Strut-tie Model Research Articles

Failure Analysis of Steel Fiber-Reinforced Concrete T-Beams without Shear Stirrups

The shear failure of a reinforced concrete member is a sudden diagonal tension failure; flexible failure is gradual, associated with significant cracks, and leads to extensive sagging. Therefore, reinforced shear rebars are commonly used to ensure that flexible failure occurs before shear failure under extreme conditions. Extensive efforts are underway to replace conventional shear reinforcements with steel fibers. Here, a nonlinear analysis of a steel fiber-reinforced concrete T-beam was performed in order to estimate the maximum shear capacity with the aid of experimental test data. A continuum-damaged plasticity model and modified compression field theory were used for nonlinear analysis. Three 360 × 360-mm web elements were selected between the shear span; changes in the principal axis caused by crack development and propagation were traced. Changes in the crack angle according to the average strain of the bottom longitudinal reinforcement and the vertical strain of the web element were also determined. For verification, a strut-tie model was used to predict shear capacity. The experimental results and the finite element analyses were in good agreement.

Experimental and analytical study on the behavior of hybrid GFRP/steel bars in reinforced concrete deep beams

Abstract The deep beam is one of the essential members of high-rise buildings structures, so the deep beams are used as a transfer girder; in walls water structures, the deep beam behavior is different from the slender beam behavior; the deep beam plane section before does not remain plane after bending. In recent years, the use of FRP as a composite material in reinforced concrete structures has been growing up to cover problems by weight of structure buildings, corrosion, repairing, and construction cost. This paper presents an experimental, analytical study to assign the variation of mechanical properties of reinforced concrete deep beams using vertical and horizontal GFRP stirrups. This paper investigates the mechanical properties of test specimens for deep beams reinforced in shear with GFRP or steel bars as web reinforcement. The deep beams are reinforced with glass fiber reinforced polymer (GFRP) in various ratios as a web reinforcement configuration (0, 0.25%, and 0.40%) rather than traditional steel web reinforcement. All tested specimens have the same span to depth ratio of 0.40 (a/d); the primary and secondary reinforcement is steel bars. The web reinforcement ratio significantly affected deep beams’ load capacity and mechanical behavior. The GFRP enhancement the mechanical behavior of the reinforced concrete deep. Increasing the GFRP web reinforcement ratio enhances the deep beam load capacity. The test results compared with the traditional ACI design method strut-tie model to demonstrate the effect of web reinforcement ratio on deep beam load capacity and strut width. The test results have been verified by ABAQUS 6.13.

Punching shear strength of reinforced concrete transfer slab-column connections with shear reinforcement

At RC transfer slab system, the load transfer from the above vertical members to the bottom columns is significantly changed, which requires two-way shear action. For structural safety, a reasonable design for two-way shear strength of RC transfer slab systems is of importance. To improve the two-way shear strength, stirrups are generally used for shear reinforcement in RC transfer slabs. However, unlike conventional structural members using single leg stirrups, lap spliced stirrups are used in the RC transfer slab due to construction difficulty. In the present study, concentric compression tests were performed on four RC transfer slabs with small shear span-to-depth ratio and shear reinforcement to investigate the two-way shear strength. The test parameters were the conventional stirrups, lap splice of stirrups, and steel truss for shear reinforcement. The two-way shear strength, failure mode, and strain distribution of reinforcement of the slab specimens were evaluated. The test results showed that the use of spliced stirrups increased the two-way shear strength of the transfer slab specimen. The two-way shear strengths of the test specimens were compared with the predictions of the current design method and the strut-tie model.

