Minimum Reinforcement Research Articles

Ductility and strength of hybrid fiber reinforced self-consolidating concrete beam with low reinforcement ratios

Based on the workability test of fiber reinforced self-consolidating concrete, this paper presents experimental study on flexural behavior of a series of fiber reinforced self-consolidating concrete beam with low reinforcement ratios. The major parameters include fiber types, fiber dosages and reinforcement ratios. The load-deflection curves of hybrid fiber reinforced RC beams and flexural ductility in comparison with steel fiber reinforced RC beams are analyzed. The investigation shows that the yield load and ultimate load of hybrid reinforced RC beam increase clearly compared to RC beam with minimum longitudinal reinforcement ratio or steel fiber reinforced RC beam, indicating positive hybrid effect. The ultimate load of 40+4kg/m3 hybrid fiber reinforced RC beam with minimum longitudinal reinforcement ratio is similar to that of RC beam with 1.5 times of minimum longitudinal reinforcement ratio. The flexural ductility of RC beam with minimum longitudinal reinforcement ratio is decreased due to fiber addition.

Efficient Shear Reinforcement Design Limits for Prestressed Concrete Beams

This study evaluates the appropriateness of the current design specifications for minimum shear reinforcement and maximum nominal shear strength for prestressed concrete members. The evaluation uses the University of Texas’ Prestressed Concrete Shear Database (UTPCSDB). The UTPCSDB contains data from 30 references published between 1954-2008, with test results from 506 tests conducted on beams with a variety of shapes. The test data indicated that none of the current minimum shear reinforcement requirements showed a clear separation between desirable and undesirable residual shear strength for prestressed concrete beams. New design provisions for minimum shear reinforcement and maximum nominal shear strength are proposed based on the empirical evidence from the database.

Minimum Reinforcement for Preventing Splitting Failure in Bottle-Shaped Struts

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고강도 콘크리트 말뚝과 기초판 접합부의 최적 철근보강량 산정

PHC 말뚝에서 강선을 노출시켜 건축물의 기초판과 연결시키는 기존 강선남김 방식은 강결합과 힌지결합의 중간형태로 공동주택(아파트)과 같은 건축구조물에 흔히 사용되는 방법이다. 그러나 이 방법은 역학적인 성능이 검증되지 않았으며 시공과정도 복잡하다. 이에 본 연구는 기존 관련 연구의 결과를 분석하고, PHC 말뚝의 콘크리트 단면적 대비 강선면적 비인 0.3%를 말뚝 접합부의 최소 철근보강량으로 선정하여 PHC 말뚝과 기초판과의 최적의 철근보강 방법을 말뚝 규격별(PHC 450, PHC 500, 및 PHC 600)로 제시하였다. PHC 말뚝과 기초판 접합부의 역학적 성능(인장강도와 전단강도)을 평가하기 위해 실물크기의 실험을 실시하였다. 그 결과, 모든 경우에 대해 요구강도를 만족하였으며 실제 적용되어도 문제가 없음을 확인하였다. 본 결과는 기존 연구에서 제시되었던 접합부의 철근 보강량보다 그 양이 대폭 감소하는 것으로 나타나 PHC 말뚝 시공 시 원가 절감에도 기여할 것으로 판단된다. Method of protruding steel bar embedded in PHC pile for connecting with foundation plate is an intermediate form of fixed and hinged connection and has often been used in architectural structures such as apartment complex. However, mechanical properties of this method have not been proved and its construction process is not simple. In this study, therefore, by analyzing previous research and by considering ratio of steel bar and concrete in PHC pile, which is minimum reinforcement of rebar, the newly optimized method of reinforcing joint of PHC pile and foundation plate is suggested with respect to PHC pile type (PHC 450, PHC 500, and PHC 600). To assess mechanical properties (ultimate tensile and shear strength) of joint of PHC pile and foundation plate, full scale experimental tests are performed. As a result, all cases are satisfied with required design criteria and can be practically applied. Our results indicate that reduction of rebar reinforcement compared to previous method would lead cost saving in PHC pile construction.

