technology transfer of structural reliability for ...utca.eng.ua.edu/files/2011/08/00231-rpt.pdf ·...

Technology Transfer of Structural Reliability for Transportation Designs

by Shen-En Chen and Yayoi Nishihama

Department of Civil and Environmental Engineering University of Alabama at Birmingham

Birmingham, Alabama

Wenshen Pong School of Engineering

San Francisco State University San Francisco, California

And

Peter S. Chen Department of Civil and Environmental Engineering

University of Illinois at Urbana Champaign Urbana, Illinois

Prepared by

UTCA University Transportation Center for Alabama

The University of Alabama, The University of Alabama at Birmingham, and The University of Alabama in Huntsville

UTCA Report Number 00231 February 2002

ii

Technical Report Documentation Page

1. Report No FHWA/CA/OR-

2. Government Accession No. 3. Recipient Catalog No.

5. Report Date May 2002

4. Title and Subtitle Technology Transfer of Structural Reliability for Transportation Designs

6. Performing Organization Code

7. Authors Shen-En Chen, Yayoi Nishihama, Wenshen Pong and Peter S. Chen

8. Performing Organization Report No. UTCA Report 00231

10. Work Unit No.

9. Performing Organization Name and Address Department of Civil and Environmental Engineering The University of Alabama at Birmingham 1075 13th Street South, Suite 321 Birmingham, Alabama 35294-4440

11. Contract or Grant No. DTRS98-0028 13. Type of Report and Period Covered Final Report; January 1, 2001 Dec 31, 2001

12. Sponsoring Agency Name and Address University Transportation Center for Alabama University of Alabama PO Box 870205 Tuscaloosa, Alabama 35487

14. Sponsoring Agency Code

15. Supplementary Notes 16. Abstract Structural reliability is a probabilistic approach to quantify the potential success of a structure to provide the design needs throughout the intended service period. Typically in structural design, reliability is factored into the random load and resistant factors. Most of the structural design specifications are slowly transitioning to the Load/Resistant Factor Design (LRFD) approach. Currently, structural reliability is not considered in most undergraduate Civil Engineering curricula in the U.S. A pilot course was developed to integrate reliability into the philosophy of structural design. To establish the course content, existing educational structural design software were used to generate simple examples to illustrate the effects of different parameters that relate to the reliability of a structure. In addition, to make the contents more relevant to the students , the short course was designed specifically relating to LRFD design for structural steel. Parametric studies were conducted and used to illustrate the effects of random load combinations in load-resistance effects, including the effects of sample sizes and of system-component correlation. This report describes the development of the pilot course, which was offered twice to professional engineers as part of the technology transfer efforts of the University Transportation Center of Alabama (UTCA). The one-day short courses were offered in the format of eight consecutive lectures taught by two instructors, and were very well received by the engineers. This project represents the UTCAs continuing effort to improve the safety and reliability of transportation infrastructure through educating the engineers within the state with innovative ideas and technology. 17. Key Words Structural reliability, technology transfer, structural safety, design, LRFD, ESD, random factors

18. Distribution Statement

19. Security Classification (of this report)

20. Security Classification (of this page)

21. No of Page

22. Price

Form DOT F 1700.7

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Contents

Contents . iii Tables . v Figures .... v Executive Summary

vi

1.0 Introduction .. 1 Background ... 1 Project Objectives . 3 Approach and Work Plan .. 3 Report Outline ... 3

2.0 Background and Literature Review .. 5

Course Survey ... 5 Structural Reliability in Engineering 10 Structural Reliability in Design Codes . 15 Textbooks for Structural Reliability . 17 Useful LRFD Websites . 17 Software for Structural Reliability. 18

3.0 UTCA Pilot Course 19

Introduction 19 UTCA Pilot Course Contents 19 Timeline 20 Teaching of Structural Reliability Concepts 21 Teaching of LRFD Structural Steel Design

21

4.0 Development of Course Projects.. 29 Introduction 29 West Point Bridge Designer (WPBD) 30 Model Generation & Problem Statements.. 30 Summary of WPBD work 37 RAM Steel Beam Design (RAM SBeam).. 37 Model Generation & Problem Statements . 37 Summary of RAM SBeam work ....... 41

iv

Contents (continued)

5.0 Proposed Reliability Course in Undergraduate Curriculum .. 43

Introduction . 43 Course Goals ..... 43 Course Contents 47 Sample Course Syllabus ... 47 Course Textbooks .. 47 Design/Computer Activities . 47 Laboratory Activities . 47 ABET Requirements . 48 Demonstration of Oral Communication Skills .. 48 Demonstration of Written Communication Skills . 48 Understanding of Ethical, Social, Economic, and Safety Considerations . 48 Estimated ABET Category Contents . 48

6.0 Discussion 49 Class Evaluation. 49 Potential Benefits .. 50 Student Involvement.. 50 Relationship to Other Research Projects 51 Limitations/Difficulties .. 51

7.0 Conclusions ..

52

8.0 Recommendation for Future Studies

53

9.0 References 54 List of Commercial Software 57

Appendix A: Course Assessment Report ... 58 Appendix B: Acknowledgements ....... 61

v

List of Tables

2-1 Survey of nationwide undergraduate/graduate curriculum for reliability courses . 6 2-2 Prime causes of failure ... 10 2-3 Classification of human errors (Melcher 1999) . 11 2-4 Error factors in observed failure cases (Melcher 1999) . 1 2-5 Coefficients of variation (Vx) for various factors (Harr, 1987) . 13 3-1 UTCA short course schedule . 20 3-2 Representative statistics for the resistance of structures produced from hot-rolled

steel elements .

23 4-1 Range of Random events using member sectional properties 32 4-2 Analysis of results from 30 samples .. 33 4-3 Comparison between LRFD and AISC based designs .. 38 5-1 Class content from CE f397-Structural Reliability from UT-Austin . 44 5-2 Class content from CE 5526-Structural Reliability from City College of New York 44 5-3 Class content from CE 810-Reliability-Based Design from Michigan State

University ...

45 5-4 Class content from CVEN 655-Structural Reliability from Texas A & M

University ...

46 5-5 Sample course syllabus .. 47 5-6 Estimated ABET category content . 48 6-1 Summary from student evaluation survey .. 49

List of Figures 2-1 Elements of reliability within the life of a structure (Nowak and Collins 2000) ... 10 3-1 Beam bending example .. 22 3-2 Dead load and live load combination for the 200 samples problem .. 23 3-3 Comparison of LRFD vs. ASD .. 25 3-4 LRFD/ASD Z ratio vs. LL/DL ratio for bending member . 27 4-1 WPBD showing bridge failure during truck crossing 31 4-2 Haupt truss bridge with member numbers . 31 4-3 Probability density function of the 30 members sample study .. 34 4-4 Reliability of the members for the 30 sample case 34 4-5 Probability density function for the 207 data . 35 4-6 Reliability measures of the 207 cases 35 4-7 Influence lines for each member for the HS20-44 truckload . 36 4-8 PFD for LRFD vs. ASD designs for 200 samples .. 39 4-9 PFD for LRFD vs. ASD designs for 50 samples 39 4-10 Cumulative density function of LRFD and ASD designs for 200 samples ... 42 4-11 Cumulative density function of LRFD and ASD designs for 50 samples . 42

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EXECUTIVE SUMMARY Structural reliability is a probabilistic approach to quantify the potential success of a structure to provide the design needs throughout the intended service period. By considering the randomness of the system factors, reliability can be used as a quantitative measure of the safety of the structure. Hence, an understanding of structural reliability is essential in warranting the utility and stability of the structure and the safety of the public/private users. Typically in structural design, reliability is factored into the random load and resistant factors. Most structural design specifications are slowly transitioning into the Load/Resistance Factor Design (LRFD) approach. Currently, structural reliability is not considered in most undergraduate Civil Engineering curricula in the U.S., even though most instructors choose to teach LRFD design specifications. A survey of over 70 undergraduate curricula found that only 1.4% of reliability-based courses are targeted at undergraduate students. This project developed a short course for practitioners who are involved in the design of transportation systems, as a means to promote and enhance an understanding of the concept of system reliability. A UTCA-sponsored pilot course was developed to integrate reliability into the philosophy of structural design. To establish the course content, research including literature reviews and work on design projects was conducted with the assistance of undergraduate students. Existing educational structural design software (West Point Bridge Designer and RAM Sbeam) was used to generate simple examples to illustrate the effects of different parameters that relate to the reliability of a structure. The materials were then integrated into a one-day short course. In addition, to make the contents more practical, the short course specifically addressed LRFD steel design, and parametric studies were conducted to show the effect of randomness in load-deflection effects, including the effects of sample sizes. Future plans are to develop the material into a full three-credit hour undergraduate class on structural reliability. Through instruction of structural reliability concepts, an awareness of structural safety design and a better appreciation of LRFD will be strengthened among future engineers. The long-term benefits of this project will be improvement in the safety of infrastructure of Alabama. It will also better equip engineers to face possible future revisions of design codes.

