A method of shakedown analysis of frames and arches

Structures, in general, are subjected to more complex load programs than those considered in the theory of limit analysis. The shakedown theory presents general theorems allowing to estimate does the structure adapt to the given load program or not. On the basis of previous general results [22] the present paper gives an approximate method of analysis of frames and arches of arbitrary solid cross-section in the case when the influence of axial forces on the stress state cannot be neglected. The problem reduces to the linear programming problem. Numerical results for a portal frame and for a circular arch of rectangular cross-section are presented. Koнcтpyкции, вooбшe, пoдвepгaют пpoгpaммaм нaгpyжeния бoлee cлoжным чeм paccмaтpивaeмыe в тeopии пpeдeльпoгo paвнoвecия. Teopия пpиcпocoблeния пpeдcтaвляeт oбшиe тeopeмы пoзвoляьщиe oцeнить пpиcпocoбляeмocть кoнcтpyкций к дaннoй пpoгpaммe нaaгpyжeния Ha ocнoвaнии пpeдьдyщнч peзyльтaгoв (22) в нacтoящeй paбoтe пpeдcтaвлeн пpиближeнныи мeтoд aнaлизa cтepжнeвыч кoнcтpyкцнй любoгo пoпepeчнoгo ceчeния в кoтopьч влияниeм oceвьч cил пpeнeбpeчь нeльзя. Pocтaвлeннaя иpoблeмa cвoдитcя к зaдaчe динeйнoгo пpoгpaммиpoвaния. Пpeдcтaвлeны чнcлeнныe peзyдьтaгь для пopтaльнoй paмь и для кpyгoвoй apкн иpямoyгoльнoгo пoпepeчнoгo ceчeния.