• Structural Engineering and Mechanics
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• v.78 no.4
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• pp.485-496
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• 2021

So far analytical methods on collapse assessment of three-dimensional (3-D) steel frames have mainly focused on a single-column-removal scenario. However, the collapse of the Federal Building in the US due to car bomb explosion indicated that the loss of multiple columns may occur in the real structures, wherein the structures are more vulnerable to collapse. Meanwhile, the General Services Administration (GSA) in the US suggested that the removal of side columns of the structure has a great possibility to cause collapse. Therefore, this paper analytically deals with the robustness of 3-D steel frames in a two-side-column-removal (TSCR) scenario. Analytical method is first proposed to determine the collapse resistance of the frame during this column-removal procedure. The reliability of the analytical method is verified by the finite element results. Moreover, a design-based methodology is proposed to quickly assess the robustness of the frame due to a TSCR scenario. It is found the analytical method can reasonably predict the resistance-displacement relationship of the frame in the TSCR scenario, with an error generally less than 10%. The parametric numerical analyses suggest that the slab thickness mainly affects the plastic bearing capacity of the frame. The rebar diameter mainly affects the capacity of the frame at large displacement. However, the steel beam section height affects both the plastic and ultimate bearing capacity of the frame. A case study on a six-storey steel frame shows that the design-based methodology provides a conservative prediction on the robustness of the frame.

• Earthquakes and Structures
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• v.14 no.2
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• pp.179-186
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• 2018

We present the accurate investigation the seismic behavior of the gravity retaining wall built near rock face based on numerical method. The retaining wall is a useful structure in geotechnical engineering, where the earthquake is a common phenomenon; therefore, the evaluation of the behavior of the retaining wall during an earthquake is essential. However, in all previous studies, the backfill behind the wall was usually approximated by a homogeneous region, while in contrast, in practice, in many cases retaining walls are used to support the soil pressure in, inhomogeneous, mountainous area. This suggests an accurate investigation of the problem, i.e., numerical analysis. The numerical results will be compared with some of recently proposed analytical methods to show the accuracy of the proposed method. We show that increasing the volume of the rock face yields decreasing the permanent horizontal displacement of the gravity retaining wall built near rock face. Besides, we see that the permanent horizontal displacement of the gravity retaining wall with homogenous backfill is more than permanent horizontal displacement of the gravity retaining wall case of the built near rock face in different frequency contents.

• Steel and Composite Structures
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• v.44 no.4
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• pp.531-543
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• 2022

An exact dynamic analytical method for free vibrations of continuous partial-interaction composite beams is proposed based on the Timoshenko beam theory. The main advantage of this method is that the independent shear deformations and rotary inertia of sub-beams are considered, which is more in line with the reality. Therefore, the accuracy of eigenfrequencies obtained by this method is significantly improved, especially for higher order modes, compared to the existing methods where the rotary angles of both sub-beams are assumed to be equal irrespective of the differences in the shear stiffness of each sub-beam. Furthermore, the solutions obtained by the proposed method are exact owing to no introduction of approximated displacement and force fields in the derivation. In addition, an exact analytical solution for the case of simply supported is obtained. Based on this, an approximate expression for the fundamental frequency of continuous partial-interaction composite beams is also proposed, which is useful for practical engineering applications. Finally, the practicability and effectiveness of the proposed method and the approximate expression are explored using numerical and experimental examples; The influence factors including the interfacial interaction, shear modulus ratio, span-to-depth ratio, and side-to-main span length ratio on the eigenfrequencies are presented and discussed in detail.

• Korean Journal of Computational Design and Engineering
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• v.14 no.1
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• pp.18-24
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• 2009

This paper proposes an analytical method of evaluating the maximum error by modeling the exact tool path for the tool traverse singular region in five-axis machining. It is known that the NC data from the inverse kinematics transformation of 5-axis machining can generate singular positions where incoherent movements of the rotary axes can appear. These lead to unexpected errors and abrupt operations, resulting in scoring on the machined surface. To resolve this problem, previous methods have calculated several tool positions during a singular operation, using inverse kinematics equations to predict tool trajectory and approximate the maximum error. This type of numerical approach, configuring the tool trajectory, requires much computation time to obtain a sufficient number of tool positions in a region. We have derived an analytical equation for the tool trajectory in a singular area by modeling the tool operation into a linear and a nonlinear part that is a general form of the tool trajectory in the singular area and that is suitable for all types of five-axis machine tools. In addition, we have evaluated the maximum tool-path error exactly, using our analytical model. Our algorithm can be used to modify NC data, making the operation smoother and bringing any errors to within tolerance.

• Structural Engineering and Mechanics
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• v.60 no.5
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• pp.795-807
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• 2016

This study tries to examine the effect of different parameters on stress analysis of infinite plates with central quasi-triangular cutout using particle swarm optimization (PSO) algorithm and also an attempt has been made to introduce general optimum parameters in order to achieve the minimum amount of stress concentration around this type of cutout on isotropic and orthotropic plates. Basis of the presented method is expansion of analytical method conducted by Lekhnitskii for circular and elliptical cutouts. Design variables in this study include fiber angle, load angle, curvature radius of the corner of the cutout, rotation angle of the cutout and at last material of the plate. Also, diagrams of convergence and duration time of the desired problem are compared with Simulated Annealing algorithm. Conducted comparison is indicative of appropriateness of this method in optimization of the plates. Finite element numerical solution is employed to examine the results of present analytical solution. Overlap of the results of the two methods confirms the validity of the presented solution. Results show that by selecting the aforementioned parameters properly, less amounts of stress can be achieved around the cutout leading to an increase in load-bearing capacity of the structure.

