Vol. 6, No 2, 2008 pp. 155 - 164
UDC 624.072.2:624.012.45/.46:534.17(045)=111 
VIBRATIONS OF CRACKED REINFORCED AND PRESTRESSED CONCRETE BEAMS
Zsolt Huszár
Budapest University of Technology and Economics Department of Structures 1111 Budapest Bertalan Lajos utca 2
Email: huszar@vbt.bme.hu
Abstract. The dynamic behaviour of bent reinforced concrete beams in elastic range is significantly influenced by cracks caused by former loads. Considering this fact a more accurate calculation of the eigenfrequencies of the beams is available. Experiments have shown that the features of vibration differ from the results obtained by the well-known linear model, if cracked zones exist. The cause of this phenomenon is that the bending rigidity of the cross-sections in the cracked range depends on the sign of the actual bending moment. Therefore the vibration shows non-linear characteristics in the elastic range as well.
The dynamic behaviour of bent prestressed concrete beams is similar. The dynamic characteristics of prestressed beams besides cracks is influenced also by the intensity and eccentricity of the axial force.
For a detailed investigation of the problem, experiments and non-linear analysis were performed. On the basis of these the virtual eigenfrequencies of the non-linear vibrations were determined.
Key words:  Vibrations, Prestressed Concrete, Beam
VIBRACIJE  ARMIRANOBETONSKIH I PRETHODNONAPREGNUTIH GREDA SA PRSLINAMA
Prsline nastale usled prethodnog opterećenja imaju značajan uticaj na dinamičko ponašanje savijenih armiranobetonskih greda u elastičnoj oblasti. S obzirom na tu činjenicu, postoje  više tačnih proračuna za sopstvene frekvencije grede. Eksperimentom se pokazuje da se vibracije razlikuju od dobro poznatog modela, ako postoji zona prslina. Uzrok ovog fenomena leži u tome da krutost na savijanje preseka u zoni prslina, zavisi od
znaka momenta svijanja. Stoga vibracije takođepokazuju  nelinearnu karakteristiku u elastičnoj oblasti. Dinamičko ponašanje savijenih prethodnonapregnutih greda je slično. Osim uticaja prslina na dinamičke karakteristike prethodnonapregnutih greda, postoje još i uticaj inteziteta opterećenja i ekscentričnost aksijalne sile.
U cilju detaljnijeg istraživanja problema urađen je eksperiment i nelinearna analiza. Na njihovoj osnovi je određena virtualna sopstvena frekvencija nelinearnih vibracija.