Effect of loading types and reinforcement ratio on an effective moment of inertia and deflection of a reinforced concrete beam Ilker Fatih Kara a , Cengiz Dundar b, * a Department of Civil Engineering, Nigde University, 51235 Nigde, Turkey b Department of Civil Engineering, Cukurova University, 01330 Adana, Turkey article info Article history: Received 4 August 2008 Received in revised form 23 December 2008 Accepted 24 January 2009 Available online xxxx Keywords: Reinforced concrete Effective moment of inertia Effective shear modulus Deflections Loads abstract In the design of reinforced concrete structures, a designer must satisfy not only the strength require- ments but also the serviceability requirements, and therefore the control of the deformation becomes more important. To ensure serviceability criterion, it is necessary to accurately predict the cracking and deflection of reinforced concrete structures under service loads. For accurate determination of the member deflections, cracked members in the reinforced concrete structures need to be identified and their effective flexural and shear rigidities determined. The effect of concrete cracking on the stiffness of a flexural member is largely dependent on both the magnitude and shape of the moment diagram, which is related to the type of applied loading. In the present study, the effects of the loading types and the reinforcement ratio on the flexural stiffness of beams has been investigated by using the com- puter program developed for the analysis of reinforced concrete frames with members in cracked state. In the program, the variation of the flexural stiffness of a cracked member has been obtained by using ACI, CEB and probability-based effective stiffness model. Shear deformation effect is also taken into account in the analysis and the variation of shear stiffness in the cracked regions of members has been considered by employing reduced shear stiffness model available in the literature. Comparisons of the different models for the effective moment of inertia have been made with the reinforced concrete test beams. The effect of shear deformation on the total deflection of reinforced concrete beams has also been investigated, and the contribution of shear deformation to the total deflection of beam have been theoretically obtained in the case of various loading case by using the developed computer program. The applicability of the proposed analytical procedure to the beams under different loading conditions has been tested by a com- parison of the analytical and experimental results, and the analytical results have been found in good agreement with the test results. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Reinforced concrete members crack at relatively low load level even with presence of reinforcement because of the very low ten- sile strength of concrete. The crack initiation and propagation is highly load dependent and have a significant effect on the stiffness and hence displacement of reinforced concrete structures. The ten- sile cracking of concrete reduces the flexural and shear stiffness of members and thus results in an increase in the deflection of rein- forced concrete members. In recent years, the serviceability of reinforced concrete struc- tures has become a much more important design consideration with the use of high strength steel and concrete coupled with more accurate and efficient analytical procedures that enabled practicing engineers to satisfy ultimate state requirements with more slender but more highly stressed structural members. When designing reinforced concrete structures, a designer must satisfy not only the strength requirements but also the serviceability requirements, and therefore the control of the deformation is important to ensure serviceability criterion. For accurate determination of member deflection, the prediction of flexural and shear stiffness of mem- bers after cracking becomes important. Therefore, an analytical model which can include the effects of nonlinearity due to the con- crete cracking on the flexural and shear stiffness of the members and accurately assess the deflections would be very useful. Deflections of reinforced concrete flexural members have been the focus of several research activities in the past decades, and as a consequent, various methods have been developed for predicting them under short-term deflection [1–4]. For calculating the deflec- tion of reinforced concrete members under working load, an empir- ical expression for the effective moment of inertia developed by Branson [5] is perhaps the most widely used, and various form of Branson formula can be found in the ACI [6] and AS 3600–1994 [7]. 0965-9978/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.advengsoft.2009.01.009 * Corresponding author. Tel.: +90 0322 3386762; fax: +90 322 3386702. E-mail address: dundar@cu.edu.tr (C. Dundar). Advances in Engineering Software xxx (2009) xxx–xxx Contents lists available at ScienceDirect Advances in Engineering Software journal homepage: www.elsevier.com/locate/advengsoft ARTICLE IN PRESS Please cite this article in press as: Kara IF, Dundar C. Effect of loading types and reinforcement ratio on an effective moment ... Adv Eng Softw (2009), doi:10.1016/j.advengsoft.2009.01.009