Simplified Shear Design Method for Concrete Beams Strengthened with Fiber Reinforced Polymer Sheets

This paper presents a simplified shear design method for reinforced concrete beams strengthened externally with fiber reinforced polymer (FRP) sheets. This design method combines both the strip method and the shear friction approach. The background of the strip method is presented in detail, including the interface shear strength curve, which is compared with some available bond test data found in the literature. A parametric study is performed to propose two simplified equations, which describe the FRP sheet contribution. This contribution is added to the discrete shear friction formulation and, by derivation, a continuous and simplified design equation is proposed. This method well describes the interaction between the concrete, the stirrups, and the FRP sheets. A variable concrete crack angle is used, which enhances the accuracy of the model. No iteration is required. The proposed design formulation gives conservative predictions with 35 experimental test results found in the literature.     

Theoretical Study of Strengthening for Increased Shear Bearing Capacity

In recent years, the use of carbon fiber reinforced polymer (CFRP) has been shown to be a competitive method for strengthening both the structural and economic performance of concrete. The method has been used for almost a decade, yet – most research undertaken has studied the flexural behavior of strengthened structures, while research on shear strengthening has been limited. The work presented in this paper focuses on CFRP shear strengthening of concrete beams. The theory presented addresses the limitations of the widely used truss model, and a refinement is suggested. A reduction factor to consider the nonuniform strain distribution over the cross section is proposed and strain limitations are prescribed for the principal strain in the concrete instead of the fiber strain, as in previous studies. The derived analytical model is compared to experimental data from tests. Fairly good agreement is found between results from tests and calculated values from theory with regard to both shear-bearing capacity and average fiber utilization.     

Does the Use of FRP Reinforcement Change the One-Way Shear Behavior of Reinforced Concrete Slabs?

For members with no transverse reinforcement, numerous models have been proposed for determining shear capacity, most often based on a statistical curve fit to experimental beam test results. The shear provisions of the Canadian code (CSA) for steel-reinforced concrete, by contrast, are based on a theoretical model, the modified compression field theory. This paper demonstrates that the CSA shear provisions for steel-reinforced members can be safely applied to members with internal fiber-reinforced polymer (FRP) bars by adjusting the term EsAs in the method to ErAr. A database of 146 shear failures of specimens reinforced with carbon, glass, or aramid FRP or steel is presented and gives an average test to predicted ratio of 1.38 with a coefficient of variation (COV) of 17.2%. The CSA code equations were optimized for the typical strain range of steel-reinforced concrete and when an equation appropriate for the wider range of strains associated with FRP is used, then a better statistical result can be achieved. Application of this expression to the database resulted in an average test to predicted strength ratio of 1.15 with a COV of 14.9%. As both methods are based on a theoretical shear model that was derived for steel-reinforced concrete and since both methods work safely, it can be concluded that the use of internal FRP bars does not change the one-way shear behavior of reinforced concrete beams and slabs without stirrups.     

Role of Fiber Reinforced Plastic Sheets in Shear Response of Reinforced Concrete Beams: Experimental and Analytical Results

The paper is principally aimed at analyzing the role of externally applied fiber reinforced plastic (FRP) sheets in the shear ultimate behavior of reinforced concrete elements. A theoretical model for predicting the shear resisting contribution of FRP sheets is illustrated. The proposal is based on a complete equilibrium/compatibility approach for reinforced concrete beams failing in shear and considers the possible interactions between the composite contribution and the resisting mechanisms of an ordinary reinforced concrete beam. The proposal is discussed and tested by means of an experimental investigation carried out on beams reinforced by glass FRP composite sheets with a shear span to depth ratio equal to 3. Further comparisons are then performed that consider the predictions of other existing approaches reported in the literature.     

