Creep in Continuous Beam Built Span-by-Span

TLDR: In this paper, the long-term variation of bending moment distribution caused by bending in a continuous beam errected sequentially in span-length sections with overhangs is analyzed.

Abstract: The long-term variation of bending moment distribution caused by creep in a continuous beam errected sequentially in span-length sections with overhangs is analyzed. A linear aging creep law is assumed. The problem involves changes of the structural system from statically determinate to indeterminate, a gradual increase in the number of redundant moments, and age differences between various cross sections. A system of Volterra integral equations for the history of support bending moments is derived. By considering infinately many equal spans, which is good enough whenever there are many spans, one can take advantage of a periodicity condition for the construction cycle; this reduces the problem to a single equation which is of a novel type in creep theory—an integral-difference equation involving time lags in the integrated unknown. The solution exhibits sudden jumps at times equal to multiples of the construction cycle. The jumps decay with time roughly in a geometric progression. Approximation of time integrals with finite sums yields a large system of simultaneous linear algebraic equations. These equations cannot be solved recurrently, step-by-step. By solving the large equation system with a computer, the effects of the duration of the construction cycle, of concrete age at assembly of span from segments and of the overhang length are studied numerically.