Almost all construction and architectural units in academic institutions offer structural design courses (Chini 1995). Much of construction education in the United States is governed by the American Council for Construction Education, commonly referred to as ACCE. The ACCE guidelines (Form 103, 2000), stipulate that construction students must take a minimum of 20 semester hours in the curriculum category of Construction Science. The Guidelines further stipulate that of these 20 semester hours, students take a minimum of six under the core subject matter entitled "Analysis and Design of Construction Systems".

As a result of these requirements, structures classes comprise between 5 and 10 percent of most construction science curriculums. It is obvious that ACCE considers structures classes to be a significant and integral part of all construction science curriculums.

Most professors that teach structures classes have an engineering background and tend to present structural concepts in the same way their professors presented the concepts to them. But it is clear that the ACCE does not envision a curriculum that focuses on training construction students to actually perform engineering calculations later in their careers. In fact, the ACCE emphasizes understanding and communication.

"The Constructor must have an understanding of the contribution of the design disciplines' processes. The Constructor must be able to communicate with the design professionals, and should be capable of participating during the planning phase of design-build projects. Construction sciences and architectural or engineering design topics selected to facilitate communications with the design disciplines and to solve practical construction problems are to be considered in this category." (ACCE, 2000)

This emphasis on understanding is consistent with a survey of construction educators done in 1995. Chini reported that "seventy eight percent of respondents believe that we should not be tied to the traditional engineering formats in teaching structures to our construction students…..More diverse subjects should be covered with less depth." (Chini 1995)

How then, have construction educators changed the content of the courses they teach to reflect the ACCE guidelines, the views of construction educators, and the recent advances in technology? The answer, interestingly, is that very little has changed. Educators continue to express dismay over students’ lack of interest and lack of understanding in these courses. Students often view structures courses as mind numbing exercises in mathematical manipulation, superimposed over stick figure sketches. (Slattery 2000, Black and Duff 1994, Williams and Hein 1990). While some educators are reporting encouraging results with digital technology (Slattery 2000, Black and Duff 1994), most are using the same ineffective pedagogy they were exposed to decades ago.

In his book on structures, J. E. Gordon describes how academe has historically taken what should be a fascinating subject, and diminished the interest and curiosity that students should naturally exhibit. Gordon points out that often the mathematical manipulations tend to obscure rather than illuminate the important structural concepts.

"By Mariotte’s time the whole subject of the behavior of materials and structures under loads was beginning to be called the science of elasticity. Since the subject became popular with mathematicians about one hundred and fifty years ago, I am afraid that a really formidable number of unreadable, incomprehensible books have been written about elasticity, and generations of students have endured agonies of boredom in lectures about materials and structures. In my opinion the mystique and mumbo-jumbo is overdone and often beside the point."

When explaining a structural concept, educators typically present the mathematical concepts first, often beginning by teaching students how to quantify a difficult concept. In reality, this is exactly the reverse of the way in which most structural engineering problems are first solved. Quantification is usually the last step of the process of understanding. For most real world problems, engineers begin by observing behavioral properties, developing engineering intuition and hypothesis, and then finally modeling a solution with mathematics. By going in reverse order, educators can bury fundamental concepts in a seeming deluge of mathematics. Students are sometimes able to "do the math" without developing a true understanding of the concept.

Faculty members have indicated a willingness to explore the use of digital or other media to enhance structural concepts. The potential advantages range from exposing students to more example problems to utilizing structural software to enhance understanding and visualization. Software may enable professors to focus more on the entire structure as opposed to teaching the design of discrete, isolated elements.

Effective educators should constantly re-evaluate course goals, objectives and instructional delivery systems. When there is a repetitive pattern of criticism and a decline in student interest, a change is required. In the following sections, a new approach to the delivery of this educational content will be presented.

Like many subjects, the teaching and learning of structures is dependent on the students’ knowledge of a relatively small number of key concepts. Topics such as stress, moment of inertia, shear, bending moment, and modulus of elasticity are key topics in any curriculum focusing on structural behavior.

In the section below, the traditional approach to the explanation of the concept of ‘Moment of Inertia’ will be contrasted with a different approach. The subject of moment of inertia has been chosen as an example, but any major structural concept would serve to contrast the two teaching styles equally well.

The learning objective is for students to be able to calculate the moment of inertia of a given geometrical shape.

Obviously, the effort required to compute the moment of inertia for the problems seen above, coupled with an appropriate explanation of the results, would take considerable time. In this traditional approach, the mathematics precedes the conceptual explanation. While the instructor is in the process of computing the moments of inertia, the students are taking notes. Since the calculations are tedious and consume most of the lecture time, the real purpose of the exercise may be obscured.

To facilitate learning, and to generate more student interest in structural topics, the authors propose a six step approach to the coverage of the key structural concepts. The same problem that was discussed previously will be presented in this manner.

The learning objectives are as follows:

1. To understand the necessity for the concept of moment of inertia.

2. To understand the role of moment of inertia in the behavior of structures.

3. To be able to calculate the moment of inertia for a given geometrical shape.

Problem Statement: Your neighbor Bill has come to you with a problem.  The contractor that built his house has used 2 x 8 floor joists to span fourteen feet and placed sixteen inches on center.  The joists have already sagged more than 1 inch, and seem to be continuing to deflect.

Bill has purchased some fourteen foot 2 x 4's and plans to jack the floor joists back into their original position.  After the 2 x 8 floor joists are raised to their original position he plans to screw a 2 x 4 to the joist as shown.  He also plans to screw the sub floor to the joists so that the plywood will act in conjunction with the beam. Bill wants you to tell him which orientation is most efficient for the 2 x 4’s, and how much all this work will improve the situation.

