- Email: [email protected]
Computer-aided instruction in structural analysis
COMPUTER-AIDED INSTRUCTION IN STRUCTURAL ANALYSIS J.u@s K. NELSON,JR-~and ARws WH& UffivCrsityof Houston. Houston, TX 77OM,U.S.A. (Receiued 18 May 1978) Abatr&-Structural Engineeringis presently in an era of rapid growth and development. Design concepts never &ought possibk have become common place. To adequately preparethestudentfor these advances, tbe engineering educatorfaces a fondue task. WItenused with flaunt, computerscan be a valuabk tool in a~mplishing this task. Three areas of am&cationare aresented de~ns~t~ utilizationof computersin the classroom. Included are sample problems in t& differenta&.
For an example in this area, consider the sample problem shown in Fig. 1. AlthourJhsomewhat simplified, this steel frame is a complete structural system examining the students knowledge of beam, column and weld design, In addition, the student must search out and identify the controlling component of the system to find the maximum load. The ABC steel code was used and must be referred to throughout the solution in order to establish the proper stress levels. Development of this type problem is very direct. After es~li~ the structural geometry the different components are analyzed individually. This analysis is done in general terms so that variable problem data can be used in the equations. This data will be provided using the random number generator. The next step is to place bounds on the randomly generated data. For this particular problem, one beam section, one column section, one weld size, and three dimensions are selected by the random number generator. Four beam sections, four column sections, and four weld sixes from which the selection is made are provided to the program in the data statements. The length ranged from IO to 24ft and L, from one-fourth to one-half L.
Structural engineering is presently in an area of rapid growth and development. Daily, new materials are used as structural elements. Design concepts never thought possible have become ~~0~1~. Examples are numerous; high-rise reinforced concrete structmes, cable-stayed bridges, aluminum alloys in the space industry, precast-prestressed concrete, skin and stringer aircraft structures. The list of advances is endless. Computer structural analysis itself is a relatively new industry, being less than 25 yr old. In order to adquately prepare the student to meet challenges of a modem world, the engineering educator faces a formidable task. In an already overcrowded academic schedule, students must be educated in an ever expanding field. The faculty itself is faced with the additional burden of updating and expanding their own skills. To ~~mplish this within existing programs, two things are needed: (1) More classroom contact time needs to be used for instruction and problem solving. (2) Students will need to do more individualizedwork outside the classroom. The computer can effectiveiy be used to accomplish this. Its speed, versatility, and avers are assets to both student and instructor. Three major uses of the computer in this regard are: (1) Randomly generated take-home problems and examinations. (2) Student exposure to computer analysis used extensively in design offices. (3) stately available ho~work solution set for both student and faculty. Take-home problems and examinations have notoriously been a license for students to cheat, Using the computer, an examination problem can be programmed in advance of intended usage. The computer will randomly select individu~ solution variable(s), other problem data, and at the same time calculate the solution set. The program can be “looped through” as many times as necessary providingeach student personal data for the examination. “Consulting” among students will still go on, but because of individualproblem data, each student is forced to actually solve the problem himself. &cause more tune is available outside the classroom, the scope of the problem can be more complex, covering several areas of structurai engineering,thus giving the student a realistic “real world” problem to solve. *Lecturerof Civil Engineering.Also: The Mfshore Company, P.O. Box 2765, Houston, TX 77001, U.S.A. *Professor of Civil Engineering.
133
Fig. 1. Steel structureexample problem.
