Aleksandar Prokić

Thin-walled beams with open and closed cross-sections

Abstract A new warping function for three-dimensional thin-walled beams is proposed that enables the analysis of structures made up of members with arbitrary open and closed cross-sections. An updated Lagrangian formulation is used to give the stiffness matrix. The method is illustrated by examples.

New finite element for analysis of shear lag

A new model of describing the shear lag phenomenon in thin-walled beams with arbitrary open or closed cross-sections is defined on the basis of the warping function proposed by Prokic. The general approach to the solution of the problem is based on the finite element method. The principle of virtual displacements has been used to give a new linear stiffness matrix. The method is illustrated by examples.

Computer program for determination of geometrical properties of thin-walled beams with open-closed section

Abstract A computer program is developed for the determination of the torsional and flexural properties of thin-walled beams with arbitrary open–closed cross-section. Graph theory is employed to establish the topological properties of multi-cellular cross-section, i.e., to automatically define independent circuits and corresponding fictitious cuts that make section open. Numerical examples calculated by the program are given in the paper.

A numerical method for free vibration analysis of beams

In this paper, a numerical method for solution of the free vibration of beams governed by a set of second-order ordinary differential equations of variable coefficients, with arbitrary boundary conditions, is presented. The method is based on numerical integration rather than the numerical differentiation since the highest derivatives of governing functions are chosen as the basic unknown quantities. The kernelsof integral equations turn out to be Greens function of corresponding equation with homogeneous boundary conditions. The accuracy of the proposed method is demonstrated by comparing the calculated results with those available in the literature. It is shown that good accuracy can be obtained even with a relatively small number of nodes.

Computer program for determination of geometrical properties of thin-walled beams with open profile

Abstract This article presents a computer program for the determination of the torsional and flexural properties of thin-walled beams with arbitrary open cross-section. The program is written in FORTRAN 77. Some numerical examples are given, with complete information about input and output.

Free Vibration Analysis of Cross-Ply Laminated Thin-Walled Beams with Open Cross Sections: Exact Solution

AbstractThe objective of the present paper is to analyze the free vibrations of thin-walled beams with arbitrary open cross section, made of cross-ply laminates with midplane symmetry, by means of an exact solution. The theory of thin-walled composite beams is based on assumptions consistent with Vlasov’s beam theory and classical lamination theory. The governing differential equations for coupled bending-torsional vibrations were obtained using the principle of virtual displacements. To simplify the coupled system of differential equations, an ideal center of gravity and shear center were introduced. In the case of a simply supported thin-walled beam, the closed-form solution for the natural frequencies of free harmonic vibrations was derived. The frequency equation, given in determinantal form, is expanded in an explicit analytical form. To demonstrate the validity of this method, the natural frequencies of nonsymmetric thin-walled beams having coupled deformation modes are evaluated and compared with r...

Flexural-torsional vibration analysis of axially loaded thin-walled beam

The present paper considers the flexure-torsion coupled vibrations of axially loaded thin-walled beams with arbitrary open cross section, by means of an exact solution. The effects of axial force, warping stiffness and rotary inertia are included in the present formulations. In the case of simply supported thin-walled beam, a closed-form solution for the coupled natural frequencies of free harmonic vibrations was derived by using a general solution of the governing differential equations of motion based on Vlasov theory. The method is illustrated by its application to two test examples, to demonstrate the effects of bending-torsion coupling and axial force on the dynamic behavior of thin-walled beams. Compared with those available in the relevant literature, numerical results demonstrate the accuracy and effectiveness of the proposed method.

Slip Modulus of Screws in Timber and Lightweight Concrete Composite Structures

NH4Cl was used to optimize the pretreatment conditions for biomass pretreatment to improve enzymatic saccharification and hemicellulose degradation of eucalyptus chips. After pretreatment, the solid substrate (SS) and pretreatment liquor (PL) were characterized, and the SS was enzymatically hydrolyzed to detect the conversion yield of cellulose (CYC). For the pretreatment using NH4Cl, the removal rate of hemicellulose reached up to 100% in some cases, but a great proportion of cellulose remained in the SS. The optimized conditions for pretreatment using NH4Cl were 0.3 M NH4Cl at 200 °C for 25 min. A comprehensive evaluation found that the most suitable severity parameter for pretreatment and enzymatic saccharification was 4.5, although a higher severity parameter could increase the CYC. XRD and FTIR analysis showed that the pretreatment had little influence on the cellulose crystalline region, and the lignin was well-retained in the pretreatment process.High biomass loading is a key technique to reduce the pretreatment cost of lignocellulosic biomass. In this work, various biomass species such as bagasse, erianthus, cedar, and eucalyptus were pretreated using an ionic liquid, 1-ethyl-3-methylimidazolium acetate, at different biomass loadings, particularly focusing on a high loading region. Cellulose structural changes in pretreated biomass were investigated via X-ray scattering and 13C solid-state nuclear magnetic resonance (SSNMR) spectroscopy. The structural behaviors roughly fell into two categories, corresponding to either grassy (bagasse and erianthus) or woody (cedar and hardwood) biomass. The grassy biomass gradually transformed from cellulose-I to cellulose-II in a monotonic manner against the biomass loading. In contrast, the transformation in the woody biomass occurred abruptly as solids was decreased within the high loadings range (50 wt% to 33 wt%). Below 33 wt%, a reformation of cellulose-I from cellulose-II proceeded readily. In terms of cellulose crystallinity, erianthus as well as bagasse showed a minimum value at 25 wt% loading, whereas the crystallinity for the woody biomass did not possess such a clear minimum. Acid hydrolysis of these pretreated biomass was also conducted and the relationship between the reactivity and the cellulose structural changes was discussed.

Bimoment Contribution to Buckling of Thin-Walled Beams with Different Boundary Conditions

AbstractIn this paper the influence of bimoment, induced by external axial loads, on the global buckling of thin-walled Z-section beams, subjected to different boundary conditions, is studied. Sinc...

Torsional buckling of thin-walled beams in presence of bimoment induced by axial loads

Original scientific paper In this paper the influence of the bimoment induced by external axial loads on the elastic torsional buckling of thin-walled beams with open cross-section is studied. The governing differential equations of a deformed thin-walled beam consistent with Vlasov’s classical assumptions are derived applying the principle of virtual displacements. It is shown that in the cross sections with lack of symmetry the bimoment can considerably affect the torsional buckling load. The obtained results are verified using ANSYS finite element software.