Effect of Detailing of Web Reinforcement on the Behavior of Bottle-shaped Struts

The effect of detailing of web reinforcement as per current design codes on the strength and serviceability behavior of bottle-shaped struts has been experimentally investigated, particularly in the context of codal minimum reinforcement requirements, by testing eleven scaled deep beams. The experimentally obtained efficiency factors of the bottle-shaped struts besides being significantly higher than the values given in the ACI 318-08 were also found to be sensitive to the amount of web reinforcement. The minimum web reinforcement requirements specified in current design codes were found to be adequate for controlling service load crack widths though the unreinforced bottle-shaped struts allowed in the ACI code were observed to violate the maximum crack width requirements. It has been shown that the transformation equation in the ACI code does not accurately represent the relationship between the strut efficiency factor and the amount of transverse reinforcement whereas a corrected version of the equation shows a clear dependence of the former on the latter.

A displacement-based seismic design procedure for concrete bridges having deck integral with the piers

A multi-step displacement-based seismic design procedure is presented and exemplified for concrete bridges having piers integral with a continuous prestressed deck, which is restrained transversely at the abutments but free to slide there longitudinally. It includes a simple estimation of inelastic deformation demands (chord or plastic hinge rotations in piers, curvatures for the deck) via elastic 5%-damped modal response spectrum analysis and normally entails very few design-analysis iterations. Prescriptive detailing and minimum reinforcement rules are relaxed. Instead, the vertical reinforcement of piers is tailored to seismic deformation demands for uniform ductility ratios across the piers, while their transverse reinforcement is detailed on the basis of explicit checks of their integrity under the design earthquake. The procedure is applied to eight different bridges with three or five spans, box girder deck and piers of various cross-sections with about equal or very different heights. Nonlinear response-history analyses are carried out under ground motions well beyond the design earthquake, in order to evaluate the seismic performance of the resulting designs and compare with that of force-based Eurocode 8 designs of the same bridge. The displacement-based procedure is shown to give more cost-effective and balanced designs than Eurocode 8, without loss in seismic performance.

Making sense of minimum flexural reinforcement requirements for reinforced concrete members

The main aims of this research were to summarize the apparent origin of current minimum reinforcement provisions, examine the margin of safety provided by existing provisions for reinforced concrete members of different sizes and shapes, and propose more consistent results than those from existing provisions. Five existing or proposed methods were included in the study. Parametric analyses show that the proposed method provides the most reasonable margins of safety among the methods examined. The study focuses on determinate reinforced concrete beams, which include only mild tensile reinforcement and no prestressing. High-strength steel and concrete were included. The study also found that, in many cases,, flexural failure at minimum reinforcement levels can be initiated by crushing of the concrete rather than the fracture of the reinforcing steel.

Creep and shrinkage behavior of high-strength concrete and minimum reinforcement ratio for bridge columns

This paper summarizes the findings of an extensive research program that examined the shrinkage and creep behavior of high-strength concrete (HSC) up to a strength of 18 ksi (124 MPa). Creep and shrinkage strains of 60 specimens were monitored for up to 2 years. The variables considered in this research were the concrete compressive strength, specimen size, curing type, age of concrete at loading, and loading stress level. Findings indicate that the current American Association of State Highway and Transportation Officials' (AASHTO) LRFD Bridge Design Specifications could be used to estimate the creep coefficient and shrinkage strain of HSC up to 15 ksi (103 MPa). However, the current AASHTO LRFD specifications do not provide appropriate predictions for concrete compressive strength greater than 15 ksi (103 MPa). A revised time-development correction factor is proposed to obtain better predictions for HSC up to 18 ksi (124 MPa). For HSC compression members, the current AASHTO LRFD specifications require an excessive amount of minimum longitudinal reinforcement to account for the long-term effects due to shrinkage and creep. Based on an analysis, a new relationship is proposed for the required minimum reinforcement ratio.

