Structural Analysis: Are We Relying Too Much on Computers Part 2: a Solution by Graham H

Structural Analysis: Are We Relying Too Much On Computers Part 2: A Solution By Graham H. Powell, Ph.D., P.E.

In Part 1 of this series of articles, I expressed the opinion that there is a serious Modeling requires an understanding problem in the way that we teach structural analysis in our universities. The main of the behavior of the various compo- problem, as I see it, is that far too much time is spent teaching the “number nents that can make up a structure,® an crunching” phase of analysis, and far too little time teaching the more important understanding of stiffness and flexibility, “modeling” and “interpretation” phases. As a consequence, students are poorly the ability to distinguish important and educated in the proper use of computers. The fault lies not with the computer, but unimportant aspects of behavior, and the with the way that structural analysis is taught. ability to create an analysis model given Basic Education for a Structural Engineer (April 2007 STRUCTURE) proposed a “toolbox” of structural elements. a course content for structural analysis. The proposed content emphasizes hand Interpretation requires a number of skills, calculation methods such as Moment Distribution and Slope Deflection, and for checking whether the analysis results mentions computers only once. In my opinion it is outdated, and it perpetuates are reasonable, for identifying the cause the problem noted above. when the results do not look reasonable, This article proposes a solution, in the formCopyright of an outline for a much different and for organizing the results in a way that course content with a different set of outcomes. This course content places much supports decision making for design. greater emphasis on the effective use of computers. Specific Skills for Modeling Outcomes 3) Given the results of a computer and Interpretation analysis, check the equilibrium Some specific skills are as follows: Consider, first, some desirable outcomes, of various components and 1) The ability to set up free bodies and for the moment consider only under- connections, using free bodies and of a wide variety of types, and graduate education. equilibrium equations. to apply equilibrium equations Before a student takes a course in struc- 4) Given the results of a computer to these free bodies to check tural analysis, I would expect that he or she analysis, check that compatibility that equilibrium is satisfied. It would first take a course in mechanics of is satisfied (i.e., check that element should be emphasized to students materials, and would also have had some deformations are consistent with that errors in setting up free instruction in statics and kinematics. I nodal displacements). bodies and applying equilibrium assume that only one semester-length 5) Explain stiffness and flexibility equations are inexcusable. course in structural analysis is required, coefficients, and stiffness and 2) The ability to use virtual work to with one additional course available as an flexibility matrices. Calculate solve simple statically determinate elective. Beyond that, a student would take stiffness and flexibility matrices graduate courses. magazinestructures (i.e. to apply the Virtual for bar and beam elements. Displacements Principle for rigid At the end of the first course, I believe 6) Explain the Direct Stiffness Sthat a T student shouldR be able to doU C T Ubodies and mechanisms)R as anE Method of structural analysis. alternative to free bodies and the following: Explain how numerical sensitivity equilibrium equations. 1) Develop a linear elastic model can cause this method to give 3) The ability to calculate internal of a fairly realistic 3D structure incorrect results.

orum actions (P, M, V) in statically composed of frame, wall and At the end of a second course, a student determinate structures, and to connection components. Run should be able to model, analyze and draw P, M, V diagrams. computer analyses for static check more complex structures with a gravity and lateral loads. Present 4) The ability to sketch deflected F wider variety of element types (including shapes for structures and structural and interpret the results. Given simple finite elements), consider dynamic components of a variety of types, beam and column strengths, loads (with a basic understanding of inertia in order to show, qualitatively, calculate strength Demand/ and damping forces, mode shapes and how a structure or structural Capacity ratios. modal superposition), and have a deeper component is likely to deform. 2) Develop a nonlinear model of a 2D understanding of the underlying theory. frame with simple plastic hinges. 5) The ability to do simple Run computer analyses for static deflection calculations for frames gravity and lateral loads, with and Broad Skills and trusses, using tools such without P-∆ effects. Explain the To satisfy the above outcomes, a stu- as Moment-Area and Williot behavior. Given beam and column dent must develop skills in modeling and diagrams. These tools require strengths and hinge rotation interpretation, be able to run an analysis, a clear understanding of the capacities, calculate strength and and have a basic understanding of the relationships between internal deformation D/C ratios. underlying theory. deformations (beam curvatures, tructural

