• Proceedings of the Korea Concrete Institute Conference
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• 2003.11a
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• pp.229-233
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• 2003

This paper describes a practical formulation of Non-Bernoulli-Compatibility Truss Model. Not only equilibrium conditions but also some approximations are employed to solve for the unknowns included in the proposed model. By assuming that the ratio of $V_a$ to V remains to be constant along the shear span, the relationship between $\alpha$ and z is mathematically established as an arch shape function. $V_m$ is also approximated to be an empirical value that is equal to the least membrane shear strength. The coefficient a is made utilizing a nonlinear finite element analysis. The adequacy of the model is examined by test results available in literatures, and the predicted values are shown to be in excellent agreement with the experimental results.

• Structural Engineering and Mechanics
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• v.38 no.5
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• pp.593-618
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• 2011

This paper deals with the problem of the determination of the response of a viscoelastic Bernoulli-Navier beam, which is resting on an elastic medium. Assuming uniaxial bending, the displacement of the beam axis is governed by an integro-differential equation. The compatibility of the displacements between the beam and the elastic medium is imposed through an integral equation. In general and in particular in the case of a Boussinesq medium, the solution has to be pursued numerically. On the contrary, in the case of a Winkler's medium the compatibility equation becomes a linear finite relationship, which allows finding an original analytical solution of the problem for both hereditary and aging behavior of the beam. Some numerical examples complete the paper, in which a comparison is made between the hereditary and the aging model for the creep of the beam.

• Structural Engineering and Mechanics
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• v.2 no.1
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• pp.1-16
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• 1994

A unified theory has recently been developed for reinforced concrete structures (Hsu 1993), subjected to the four basic actions - bending, axial load, shear and torsion. The theory has five components, namely, the struts-and-ties model, the equilibrium (or plasticity) truss model, the Bernoulli compatibility truss model, the Mohr compatibility truss model and the softened truss model. Because the last three models can satisfy the stress equilibrium, the strain compatibility and the constitutive laws of materials, they can predict not only the strength, but also the load-deformation history of a member. In this paper the five models are summarized to illustrate their intrinsic consistency.

• Journal of the Korea Concrete Institute
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• v.18 no.3 s.93
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• pp.379-388
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• 2006

This paper presents a model for evaluating the contribution by arch action to shear resistance in shear-critical reinforced concrete beams. Based on the relationship between shear and bending moment in beams subjected to combined shear and bending, the behavior of a beam is explicitly divided into two base components of the flexural action and the tied arch action. The compatibility condition of the shear deformation that deviates from Bernoulli bending plane is formulated utilizing the smeared truss idealization with an inclined compression chord. The Modified Compression Filed Theory is employed to calculate the shear deformation of the web, and the relative axial displacements of the compression and the tension chord by the shear flow are also calculated. From this shear compatibility condition in a beam, the shear contribution by the arch action is numerically decoupled. Then the validity of the model is examined by applying the model to some selected test beams in literatures. The results may confirm the rationale of the proposed behavioral model.

• Proceedings of the Korea Concrete Institute Conference
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• 2006.05a
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• pp.362-365
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• 2006

This paper presents a model for evaluating the contribution by arch action to shear resistance in shear-critical RC beams. Based on the relationship between shear and bending moment in beams subjected to combined shear and bending, The behavior of a beam is explicitly divided into two base components of the flexural action and the tied arch action. The compatibility condition of the shear deformation that deviates from Bernoulli bending plane is formulated utilizing the smeared truss idealization with an inclined compression chord. From this shear compatibility condition in a beam, the shear contribution by the arch action is numerically decoupled.

