Rectangular Stress Block Parameters Research Articles

Development of stress block parameters for ultra high performance concrete

Extensive literature exists on mix design, production methods, and the structural behavior of ultra-high-performance concrete elements (UHPC). Numerous studies in these domains have significantly contributed to our comprehension of UHPC. Nevertheless, a notable research lacuna persists in formulating rectangular stress block parameters tailored specifically for UHPC. This gap arises from the predominant reliance on prevailing standard codes and guidelines, which are founded on experimental data derived from normal concrete, rendering them inadequately applicable to the design of UHPC structures. This paper addresses this research gap by proposing novel rectangular stress block parameters explicitly designed for UHPC. The compression stress block is derived by modeling the stress–strain response and evaluating the shape factor. Simultaneously, the tension stress block is developed by modeling responses during the linear elastic phase, fiber activation, and fiber activation stages using stress versus crack width relationships. The derived relationships considering strength, reinforcement index, and fiber efficiency satisfactorily predict the moment capacity of UHPC beams with varying fiber dosages and geometrical dimensions. The proposed stress block parameters, denoted as alpha and beta, are presented for compression strength ranging up to 200 MPa and found suitable for designing structural members using UHPC.

Analytical study and design approach of the axial and flexural response of reinforced masonry columns confined with FRP jackets

Using fiber-reinforced polymer (FRP) wraps has proven to be an effective and optimized confinement technique to upgrade the axial and flexural capacity of reinforced concrete (RC) and reinforced masonry (RM) columns. The axial capacity of FRP-confined masonry depends on both the compressive strength of masonry before strengthening and the confinement pressure provided by the FRP jacket. This study proposes a simplified methodology to design and analyze prismatic fully grouted reinforced masonry columns (RMCs) strengthened with FRP Jackets. The proposed design methodology included an analytical confinement model to predict the compressive strength gain in RMCs due to the effective confinement pressure provided by FRP jackets. The proposed procedure was also designed to predict the nominal capacity of RMCs for practical design applications, with columns subjected to both axial loading and bending moment. The essential parameters to perform detailed section analysis were established, and suggested expressions were proposed to obtain the parameter values. Practical values for the equivalent rectangular stress block parameters were proposed. The theoretical axial force-moment interaction diagrams obtained by the proposed procedure were compared with available experimental data. The experimental test results were in good agreement with the analytical predictions by a reasonable marginal error. Furthermore, the effect of five design variables on the axial-flexural interaction of FRP-wrapped RMCs was investigated. The variables considered in the parametric study were the number of FRP layers, radius of the corners, stiffness of the FRP composite, cross-sectional aspect ratio, and masonry compressive strength. The results showed that increasing the FRP layers, corner radius, and FRP jacket stiffness significantly enhanced the axial capacity of the FRP-confined RMCs. However, the increase in the masonry compressive strength and cross-sectional aspect ratio negatively affected the axial capacity gain ratio of FRP-strengthened RMCs.

Flexural Strength and Behavioral Study of High-Performance Concrete Beams using Stress-Block Parameters

Most of the existing codes are using stress block parameters which were derived for normal strength concrete. Rectangular stress-block parameters used for normal strength concrete cannot be used safely for higher grade concrete like HPC, hence new stress-block parameters are established from the experimental investigations. Theses parameters can be made very much useful in the design of HPC members. Present research aims at behaviour study of HPC using stress block parameters. High performance concrete single span beams were tested under monotonic four-point bending. Considering the experimental stress-strain curves of HPC for grade 60, 80 and 100 MPa, an idealized stress block curve is established and the stress block parameters are derived. Based on the idealized stress block curve, the equations for ultimate moment of resistance, depth of neutral axis, limiting moment of resistance and maximum depth of neutral axis are proposed. Based on the observation of experimental load deformation curves, an ideal load deformation curve is proposed, which follows four significant events identified as, first cracking, yielding of reinforced steel, crushing of concrete with spalling of cover and ultimate failure. The predicted values compare well with the experimental values. The average location of the first crack observed was at 0.535 times the span of the beam from the left support of the observer in the tension zone.

