Symmetric Point Loads Research Articles

Experimental Behavior of the Curved Continuous Twin I-Girder Composite Bridge with a Precast Concrete Slab Subjected to Bending, Shear, and Torsion

In order to investigate the mechanical behavior, ultimate load carrying capacity, and failure mode of the intact curved continuous twin I-girder composite bridge (TGCB) with a precast concrete slab, one curved continuous composite bridge model with a scale ratio of 1 : 5 of a prototype bridge was designed and manufactured considering the influence of the construction sequence. Four symmetric point loads’ test was carried out. In this paper, load-deflection relationship and strain development of steel girders, concrete slab, and reinforcement at key sections were tested and analyzed. Failure mode, crack development, and major crack width at the top surface of the concrete slab in the hogging moment region were also reported. The experimental results demonstrated that the load capacity under the initial cracking level, cracking level with the width of 0.2 mm, and steel girder yielding state is about 1.7, 5.0, and 6.3 times of the design load, respectively. Due to the influence of curvature, the stiffness of the external girder is less than that of the internal girder. However, the ultimate bearing capacity is basically the same, approximately 13.6 times of the design load. During the loading process, plastic hinge was first observed at the intermediate support section as a result of the hogging moment which should be emphasized in design. The local buckling took place after yielding, indicating a class 2 section according to Eurocode 4. In addition, the TGCB had good ductility since the displacement ductility coefficients of the external and internal girders were 4.40 and 4.06, respectively.

The floating plate–load system: a new stability problem

The interesting problem of a flat elastic plate and a weight which would sink individually but may float as a system is presented. Using beam and plate theories, the two-dimensional strip and the circular disc are solved exactly for the minimum width for which the system would float. Three types of loading are considered: a centered point load, two symmetric point loads or a ring load, and a continuous uniform load. These problems represent a new class of stability problems which illustrate the interaction of load, elasticity, and hydrostatics.

Elastic analysis of interfacial stresses in prestressedPFGM-RC hybrid beams

In this paper, the problem of interfacial stresses in damaged reinforced concrete beams strengthened with bonded prestressed functionally graded material plate and subjected to a uniformly distributed load, arbitrarily positioned single point load, or two symmetric point loads is developed using linear elastic theory. The adopted model takes into account the adherend shear deformations by assuming a linear shear stress through the depth of the damaged RC beam. This solution is intended for application to beams made of all kinds of materials bonded with a thin FGM plate. The results show that there exists a high concentration of both shear and normal stress at the ends of the functionally graded material plate, which might result in premature failure of the strengthening scheme at these locations. Finally, numerical comparisons between the existing solutions and the present new solution enable a clear appreciation of the effects of various parameters of the beams on the distributions of the interfacial stresses.

Analytical analysis of the interfacial shear stress in RC beams strengthened with prestressed exponentially-varying properties plate

In this paper, a closed-form rigorous solution for interfacial shear stress in simply supported beams strengthened with bonded prestressed E-FGM plates and subjected to an arbitrarily positioned single point load, or two symmetric point loads is developed using linear elastic theory. This improved solution is intended for application to beams made of all kinds of materials bonded with a thin plate, while all existing solutions have been developed focusing on the strengthening of reinforced concrete beams, which allowed the omission of certain terms. The theoretical predictions are compared with other existing solutions. Finally, numerical results from the present analysis are presented to study the effects of various parameters of the beams on the distributions of the interfacial shear stresses. The results of this study indicated that the E-FGM plate strengthening systems are effective in enhancing flexural behavior of the strengthened RC beams.

Behavior of continuous steel-concrete composite beams with web openings

In order to investigate the mechanical performance and load carrying capacity of continuous steel-concrete composite beams with web openings, five continuous composite beams with web openings and a contrasting continuous composite beam without web openings were tested through two symmetric point loads. Nonlinear finite element analysis was also conducted, in which the slab thickness and the reinforcement ratio of slabs were selected as the major parameters. The main results of this test were concluded as follows: (1) Web openings not only decrease the stiffness and ultimate load carrying capacity of continuous composite beams but also give rise to the redistribution of vertical shear force between the cross section of the steel beam and the concrete slab at the web opening region. (2) The plane hypothesis is not satisfied at the web opening region. The failure mode of continuous composite beams with web openings is the shear failure of concrete slab in the region near the opening, and the result also indicates that the shear bearing capacity at the span with web openings become a critical factor in controlling design. (3) Meanwhile, by increasing the thickness and reinforcement ratio of a concrete slab, the ultimate load carrying capacity and ductility of continuous composite beams increased, which can be used to the enhancement of web opening region. (4) In addition, based on the experimental results, a finite element mode was established for composite beams with web openings, and good agreement was obtained between the tested results and the numerical results.

Flexure Behavior of High Strength Concrete (HSC) Beams Reinforced With Carbon Fiber Reinforced Polymer (CFRP) Rebars With and Without Chopped Carbon Fiber (CCF)

The flexure strength and behavior of high strength concrete beams reinforced with carbon fiber reinforcement (CFRP) rebars with and without chopped carbon fiber (CCF) were investigated by conducting flexural testes on a total of 27 simply supported HSC beams under two symmetrical point loads. The main parameters considered in the study were the reinforcement ratio ρ, compressive strength of the concrete f`c and volume fraction of chopped carbon fiber Vf. It can be seen from the experimental results that the maximum carrying capacity increases as the reinforcement ratio, concrete compressive strength and the volume fraction of copped carbon increases. Crack spacing of the fiber reinforced concrete (FRC) beams was about 20% smaller than plain concrete beams at service load (30% of ultimate load). Addition of fibers significantly improves the system’s ductility; nonetheless the ductility index depends on amount of reinforcement (higher reinforcement allows for lower deformation, thus a lower ductility index) obtained.

