Open Ended Problems in Mechanics of Materials





Problem solving is one learning activity that is extensively employed by engineering educators. “Problem-solving is defined as a process used to obtain a best answer to an unknown or a decision subject to some constraints” (Mourtos 2004). Through problem solving students learn to apply the theoretical equations in both hypothetical and real-world scenarios. Assigning problem sets provides students the opportunity to test their understanding of the theory and concepts. The type of problems assigned to students addresses various levels of thinking and outcomes. Traditionally, problems are designed with given parameters and students are required to determine an unknown quantity. The solution usually involves substitution of known values to an equation to solve for the unknown parameter. Problems of this type are said to be “close-ended.” Close-ended questions usually have a unique answer and the procedure of obtaining the answer is limited or straight-forward. Close-ended problems address lower levels of thinking (based on Bloom’s taxonomy) like “remembering”, “understanding” and “applying” and some higher mode of thinking like “analyzing”.



To address higher levels of thinking like “evaluating” and “creating” and transformative outcomes experienced in the real-world, “open-ended” questions should also be included in the problem sets. Sobek and Jain (2004) emphasized the need for open-ended problems. “Employers look for engineers who are effective at solving open-ended problems. Engineering accreditation demands evidence that students can tackle open-ended problems proficiently.” Open-ended problems address considerably the student outcomes on “an ability to recognize, formulate, and solve civil engineering problems” and “an ability to engage in lifelong learning.” Open-ended questions are usually ill-defined and there may be more than one valid approach to obtain the solution. As a matter of fact, the solution may not be unique because of varying assumptions made regarding some parameters. Mourtos (2004) noted in their study that “traditional exercises (close-ended) found in most engineering texts, although useful, do not adequately prepare engineering students for real-world problems. Students seem to have great difficulty approaching these (open-ended) problems; however, they also seem to enjoy the challenge and perform reasonably well if given proper guidance.”

Problem : If you were to install a

steel Z-purlin, which arrangement

would you choose to maximize the

moment capacity of the section?

In the problem sets in my structural analysis course, open-ended problems are given. The problem shown about a Z-purlin is related to analysis of beams due to unsymmetrical bending which is similar to a problem by Singer. Deciding on the most effective set-up of the Z-section whether upright or inverted would require application of concepts in moment of inertia, equilibrium, bending moment and elastic bending stress analysis. There are various ways of determining the more efficient arrangement of the Z-section. You may compute which arrangment has the larger moment capacity. You can assume a moment and compute the maximum stresses and compare.

References:

Mourtos, N. et al. (2004). “Open-ended problem solving skills in thermal-fluids engineering,” Global Journal of Egg Education, UICEE

Sobek, D and Jain V. (2004). “The Engineering Problem Solving Process: Good for Students?” Proc.2004 American Society for Engineering Education (ASEE) Annual Conference & Exposition

NOTE: An updated version of this article - "Challenging Students' Thinking Through Open-ended Problems" was published as e-notes in The Philippine Engineering Education (Vol. 1, No. 1, Sept 2013) - the official news magazine of the Philippines Association for Technological Education (PATE).

Using Visual Gobbets in Teaching

A gobbet is “an extract of text, a passage of literature, an image, a cartoon, a photograph, a map or an artifact provided as a context for analysis, translation or discussion in an assessment” (Chan 2008). “The student’s task is to identify the gobbet, explain its context, say why it is important, what it reminds them of or whatever else you would like them to comment on” (Biggs and Tang 1999). Gobbets are usually used for assessment.

I used "visual" gobbets in my class in Theory of Structures and Earthquake Engineering. Here are some examples.

In my first meeting in Theory of Structures-I, as my review of basic concepts in Statics and Mechanics of Deformable Bodies, I displayed an image of a beam bridge  and posed the problem to the students: “if you are required to design a simple beam bridge to cross a river, what information would you gather to accomplish your task and how would you use the information?

A Gobbet on Simple Beam Analysis & Design

 The responses from this gobbet include span length, beam material, weight of the person(s), number of persons crossing the bridge at one time, shape and size of the beam, soil type at the beam ends and cost. After listing their responses, I asked them on how the items in the list will be used in the analysis and design of the beam bridge. From this exercise, the students were able to reflect and learned about the relationship of the listed items to concepts in Statics and Mechanics of Deformable Bodies.

• A beam bridge can be modelled as a simple beam with length, L and the weights represented as concentrated loads
• Analysis means solving for reactions and maximum internal forces – moment and shear
• The type of material will specify the material strength (allowable stresses) and mechanical properties (modulus of elasticity)
• Designing the beam means determining the shape and size of the beam
• Various types of design can be done for comparison (strength, cost)

Another gobbet in my Earthquake Engineering class was included in an exam to assess the students’ understanding of structural failure due to earthquakes. This is an exercise on post-earthquake evaluation usually conducted by structural engineers (ASEP) after the occurrence of an earthquake. The students are shown photos of a building damaged due to earthquake. A description of the observed damage is also given. The students are required to assess the condition of the building based on the photos and description and recommend the appropriate post-earthquake posting (Safe, Limited Entry or Unsafe).



 "Safe", "Limited Entry" or "Unsafe"?
nisee.berkely.edu



The third example of a gobbet exercise which I called “Scaling an Earthquake” was applied in the Earthquake Engineering course. One of the learning outcomes of the course is familiarization with the PHIVOLCS Earthquake Intensity Scale (PEIS). A series of photos were displayed to the class and the following problem was posted: “You are tasked to determine the intensity of the earthquake using PEIS. Assign the intensity scale for each photo. Explain your answer.” In this exercise, the students have to read and understand carefully the descriptors for each intensity scale in PEIS and relate them to the photos. 

Rate the Intensity Scale of this Earthquake
                     http://woldcnews.com/

References

Biggs, J. and Tang, C. (1999). Teaching for Quality Learning at University, McGraw-Hill Open University Press
Chan C. (2008) “Assessment: Gobbets”, Assessment Resource Centre, University of Hong Kong [http://arc.caut.hku.hk]: Available: Accessed: 8/27/2012