a framework for adaptive e-learning for continuum ...

A FRAMEWORK FOR ADAPTIVE E-LEARNING FOR CONTINUUM MECHANICS AND STRUCTURAL ANALYSIS Juan Carlos Mosquera1, Luis Francisco Plaza2, Beatriz González3 1,2

Univ Politécnica de Madrid (UPM), Dept Mecánica de Medios Continuos y T.Estr. (SPAIN) 3 Univ Politécnica de Madrid (UPM), Escuela de Ingeniería Civil (SPAIN)

Abstract This paper presents a project for providing the students of Structural Engineering with the flexibility to learn outside classroom schedules. The goal is a framework for adaptive E-learning based on a repository of open educational courseware with a set of basic Structural Engineering concepts and fundamentals. These are paramount for students to expand their technical knowledge and skills in structural analysis and design of tall buildings, arch-type structures as well as bridges. Thus, concepts related to structural behaviour such as linearity, compatibility, stiffness and influence lines have traditionally been elusive for students. The objective is to facilitate the student a teachinglearning process to acquire the necessary intuitive knowledge, cognitive skills and the basis for further technological modules and professional development in this area. As a side effect, the system is expected to help the students improve their preparation for exams on the subject. In this project, a web-based open-source system for studying influence lines on continuous beams is presented. It encompasses a collection of interactive user-friendly applications accessible via Web, written in JavaScript under JQuery and Dygraph Libraries, taking advantage of their efficiency and graphic capabilities. It is performed in both Spanish and English languages. The student is enabled to set the geometric, topologic, boundary and mechanic layout of a continuous beam. While changing the loading and the support conditions, the changes in the beam response prompt on the screen, so that the effects of the several issues involved in structural analysis become apparent. This open interaction with the user allows the student to simulate and virtually infer the structural response. Different levels of complexity can be handled, whereas an ongoing help is at hand for any of them. Students can freely boost their experiential learning on this subject at their own pace, in order to further share, process, generalize and apply the relevant essential concepts of Structural Engineering analysis. Besides, this collection is being added to the "Virtual Lab of Continuum Mechanics" of the UPM, launched in 2013 (http://serviciosgate.upm.es/laboratoriosvirtuales/laboratorios/medios-continuos-enconstrucci%C3%B3n). Keywords: Teaching Innovations, Classroom Applications, Educational Software, Structural analysis, Continuous beams.

1

INTRODUCTION

Information and Communication Technology (ICT) tools have been applied for e-Learning in a number of traditional subjects. However, structural analysis should be considered as a special case. Computer-based learning-aid packages, with the aim of developing a ‘feel’ for structural understanding, have boasted widespread use since the 1980s. Some of them even included selfevaluation systems and attempts for rubrics [4]. With the advent of the Internet, ICT tools enable the information to be accessed directly and quickly. Structural engineering educators often lack available time and resources to adequately present the fundamentals and techniques of Structural Analysis. This is particularly true for advanced engineering elective courses. Indeed, some advanced matters such as the design of connections in steel structures in detail is a pending task. The use of innovative computer tools in teaching and learning Continuum Mechanics is a matter of great concern. It allows students to enhance their understanding of the behaviour of complex structural systems.

Various attempts have being implemented during the last decade. They encompass simple spreadsheets, even with advanced programming such as VBA [1], scientific programming environments (MatLab, Octave, Mathematica, MathCad…), specific ad hoc computer programs [2] and autonomous learning systems through virtual platforms [3], among others. Likewise, recent alluring frameworks, gathered under concepts such as OpenCourseWare or MOOCs open up new horizons. A framework for adaptive E-learning based on distributed re-usable learning activities is currently under development at the Continuum Mechanics and Structural Analysis of the Technical University of Madrid (UPM). A web classroom application which adapts the presentation of educational material according to Civil Engineering students' learning needs is presented in this paper. The teaching-learning of influence lines for Structural Analysis students is a subject of paramount relevance as well as difficult to understand. So, a web-based system that helps the student to achieve both the basic understanding and the practical design rules and criteria is intended in this repository. The goal of the project is to keep the power of educational material repositories updated in order to enhance the experiential learning of students in such a practical discipline as is Civil Engineering.

