Robust-to-Change Stiffness Allocation for Tall Structures
Publication: Journal of Engineering Mechanics
Volume 142, Issue 3
Abstract
A computational procedure for robust-to-modeling and robust-to-change design of structural systems is proposed with application to planar rigid frames. A structure is considered robust when it is least sensitive to changes that alter its system coefficients (stiffness matrix for static loading). The upper limits of change from perturbations in the stiffness matrix are available from linear algebra; however, what is not clear is an ideal pattern of material allocation throughout the structure, or a preferred preliminary model from a set of viable models, such that it results in a final design that has low error bounds while satisfying the limit states of performance and safety. Because gradient-based optimization is not feasible, the authors rely on statistical simulation techniques to study the variation of error upper bounds in structural response when the system is subjected to changes in its components (elasticity, cross-sectional dimensions, member lengths). Application of the methodology to lateral design of a set of multistory rigid frames shows that initial models with uniform material distribution over their height produce more tolerant designs. Along the way, the authors analytically present the necessary condition for making multiobjective design (also known as performance-based design) of multistory frames with a single objective. The procedures have the potential of saving time and resources during the lengthy design projects and creating structures that are more tolerant to change, hence improving their resiliency and lifespan.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The work reported here was performed while the first author was with the Department of Mathematics at Southern Methodist University. The assistance of the department in providing computational resources needed for this work is acknowledged. Discussions with and comments by Professors James L. Beck of the California Institute of Technology and Konstantin Zuev of the University of Liverpool have been very insightful and are appreciated. The comments and the critique of the anonymous reviewers improved the paper. We are grateful for their review.
References
ACI (American Concrete Institute). (2011). “Building code requirements for structural concrete and commentary.” Farmington Hills, MI.
AISC (American Institute of Steel Construction). (2010). “Steel construction manual.” Chicago.
Alimoradi, A. (2004). “Probabilistic performance-based seismic design automation of nonlinear steel structures using genetic algorithms.” Ph.D. thesis, Univ. of Memphis, Memphis, TN.
Ang, A. H.-S. (1973). “Structural risk analysis and reliability-based design.” J. Struct. Div., 99(9), 1891–1910.
Arnold, C., and Reitherman, R. (1982). Building configuration and seismic design, Wiley.
Asadpoure, A., Tootkaboni, M., and Guest, J. (2011). “Robust topology optimization of structures with uncertainties in stiffness–Application to truss structures.” Comput. Struct., 89(11-12), 1131–1141.
Au, S. (2005). “Reliability-based design sensitivity by efficient simulation.” Comput. Struct., 83(14), 1048–1061.
Beck, J. (2013). “Bayesian system identification and response predictions robust to modeling uncertainty.” ICOSSAR 2013, International Association for Structural Safety and Reliability, New York.
Beck, J., and Au, S. (2002). “Bayesian updating of structural models and reliability using Markov chain Monte Carlo simulation.” J. Eng. Mech., 380–391.
Beck, J. L., et al. (1997a). “A methodology for reliability-based multi-criteria optimal structural design.” Structural Safety and Reliability: Proc., ICOSSAR ‘97, the 7th Int. Conf. on Structural Safety and Reliability, Balkema, Rotterdam, Netherlands, 1113–1120.
Beck, J. L., et al. (1997b). “A performance-based optimal structural design methodology.”, California Institute of Technology, Earthquake Engineering Research Laboratory, Pasadena, CA.
Chen, W., and Lewis, K. (1999). “Robust design approach for achieving flexibility in multidisciplinary design.” AIAA J., 37(8), 982–989.
Chopra, A. K. (2011). Dynamics of structures, Prentice Hall, NJ.
Clough, R., and Penzien, J. (1975). Dynamics of structures, McGraw-Hill.
Cornell, C. A., and Krawinkler, H. (2000). “Progress and challenges in seismic performance assessment.” PEER Center News, 3(2), 1–4.
Der Kiureghian, A., and Liu, P. (1986). “Structural reliability under incomplete probability information.” J. Eng. Mech., 85–104.
Doltsinis, I., and Kang, Z. (2004). “Robust design of structures using optimization methods.” Comput. Methods Appl. Mech. Eng., 193(23–26), 2221–2237.
DuChateau, P., and Zachman, D. (1989). Applied partial differential equations, Harper and Row, New York.
Ellingwood, B., and Galambos, T. V. (1982). “Probability-based criteria for structural design.” Struct. Saf., 1(1), 15–26.
Ellingwood, B. R. (1994). Probability-based codified design: Past accomplishments and future challenges. Struct. Saf., 13(3), 159–176.
Ern, A., and Guermond, J.-L. (2004). “Evaluation of the condition number in linear systems arising in finite element approximations.”, Texas A&M Univ., College Station, TX.
Frangopol, D., Corotis, R., and Rackwitz, R. (1997). “Reliability and optimization of structural systems.” Pergamon, Padstow, Cornwall.
Haftka, R. (1990). “Stiffness-matrix condition number and shape sensitivity errors.” AIAA J., 28(7), 1322–1324.
Haldar, A., and Mahadevan, S. (1999). Probability, reliability and statistical methods in engineering design, 1st Ed., Wiley, New York.
Higham, N. (1994). “A survey of componentwise perturbation theory in numerical linear algebra.” W. Gautschi, ed., Proc., Symp. in Applied Mathematics, Vol. 48, American Mathematical Society, Providence, RI, 49–77.
Hjelmstad, K. (2005). Fundamentals of structural mechanics, Springer, New York.
Katafygiotis, L., and Zuev, K. (2008). “Geometric insight into the challenges of solving high-dimensional reliability problems.” Probab. Eng. Mech., 23(2–3), 208–218.
Papadimitriou, C., Beck, J. L., and Katafygiotis, L. S. (1997). “Asymptotic expansions for reliabilities and moments of uncertain dynamic systems.” J. Eng. Mech., 1219–1229.
Paulay, T., and Priestley, M. J. N. (1992). Seismic design of reinforced concrete and masonary buildings, Wiley.
Salmon, C., Johnson, J., and Malhas, F. (2008). Steel structures: Design and behavior, Prentice Hall, New York.
Scott, M. (2012). “Evaluation of force-based frame element response sensitivity formulations.” J. Struct. Eng., 72–80.
Song, J., and Der Kiureghian, A. (2003). “Bounds on system reliability by linear programming.” J. Eng. Mech., 627–636.
Sorensen, J., Kroon, I., and Faber, M. (1994). “Optimal reliability-based code calibration.” Struct. Saf., 15(3), 197–208.
Taflanidis, A., and Beck, J. (2010). “Reliability-based design using two-stage stochastic optimization with a treatment of model prediction errors.” J. Eng. Mech., 1460–1473.
Vanmarcke, E. H. (1973). “Matrix formulation of reliability analysis and reliability-based design.” Comput. Struct., 3(4), 757–770.
Watkins, D. (2010). Fundamentals of matrix computations, Wiley, New York.
Wells, M. (2005). Skyscrapers structure and design, Laurence King Publishing, London.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 142 • Issue 3 • March 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Feb 8, 2015
Accepted: Sep 14, 2015
Published online: Nov 20, 2015
Published in print: Mar 1, 2016
Discussion open until: Apr 20, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.