Moment of Inertia, or "I", is a property of a cross section. It has many applications. The property is difficult to visualize because it has units of inches raised to the fourth power. In the example we are about to work, moment of inertia is a measure of the resistance of the beam to deflection.

Moment of inertia does not vary linearly due to changes in the depth of a cross-section. For example, doubling the depth of a rectangular beam cross-section will result in an 8 fold increase in moment of inertia. To maximize moment of inertia, move as much of the material as far from the centroid as possible.

A software product called "Shape Builder" by I.E.S. systems is used to allow the instructor to calculate moment of inertia (and many other properties) as fast as the instructor can create the shape on the computer. Both shapes shown can be created in less than two minutes. The software is essentially a drawing package, with all the standard steel and wood shapes built into it. As soon as the operator completes the drawing, the moment of inertia of the assembled section is automatically displayed. The solution is presented in Table 2.

Since all of the computations shown in this approach are done by the software, the instructor can fulfill most of the learning objectives in less than 10 minutes. Utilizing the software saves significant class time and gives the students and the instructor time to explore other options not possible with a traditional approach. The instructor can quickly summarize the results of the various configurations as shown in Table 3.

Instead of simply quantifying an esoteric cross-sectional property, the students learn about constructing efficient cross-sections for beams. If the floor joists are jacked up and the 2 x 8 joist is then glued and screwed to the sub floor (Option 1), the moment of inertia is increased (and the deflection decreased) by almost a factor of three. To further reduce deflection, a 2 x 4 can be attached to the side of the joist as shown in Option 2, increasing the moment of inertia by almost 5 times the original. If the 2 x 4 is placed on the bottom of the joist (Option 3) the strength of the system is almost 7 times the original strength.

In this problem, it would be appropriate to mathematically recalculate the moment of inertia for various other combinations of wood members comprising typical floor systems. At the end of the lecture, the students would hopefully understand the need for the concept of moment of inertia and its role in the deflection of beams. By using an example, the significance of moment of inertia to a column may be taught in a similar fashion. With a little bit of practice the students should be able to calculate moment of inertia for any given composite shape.

A Comment on the Math…………

Some instructors argue that the rigor of mathematical calculations enhances problem solving capabilities of students; others feel strongly that the structural concepts could be taught without any mathematical calculations. Hence phase 5 is an option the instructor must adapt based on his/her point of view.

There is obvious and demonstrable value in having students participate in a process that demands organization of complex material, precision of calculation, and the presentation and quantification of values. The question that logically follows is whether this necessary portion of the educational process should be confined to topics covered in structures courses.

When learning the topic of moment of inertia (and most other structural concepts), students traditionally spend the bulk of their study time working problems that deal with the calculation of the magnitude of the property. Is it possible that this traditional approach is an inefficient use of time and effort? Is it possible that placing so much focus on the mathematics is counterproductive and actually obscures the real meaning of the concept?

Perhaps it is time for structural educators to give serious consideration to significantly reducing or even eliminating this student perceived drudgery. When considering moment of inertia, it is unlikely that these mathematical gymnastics provide any real bridge to understanding. Furthermore, because so many software packages quickly and easily provide this information, few outside of the educational community (including engineers) will ever actually perform these calculations.

If one of the primary goals of the structures sequence is to force students to learn complex processes, then the mathematics are rightfully positioned in the structures courses. If, however, the goals of the classes are to promote understanding of the structural concepts, the instructor should reevaluate the traditional methods of presenting the material.

Discuss the learning objectives with the students again and the relevance of moment of inertia to their understanding of structures. The exercise of testing students is to verify that students have indeed understood the concept and can apply their knowledge to solve real world problems. Testing the students only on the mathematics does not prove that they can apply their knowledge to an actual situation. Hence the students must be tested with similar problems that not only test their ability to do the mathematics correctly but also that they can apply the concept to a real world problem

The American Council for Construction Education (ACCE) requires accredited construction programs in the United States to devote significant educational effort to the "Analysis and Design of Construction Systems". Topics within these courses are often taught in the same way they are taught in engineering curriculums. Although there is nothing inherently wrong with using an established educational model, there is documented dissatisfaction with the way the structures courses are taught to construction students. The ACCE recommendations clearly state that a pedagogical emphasis should be placed on a basic understanding of the principles, as opposed to spending large amounts of time perfecting mathematical quantification.

By reorganizing and restructuring the way the information is delivered, professors can do fewer problems and spend more time playing the "what if" games to help students understand the key structural concepts. Furthermore, recent advances in technology provide professors even greater opportunity to explain difficult structural concepts quickly and easily.

The real challenge for the future is to clearly identify those principles that are most pertinent to the construction student’s understanding of structural behavior. After these principles are identified, a statistically relevant mechanism needs to be developed that will allow educators to measure the students true understanding of these principles.

Black R. G. and Duff S. (1994), A Model for Teaching Structures: Finite Element Analysis in Architectural Education, Journal Architectural Education, Vol. 48, Issue 1 - September 1994

Chini S. A. (1995), Survey of the Structures Courses Offered by ASC School Members, ASC Proceedings.

Gordon, James Edward, (1978), Structures: or, why things don’t fall down. ISBN 0-306-80151-5 (pbk.) p. 28

Saddik W. F. (2000), Evaluating Construction Software Without Getting Burned, [WWW document]. URL http://www.cbczine.com/articles/selecting/eval_p2.asp

Slattery T. K. (2000), Design by Analysis Tool for Teaching Formwork Design, ASC Proceedings.

Williams S. and Hein M. (1990), Rethinking the Structures Curriculum, ASC Proceedings.