Nonlinear fracture mechanics investigation on the ductility of reinforced concrete beams

In the present paper, a numerical algorithm based on the finite element method is proposed for the prediction of the mechanical response of reinforced concrete (RC) beams under bending loading. The main novelty of such an approach is the introduction of the Overlapping Crack Model, based on nonlinear fracture mechanics concepts, to describe concrete crushing. According to this model, the concrete dam- age in compression is represented by means of a fictitious interpenetration. The larger is the interpenetration, the lower are the transferred forces across the damaged zone. The well-known Cohesive Crack Model in tension and an elastic-perfectly plastic stress versus crack opening displacement relationship describing the steel reinforcement behavior are also integrated into the numerical algorithm. The application of the proposed Cohesive-Overlapping Crack Model to the assessment of the minimum reinforcement amount neces- sary to prevent unstable tensile crack propagation and to the evaluation of the rotational capacity of plastic hinges, permits to predict the size-scale effects evidenced by several experimental programs available in the literature. According to the obtained numerical results, new practical design formulae and diagrams are proposed for the improvement of the current code provisions which usually disregard the size effects.

철근콘크리트 기둥의 성능기반설계를 위한 주철근비

The longitudinal reinforcement ratio for the performance-based design of columns was studied. Unlike the existing design codes using uniform minimum reinforcement ratio and effective stiffness for all columns, the longitudinal reinforcement ratio of columns was defined as the function of various design parameters. To evaluate the minimum reinforcement ratio, two conditions were considered: 1) prevention of passive yielding of compression re-bars due to the creep and shrinkage of concrete under sustained service loads; and 2) ultimate flexural strength greater than the cracking moment capacity to maintain the ductility of columns for earthquake design. In addition, the effective flexural stiffness of columns for structural analysis was determined according to the longitudinal reinforcement ratio. The design method addressing the three criteria was proposed. The proposed method was applied to a design example.

Factors affecting web-shear capacity of deep hollow-core units

Shear-strength estimates for precast, prestressed hollow-core units in the United States follow the shear recommendations of the American Concrete Institute's (ACI's) Committee 318. These recommendations are based on experimental research done mainly on members other than hollow-core units, and they have been extended to hollow-core units based on a limited amount of hollow-core shear tests. Recent shear tests that several U.S. manufacturers have performed on thick hollow-core units (units with depths larger than 12 in. [300 mm]) have indicated failures in the web at forces smaller than those predicted by Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05). Similar observations have been made by researchers in Europe, where web-shear provisions are similar in nature to those in ACI 318-05. As a stopgap measure, ACI 318-08 waives the exception on minimum shear reinforcement for hollow-core units deeper than 12.5 in. (318 mm). An analytical research program at the University of Minnesota investigated the reasons that thicker hollow-core units fail at lower shear forces than those predicted using the ACI 318-05 provisions. This paper summarizes the findings of the analytical program, including comparisons of the ACI 318-05, Eurocode No. 2: Design of Concrete Structures-Part 1: General Rules and Rules for Buildings, the modified compression field theory, the American Association of State Highway and Transportation Officials' AASHTO LRFD Bridge Design Specifications, and Yang's shear prediction methods.

Design of shear reinforcement for thick plates using a strut-and-tie model

The strut-and-tie method is a rational approach to structural concrete design that results in a uniform and consistent design philosophy. A strut-and-tie model has been developed to model the punching-shear behaviour of thick concrete plates. This model provides a quick and simple approach to check the punching-shear behaviour. Thick concrete slabs (250–500 mm) without shear reinforcement can exhibit brittle shear failure under a central force and an unbalanced moment. Shear reinforcement has proven to be very effective in preventing such failures. The developed strut-and-tie model has also been used to evaluate the minimum shear reinforcement required to prevent brittle shear failure of two-way slabs in the vicinity of concentrated loads. The strut-and-tie model for symmetric punching consists of a “bottle-shaped” compressive zone in the upper section of the slab depth, leading to a “rectangular-stress” compressive zone in the lower section of the slab depth. Inclined shear cracking develops in the bottle-shaped zone prior to failure in the lower zone. Cracking in the bottle-shaped zone is related to the splitting tensile strength of concrete.