134
J. K. NELSON.JR and A. WHITE
Column height ranged from 10to 18ft. The sections used as data and the range of the different dimensions is somewhat arbitrary, however consideration needs to be given to providing a wide range of possibilities for the student as well as keeping the various items compatible with each other. For the example shown in Fig. 1, the sections and dimensions were selected so that their random combination would result in cases of maximum allowable stress using compact sections as well as reduced allowable stress due to lateral beam buckling and column interaction. Parameters were chosen so that the maximum load the structurecan carry will not be dominated solely by beam or column strength but rather a reasonable distribution of each. Input data needs to be selected so that an even distribution occurs. The equations for de&mining the allowable stresses were taken directly from the AISC Code. After the applicable equations are identified and the d&rent parameters selected, they are coded for the computer. The tlowchart for such a program is shown in Fig. 2 and the code listingfor the problemdiscussedhere is shown in the Appendix along with a typical set of output.The sketchreferredto in the output is Fig. 1. Exams of this type need not be left to the instructorto develop as they offer an excellent opportunity for the advanced senior or a graduate student in a special problem course. Examinations can effectively be developed by these students. Ben&it to the student lies in four areas: (1) Involvementin comprehensiveevaluationof the probkmstatenwntto gain maximumdesignoptions. (2) Detailed review of code requirements for design. (3) Exposure to programmingand practice developing probkm solving logic. (4) Exposure to program documentation requirements. This particular problem was developed by a graduate student in the non-thesis program as part of his graduation requirements. This fuMlkd the requirement for a special project. AIthough the particular problem shown here is for a steel structure, there are opportunities in all areas of structural engineering, similar problems can be developed for concrete and timber structures. In statics, strength of materials, and theory of structures courses, problems of an equally general nature can be generated randomly using the computer. This type examination
greatly enhances the students transition from “classroom design” to the design office. The second use of computers in the classroom involves already available programs such as STRESS, STRUDL, NASTRAN, AYSYS, and others commonly used in design offices. By integrating these or similar programs into course work, the student can gain an understanding of the operational features of structural analysis programs, the limitationsof computer structural analysis and the behavior of structures through easily changed section properties and loads. A typical area of application would be a course in theory of structures or indeterminate structures. Here the student learns numerous classical, theoretical methods of analysis. This is essential to become a well versed engineer. But much analysis, especially of larger, more complex structures, is being done on the computer. The student should be equally aware of this method of analysis. For any given problem, a student could develop a long-hand numerical solution and also a computer solution. By doing this, several things are accomplished. Firstly, some of the “black-box magic” is taken out of the computer. It is readily seen that the machine cannot do anything that cannot be done by hand, given enough time. Secondly, a feeling for the precision of computer analysis is realized. Precision and accuracy of output data is only as good as that of the input data. Conditioning of a solution also affects the accuracy of the output. These are all considerations users need to be aware of. Thirdly, through several problems of this type, a student can gain an understandingof when a computer solution is just&d. For a trivial problem, he will see that a long-hand solution is by far the quickest, and for highly complex problems that a computer solution is the most desirable. For problems in between, he will have developed some judgement to determine which method
Fig. 2. System flowchart.
Fig. 3. Special problem description.
Computer-aided instruction in structural analysis
9
200”
tamy-
,ldwK Fig. 4. Special problem detail.
of solution is more desirable. By instruction of this type, the student will most likely view the computer as a “tool of the trade” rather than a nemesis. Consider the problem shown in Figs. 3 and 4 that was used in CIE 337, Theory of Structures. The course was structured such that students studied determinate, deflection, and indeterminate theory of trusses in sequence. This particular problem was assigned after the discussion of indeterminate trusses. With few exceptions this was the elementary students first exposure to a realistic structural system. To this point, most of the textbook problems he has solved have been contrived and not directly applicable to a real-world situation. In order to make their education more m6aningfuland to aid the transition from the classroom to the office, the student needs to be aware of and to solve practical problems. To date reception to this type problem by students has been excellent. The quality of work sub mitted and the accuracy of the solution has been far better than normally submitted on homework. With such problems, this instructor emphasizes that he is the client and the student is the consultant; future contracts depend on the quality of the work being submitted now. In assigningthis particular problem four end results were desired: (1) Exposure of the student to a complete structural system. (2) Exposure of the student to moving loads and force envelopes. (3) Appreciation by the student of computer structural analysis. (4) Understanding by the student of the behavior of indeterminate structures when section properties are altered. Development of a special problem of this type is very straight forward. The instructor first needs to arrive at the geometry of the structure and then perform trial analyses using the computer to arrive at appropriate