Axial load–moment interaction diagram of full-scale circular LWSCC columns reinforced with BFRP and GFRP bars and spirals: Experimental and theoretical investigations

No research has yet been reported on the behavior of lightweight-aggregate self-consolidating concrete (LWSCC) columns reinforced with fiber-reinforced polymer (FRP) bars. LWSCC can be of great interest for reducing dead loads, section dimensions, and project costs, especially for precast elements. This paper presents, for the first time, the test results of a study conducted on 12 circular LWSCC columns reinforced with two types of FRP bars: basalt FRP (BFRP) and glass FRP (GFRP). In addition, columns with steel reinforcement were introduced into the test matrix as references. A mix design for the LWSCC with an equilibrium density of 1,807 kg/m3 and compressive strength of 52 MPa was developed and used to cast the columns. The columns were tested under concentric and eccentric loading. The test variables were the eccentricity-to-diameter ratio, and the type of reinforcement (steel versus GFRP and BFRP). The study was conducted to investigate whether the type of concrete and reinforcement affect the column performance and to develop the experimental load–moment interaction diagram. The load–strain behavior for the concrete, bars, and spirals; the load-deformation curves (axial and lateral); and the experimental P–M interaction diagrams are presented. An analytical study was conducted to predict the axial–flexural capacity. The effect of concrete density was considered in the analysis based on parameters in the codes for conventional and modified rectangular stress blocks. The test results indicate that the LWSCC columns with BFRP and GFRP reinforcement had behavior and strength comparable to their steel-reinforced counterparts when tested under different levels of eccentricity. The analytical results show that the column capacity was sensitive to variations in the rectangular stress-block parameters. Lastly, this study demonstrated the effectiveness of integrating GFRP and BFRP reinforcement into lightweight-aggregate concrete would play a role in producing lighter and more durable concrete members for precast applications.

Rectangular Stress-block Parameters for Fly-ash and Slag Based Geopolymer Concrete

Although there has been a numerous quantity of studies investigating the mechanical properties of geopolymer concrete (GPC), parameters for designing GPC structures are still not systematically investigated and carefully justified. ACI rectangular stress-block parameters are able to predict well the strength of conventional concrete structures but their applicability for GPC is questionable. This study aims to establish new sets of rectangular stress-block parameters for GPC with a broad range of the compressive strength up to 66 MPa. The proposed rectangular stress-block parameters in this study are based on two analytical concrete stress-strain models and measured curves from previous studies of GPC materials. The results from this study show that the use of ACI recommendations for concrete structure in designing GPC beams is still acceptable with high accuracy. However, the axial load-carrying capacity of GPC columns computed by ACI parameters deviate significantly from the experimental results while the proposed parameters provide a good correlation with these experimental data. The significant difference is mainly due to the modification of k3, which is the ratio of concrete strength in real structures to standard cylinder samples. This study suggests that the assumption of k3 = 0.9 in previous studies for conventional Portland concrete is not suitable for use in deriving the stress-block parameters of GPC. In some cases, this ratio should be reduced to 0.7 depending on the curing condition.

Rectangular Stress-Block Parameters for Bending Design of Reinforced UHTCC Beam

The full replacement of plain concrete with ultra-high toughness cementitious composite (UHTCC) in structural members can obtain the enhanced structural performance over traditional concrete structures because of its prominent advantages such as the markedly ductile deformation capacity after post-cracking and excellent damage tolerance ability. In the current article, aimed at setting up the theoretical formula for the practical use in the bending design of reinforced beam made of UHTCC, the equivalent parameters introduced in rectangular stress block approach are analytically determined. Two existing models in compression for UHTCC, i.e., bilinear model and parabolic line then horizontal line (nonlinear model) are adopted in the derivation of the equivalent parameters. By comparing moment-curvature curve obtained from the experiment with the calculated one, the nonlinear model is verified to be rational and could predict bending capacity with sufficient accuracy. Further comparison between moment-curvature curves calculated according to two compression models shows that the nonlinear model can give a bending response prediction with almost the same accuracy as the bilinear model. Finally, it is suggested that, in the case that nonlinear compression model is adopted for the compressive behavior in UHTCC, the equivalent parameters α=0.8 and β=1.0 could be used to estimate ultimate load bearing capacity of reinforced UHTCC beam.