Shear Behavior of Steel Fiber-Reinforced Concrete Beams without Stirrup Reinforcement

This paper investigates the behavior of steel fiber-reinforced concrete (SFRC) beams in shear, as well as the possibility of using steel fibers as minimum shear reinforcement. In the study, 28 simply supported beams with a shear span-to-effective depth ratio of approximately 3.5 were subjected to a monotonically increased, concentrated load. The target concrete compressive strength for all of the beams was 41 MPa (6000 psi). The studied parameters included beam depth, fiber length, fiber aspect ratio, fiber strength, and fiber volume fraction. Three types of steel fibers were considered, all with hooks at their ends. The behavior of beams failing in shear prior to or after flexural yielding was also investigated by varying the longitudinal reinforcement ratio. Compared to reinforced concrete (RC) beams without stirrup reinforcement, the use of hooked steel fibers in a volume fraction greater than or equal to 0.75% led to an enhanced inclined cracking pattern and a substantial increase in shear strength.

Influence of Effective Depth on Shear Strength of Concrete Beams—Experimental Study

Laboratory tests of reinforced concrete beams without shear reinforcement have shown that the shear strength (in terms of average shear stress) decreases as the size (depth) of the member increases. This paper discusses the results of experimental research performed to test the hypothesis that the effective depth influences the shear strength of reinforced concrete flexural members that do not contain web reinforcement in the range of overall depth between 12 to 36 in. (610 to 900 mm) where ACI 318-08 does not require skin reinforcement. The results of tests on eight simply supported reinforced concrete beams without shear and skin reinforcement are described, discussed, and correlated herein. The longitudinal reinforcement ratio was approximately 1.25%. The target concrete compressive strength was 10, 000 psi (70 MPa). The beam width varied between 8 and 24 in. (203 and 610 mm). All of the beams were simply supported and monotonically loaded in increments at midspan up to destruction. The shear span-depth ratio was maintained at 3.0. Test results show a reduction in shear strength with increasing effective depth; however, significant differences in behavior were observed between the 12 in. (305 mm) specimens and the larger specimens in terms of the amount of flexural cracking, crack progression, load-displacement, and load-strain measurements despite holding other traditionally considered influential parameters constant. These differences suggest that the reduction in shear strength was influenced not only by a size effect but also by differences in behavior and mode of shear transfer at failure (beam action versus arch action). For the beams tested in this study, flexural crack spacing did not scale with beam size. The change in ACI 318-08 restricting isolated beams without minimum shear reinforcement to heights not greater than 10 in. (250 mm) is supported by the findings of this study.

Seismic collapse risk of precast industrial buildings with strong connections

AbstractA systematic seismic risk study has been performed on some typical precast industrial buildings that consists of assemblages of cantilever columns with high shear‐span ratios connected to an essentially rigid roof system with strong pinned connections. These buildings were designed according to the requirements of Eurocode 8. The numerical models and procedures were modified in order to address the particular characteristics of the analyzed system. They were also verified by pseudo‐dynamic and cyclic tests of full‐scale large buildings. The intensity measure (IM)‐based solution strategy described in the PEER methodology was used to estimate the seismic collapse risk in terms of peak ground acceleration capacity and the probability of exceeding the global collapse limit state. The effect of the uncertainty in the model parameters on the dispersion of collapse capacity was investigated in depth. Reasonable seismic safety (as proposed by the Joint Committee on Structural Safety) was demonstrated for all the regular single‐storey precast industrial buildings addressed in this study. However, if the flexural strength required by EC8 was exactly matched, and the additional strength, which results from minimum longitudinal reinforcement, was disregarded as well as large dispersion in records was considered, the seismic risk might in some cases exceed the acceptable limits. Copyright © 2009 John Wiley & Sons, Ltd.

Comparison between ACI 318-05 and Eurocode 2 (EC2-94) in flexural concrete design

The two major widely used building design code documents of reinforced concrete structures are the ACI 318-05 and Eurocode for the Design of Concrete Structures EC2. Therefore, a thorough comparative analysis of the provisions of these codes is required to confirm their validity and identify discrepancies in either code. In this context, provisions of flexural computations would be particularly attractive for detailed comparison. The provisions of safety concepts, design assumptions, cross-sectional moment capacity, ductility, minimum and maximum reinforcement ratios, and load safety factors of both the ACI 318-05 and EC2 is conducted with parametric analysis. In order to conduct the comparison successfully, the parameters and procedures of EC2 were reformatted and defined in terms of those of ACI 318-05. This paper concluded that although the adopted rationale and methodology of computing the design strength is significantly different between the two codes, the overall EC2 flexural provisions are slightly more conservative with a little of practical difference than those of ACI 318-05. In addition, for the limit of maximum reinforcement ratio, EC2 assures higher sectional ductility than ACI 318-05. Overall, EC2 provisions provide a higher safety factor than those of ACI 318-05 for low values of Live/Dead load ratios. As the ratio increases the difference between the two codes decreases and becomes almost negligible for ratios higher than 4.