Structural Forum is intended to stimulate thoughtful dialogue and debate among structural engineers and other participants in the discussion on topics of current importance to structural engineers S design and construction process. Any opinions expressed in Structural Forum are those of the author(s) and do not necessarily reflect the views of NCSEA, CASE, SEI, C 3 Ink, or the STRUCTURE® magazine Editorial Board.

STRUCTURE magazine 20 December 2008 bar extensions, etc.) and external treated largely as a black box – we can assume ment stiffnesses into a structure stiffness, to displacements. In my opinion, the that it is done correctly, and we do not need know that a large set of equations must be ability to calculate deflections using to worry about the details. solved, and a few other things. These can be virtual work (i.e., using the Virtual Obviously, however, when an engineer explained using physical reasoning, with no Forces Principle) is not an essential uses an analysis method, he or she should need for elaborate mathematics. Compared skill – it requires a lot of effort to have an understanding of the theoretical with the complexities of modeling and in- learn, it does not help a student to and computational basis of that method. terpretation, the Direct Stiffness Method is develop a “feel” for structural The question is: how much detail do we not difficult to understand. The® full details behavior, and I have not found it need to teach? can be left to advanced graduate courses. to be particularly useful. In my opinion, we do not need to go into It is also important for students to recognize 6) The ability to calculate stiffnesses and a lot of detail for undergraduate students. A that the Direct Stiffness Method is not fool- flexibilities for structural components student needs to understand the concepts of proof. A common problem occurs when of a variety of types, and to understand stiffness and flexibility, to know about stiff- an element in a structure is assumed to be the importance of stiffness and ness coefficients and stiffness matrices, to extremely stiff, and an inexperienced engineer flexibility. This can be done for most understand the process for assembling ele- makes that element astronomically stiff (for components using the above skills. It should include the ability to calculate stiffnesses and flexibilities for simple Copyright components in series and in parallel (i.e. adding stiffnesses for components in parallel, and adding flexibilities for components in series). 7) The ability to apply common sense, for example by recognizing when Now a calculated deflection is obviously too large or too small, or that the Powder Available! proportions of a structural member •Square 2"–7" are obviously unrealistic. 1 •Rectangle 3"x1 /2"–10"x4" These skills are needed mainly to understand structural behavior (for example, how forces Primed •Round 2 NPS–8 NPS are transmitted through connections), and to •Square, Rectangle & Round in a wide variety of gauges. check that computer results are reasonable.

These skills may occasionally be used to analyze visit ADVERTISEMENT Information, - For Advertiser simple structures by hand, but a structure must Tubing be very simple before hand analysis is moremagazine EPOX Z KOTE: efficient than computer analysis. I haveS not included T the ability toR analyze a U C T U R E statically indeterminate structure by hand. In my opinion this is something that an engineer CutCut it.it. will never be required to do, so it is not a useful skill. In my practice, I use equilibrium equations all the time; I sketch deflected WeldWeld it.it. www. shapes often, and I frequently do simple STRUCTUREmag deflection calculations. I never use moment distribution or other classical methods to PaintPaint it.it. analyze a statically indeterminate structure. .org These methods are of interest to a historian, but to teach them is, I believe, a waste of a student’s valuable time and energy. There ShipShip it.it. are much more useful, and more interesting, things to teach. Are you ready to uncover more profit? Skills for Number Crunching • Weld spatter doesn’t stick The number crunching phase, as I have defined • No VOC’s or harmful fumes it, includes both theory and computation. In • No special welding procedures the present era, the method that is used for • Reduces cleaning & preparation virtually all analyses is the Direct Stiffness • Compatible with powder & paint systems Method, and the computation is always done • Save space, store EPOX Z KOTE outdoors! by computer The engineer defines the model, but a computer program forms the element Division of the John Maneely Company USA 800-733-5683 CANADA 800-265-6912 stiffnesses, assembles them, sets up the loads, MADE WITH PRIDE solves the equations, etc. This process can be - IN AMERICA - [email protected] www.atlastube.com

