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Is Shaping Structures: Statics rigorous enough for use in
an engineering program? 
It would be easy to dismiss Shaping Structures: Statics as
being "soft" and something less than rigorous. For one thing, all those
beautiful photographs and drawings would seem to indicate a "touchy-feely"
approach. And then there are the graphical solutions, which are 98% to 99% accurate rather
than 100%. Furthermore, the book gives a lot of space and attention to such
nonmathematical matters as preliminary design, form-finding, detailing, and planning the
construction process. The book even talks about aesthetics, for goodness sake! How
can it possibly be suitable for use in a structural engineering curriculum? Consider the
following points:
Shaping Structures: Statics teaches engineering
students to design structures and get them built, not just to check member sizes.
Shaping Structures: Statics presents a coherent, continuous picture of the whole
process of designing a structure in every chapter. Every other statics textbook in print
teaches how to find forces in structures and nothing else--nothing on how to find good
form for a structure, how to detail it, how to get it built, all things that every
structural engineer needs to know. European engineering programs feature sustained design
experiences in which students invent and develop structures to fit open-ended problem
statements. Most U.S. schools still don't do that, despite the warnings of many
leading engineering educators that students must be taught to design, not just to
calculate. Many students of structural engineering in America today graduate from their
universities never having designed even a single rudimentary structure, but only having
done repeated analyses of fragments of structures that were designed by other people.
Engineering is neither science nor mathematics; it's design. Design is the
process of starting with a problem statement and a blank sheet of paper and ending up with
a built solution that works. Shaping Structures: Statics is the only statics text
that teaches students to design.
Shaping Structures: Statics
presents graphical solution techniques that are ideal partners for
finite element analysis. The question
is sometimes asked, why introduce graphical analysis of structures,
which can lead to errors in force values that run as high as 1%
to 2%, in an era when finite element analysis by computer is available
in every engineering school? The answer is perhaps not obvious,
but it's very important: Finite element analysis is purely
quantitative and wholly uncritical. It will give useful results
for a very badly-shaped structure as well as for a well-shaped one,
and it will give the designer no clue that the shape is bad. Graphical
analysis, on the other hand, always finds good shapes for cables
and arches, and is easily made to do so for trusses. Even when used
to analyze a truss of predetermined shape, it gives an immediate
reading of the relative efficiency of the shape, and it shows clearly
why forces are excessive in a badly shaped truss and how to change
the shape to reduce them. A student who is taught to use graphical
analysis for preliminary design and FEA for more detailed analysis
will soon find that structures shaped by graphical methods will
show consistently low stresses in FEA, whereas structures that are
shaped entirely by eye and intuition often will not.
Keep in mind, too, that all numerical and computer-based methods of
analysis are based on graphical models. The parallelogram model for adding force vectors
is a graphical device. Shear force and bending moment diagrams originally were plotted
graphically. All the formulas we know and love, and all the computer programs for
structural analysis, had their origins in graphical understandings. Doing the calculations
purely by numbers or by computer means that the diagrams that really explain the structure
are hidden from view and cannot be consulted for the wisdom that they can communicate to
the designer. As for a potential error of 2% or 3% in graphical calculations: How accurate
are the live load values that you use in your numerical calculations? The true live loads
on a structure often range between 0% and 200% of the values that we take from a building
code. Given this range, an error of 10% in calculating forces would be of no consequence,
and you'd have to draw the diagrams freehand to get that big an error. A 2% or 3%
error is infinitesimal when measured against the huge uncertainty of our load estimates.
Every photograph in Shaping Structures: Statics has a
pedagogical function. Most of the photographs serve to demonstrate to the student that
the principle or technique that he or she is learning is related to real structures. This
is highly motivational: The student looks at the picture and suddenly realizes that he or
she knows how to find form and forces for such a structure. When so many of these real
structures are so beautiful, it soon becomes apparent to the student that efficiency and
beauty are closely linked.
The math is all there in Shaping Structures: Statics.
In a conventional statics text, the math is often the only thing that stands out from the
page layout, and we tend to notice it more. In our text, the drawings and photographs tend
to catch the reader's eye, making the equations less obvious. But they are there. We
even derive and demonstrate two different mathematical approaches to quantifying form and
forces in parabolic structures, which is one more than most books do. It's true that
we don't cover centroids and moments of inertia in this book. That's because we
know that students learn a subject most easily and efficiently when they feel a need for
it and can put it to work as soon as they learn it. They don't need these two
subjects until their next term's study of structures in bending, which is where we
will introduce them.
Shaping Structures: Statics teaches critical thinking to
engineering students. Every statics text teaches students to find the forces in a
truss. But what text other than ours takes the time to explore how a truss functions, how
to distinguish good truss forms from bad, and how to find good forms for trusses? The
student who has completed study of this book is already an astute critic of long-span
structures of every type.
Shaping Structures: Statics is rigorous in presenting the
entire context of structural design. Webster notes that the word "rigor"
comes from a root word meaning "stiff." He then offers, in this order, the
following synonyms: "harsh inflexibility; severity; the quality of being unyielding
or inflexible; strictness; severity of life; austerity;" and so on, then finally,
"strict precision; exactness." Do these words describe you and your teaching
style? None of these qualities, not even the last of them, is characteristic of a good
structural engineer (or teacher). A good engineer has the mental flexibility to find a
good design solution and the wisdom to realize that precision and exactness are qualities
that do not reflect the approximate nature of our load assumptions and analyses.
Perhaps you teach a very complete, no-nonsense course in
calculations of structural steel or reinforced concrete structures. Is it rigorous, in the
good sense of the word? Not if it doesn't cover aspects of the structural design
process other than the mathematics. Thousands of engineers languish in the boredom of
back-desk jobs, victims of their inability to do anything other than calculate. The front
desks are occupied by the rare engineers who know how to find good forms for structures
and how to get them built. True rigor means educating your engineering students to occupy
the front desks. The people at the front desks not only make more money, they're a
lot happier. And they, not the ones who merely calculate, are the people who create the
world's structures. |