Model for Dynamic Analysis of Wood Frame Shear Walls

A discrete three-degree-of-freedom model of a wood frame shear wall has been developed that is suitable for design-type analyses. The model captures the salient features of the wall response, is amenable to exact closed-form solution, and has the flexibility to account for variations in wall geometry, framing and sheathing materials, fastener type, and spacing. Sheathing-to-stud connections are modeled using a linear viscoelastic element; a method is presented for determining the connection properties using the results of full-scale shear wall tests and a closed-form solution for the test excitation. Results show that the model accurately predicts the hysteretic behavior of the wall for low to moderate displacements; at larger displacements the linear model captures the overall behavior (effective stiffness and energy dissipation), but, as would be expected, fails to predict the pinched hysteresis observed in the tests. Finally, a response spectrum analysis is conducted of a single-story wood frame structure to demonstrate how the model can be used for design-type analyses.     

Maximum Shear Strength of RC Beams Retrofitted in Shear with FRP Composites

In reinforced concrete (RC) beams strengthened in shear with fiber-reinforced polymer (FRP), crushing of the web can be a potential mode of failure. The guidelines provided by codes and standards for the design of structures strengthened with externally bonded FRP recommend limiting the maximum shear strength to avoid such an undesirable failure scenario. However, these limitation provisions are not based on specific research studies performed on beams strengthened in shear with FRP. Rather, they simply duplicate provisions used in conventional concrete codes and standards. The main objective of this research study is to assess the suitability of the limits specified by the guidelines, and propose, if necessary, an alternative equation as an upper limit for shear strength against web crushing failure in such structures. To this end, an analytical approach was developed based on the static theorem of the theory of plasticity. The predictions of the equations resulting from this approach were compared with those obtained from tests reported in the literature and with those predicted by ACI Committee 440-02, Canadian Standard S6-06, and the European recommendations fib TG 9.3. The study shows that the current ACI Committee 440-02 and Canadian Standards provisions are overly conservative and therefore need to be reviewed.     

Shear Strength of Fiber-Reinforced Sands

Soil reinforcement using discrete randomly distributed fibers has been widely investigated over the last 30 years. Several models were suggested to estimate the improvement brought by fibers to the shear strength of soils. The objectives of this paper are to (1) supplement the data available in the literature on the behavior of fiber-reinforced sands; (2) study the effect of several parameters which are known to affect the shear strength of fiber-reinforced sands; and (3) investigate the effectiveness of current models in predicting the improvement in shear strength of fiber-reinforced sand. An extensive direct shear testing program was implemented using coarse and fine sands tested with three types of fibers. Results indicate the existence of a fiber-grain scale effect which is not catered for in current prediction models. A comparison between measured and predicted shear strengths indicates that the energy dissipation model is effective in predicting the shear strength of fiber-reinforced specimens in reference to the tests conducted in this study. On the other hand, the effectiveness of the predictions of the discrete model is affected by the parameters of the model, which may depend on the test setup and the procedure used for mixing the fibers.     

Shear Analysis of Concrete with Brittle Reinforcement

The design of steel-reinforced concrete relies on lower-bound plasticity theory, which allows an equilibrium-state to be postulated without considering compatibility. This is of particular benefit in shear design, due to the complexity of shear-transfer, where simplified models such as the truss analogy are used. Lower-bound plasticity theory, however, relies on stress-redistribution. If brittle reinforcement [such as fiber-reinforced-plastic (FRP)] is used in concrete, lower-bound plasticity theory cannot be applied. This paper studies how compatibility, equilibrium, and the material constitutive laws can be combined to establish the actual conditions within an FRP-reinforced beam subjected to shear. A crack-based analysis is proposed to model shear failure in a beam with brittle reinforcement. The analysis is used to illustrate the importance of satisfying compatibility requirements, and the results are contrasted with the current shear design proposals for FRP-reinforced concrete.     

