Mechanika Sprężonych i Zbrojonych Konstrukcji Prętowych w Ujęciu Reologicznym - Wiśniewski, Z. (Engineering Transactions, 1962)
The results of Refs. [1] and [2] are used to obtain accurate effective closed and possibly general rheomechanical solutions for bar structures reinforced and prestressed in any manner, by means of methods of the matricial calculus and Laplace transformation. The functions expressing the creep and shrinkage are assumed in the form (1.1), (1.2), (1.3). Sections 2 and 3 bring equations for stresses, strains, deflections, displacements, and rotations elements which can be treated separately of any reinforced and prestressed structure composed of as flat bars loaded in their principal planes only. They may be flat beams, frames, arches, lattices or three-dimensional structures such as plate structures, high section beams or gridworks, statically determinate or indeterminate, The (generalized) redundant forces X(t) are resolved into the irreversible part Hr(t) correspond- ing to the durable retarded deformation (5.6) and the reversible part Rk (t) corresponding to the elastic transitory strains. The generalized forces Xx (t) are expressed in the functional form 8 the load function Fr is given in the cases of prestressing (6.18) or the recurrence form (7.5). In Sec. Fis, external load Fiq, movement of the support and the action of temperature Fire and concrete shrinkage. Constant and linear periodic and asymptotic hanges of loads and movements of the supports and temperatures are discussed. In Section 9 some particular cases are considered: structures with one layer of reinforcement (9.1), continuous beams (9.3), lattices (9.5), centrally prestressed lattices with constant cross-sectional area of the reinforcement and systems with one redundant force as unknown. The symmetry condition (6.19) of the matrices (6.5), (6.6) of the coupled system h and ón are formulated as well as a con- clusion concerning the general asymmetry of the matrix (6.16) of the uncoupled system wnl. The assumption of K. Sattler [7], [11] is verified in the particular case (9.4).