays (FPAAs) provide a method for rapidly pro- totyping analog systems. Currently available commercial and academic FPAAs are typically based on operational amplifiers (or other similar analog primitives) with only a few computational elements per chip. While their specific architectures vary, their small sizes and often restrictive interconnect designs leave current FPAAs limited in functionality, flexibility, and usefulness. Recent advances in the area of floating-gate transistors have led to an analog technology that is very small, accurately programmable, and extremely low in power consumption. By leveraging the advantages of floating-gate devices, a large-scale FPAA is designed that dramatically …


A Ray-Based Investigation Of The Statistical Characteristics And Efficient Representation Of Multi-Antenna Communication Channels, Gus Ryan German Jul 2004

A Ray-Based Investigation Of The Statistical Characteristics And Efficient Representation Of Multi-Antenna Communication Channels, Gus Ryan German

Theses and Dissertations

Multi-antenna communication systems are attracting research interest as a means to increase the information capacity, reliability, and spectral efficiency of wireless information transfer. Ray-tracing methods predict the behavior of wireless channels using a model of the propagation environment and are a low-cost alternative to direct measurements. We use ray tracing simulations to validate the statistical time and angle of arrival characteristics of an indoor multipath channel and compare model parameter estimates with estimates derived from channel sounding measurements. Ray tracing predicts the time and angle clustering of multipaths observed in the measurements and provides model parameter estimates which are closely …


Assuring Power In A Disaster And Providing Energy Security, Florida Solar Energy Center, William Young Jul 2004

Assuring Power In A Disaster And Providing Energy Security, Florida Solar Energy Center, William Young

FSEC Energy Research Center®

Daily use of a myriad of electrical and electronic devices has contributed to a steadily increasing dependence on electric power. The degree of importance of electricity is temporarily highlighted with any type of power outage, whether caused by a disaster as destructive as a Hurricane Andrew or as minor as an afternoon thunderstorm knocking down local utility lines. After September 11, terrorism added a new dimension to our definition of energy security. While the American public is dependent on utility providers to meet energy needs, it is the right and the responsibility of each citizen to become aware of energy …


A Modal Pushover Analysis Procedure To Estimate Seismic Demands For Unsymmetric-Plan Buildings, Anil K. Chopra, Rakesh K. Goel Jul 2004

A Modal Pushover Analysis Procedure To Estimate Seismic Demands For Unsymmetric-Plan Buildings, Anil K. Chopra, Rakesh K. Goel

Civil and Environmental Engineering

An Erratum has been published for this article in Earthquake Engng. Struct. Dyn. 2004; 33:1429.

Based on structural dynamics theory, the modal pushover analysis (MPA) procedure retains the conceptual simplicity of current procedures with invariant force distribution, now common in structural engineering practice. The MPA procedure for estimating seismic demands is extended to unsymmetric‐plan buildings. In the MPA procedure, the seismic demand due to individual terms in the modal expansion of the effective earthquake forces is determined by non‐linear static analysis using the inertia force distribution for each mode, which for unsymmetric buildings includes two lateral forces and torque at …