Thermo-Chemo-Mechanical Model for Concrete. II: Damage and Creep

In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. This paper presents the formulation and assessment of the mechanical aspects of the model. Short- and long-term mechanical behaviors are modeled via a viscoelastic damage model that accounts for the aging effects. The short-term model is based on the framework of the continuum damage mechanics theory. A novel normalized format of the damage model is proposed, so that the phenomenon of aging is accounted for in a natural fashion. Long-term effects are included by incorporating a creep model inspired in the microprestress-solidification theory.     

Model for Reinforced Concrete Members under Torsion, Bending, and Shear. I: Theory

A model has been developed that can predict the load-deformation response of a reinforced concrete (RC) member subjected to torsion combined with bending and shear to spalling or ultimate capacity. The model can also be used to create interaction surfaces to predict the failure of a member subjected to different ratios of applied torsion, bending, and shear. The model idealizes the sides of an reinforced concrete member as shear “wall panels.” The applied loads are distributed to the wall panels as uniform normal stresses and uniform shear stresses. The shear stress due to an applied torsional moment and shear force are summed over the thickness of the shear flow zone. Stress-strain relationships are adopted for tension stiffening and softened concrete in compression. The crack alignment rotates to remain normal to the principal tensile stress and the contribution of concrete in shear is neglected. The model has been validated by comparing the predicted and experimental behavior of members loaded under torsion combined with different ratios of bending and shear. The torque-twist behavior, reinforcement stress, and concrete surface strain predicted by the model were in agreement with experimental results.     

砂卵石土的剪切流变特性研究

应用RYL-600岩石剪切流变仪对长沙市某边坡砂卵石土试样进行剪切流变试验,分析砂卵石土的剪切流变特性。试验表明正应力越高时,能够引起砂卵石土试件发生剪切流变破坏的剪切应力也随之增高。砂卵石土剪切流变在低于长期抗剪切强度的应力作用下,表现出黏弹特性;在高于长期强度的应力作用下,表现出黏弹塑性。应用五元黏弹性模型与VR黏塑性模型串联得到的黏弹塑性模型对砂卵石土全程流变曲线进行模拟,将拟合结果与试验数据进行分析比较,验证了新模型具有正确性和合理性,这对砂卵石土工程具有重要的指导意义和参考价值。     

Wedge type creep damage in low cycle fatigue

A model is proposed to quantify the accumulation of wedge type creep damage in low cycle fatigue. It is proposed that such damage is produced primarily during the ramp periods of the cycle. Equations are developed for estimating incremental accumulation of damage per cycle in fully reversed, multiaxial loading. The rate of accumulation of damage depends on the strain-rate, the temperature, and the microstructure. The analysis is kept simple by making physically reasonable assumptions. Cycles to failure are predicted by invoking a fracture criterion. The model is applied to two sets of data; one set is a well characterized life test data on an aluminum alloy, and the other is phenomenological data on austenitic stainless steels. In both cases the predictions are good enough to prompt further experimental evaluation of the model. This paper deals with only one mechanism of creep-fatigue interaction. Other mechanisms of failure,e.g., ‘r’ type cavitation, or fatigue crack initiation and propagation, are also viable. The model described here may be expected to apply only under those conditions when wedge damage is the dominant failure mechanism.     

Shear Strength of One-Way Concrete Slabs Reinforced with Fiber-Reinforced Polymer Composite Bars

This paper evaluates the shear strength of one-way concrete slabs reinforced with different types of fiber-reinforced polymer (FRP) bars. A total of eight full-size slabs were constructed and tested. The slabs were 3,100?mm?long×?1,000?mm?wide×200?mm?deep. The test parameters were the type and size of FRP reinforcing bars and the reinforcement ratio. Five slabs were reinforced with glass FRP and three were reinforced with carbon FRP bars. The slabs were tested under four-point bending over a simply supported clear span of 2,500 mm and a shear span of 1,000 mm. All the test slabs failed in shear before reaching the design flexural capacity. The experimental shear strengths were compared with some theoretical predictions, including the JSCE recommendations, the CAN/CSA-S806-02 code, and the ACI 440.1R-03 design guidelines. The results indicated that the ACI 440.1R-03 design method for predicting the concrete shear strength of FRP slabs is very conservative. Better predictions were obtained by both the CAN/CSA-S806-02 code and the JSCE design recommendations.     

