• Journal of the Korea Concrete Institute
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• v.19 no.2
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• pp.199-207
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• 2007

Strut-and-tie models for noncontact lap splices are presented and parameters affecting the effective lap length $(l_p)$ and the splice strength are discussed in this paper. The effective lap length along which bond stress is developed is shorter than the whole lap length. The effective lap length depends on the transverse reinforcement ratio $({\Phi})$ and the ratio of spacing to lap length $({\alpha})$. As the splice-bar spacing becomes wider, the effective lap length decreases and, therefore, the splice strength decreases. The influence of the ratio ${\alpha}$ on the effective lap length becomes more effective when the transverse reinforcement ratio is low. Because the slope of the strut developed between splice-bars becomes steeper as the ratio ${\Phi}$ becomes lower, the splice-bar spacing significantly affects the effective lap length. The proposed strut-and-tie models for noncontact lap splices are capable of considering material and geometric properties and, hence, providing the optimal design for detailing of reinforcements. The proposed strut-and-tie model can explain the experimental results including cracking patterns and the influence of transverse reinforcements on the splice strength reported in the literature. From the comparison with the test results of 25 specimens, the model can predict the splice strengths with 11.1% of coefficient of variation.

• Journal of the Korea institute for structural maintenance and inspection
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• v.18 no.1
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• pp.31-39
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• 2014

In order to design rigid zone area of frame structures, it is important to predict the direction change of internal stresses according to the bending moment acting on the joint region. In this study, it was examined whether current highway bridge design standards are useful to design different types of rigid joints having a various haunch shapes. In addition, stress distributions of inside of various rigid joints were inspected using the linear elastic finite element analysis. Based on the results of finite element analysis, the strut-tie models to design rigid joints are proposed. Suggested by this study, the strut-tie models have a same level of accuracy to a linear elastic finite element analysis. The proposed strut-tie models will be useful to design reinforcement details of rigid joints having a various haunch types.

• Computers and Concrete
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• v.25 no.5
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• pp.461-470
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• 2020

This paper presents a numerical study on structural behavior of hammer head pier cap beams, extended on verges and reinforced with carbon fiber reinforced polymer (CFRP) plates. A 3-D finite element (FE) model along with a simplified analytical model are presented. Concrete damage plasticity (CDP) was adapted in the FE model and an analytical approach predicting the CFRP anchor strength was adapted in both FE and analytical model. Total five quarter-scaled pier cap beams with various CFRP reinforcing schemes were experimentally tested and analyzed with numerical approaches. Comparison between experimental results, FE results, analytical results and current ACI guideline predictions was presented. The FE results showed good agreement with experimental results in terms of failure mode, ultimate capacity, load-displacement response and strain distribution. In addition, the proposed strut-and-tie based analytical model provides the most accurate prediction of ultimate strength of extended cap beams among the three numerical approaches.

• Advances in Computational Design
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• v.1 no.1
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• pp.61-77
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• 2016

Seismic performance of structures depends on the force flow mechanism inside the structure. Discontinuity regions, like beam-column joints, are often affected during earthquake event due to the complex and discontinuous load paths. The evaluation of shear strength and identification of failure mode of the joint region are helpful to (i) define the strength hierarchy of the beam-column sub-assemblage, (ii) quantify the influence of different parameters on the behaviour of beam-column joint and, (iii) develop suitable and adequate strengthening scheme for the joints, if required, to obtain the desired strength hierarchy. In view of this, it is very important to estimate the joint shear strength and identify the failure modes of the joint region as it is the most critical part in any beam-column sub-assemblage. One of the most effective models is softened strut and tie model which was developed by incorporating force equilibrium, strain compatibility and constitutive laws of cracked reinforced concrete. In this study, softened strut and tie model, which incorporates force equilibrium equations, compatibility conditions and material constitutive relation of the cracked concrete, are used to simulate the shear strength behaviour and to identify failure mechanisms of the beam-column joints. The observations of the present study will be helpful to arrive at the design strategy of the joints to ensure the desired failure mechanism and strength hierarchy to achieve sustainability of structural systems under seismic loading.

• Proceedings of the Korea Concrete Institute Conference
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• 2008.11a
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• pp.265-268
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• 2008

Slab-column joints have been used in the constructions of many structures and buildings. However, as the prediction of the failure behavior and ultimate strength of the joints subjected to lateral loadings is very difficult, the current building and structural design codes do not explain the failure behavior of the joints clearly. In this study, the applicability of the 3-dimensional grid strut-tie model approach, suggested for analysis and design of 3-dimensional structural concrete with disturbed regions, to the ultimate analysis and design of the joints is examined by evaluating the failure strengths of 43 slab-column joints tested to failure. The validity of the 3-dimensional grid strut-tie model approach is also verified by comparing the strength evaluation results with those by ACI 318-05 and FIB 1999.

