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Stability Fun

The nonlinear analysis capabilities of MASTAN2 provide students the opportunity toperform a wide range of investigations into the behavior of structural members andsystems. With this in mind, the below learning modules are intended for use in

undergraduate and or graduate level steel design or structural stability courses. !fcourse, practicing engineers are also encouraged to continue their education bycompleting these e"ercises.

Although the modules can be completed with MASTAN2, they have been prepared ingeneric form so that other nonlinear analysis software could be employed. #achmodule is provided as $%& and Microsoft Word 'les along with accompanyingMicrosoft #"cel spreadsheets. (n addition to instructions, )uestions, and suggestionsfor further study, these 'les include lin*s to videos that show MASTAN2 in action.&or those employing MASTAN2, completion of the Tutorial is strongly encouragedbefore attempting the below modules. #n+oy -- on /iemian, 0uc*nell

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Learning Module 1 - Elastic Column Buckling and the Efect o EndRestraint 1sing a critical load analysis, the elastic e"ural buc*ling strength of a column withvarious degrees of end restraint is investigated.

Learning Module ! - Factors "n#uencing the Fle$ural Buckling Strength oCom%ression Members1sing computational analysis as a virtual laboratory, the main factors that impactthe e"ural buc*ling strength of steel wide- ange sections with nonslenderelements are investigated. These factors include member slenderness, materialnonlinearity, initial imperfections in geometry 3out-of-straightness4, and residualstresses. 5omputed strengths are presented in the form of column curves, which arefurther compared with the corresponding nominal strength curve de'ned in 5hapter# of the A(S5 Speci'cation for Structural Steel 0uildings 326764.

Learning Module & - Efecti'e Length (- actors or Frame Members#8ective length 9-factors for compression members in frames are investigated. (naddition to studying cases of sidesway inhibited and uninhibited, elastic andinelastic buc*ling is e"plored. 5omputational results are compared with alignmentchart methods.

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Learning Module ) - Factors "n#uencing the Strength o Fle$ural Members1sing computational analysis as a virtual laboratory, the main factors that impactthe ma+or-a"is e"ural strength of steel wide- ange sections with compact elementsare investigated. These factors include unbraced length, partial yieldingaccentuated by the presence of residual stresses, and initial imperfections in

geometry 3out-of-straightness4. Strength limit states de'ned by full yielding of thecross-section 3plastic hinge4 and elastic inelastic lateral torsional buc*ling arestudied. 5omputed strengths are presented in the form of beam strength curves,which are further compared with the corresponding nominal strength curve de'nedin 5hapter & of the A(S5 Speci'cation for Structural Steel 0uildings 326764.

Learning Module * - Lateral-+orsional Buckling o Beams ,ith Momentradient

The in uence of moment gradient on the lateral-torsional buc*ling capacity of

compact wide- ange beams is studied. #)uivalent uniform moment factors 5b bac*-calculated from computational analyses are compared with values computed usingtwo longstanding e)uations, one appearing in 5hapter & of the A(S5 Speci'cation forStructural Steel 0uildings 326764 and the other in the commentary to theSpeci'cation

Learning Module . - Beam /esign by Elastic and "nelastic 0nalyses The design of a laterally braced beam of compact section is investigated usingelastic and inelastic analyses. (n addition to observing di8erences in load carrying

capacity and e:ciency, force and moment redistribution as a result of memberyielding is e"plored.

Learning Module - Second-order 23-4 and 3-56 E ectsSecond-order e8ects in beam-columns are investigated. esults obtained usingrigorous second-order elastic analyses are compared with appro"imate momentamplification factors. 0oth $-; and $-< effects are observed.

Learning Module 7 - Strength o Beam-Columns The strength of beam-columns is investigated for various combinations of a"ialforce and bending moment. 0oth ma+or- and minor-a"is e"ure of steel wide- angesections with compact elements are investigated. Nominal strength curves perre)uirements of 5hapter = of the A(S5 Speci'cation for Structural Steel 0uildings326764 are compared with results obtained using second-order inelastic analyses.

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Strength limit states de'ned by elastic inelastic e"ural and lateral torsionalbuc*ling as well as full yielding of the cross-section 3plastic hinge4 are studied.

Learning Module 8 - /esign by the /irect 0nalysis Method The design of a portal frame is investigated for two options available within the%irect Analysis Method as de'ned in 5hapter 5 of the A(S5 Speci'cation forStructural Steel 0uildings 326764. igorous second-order analyses are employed tochec* the ade)uacy of compact doubly symmetric members sub+ect to e"ure anda"ial force.