Two-way shear strength of reinforced concrete transfer slab-column connections

In high-rise wall-type residential buildings, thick RC transfer slabs have been widely used for parking space or public space. Despite the different behavior from thin RC flat slab, design methods for thin RC flat slab are applied to the thick RC transfer slab, due to the limited literature on the two-way shear behavior of RC transfer slab systems with small shear span-to-depth ratio. In the present study, concentric compression tests were performed on eight RC transfer slabs with small shear span-to-depth ratio to investigate the two-way shear strength. The test parameters were the concrete strength, shear span-to-depth ratio, slab thickness, and reinforcement ratio of the slab. The two-way shear strength, deformation capacity, failure mode, and strain distribution of slab rebars of the slab specimens were evaluated. The test results showed that the use of high-strength concrete or large reinforcement ratio increased the two-way shear strength of the transfer slab specimens. However, the transfer slab specimen having large slab thickness without sufficient reinforcement was susceptible to punching shear failure, showing insignificant strength increment. The two-way shear strengths of the test specimens were compared with the predictions of the current design method and the strut-tie model.

Suggestion, Shear Tests, and Analysis by Strut-Tie Model of Modified Double-Tee Slabs

Suggestion, Shear Tests, and Analysis by Strut-Tie Model of Modified Double-Tee Slabs

2차원 격자 스트럿-타이 모델 방법에 의한 철근콘크리트 깊은 보의 파괴강도 예측

2차원 격자 스트럿-타이 모델 방법에 의한 철근콘크리트 깊은 보의 파괴강도 예측

Strength of Concrete Struts in Three-Dimensional Strut-Tie Models

AbstractThe design of structural concrete using strut-tie models requires establishing the effective strength of concrete struts, ensuring sufficient anchorage of reinforcing bars in nodal zones, and the geometric compatibility of the strut-tie model within the member geometry. In this paper, a consistent and general method applicable to three-dimensional (3D) strut-tie models is presented. The proposed method includes the effects of 3D stresses associated with tensile strains in reinforcing bars crossing a strut, strut length, deviation angle between strut orientation and compressive principal stress flow, compressive strength of concrete, and degree of confinement provided by reinforcement. The proposed method is implemented and then verified using data from 115 reinforced concrete pile caps tested to failure.

Strength of Concrete Struts for Strut-Tie Model Design of Reinforced Concrete Beams with Shear Span-to-Effective Depth Ratio of Less than 3.0

Strength of Concrete Struts for Strut-Tie Model Design of Reinforced Concrete Beams with Shear Span-to-Effective Depth Ratio of Less than 3.0

Strut-tie model for two-span continuous RC deep beams

In this study, a simple indeterminate strut-tie model which reflects complicated characteristics of the ultimate structural behavior of continuous reinforced concrete deep beams was proposed. In addition, the load distribution ratio, defined as the fraction of applied load transferred by a vertical tie of truss load transfer mechanism, was proposed to help structural designers perform 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 was introduced to ensure the 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 compressive strength of concrete were reflected upon. To verify the appropriateness of the present study, the ultimate strength of 58 continuous reinforced concrete deep beams tested to shear failure was evaluated by the ACI 318M-11\'s strut-tie model approach associated with the presented indeterminate strut-tie model and load distribution ratio. The ultimate strength of the continuous deep beams was also estimated by the experimental shear equations, conventional design codes that were based on experimental and theoretical shear strength models, and current strut-tie model design codes. The validity of the proposed strut-tie model and load distribution ratio was examined through the comparison of the strength analysis results classified according to the primary design variables. The present study associated with the indeterminate strut-tie model and load distribution ratio evaluated the ultimate strength of the continuous deep beams fairly well compared with those by other approaches. In addition, the present approach reflected the effects of the primary design variables on the ultimate strength of the continuous deep beams consistently and reasonably. The present study may provide an opportunity to help structural designers conduct the rational and practical strut-tie model design of continuous deep beams.

