Processing load and the use of concrete representations and strategies for solving linear equations

This paper is a report of students' responses to instruction which was based on the use of concrete representations to solve linear equations. The sample consisted of 21 Grade 8 students from a middle-class suburban state secondary school with a reputation for high academic standards and innovative mathematics teaching. The students were interviewed before and after instruction. Interviews and classroom interactions were observed and videotaped. A qualitative analysis of the responses revealed that students did not use the materials in solving problems. The increased processing load caused by concrete representations is hypothesised as a reason.

Performance comparison of VSC-based shunt and series compensators used for load voltage control in distribution systems

In this paper, the performance of voltage-source converter-based shunt and series compensators used for load voltage control in electrical power distribution systems has been analyzed and compared, when a nonlinear load is connected across the load bus. The comparison has been made based on the closed-loop frequency resopnse characteristics of the compensated distribution system. A distribution static compensator (DSTATCOM) as a shunt device and a dynamic voltage restorer (DVR) as a series device are considered in the voltage-control mode for the comparison. The power-quality problems which these compensator address include voltage sags/swells, load voltage harmonic distortions, and unbalancing. The effect of various system parameters on the control performance of the compensator can be studied using the proposed analysis. In particular, the performance of the two compensators are compared with the strong ac supply (stiff source) and weak ac-supply (non-still source) distribution system. The experimental verification of the analytical results derived has been obtained using a laboratory model of the single-phase DSTATCOM and DVR. A generalized converter topology using a cascaded multilevel inverter has been proposed for the medium-voltage distribution system. Simulation studies have been performed in the PSCAD/EMTDC software to verify the results in the three-phase system.

Cognitive load and assembly tasks : effect of instructional formats on learning assembly procedures

The study investigated the effect on learning of four different instructional formats used to teach assembly procedures. Cognitive load and spatial information processing theories were used to generate the instructional material. The first group received a physical model to study, the second an isometric drawing, the third an isometric drawing plus a model and the fourth an orthographic drawing. Forty secondary school students were presented with the four different instructional formats and subsequently tested on an assembly task. The findings indicated that there may be evidence to argue that the model format which only required encoding of an already constructed three dimensional representation, caused less extraneous cognitive load compared to the isometric and the orthographic formats. No significant difference was found between the model and the isometric-plus-model formats on all measures because 80% of the students in the isometric-plus-model format chose to use the model format only. The model format also did not differ significantly from other groups in total time taken to complete the assembly, in number of correctly assembled pieces and in time spent on studying the tasks. However, the model group had significantly more correctly completed models and required fewer extra looks than the other groups.

Cognitive load and mental rotation : structuring orthographic projection for learning and problem solving

Cognitive load theory was used to generate a series of three experiments to investigate the effects of various worked example formats on learning orthographic projection. Experiments 1 and 2 investigated the benefits of presenting problems, conventional worked examples incorporating the final 2-D and 3-D representations only, and modified worked examples with several intermediate stages of rotation between the 2-D and 3-D representations. Modified worked examples proved superior to conventional worked examples without intermediate stages while conventional worked examples were, in turn, superior to problems. Experiment 3 investigated the consequences of varying the number and location of intermediate stages in the rotation trajectory and found three stages to be superior to one. A single intermediate stage was superior when nearer the 2-D than the 3-D end of the trajectory. It was concluded that (a) orthographic projection is learned best using worked examples with several intermediate stages and that (b) a linear relation between angle of rotation and problem difficulty did not hold for orthographic projection material. Cognitive load theory could be used to suggest the ideal location of the intermediate stages.

Statistical analyses of weigh-in-motion data for bridge live load development

This paper discusses the statistical analyses used to derive bridge live loads models for Hong Kong from a 10-year weigh-in-motion (WIM) data. The statistical concepts required and the terminologies adopted in the development of bridge live load models are introduced. This paper includes studies for representative vehicles from the large amount of WIM data in Hong Kong. Different load affecting parameters such as gross vehicle weights, axle weights, axle spacings, average daily number of trucks etc are first analyzed by various stochastic processes in order to obtain the mathematical distributions of these parameters. As a prerequisite to determine accurate bridge design loadings in Hong Kong, this study not only takes advantages of code formulation methods used internationally but also presents a new method for modelling collected WIM data using a statistical approach.

Vulnerability assessment of reinforced concrete columns subjected to vehicular impacts

