Elsevier

Construction and Building Materials

Volume 192, 20 December 2018, Pages 357-365
Construction and Building Materials

Rational modeling for cracking behavior of RC slabs in composite beams subjected to a hogging moment

https://doi.org/10.1016/j.conbuildmat.2018.10.163Get rights and content

Highlights

  • Efficient model is developed for predicting the cracking behavior of composite beams.

  • Rational modeling parameters for the fiber beam-column model are suggested.

  • The shrinkage effect should be considered in the prediction of the crack width.

  • The average crack spacing is dominated by the transverse reinforcement spacing.

Abstract

Cracking of the reinforced concrete (RC) slab is a critical problem for a composite beam subjected to a hogging moment, which hinders its application to indeterminate composite structural systems. An efficient numerical method based on the fiber beam-column model is developed for predicting the full-process nonlinear crack width development of composite beams. Several significant modeling issues involving the modeling strategies, selection of material constitutive laws, consideration of shrinkage effect, and determination of average crack spacing are discussed in detail. Rational modeling parameters are recommended and validated by several previous experiments: (i) the slight mesh-dependency can be neglected, and the midpoint integration rule with 6 and 4 uniformly distributed fibers for the slab concrete and the steel beam web, respectively, can give results with sufficient accuracy; (ii) the crack width–load curve obtained through FE analysis should be modified to rationally consider the shrinkage effect of the slab concrete with the initial shrinkage strain of about 300 με; (iii) it is rational to select the value of the average crack spacing as the transverse reinforcement spacing of the RC slab; and (iv) the constitutive laws of the tensile slab concrete and reinforcement have minor influence on the global crack width–load response, especially in the stage after the stabilization of the cracking distances. The selected smeared material constitutive laws are recommended to give a smooth and rational curve for the stage before stabilized cracking.

Introduction

Composite beams of steel and concrete have been widely accepted by the engineering community in many countries as a means for realizing a high-performance structure. Because of their higher span/depth ratio, less deflection, lower self-weight and more efficient construction compared with conventional reinforced concrete (RC) beams, composite beams provides an attractive alternative to overcome some critical design difficulties. Nevertheless, cracking of the RC slab in a composite beam subjected to a hogging moment may significantly decrease the structural stiffness and durability, and thus it is still a critical problem hindering application for many indeterminate composite structural systems such as continuous and frame composite structures.

In recent years, considerable attention has been paid to the cracking behavior of composite beams subjected to a hogging moment in the literature. Some basic facts concerning the cracking mechanisms were revealed by Allison in 1980 [1]. Then, the steel–concrete interface behavior, effective flange width, long-term behavior, and fatigue behavior were investigated by many investigators (Fabbrocino et al. [2]; Loh et al. [3]; Nie et al. [4]; Aref et al. [5]; Ryu et al. [6]; Fan et al. [7]; Lin and Yoda [8]). The feasibility of the use of prestress for cracking control of continuous composite beams is also discussed by Ayyub et al. [9], Nie et al. [10], and Chen et al. [11]. The crack width is one of the most direct and important indexes reflecting the serviceability, durability and damage of structures. Thus, on the basis of previous extensive researches, some simplified design formulas for crack width control in routine practice were provided in Eurocode 4 [12]. However, for the composite beams under monotonically applied hogging moment loading, it is still difficult to accurately predict the whole evolution process of nonlinear cracking behavior.

Among various available numerical models, the fiber beam-column model is believed as one of the most promising tools for nonlinear analysis of composite beams because of its high numerical efficiency, good accuracy and wide applicability [13]. However, for the full-process crack width prediction of composite beams by using the fiber beam-column model, no successful attempt is available in the literature because the following critical issues concerning the rational modeling parameters have not be fully addressed: (i) Modeling strategies. An appropriate element mesh scheme and an efficient section discretization strategy have not be clarified to ensure a reliable prediction of crack width. (ii) Material constitutive laws. The tension stiffening effect significantly influences the cracking behavior of RC slabs in composite beams. Considerable empirical constitutive models with different profiles of descending branches were developed by researchers [14], [15], [16], [17], [18], [19] for considering tension stiffening in RC members, but no recommendation in the selection of constitutive laws was made for modeling the tension stiffening of RC slabs in composite beams. (iii) Shrinkage effect. Previous experiments [1] demonstrated that the shrinkage effect of the concrete in composite beams leads to a reduction in load needed to crack the member and an increase in crack width. However, previous fiber beam-column models [13], [20] cannot take into account the shrinkage effect, and therefore they can only trace the global behavior rather than the microscopic cracking behavior of composite beams. (iv) Average crack spacing. The average crack spacing is a critical factor bridging the average tensile strain of concrete to the crack width. In spite of an analogy between the RC slab in the composite beam and the RC member subjected to pure axial load, the formula for the latter is not suitable for the former as demonstrated by recent experimental researches [8]. A more solid understanding of the cracking mechanism for composite beams is necessary for developing a rational formula for determining the average crack spacing.

The primary objective of this paper is to develop an efficient numerical method for predicting the full-process nonlinear crack width development, i.e. the crack width–load relation subjected to monotonic loading, of composite beams under a hogging moment. A self-developed fiber beam-column element [13] is used, and special attention is paid to the critical modeling issues involving the modeling strategies, selection of material constitutive laws, consideration of shrinkage effect, and determination of average crack spacing. Rational modeling parameters are finally recommended for simulating the cracking behavior of RC slabs in composite beams subjected to hogging moments, the fidelity of the proposed model is validated by several previous experiments.

Section snippets

Fiber beam-column model

As shown in Fig. 1, a composite beam subjected to a hogging moment can be rationally modeled using efficient fiber beam-column elements with distributed plasticity. Either force-based or displacement-based element [21], [22] can be used with corresponding modeling schemes. In the present study, the self-developed program for nonlinear analysis of composite structures COMPONA-MARC [13], [20] is used. The fiber beam-column element in this program is developed from the Type 98 element, a standard

Test specimens for numerical simulation

From the limited range of experimental results available in the literature, four composite beam specimens tested by Lin et al. [31], Nie et al. [27], and Fan et al. [37] are selected to validate the proposed model. The critical modeling parameters are supposed to be discussed in detail for giving rational suggestions. In these tests, simply supported composite beams were subjected to the negative moment monotonically applied over their entire span, which are considered to approximately simulate

Conclusions

This paper discusses the rational modeling parameters in utilizing the fiber beam-column model for full-process crack width prediction of composite beams under monotonically applied hogging moment loading. The proposed modeling procedure with reasonable model parameters is found to give good predictions of experimental crack width–load responses. The recommendations for rational modeling of cracking behavior of RC slabs in composite beams are concluded as follows:

  • 1.

    When a displacement-based

Conflict of interest

None.

Acknowledgments

The writers gratefully acknowledge the financial support provided by the National Key Research Program of China (2017YFC0703804)

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