• Smart Structures and Systems
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• v.4 no.1
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• pp.67-84
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• 2008

The present contribution is concerned with the static and dynamic stability of a piezo-laminated Bernoulli-Euler beam subjected to an axial compressive force. Recently, an inconsistent derivation of the equations of motions of such a smart structural system has been presented in the literature, where it has been claimed, that an axial piezoelectric actuation can be used to control its stability. The main scope of the present paper is to show that this unfortunately is impossible. We present a consistent theory for composite beams in plane bending. Using an exact description of the kinematics of the beam axis, together with the Bernoulli-Euler assumptions, we obtain a single-layer theory capable of taking into account the effects of piezoelectric actuation and buckling. The assumption of an inextensible beam axis, which is frequently used in the literature, is discussed afterwards. We show that the cited inconsistent beam model is due to inadmissible mixing of the assumptions of an inextensible beam axis and a vanishing axial displacement, leading to the erroneous result that the stability might be enhanced by an axial piezoelectric actuation. Our analytical formulations for simply supported Bernoulli-Euler type beams are verified by means of three-dimensional finite element computations performed with ABAQUS.

• Journal of Korean Society of Steel Construction
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• v.15 no.3
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• pp.251-259
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• 2003

In this paper, an analytical approach hwas been conductsed to clarify the relationships between the axial force and the deformation capacity of steel- encased reinforced- concrete beam-columns. The analytical model was defined as a cantilever. Several parameters influencing the inelastic performance of the beam-columns were selected, as follows: including encased steel area ratios, and sectional shapes of the encased steel, material strengths, and shear-span- to-depth ratios. The Analytical results of the analysis showed that the axial force had to have a maximum limit to ensure the stable behavior of a steel- encased reinforced- concrete beam-column when it was subjected to both axial and repeated lateral loading under a constant rotation angle amplitude. The maximum axial force of the beam-column to be resisted under cyclic lateral loading was defined as the stable-limit axial force to ensure the required rotation angle amplitude. The Analytical results of the analysis indicate that the stable-limit axial load ratio increases as the steel strength increases or as the compressive strength of the concrete decreases. The stable-limit axial load ratio decreases as the encased steel ' s sectional area increases in the case of a 1-shaped sections and it is almost not influenced by the steel sectional area in the case of a cross-shaped section.

• Steel and Composite Structures
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• v.4 no.2
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• pp.77-94
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• 2004

Steel beam-to-column joints are often subjected to a combination of bending and axial forces. The level of axial forces in the joint may be significant, typical of pitched-roof portal frames, sway frames or frames with incomplete floors. Current specifications for steel joints do not take into account the presence of axial forces (tension and/or compression) in the joints. A single empirical limitation of 10% of the beam's plastic axial capacity is the only enforced provision in Annex J of Eurocode 3. The objective of the present paper is to describe some experimental and numerical work carried out at the University of Coimbra to try to extend the philosophy of the component method to deal with the combined action bending moment and axial force.

• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.699-715
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• 2010

This paper investigates the structural responses of axially restrained steel beams under fire conditions by a nonlinear finite element method. The axial restraint is represented by a linear elastic spring. Different parameters which include beam slenderness ratio, external load level and axial restraint ratio are investigated. The process of forming a mid-span plastic hinge at the mid-span under a rising temperature is studied. In line with forming a fully plastic hinge at mid-span, the response of a restrained beam under rising temperature can be divided into three stages, viz. no plastic hinge, hinge forming and rotating, and catenary action stage. During catenary action stage, the axial restraint pulls the heated beam and prevents it from failing. This study introduces definitions of beam limiting temperature $T_{lim}$, catenary temperature $T_{ctn}$ and warning time $t_{wn}$. Influences of slenderness ratio, load level and axial restraint ratio on $T_{lim}$, $T_{ctn}$ and $t_{wn}$ are examined.

• Journal of Mechanical Science and Technology
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• v.20 no.2
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• pp.191-196
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• 2006

This paper presents the application of techniques of differential transformation method (DTM) to analyze the transverse vibration of a uniform Euler-Bernoulli beam under varying axial force. The governing differential equation of the transverse vibration of a uniform Euler-Bernoulli beam under varying axial force is derived and verified. The varying axial force was extended to the more general case which was high polynomial consisted of many terms. The concepts of DTM were briefly introduced. Numerical calculations are carried out and compared with previous published results. The accuracy and the convergence in solving the problem by DTM are discussed.