1

Section 1.0 Introduction

Background The science of transportation infrastructure design deals with the moving of the public mass from point A to point B, and is congruently divided into two important components: 1) the design of the physical structural system and 2) the planning and management of the flows of traffic. These two complementing studies encompass nearly every aspect of transportation engineering and are distinguishable through the science and mathematics involved. Traffic engineering and transportation planning deal with characterization and forecast of traffic flows using complex and abstract mathematical concepts. The design of physical structural systems, such as transportation facilities, on the other hand, is typically marked by the precision of the Laws of Physics and the theoretical explicit mathematics of easily quantifiable elements. Over the years, however, as a result of the recognition of the importance of incorporating randomness of the physical elements, evolution of the design philosophy of the physical structural systems has slowly transitioned into abstract mathematics. Consequently, probabilistic structural design approaches have been introduced into many aspects of physical transportation facility designs. Naturally, probabilistic structural design approaches underlie the concept of structural reliability, which is defined as the ability of a structure to fulfill its design purposes for a specified design life. Simply put, reliability is a measure of the probability of success for a structure for all its intended applications. Hence, the study of structural reliability is concerned with the calculation and prediction of the limiting probability states for an engineered structure at any stage of its life cycle (Galambos et al. 1982, Ellington et al. 1982, 1991, 1996 and 1999, Rosowsky et al. 1991, 1992 and 1994, Harr 1987, Marek et al. 1996, Melcher 1999 and Nowak and Collins 2000). The introduction of Structural Reliability becomes essential, as we understand more about the random nature of the physical world that we live in and the existing limitations in modeling and quantifying this randomness. Accordingly, we engage in the study of structural reliability to establish a better grasp of the explicit quantity of the safety level of the end design product to provide a more responsible recommendation to the client. Currently, the concepts of reliability are slowly being incorporated into all physical designs of transportation facilities, may it be the design of a bridge, a highway pavement or an airport runway. These reliability concepts have become an integral part of the design specifications in concrete, steel and other construction materials. The processes to establish a structural product from planning, designing, testing, building and operating, all constitute a part of the life cycle of the structural product. In recent years, most design guidelines, such as the AASHTO Bridge Design Specification (American Association of State Highway and Transportation Officials 1998), the AISC Steel Design Code (American Institute of Steel Construction 1994) and the ACI Concrete Design Code (American Concrete Institute 1999), have gradually changed their design

2

philosophies as probabilistic calculations are established and are integrated into the design codes in the forms of Load Factors (LF) and Resistance Factors (RF). The Northridge, California, earthquake showed the engineering community that there was a need to improve the current design load factors for structural design. In fact, since Load and Resistance Factor Design (LRFD) design codes require realistic (empirical) data for calibrating the reliability parameters, a continuous scheme for modifying design codes is necessary. Without a proper understanding of the underlying philosophy of the reliability approach, the professional community may be hesitant in adopting the new design specification. This potential problem should be rectified as early as possible, such as through a required undergraduate course in reliability, so that students may gain an early appreciation for reliability within structures. The transformation from Allowable Stress Design (ASD) or Working Stress Design (WSD) to LRFD indicates the great demand for safer and more economical designs. However, the design codes along with the integrated load factors do not necessarily transfuse a proper understanding of the underlying concepts of Structural Reliability. Since LRFD may or may not end up in conservative designs, without a proper understanding of the underlying philosophy, reliability-based designs may be highly under-valued. Structural mechanics courses constitute a significant portion of the senior- level Civil Engineering undergraduate curriculum in the United States. Depending on the instructors preference, structural design may be taught in either LRFD or ASD. Traditionally, design classes have focused only on how to use design codes and the mechanical principles, and not on the underlying reliability concepts. Structural reliability is more than LRFD design - students must learn not only how to perform load-factored design, but also what reliability encompasses. Students will then begin to acquire insights in understanding what reliability means when they began to understand the logical algorithms of developing reliability codes. However, in most institutions, Structural Reliability has only been taught as a special- topic course at the graduate level or as an undergraduate elective course. Since LRFD has been adopted by most design codes, this important concept should be embraced early on in the undergraduate curriculum, for students to develop an apprecia tion and better understanding of the quantitative measures of structural safety. To this end, an undergraduate Structural Reliability course that encompasses simple modeling and design class project is proposed. A study has been undertaken to develop the teaching content and associated materials for such a course. This course would provide simple and interesting design projects using computer simulations, and would facilitate students with hands-on exercises in conducting a probabilistic study of the design of simple structures. This report describes the development of the course materials for this class, which was first offered as a UTCA (University Transportation Center for Alabama) technology-transfer short course to professional engineers. This short course integrated LRFD structural steel design and the concepts of reliability into an eight- lecture course on a single-day basis. Two design projects have been developed for the course using the West Point Bridge Designer (WPBD) (Ressler 2000) and the RAM Steel Beam Design (RAM SBeam) (RAM International 1999) software.

3

The developed course materials also include lecture-length PowerPoint presentations and class notes. Project Objectives The objective of this study is to promote the knowledge of struc tural reliability so that there will be an improvement of understanding reliability concepts and the probabilistic design approach. This understanding will ultimately become a useful tool for future engineers to grasp more advanced design concepts, to develop a sense of reliability, and to improve client relationships by providing the clients with a more definite measure of the reliability of their structures. Approach and Work Plan This project involved literature reviews, a well-designed short course, and the integration of the course materials into a potential future undergraduate reliability course. The short course was a part of the UTCA technology transfer efforts and was offered as a continuing education course. The following seven tasks encompassed the scope of this project:

1. Course Preparation (literature research, class projects, class materials, syllabus development, etc)

2. Advertisement (course announcement) 3. Pilot course implementation 4. Course evaluation 5. Formal course implementation 6. Establishment of the outline and syllabus for future undergraduate reliability course. 7. Revision and improvement based on feedback. 8. Final report and course material submission.

To investigate the extent of reliability being taught in the undergraduate curriculum, over 250 web sites for civil engineering departments nationwide were surveyed for relevant courses in the undergraduate and graduate curricula. To develop the course material, exhaustive literature was collected. The collected materials include published textbooks, journal papers and relevant contents from various reliability-related Internet sites. Two design examples were developed to help students appreciate the importance of the simulation and data generation process in establishing reliability indices. These design examples can be used for future course projects, thus engaging students in hands-on development of reliability-based designs. Two simulation software products were used in the development of the design examples. The selection of the two programs was largely based on simplicity and availability. An undergraduate student was hired to help process data and establish reliability parameters for each design problem. Report Outline Section 2 of this report presents a review of reliability-related literature and survey results of the course contents of reliability courses offered in four-year colleges nationwide. Section 3

4

describes the short course and the material taught in the UTCA technology transfer/continuing education course (UTCA pilot course), including the timeline of the project. Section 4 outlines the development of the design projects for this course. Based on the results of the UTCA pilot course, a reliability course for undergraduate curriculum is outlined and a syllabus prepared. This is described in Section 5. Section 6 discusses the outcome of this study and the course evaluations from the students. Finally, Section 7 summarizes this study, and recommendations for future studies and an implementation plan are presented in Section 8.

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Section 2.0

Background and Literature Review

Course Survey A survey has been conducted of the syllabi from available reliability courses collected from the Internet web sites of 250 institutions in the US. This survey is limited to the courses offered within the civil engineering curriculum. Undergraduate courses that teach general probability and statistics, which encompass most of the schools surveyed, are not considered. Consideration instead is focused on course descriptions that emphasize reliability concepts. According to this survey, a total of 70 schools offer reliability- related courses. These courses may be titled as probabilistic methods, reliability, safety and risk analysis or uncertainty analysis. Table 2-1 shows the list of schools and the associated course(s) offerings. The list includes the course title, focus area and the Web site link. Also included in the table is the level of students that the courses are targeted at, namely graduate students (G), undergraduate students (UG) or both (UG/G). The results show that 50% of all reliability-related courses are focused on general reliability theories, 47.2% are on general probabilistic methods, and only 2.8% are specifically addressing Structural/Geotechnical mechanics design. With the exception of 9 schools, almost all the reliability courses are offered at the graduate level. Only 1.4 % of all reliability-related courses are targeted at undergraduate students. The results indicated a lack of structural reliability-related courses in the undergraduate Civil Engineering curriculum. As mentioned in the Introduction (Section 1), the current trend of integrating reliability concepts with physical transportation facility designs, in particular in the establishment of LRFD design codes (i.e. American Association of State Highway and Transportation Officials 1998, American Concrete Institute 1999 and American Institute of Steel Construction 1994), require Civil Engineering students to have a basic understanding of the underlying principles in this design philosophy. The results of this survey support the hypothesis of this study, that is, there is an urgent need to offer a reliability course within the undergraduate curriculum. Most civil engineering undergraduate curricula encompass at least four mechanics-related courses (statics, dynamics, strength of materials and at least one structural design course). The structural design courses typically teach students to design a structure based on the design specifications, which may based on either allowable strength-based design (ASD) or load resistance factor-based design (LRFD). In practice, selection is primarily based on the kind of material, i.e., whether steel, reinforced concrete, etc. The available materials and governing codes typically dictate the design approach. It is unlikely that instructors have time to cover the basis of the design specifications under these curricula. Therefore, a course that uses simple examples to illustrate structural safety, reliability concepts and the underlying philosophies of LRFD design codes early in the undergraduate curriculum can be very beneficial to undergraduate students who are interested in developing Structural/Geotechnical/Transportation engineering specialties.