STRUCTURE magazine 21 December 2008

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Blank Page.indd 1 7/31/2008 3:41:11 PM example, by specifying an area of 1020 units for a very stiff bar). Such errors can cause numerical Example Exercise – Source of Deflections inaccuracy in the equation solving part of the in a Moment Frame Direct Stiffness Method. Students need to understand the basics of the numerical procedure, Consider a simple moment frame as shown. to avoid making such elementary mistakes.

Basic Studies Computer Programming Skills® 1) Analyze the frame, by computer, with Area to see why. Discuss how pinned In my opinion, most courses in structural very stiff columns and deformable and fixed (moment-resisting) supports analysis spend too much time on the num- beams (Figure b). Look at the roof drift might be provided in an actual frame. ber crunching phase. Among other things, and explain the deflected shape. Discuss whether such fixed supports it is not uncommon to require students to 2) Analyze with very stiff beams and might really be rotationally rigid. write computer programs to implement the deformable columns (Figure c). Again 2) Vary the beam and column sizes Direct Stiffness Method (and possibly other look at the roof drift and explain the within practical ranges. Discuss methods). The programming effort can be deflected shape. practical span-to-depth ratios. substantial and at the undergraduate level 3) Compare the roof drifts to get an idea 3) For the case with deformable beams, I do not believe that this is a good use of a of how much of the frame deflection add stiffCopyright end zones to the beams, to student’s time – there are more important originates in the columns and how account for increased stiffness in the things to teach. much in the beams. connection region. See how much this This does not mean, however, that under- 4) Analyze with deformable beams and increases the stiffness. Compare the graduate students should not be encouraged deformable columns. Look at the roof bending moments at the column face to use computers. Many tasks in the modeling drift and the deflected shape. See if the and column centerline. and interpretation phases involve equilibrium, roof drift is the sum of drifts from the 4) For typical steel member sizes, analyze compatibility and other calculations. Usually previous analyses. There is no reason with very stiff beams and columns the calculations can be done quickly by hand, why it should be equal to the sum, but and deformable panel zones in the but sometimes it can be more efficient to de- it should be close. connections. See how much of the velop solutions in computer programs such as 5) Perform equilibrium checks on the deflection originates in the panel zones. Mathcad and Matlab. I believe that students results. For example, given the column 5) Make the stiff columns astronomically should be encouraged to use such programs shear forces get the story shears and stiff. The results will be garbage. Show when it is appropriate. compare with the shears from the that if the stiffness ratio between lateral loads. beams and columns exceeds the 6) For the cases in Figures b and c, check precision of the computer, accuracy is Instructional Method the deflections by hand. This can lost. Progressively reduce the column I believe that the best and quickest way for easily be done using direct geometry magazinestiffness and show that correct results a student to learn structural analysis is to do and standard cantilever and beam are ultimately obtained. Show that if structural analysis. Sflexibilities (deflectionT = 3PL /3EIR for a Uthe column stiffnessC is 100 or moreT OnU the first day of theR first course, Egive -ev cantilever with an end load, deflection times the beam stiffness, there is not ery student a computer program and begin = PL3/12EI for sway of a column much difference in the results. assigning analysis exercises along the lines of fixed top and bottom, end rotation = 6) Instead of very stiff columns, use rigid those listed in Part 1 of this article. Using ML/6EI for a beam). link constraints to make the columns such exercises, teach how to model structures 7) For the case in Figure b, given the roof truly rigid. Note that there are no and how to check the analysis results. Explain drift, calculate the beam end rotations, numerical sensitivity issues. Note that the behavior of frame and wall components and use the beam stiffnesses to calculate when the columns are very stiff the under bending and shear, and how to model the end moments. Confirm that they computer calculates P,M,V values for this behavior. Show how to use the virtual agree with the computer results. the columns, but that when rigid link displacements principle, and tools such as constraints are used the computer Moment-Area and Williot diagrams. Show Some Additional Studies calculates zero P,M,V values. how stiffness and flexibility matrices can be formed for simple elements, and how 1) For the case with stiff beams, consider stiffness and flexibility can be calculated for both pinned and fixed supports for components in series and parallel. Explain the the bottom story physical basis of the Direct Stiffness Method, columns. Show explain the P-∆ effect (equilibrium in the that the first deformed configuration), and introduce story with pinned simple inelastic behavior (e.g. plastic hinge supports is four concepts). Do this within the framework of a times more flexible series of exercises that require skills in model- than with fixed ing, analysis and interpretation. supports. Look With this approach, a student can pro- at the bending gressively develop the required skills, and moment diagrams also develop a “feel” for structural behavior. and use Moment (a) (b) (c) The hands-on approach also helps to keep students interested.