• Structural Engineering and Mechanics
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• v.12 no.6
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• pp.685-698
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• 2001

In this paper, a general method for the automatic search for Strut-and-Tie (S&T) models representative of possible resistant mechanisms in reinforced concrete elements is proposed. The representativeness criterion here adopted is inspired to the principle of minimum strain energy and requires the consistency of the model with a reference stress field. In particular, a highly indeterminate pin-jointed framework of a given layout is generated within the assigned geometry of the concrete element and an optimum truss is found by the minimisation of a suitable objective function. Such a function allows us to search the optimum truss according to a reference stress field deduced through a F.E.A. and assumed as representative of the given continuum. The theoretical principles and the mathematical formulation of the method are firstly explained; the search for a S&T model suitable for the design of a deep beam shows the method capability in handling the reference stress path. Finally, since the analysis may consider the structure as linear-elastic or cracked and non-linear in both the component materials, it is shown how the proposed procedure allows us to verify the possibilities of activation of the design model, oriented to the serviceability condition and deduced in the linear elastic field, by following the evolution of the resistant mechanisms in the cracked non-linear field up to the structural failure.

• Biomaterials and Biomechanics in Bioengineering
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• v.3 no.1
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• pp.1-14
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• 2016

Well-ordered porous materials are very promising in orthopedics since they allow tailoring the mechanical properties. Finite element (FE) analysis is commonly used to evaluate the mechanical behavior of well-ordered porous materials. However, FE results generally differ importantly from experimental data. In the present article, three types of manufacturing irregularities were characterized on an additive manufactured porous titanium sample having a simple cubic unit-cell: strut diameter variation, strut inclination and fractured struts. These were included in a beam FE model. Results were compared with experimental data in terms of the apparent elastic modulus (Eap) and apparent yield strength (SY,ap). The combination of manufacturing irregularities that yielded the closest results to experimental data was determined. The idealized FE model resulted in an Eap one order of magnitude larger than experimental data and a SY,ap almost twice the experimental values. The strut inclination and fractured struts showed the strongest effects on Eap and SY,ap, respectively. Combining the three manufacturing irregularities produced the closest results to experimental data. The model also performed well when applied to samples having different structural dimensions. We recommend including the three proposed manufacturing irregularities in the FE models to predict the mechanical behavior of such porous structures.

• Structural Engineering and Mechanics
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• v.73 no.5
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• pp.515-527
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• 2020

This paper presents a stress field approach for the shear capacity of stirrup-reinforced concrete beams that explicitly incorporates the contribution of principal tensile stresses in concrete. This formulation represents an extension of the variable strut inclination method adopted in the Eurocode 2. In this model, the stress fields in web concrete consist of principal compressive stresses inclined at an angle θ combined with principal tensile stresses oriented along a direction orthogonal to the former (the latter being typically neglected in other formulations). Three different failure mechanisms are identified, from which the strut inclination angle and the corresponding shear strength are determined through equilibrium principles and the static theorem of limit analysis, similar to the EC-2 approach. It is demonstrated that incorporating the contribution of principal tensile stresses of concrete slightly increases the ultimate inclination angle of the compression struts as well as the shear capacity of reinforced concrete beams. The proposed stress field approach improves the prediction of the shear strength in comparison with the Eurocode 2 model, in terms of both accuracy (mean) and precision (CoV), as demonstrated by a broad comparison with more than 200 published experimental results from the literature.

• Advances in concrete construction
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• v.16 no.4
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• pp.217-230
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• 2023

Methods for designing the post-tensioned anchorage zones at ultimate limit state has been specified in current design codes based on strut-and-tie models (STM). However, it is still not clear how to estimate the serviceability behavior of the anchorage zones. The serviceability is just indirectly taken into account by means of the reasonable reinforcement detailing. To address this issue, this paper is devoted to developing a modified strut-and-tie model (MSTM) to predict the behavior of concentric anchorage zones throughout the loading process. The principle of stationary complementary energy is introduced into STM at each load step to satisfy the compatibility condition and generate the unique MSTM. The structural behavior of anchorage zones can be achieved based on MSTM from loading to failure. Simplified formulas have been proposed to estimate the first cracking load, bearing capacity and maximum crack width with the consideration of the details of reinforcement bursting bars. The proposed model provides a definite method to control the bursting crack width in concentric anchorage zones. Four specimens with different bearing plate ratios have been designed and tested to validate the proposed method.

• Journal of the Korea Concrete Institute
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• v.23 no.1
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• pp.3-12
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• 2011

The structural behavior of continuous reinforced concrete deep beams is mainly controlled by the mechanical relationships associated with the shear span-to-effective depth ratio, flexural reinforcement ratio, load and support conditions, and material properties. In this study, a simple indeterminate strut-tie model which reflects characteristics of the complicated structural behavior of the continuous deep beams is presented. In addition, the reaction and load distribution ratios defined as the fraction of load carried by an exterior support of continuous deep beam and the fraction of load transferred by a vertical truss mechanism, respectively, are proposed to help structural designers for the analysis and design of continuous reinforced concrete deep beams by using the strut-tie model approaches of current design codes. In the determination of the load distribution ratio, a concept of balanced shear reinforcement ratio requiring a simultaneous failure of inclined concrete strut and vertical steel tie is introduced to ensure a ductile shear failure of reinforced concrete deep beams, and the primary design variables including the shear span-to-effective depth ratio, flexural reinforcement ratio, and concrete compressive strength are implemented after thorough parametric numerical analyses. In the companion paper, the validity of the presented model and load distribution ratio was examined by applying them in the evaluation of the ultimate strength of multiple continuous reinforced concrete deep beams, which were tested to failure.