6

Table 2-1 Survey of nationwide undergraduate/graduate curriculum for reliability courses School Name Course Title Focus UG/G web site

1

California State Polytechnic University, Pomona

Engineering Probability and Statistics Manufacturing

http://www.csupomona.edu/~engineering/programs/details/IME/ime_course_outlines/ime_course_syllabi.pdf

2

California State University, Long Beach

Probabilistic and Statistical Methods in Engineering Applications

General probabilistic methods

G http://www.csulb.edu/~janicej/catalog-98-99/civil.pdf

3 Carnegie Mellon University

Probability and Estimation Methods for Engineering Systems


G http://www.ce.cmu.edu/descriptions/12-704.html

4

Case Western Reserve University

Structural Reliability Structural Reliability G http://ecivwww.cwru.edu/civil/gclass_struct.html

5 City College of New York Structural Reliability

Structural Reliability G

http://www-ce.engr.ccny.cuny.edu/course/ce5526/ce5526.html

6 Clemson University Reliability

Structural Reliability G http://www.grad.clemson.edu/catalog/es7.htm#Civil

7 Cooper Union Stochastic concepts in civil engineering


G http://www.cooper.edu/engineering/civil/catalog.html

8 Cornell University

Risk Analysis and Management

Structural Reliability

G http://www.cuinfo.cornell.edu/Academic/Courses/CoSdetail.phtml?college=ENG&number=597&prefix=CEE&title=Risk+Analysis+and+Management

9 Duke University

Engineering Systems Reliability, Safety, and Risk Assessment


http://www.registrar.duke.edu/ACES/course_descrip/CE.html

10 Florida Atlantic University

Probability Models for Engineers


G http://www.me.fau.edu/current/ProbMod.pdf

11 Florida Atlantic University

Structural Reliability and Random Vibrations

Structural Reliability G http://www.me.fau.edu/current/Structrel.pdf

12 Florida Institute of Technology

Stochastic operations research models


G http://www.fit.edu/AcadRes/engsci/civil/civil.html

13 Georgia Institute of Technology

Probability and Statistics for Civil Engineering


G http://www.oscarweb.gatech.edu/catalog/semester/CEE/CEE6231.html

14 Illinois Institute of Technology

Structural Reliability and Probabilistic Bases of Design

Structural Reliability G http://www.iit.edu/~ce/course_desc.html

15 Massachusetts Institute of Technology

Probability and Statistics in Engineering


G http://student.mit.edu/@8937072.23297/catalog/m1b.html

16 Massachusetts Institute of Technology

Systems Simulation risk and probability

G http://student.mit.edu/@8937072.23297/catalog/m1b.html

7

Table 2-1 Survey of nationwide undergraduate/graduate curriculum for reliability courses (continued)

17 Michigan State University

Reliability-Based Design

Structural Reliability G http://www.egr.msu.edu/~wolff/ce810/syllabusfs00.htm

18 Michigan Technological University

Probabilistic Analy & Rel


G http://www.civil.mtu.edu/course.htm

19 North Carolina State University

Probabilistic Methods of Structural Engineering


G http://www2.acs.ncsu.edu/reg_records/crs_cat/CE.html#CE724

20 Northeastern University Applied Probability


http://www.coe.neu.edu/Depts/CIV/civil/FrontPage/GradCourses.htm

21 Northwestern University

Uncertainty Analysis in Civil Engineering


G http://www.civil.northwestern.edu/

22 Ohio State University

Construction Risk and Decision Analyses


http://www.ureg.ohio-state.edu/course/spring/book3/B105.htm

23 Oregon State University

Probabilistic Structural Engineering

Structural Reliability G http://www.ccee.orst.edu/programs/graduate/structgrad.html

24 Polytechnic University

Analysis of Uncertainty in Civil Engineering


G http://www.poly.edu/cee/academics.htm

25 Purdue university Stochastic concepts and methods in civil engineering


UG http://www.ecn.purdue.edu/ECN/course_info/index?action=display_course_list&abbrev=CE&designator=392&detail=4&semester=200210

26 Santa Clara University Reliability of Engineering Systems


G http://www.engr.scu.edu/undergrad/ceng.html

27 Stanford University Structural Reliability


http://www.stanford.edu/dept/registrar/bulletin/pdf/CivilEng.pdf

28

Syracuse University Structural Reliability

Structural Reliability G http://www.ecs.syr.edu/dept/cie/welcome/cie%20home.htm

29 Texas A&M University

Structural Reliability Structural Reliability UG/G http://ceprofs.civil.tamu.edu/jyao/655-syl%5C655-00c.htm

30 Washington State University

Strucutral Reliability Structural Reliability G http://www.ce.wsu.edu/CEabout/ceacademic/cegraduate/cegradclist/gradcourselist.htm

31

Washington State University

Probabilistic Methods in Structural Design


G http://woodhead.ce.wsu.edu/CE531/ce531.pdf

32 University of Alabama, Birmingham

Civil Engineering Analysis General probability methods

UG http://main.uab.edu/show.asp?durki=39473

33 University of Alabama, Tuscaloosa

Statistical Application in Civil Engineering

Structural Reliability G http://civil.eng.ua.edu/frames4.html

34 University of Arizona

Probabilistic Methods in Geotechnical Engineering

Geotechnical engineering G http://catalog.arizona.edu/2000-01/courses/004/CxEx.html

35 University of California, Berkeley

Structural Reliability Structural Reliability

http://www.ce.berkeley.edu/Programs/Structure/Book/courses/CE229.htm

36 University of California, Davis

Probabilistic Design and Optimization


G http://registrar.ucdavis.edu/UCDWebCatalog/Programs/eci/courses.htm

37 University of California, San Diego

Statistics, Probability and Reliability


UG http://www.structures.ucsd.edu/Courses/SE125.shtml


8

38 University of Cincinnati Reliability Analysis

Structural Reliability G http://www.eng.uc.edu/dept_cee/courses/

39 University of Cincinnati Reliability of CEE systems General probabilistic methods

G http://www.uc.edu/courses/engineering.pdf

40 University of Colorado at Boulder

Structural Reliability Structural Reliability G http://civil.colorado.edu/web/course/CVEN5555.html

41 University of Detroit Mercy

Engineering Risk-Benefit Analysis


- http://ids.udmercy.edu/mpd525_w00/syllabus.cfm

42 University of Idaho

Reliability of Engineering Systems


G http://www.uidaho.edu/catalog/6ce.html

43

University of Illinois at Urbana - Champaign

Engineering Decision and Risk Analysis


UG http://cee.ce.uiuc.edu/Course_Listings.asp

44 University of Iowa

Probabilistic Methods in Hydroscience Hydrology UG http://www.cee.engineering.uiowa.edu/courselist.html

45 University of Maine

Probabilistic Methods in Structural and Geotechnical Engineering

Structural and Geotechnical Engineering

G http://www.umeciv.maine.edu/ce/student/courses/course.htm

46

University of Maryland, College Park


G http://ctsm.umd.edu/ayyub/courses/ence615/index.htm

47 University of Massachusetts Lowell

Probability & Statics for Engineering


UG http://www.eng.uml.edu/Dept/civ/UnderGrad/syllabus/Syllabus14286.htm

48 University of Memphis Probabilistic Methods in Engineering


G http://www.ce.memphis.edu/grad/grad_courses.html

49 University of Miami Structural Reliability


http://www.eng.miami.edu/cgi-bin/Co E/show_course?CAE+612

50

University of Michigan, Ann Arbor

Reliability of structural Systems


http://www.engin.umich.edu/students/courses/catalog/CEE517.html

51

University of Minnesota


G http://www.ce.umn.edu/courses/ce8461/

52 University of Mississippi Probabilistic Analysis and Design


UG http://www.olemiss.edu/depts/civil_eng/undergraduate/ucourses.html

53 University of New Orleans

Reliability Analysis in Civil Engineering

Structural Reliability G http://www.uno.edu/~engr/civil/new/courses.html

54 University of Notre Dame

Structural Reliability and Probabilistic

Structural Reliability G http://www.nd.edu/~cegeos/gradprog2/cegradcours2.html

55 University of Oklahoma

Reliability in Engineering Design Manufacturing G

http://www.ou.edu/bulletins/courses/industrial_engineering_courses.htm

56 University of Rhode Island

Probabilistic Methods in Structural Engineering

Structural Reliability G http://cveserver.cve.uri.edu/academics/courses/index.htm

