GBT-based buckling analysis of thin-walled members with non-standard support conditions

This paper reports on the use of a recently developed Generalised Beam Theory (GBT) formulation, and corresponding finite element implementation, to analyse the local and global buckling behaviour of thin-walled members with arbitrary loading and support conditions — this formulation takes into account longitudinal normal stress gradients and the ensuing pre-buckling shear stresses. After presenting an overview of the main concepts and procedures involved in the performance of a GBT-based (beam finite element) member buckling analysis, one addresses in detail the incorporation of non-standard support conditions, such as (i) full or partial localised displacement or rotation restraints, (ii) rigid or elastic intermediate supports or (iii) end supports corresponding to angle connections. In order to illustrate the application and capabilities of the proposed GBT-based approach, one presents and discusses numerical results concerning cold-formed steel (i) lipped channel beams and (ii) lipped I-section beams and columns with various “non-standard” support conditions — while the beams are acted by uniformly distributed or mid-span point loads, applied at the shear centre axis, the columns are subjected to uniform compression. In particular, it is possible to assess the influence of the different support conditions on the beam and column buckling behaviour (critical buckling loads and mode shapes). For validation purposes, most GBT-based results are compared with values yielded by shell finite element analyses carried out in the code Ansys.     

基于广义梁理论的非线性材料薄壁受压构件屈曲荷载计算方法

提出适用于非线性材料的广义梁理论屈曲荷载计算方法,并对不锈钢薄壁受压构件屈曲荷载进行计算验证。通过定义材料非线性应力应变关系和瞬时弹性模量,对传统线弹性广义梁理论进行修正,建立非线性材料薄壁构件受压屈曲荷载计算方法,推导不锈钢薄板受压局部屈曲、冷弯薄壁不锈钢卷边槽形柱畸变屈曲及箱形不锈钢长柱弯曲屈曲荷载计算公式,并与既有试验数据对比。经验证,线弹性分析方法不适用于不锈钢材料;提出的修正GBT法具有较高精度,且本构关系采用变形法则结果偏于安全,可用于不锈钢等非线性金属材料薄壁构件受压屈曲荷载的确定,为研究和设计提供理论指导。     

Buckling mode identification of perforated thin-walled members by using GBT and shell FEA

The paper presents an original method based on the Generalised Beam Theory (GBT) whereby the general buckling modes, provided by the shell Finite Element Analysis (SFEA) of perforated thin-walled members, are expressed in terms of the fundamental (pure) buckling types (global, distortional and local). The contribution of each pure buckling mode to a coupled instability can be quantified, allowing a better understanding of the member buckling behaviour and post-buckling strength reserve. The main advantage of this method lies in using only the GBT cross-sectional pure deformation modes instead of member pure modal shapes. There are no restrictions regarding the element cross-sectional shape, loading and boundary conditions.     

The vibration behaviour of thin-walled regular polygonal tubes

This paper addresses the free vibration behaviour of single-cell thin-walled tubes with regular convex polygonal cross-section (RCPS) and provides an extensive analysis of the resulting natural frequencies and associated vibration mode shapes. A semi-analytical approach is adopted, which is based on the generalised beam theory (GBT) specialisation for RCPS recently proposed by Gonçalves and Camotim (2013) [1] and subsequently employed to obtain insightful conclusions concerning the buckling behaviour of RCPS tubes (Gonçalves and Camotim (2013) [2], [3]). This approach makes it possible to obtain closed-form analytical solutions and also acquire in-depth knowledge concerning the mechanics of the vibration problem, through the well-known GBT modal decomposition features. Attention is paid to local (plate-like), extensional, torsional and distortional vibration modes, as well as their interaction.     

Distortional buckling formulae for cold-formed steel C and Z-section members: Part I—derivation

This paper presents the derivation of generalised beam theory (GBT)-based fully analytical formulae to provide distortional critical lengths and bifurcation stress resultant estimates in cold-formed steel C and Z-section members (i) subjected to uniform compression (columns), pure bending (beams) or a combination of both (beam–columns), (ii) with arbitrary sloping single-lip stiffeners and (iii) displaying four end support conditions. These formulae incorporate genuine folded-plate theory, a feature which is responsible for their generality and high accuracy. After a brief outline of the GBT fundamentals and linear stability analysis procedure, the main concepts and steps involved in the derivation of the distortional buckling formulae are described and discussed. Moreover, the paper also includes a few remarks concerning novel aspects related to the distortional buckling behaviour of Z-section beams and C-section beam–columns, which were unveiled by the GBT-based approach. Finally, note that, in a companion paper [Thin-Walled Struct., 2004 doi: 10.1016/j.tws.2004.05.002], the formulae derived here are validated and their application, accuracy and capabilities are illustrated. In particular, the GBT-based estimates are compared with exact results and, when possible, also with values yielded by the formulae developed by Lau and Hancock, Hancock, Schafer and Teng et al.     