section properties. Often this can be accomplishedon the initial run based upon experience. Generally no more than two computer runs are needed. The computer program used to run the problems is mostly dependent upon what is available on the computer system to be used for the analysis. There are many commercially available software systems compatible with most machines on the market. This instructor has used ASACS, a problem-oriented analysis package that he developed as a thesis at the University of Houston. The key is to select a program that can efficiently handle small problems. Using ASACS as an example, each run costs approximately 5Oc for the problem presented here. Another area of applicationfor this type of problem is rigidly framed structures. A suggested approach is to have the students analyze the structure by hand using two classical methods of analysis (elastic energy, slope deflection, or moment distribution)and reanalyze it using the computer. Various loads can be applied and section properties changed as before. The third use of computers in the classroom is predominately a tool for the instructor, but has equal application for the student as well. Also, this particular application is geared mostly to analysis courses such as Theory of Structures or Statics. Often homework problems are assigned before they at6 solved. An assignment is freshest in the students mind and knowledge of the correct solution wig benefit him most when the assignment is turned in. The instructor can solve the problem on a computer in a minimal amount of time, thereby having the solutions ready when the problems are due. With homework probkms there is an advantage in providing the correct solution when an assignment is given.This gives the studentan objectiveto worktoward and also indicatesthe need for additional help in certain areas. Using the computer augm6nts the instructor’s ability to consistently provide the solution early as less of his time will be required. By encouraging the student to check his solution on the computer, the student gains knowledgeof the correct solution, a feel for computer structural analysis, and the desire to turn in a correct solution. The desire is a by-product not directly output by the machine. It comes from basic pride intrinsic to each student when a prob lem is correctly solved. An individual is more likely to check and rework a problem to obtain the correct solution, knowingwhat the solution is, than submit erroneous work. When used with forethought, the computer is a powerful tool in the classroom. It frees some faculty time that can be better used for consulting with students and educational development. Students gain knowledge and experience in another method of analysis, one that will be used extensively in their later careers.
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9
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For an example in this area, consider the sample problem shown in Fig. 1. AlthourJhsomewhat simplified, this steel frame is a complete structural system examining the students knowledge of beam, column and weld design, In addition, the student must search out and identify the controlling component of the system to find the maximum load. The ABC steel code was used and must be referred to throughout the solution in order to establish the proper stress levels. Development of this type problem is very direct. After es~li~ the structural geometry the different components are analyzed individually. This analysis is done in general terms so that variable problem data can be used in the equations. This data will be provided using the random number generator. The next step is to place bounds on the randomly generated data. For this particular problem, one beam section, one column section, one weld size, and three dimensions are selected by the random number generator. Four beam sections, four column sections, and four weld sixes from which the selection is made are provided to the program in the data statements. The length ranged from IO to 24ft and L, from one-fourth to one-half L.
Structural engineering is presently in an area of rapid growth and development. Daily, new materials are used as structural elements. Design concepts never thought possible have become ~~0~1~. Examples are numerous; high-rise reinforced concrete structmes, cable-stayed bridges, aluminum alloys in the space industry, precast-prestressed concrete, skin and stringer aircraft structures. The list of advances is endless. Computer structural analysis itself is a relatively new industry, being less than 25 yr old. In order to adquately prepare the student to meet challenges of a modem world, the engineering educator faces a formidable task. In an already overcrowded academic schedule, students must be educated in an ever expanding field. The faculty itself is faced with the additional burden of updating and expanding their own skills. To ~~mplish this within existing programs, two things are needed: (1) More classroom contact time needs to be used for instruction and problem solving. (2) Students will need to do more individualizedwork outside the classroom. The computer can effectiveiy be used to accomplish this. Its speed, versatility, and avers are assets to both student and instructor. Three major uses of the computer in this regard are: (1) Randomly generated take-home problems and examinations. (2) Student exposure to computer analysis used extensively in design offices. (3) stately available ho~work solution set for both student and faculty. Take-home problems and examinations have notoriously been a license for students to cheat, Using the computer, an examination problem can be programmed in advance of intended usage. The computer will randomly select individu~ solution variable(s), other problem data, and at the same time calculate the solution set. The program can be “looped through” as many times as necessary providingeach student personal data for the examination. “Consulting” among students will still go on, but because of individualproblem data, each student is forced to actually solve the problem himself. &cause more tune is available outside the classroom, the scope of the problem can be more complex, covering several areas of structurai engineering,thus giving the student a realistic “real world” problem to solve. *Lecturerof Civil Engineering.Also: The Mfshore Company, P.O. Box 2765, Houston, TX 77001, U.S.A. *Professor of Civil Engineering.