Columns are one of the key load bearing elements that are highly susceptible to vehicle impacts. The resulting severe damages to columns may leads to failures of the supporting structure that are catastrophic in nature. However, the columns in existing structures are seldom designed for impact due to inadequacies of design guidelines. The impact behaviour of columns designed for gravity loads and actions other than impact is, therefore, of an interest. A comprehensive investigation is conducted on reinforced concrete column with a particular focus on investigating the vulnerability of the exposed columns and to implement mitigation techniques under low to medium velocity car and truck impacts. The investigation is based on non-linear explicit computer simulations of impacted columns followed by a comprehensive validation process. The impact is simulated using force pulses generated from full scale vehicle impact tests. A material model capable of simulating triaxial loading conditions is used in the analyses. Circular columns adequate in capacity for five to twenty story buildings, designed according to Australian standards are considered in the investigation. The crucial parameters associated with the routine column designs and the different load combinations applied at the serviceability stage on the typical columns are considered in detail. Axially loaded columns are examined at the initial stage and the investigation is extended to analyse the impact behaviour under single axis bending and biaxial bending. The impact capacity reduction under varying axial loads is also investigated. Effects of the various load combinations are quantified and residual capacity of the impacted columns based on the status of the damage and mitigation techniques are also presented. In addition, the contribution of the individual parameter to the failure load is scrutinized and analytical equations are developed to identify the critical impulses in terms of the geometrical and material properties of the impacted column. In particular, an innovative technique was developed and introduced to improve the accuracy of the equations where the other techniques are failed due to the shape of the error distribution. Above all, the equations can be used to quantify the critical impulse for three consecutive points (load combinations) located on the interaction diagram for one particular column. Consequently, linear interpolation can be used to quantify the critical impulse for the loading points that are located in-between on the interaction diagram. Having provided a known force and impulse pair for an average impact duration, this method can be extended to assess the vulnerability of columns for a general vehicle population based on an analytical method that can be used to quantify the critical peak forces under different impact durations. Therefore the contribution of this research is not only limited to produce simplified yet rational design guidelines and equations, but also provides a comprehensive solution to quantify the impact capacity while delivering new insight to the scientific community for dealing with impacts.

Performance load testing and structural adequacy evaluation of road bridge decks

Many ageing road bridges, particularly timber bridges, require urgent improvement due to the demand imposed by the recent version of the Australian bridge loading code, AS 5100. As traffic volume plays a key role in the decision of budget allocations for bridge refurbishment/ replacement, many bridges in low volume traffic network remain in poor condition with axle load and/ or speed restrictions, thus disadvantaging many rural communities. This thesis examines an economical and environmentally sensible option of incorporating disused flat rail wagons (FRW) in the construction of bridges in low volume, high axle load road network. The constructability, economy and structural adequacy of the FRW road bridge is reported in the thesis with particular focus of a demonstration bridge commissioned in regional Queensland. The demonstration bridge comprises of a reinforced concrete slab (RCS) pavement resting on two FRWs with custom designed connection brackets at regular intervals along the span of the bridge. The FRW-RC bridge deck assembly is supported on elastomeric rubber pads resting on the abutment. As this type of bridge replacement technology is new and its structural design is not covered in the design standards, the in-service structural performance of the FRW bridge subjected to the high axle loadings prescribed in AS 5100 is examined through performance load testing. Both the static and the moving load tests are carried out using a fully laden commonly available three-axle tandem truck. The bridge deck is extensively strain gauged and displacement at several key locations is measured using linear variable displacement transducers (LVDTs). A high speed camera is used in the performance test and the digital image data are analysed using proprietary software to capture the locations of the wheel positions on the bridge span accurately. The wheel location is thus synchronised with the displacement and strain time series to infer the structural response of the FRW bridge. Field test data are used to calibrate a grillage model, developed for further analysis of the FRW bridge to various sets of high axle loads stipulated in the bridge design standard. Bridge behaviour predicted by the grillage model has exemplified that the live load stresses of the FRW bridge is significantly lower than the yield strength of steel and the deflections are well below the serviceability limit state set out in AS 5100. Based on the results reported in this thesis, it is concluded that the disused FRWs are competent to resist high axle loading prescribed in AS 5100 and are a viable alternative structural solution of bridge deck in the context of the low volume road networks.

Adaptive and optimal under frequency load shedding

Power systems in many countries are stressed towards their stability limit. If these stable systems experience any unexpected serious contingencies, or disturbances, there is a significant risk of instability, which may lead to wide-spread blackout. Frequency is a reliable indicator for such instability condition exists on the power system; therefore under-frequency load shedding technique is used to stable the power system by curtail some load. In this paper, the SFR-UFLS model redeveloped to generate optimal load shedding method is that optimally shed load following one single particular contingency event. The proposed optimal load shedding scheme is then tested on the 39-bus New England test system to show the performance against random load shedding scheme.

Load modelling : induction motors

Modelling the power systems load is a challenge since the load level and composition varies with time. An accurate load model is important because there is a substantial component of load dynamics in the frequency range relevant to system stability. The composition of loads need to be charaterised because the time constants of composite loads affect the damping contributions of the loads to power system oscillations, and their effects vary with the time of the day, depending on the mix of motors loads. This chapter has two main objectives: 1) describe the load modelling in small signal using on-line measurements; and 2) present a new approach to develop models that reflect the load response to large disturbances. Small signal load characterisation based on on-line measurements allows predicting the composition of load with improved accuracy compared with post-mortem or classical load models. Rather than a generic dynamic model for small signal modelling of the load, an explicit induction motor is used so the performance for larger disturbances can be more reliably inferred. The relation between power and frequency/voltage can be explicitly formulated and the contribution of induction motors extracted. One of the main features of this work is the induction motor component can be associated to nominal powers or equivalent motors