2

METHODOLOGY

The proposed work aims to boost students’ both receptive and productive skills while learning the fundamentals of Structural Analysis. The starting point is the concern on the difficulty that a large percentage of the students encounter in acquiring the knowledge of the basic principles of behaviour of some typologies of structures which are frequent in civil engineering constructions. The formal object is the combination of web-based tools for adaptive learning with open source projects and open educational resources (ORE). The application of ORE [5] to this project may contribute to enhancing students’ capabilities for envisaging the behaviour of continuous beams. This entails mastering concepts such as stiffness, force transmission, support conditions, moving loads or unfavourable load combinations. In addition, students’ spatial reasoning skills may become enhanced, in order to identify the critical sections and forecast the worst combinations of loading on a beam. At the current stage, this E-learning system is complementary to the formal training imparted at the Civil Engineering School at the Universidad Politécnica de Madrid (CES-UPM). The system is under development, granted by the UPM, as a standalone site. It will eventually be embodied into the Virtual 1 Lab of Continuum Mechanics .

2.1

Project overview and expected benefits

The project seeks to increase the quality of the structural engineering education available to CESUPM students. The technology utilized allows the web application to be used in the classroom for illustrating and animating structural behaviour. Also, the system facilitates that students work remotely either alone or in team, so that they can learn at their own pace. In addition, the project will provide CES-UPM students with onsite training during its implementation. The implementation of the proposed work starts with an introductory workshop for students, in order to enhance their learning environment. The resources required for users to take advantage of the eLearning system consist of any personal, laptop or convertible notebook computer or tablet PC; they may be used in course lecture preparation and presentation. They allow instructors to combine the benefits of an attractive electronic lecture presentation with the ability to signal and jot down directly on the screen, remark relevant issues or address student queries. A number of illustrative examples of structural analysis and behaviour will be modelled using this procedure and integrated into the current curriculum. The graphics capabilities and animation features 2 3 provided with by jQuery and Dygraphs will be used to illustrate such things as: 1

http://serviciosgate.upm.es/laboratoriosvirtuales/laboratorios/medios-continuos-en-construcci%C3%B3n

2

http://jquery.com/

3

http://dygraphs.com/

• Load position-dependent behaviour of the beam. • Worst load combinations on a given structure. • Envelopes for both the largest positive and negative bending moments. • Difference between influence lines and distributions of internal forces due to a set of loads. • Simple procedures for calculating the maximum bending moment in a continuous beam due to a set of moving loads (vehicles). The system is freely available through any Internet browser, although Google Chrome and Mozilla-based browsers are recommended. The syntax and methodology is easily upgradeable and transferable to other disciplines.

2.2

Influence lines in engineering design

Some types of structures are designed to carry transient service loads. For example, a building structure must be designed to withstand the worst combination of both fixed and live loads. These often encompass snow, wind, movable equipment or walking people. Other frequent forms of spatiallyvarying loads are pedestrians crossing footbridges, travelling cranes on crane beams, vehicles or trains on bridges and viaducts. Design engineers are concerned with the maximum values of the internal forces and displacements at various sections. Then, an important issue arises: determining the critical positions of the loads with respect to the structure. The effects of loads that may occupy different positions on a structure can be studied through the concept of influence lines. For practical purposes, these moving loads are assumed to shift at such a slow rate that dynamic effects (such as vibrations and oscillating stresses) can be neglected [6]. The concept of influence lines is a valuable tool that allows the study of the effects of loads that occupy different positions on a structure. Influence lines give the value, at a given point in a structure, of any response function such as deflection, rotation, shear force, bending moment and support reactions for all possible positions of a travelling unit load. Two alternative methods are available for obtaining an influence line: 

Application of the Mueller-Breslau principle, by virtue of Maxwell's reciprocal theorem. This method which leads directly to the shape of the influence line, rather than its mathematical expression. Fig. 1 shows the reciprocal states an example for a two-span continuous beam.