9


57

University of Southern California

Risk Analysis in Civil Engineering


G http://www-classes.usc.edu/engr/ce/408/syllabus.html

58

University of Tennessee at Knoxville

Reliability of Constructed Systems

Structural Reliability G http://www.engr.utk.edu/civil/courses/ce680.htm

59

University of Tennessee at Knoxville

Risk Analysis in Civil & Environmental Engineering


G http://www.engr.utk.edu/civil/courses/ce580.htm

60

University of Texas at Arlington

Reliability and Advanced Quality Control Topics Manufacturing G http://www.uta.edu/ie/gcourses.htm

61

University of Texas at Austin

Structural Reliability Structural Reliability UG http://www.ce.utexas.edu/academic/classes/archive/sum00/CEf397_Manuel_2000su/CEf397_Manuel_2000su.htm

62 University of Toledo Advanced Engineering Systems Modeling


UG http://www.eng.utoledo.edu/civil/classes/c 4710.html

63 University of Utah Applied Probability and Statistics


UG/G http://www.civil.utah.edu/

64 University of Virginia Risk and Reliability in Structural Engineering


http://www.cs.virginia.edu/%7Ecivil/degree%20programs/structures/smdc.html

65 University of Washington

Reliability and Design Structural Reliability G http://www.washington.edu/students/crscat/cee.html

66 University of Wisconsin, Madison

Probabilistic Methods in Structural Engineering

Structural Reliability G http://www.engr.wisc.edu/cee/courses/cee640.html

67 Utah State University Structural Reliability Structural Reliability G http://www.engineering.usu.edu/cee/classes.html

68 Vanderbilt University

Probability Models in Engineering Design


G http://www.vanderbilt.edu/catalogs/grad/Grad11.html

69 Villanova University

Probability concepts EGR General probabilistic methods

UG/G http://www.catalog.villanova.edu/courses/cee.html

70 Virginia Tech Reliability methods in structures and mechanics


http://www.ce.vt.edu/courses/coursedetails.asp?index=124&course=5494

10

Structural Reliability in Engineering Structural reliability accounts for the ability of the structure to fulfill its design purposes throughout a certain design life. Measures of structural reliability come from every process that constitutes the life of a structure (Figure2-1):

Most of these measures are random in nature; hence, probabilistic methods are required to quantify the participation of these different random variables in the design in order to determine the overall system stability. Sources of errors that may affect the reliability of a structure may come from humans (i.e. negligence, approximation, lack of knowledge or pure greed) or from nature (i.e. snow, ice, earthquake, fire, traffic or other loads). Table 2-2 shows the prime causes of structural failures (Melcher 1999):

Table 2-2 Prime causes of failure

Cause Percent Inadequate appreciation of loading conditions or structural behavior

Mistakes in drawing or calculations Inadequate information in contract documents or instructions

Contravention of requirements in contact documents or instructions Inadequate execution of erection procedure

Unforeseeable misuse, abuse and/or sabotage, catastrophe, deterioration Random variation in loading, structure, materials, workmanships etc.

Others

43 7 4 9 13 7 10 7

Figure 2-1 Elements of reliability within the life of a structure (Nowak and Collins 2000)

Designing Testing Build- ing

Using Planning

Owner/designer Interaction

Existing limited information

Information Not

Available

Limitation of designer

Limitation in analysis

Design load assumptions

Design resistance

assumptions

Future change of

conditions

Limitations in test methods

Representation of test samples

Control in testing practice

Limited full-scale testing

Construction process

Designer/ contractor interact

Change of conditions

Intentional alterations

Inadequate

Inspection

User abuse

Limited records of failures

Environmental effects

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Table 2-3 shows the various likely sources of human errors (Melcher 1999). Other than natural disasters, human errors contribute the most to structural failures.

Table 2-3 Classification of human errors (Melcher 1999)

Error type Human variability Human error Gross human error Failure process

In a mode of behavior against which the structure was designed

In a mode of behavior against which the structure was not designed

Mechanism of error

One or more errors during design, documentation, construction and/or use of the structure

Engineers ignorance or oversight of fundamental behavior. Professions ignorance of fundamental behavior

Possibility of analytic representation

High

Medium

Low

Table 2-4 shows the observed causes of common errors; with ignorance, carelessness and negligence comprising the highest of the error factors (35%):

Table 2-4 Error factors in observed failure cases (Melcher 1999)

Factor Percent Ignorance, carelessness, negligence Forgetfulness, errors, mistakes Reliance upon others without sufficient c ontrol Underestimation of influences Insufficient knowledge Objectively unknown situations (unimaginable?) Remaining

35 9 6 13 25 4.8

Another critical source of human error comes from the lack of knowledge (25%). This is a critical aspect that needs to be acknowledged. Technology is changing at a rapid speed, making it difficult for the design/construction industry to catch up. Most of these error factors are difficult to quantify and are classified as random variables. To ensure structural safety, the design of a structure requires the establishment of limit states to account for these likely sources of errors. Structural safety is achieved when the structure performs without exceeding the limit states. A limit state, represented by a mathematical function, is a boundary between desired and undesired performance of a structure. The limit state may be established at the component level or the system level. Structural reliability utilizes probabilistic quantification of these limit states to determine the likely failure of a structure as a result of either collapse of a structural component or the structure as a system. Probabilistic methods require the statistical quantification of the different random variables participating in the system stability. Fundamentally, a structure or a structural component is considered to have failed, if the load (L) applied to the structure exceeds its capacity to resist load (R):

12

(2-1) To establish the limit states, the variation of the different random variables must be known, which are typically accounted for by a coefficient of variation (VX). This variation can be determined by collecting data on the occurrences of the variable and identifying the statistical parameters (standard devia tion, X, and mean, X) of the particular random variable: (2-2) Table 2-5 shows the coefficients of variation (VX) for various factors that may involve in design:

LimitRL =/

x

xxV

=

13

Table 2-5 Coefficients of variation (VX) for various factors (Harr, 1987)

Parameter Coefficient of variation %

Sources

Porosity Specific gravity Water content Silty clay Clay Degree of saturation Unit weight Coefficient of permeability Compressibility factor Preconsolidation pressure Compression index Sandy clay Clay Standard penetration test Standard cone test Friction angle f Gravel Sand c, strength parameter (cohesion) Dead load Live load Snow load Wind load Earthquake load Structural steel Tension members, limit state, yielding Tension members, limit state, tensile strength Compact beam, uniform moment Beam, column Plate, girders, flexure Concrete Flexure, reinforced concrete, grade 60 Flexure reinforced concrete, grade 40 Flexure, cast-in-place beams Short column Thickness Flexural strength Crushing strength Flow velocity Moisture Density Compressive strength Flexural strength Glue-laminated beams Live load Snow load

Soil 10 2

20 13 10 3

(240 at 80% saturation to 90 at 100% saturation)

16 19

26 30 26 37 7 12 40

Struct. Loads, 50-Yr Max 10 25 26 37

>100

Structural Resistance

11 11 13 15 12

11 14

8-9.5 12-16

Ice 17 20 13 33

Wood

3 4 19 19

18 18

Schultze (1972) Padilla and Vanmarcke (1974) Padilla and Vanmarcke (1974) Fredlund and Dahlman (1972) Fredlund and Dahlman (1972) Hammitt (1966) Nielsen et al. (1973) Padilla and Vanmarcke (1974) Padilla and Vanmarcke (1974) Lumb (1966) Fredlund and Dahlman (1972) Schultze (1975) Schultze (1975) Schultze (1972) Schultze (1972) Fredlund and Dahlman (1972) Ellingwood et al. (1980) Ellingwood et al. (1980) Ellingwood et al. (1980) Ellingwood et al. (1980) Ellingwood et al. (1980) Ellingwood et al. (1980) Ellingwood et al. (1980) Ellingwood et al. (1980) Ellingwood et al. (1980) Ellingwood et al. (1980) Ellingwood et al. (1980) Ellingwood et al. (1980) Ellingwood et al. (1980) Ellingwood et al. (1980) Bercha (1978) Bercha (1978) Bercha (1978) Bercha (1978) Borri et al. (1983) Borri et al. (1983) Borri et al. (1983) Borri et al. (1983) Galambos et al. (1982) Galambos et al. (1982)