Shear Resistance of FRP RC Beams: Experimental Study

This study investigates the shear behavior of concrete beams reinforced with fiber-reinforced polymer (FRP) reinforcement. Six beams were subjected to two successive phases of testing. Half of the beams were reinforced in flexure with conventional steel reinforcement, while the other half were reinforced with glass fiber bars. Different shear span to depth ratios, ranging from 1.1 to 3.3, were analyzed in order to study the variation in the shear behavior of beams characterized by different types of shear failure. No shear reinforcement was provided in the first phase of testing, while in the second phase, just enough glass and carbon shear reinforcement was provided to enable failure due to shear. The results of these tests are presented and compared to predictions according to the design recommendations proposed by the ACI and the Institution of Structural Engineers, U.K. The results of this study show that these approaches, which are based on modifications of equations derived for steel reinforcement, underestimate the contribution of the concrete and the shear reinforcement to the total shear capacity of FRP RC beams. It is shown that both approaches can be modified to become less conservative.     

Experimental Behavior of Bridge Beams Retrofitted with Postinstalled Shear Connectors

A number of older bridges were constructed with floor systems consisting of a noncomposite concrete slab over steel girders. A potentially economical means of strengthening these floor systems is to connect the existing concrete slab and steel girders with postinstalled shear connectors to permit the development of composite action. This paper presents the results of an experimental investigation of this concept. Five large-scale noncomposite beams were constructed, and four of these were retrofitted with postinstalled shear connectors and tested under static load. The retrofitted composite beams were designed as partially composite with a 30% shear connection ratio. A noncomposite beam was also tested as a baseline specimen. Test results showed that the strength and stiffness of existing noncomposite bridge girders can be increased significantly. Further, excellent ductility of the strengthened partially composite girders was achieved by placing the postinstalled shear connectors near zero-moment regions to reduce slip demand on the connectors. The test results also showed that current simplified design approaches commonly used for partially composite beams in buildings provide good predictions of the strength and stiffness of partially composite bridge girders strengthened using postinstalled shear connectors.     

Concrete Contribution to the Shear Resistance of Fiber Reinforced Polymer Reinforced Concrete Members

Seven beams were tested in bending to determine the concrete contribution to their shear resistance. The beams had similar dimensions and concrete strength and were reinforced with carbon fiber reinforced polymer bars for flexure without transverse reinforcement. They were designed to fail in shear rather than flexure. The test variables were the shear span to depth ratio, varying from 1.82 to 4.5, and the flexural reinforcement ratio, varying from 1.1 to 3.88 times the balanced strain ratio. The test results are analyzed and compared with the corresponding predicted values using the American Concrete Institute, the Canadian Standard, and the Japan Society of Civil Engineers (JSCF) fiber reinforced polymer design recommendations. Based on these results and previous experimental data, it is shown that the ACI recommendations are extremely conservative whereas the Canadian and JSCE recommendations, albeit still conservative, are in closer agreement with the experimental data. Overall the Canadian Standard’s predictions are in better agreement with experimental data than the JSCE predictions.     

Finite Element Response Sensitivity Analysis of Steel-Concrete Composite Beams with Deformable Shear Connection