• Earthquakes and Structures
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• v.22 no.3
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• pp.231-243
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• 2022

Beam-column joints (BCJs) are recognized among the most crucial zones in reinforced concrete structures, as they are the critical elements subjected to a complex state of forces during a severe earthquake. Under such conditions, BCJs exhibit behaviors with impacts that extend to the whole structure and significantly influence its ductility and capability of dissipating energy. The focus of this paper is to investigate the effect of undamaged transverse beam (secondary beams) on the ductility of concrete BCJs reinforced with conventional steel and shape memory alloys bars using pushover analysis at tip of beam under different axial load levels at the column using a nonlinear finite element model in ABAQUS environment. A numerical model of a BCJ was constructed and the analysis outcomes were verified by comparing them to those obtained from previous experiments found in the literature. The comparison evidenced the capability of the calibrated model to predict the load capacity response of the joint. Results proved the ability of undamaged secondary beams to provide a noticeable improvement to the ductility of reinforced concrete joints, with a very negligible loss in load capacity. However, the effect of secondary beams can become less significant if the beams are damaged due to seismic effects. In addition, the axial load was found to significantly enhance the performance of BCJs, where the increase in axial load magnified the capacity of the joint. However, higher values of axial load resulted in greater initial stiffness of the BCJ.

• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.717-733
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• 2010

The dynamic stiffness matrix is formulated for an axially loaded slender double-beam element in which both beams are homogeneous, prismatic and of the same length by directly solving the governing differential equations of motion of the double-beam element. The Bernoulli-Euler beam theory is used to define the dynamic behaviors of the beams and the effects of the mass of springs and axial force are taken into account in the formulation. The dynamic stiffness method is used for calculation of the exact natural frequencies and mode shapes of the double-beam systems. Numerical results are given for a particular example of axially loaded double-beam system under a variety of boundary conditions, and the exact numerical solutions are shown for the natural frequencies and normal mode shapes. The effects of the axial force and boundary conditions are extensively discussed.

• Journal of Korean Society of Steel Construction
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• v.17 no.5 s.78
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• pp.605-615
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• 2005

Experimental and analytical work was conducted to investigate the relations of axial force and deformational capacity of concrete-filled square steel tube columns. The test series consisting of 36 columns were tested under the constant axial load and horizontal cyclic load. The axial force of the columns that resisted under the cyclic lateral load was defined as a certified strength of limit axial force. The analytical model was defined as a cantilever beam-column. The axial force of the beam-column that resisted under the cyclic lateral load was defined as an accumulated certified strength of limit axial force. The purpose of this study is to investigate the certified strength of limit axial force of concrete-filled steel tube beam-columns, which were subjected to both axial and lateral load condition corresponding to a given constant rotation angle. Another purpose of this study is to discuss the comparison of the certified strength of limit axial force of concrete and the accumulated certified strength of limit axial force of concrete-filled steel tube columns.

• 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 Monitoring and Maintenance
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• v.4 no.2
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• pp.153-173
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• 2017

An improved method is presented to estimate the axial force of a bar member with vibrational measurements based on modified Timoshenko beam theory. Bending stiffness effects, rotational inertia, shear deformation, rotational inertia caused by shear deformation are all taken into account. Axial forces are estimated with certain natural frequency and corresponding mode shape, which are acquired from dynamic tests with five accelerometers. In the paper, modified Timoshenko beam theory is first presented with the inclusion of axial force and rotational inertia effects. Consistent mass and stiffness matrices for the modified Timoshenko beam theory are derived and then used in finite element simulations to investigate force identification accuracy under different boundary conditions and the influence of critical axial force ratio. The deformation coefficient which accounts for rotational inertia effects of the shearing deformation is discussed, and the relationship between the changing wave speed and the frequency is comprehensively examined to improve accuracy of the deformation coefficient. Finally, dynamic tests are conducted in our laboratory to identify progressive axial forces of a steel plate and a truss structure respectively. And the axial forces identified by the proposed method are in good agreement with the forces measured by FBG sensors and strain gauges. A significant advantage of this axial force identification method is that no assumption on boundary conditions is needed and excellent force identification accuracy can be achieved.