14

In structural reliability, the performance of a structure is defined as a performance function (g): ( ) LRLRg =, (2-3) where R, the total resistance term, is expressed as a function of its statistical sum of all its constituents: += RRR ZR (2-4) where R and X are the same statistical parameters for the ZR parameter that contributes to the total resistance. Similarly, the total load term can be expressed as the sum of its constituents: += LLL ZL (2-5) After significant mathematical derivation (not shown here), a generalized reliability index can then be expressed as:

22LR

LR

+

= (2-6)

Structural Reliability as a science is not limited to the structural design of civil structures. In fact, most of its applications are related to the design of system measures for manufacturing processes. The repetitive production process in manufacturing allows the generation of a significant database for the statistical studies needed to generate reliability measures. However, for structural engineering applications, the database for the statistical study is more difficult to generate. The conservatism in the previous design codes has already eliminated the possibility of structured failure under normal conditions. Hence, it makes it even more difficult to sell reliability-based designs. The establishment of reliability for civil engineering structures is difficult because of the following reasons:

1. All civil engineering structures are one-of-a-kind; 2. There is a general lack of records of failure (conservative design approach); 3. Lack of full-scale models; 4. Difficult to control quality; 5. Difficult to control boundary variables; 6. Difficult to promote probability-based analysis;

Other than design specifications, structural reliability is also useful for studies of specific structural behaviors (Moses and Derma 1987, Nowak and Carr, 1985) or damage failure assessments (Juang et al. 1999).

15

Structural Reliability in Design Codes Key arguments that lead to the promotion of reliability-based design specifications are that:

1. LRFD design provides a better measure of safety, while ASD design does not provide an accurate indication of safety;

2. LRFD design uses multiple load factor combinations, which typically leads to economical design;

3. LRFD may make design of all materials more compatible; 4. The rationality of LRFD has always been attractive; 5. Most national codes are leaning toward the adoption of LRFD; and 6. There is a direct relationship to strength testing in the laboratory.

As a result, there is a general increased interest in learning structural reliability. In classical Allowable Stress Design (ASD), the limit state is typically assigned a factor of safety (FS). As long as the design load of the structure does not exceed the resistance increased by the factor of safety, then the structure will be in good condition. In ASD design, factors of safety are integrated into the load and strength calculations at the component level, such as tension, compression and response of a member. The factor of safety is typically determined by and based upon experience and reasoning. By limiting the permissible load by a fraction, the safety of the structure is ensured. Recognizing the random nature of the various elements that contributes to the safety of a structure, a reasonable size sample of the different elements can be collected to statistically quantify L and R. The development of structural reliability in Civil Engineering is almost exclusive to the development of LRFD (Load Resistance Factored Design) code, which is based on the probability-based limit-states design (PBLSD). PBLSD requires the establishment of statistical parameters of each of the random variables, and hence needs extensive data collection and the establishment of the load factor (LF) and the resistance factor (RF) for the design of various types of structures. A set of equations such as the following is common for the establishment of the design code: ++= iiqD QQDR (2-7) where R is the code-specified resistance, D and Q are code-specified dead and live loads; is the resistance factor; and Q, D and i are the load factors. Contributors to the load factors may be earthquakes, tornados, traffics, winds, rains or snow. Each of the load factors is determined individually and is a function of its demographic distribution. In particular, due to recent earthquakes, a new zoning distribution has been established for determining the earthquake load factor (ASCE 7-98, 2000). In reliability-based design, it is very important to consider the unique nature of the material as well as the overall structure to be built. The material properties (Bulleit et al. 1993, 1995, Philpot et al. 1993, 1994, Rosowsky et al. 1994), construction process (Rosowsky 1996), different combinations of loads (Ellingwood et al. 1982, Galambos et al. 1982, Ellingwood and

16

Rosowsky 1991, 1996, Ellingwood and Tekie 1999, Byers 1997(1), 1997 (2), Hwang and Nowak 1991, Nowak and Hong 1991), seismic loads (Ghosn and Moses 1985, Han and Wen 1997(1), 1997(2)), environmental impact (Frangopol et al. 1997, Rosowsky and Fridley 1992), structure type (Casas 1997, Nowak and Lind 1979, Tabsh and Nowak 1991, Rosowsky and Ellingwood 1992, Nowak et al. 1994, Rajeev and Krishnamoorthy 1997, Koskisto and Ellingwood 1997), connection designs (Nowak and Regupathy 1984) and system-component relations (Rosowsky and Ellingwood 1991, Philpot et al. 1995, Keil 2000, Kirkham and Miller 2000) are all critical elements in reliability considerations. In developing LRFD design code, the random variables involved in the process of the establishment (such as the consideration of material variation, uncertainty in mechanical design methods, construction negligence, etc.) and utility (such as the variation in wind and live loads, the duration of loads, etc.) of a structure are all factored into the load or resistance factors. For example, in Ellingwood and Rosowskys (1991) study of the effect of load for wood construction, they noted that wood is a natural material with variable mechanical properties and is sensitive to the load application and duration. The benefit of the LRFD design code is questionable because of the following:

1) It does not directly measure the reliability of the design since the random variables are factored into LF and RF, the actual reliability is not measured. Nowhere in any of the design codes is there a mention or a requirement of safety quantification. This discrepancy in the design philosophy and the actual code establishment is inherent in the current cookbook approach in structural design practice.

2) It requires constant modifications or updates - if there is a general change in engineering

practice, such as the development of a new material, then there is a need to revise the design code, either partially or in its entirety,

3) It is based on limited data the establishment of LF and RF requires reasonably large

databases. However, they are not always available for civil engineering structures for two reasons. First, we do not usually collect data in actual practice; second every civil structure is considered unique. Unlike the manufacturing industry, repetitive and conformable designs are rare in civil engineering.

Based on the above three arguments, it is foreseeable that future improvement of the design codes would require an equal amount of effort to modify the code as when it was originally designed. Engineers will be required to continue to improve their knowledge through the design, modification and upgrade of codes. On the other hand, following the tradition of code establishment, the LRFD design code is relatively simple to use and is superior to the ASD design approach.

17

Textbooks for Structural Reliability Though there are numerous textbooks available for the teaching of general reliability (for example, Ang and Tan, 1985, OConner 1991, Lewis 1996, Ayyub and McCuen, 1997 and Carter, 1997), textbooks suitable for teaching structural reliability for undergraduates are very limited. Harr (1987) introduces very general reliability concepts but includes practical engineering applications such as geotechnical and structural applications. Nowak and Collins (2000) provide the most comprehensive discussion, and perhaps the most ideal for teaching, on the development of LRFD design specifications from probabilistic design methods. Mechner (1999), on the other hand, gives a more comprehensive discussion on the application of probabilistic methods in design of structures. He also provides a comparison between the different design codes, such as the European codes, the Canadian National Building Code and the LRFD codes. More in-depth discussions on the specific developments of different aspects of structural reliability theories can be found in Hart (1982) and Wen (1995) for load modeling, Ross (1997) for simulation, and Thoft-Christianson and Baker (1982, 1986) for structural reliability theories and applications. Marek, Gustar and Anagnos (1996) published a focused study on the use of computer simulations in reliability assessment. This particular book provides numerous examples of how to determine reliability indices for structures through the use of software. Useful LRFD Web Sites There are several useful web sites available on the Internet where students can freely access introductory information on the LRFD design methods: Thacker, B., and Millwater, H. "NESSUS: A New Tool for Safer Structure." http://www.swri.org/3pubs/papers/d06/probmech.htm. LRFD Calibration for Wood Bridges. http://www-personal.engin.umich.edu/~nowak/projects/lrfd_calibration_wood.htm Control of Truck Loads on Bridges. http://www-personal.engin.umich.edu/~nowak/projects/control_truck_loads.htm Control System for Live Load and Live Load Effects on Bridges. http://www-personal.engin.umich.edu/~nowak/projects/contro_system_live_load.htm Development of a Produce for Efficient Evaluation of Bridge Decks. http://www-personal.engin.umich.edu/~nowak/projects/evaluation_bridge _decks.htm LRFD Primer. http://www.lrfd.com/Loads.htm LRFD Primer. http://www.lrfd.com/Concrete.htm Structural Reliability Analysis. http://insdel.snu.ac.kr/~ohk/reliability.html

18

Software for Structural Reliability Commercial computer programs for the study of structural reliability are available, including CAREL, COSSAN, PROBAN, ISPUD, NESSUS and STRUREL. NESSUS is capable of both stochastic finite element and boundary analyses for structural simulations. Most of these programs are able to conduct Monte Carlo simulations and structural reliability analyses. However, the commercial packages are either too expensive or too extensive for undergraduate study. Marek, Gustar and Anagnos (1996) published simpler versions of general structural reliability analyses programs: ResCom for the evaluation of a single-component load effects on a simply supported beam; LoadCom for load effect combination analysis for up to 6 load combinations; DamAc- for the effects of accumulated damage with load history on the strength of a wood member; and AntHill for using the anthill method to solve several reliability assessment problems. Most of these programs involve extensive probabilistic studies and powerful data presentations, and they are suitable for upper level reliability courses. But the process of random data generation and fundamental reliability index establishment are transparent to the users; hence, the literature search results indicate that currently, there are no simple computer programs that are suitable for undergraduate students with limited structural analysis background. In addition, they may not be suitable for undergraduate students or for the UTCA short course.