1

𝑀𝑓𝐼 (𝐷)

A

Selected point

B

F

C

(I)

C

(II)

D

x

θII=1

A

B

F

D

x 15,0

10,0

Fig. 1: Application of the reciprocal theorem for obtaining the influence line for bending moment at D. 

Application of the plain definition, this is to say, placing a unit point load on a generic position and calculating the desired response function at a given point.

So, the derivation of the influence line for bending moment a D yields the analytical expression given in Table 1: Table 1: Influence line for bending moment at section D.

Mathematical expression of bending moment at D

M f ( B) 

2.3



x 525  x 2 1500



Valid range in AD

11250  975 x  x 2 M f ( B)  1500

in DB

M f ( B)  0.2 x  0.03x 2  0.001x3

in BC

Features and operation

The access to the list of contents of the repository is granted through a web browser. Once the user has selected the topic and an exercise, then starts a sequence consisting of statement, solving, solution, rubric and feedback. Interactivity with the system allows the user moving back and forth through the application, including a help system which provides with ad hoc hints, remarks and comments at each solving step. At the statement stage, the user can set the data values and physical properties of the structural system, this is to say, the lengths of spans, support conditions at beam ends and flexural stiffness. Then the structural system is plotted. Graphic issues on any problem are based on the advanced properties of jQuery and Dygraphs. Thus, the student handles a stable environment that leads to the solution of any given set of user-defined data. Practical conclusions regarding the beam behaviour under moving loads can be easily drawn. A set of problems with increasing complexity has been configured, of which a short sample is shown below.

2.3.1 Two-span continuous beam: Influence lines for bending moment at both mid-spans. This simple case involves a beam with constant cross-section and pinned supports and ends. It is of interest to study the variation of the bending moment at midpoints of both spans as a unit load moves along the beam ABC. The main purpose of this exercise is to understand the derivation and the meaning of the diagram ordinates. So, other aspects which would add complexity, such as non-prismatic sections, clamping of flexible supports at beam ends, are neglected. This information is useful in finding the absolute maximum bending moments (i.e., either positive or negative) at such points when a uniformly distributed load can occupy any region of the beam. The lengths of the two spans are defined by user (Fig. 2). Those values directly affect the beam response since the larger the span, the larger its response functions, this is to say, maximum response values are usually expected to occur. Once the user clicks the “Calculate” button, the system discerns if the maximum bending moment occurs at the midpoint of the span AB or at that of the span BC (Fig. 3). Afterwards the system shows the regions that the distributed load must occupy in order to achieve the maximum absolute values of bending moments at both midpoints.

Fig. 2: Problem statement of the influence line for bending moment at mid-spans of a two-span beam.

Fig. 3: Maximum bending moment values at mid-spans and occupied regions with uniform load.

The requested influence lines are plotted on the screen. Both abscissae and ordinates can be directly read for any point in the structures (Fig. 4). Besides, pop-up hints can appear any time the user requires so (Fig. 5). Additional on-the-run hints are available for the student to understand the basics and the fundamentals that lead to the results obtained (Fig. 6). As the user changes the data by swapping the lengths between spans, the effects become apparent. So, some design rules can be easily drawn, in particular, the significance of the ratio between the lengths of the spans.

Fig. 4: Influence line diagram. Ordinates are shown as the mouse pointer moves.

Fig. 5: Online hints and theoretical issues for enhancing comprehension.

Fig. 6: Explanations directly available at each step of the solving procedure.

2.3.2

Two-span continuous beam: maximum values for bending moment at any point when a point load moves along the beam.

