ELSEVIER S0141-0296(96)00028-4 Engineering Strtu'mres, Vol. 19. No. I, pp. 2 18, 1997 Copyright 7~ 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0141 0296/97 $[7.00 + 0.0I) Effects of repeated loading on creep deflection of reinforced concrete beams C. G. Koh, K. K. Ang and L. Zhang Department of Civil Engineering, National University cf Singapore, Kent RMge, 0511 Singapore, Singapore (Received October 1995: revised version accepted January 1996) This paper presents a computational procedure to predict deflec- tions of reinforced concrete beams subjected to repeated loading in addition to sustained static loading. A semi-empirical constitutive model is adopted to account for the effects of creep (basic, drying and cyclic) and shrinkage. A numerical iterative procedure is pro- posed to update the stress and total strain of each layer. Numerical results are compared with available experimental results as well as results obtained by some analytical methods. The comparison shows that the proposed procedure accounts for more parameters than other methods considered and is generally in better agree- ment with the experimental results. Parametric studies are carried out to study the effects of various parameters including the exci- tation frequency and concrete composition. Copyright © 1996 Elsevier Science Ltd. Keywords: beams, creep, deflection, reinforced concrete, repeated loading, dynamics 1. Introduction Creep of concrete under a sustained static load is a well known phenomenon. Much research has been carried out in this context ~'2. Under actual operating conditions, however, many structures are subjected to dynamic loading in addition to static loading. Dynamic loadings are often cyc- lic in nature, such as traffic loads on highway bridges, wave loads on offshore structures and wind loads on slender buildings. Under cyclic loading particularly of many rep- etitions, creep is accelerated. In some early works, Avram 3 found that, for the same total duration, the deformation under repeated loading was significantly greater than that under a sustained loading. Snowdon 4, Sparks and Menzies 5, Lovegrove and Salah 6, and Shinzo et (.1.1. 7 have carried out primarily experimental investigations to study the behav- iour of reinforced concrete beams under repeated loading. Their results showed that reinforced concrete beams sub- jected to repeated loading might suffer from excessive deflection not predicted if only static loading was con- sidered. It was noted that the deflection of reinforced con- crete members increased with the number of load rep- etitions. Several attempts have been made by researchers to describe the complicated cyclic creep phenomenon of con- crete. Whaley and Neville s proposed a simple cyclic creep model, expressing cyclic stress as the sum of a mean stress component (cr,~ ...... ) and a component dependent upon the stress peak-to-peak amplitude (O-pp). They reported that the calculated results agreed reasonably well with experimental data only when o- ....... < 0.45H and ~rpp < 0.3f~'. For higher o-, ..... or O-pp,the departure of their model from the observed data becomes considerable. Some factors known to influ- ence creep, such as relative humidity, member shape of specimen, loading frequency and age at loading, were not considered. Balaguru and Shah '~ adopted Whaley and Nevil- le's cyclic creep model in their deflection prediction, In their method, the deflections are calculated from the knowl- edge of the average effective moment of inertiaU( The reduction in stiffness after N load cycles is approximately computed in accordance with the creep strain at that time. Shrinkage, an important factor, was not taken into account. Later, Balaguru ~ extended their method to predict the deflection of partially prestressed concrete members. How- ever, the constants used to develop the predictive equations in their analysis were based on a limited number of data and may not be applicable to beams subjected to very high- cycle loading. In a series of systematic studies, Bakant and Panula ~2 r used optimization techniques to fit numerous test data avail- able in the literature and proposed a practical model, namely the BP model, for predicting creep and shrinkage 2