Global buckling analysis of plane and space thin-walled frames in the context of GBT

This paper reports research work concerning the use of Generalised Beam Theory (GBT) to analyse the global buckling behaviour of plane and space thin-walled frames. Following a brief overview of the main concepts and procedures involved in the performance of a GBT buckling analysis, one presents in detail the formulation and numerical implementation of a GBT-based beam finite element that includes only the first four (rigid-body) deformation modes — namely, one describes (i) the kinematical models developed to simulate the warping transmission at frame joints connecting two or more non-aligned U- and I-section members, (ii) the procedures adopted to handle the effects stemming from the non-coincidence of the member centroidal and shear centre axes (cross-sections without double symmetry), and (iii) the definition of joint elements, which involves providing a relation between the connected member GBT degrees of freedom and the joint generalised displacements. Finally, one presents and discusses numerical results that make it possible to illustrate the application and show the capabilities of the above GBT-based finite-element formulation and implementation. For validation purposes, the GBT-based results (critical buckling loads and mode shapes) are also compared with values yielded by shell (mostly) and beam finite element analyses carried out in the code ANSYS.     

Modal decomposition of thin-walled member collapse mechanisms

Following recent investigations on the decomposition of elastic buckling modes into combinations of structurally meaningful deformation modes, this work presents a novel extension of the above procedure to elastic–plastic collapse mechanisms and highlights the relevant role that this concept may play in the mechanical knowledge/interpretation of thin-walled member failures. In order to achieve the sought decomposition, a code based on a Generalised Beam Theory (GBT) formulation developed to perform first-order elastic–plastic analyses of thin-walled members is employed. Five illustrative examples are presented and discussed, and the results displayed, namely load-deflection curves, deformed configurations and stress contours, are validated through the comparison with values provided by shell finite element analyses. The most relevant modal results addressed consist of (i) load-deflection curves determined on the basis of pre-selected deformation mode sets, (ii) modal participation diagrams and (iii) modal amplitude functions. These results make it easy to characterise and interpret the mechanics associated with the thin-walled member elastic–plastic failures (as well as with the various loading stages), which may be of great importance in the improvement/development of existing/new design methods (e.g, yield-line theory, direct strength method).     

GBT formulation to analyse the buckling behaviour of thin-walled members with arbitrarily ‘branched’ open cross-sections

This paper presents the derivation, validates and illustrates the application of a Generalised Beam Theory (GBT) formulation developed to analyse the buckling behaviour of thin-walled members with arbitrarily ‘branched’ open cross-sections. Following a brief overview of the conventional GBT, one addresses in great detail the modifications that must be incorporated into its cross-section analysis procedure, in order to be able to handle the ‘branching’ points — they concern mostly issues related to (i) the choice of the appropriate ‘elementary warping functions’ and (ii) the determination of the ‘initial flexural shape functions’. The derived formulation is then employed to investigate the local-plate, distortional and global buckling behaviour of (i) simply supported and fixed asymmetric E-section columns and (ii) simply supported I-section beams with unequal stiffened flanges. For validation purposes, several GBT-based results are compared with ‘exact’ values, obtained by means of finite strip or shell finite element analyses.     

Web buckling study of the behaviour and strength of perforated steel beams with different novel web opening shapes

This paper presents an experimental and analytical study on the behaviour of perforated steel beams with closely spaced web openings. Seven specimens including two typical cellular beams (i.e. circular web openings) and five perforated beams with novel web opening shapes were tested to investigate the failure mode and load strength of the web-post between two adjacent web openings. Fourteen numerical test specimens were developed and analysed by the finite element method and the results were compared with the full scale experiments. The effect of web opening spacing/web opening depth of web-posts was studied to investigate the effective ‘strut’ action of the web-post buckling. The effect of the web opening depth/web thickness was also studied to investigate the stability (slenderness) of the web-post subjected to vertical shear load. Two hundred and twenty-fine elastic-plastic finite element analyses were then employed in a comprehensive parametric study to propose an empirical formula which predicts the ultimate vertical shear load strength of web-posts formed from the particular web opening shapes.Perforated beams with standard circular, hexagonal and elongated web openings are mostly used nowadays. Various non-standard web opening shapes are introduced through this paper for first time. These new pioneering web opening shapes improve the structural performance of the perforated beams when examined under the web-post buckling failure mode. In addition, the manufacturing procedure of these non-standard web openings show great advantage in comparison with the manufacturing way of the more popular cellular beams.     