STRUCTURE magazine 22 December 2008 An Example Exercise Conclusion An example exercise is provided (see page ally considered only in advanced courses. I The goal of courses in structural analysis 22), which could be the first exercise to be believe this is a mistake. should be to educate young engineers to assigned in a first undergraduate course. Beyond these basic graduate courses there can, analyze complex structures using modern meth- This exercise can be used to introduce and should, be a number of advanced courses, ods, and to understand what they are doing stiffness concepts and the Direct Stiffness including finite element theory, advanced and why they are doing it. I believe that most Method, show how simple equilibrium and dynamics, advanced nonlinear analysis, and structural analysis courses in our universities compatibility tools can be used to check the computer programming for structural analysis. fail to achieve this goal. The first part® of this analysis results, and get a student thinking These should be PhD level courses, for the article describes the problem, and this second about structural behavior. relatively small number of students who need part proposes a solution. There are many other exercises that can a deeper theoretical understanding. We are doing a disservice to both our students be assigned, illustrating different aspects of and the profession. It is time to modernize structural behavior and serving as a framework Matrix Methods our courses, and provide our students with for developing a variety of skills. A semester In the April 2007 article Basic Education truly useful skills.▪ course might cover a half dozen exercises. for a Structural Engineer, the course content included a “Matrix Methods” course. This Graduate Courses impliesCopyright that the earlier courses do not use Graham Powell, Ph.D., P.E. is professor At the graduate level, there are likely to be a matrices, and/or that matrix methods are emeritus of Structural Engineering at number of analysis courses. I believe that there somehow distinct from other methods. I the University of California at Berkeley. should be two basic courses, with roughly the think this is a mistake. There is really no such Over his career, Professor Powell has same aims as the above two undergraduate thing as a “matrix method” – only matrix developed, or supervised the development courses, but at a higher level. These courses notation, which applies to all methods and of, several computer programs that have should include dynamic loads, nonlinear behav- should be used whenever it is appropriate. been used widely in research and industry. ior, some basic finite elements, and comparison He currently works as a consultant to of P-∆ and true large displacement effects. Licensing Examinations Computers and Structures Inc., developing In my opinion, both dynamic loads and Currently, the structural analysis sections of and supporting the CSI PERFORM nonlinear behavior should be included in professional licensing examinations require computer program. Professor Powell may be these basic courses. In most graduate pro- analysis of statically indeterminate structures reached at [email protected]. grams, dynamics is taught as a separate by hand. Why? To get a driver’s license do you discipline and nonlinear behavior is usu- have to show that you can ride a horse? S T Rmagazine ADVERTISEMENTU - For Advertiser CInformation, visit www. STRUCTUREmagT.org U R E

STRUCTURE magazine 23 December 2008

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