19

Section 3.0 UTCA Pilot Course

Introduction To develop a fully extended undergraduate course in structural reliability, a pilot course was first established. The pilot course allowed experimentation on the course contents and modifications based on students feedback. The UTCA pilot course was designed to teach students the principles of structural reliability by using structural steel design as an example. This course was intended as part of the UTCA technology transfer course for continuing education for professional engineers. The full 8 contact hours qualifies for a 0.5 CEU accreditation. Two instructors were involved in the teaching of this course: Dr. Shen-En Chen of UAB and was responsible for the materials on system reliability and Dr. Wenshen Pong of SFSU (San Francisco State University), who is specialized in Earthquake engineering, especially in damper design for steel structures, taught the structural steel design. Since most of the students were professional engineers and graduate students, the course content was structured with more in-depth discussions on structural steel connections. Four years after the Northridge earthquake, extensive research and development have been applied to improve the design of steel structure connections. These new designs are slowly being incorporated into new steel design codes. The engineering community has indicated a need to improve the current load factors for structural steel design. The selection of an earthquake design specialist (Dr. Wenshen Pong) in teaching the structural steel LRFD design allowed new fertile concepts regarding the future development of the load factors into the course content. Dr. Pongs participation demonstrates UTCAs outreach and utility of experts outside of the state of Alabama. UTCA Pilot Course Contents Table 3-1 outlines the schedule of the one-day short course, which interlaces the teaching of reliability concepts and structural steel LRFD design. The goal was to use structural steel LRFD design to illustrate the application of reliability concepts in the development of a specific LRFD code. This was followed by a comparison of the two different fundamental design philosophies (ASD and LRFD) for steel structures. An overview of the differences between the AISC, ASD, and LRFD Steel Design Codes was also presented. A review of probability, statistics and the development of system reliability was then conducted. Afternoon sessions were focused on system/component relationships, including discussions of behaviors of structural members and their relationships to the overall structural performance, and also the quantification of system reliabilities as well as simulation methods. The course concluded with design examples using RAM SBeam and West Point Bridge Designer (WPBD). Students were asked to gene rate data using the two programs to calculate structural reliabilities.

20

Table 3-1. UTCA short course schedule

8:30am - 9:20am Introduction (Chen)

9:30am - 10:20am LRFD & ASD (Pong)

10:30am - 11:20am Review of probability (Chen)

11:30am - 12:20pm Steel design - LRFD (Pong)

12:30pm - 1:20pm Lunch

1:30pm - 2:20pm Connection considerations (Pong)

2:30pm - 3:20pm System reliability (Chen)

3:30pm - 4:20pm Design examples (Pong)

4:30pm - 5:20pm Reliability example (Chen)

Timeline The UTCA project started in October of 2000. The first quarter was spent in preparing the course materials (including PowerPoint presentations for all eight lectures) and reviewing the applicable literature. The first class project, using the WPBD software (Ressler, 2000) with 30 design examples, was generated. The Professional Development Department at UAB was asked to help distribute the course announcement flyers. The first course was offered on December 14, 2000 with three professional engineers and four graduate students participating in the class. The low enrollment was probably the result of poor promotion strategy. The short course was offered in the Multi-media lab of the Business and Engineering College building at UAB. Three computer programs were used as teaching tools: RAM SColumn, RAM SBeam (Ram International 1999) and the WPBD. More examples were generated during the second quarter, including 200 West Point Bridge Designer data examples. Dr. Peter Chen of UIUC (University of Illinois at Urbana Champaign) was invited to assist in the statistical analysis of the design data. This study allowed investigation of the effects of the sample size on the random distribution and reliability of the bridge design. Due to the time constraint for the short course, RAM SColumn was dropped from the course material. The emphasis is in developing design projects using RAM SBeam. The second course was delayed to the fourth quarter of 2001. Most of the work during the third quarter was spent developing short course materials, including revising the entire PowerPoint presentations, and conducting a study on using influence line analysis to determine the critical members on the West Point Bridge example. A conference paper entitled: Teaching Reliability to Structural Engineers by Chen, Pong, Chen and Nishihama, was submitted and accepted for publication and presentation at the First International Colloquium on Engineering Education to be held in Berlin, Germany. The colloquium, unfortunately, was cancelled due to the terrorist attack on the New York World Trade Center and the Pentagon on September 11, 2001. The paper was subsequently submitted to the annual American Society of Engineering Education (ASEE) Southeast Section Conference to be held on the April 7-9, 2002 at the University of Florida.

21

The second short course was offered during the fourth quarter, on November 16, 2001, with four graduate students and two professionals participating. Revised lecture notes were distributed out to the participants. To promote the second course, an extensive mailing list from the Continue Education Department was used. More than 100 promotional materials have been sent. However, due to erroneous information in the mailing list, over 70 % of the mailed materials were returned. Teaching of structural reliability concepts The lecture started with an introduction of the reliability concept, which is a measure of safety in a structure. A discussion on what contributes to the safety of a structure then followed, and included an overview of the likely sources of error from the different stages of the establishment of the structure that may contribute to the safety of a structure. Since most of these errors are random in nature, they can be identified as random variables and probabilistic methods can be used to quantify them. During the introduction, a brief overview of Structural Reliability and Random Variables was presented. A detailed discussion on the components that contribute to structural reliability and that are involved in the different stages of planning and construction was presented. A brief introduction of the course content, including the two design projects, was then presented. This was followed by a description of safety analysis, and of the establishment of limit states and system concept. The first lecture ended with a discussion on the current availability of structural reliability-related courses, books and software. Basic concepts in Probability and Statistics were presented in relation to structural mechanics. One example was about how a possible event can be related to the distribution within the sample space for a particular problem. Its Probability Density Functions (PDF) and its Cumulative Distribution Functions (CDF) could be used to describe the dis tribution of the random events. Using a beam-bending problem (Figure 3-1), the characteristics of the basic functions were described. The steel beam was assumed to be simply supported and under uniformly distributed dead and live loads.

22

The example used randomly generated load combinations and computer analysis to determine the most economical design. Figure 3-2 shows the scatter plot of different combinations of dead and live loads. Details of the design problem are described in Section 4. A random variable was then introduced along with its statistical parameters such as the variance, expected values, standard deviation and coefficient of variation. The different distributions of random variables such as uniform normal distribution, lognormal, Gamma distribution, etc. were also briefly described. Representative statistics parameters for quantifying hot-rolled steel components are presented in Table 3-2.

DL

LL

= DL + LL

Fixed Span, L

2L

8

2L

Figure 3-1 Beam bending example

Sample Beam

Shear Diagram

Moment Distribution

23

Table 3-2 Representative statistics for the resistance of structures produced from hot-rolled steel elements

Element type P VP M VM F VF *R VR Tension member, yielding

1.00 0 1.05 0.10 1.00 0.05 1.05 0.11

Tension member, ultimate

1.00 0 1.10 0.10 1.00 0.05 1.10 0.11

Compact beam, uniform moment

1.02 0.06 1.05 0.10 1.00 0.05 1.07 0.13

Compact beam, continuous

1.06 0.07 1.05 0.10 1.00 0.05 1.11 0.13

Elastic beam, lateral-torsional buckling

1.03 0.09 1.00 0.06 1.00 0.05 1.03 0.12

Inelastic beam, lateral-torsional buckling

1.06 0.09 1.05 0.10 1.00 0.05 1.11 0.14

Plate girders, flexure 1.03 0.05 1.05 0.10 1.00 0.05 1.08 0.12

Beam columns 1.02 0.10 1.05 0.10 1.00 0.05 1.07 0.15 *The nominal resistance used to determine the bias factor is based on an older version of the AISC steel design code. These values may change slightly if nominal resistances based on later version of the AISC code (or other steel design codes) are used. (Ellingwood, Galambos, MacGregor, and Cornell, 1980)

Limit states, performance functions and their tie to the probability of structural failure and reliability measures (indices) were presented, followed by a detailed reliability example (class project) prepared using data generated from the RAM SBeam (RAM International 1999) design software. Calculation of the reliability indices was demonstrated using this example.

