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Stability: Using Computer Software as a Virtual Lab for Learning Structural Stability
2012 Educator Session Presentation - April 18, 2012
by Ronald D. Ziemian, Ph.D., Bucknell University
Due to its significant strength-to-weight ratio, the use of steel often results in structural systems composed of fairly slender members and cross sections. As a result, the associated design process requires a fundamental understanding of structural stability. In addition, or as an alternative to differential equations and experimental testing, nonlinear analysis can provide opportunities for learning many important concepts related to designing for stability. Based on educational software that is available at no cost, several learning modules have been developed that can provide a virtual lab for better understanding topics such as elastic and inelastic flexural and lateral-torsional buckling, inelastic force redistribution, local buckling, and second-order effects.
To download the software or more information on this topic, visit Ron Ziemian's website: http://www.mastan2.com/stabilityfun.html.
Ziemian's 2012 NASCC Educator Session presentation is provided below along with several learning modules that he has created for learning structural stability.
Presentation Slides (27 MB)
Learning Modules 1-9 (4 MB)
Individual Learning Modules:
Learning Module 1 - Elastic Column Buckling and the Effect of End Restraint (863 KB)
Using a critical load analysis, the elastic flexural buckling strength of a column with various degrees of end restraint is investigated.
Learning Module 2 - Factors Influencing the Flexural Buckling Strength of Compression Members (329 KB)
Using computational analysis as a virtual laboratory, the main factors that impact the flexural buckling strength of steel wide-flange sections with nonslender elements are investigated. These factors include member slenderness, material nonlinearity, initial imperfections in geometry (out-of-straightness), and residual stresses. Computed strengths are presented in the form of column curves, which are further compared with the corresponding nominal strength curve defined in Chapter E of the AISC Specification for Structural Steel Buildings (2010).
Learning Module 3 - Effective Length K-factors for Frame Members (729 KB)
Effective length K-factors for compression members in frames are investigated. In addition to studying cases of sidesway inhibited and uninhibited, elastic and inelastic buckling is explored. Computational results are compared with alignment chart methods.
Learning Module 4 - Factors Influencing the Strength of Flexural Members (444 KB)
Using computational analysis as a virtual laboratory, the main factors that impact the major-axis flexural strength of steel wide-flange sections with compact elements are investigated. These factors include unbraced length, partial yielding accentuated by the presence of residual stresses, and initial imperfections in geometry (out-of-straightness). Strength limit states defined by full yielding of the cross-section (plastic hinge) and elastic/inelastic lateral torsional buckling are studied. Computed strengths are presented in the form of beam strength curves, which are further compared with the corresponding nominal strength curve defined in Chapter F of the AISC Specification for Structural Steel Buildings (2010).
Learning Module 5 - Lateral-Torsional Buckling of Beams with Moment Gradient (622 KB)
The influence of moment gradient on the lateral-torsional buckling capacity of compact wide-flange beams is studied. Equivalent uniform moment factors Cb back-calculated from computational analyses are compared with values computed using two longstanding equations, one appearing in Chapter F of the AISC Specification for Structural Steel Buildings (2010) and the other in the commentary to the Specification.
Learning Module 6 - Beam Design by Elastic and Inelastic Analyses (281 KB)
The design of a laterally braced beam of compact section is investigated using elastic and inelastic analyses. In addition to observing differences in load carrying capacity and efficiency, force and moment redistribution as a result of member yielding is explored.
Learning Module 7 - Second-order (P-Δ and P-δ) Effects (330 KB)
Second-order effects in beam-columns are investigated. Results obtained using rigorous second-order elastic analyses are compared with approximate moment amplification factors. Both P-Δ and P-δ effects are observed.
Learning Module 8 - Strength of Beam-Columns (336 KB)
The strength of beam-columns is investigated for various combinations of axial force and bending moment. Both major- and minor-axis flexure of steel wide-flange sections with compact elements are investigated. Nominal strength curves per requirements of Chapter H of the AISC Specification for Structural Steel Buildings (2010) are compared with results obtained using second-order inelastic analyses. Strength limit states defined by elastic/inelastic flexural and lateral torsional buckling as well as full yielding of the cross-section (plastic hinge) are studied.
Learning Module 9 - Design by the Direct Analysis Method (306 KB)
The design of a portal frame is investigated for two options available within the Direct Analysis Method as defined in Chapter C of the AISC Specification for Structural Steel Buildings (2010). Rigorous second-order analyses are employed to check the adequacy of compact doubly symmetric members subject to flexure and axial force.