Stress-Block Parameters for Unconfined and Confined Concrete Based on a Unified Stress-Strain Model

Equations to obtain equivalent rectangular stress-block parameters for unconfined and confined concrete are derived for rapid (hand) analysis and design purposes. To overcome a shortcoming of existing commonly used stress-strain models that are not easy to integrate, a new stress-strain model is proposed and validated for a wide range of concrete strengths and confining stresses. The efficacy of the equivalent rectangular stress-block parameters is demonstrated for hand calculations in predicting key moment-curvature results for a confined concrete column. Results are compared with those obtained from a computational fiber-element analysis using the proposed stress-strain model and another widely used existing model; good agreement between the two is observed.

Proposal for Concrete Compressive Strength up to 18 ksi (124 MPa) for Bridge Design

An extensive experimental and analytical research program was undertaken to recommend revisions to extend the applicability of flexural and compression design provisions for reinforced and prestressed concrete members of the AASHTO LRFD Bridge Design Specifications to concrete compressive strengths up to 18 ksi (124 MPa). The recommended provisions are intended to be seamless and unified over the full range of concrete strengths. The experimental program included tests of material properties; flexural, axial compression, and combined axial and flexure tests of reinforced concrete members; and flexural tests of prestressed concrete members. From the measured test results and the analytical study came several recommendations to revise the specifications; these include modulus of elasticity, modulus of rupture, creep and shrinkage, rectangular stress block parameters for flexural design, minimum area of prestressed, and nonprestressed longitudinal reinforcement for compression members and prestressed girders. The 4-year research program was sponsored by NCHRP and TRB.

Ductility enhancement of reinforced concrete thin walls

The ductility of reinforced concrete bearing walls subjected to high axial loading and moment can be enhanced by improving the deformability of the compression zone or by reducing the neutral axis depth. The current state-of-the-art procedure evaluating the confinement effect prompts a consideration of the spaces between the transverse and longitudinal reinforcing bars, and a provision of tie bars. At the same time, consideration must also be given to the thickness of the walls. However, such considerations indicate that the confinement effect cannot be expected with the current practice of detailing wall ends in Korea. As an alternative, a comprehensive method for dimensioning boundary elements is proposed so that the entire section of a boundary element can stay within the compression zone when the full flexural strength of the wall is developed. In this comprehensive method, the once predominant code approach for determining the compression zone has been advanced by considering the rectangular stress block parameters varying with the extreme compression fiber strain. Moreover, the size of boundary elements can also be determined in relation to the architectural requirement.

Early Cover Spalling in High-Strength Concrete Columns

The American Concrete Institute (ACI) 318-02 provisions for stress block parameters were derived using normal-strength concrete column tests. Azizinamini et al. in 1994, Ibrahim and MacGregor in 1996, Bayrak in 1999 have reported that the use of current ACI stress block parameters results in estimations that are not conservative for high-strength concrete column sections. This was mainly attributed to the early cover spalling in high-strength concrete columns. In this paper, a numerical procedure for simulating premature cover spalling in high-strength concrete columns (66 MPa<\if′\dc<140 MPa) is presented. The proposed method for nominal moment capacity calculation employs rectangular stress block parameters and an analytically derived strength reduction parameter to integrate the effect of early cover spalling into the design process. Although the proposed method for moment capacity calculation is analytically derived, its results are validated with the experimental data from 224 column tests reported in the literature. Twenty-four of the 224 tests were conducted by Bayrak as part of a comprehensive research program in which the behavior of reinforced concrete columns was studied and provided the motivation for the research reported here. ACI 318-02 provisions for stress block parameters are critically examined using the experimental data from 224 tests. It is concluded that the ACI stress block parameters do not result in conservative estimations for the moment capacity of high-strength concrete column sections failing in compression. However, the proposed technique results in conservative estimations of strength for high-strength concrete column designs as well as normal strength concrete column designs.

Determination of rectangular stress block parameters for high performance concrete

Despite so much research on high performance concrete, the properties of this concrete are not known as well as those of ordinary concrete. There have been a lot of equations, rules and suggestions in the codes which are used in the design of reinforced concrete and prestressed concrete structures. They are obtained from experimental studies made on concrete that have compressive strength of less than about 40 MPa. It is not exactly known whether they could be used in the design of structures constructed by using high performance concrete. Therefore in this study, stress-strain and equivalent block parameters were obtained from experimental stress-strain diagrams for calculation of high performance reinforced concrete beams in flexure. The conclusions obtained from this study showed that determined rectangular stress block parameters can be used in the design of high performance reinforced concrete members in flexure.