The proposed tool provides the student with some features for highlighting crucial differences between various types of response functions in the beam. For instance, most students usually get soon familiar with the procedure to obtain both the internal forces diagrams for a beam under certain load conditions and the influence line for a certain internal force at a specific point. However, a number of them tend to confound the interpretations of such diagrams. This concern is one of tasks of this web-based learning assistant. So, an example is shown below (Fig. 7). For the same two-span continuous beam, two simultaneous charts appear on the screen. The left chart of Fig. 7 shows the influence line for bending moment at the point specified where the mouse cursor is located (at 10.85m from the left end). Some tips on the run are available upon request in case the user needs additional information. The right chart shows the internal forces diagrams (bending moment and shear optionally) for the beam when the point unit load is in the position selected on the left chart, related to the mouse pointer position.

Fig. 7: Influence line for bending moment at any point (left), internal forces diagrams (right).

3

RESULTS AND ACHIEVEMENT INDICATORS

The system is just in progress at its initial stages. The first indicators will be measured after the spring semester of 2015. The system starts with a presentation in classroom and an introductory workshop for students. Some planned lectures will include the use of this resource. Students will be actively involved in the usage of this tool. First, a group of them are invited to calculate by-hand several types of influence lines. Second, another group will directly apply this tool as the basic theory is being explained. Onsite training for CES-UPM students during implementation of this tool is available. Comparison between the levels of learning achieved is the first criterion to be measured. This will be used for enhancing and updating the learning environment. In an end-of-semester survey, students will be asked how often they used this tool and resources in the classroom and at home, in order to reshape or adapt it to their specific needs. This will serve as a measurement of the student learning progress and of the effectiveness of this tool. The survey is related with the following questions: 

For which subjects in the syllabus is the exercise useful?



The level of difficulty of the exercise and the time it takes to be done.



Any desirable information for handling errors or improving the learning of the exercise.



The content of a practical rubric that facilitates the correction of the exercise.



The usability and ease of the system.



Suggestions for improving the content of the repository.

The activity is expected to increase its autonomous learning level during the two next semesters.

4

CONCLUSIONS

This paper presents a web classroom application, currently in progress, based on a flexible, innovative and customisable methodology with the aim of responding to the needs of current Structural Analysis students. This free repository encompasses a range of topics on the basics and applications of influence lines on continuous beams. It includes a collection of exercises and problems in which the user can freely set the beam layout, the loading and boundary conditions. The system promptly shows the beam response and highlights the most critical sections for the given load condition. Also, theoretical and practical issues are easily available upon user’s convenience in each web page. Indeed, the critical positions of loads with relation to the structural response help the student to establish some design criteria. A subset with some sample cases has already been tested by a few students. They can configure their own individual learning pace and post queries relating to the course anytime on an online Forum, regularly monitored either by tutors or other students. The opinions and feedbacks hereby gathered are being very useful. This repository is currently being enlarged to include more resources.

5

ACKNOWLEDGEMENTS

The authors want to express their gratitude to the UPM for the support and facilities given under the Innovative Tools for Learning Programme.

REFERENCES [1]

El-Sawy, K.M. Sweedan, A. (2010). Innovative use of computer tools in teaching structural engineering applications. Australasian Journal of Engineering Education 16(1), pp 35-54.

[2]

Pedron, C. (2006). An Innovative Tool for Teaching Structural Analysis and Design. Institute of Structural Engineering, Suisse Federal Institute of Technology.

[3]

Marcé-Nogué, J., Gil, L., Pérez, M. A., Sánchez, M. (2013). Self-assessment exercises in Continuum Mechanics with autonomous learning. Journal of Technology and Science Education. 3(1), pp. 23-30.

[4]

Oxley, A. (1984). Computer‐Assisted Learning (CAL) of Structural Analysis. Innovations in Education & Training International. Ed Taylor&Francis 21(3)

[5]

UNESCO (2012). World Open Educational Resources (OER) Congress 2012 Paris OER Declaration. Retrieved from: www.unesco.org/new/fileadmin/MULTIMEDIA/HQ/CI/CI/pdf/Events/English_Paris_OER_Declar ation.pdf.

[6]

Megson, T.H.G. (2005). Structural and Stress Analysis, 2 ed. Elsevier ButterworthHeinemann.

nd