133
Fig. 1. Steel structureexample problem.
134
J. K. NELSON.JR and A. WHITE
Column height ranged from 10to 18ft. The sections used as data and the range of the different dimensions is somewhat arbitrary, however consideration needs to be given to providing a wide range of possibilities for the student as well as keeping the various items compatible with each other. For the example shown in Fig. 1, the sections and dimensions were selected so that their random combination would result in cases of maximum allowable stress using compact sections as well as reduced allowable stress due to lateral beam buckling and column interaction. Parameters were chosen so that the maximum load the structurecan carry will not be dominated solely by beam or column strength but rather a reasonable distribution of each. Input data needs to be selected so that an even distribution occurs. The equations for de&mining the allowable stresses were taken directly from the AISC Code. After the applicable equations are identified and the d&rent parameters selected, they are coded for the computer. The tlowchart for such a program is shown in Fig. 2 and the code listingfor the problemdiscussedhere is shown in the Appendix along with a typical set of output.The sketchreferredto in the output is Fig. 1. Exams of this type need not be left to the instructorto develop as they offer an excellent opportunity for the advanced senior or a graduate student in a special problem course. Examinations can effectively be developed by these students. Ben&it to the student lies in four areas: (1) Involvementin comprehensiveevaluationof the probkmstatenwntto gain maximumdesignoptions. (2) Detailed review of code requirements for design. (3) Exposure to programmingand practice developing probkm solving logic. (4) Exposure to program documentation requirements. This particular problem was developed by a graduate student in the non-thesis program as part of his graduation requirements. This fuMlkd the requirement for a special project. AIthough the particular problem shown here is for a steel structure, there are opportunities in all areas of structural engineering, similar problems can be developed for concrete and timber structures. In statics, strength of materials, and theory of structures courses, problems of an equally general nature can be generated randomly using the computer. This type examination
greatly enhances the students transition from “classroom design” to the design office. The second use of computers in the classroom involves already available programs such as STRESS, STRUDL, NASTRAN, AYSYS, and others commonly used in design offices. By integrating these or similar programs into course work, the student can gain an understanding of the operational features of structural analysis programs, the limitationsof computer structural analysis and the behavior of structures through easily changed section properties and loads. A typical area of application would be a course in theory of structures or indeterminate structures. Here the student learns numerous classical, theoretical methods of analysis. This is essential to become a well versed engineer. But much analysis, especially of larger, more complex structures, is being done on the computer. The student should be equally aware of this method of analysis. For any given problem, a student could develop a long-hand numerical solution and also a computer solution. By doing this, several things are accomplished. Firstly, some of the “black-box magic” is taken out of the computer. It is readily seen that the machine cannot do anything that cannot be done by hand, given enough time. Secondly, a feeling for the precision of computer analysis is realized. Precision and accuracy of output data is only as good as that of the input data. Conditioning of a solution also affects the accuracy of the output. These are all considerations users need to be aware of. Thirdly, through several problems of this type, a student can gain an understandingof when a computer solution is just&d. For a trivial problem, he will see that a long-hand solution is by far the quickest, and for highly complex problems that a computer solution is the most desirable. For problems in between, he will have developed some judgement to determine which method
Fig. 2. System flowchart.
Fig. 3. Special problem description.