프리스트레스트 콘크리트 보의 부정정 스트럿-타이 모델

이 논문에서는 스트럿-타이 모델을 이용한 프리스트레스트 콘크리트 보의 해석 및 설계 시 프리스트레스트 콘크리트 보의 비선형 파괴거동 특성 및 복잡한 하중전달 메커니즘을 합리적인 방법으로 반영할 수 있는 단순한 형태의 부정정 스트럿-타이 모델을 제안하였다. 또한 현행 설계기준서의 스트럿-타이 모델 규정을 이 연구에서 제안한 부정정 스트럿-타이 모델에 접목시켜 프리스트레스트 콘크리트 보의 해석 및 설계를 수행할 수 있는 부정정 스트럿-타이 모델의 하중분배율을 제안하였다. 이 연구에서 제안한 부정정 스트럿-타이 모델 및 하중분배율의 적합성을 검증하기 위해 파괴실험이 수행된 47개의 프리스트레스트 콘크리트 보의 극한강도를 평가하였으며, 그 결과를 현행 설계기준서의 스트럿-타이 모델 방법에 의한 평가결과와 비교분석 하였다. In this study, a statically simple indeterminate strut-tie model is proposed for the rational analysis and design of simply supported prestressed concrete beams by reflecting all characteristics of nonlinear structural behavior and load transfer mechanisms. In addition, a load distribution ratio that allows to transform the proposed indeterminate strut-tie model to a determinate model is also suggested to help structural designers conduct the structural analysis and design of simply supported prestressed concrete beams by using the strut-tie model method of current design codes. For verifying of the validity of the proposed model and load distribution ratio, the ultimate strengths of 47 simply supported prestressted concrete beams tested to failure were estimated and the results were compared with those by the strut-tie model methods of current design codes.

Nonlinear Lattice-Based Model for Cyclic Analysis of Reinforced Normal and High-Strength Concrete Columns

As a practical approach, the strut-tie model has been widely used, but not able to inform deformational responses of the structures. A lattice model is a good alternative as a nonlinear prediction since it can provide information on strength as well as deformation in concrete structures. In this study, a two-dimensional lattice-based model of RC columns is newly formulated in normal and high-strength concrete. Constitutive laws of concrete have been attempted by including the confinement effect of normal concrete and high-strength concrete. The effective width of concrete struts is determined by the principle of minimization of the strain energy based on the preanalysis. Cyclic analyses of reinforced normal and high-strength concrete columns are compared with several experiments. The results demonstrated that the strengths, deformations, and hysteretic behaviors were well matched with those of experiments, and the proposed model was useful in seismic assessment and performance-based design of RC structures.

스트럿-타이 모델의 절점 폭 변화에 따른 설계 비교

In the Strut-Tie-Model(STM), the width of a node is important in both analysis and design. Its effects on the force distribution at truss analogy system. In addition, it effects the verification of all struts and nodes, which need to be checked to satisfy the code of design. Code here refers to the ACI-318 code. Four methods were used to define the width of node: 1) effective depth is assumed to equal to 0.9 of the overall depth of beam, 2) moment equilibrium 3) assumption of the width of node at the bottom equal to 380mm, and 4) the new proposed method by this study. 106 selected samples of a parametric study obtained from the four methods were analyzed. Because total steel requirement from these four methods are similar, the easiest would be a good choice for a time saving calculation.

An Indeterminate Strut-Tie Model and Load Distribution Ratio for Reinforced Concrete Corbels

