• Proceedings of the Korea Concrete Institute Conference
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• 2006.11a
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• pp.269-272
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• 2006

The anchorage zone of prestressed concrete members is a critical region where a large concentrated force due to prestressing by tendons is introduced. In this study, the ACI, AASHTO LRFD, CEB-FIP design criteria and the nonlinear strut-tie model approach are applied to the ultimate strength analysis of simple anchorage zones of 18 post-tensioned concrete members tested to failure. From the result of ultimate strength analysis, the advantages and disadvantages of each method are compared and discussed.

• 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.7 no.4
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• pp.159-169
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• 2003

In the ACI Code, the empirical equations governing deep beam design are based on low-strength concrete specimens with $f_{ck}$ in the range of 14 to 40MPa. As high-strength concrete(HSC) is becoming more and more popular, it is timely to evaluate the application of HSC deep beam. For the shear strength prediction of HSC deep beams, this paper proposed Softened Strut-and-Tie Model(SSTM) considered HSC and bending moment effect. The shear strength predictions of the proposed model, the Appendix A Strut-and-Tie Model of ACI 318-02, and Eq. of ACI 318-99 11.8 are compared with the experimental test results of 4 deep beams and the collected experimental data of 74 HSC deep beams, compressive strength in the range of 49~78MPa. The proposed SSTM performance consistently reproduced 74 HSC deep beam measured shear strength with reasonable accuracy for a wide range of concrete strength, shear span-depth ratio, and ratio of horizontal and vertical reinforcement.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.4
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• pp.2406-2413
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• 2014

Since clear span-to-depth ratio is used to define what is so called a deep beam, it is an important parameter ratio for study about deep beam. Deep beams can be designed by flexure design method, and shear provided by concrete ($v_c$) and by steel ($v_s$) for deep flexure members are provided in ACI 318-99 [1]. But in later version of ACI (from ACI 318-02) it is not provided and deep beams shall be designed either by taking into account nonlinear distribution of strain or by Appendix A of Strut-and-Tie Models (STM). The trend of deep beam design seems to be familiar with strut-and-tie model, but ACI traditional design is not forgotten. By comparing these two method, there should a point which definitely explain the different between the two methods. In this study, 68 samples result of steel, after reinforcement arrangement, are taken to be analyzed.

• Journal of the Korea Concrete Institute
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• v.13 no.6
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• pp.602-609
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• 2001

A strut-and-tie model was proposed to predict the shear strength of RS beam which is a hybrid steel beam with reinforced concrete ends. The proposed model is capable of considering the concrete softening effects due to diagonal shear cracks at the embedded area of steel in concrete. It can predict tile failure strength of RS beam from the mathematical formulations which are based on equilibrium, compatibility, and the constitutive laws of cracked reinforced concrete. The previous experimental results of 15 RS beams were analyzed with the proposed model and the analytical results were also compared with formulas currently available. The comparison revealed that the proposed model can predict the strength of RS beam better than the others. The average ratio of experimental strengths to analytical results was 1.02 and the standard deviation was 0.126.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.3
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• pp.165-172
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• 2019

In this study, the shear strength of prestressed concrete deep beams is predicted using finite element analysis, and the variation in the shear strength according to the degree of prestressing is investigated. Numerical analysis results are compared with results obtained by the strut-and-tie model and associated experiments. Numerical analyses are performed on prestressed concrete deep beams with different values of concrete strength, effective prestress, ratio of tensile reinforcement, and shear span to effective depth ratio. The shear strength predicted by the numerical analysis is similar to the experimental value obtained, with an error of less than 5%. However, the strut-and-tie model highly overestimated the shear strength of prestressed concrete deep beams with a concentrated loading area. The ultimate shear capacity of prestressed concrete deep beams increased linearly with increasing prestresss applied to the tendon.

• 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.

• 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.

• 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.17 no.1
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• pp.141-156
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• 2016

The search for new structural systems capable of associating performance and safety requires deeper knowledge regarding the mechanical behavior of structures subject to different loading conditions. The Strut-and-Tie Model is commonly used to structurally designing some reinforced concrete elements and for the regions where geometrical modifications and stress concentrations are observed, called "regions D". This method allows a better structural behavior representation for strength mechanisms in the concrete structures. Nonetheless, the topological model choice depends on the designer's experience regarding compatibility between internal flux of loads, geometry and boundary/initial conditions. Thus, there is some difficulty in its applications, once the model conception presents some uncertainty. In this context, the present work aims to apply the Strut-and-Tie Model to nonlinear structural elements together with a topological optimization method. The topological optimization method adopted considers the progressive stiffness reduction of finite elements with low stress values. The analyses performed could help the structural designer to better understand structural conceptions, guaranteeing the safety and the reliability in the solution of complex problems involving structural concrete.