Free vibration and buckling of heavy column with regular polygon cross-section

This paper deals with the free vibration and buckling of heavy column, considering its own self-weight. The column has a regular polygonal cross-section with a constant area. The column is applied to an external axial load as well as the self-weight. The five end conditions of the column are considered. Based on equilibrium equations of the column element, differential equations governing the vibrational and buckled mode shapes of column are derived. In solution methods, differential equations are numerically integrated by the direct integration method and eigenvalues of the natural frequency, buckling load and self-weight buckling length are calculated by the determinant search method. The numerical results of this study were in good agreement with those of the reference. Parametric study of the end condition, side number and self-weight on the natural frequency and buckling load was carried out.

Buckling of Tapered Heavy Columns with Constant Volume

This paper studies the buckling of standing columns under self-weight and tip load. An emphasis is placed on linearly tapered columns with regular polygons cross-section whose volume is constant. Five end conditions for columns are considered. The differential equation governing the buckling shapes of the column is derived based on the equilibrium equations of the buckled column elements. The governing equation is numerically integrated using the direct integration method, and the eigenvalue is obtained using the determinant search method. The accuracy of the method is verified against the existing solutions for particular cases. The effects of side number, taper ratio, self-weight, and end condition on the buckling load and mode shape are investigated. The contribution of self-weight acting alone to the buckling response is also explored. For a given column volume, especially, the buckling length and its stress distribution of the columns with different geometries and end conditions are estimated.

Buckling length of reinforced concrete columns in non-sway constructions

The paper presents a comparison of methods of determining the buckling length of reinforced concrete columns in non-sway frames. The comparison was made on the basis of guidelines issued by Poland some EU countries, USA and India. Differences in approaches and values of buckling length coefficients of columns calculated according to these guidelines are shown. An example of the calculation of column buckling length coefficients on selected multi-span, multi-storey non-sway frames is given.

Built-up CFS column with lacings and battens

The built-up columns are generally used in industrial buildings, either as posts for cladding when their buckling length is very long, or as columns supporting a crane girder. The built-up columns are composed usually of two parallel chords interconnected by lacings or battens. In the paper the special type of built-up column will be analysed from Llentab Company. It consists from four parallel chords with cold-formed C cross-sections which are interconnected by lacing in one plane and by battens in four perpendicular planes. Such types of columns are especially convenient for the relatively high light steel halls. Analysis of the behaviour of such column will be performed: a) on the model with smeared equivalent bending and shear stiffness’s using analytical solution, b) on the discrete model using FEM and commercial program ANSYS. The theory of the second order taking into account the initial imperfections and the shear deformations will be employed.

Study of Column Buckling Lengths of Braced and Unbraced Frames in Fire Situations

<p>The problem of fire resistance of steel structures is still a very actual topic, because there is a need to suitably evaluate the fire resistance and safety of structures exposed to fire hazard. Rules given in the parts of structural Eurocodes devoted to fire design do not cover all relevant design issues. In the case of the buckling resistance of steel columns exposed to fire the Eurocode gives rules only for braced frames in which each storey comprises a separate fire compartment, where it is possible to reduce the buckling length to 0.5L (intermediate storey) or 0.7L (top storey) thanks to the fact, that the hot column is „fixed“ to the cold ones in the storeys above and under. For the case of unbraced frames there are no special rules, the columns should be verified with the procedures as for normal temperature design. Several authors dedicated their efforts to the problem of modelling the real behaviour of entire frame buildings in fire situation. The aim of this paper is to show the behaviour of braced and unbraced frame structure by simple analysis with a FEM programme and to compare the results with some other procedures from the literature.</p>

PLIENINIŲ TINKLINIŲ ARKINIŲ PĖSČIŲJŲ TILTŲ TINKLELIO LYGINAMOJI ANALIZĖ / COMPARATIVE NET ANALYSIS OF THE PEDESTRIAN STEEL NETWORK ARCH BRIDGES

Network arch bridges as a new structural form were invented in the middle of 21st century, describing the row of hangers which intersect each other two or more times. The bending moments in the arch and grinder are approximately ten times smaller due to network hangers arrangement. Additionally, an arch buckling length is smaller comparing with traditional vertical hangers, due to the slope of hangers in the network. However, the search pattern of the net rational angle, other composite parameters, and strain-strain state includes only automotive and rail traffic network arched bridges. This paper presents a geometric analysis of the behaviour of network arch pedestrian steel bridges and geometrical parameters of hangers net. Santrauka Tinkliniai arkiniai tiltai – tai XX a. viduryje atsiradusi nauja konstrukcinė tilto forma, apibūdinama mažiausiai dviem eilėmis pasvirusių pakabų, prasilenkiančių viena su kita. Dėl kryžminio pakabų tinklelio arkoje ir standumo sijoje pasireiškia apie 10 kartų mažesni lenkimo momentai nei tradiciniame arkiniame tilte su vertikaliomis pakabomis. Taip pat dėl pasvirusių pakabų tokių tiltų arkos skaičiuojamasis ilgis yra mažesnis nei tradicinių. Pažymėtina, kad tinklelio racionalaus kampo bei kitų komponuojamųjų parametrų paieškos spektras daugelyje tyrimų apima tik automobilių ar geležinkelio eismo paskirties tinklinius arkinius tiltus. Šiame straipsnyje pateikta plieninių tinklinių arkinių pėsčiųjų tiltų elgsenos analizė ir pakabų tinklo geometrinių parametrų paieška.

Buckling length of a frame member

In steel frame design, the definition of buckling lengths of members is a basic task. Computers can be used to calculate the eigenmodes and corresponding eigenvalues for the frames and using these the buckling lengths of the members can be defined using Euler's equation. However, it is not always easy to say, which eigenmode should be used for the definition of the buckling length of a specific member. Conservatively, the lowest positive eigenvalue can be used for all members. In this paper, methods to define the buckling length of a specific member is presented. For this assessment, two ideas are considered. The first one uses geometric stiffness matrix locally and the other one uses strain energy measures to identify members taking part in a buckling mode. The behaviour of the methods is shown in several numerical examples. Both methods can be implemented into automated frame design, removing one big gap in the integrated design. This is essential when optimization of frames is considered.

Probabilistic Verification of Structural Stability Design Procedures

Introduction: This contribution presents a comparison of three methods of the statistical computation of the design load-carrying capacity of a steel plane frame. Two approaches of the European Standard Eurocode 3 and one stochastic approach are applied. The stochastic approach takes into account the random influence of all imperfections and can be applied to the reliability verification of design according to Eurocode 3. Methods: The columns and beams in the steel frame are modelled with beam elements using the stability solution with buckling length and the geometrically nonlinear solution. The stochastic computational model is based on the geometrically nonlinear solution and on the random influence of initial imperfections, whose random samplings are simulated using the Monte Carlo method. Results and Conclusion: The design load-carrying capacity of the steel plane frame computed using the stability solution with buckling length is in good agreement with the stochastic solution in which the design value is calculated as 0.1 percentile. On the contrary, the geometrically nonlinear solution according to Eurocode 3 gives the lowest (safest) values of design load-carrying capacity.