The behavior of steel-concrete composite beams is strongly influenced by the type of shear connection between the steel beam and the concrete slab. For accurate analytical predictions, the structural model must account for the interlayer slip between these two components. In numerous engineering applications (e.g., in the fields of structural optimization, structural reliability analysis, and finite element model updating), accurate response sensitivity calculations are needed as much as the corresponding response simulation results. This paper focuses on a procedure for response sensitivity analysis of steel-concrete composite structures using displacement-based locking-free frame elements including deformable shear connection with fiber discretization of the cross section. Realistic cyclic uniaxial constitutive laws are adopted for the steel and concrete materials as well as for the shear connection. The finite element response sensitivity analysis is performed according to the direct differentiation method. The concrete and shear connection material models as well as the static condensation procedure at the element level are extended for response sensitivity computations. Two steel-concrete composite structures for which experimental test results are available in the literature are used as realistic testbeds for response and response sensitivity analysis. These benchmark structures consist of a nonsymmetric, two-span continuous beam subjected to monotonic loading and a frame subassemblage under cyclic loading. The new analytical derivations for response sensitivity calculations and their computer implementation are validated through forward finite difference analysis based on the two benchmark examples considered. Selected sensitivity analysis results are shown for validation purposes and for quantifying the effect and relative importance of the various material parameters in regards to the nonlinear monotonic and cyclic response of the testbed structures.     

Rational Approach to Shear Design in Fiber-Reinforced Polymer-Prestressed Concrete Structures

The use of plasticity-based shear design methods for fiber-reinforced polymer (FRP) reinforced and prestressed concrete, as they are used at present, is inappropriate in the long term. In particular, the use of a plasticity-based truss model for shear behavior seems to be unsound, as reliance is placed on a predominantly elastic zone to redistribute stresses. A better approach to shear design would be to employ a model incorporating force equilibrium and compatibility of strains so that the elastic properties of the FRP could be included rationally. This would help to develop a real understanding and form a basis on which new guides and codes could be founded. In tandem with a more rational analytical approach, new configurations and types of FRP reinforcement need to be developed and researched so that these materials can be used more efficiently. An analytical approach to investigate the shear response of FRP-reinforced and -prestressed concrete has been developed, based on equilibrium and compatibility across a shear discontinuity. The analytical model presented here was developed in conjunction with an experimental program. Correlation between the analytical and experimental results is good and more accurate than the current guideline provisions for concrete beams containing FRP reinforcement.     

Concept and Finite-Element Modeling of New Steel Shear Connectors for Self-Centering Wall Systems

Self-centering precast concrete walls have been found to provide excellent seismic resistance. Such systems typically exhibit low energy dissipation, requiring supplementary dissipating components to improve their seismic performance. Mild steel shear connectors can provide an economical energy dissipating element. The design and analysis of steel shear connectors for a new precast wall system has been undertaken. A series of finite-element analyses were conducted to investigate the behavior of different types of connectors. Emerged from these analyses is a oval-shaped connector (O-connector) that provided satisfactory force-displacement behavior and appeared well suited for the new wall system in high seismic regions. An extensive experimental test program was then conducted to verify the performance of the chosen O-connector, which confirmed the expected response with sufficient energy dissipation. The experimental data demonstrated good correlation with the finite-element model developed, providing satisfactory confidence in the finite-element technique used for the development of the different connectors.     

Determination of Shear and Bulk Moduli of Viscoelastic Solids from the Indirect Tension Creep Test

Because of its efficiency in analyzing complex viscoelastic problems, the finite-element (FE) analysis has been widely used to identify the time- and rate-dependent effects of viscoelastic materials on various structural conditions. When performing the FE analysis on a viscoelastic structure, most FE programs require fundamental material properties, shear and bulk moduli, of the given viscoelastic material as their input. However, the shear and bulk modulus tests are difficult to perform, so they have been commonly estimated from a single material test on the basis of the assumption that the Poisson’s ratio of viscoelastic materials is a time-independent constant. Such an assumption, however, might not be suitable because the Poisson’s ratio of the viscoelastic materials is also a function of time. Therefore, this study developed computation algorithms for determining the time-dependent Poisson’s ratio and shear and bulk moduli of asphalt mixtures, which have been well recognized as a viscoelastic material, by employing the indirect tension testing system. The shear and bulk moduli determined by the developed approach appear to be reasonable and realistic. Their applicability and reliability were also verified by comparing experimental data to the results of the FE analysis performed on the same circular specimen as that used in the indirect tension creep test.