Exact least-volume trusses for two symmetric point loads and unequal permissible stresses in tension and compression

In this Authors' Reply previously presented solutions are extended to unequal permissible stresses in tension and compression, comments are made on the lack of adjoint displacement fields in so-called O-regions (memberless regions), and some computational details are explained.

Interfacial stress analysis of steel beams reinforced with bonded prestressed FRP plate

In this paper, a closed-form rigorous solution for interfacial stress in simply supported beams strengthened with bonded prestressed FRP plates and subjected to a uniformly distributed load, arbitrarily positioned single point load, or two symmetric point loads is developed using linear elastic theory and including the variation in FRP plate fibre orientation. The results show that there exists a high concentration of both shear and normal stress at the ends of the laminate, which might result in premature failure of the strengthening scheme at these locations. A parametric study has been conducted to investigate the sensitivity of interface behavior to parameters such as laminate and adhesive stiffness, the thickness of the laminate and the fibre orientations where all were found to have a marked effect on the magnitude of maximum shear and normal stress in the composite member.

Finite element non-linear analysis of reinforced concrete beams with openings

In this study, behaviour of reinforced concrete beams containing rectangular openings, subjected to two symmetrical point loads and simply supported at its ends are studied under increasing loads by nonlinear finite element method and effects of the loss of section due to openings on the load-carrying capacity of the beams and the necessary conditions in design are investigated. Numerical solutions are explained for various opening locations and numbers on two groups of beams with web reinforcement and without. The effects of the web openings and web reinforcement on the load-carrying capacity of the beams are investigated. According to the results obtained, it is observed that the loadcarrying capacity of the beams is affected positively provided that web openings are arranged close to the tension zone in the middle of the span and to the compression zone at the support and the ultimate strength of the beams increases in case of reinforcing the sides of the openings.

Static buckling appraisal of an echinodome

The buckling behavior of an underwater shell of revolution structure of optimum form—an echinodome—is examined under axisymmetric and symmetric point loads both experimentally and theoretically. For the concentrated loadings, experimental predictions of critical buckling are based on the Southwell technique and a possible alternative method is suggested. Bifurcation and nonlinear collapse buckling analyses are described theoretically. Within the bifurcation investigation both linear and nonlinear approaches are included. The effects of base fixity on the instability of the structure are considered. Comparisons are made with earlier external-pressure loading effects and the relative significance of the two forms of loading are discussed.

Debonding of Steel Plate‐Strengthened Concrete Beams

The behavior of damaged concrete beams strengthened by externally bonded steel plates is analytically investigated using linear elastic fracture mechanics and the finite element method. The study includes investigation of the failure by interface debonding of the steel plate and the adhesive layer due to interfacial shear stress which exists at the interface. The principles of the conservation law of elasticity are used to determine the critical strain energy release rate required to cause the interfacial crack to propagate. Simply supported beams under monotonically increasing symmetrical loads are considered exclusively. It is found that the failure by debonding is dependent on the stress near the interfacial crack tip and on the critical strain energy release rate required for crack propagation. For the beam size [4×4×96in. (101.6×101.6×2,438.4mm)] and the loading configuration [two symmetrical point loads spaced 24 in. (609.4 mm) apart] studied in this investigation, the results indicates that the mos...

Shear Strength of Ferrocement Beams

An experimental investigation was carried out on a total of 28 simply supported ferrocement I-beams loaded in flexure under two symmetrical point loads. The major parameters considered in the study were the shear span-to-depth ratio a/h, compressive strength of the mortar, and amount of longitudinal and transverse reinforcement. The results of these tests are presented and discussed. Test results indicate that the beams fail in shear only when the a/h is less than or equal to 1.5. Beyond this value, failure occurs in flexure. Analyses are presented to predict the cracking and ultimate strength of such beams in shear as well as flexure. A comaprison of theoretical predictions with experimental results shows good agreement.

A homotopy method applied to elastica problems

The inverse problem in nonlinear (incompressible) elastica theory, where the end positions and inclinations rather than the forces and moment are specified, is considered. Based on the globally convergent Chow-Yorke algorithm, a new homotopy method which is simple, accurate, stable, and efficient is developed. For comparison, numerical results of some other simple approaches (e.g. Newton's method based on shooting or finite differences, standard embedding) are presented. The new homotopy method does not require a good initial estimate, and is guaranteed to have no singular points. The homotopy method is applied to the problem of a circular elastica ring subjected to N symmetrical point loads, and numerical results are given for N = 2,3,4.

The diagonal cracking strength of continuous prestressed concrete beams

Synopsis Results of tests on 20 two-span un bonded prestressed concrete I beams failing infiexure and shear under symmetrical point loads are presented. Under shear failure, the mechanism offailure being that of diagonal tension cracking only, a fracture criterion suitable for concrete is adopted to predict this cracking strength. Various existing methods of predicting the cracking strength of pre-tensioned and post-tensioned I beams are compared with the present proposal.