철근콘크리트 코벨의 파괴거동은 코벨의 전단경간비 및 주인장 철근비를 포함한 여러 변수들로 인해 복잡하다. 이 논문에서는 철근콘크리트 코벨의 강도 및 거동 특성을 논리적이고 합리적인 방법으로 반영하여 전단경간비가 1.0 이하인 철근콘크리트 코벨을 설계할 수 있는 단순한 형태의 1차 부정정 트러스 구조의 스트럿-타이 모델을 제안하였다. 또한 부정정 스트럿-타이 모델을 정정 트러스 구조의 스트럿-타이 모델로 변환시켜 현행 스트럿-타이 모델 설계기준에 의한 코벨의 설계를 가능하게 하는 하중분배율을 제안하였다. 하중분배율 결정 시 스트럿과 타이의 재료적 비선형 거동을 고려할 수 있는 부정정 스트럿-타이 모델의 비탄성 구조해석을 통해 철근콘크리트 코벨의 강도 및 거동을 지배하는 전단경간비, 주인장 철근비, 수직하중에 대한 수평하중의 비, 그리고 콘크리트의 압축강도 등의 주요설계변수들의 영향을 반영하였다. 이 연구에서 제안한 부정정 스트럿-타이 모델 및 하중분배율의 적합성을 검증하기 위해 파괴실험이 수행된 다수의 철근콘크리트 코벨의 극한강도를 평가하였으며, 그 결과를 ACI 318-11의 전통적인 설계기준 및 정정 트러스 구조의 스트럿-타이 모델을 기반으로 하는 현행 주요 설계기준의 스트럿-타이모델 방법에 의한 평가결과와 비교분석하였다. The ultimate behavior of reinforced concrete corbel is complicated due to the primary design variables including the shear span-to-effective depth ratio a/d, flexural reinforcement ratio, load condition, and material properties. In this study, a simple indeterminate strut-tie model reflecting all characteristics of the ultimate strength and complicated structural behavior is proposed for the design of the reinforced concrete corbels with shear span-to-effective depth ratio of <TEX>$a/d{\leq}1$</TEX>. A load distribution ratio, defined as the fraction of applied load transferred by horizontal truss mechanism, is also proposed to help structural designers perform the design of reinforced concrete corbels by using the strut-tie model approaches of current design codes. For the development of the load distribution ratio, numerous material nonlinear finite element analyses of the proposed indeterminate strut-tie model were conducted by changing primary design variables. The ultimate strengths of reinforced concrete corbels tested to failure were evaluated by incorporating the proposed strut-tie model and load distribution ratio into the ACI 318-11's strut-tie model method. The validity of the proposed model and load distribution ratio was examined by comparing the strength analysis results with those by the ACI 318-11's conventional design method and strut-tie model methods of current design codes.

Effective Strengths of Concrete Struts in Strut-Tie Models of Reinforced Concrete Corbels

스트럿-타이 모델 방법은 철근콘크리트 코벨의 극한강도 해석 및 설계에 매우 효과적이다. 그러나 스트럿-타이 모델 방법을 이용한 철근콘크리트 코벨의 정확한 해석 및 안전한 설계를 위해서는 스트럿의 유효강도를 정확하게 결정하여야 한다. 이 연구에서는 여러 연구문헌에서 제안된 철근콘크리트 코벨의 대표적인 세 종류의 스트럿-타이 모델을 활용하기 위하여 철근콘크리트 코벨의 기하학적 형상, 수직 및 수평 하중의 조합 비, 그리고 휨철근 및 수평전단철근 비 등 주요 설계변수들의 영향을 정확하게 반영할 수 있는 스트럿 유효강도 식을 개발, 제안하였다. 현행 여러 설계기준서의 스트럿 유효강도 식과 이 연구에서 제안한 유효강도 식을 이용하여 파괴실험이 수행된 243개 철근콘크리트 코벨의 극한강도를 평가하였으며, 그 결과의 비교분석을 통해 이 연구에서 제안한 스트럿 유효강도 식의 적합성을 평가하였다. The strut-tie model approach has proven to be effective in the ultimate analysis and design of structural concrete with disturbed regions. For the reliable analysis and safe design of the structural concrete, however, the effective strengths of concrete struts must be determined accurately. In this study, the equations of the effective strengths of concrete struts, which are useful for the three types of determinate and indeterminate strut-tie models of reinforced concrete corbels, were proposed. The effects of shear span-to-effective depth ratio, the vertical-to-horizontal force ratio, and flexural and horizontal shear reinforcement ratios were reflected in the development of the proposed equations. To examine the appropriateness of the proposed and existing equations, the ultimate strengths of 243 reinforced concrete corbels tested to failure were evaluated by using the three types of corbel strut-tie models.