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12

Live load (k/ft)

Dea

d lo

ad (

k/ft

)

Dead load vs. Live load (200 samples) Median

Mean

Figure 3-2 Dead load and live load combination for the 200 sample problem

24

The system reliability concept was presented along with a brief discussion of the different types of possible system-component combinations. The lecture then turned to the discussion of design code development. Links between ASD, LRFD and performance-based design philosophies were discussed. Different levels of code development, including the necessity of code calibration, were also discussed; where the development of the bridge design code was used to illuminate the process of code development. Finally, the class project using West Point Bridge Design (WPBD) software was used to illustrate the calculation of system reliability. Students were asked to hand calculate some simple data. Teaching of LRFD Structural Steel Design The goal of the Structural Steel Design lecture was to use a steel structure as an example to illustrate the differences between the ASD and LRFD design codes. Four lectures encompassing the design of steel structure using LRFD design specification of different structural components were coupled with design examples. The course material was revised into four one-hour lectures. Some important tables and charts were extracted from the AISC Steel design code (AISC 1999). The American Institute of Steel Construction has adopted the LRFD specification in 1984 (AISC, 1984). It is calibrated with the 1978 AISC ASD specification, is based on a probabilistic model, and has been evaluated based on judgments of experienced design engineers. The limit states used in the design code include both strength (i.e. ductile strength, buckling, fatigue, fracture, overturning and sliding, etc) and serviceability (i.e. deflection, vibration, permanent deformation and cracking). The design concept is based on the establishment of resistance factor and factored loads. The lecture started with a brief discussion on why the LRFD design approach is needed in steel design:

1) ASD is an approximate way to account for what LRFD does in a more rational way; 2) Using multiple load factor combinations should lead to economy; 3) LRFD makes design of all materials more compatible; 4) Safer structures may result under LRFD; 5) LRFD is especially relevant for seismic design; 6) LRFD uses appropriate combinations of loading for strength and serviceability criteria; 7) LRFD is consistent with the trend toward limit state design; 8) The rationality of LRFD has always been attractive; 9) LFRD is consistent with specifications for other methods; and 10) LFRD is easily adaptable to test data.

The designs of members (tension and compression) and connections were organized into separate topics. A comparison of the LRFD and ASD designs for tension and compression members was offered at the beginning of these topics.

25

For beam bending, ASD design requires that:

Where PD and PL are the dead and live loads. Fy is the nominal steel strength and Ag is the gross sectional area. 0.6 is equivalent to the factor of safety. For ultimate load design, Fu, ASD has similar requirements for a certain nominal net area, An:

nuLD AFPP 5.0

26

Defining the gross area as a weight function to compare the ASD and LRFD designs:

)/(5.1

)/(6.12.1

DL

DL

ASD

LRFD

PPPP

WeightWeight +

= (3-5)

Figure 3-3 shows that the LRFD design is more conservative for a lower live load vs. dead load ratio. The design advantage is minimized at a ratio of three. Examples of tension members were used to describe the determination of critical path based on fracture criteria for design. The limit states for a tension member, therefore, may be either yielding or a combination of fracturing and yielding. The design engineer should determine the most critical limit state. Examples of column designs (compression members) for both ASD and LRFD specifications were demonstrated using a specified dead load (PD = 299 kips) and live load (PL = 38 kips) combination. With a constant effective length of 12 ft, it was shown that ASD (W1253) requires a larger section than LRFD (W1250). More than 4 examples were prepared for illustrating column design. Similar comparisons between ASD and LRFD design are also presented for beam members. Chapter F of the AISC LRFD specification (AISC 1994) identifies four possible limit states for beam members:

1. Flexural yielding and buckling; 2. Shear yielding and fracture; 3. Deflection; 4. Weak axis bending.

For a compact section with full lateral support (no buckling), the flexural design strength is controlled by member yielding:

ypnnb ZFMMM 9.09.09.0 === (3-6) where Mn is the nominal flexural capacity, Mp is the plastic moment and Z is the plastic section modulus. For LRFD specification, the requirement would be:

ZFMM yLD 9.06.12.1

27

SFMM yLD 66.0

28

The lecture content also included the design of composite members such as steel/concrete composite sections. For composite beams, the nominal flexural capacity should be determined with consideration of the plastic stress distribution. Shear connections, partial composite action and deflection were also discussed. Composite columns were also included in the discussion. The last section of structural steel design was a comprehensive list of examples, which provides the flexibility for the instructor to add or omit materials, based on time allowance.

29

Section 4.0 Development of Course Projects

Introduction A very important component in teaching reliability courses is to make students aware of the numerical simulation and random data generation processes in establishing the statistical parameters for reliability. Most engineering designs are now computer based. However, the proper selection of the right parameters for input remains a tricky business. Using the concepts of random variables, simulation of probabilistic distributions of each critical input parameter in a design can be performed. To illustrate this concept in the UTCA short course, two design examples have been developed. These design examples can be used for future course projects that engage students in hands-on development of reliability-based designs. To develop the two design examples, simulation software for structural behavior was used. Selection of the two design programs was largely based on their simplicity of application and their availability. Two reasons that the simulation software should be kept as simple as possible are as follows: 1) the UTCA short course does not allow time to teach the underlying background materials such as matrix analysis and finite element methods; and 2) it is assumed that undergraduate students that will be taking this class may only have the fundamental mechanics courses (Statics, Dynamics and Strength of Material). Hence, computer programs should use less complicated data that require a minimal mechanics background for the student. Criteria for the design examples are: 1) comprehensible for undergraduate students and 2) easy for simulation. Based on these criteria, the West Point Bridge Designer (developed by the US Military Academy, Ressler 2000) and the RAM SBeam software (Ram International 1999) were selected for simulating structural behavior. The WPBD program is used to illustrate the effects of individual member resistance on structural stability. The RAM SBeam program, on the other hand, allows different load combinations; hence it is used to illustrate effects of variable loads on structural reliability. Monte Carlo simulation using randomly generated cases are then used to illustrate the computation of reliability parameters and to study the probabilistic effects on structural reliability. The objectives of the design projects are:

1) To demonstrate the process of computer simulation and random data generation for reliability analysis;

2) To show the effect of the size of the sample population on the results of analysis; 3) To explain separately the effects of load and resistance variance on the stability and

reliability of a structure; 4) To compare the results based on ASD and LRFD design principles;

30

West Point Bridge Designer (WPBD) WPBD is a popular program for illustrating the underlying concepts of truss bridge stability under a standard AASHTO H20-44 truckload (Ressler 2000). Each of the members is pin-connected. To make the bridge more realistic, it is equipped with concrete deck, floor beam and asphalt riding surface. To illustrate the effect of ind ividual members on the stability of the structure as a whole, static structural analysis using the truckload is performed in the WPBD software to determine if the bridge would fail under the load test. The system mechanism is such that a single member failure would cause the collapse of the entire bridge. WPBD provides not only for interactive design of a steel highway truss bridge but also tensile and compressive stresses of each member and animated displays of the truck crossing and of bridge failure. WPBD allows the selection of different materials and member sizes. A simplified budget is also provided for every design, including labor and material costs. Students can model a bridge and test it for structural adequacy and cost minimization. Also, users learn about engineering design as they construct an efficient and effective virtual bridge by using different member dimensions as input variables. Using the WPBD, two design issues are addressed: suppose a member is designed with randomized sectional dimensions:

1. What is the probability that the failure of a member will cause the bridge to fail? 2. What is the system reliability due to the change of a single particular member?

Figure 4-1 shows the WPBD program with the standard truck crossing the bridge. When a member is not designed adequately, the program will show the bridge failure (member buckling). Different colors represent the stresses within a member: the members that are under the compression are shown in red and the members that are under tension are shown in blue. The intensity of the color represents the stress level. For example, the bridge shown in Figure 4-1 is a Herman Haupt Memorial Bridge, which has 21 members. Figure 4-1 shows that member 20 failed in tension, and as a result the whole bridge collapsed. The thickness of each member indicates the relative cross-sectional size. Model Generation & Problem Statements For the classroom example, a truss bridge (the Herman Haupt bridge) with 21 bar-elements was used. Figure 4-2 shows the truss bridge with labeled member numbers. The span of the bridge is 24 m, the height is 5 m, and the width of the bridge is about 10 m. The original design consisted of members of 120 mm 120 mm cross-section, except for members No. 11 and 21, which are 140 mm 140 mm cross-section. This configuration gives an economical and safe design. A Monte Carlo simulation is then conducted using randomly generated numbers to choose member numbers and section sizes. The random number generator assumes a normal distribution. The member cross-section dimensions are limited to the range from 10 mm 10 mm to 140 mm 140 mm. The program is then executed to determine if the bridge would hold under the new design. The results include thirty generated samples.

