Best in 5 Minutes: Improving Students' Conceptual Understanding of Arch Construction and Behavior Using Physical Models of Masonry Arches in a Classroom Exercise

Rachel Herring Sangree; Benjamin W. Schafer

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Conference: 2020 ASEE Virtual Annual Conference Content Access
Location: Virtual On line
Publication Date: June 22, 2020
Start Date: June 22, 2020
End Date: June 26, 2021
Conference Session: Best in 5 Minutes: Demonstrating Interactive Teaching Activities
Tagged Divisions: Civil Engineering and Environmental Engineering
Page Count: 8
DOI: 10.18260/1-2--34211
Permanent URL: https://peer.asee.org/34211
Download Count: 557

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Paper Authors

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Rachel Herring Sangree Johns Hopkins University

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Rachel H. Sangree is a Senior Lecturer in the Department of Civil and Systems Engineering at Johns Hopkins University, where she teaches courses in structural engineering, serves as Director of Undergraduate Studies, and manages the part-time Master of Civil Engineering program through Johns Hopkins’ Engineering for Professionals. Dr. Sangree holds BS and MS degrees in Civil Engineering from Bucknell University and a PhD in Civil Engineering from Johns Hopkins University. Before beginning her PhD program, she worked as a design engineer in the bridge design group at Whitman, Requardt, and Associates, LLP in Baltimore, Maryland. While there, she had the opportunity to design a replacement floor system for a 1933 Pratt truss bridge over the Patapsco River, beginning a life-long interest in historic bridges which she hopes to pass on to future generations of civil engineering students.

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Benjamin W. Schafer Johns Hopkins University

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Professor in the Department of Civil and Systems Engineering at Johns Hopkins University.

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Abstract

The best works of structural engineering strive to find balance among efficiency (the best use of natural resources), economy (the best use of public funds), and elegance (a structure’s aesthetic quality or cultural significance) – all under the umbrella of safety and serviceability. In [Name of Course], a course offered in the Department of Civil Engineering at [Name of Institution], instructors take students on a semester-long tour of exemplary works of structural engineering around the world – works whose designers achieved such balance – so that students might in the future be able to independently evaluate works of structural engineering. The course is based on one developed and taught by Professor David Billington at Princeton University for many years, and like Professor Billington, the instructors of this course rely heavily on slide lectures in the style of an art history course. As much as possible, however, we engage the students in hands-on activities in the classroom to help demonstrate the lessons and stories told in the slides.

The first activity of the semester attempts to demonstrate the balance between efficiency and economy, using masonry arches as an example. In two small groups, students are timed as they construct arches out of pre-cut wood voussoirs. One group constructs a semi-circular arch – favored in ancient times by the Romans for its simple geometry and ease of construction. Another group constructs a parabolic arch – an evolved, funicular form whose efficiency was most elegantly expressed by Robert Hooke in 1675: as hangs the flexible line, so but inverted will stand the rigid arch. Once constructed, the two arches have the same span, rise, and most importantly ring thickness so while the students are able to construct the semi-circular arch much more quickly than the parabolic arch (demonstrating economy of construction), they find in the end (when a third person applies load simultaneously to the two arches) that the parabolic arch is more efficient – that is, a larger ring thickness would be needed by the semi-circular arch if it was to support the same amount of load.

For this “Best in 5 Minutes” presentation, we will bring the arches to the conference, take volunteers from the audience, and run the exercise as we would in class. We will also provide AutoCAD drawings of the arches to anyone who wishes to make their own!

Citation
Format

Sangree, R. H., & Schafer, B. W. (2020, June), Best in 5 Minutes: Improving Students' Conceptual Understanding of Arch Construction and Behavior Using Physical Models of Masonry Arches in a Classroom Exercise Paper presented at 2020 ASEE Virtual Annual Conference Content Access, Virtual On line . 10.18260/1-2--34211

TY  - CPAPER
AB  - The best works of structural engineering strive to find balance among efficiency (the best use of natural resources), economy (the best use of public funds), and elegance (a structure’s aesthetic quality or cultural significance) – all under the umbrella of safety and serviceability.  In [Name of Course], a course offered in the Department of Civil Engineering at [Name of Institution], instructors take students on a semester-long tour of exemplary works of structural engineering around the world – works whose designers achieved such balance – so that students might in the future be able to independently evaluate works of structural engineering.  The course is based on one developed and taught by Professor David Billington at Princeton University for many years, and like Professor Billington, the instructors of this course rely heavily on slide lectures in the style of an art history course.  As much as possible, however, we engage the students in hands-on activities in the classroom to help demonstrate the lessons and stories told in the slides.  

The first activity of the semester attempts to demonstrate the balance between efficiency and economy, using masonry arches as an example.  In two small groups, students are timed as they construct arches out of pre-cut wood voussoirs.  One group constructs a semi-circular arch – favored in ancient times by the Romans for its simple geometry and ease of construction.  Another group constructs a parabolic arch – an evolved, funicular form whose efficiency was most elegantly expressed by Robert Hooke in 1675: as hangs the flexible line, so but inverted will stand the rigid arch.  Once constructed, the two arches have the same span, rise, and most importantly ring thickness so while the students are able to construct the semi-circular arch much more quickly than the parabolic arch (demonstrating economy of construction), they find in the end (when a third person applies load simultaneously to the two arches) that the parabolic arch is more efficient – that is, a larger ring thickness would be needed by the semi-circular arch if it was to support the same amount of load.  

For this “Best in 5 Minutes” presentation, we will bring the arches to the conference, take volunteers from the audience, and run the exercise as we would in class.  We will also provide AutoCAD drawings of the arches to anyone who wishes to make their own!

AU  - Rachel Herring Sangree
AU  - Benjamin W. Schafer
CY  - Virtual On line 
DA  - 2020/06/22
PB  - ASEE Conferences
TI  - Best in 5 Minutes: Improving Students' Conceptual Understanding of Arch Construction and Behavior Using Physical Models of Masonry Arches in a Classroom Exercise
UR  - https://peer.asee.org/34211
DO  - 10.18260/1-2--34211
ER  -