Strut-Tie Model Approach Associated with 3-Dimensional Grid Elements for Design of Structural Concrete - (II) Validity Evaluation

현 논문에서는 전편 논문에서 제안한 3차원 격자요소를 활용하는 스트럿-타이 모델 방법의 타당성 및 효율성을 검증하기 위해 파괴실험이 수행된 13개의 슬래브-기둥 접합부 및 51개의 비틀림 보 등의 극한강도를 평가하였으며, 또한 3축 방향의 하중을 받는 교각코핑부에 대한 설계를 수행하였다. 현 연구의 방법에 의한 철근콘크리트 슬래브-기둥 접합부 및 비틀림 보의 극한강도 평가결과는 실험결과, ACI 318 설계기준을 비롯한 세계 주요설계기준, 그리고 몇몇 연구자의 방법에 의한 평가결과 등과 비교하여 현 연구방법의 타당성을 검증하였다. 교각코핑부의 설계결과는 ACI 318 설계기준의 단면법 및 AASHTO-LRFD의 스트럿-타이 모델 설계기준에 의한 설계결과와 비교하여 그 결과의 타당성을 검토하였다. In this study, the ultimate strengths of 13 slab-column joints and 51 torsional beams were evaluated to verify the validity of the strut-tie model approach presented in the companion paper. In addition, the design of the bridge pier subjected to multiple load combinations with longitudinal and lateral loads was conducted. The analysis results were compared with those by the provisions of BS 8110, ACI 318, and AASHTO-LRFD. The design results of the bridge pier were also compared with those by the provisions of ACI 318's sectional design method and AASHTO-LRFD's strut-tie model method.

Strut-Tie Model Approach Associated with 3-Dimensional Grid Elements for Design of Structural Concrete - (I) Proposal of Approach

Strut-Tie Model Approach Associated with 3-Dimensional Grid Elements for Design of Structural Concrete - (I) Proposal of Approach

철근콘크리트 파일캡의 해석 및 설계를 위한 개선 3차원 스트럿-타이 모델

철근콘크리트 파일캡의 설계 시 사용되고 있는 현행 설계기준의 단면법 및 스트럿-타이 모델 방법은 각각 B-영역으로 이루어진 철근콘크리트 구조부재의 거동과 2차원 응력교란영역을 갖는 철근콘크리트 구조부재의 거동에 기초한 것으로, 이를 응력교란영역(D-영역)을 갖고 3차원 거동이 지배적인 철근콘크리트 파일캡의 설계에 적용하는 것은 적절하지 않다. 이 연구에서는 3축 응력을 받는 콘크리트 스트럿 및 절점영역의 강도특성과 철근이 배치되지 않은 인장영역에서의 콘크리트 타이의 하중저항능력 등을 반영하여 철근콘크리트 파일캡을 합리적으로 설계할 수 있는 개선 3차원 스트럿-타이 모델을 제안하였다. 파괴실험이 수행된 78개 철근콘크리트 파일캡 시험체의 극한강도를 현행 설계기준의 단면법 및 스트럿-타이 모델 방법, 그리고 이 연구의 개선 3차원 스트럿-타이 모델을 이용하여 평가하였으며, 그 결과의 비교분석을 통해 스트럿-타이 모델 방법 적용 시의 3차원 거동 및 하중전달 메커니즘을 묘사하기 위한 적절한 구성요소의 필요성과 이 연구에서 제안한 개선 3차원 스트럿-타이 모델의 타당성을 검증하였다. The sectional methods of current design codes have been broadly used for the design of various kinds of reinforced concrete pile caps. Lately, the strut-tie model approach of current design codes also became one of the attracting methods for pile caps. However, since the sectional methods and the strut-tie model approach of current design codes have been established by considering the behaviors of structural concrete without D-regions and two-dimensional concrete structures with D-regions, respectively, it is inappropriate to apply the methods to the pile caps dominated by 3-dimensional structural behavior with disturbed stress regions. In this study, the refined 3-dimensional strut-tie models, which consider the strength characteristics of 3-dimensional concrete struts and nodal zones and the load-carrying capacity of concrete ties in tension regions, are proposed for the rational analysis and design of pile caps. To examine the validity of the proposed models and to verify the necessity of appropriate constituent elements for describing 3-dimensional structural behavior and load-transfer mechanism of pile caps, the ultimate strength of 78 reinforced concrete pile caps tested to failure was examined by the proposed models along with the sectional and strut-tie model methods of current design codes.