31

Figure 4-1. WPBD showing bridge failure during truck crossing

Figure 4-2. Haupt truss bridge with member numbers

11

1 2 3 4 5 6

8 7 9 10

12

13

14

15

16

17

18

19 21

20

32

Table 4-1 Range of Random Events Using Member Sectional Properties

Random Events Sectional property E1 0~100 mm E2 101~200 mm E3 201~300 mm E4 301~400 mm E5 401~500 mm

Table 4-1 shows the random events defined for the different member sizes. The random variables involved are the member number (N) and the dimension range (E). The outcome of analysis is bridge failure or safety (S). The probability that a member gets selected is then P(N) = 1/21 = 0.048, the probability that a section range may be selected is then P(E) = 1/5 = 0.2, and the probability of a bridge failure is then P(S) = 1 / 2 = 0.5. Table 4-2 shows the results from the 30 sample tests, where column 1 shows the test number, column 2 is the member selected, column 3 is the actual member size selected, and columns 4 and 5 are the maximum tensile or compressive forces in the member, respectively. Column 6 shows whether the member has failed (1) or passed the load test (2). With 14 failures, the 30 sample tests show a bridge reliability of (30-14)/30 = 54%. Figure 4-3 shows the Probability Density Functions (PDF) of the 21 members that were selected. This demonstrates that member 18 has the highest occurrence rate. From the 30 samples, the percentage of success (used as a measure of structural reliability) was then determined. Figure 4-4 shows the reliability of the 30 samples, from which it is shown that Members 12 and 18 have the highest reliability (10 %). Members 2, 3, 4, 7, 8, 9, 14, 15, 17, 19 and 20 are shown to have the lowest reliability (0 %). However, obviously this is misleading due to the small size of the sample population. For example, some of the members (Members 8 and 19 and 20) were not selected. The question about the sample size can then be answered by generating another set of 207 data points. Figure 4-5 shows the PDF for the set of 207 data points. Again, it is shown that Member 18 has the highest occurrence and Member 2 has the second highest occurrence rate, whereas Member 20 has the lowest occurrence rate. In this case, all members have been selected at least three times.

33

Table 4-2. Analysis of results from 30 samples

Test Member Sectional size (mm)

Tension (kN) Compression (kN)

*Fail/Pass

1 12 300 742.3 2 2 10 300 -577.3 1 3 18 100 454.1 2 4 10 100 -558.8 2 5 21 90 -892.4 2 6 16 90 481.3 2 7 4 200 1066.8 1 8 18 50 453.5 2 9 11 50 -945.2 1 10 1 500 624.2 2 11 12 400 753.6 2 12 11 100 -947.7 1 13 18 200 456.5 1 14 14 300 503.2 1 15 18 300 460.5 1 16 2 300 969.9 1 17 7 400 -627.6 1 18 6 300 569.6 2 19 3 300 1086 1 20 18 90 454 2 21 13 300 -668.8 2 22 5 100 923.5 2 23 17 300 52 -305.7 1 24 4 300 1086 1 25 12 200 734.3 2 26 2 400 991.4 1 27 16 300 501 1 28 11 400 -997 2 29 9 300 -952 1 30 15 500 -370.9 1

*Fail=1, Pass=2

34

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Member number

occu

ranc

e %

Figure 4-3. Probability density function of the 30 member sample study

3.33

3.33 0.00 0.00 0.00 3.33 3.33

0.00 0.00 0.00 3.33

10.00

0.00 3.33 3.33

0.00 3.33

0.00

10.00

0.00

0.00

30 samples

Figure 4-4. Reliability of the members for the 30 sample case

35

Figure 4-6 shows the reliability measure of each member for the 207 cases. It is shown that the lowest probability of the bridge failure due to a change of dimensions of a randomly selected single member (most reliable) is 7.73 % (member 18), and the most critical member (least reliable) is 21 (0%). Member 21 was selected five times, and it failed all five times. Other critical members are 11 (0.48 %), 15 (0.48 %) and 7 (0.48 %). Obviously, the accuracy of the results has been improved with a bigger sample size. The accuracy of the results can be further improved with more data. Typically, a realistic structure will have to generate millions of data points to generate reliability indices. This formidable task can easily be accomplished by automating the sample tests. In real life, sample tests are limited because of the associated costs, so behavior of large bridge components are typically determined by using computer simulation.

4.35 0.48

3.38 2.90 4.83 2.42 1.93 3.38

0.48 1.45 2.42 2.42

0.48 0.97

0.00 3.38 2.90

3.38

7.73

0.97

0.97

207 samples

Figure 4-6. Reliability measures of the 207 cases

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

MEMBER No.

OC

CU

RA

NC

ES

Figure 4-5. Probability density function for the 207 data

36

In this example, there were 101 failures in the 207 trials. Hence, the overall performance of the bridge was 101/207=0.49 or 49 %, which gives a reliability of 51 % for the entire system. The reliability of individual members in this case varies. This example illustrates the effects of individual members on the system reliability and of the size of sampling population. Influence lines for bridge members were then hand-calculated and drawn to check the maximum forces that the combined loads may apply to the system. Figure 4-7 shows that Member 11 experienced the highest compression value when the head of a H20-44 truckload is located at the joint between members 2 and 3 (which is located 8.0 m from the far left side). The stiffness is measured by the slenderness ratio (the ratio of the length of a member to its smallest radius of gyration). As a member becomes longer, or as its slenderness ratio increases, a larger cross sectional area is required to withstand the same load since the danger of buckling increases. The results of the influence- line show that members 2, 3, 11 and 17 experience the highest loads in tension or compression. The influence line only gives the amount of force experienced by the bridge and does not reflect the reliability of the bridge in general. However, if this force exceeds the tensile or compressive strength of the member, which are functions of the cross-sectional dimension of the member, then the member will not be safe. Hence, if the sectional properties of these members are reduced, there is a good likelihood that these members will fail first.

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 1 2 3 4 5 6 7 8 9

Case Number

Axi

al F

orce

(ki

ps)

Member 1

Member 2

Member 3

Member 4

Member 5

Member 6

Member 7

Member 8

Member 9

Member 10

Member 11

Member 12

Member 13

Member 14

Member 15

Member 16

Member 17

Member 18

Member 19

Member 20

Figure 4-7. Influence lines for each member for the HS20-44 truckload

37

Summary of WPBD Work The results of this study indicated that the 30-samples have a reliability of 54 %. As the sample size increases to 207 samples, the reliability becomes 51 %. This is closer to the theoretical probability of success of 50 %, given that any single member failure will lead to the failure of the entire system. In this example, the likely event of a particular element changing is independent of the changes in the dimension of the member. Both results show that member 18 is the most reliable member, whereas, the two tests do not agree on the least reliable member. RAM Steel Beam Design (RAM SBeam) This example studied the difference between safety factor-based design and reliability-based design. RAM SBeam is a powerful design software for structural engineers. It can be used for design and analysis of steel composite and noncomposite beams with various boundary conditions. The program has a fully interactive Windows95/NT interface and full- integration of ASD and LRFD design specifications. Optimized designs using ASD and LRFD specifications were studied using the RAM SBeam software (Ram International 1999). After entering data such as dead load, live load, and beam length, RAM SBeam can determine the smallest stable sections using a prescribed structural member database. Model Generation & Problem Statements In this example, different combinations of live load and dead loads are used as random variables. Figure 3-1 shows a simply supported beam under both live (LL) and dead loads (DL). The range of the dead load was between 0.0236 kN/m and 14.550 kN/m with a mean of 7.990 kN/m and standard deviation of 3.970 kN/m. The range of the live load was between 0.2363 kN/m and 145.50 kN/m with a mean of 73.334 kN/m and standard deviation of 42.410 kN/m. These loads were then applied to an A36 steel I-beam with a 10.67 m simple span. Two sets of data were generated: the first set had 50 data points and the second set had 200 data points. Both ASD and LRFD design specification analyses were conducted for the different load combinations. Then, optimized designs of ASD and LRFD for different load combinations were conducted. Table 4-3 shows the results of the 50 and the 200 sample tests for the previously selected 30 sample members. Column 1 in the table shows the 30 selected members followed by the results from the LRFD design with 50 sample

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