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Structural Performance of RC Beams containing Tension-Only Nodes
- Manuel Alejandro Fernández-Ruiz^{1}Email authorView ORCID ID profile,
- Luisa María Gil-Martín^{1} and
- Enrique Hernández-Montes^{1}
https://doi.org/10.1186/s40069-018-0228-9
© The Author(s) 2018
Received: 16 December 2016
Accepted: 3 November 2017
Published: 30 January 2018
Abstract
Strut and Tie (S&T) models are used for the design of what are known as “discontinuity regions” in reinforced concrete (RC) structures. Building codes such as ACI-318 and Eurocode 2 do not give information on the nodes that only connect ties in S&T models (called TTT or tension-only nodes). However, their use is not explicitly prohibited in the design of RC structures. In this work, a comparison between solutions which have been designed both considering and not considering TTT nodes is evaluated. Four RC beams (designed with and without TTT nodes) were subjected to three-point bending. Experimental results show that TTT nodes are a good design solution for special cases of discontinuity regions in RC structures. However, the experimental campaign has proven that this type of node is more vulnerable to errors during construction than solutions designed without TTT nodes.
Keywords
1 Introduction: Continuity and Discontinuity Regions
Strut and tie (S&T) models (Schlaich et al. 1987) may be used for the design in the ultimate limit state (ULS) of discontinuity regions [ACI-318 §23 (ACI Committee 318 2014) and Eurocode 2 §5.6.4(1) (CEN 2004)] in Reinforced Concrete (RC) structures. The S&T method is based on the lower bound plasticity theorem. As an unlimited number of possible S&T models can be inserted into a discontinuity region, a correct definition of the S&T model during the design process is key for a good estimation of the load-carrying capacity of the corresponding RC member (Kassem 2015; Choi et al. 2012).
Nodal zones in a S&T model are a design idealization of a more complex stress state in the regions where the demand is concentrated, due to a change in the load path (Yun 2006).
Several S&T models, compatible with both the geometry and reinforcement, have been analyzed by authors but only the ones represented in Fig. 3 are going to be considered in this work. All of them satisfy the ACI (ACI Committee 318 2014) requirements on angles between struts and ties, the length of the ties is at a minimum in order to avoid excessive deflections, and in both of them, the yielding of the ties happens before the failure of the struts.
2 Materials and Methods: Design with TTT Nodes
Theoretically a S&T model could include TTT (or tension-only) nodes, but the reality is that there are no specific recommendations in structural codes for concrete, such as ACI-318 (ACI Committee 318 2014) and Eurocode 2 (CEN 2004). Furthermore, there are few pieces of research and documents like that of Bergmeister et al. (Bergmeister et al. 1993), that recognize the possibility of using TTT nodes in the design of RC structures.
Specimens A-I and A-II are slightly different. The stirrup corresponding to the TTT node 12 of specimen A-II (see Fig. 3a) was positioned 1.8 cm from the change of direction of the bent longitudinal bars. This node is called “defective TTT node” hereafter. However, specimens B-I and B-II are identical.
3 Results and Discussion
3.1 S&T Model
The width of struts was computed following AASHTO prescriptions (AASHTO 2012) and the structural capacity of struts, ties and nodes was computed according to ACI-318 (ACI Committee 318 2014) (see Appendix). According to ACI-318 (ACI Committee 318 2014), if more than three forces act on a nodal zone it can be assumed that all of them act through the same point or, alternatively, some of them can be resolved to form three intersecting forces. Due to the high value of the angles between the axis of the truss members of both S&T models proposed in Fig. 3, the first option has been adopted in this work.
P_{ yield,S&T } is the load at midspan that causes first yielding in any nodal region, strut or tie, which has been obtained from the S&T analysis which takes the actual yield strength of steel into account. For the models represented in Fig. 3, P_{ yield,S&T } is 74.5 kN for type A specimens and 71.6 kN for type B specimens. In the case of type A specimens, P_{ yield,S&T } corresponds to the yielding of the tie between the nodes 7 and 10 (see Fig. 3a). In the case of type B specimens, the value of P_{ yield,S&T } corresponds to the yielding of the tie between the nodes 5 and 8 and its symmetrical counterpart (the tie between the nodes 10 and 14), see Fig. 3b.
3.2 Experimental Results
Summary of test results.
Specimen | P _{ yield,S&T } | P _{ yield,exp } |
---|---|---|
A-I | 74.5 | 84.5 |
A-II^{a} | 74.5 | 69.6 |
B-I | 71.6 | 88.4 |
B-II | 71.6 | 86.6 |
Positioning the stirrup wrongly (in this case, a displacement around 20 mm) in the TTT node provoked a reduction in the yield load of the beam of around 18% (see Table 1). Specimens A-I, B-I and B-II had a similar P_{ yield,exp }, even though 32% in the weight of reinforcing steel was saved in the case of A-I compared with type B specimens.
As was expected, the yield loads estimated using the S&T models were slightly lower than the corresponding experimental results (see Table 1) in all cases except for specimen A-II (the specimen with the defective TTT node). The accuracy of the yield load obtained from the S&T models presented in Fig. 3 depends on how well they represent the internal stresses of the tested beams. Results corresponding to specimen A are closer to the experimental ones than those of specimen B, meaning that the first model more accurately represents the internal behavior of the beam.
As the applied load increases, the internal stresses of the beam change. The appearance of load transfer mechanisms different from those considered in the S&T models presented in Fig. 3 could explain the difference between analytical and experimental values.
4 Conclusions
The main structural codes, such as ACI-318 and Eurocode 2 do not provide design guidelines for TTT nodes. Four RC beams with varying cross-sections designed using S&T models including (A-I and A-II specimens) and not including (B-I and B-II specimens) tension-only nodes were subjected to three-point bending in the Structures Laboratory of the University of Granada.
Experimental results showed that elements including TTT nodes are more vulnerable to errors during construction than models that do not include TTT nodes. Specimen A-II (with a defective TTT node) had a 18% reduction of the yield load compared with specimen A-I (without a defective TTT node).
Specimen A-I had a yielding capacity similar type B specimens (with even a saving of 32% in the weight of steel).
Two S&T models, both considering and not considering TTT nodes were proposed to predict the yielding capacity of A and B specimens in Fig. 3. Both the yielding capacities and the failure modes obtained from S&T models and experimental tests were in reasonable correlation.
Tension-only nodes can be considered in the design of discontinuity regions in RC members in some cases (like the one presented) but a more exhaustive control during the construction procedure is required.
Declarations
Acknowledgements
The authors would like to acknowledge the financial support provided by the University of Granada in the form of a PhD fellow (FPU Grant) to the first author.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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