• Structural Engineering and Mechanics
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• v.72 no.2
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• pp.217-227
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• 2019

The methodology known as "shape sensing" allows the reconstruction of the displacement field of a structure starting from strain measurements, with considerable implications for structural monitoring, as well as for the control and implementation of smart structures. An approach to shape sensing is based on the inverse Finite Element Method (iFEM) that uses a variational principle enforcing a least-squares compatibility between measured and analytical strain measures. The structural response is reconstructed without the knowledge of the mechanical properties and load conditions but based only on the relationship between displacements and strains. In order to efficiently apply iFEM to the most common structural typologies of civil engineering, its formulation according to the kinematical assumptions of the Bernoulli-Euler theory is presented. Two beam inverse finite elements are formulated for different loading conditions. Depending on the type of element, the relationship between the minimum number of required measurement stations and the interpolation order is defined. Several examples representing common applications of civil engineering and involving beams and frames are presented. To simulate the experimental strain data at the station points and to verify the accuracy of the displacements obtained with the iFEM shape sensing procedure, a direct FEM analysis of the considered structures is performed using the LUSAS software.

• Journal of the Korea Concrete Institute
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• v.18 no.6 s.96
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• pp.819-825
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• 2006

The objective of the present study is to verify the validity of a new truss model for evaluating the contribution by arch action to shear resistance in shear-critical reinforced concrete beams. The new truss model is based on the relationship between shear and bending moment in a beam subjected to combined shear and bending. The compatibility condition of the shear deformation that deviates from Bernoulli bending plane is formulated utilizing the smeared truss idealization with an inclined compression chord. The Modified Compression Filed Theory is employed to calculate the shear deformation of the web, and the relative axial displacements of the compression and the tension chord by the shear flow are also calculated. From this shear compatibility condition in a beam, the shear contribution by the arch action is numerically decoupled. Then the validity of the model is examined by applying the model to some selected test beams in literatures. On the basis of the analytical results, the contribution by the web to shear resistance can be constant and have an excellent linear correlation with the web reinforcement ratio. The present decoupling approach may provide a simple way for the assessment of the role of each parameter or mechanism that affects the ultimate shear behavior of reinforced concrete beams.

• Steel and Composite Structures
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• v.38 no.3
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• pp.257-270
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• 2021

This paper presents a displacement-based numerical methodology following the Euler-Bernoulli theory to simulate the 2 nonlinear behavior of steel structures. It is worth emphasizing the adoption of co-rotational finite element formulations considering large displacements and rotations and an inelastic material behavior. The numerical procedures proposed considers plasticity concentrated at the finite elements nodes, and the simulation of the steel nonlinear behavior is approached via the Strain Compatibility Method (SCM), where the material constitutive relation is used explicitly. The SCM is also applied in determining the sections bearing capacity. Moreover, the present numerical approach is not limited to a specific structural member cross-sectional typology, with the residual stress models introduced explicitly in subareas of steel cross-sections generated by a 2D discretization. Finally, results consistent with the literature and with low processing time are presented.

• Advances in Computational Design
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• v.5 no.4
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• pp.397-416
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• 2020

Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned - clamped (P-C), axial hinge - pinned (AH-P), axial hinge - clamped (AH-C), pinned - shear hinge (P-SHH), pinned - shear force released (P-SHR), axial hinge - shear force released (AH-SHR) and axial hinge - shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.

• Structural Engineering and Mechanics
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• v.30 no.2
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• pp.165-176
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• 2008

In this paper, a new iterative method for solving vehicle-bridge interaction problems is proposed. Iterative methods have advantages over the non-iterative methods in that it is not necessary to update the system matrix for a given wheel location, and the method can be applied for a new type of car or bridge with few or no modifications. In the proposed method, the necessity of system matrices update is eliminated using the equivalent interaction force acting on the bridge, which is obtained iteratively. Ballast stiffness is included in the interaction forces and the geometric compatibility at the contact points are used as convergence criteria. The bridge is considered as an elastic Bernoulli-Euler beam with surface irregularity and ballast stiffness. The moving vehicle is modeled as a multi-axle mass-spring-damper system having many degrees of freedom depending on the number of axles. The pitching effect, which is the interaction effect between the rear and front wheels when a vehicle begins to enter or leave the bridge, is also considered in the formulation including extended ground boundaries having surface irregularity and ballast stiffness. The applicability of the proposed method is illustrated in the numerical studies.