Computer-aided instruction in structural analysis
9
200”
tamy-
,ldwK Fig. 4. Special problem detail.
of solution is more desirable. By instruction of this type, the student will most likely view the computer as a “tool of the trade” rather than a nemesis. Consider the problem shown in Figs. 3 and 4 that was used in CIE 337, Theory of Structures. The course was structured such that students studied determinate, deflection, and indeterminate theory of trusses in sequence. This particular problem was assigned after the discussion of indeterminate trusses. With few exceptions this was the elementary students first exposure to a realistic structural system. To this point, most of the textbook problems he has solved have been contrived and not directly applicable to a real-world situation. In order to make their education more m6aningfuland to aid the transition from the classroom to the office, the student needs to be aware of and to solve practical problems. To date reception to this type problem by students has been excellent. The quality of work sub mitted and the accuracy of the solution has been far better than normally submitted on homework. With such problems, this instructor emphasizes that he is the client and the student is the consultant; future contracts depend on the quality of the work being submitted now. In assigningthis particular problem four end results were desired: (1) Exposure of the student to a complete structural system. (2) Exposure of the student to moving loads and force envelopes. (3) Appreciation by the student of computer structural analysis. (4) Understanding by the student of the behavior of indeterminate structures when section properties are altered. Development of a special problem of this type is very straight forward. The instructor first needs to arrive at the geometry of the structure and then perform trial analyses using the computer to arrive at appropriate
section properties. Often this can be accomplishedon the initial run based upon experience. Generally no more than two computer runs are needed. The computer program used to run the problems is mostly dependent upon what is available on the computer system to be used for the analysis. There are many commercially available software systems compatible with most machines on the market. This instructor has used ASACS, a problem-oriented analysis package that he developed as a thesis at the University of Houston. The key is to select a program that can efficiently handle small problems. Using ASACS as an example, each run costs approximately 5Oc for the problem presented here. Another area of applicationfor this type of problem is rigidly framed structures. A suggested approach is to have the students analyze the structure by hand using two classical methods of analysis (elastic energy, slope deflection, or moment distribution)and reanalyze it using the computer. Various loads can be applied and section properties changed as before. The third use of computers in the classroom is predominately a tool for the instructor, but has equal application for the student as well. Also, this particular application is geared mostly to analysis courses such as Theory of Structures or Statics. Often homework problems are assigned before they at6 solved. An assignment is freshest in the students mind and knowledge of the correct solution wig benefit him most when the assignment is turned in. The instructor can solve the problem on a computer in a minimal amount of time, thereby having the solutions ready when the problems are due. With homework probkms there is an advantage in providing the correct solution when an assignment is given.This gives the studentan objectiveto worktoward and also indicatesthe need for additional help in certain areas. Using the computer augm6nts the instructor’s ability to consistently provide the solution early as less of his time will be required. By encouraging the student to check his solution on the computer, the student gains knowledgeof the correct solution, a feel for computer structural analysis, and the desire to turn in a correct solution. The desire is a by-product not directly output by the machine. It comes from basic pride intrinsic to each student when a prob lem is correctly solved. An individual is more likely to check and rework a problem to obtain the correct solution, knowingwhat the solution is, than submit erroneous work. When used with forethought, the computer is a powerful tool in the classroom. It frees some faculty time that can be better used for consulting with students and educational development. Students gain knowledge and experience in another method of analysis, one that will be used extensively in their later careers.
Computer program and selected output
9
1C 11
135
J. K. NELSON.JR. and A. WHY ~~1.r~,1~,7.?,7~~..3~.5,5.1?,21.~,b.~1~1.5~~1.~5~3.~9~b.~~~~7.1~ ~SO.,lL.'.l*5?.3Q' .rhL.?rS.lQ,S*.L,1L.I QATA TWAWRI 'U21XL4'. ‘W?4Xbl’r RATA l"lA(wFCI 'U9X31' , 'VlOXLQ', 5)AT4 uIO.?~,~.~'S,~.S,O.~~~/ OATA WF4tLI 'qSA*' r'COLUW'r '#LO'
099
50
TO
To
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LSIQYG M*QYG(Il) tQ'J';=l'W*Il
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