An Indeterminate Strut-Tie Model and Load Distribution Ratio for RC Deep Beams- (II) Validity Evaluation

In this study, the ultimate strength of 234 simply supported reinforced concrete deep beams tested to shear failure was evaluated by the ACI 318M-08's strut-tie model approach implemented with the indeterminate strut-tie model and load distribution ratio of the companion paper. The ultimate strength of the deep beams was also estimated by using the experimental shear strength models, the theoretical shear strength models, and the current strut-tie model design codes. The validity of the presented indeterminate strut-tie model and load distribution ratio was examined through the comparison of the strength analysis results classified according to the primary design variables of shear span-to-effective depth ratio, flexural reinforcement ratio, and compressive strength of concrete. The present study associated with the indeterminate strut-tie model and load distribution ratio evaluated the ultimate strength of 234 deep beams fairly accurately compared with those by other approaches. In addition, the present approach reflected the effects of the primary design variables on the ultimate strength of deep beams consistently and accurately.

An Indeterminate Strut-Tie Model and Load Distribution Ratio for RC Deep Beams - (I) Model &amp; Load Distribution Ratio

The ultimate strength of simply supported reinforced concrete deep beams is governed by the capacity of the shear resistance mechanism. The structural behavior of the deep beams is controlled mainly by the mechanical relationships between the primary design variables including shear span-to-effective depth ratio, flexural reinforcement ratio, and the compressive strength of concrete. In this study, a simple indeterminate strut-tie model which reflects all characteristics of the ultimate strength and behavior of the deep beams was presented. A load distribution ratio, defined as the fraction of load transferred by a truss mechanism, was also proposed to help structural designers perform the rational design of 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 which ensures the ductile shear design of the deep beams was introduced, and the effect of the primary design variables was reflected through numerous numerical analyses of the presented indeterminate strut-tie model. In the companion paper, the validity of the presented model and load distribution ratio was examined by applying them to the evaluation of ultimate strength of 234 simply supported reinforced concrete deep beams tested to failure.

연속지지 RC 깊은 보의 부정정 스트럿-타이 모델 및 하중분배율 (II) 적합성 평가

In this study, ultimate strengths of 51 continuous reinforced concrete deep beams were evaluated by the ACI 318M-08`s strut-tie model approach implemented with the presented indeterminate strut-tie model and load distribution ratio of the companion paper. The ultimate strengths of the continuous deep beams were also estimated by the shear equations derived based on experimental results, conventional design codes based on experimental and theoretical shear strength models, and current strut-tie model design codes. The validity of the presented strut-tie model and load distribution ratio was examined through the comparison of the strength analysis results classified according to the primary design variables of shear span-to-effective depth ratio, flexural reinforcement ratio, and concrete compressive strength. The present study results of ultimate strengths obtained using the indeterminate strut-tie model and load distribution ratio of the continuous deep beams agree fairly well with those obtained using other approaches. In addition, the present approach reflected the effect of the primary design variables on the ultimate strengths of the continuous deep beams consistently and accurately. Therefore, the present study will help structural designers to conduct rational and practical strut-tie model designs of continuous deep beams.