Plastic deformations of steel frame: statics and dynamics

When all deformations of a column are elastic, transverse deflections of the column depend on transverse force and axial displacements depend on axial force only. These classical dependences are unsuitable for elastic-plastic deformations. Plastic deformations develop in columns when steel frame is influenced by extreme action. When a steel column is in the elastic-plastic state, the distribution of elastic and plastic deformations in the cross-section depends on both the bending moment and compressing force. The ideal elastic-plastic material is assumed in this investigation (Prandtl stress – strain diagram). If the shape of the column section is double tee, flange width is neglected with respect to web height, but the area of the flange cross-section is assumed a constant. Single-sided or double-sided yield depends on the moment and force, and therefore curvature and the axial strain of the column can be calculated when yielding dependences are determined. Transverse and axial displacements of the highest point of the column are deduced by integration and depend on two arguments: bending force and axial force. These dependences are essentially non-linear, so linear approximations can be assessed for some vicinity of axial force and bending moment values. When axial force is a constant and transverse force increases, both axial and transverse displacements tend to increase. If transverse force is a constant and axial force increases, both displacements increases but dependence lines remain different and depend on cross-section shape parameter equal to the ratio of the flange area and the area of the whole cross-section. A distinguished feature of plastic deformations is dependence on the history of loading a frame of which can be selected in an arbitrary way by an investigator if a quasi-static solution is under examination. The loading of a frame and inertia forces have to be deduced if dynamic analysis is studied. Not only the ultimate result but also the way of approaching a plastic piston – plastic hinge is important. The bended and compressed column is the structure when inelastic dynamic analysis is really important. Plieninio rėmo plastinės deformacijos: statika ir dinamika Santrauka Plastinės deformacijos atsiranda, kai plieninį rėmą veikia ekstremalios apkrovos. Jei plieninėje kolonoje yra tampriosios ir plastinės deformacijos, tai įtempių išsidėstymas skerspjūvyje priklauso nuo lenkimo momento ir gniuždymo jėgos. Vienpusis arba dvipusis takumas priklauso nuo momento ir ašinės jėgos, todėl kolonos kreivis ir ašinė santykinė deformacija gali būti apskaičiuoti, kai takumo priklausomybės nustatytos. Aukščiausio kolonos taško ašinis ir skersinis poslinkiai apskaičiuojami integruojant ir priklauso nuo dviejų argumentų: lenkimo jėgos ir gniuždymo jėgos. Svarbi savybė, susijusi su plastinėmis deformacijomis, yra jų priklausomybė nuo apkrovimo istorijos, t. y. nuo apkrovimo eigos. Jei tiriamoji problema yra kvazistatinė, tai apkrovimo eiga gali būti paties tyrėjo laisvai parenkama. Jei tiriama plieninio rėmo dinamika, tai rėmo apkrova, inercijos jėgos turi būti atrasti. Ne tik ribinė reikšmė, bet ir artėjimo kelias prie plastinio stūmoklio – plastinio lanksto – turi būti atrastas ir yra svarbus. Lenkiama ir gniuždoma kolona yra viena iš konstrukcijų, kuriai dinaminė analizė svarbi. First Published Online: 16 May 2013 Reikšminiai žodžiai: plieninis rėmas, plastiškumas, gniuždoma kolona, lenkiama kolona, statika, dinamik

Elastic Foundation Displacement Approximations

Interaction of an elastic foundation and structures like beams, plates and frames plays an essential role in investigating soil media in contact and impact mechanics. The solution to this interaction problem is complicated even the foundation is assumed as a linear elastic medium. E. Winkler suggested the fair representation of the foundation in 1867, and then, to bring it closer to reality, an interaction between the spring elements was introduced. In this paper, a relatively simple membrane-spring system is investigated, where an ideal gas is added under or above the membrane. In many cases, this constant pressure in the cavity modifies the solution and accuracy of the approximation is significantly increased. The cases of concentrated normal force and uniform distributed load are examined. The results of elastic half-space line displacements and the membrane displacements are presented