• 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.

• 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.

• 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.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.10a
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• pp.456-461
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• 1998

This paper presents the results from a combination of strut-and-tie model and analytical study that investigated the ultimate strength of wall system with frame supports. Strut-and-tie models show reasonable force flows and upper bound solution is compared to the results from FEM analysis. The results shows that two main parameters - transfer girder depth and column width - yield good estimation of the ultimate strength of the system. Vertical and horizontal reinforcements of the transfer girder add few strength to the whole system. The proposed design strength formula shows good agreement with the results from FEM analysis.

• 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.

• Proceedings of the Korea Concrete Institute Conference
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• 2002.05a
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• pp.817-822
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• 2002

In this paper, the strengthening analysis by strut-tie model for strengthened shear failed RC deep beam by the so-called the Steel Clamping Unit (SCU), which is a strengthening equipment, is carried out. The analysis considers the span-to-depth ratio, the existence of prestressing and stirrup, the shape of shear crack, and the strengthening position of the SCU. Based on analytical results, optimized strengthening analysis and design are carried out by investigating the behavior of the strengthened deep beams. The comparison between analytical results and experimental results shows that optimum strengthening effect by the SCU can be obtained when compressive strut zone created by SCU is away from major shear crack of the beam as far as possible.

• Structural Engineering and Mechanics
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• v.38 no.4
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• pp.385-403
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• 2011

Continuous deep girders which transmit the gravity load from the upper wall to the lower columns have frequently long end shear spans between the boundary of the upper wall and the face of the lower column. This paper presents the results of tests and analyses performed on three 1:2.5 scale specimens with long end shear spans, (the ratios of shear-span/total depth: 1.8 < a/h < 2.5): one designed by the conventional approach using the beam theory and two by the strut-and-tie approach. The conclusions are as follows: (1) the yielding strength of the continuous RC deep girders is controlled by the tensile yielding of the bottom longitudinal reinforcements, being much larger than the nominal strength predicted by using the section analysis of the girder section only or using the strut-and-tie model based on elastic-analysis stress distribution. (2) The ultimate strengths are 22% to 26% larger than the yielding strength. This additional strength derives from the strain hardening of yielded reinforcements and the shear resistance due to continuity with the adjacent span. (3) The pattern of shear force flow and failure mode in shear zone varies depending on the amount of vertical shear reinforcement. And (4) it is necessary to take into account the existence of the upper wall in the analysis and design of the deep continuous transfer girders that support the upper wall with a long end shear span.

• Computers and Concrete
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• v.15 no.3
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• pp.357-372
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• 2015

This study reports the test results of twelve reinforced concrete deep beams. The deep beams were tested with loads applied through and supported by columns. The main variables studied were the shear span-to-depth ratios, and the horizontal and vertical stirrups. The shear strengths can be effectively enhanced for deep beams reinforced with both horizontal and vertical stirrups. The test results indicate the shear strengths of deep beams increase with the decrease of the shear span-to-depth ratios. The normalized shear strengths of the deep beams did not increase proportionally with an increase in effective depth. An analytical method for predicting the shear strengths of deep beams is proposed in this study. The shear strengths predicted by the proposed method and the strut-and-tie model of the ACI Code are compared with available test results. The comparison shows the proposed method can predict the shear strengths of reinforced concrete deep beams more accurately than the strut-and-tie model of the ACI Code.