An appraisal of the ACI strut efficiency factors

The strut-and-tie modelling recommendations of the American Concrete Institute (ACI) 318-08 Appendix A are widely followed for the design of disturbed regions in concrete structures. In this investigation, an experimental appraisal of the ACI 318-08-recommended efficiency factors for prismatic and bottle-shaped struts has been carried out and inconsistency in the recommendations for bottle-shaped struts highlighted. It has been demonstrated that a bottle-shaped strut is in no way inferior to a prismatic strut in terms of strength and, consequently, the efficiency factor of bottle-shaped struts needs to be revised. An error in the ACI 318-08-recommended formulation for minimum effective transverse reinforcement in reinforced bottle-shaped struts is identified and corrected.

Failure mechanisms governing reinforcement length of geogrid reinforced soil retaining walls

Current design practice of reinforced soil retaining walls is based on the limit equilibrium approach. The walls are designed for both external and internal stability criteria. Design reinforcement length should be such that minimum required safety factors are fulfilled for all failure modes. Most agencies require minimum reinforcement length equal to 70 percent of wall height. However, it is not always possible to have enough space behind a wall to accommodate these required reinforcement lengths due to an existing natural rock formation, man-made shoring system, or the presence of another reinforced soil retaining wall. This study was performed to investigate governing failure mode in determining the required minimum reinforcement length and also to investigate the possibility of shortening the specified minimum reinforcement lengths. Effect of different parameters involved in the design of reinforced soil retaining walls on the required minimum reinforcement length and the governing failure mode were studied. Parameters considered included wall height, surcharge, reinforcement vertical spacing, reinforced soil properties, backfill/retained soil properties, and foundation soil properties. Results indicated that both external and internal failure modes can be governing criteria in determining the required minimum reinforcement length depending on the parameters involved for a specific wall. In addition, it may be possible to use reinforcement lengths as low as almost 50 percent of the wall height, instead of 70 percent as required by many agencies around the world. This paper presents the results of parametric studies conducted, including the effect of different parameters on the required minimum reinforcement length and the governing failure criteria.

Shear Strength Evaluation of Concrete Bridge Girders

This paper presents a shear strength evaluation procedure for structural concrete girders that contain at least minimum transverse reinforcement. This procedure is similar to the 2008 American Association of State Highway and Transportation Officials Load & Resistance Factor Design (AASHTO LRFD) shear design method except that it does not require trial-and-error for shear strength evaluation and provides more insight by providing information about different shear failure modes involving stirrups yielding, diagonal crushing of concrete, and longitudinal reinforcement yielding. The procedure is simple enough to be implemented into a small computer program for checking numerous sections along a bridge girder. To validate the proposed method, shear strength predictions are compared with results from strength tests on reinforced and prestressed concrete beams, as well as predictions from shear design methods in AASHTO LRFD and American Concrete Institute 318. The proposed procedure is used to evaluate the shear strength of girders in three existing bridges with prestressed concrete I-girders, prestressed concrete box-girders, and reinforced concrete channel-girders. Results from the validation tests and demonstrations compare well with results from previous tests and models.

External beam–column joints: design to Eurocode 2

In practice external beam–column joints are seldom designed for monotonic loading. The current authors believe that this is an oversight which should be addressed. This paper presents a simple strut and tie model for the analysis and design of external reinforced concrete beam–column joints. The strut and tie model is developed from first principles using the concrete design strengths given in Eurocode 2. The main difficulty in developing strut and tie models for beam–column joints is in determining the node dimensions. The novel feature of the authors' analysis is that the joint strength is related to the flexural capacity of the beam at the face of the column which is defined in terms of the maximum moment which can be transferred through the joint into the upper and lower columns. The model is shown to give better predictions of joint shear strength than existing simple design models. A case study is presented which shows that it is often sufficient to provide only minimum shear reinforcement in beam column joints.