• International Journal of Precision Engineering and Manufacturing
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• v.2 no.3
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• pp.47-53
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• 2001

This paper investigates the characteristics of interlaminar fracture toughness of foam core sandwich structures under opening mode by using the double cantilever beam (DCB) specimens which are Carbon/Epoxy and foam core composites. Instead of using a DCB specimen of symmetric geometry, a non-symmetric DCB specimen was used to calculate the interlaminar fracture toughness. Three approaches for calculating the energy release rate(G$\sub$IC/) were used and fracture toughness of foam core sandwich structures made by autoclave, vacuum bagging and hotpress were compared. Experiment, analysis using nonlinear beam bending theory, and numerical work by FEM methods were performed. Bonding surface compensation and equivalent moment of inertia were used to calculate the energy release rate in nonlinear analytical work. Conclusions of experimental, nonlinear analytical and FEM methods were compared. It is, also, shown that the vacuum bagging forming can substitute the method of autoclave without serious loss of Mode I energy release rate(G$\sub$I/).

• Proceedings of the Korean Nuclear Society Conference
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• 1995.05b
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• pp.643-650
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• 1995

A numerical method for treating transient diffusion Involving change of phase is presented. In other methods of dealing with this class of problems, the mass flux balance at the moving phase boundary requires explicit treatment of two distinct phases. The technique, originating from the apparent heat capacity method in transient heat conduction with the phase change, avoids the difficulty by transferring the concentration discontinuity at the boundary to smoothed physical property variations near the moving front. This technique accomodates the nonlinearities which preclude use of analytical solutions. It was tested against known analytical solutions for simple cases and turned out to be quite accurate.

• Computers and Concrete
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• v.19 no.5
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• pp.509-514
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• 2017

Concrete retaining walls are the most common types of geotechnical structures for controlling instable slopes resulting from lateral pressure. In analytical stability, calculation of the concrete retaining walls is regarded as a rigid mass when its safety is required. When cracks in these structures are created, the stability may be enforced and causes to defeat. Therefore, identification, creation and propagation of cracks are among the important steps in control of lacks and stabilization. Using the numerical methods for simulation of crack propagation in concrete retaining walls bodies are among the new aspects of geotechnical analysis. Among the considered analytical methods in geotechnical appraisal, the boundary element method (BEM) for simulation of crack propagation in concrete retaining walls is very convenient. Considered concrete retaining wall of this paper is Pars Power Plant structured in south side in Assalouyeh, SW of Iran. This wall's type is RW6 with 11 m height and 440 m length and endurance of refinery construction lateral forces. To evaluate displacement and stress distributions (${\sigma}_{1,max}/{\sigma}_{3,min}$), the surrounding, especially in tip and its opening crack BEM, is considered an appropriate method. By considering the result of this study, with accurate simulation of crack propagation, it is possible to determine the final status of progressive failure in concrete retaining walls and anticipate the suitable stabilization method.

• Smart Structures and Systems
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• v.21 no.5
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• pp.583-590
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• 2018

Nowadays, many tunnels have been commissioned for several decades, which require effective inspection methods to assess their health conditions. The ambient vibration test has been widely adopted for the damage identification of concrete structures. In this study, the vibration characters of tunnel lining shells built with forepoling method was analyzed based on the analytical solutions of the Donnell-Mushtari shell theory. The broken rock, foreploing, rock-concrete contacts between rock mass and concrete lining, was represented by elastic boundaries with normal and shear stiffness. The stiffness of weak contacts has significant effects on the natural frequency of tunnel lining. Numerical simulations were also carried out to compare with the results of the analytical methods, showing that even though the low nature frequency is difficult to distinguish, the presented approach is convenient, effective and accurate to estimate the natural frequency of tunnel linings. Influences of the void, the lining thickness and the concrete type on natural frequencies were evaluated.

• Structural Engineering and Mechanics
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• v.43 no.5
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• pp.561-582
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• 2012

Despite popularity of FEM in analysis of static and dynamic structural problems and the routine applicability of FE softwares, analytical methods based on simple mathematical relations is still largely sought by many researchers and practicing engineers around the world. Development of such analytical methods for analysis of free vibration of non-prismatic beams is also of primary concern. In this paper a new and simple method is proposed for determination of vibration frequencies of non-prismatic beams under variable axial forces. The governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single variable equation in terms of location. Through repetitive integrations, integral equation for the weak form of governing equation is derived. The integration constants are determined using the boundary conditions applied to the problem. The mode shape functions are approximated by a power series. Substitution of the power series into the integral equation transforms it into a system of linear algebraic equations. Natural frequencies are determined using a non-trivial solution for system of equations. Presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic beams. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained to those obtained using available finite element software.