Vol.9, No 1, 2011 pp. 89 - 104
UDC 004+624.042.8:624.071.3=111
DOI: 10.2298/FUACE1101089Z
MATRIX FORMULATION OF DYNAMIC DESIGN OF STRUCTURES WITH SEMI-RIGID CONNECTIONS
Dragan Zlatkov1*, Slavko Zdravković1, Biljana Mladenović1, Radoslav Stojić2
1University of Niš, Faculty of Civil Engineering and Architecture, Serbia
2Metropolitan University, Belgrade, Serbia
E-mail:* dragan.zlatkov@gaf.ni.ac.rs
The structures with semi-rigid connections comprise systems with the connections in joints which are not absolutely rigid, but allow, in general, some relative movements in directions of generalized displacements. Such type of connections is considered very little, or not at all, in designing of structures in today's engineering practice. If the influence of rigidity of semi-rigid connections is underestimated, and they are treated in the design as pinned, it has a negative impact on cost of a structure. But if it is overstated, the calculation results are not on the side of safety, what is reflected on bearing capacity, durability and stability, especially in the case of precast structures. Therefore Eurocodes take due account to the structures with semi-rigid connections. Matrix formulation of the analysis of systems with semi-rigid connections opens wide possibilities for relatively easy calculation by use of computers that is shown by example of seismic design. The interpolation functions, stiffness matrix, equivalent load vectors, and the consistent mass matrix are presented in this paper, particularly with an emphasis on systems with semi-rigid connection.
Key words: matrix formulation, semi-rigid connections, structure, software, dynamic design.
MATRIČNA FORMULACIJA DINAMIČKOG PRORAČUNA KONSTRUKCIJA SA POLUKRUTIM VEZAMA
U konstrukcije sa polukrutim vezama ubrajaju se sistemi kod kojih veze štapova u čvorovima nisu apsolutno krute, već dozvoljavaju, u opštem slučaju, izvestan stepen relativne pomerljivosti u pravcima generalisanih pomeranja. U današnjoj inženjerskoj praksi pri projektovanju konstrukcija vrlo se malo, ili ni malo, o tome vodi računa. Ukoliko je uticaj polukrutih veza potcenjen a one se u proračunu tretiraju kao zglobne, to se negativno odražava na ekonomičnost konstrukcije, a ukoliko je precenjen rezultati proračuna nisu na strani sigurnosti što se odražava na nosivost, trajnost i stabilnost, posebno kod montažnih konstrukcija. Evrokodovi ovim konstrukcijama posvećuju dužnu pažnju. Matrična formulacija analize sistema sa polukrutim vezama štapova otvara široke mogućnosti za relativno jednostavan i brz proračun konstrukcija uz primenu elektronskih računara, što je pokazano na primerima seizmičkog proračuna. U radu su date interpolacione funkcije, matrice krutosti i vektor ekvivalentnog opterećenja, kao i konzistentne matrice masa za sisteme sa krutim i polukrutim vezama štapova u čvorovima.
Ključne reči: matrična formulacija, polukrute veze, konstrukcija, kompjuterski program, dinamički proračun