CFD analysis of ventilation effectiveness in a public transport interchange

A study was conducted into the ventilation effectiveness of a ventilation system within a public transport interchange (PTI) in Hong Kong. A computational fluid dynamics (CFD), steady state computational model of the PTI was used to investigate and predict the typical pollutant emission pattern for buses. In Hong Kong, the displacement ventilation (DV) scheme is often employed for the PTI. The numerical simulation investigates the effectiveness of the DV system in removing pollutants from the occupied zone. An alternative model is proposed where the supply is located at the ceiling and the exhausts are located at the lower part of the columns. It was found that both systems could adequately ventilate the PTI; however, the ceiling based air supply system is able to provide improved thermal comfort and indoor air quality (IAQ).     

Energy and exergy analysis of prosumers in hybrid energy grids

Surplus energy can be a recurrent phenomenon in zero-energy buildings (ZEBs) with onsite generation systems, usually resulting in the export of excess electricity. Yet, converting electricity into heat and exporting it could improve the overall energy balance. This study analyses the energy and exergy performance of a Finnish nearly zero-energy building (nZEB) as a heat and electricity prosumer, and proposes alternative energy topologies to improve energy and exergy levels, primary energy demand and CO₂ emissions. The results show that increasing the installed capacity of the photovoltaic systems would lead to zero energy, exergy, emissions and a balance of primary energy. However, by instead using the surplus electricity to drive a heat pump and export heat, the currently installed capacity would lead to a net energy export of over 4000?kWh/a. Thus, energy conversion could significantly enhance the contribution from heat and electricity prosumers to smart energy grids, though not without affecting other criteria. Two management strategies arise: favouring heat export improves the net energy and CO₂ emissions reduction but lessens the net exergy, while favouring electricity export improves the net exergy and primary energy reduction. The findings highlight that energy conversion can enhance nZEB performance and its exchange with hybrid grids.     

Life-cycle cost analysis of highway noise barriers designed with photocatalytic cement

This study examines the environmental and economic feasibility of concrete noise barriers containing photocatalytic cement using a life-cycle cost analysis (LCCA). Photocatalytic concrete contains titanium dioxide (TiO₂) which allows for the oxidation of air pollutants to occur on the surface of the building material. Design variables studied include the cementing material type (general use (GU) cement, ground granulated blast furnace slag (GGBFS) used as cement replacement, and photocatalytic (PCAT) cement), and the thickness of a photocatalytic concrete cover. The LCCA accounts for the CO₂ and NO_x generated during manufacturing and the NO_x (NO, NO₂) oxidised during the life of barriers containing photocatalytic concrete. A key outcome from this study revealed that at a 40-year service life, assuming a 6 mg/h/m² NO_x degradation rate, a barrier designed with 100%GU cement and a 25 mm photocatalytic concrete cover has an annual cost that is 7%, 30%, and 36% greater than the 100%GU, 35% and 50%GGBFS barriers without a photocatalytic cover, respectively. Results of this analysis also indicated that the application of a 25 mm photocatalytic concrete cover to concrete containing 35 and 50%GGBFS is more economically feasible than 100%GU concrete, irrespective of the service life and pollution degradation rate.     

Phylogenetic analysis of the bacterial community in a full scale autothermal thermophilic aerobic digester (ATAD) treating mixed domestic wastewater sludge for land spread

The bacterial community associated with a full scale autothermal thermophilic aerobic digester (ATAD) treating sludge, originating from domestic wastewater and destined for land spread, was analysed using a number of molecular approaches optimised specifically for this high temperature environment. 16S rDNA genes were amplified directly from sludge with universally conserved and Bacteria-specific rDNA gene primers and a clone library constructed that corresponded to the late thermophilic stage (t = 23 h) of the ATAD process. Sequence analyses revealed various 16S rDNA gene sequence types reflective of high bacterial community diversity. Members of the bacterial community included α- and β-Proteobacteria, Actinobacteria with High G + C content and Gram-Positive bacteria with a prevalence of the Firmicutes (Low G + C) division (class Clostridia and Bacillus). Most of the ATAD clones showed affiliation with bacterial species previously isolated or detected in other elevated temperature environments, at alkaline pH, or in cellulose rich environments. Several phylotypes associated with Fe(III)- and Mn(IV)-reducing anaerobes were also detected. The presence of anaerobes was of interest in such large scale systems where sub-optimal aeration and mixing is often the norm while the presence of large amounts of capnophiles suggest the possibility of limited convection and entrapment of CO₂ within the sludge matrix during digestion. Comparative analysis with organism identified in other ATAD systems revealed significant differences based on optimised techniques. The abundance of thermophilic, alkalophilic and cellulose-degrading phylotypes suggests that these organisms are responsible for maintaining the elevated temperature at the later stages of the ATAD process.