Stiffness Assessment of Cracked Reinforced Concrete Beams Based on a Fictitious Crack Model
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pISSN 1226-7988, eISSN 1976-3808 www.springer.com/12205
DOI 10.1007/s12205-020-2056-0
Structural Engineering
Stiffness Assessment of Cracked Reinforced Concrete Beams Based on a Fictitious Crack Model Chunyu Fu
a
, Yin Zhu
a
, and Dawei Tong
a
a
Dept. of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China
ARTICLE HISTORY
ABSTRACT
Received 12 November 2019 Revised 23 April 2020 Accepted 13 September 2020 Published Online 30 November 2020
A fictitious crack model is introduced into cracked reinforced concrete beams to assess the changing beam stiffness under loads. Firstly, nonlinear concrete stress distributions near cracks are built based on the model. Then the stress of the steel bar at the cracked section is considered as cohesive stress. The concrete and steel stresses are substituted into the equilibrium equations of forces to solve the concrete stress. Based on the solution, the section inertias are estimated by iterating the calculation of the cracking open displacement, and finally the beam stiffness is assessed. Experimental data from seven concrete beams after cracking are adopted to validate the effectiveness of the proposed method, and the results show that the fictitious cracks ahead of actual cracks increase their depth with the load, which will raise the neutral axis and change the inertias of cracked sections and their neighboring sections. These changes are taken into account in the stiffness assessment, so the results predicted by the proposed method are shown to coincide well with the nonlinear deflections measured in the experiments.
KEYWORDS Reinforced concrete beams Fictitious crack Beam stiffness Nonlinear stress Force equilibrium
1. Introduction Deflection control is an important objective in the design of reinforced concrete beams. However, the concrete in these beams is easy to crack due to its low tensile strength, which has a great effect on the beam stiffness through altering the bearing area of cross sections. So in recent decades, how to assess the stiffness of cracked concrete beams became a hot topic of civil engineering. The effective inertia of cross sections was early proposed for the stiffness control of the cracked reinforced concrete beams in design. Branson (1965) proposed a model for the effective inertia using a weighted average of the fully cracked inertia and the uncracked inertia. But the comparison with experimental data showed that the instantaneous deflections of reinforced concrete beams and slabs after cracking were underestimated in Branson’s model (Gilbert, 2007; Gribniak et al., 2013). Bischoff (2005) developed Branson’s model by using empirical parameters that decrease the ratio of the uncracked inertia to the cracked inertia, which was suggested by the fib Model Code (CEB-FIP, 2012). Kalkan and Lee (2013) compared these models, and found that Bischoff’s model produced more conservative results for CORRESPONDENCE Chunyu Fu
[email protected]
ⓒ 2020 Korean Society of Civil Engineers
heavily-reinforced concrete beams. The
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