Cross-section Of Members Research Articles

Application of Multiple Linear Regression Method in Steel Column Design under Combined Loading

The article explores using multiple linear regression (MLR) approach to predict the cross-section of beam-column steel members. These members are complex in design, as they must withstand bending and axial forces. The design process involves multiple safety checks according to design standards. The first step in the design procedure is to calculate and verify the axial capacity of the member. Following that, the flexural capacity is calculated. Finally, the combined load capacity is examined, often involving a trial-and-error process. If the initially selected section cannot withstand the applied forces, a new section must be chosen, and the calculations must be repeated. This study employs a multiple linear regression approach to investigate the relationship between member properties (such as length and cross-section) and load design parameters (axial and bending forces). The primary objective is to predict the beam-column steel member’s elastic section modulus (Sx). The regression equation derived from the study is as follows: Sx = 18.000L + 6.839Pr + 47.193Mr – 129.093, with an R-square value of 0.985. The histogram of the equation exhibits symmetry and a standard distribution, while the typical probability plot demonstrates a relatively linear trend. Two examples are presented to evaluate the efficiency of the regression equation. The first example confirms the efficiency of the equation by determining the cross-sectional size by employing the regression equation and using it to verify the safety according to EIT design standards. The second example is the application of the equation for estimating the size of other types of steel members. This study suggests that the regression equation can effectively predict the size of beam-column steel members, providing reliable results for practical design applications.

Optimization of Cold-Formed Thin-Walled Cross-Sections in Portal Frames

Portal frames with built-up cold-formed cross-sections hold significant potential; however, there is a notable gap in the analysis of cross-section types and connections. In this study, an optimization algorithm was developed for the closed cross-sections of portal frame members. An optimization algorithm was tested against optimized open cold-formed cross-sections. The results indicated a portal frame volume up to 38% lower where members were assembled of optimal closed cross-sections when compared to frames with optimal open cross-sections. Parametric analysis was carried out, where two types of cross-sections were examined: Type A, with four web stiffeners bent inwards, and Type B, with four web stiffeners bent outwards. The optimization was conducted using a Genetic Algorithm in MATLAB R2022b. Portal frames with optimal Type B cross-sections had a volume that was up to 22% lower when compared to frames with optimal Type A cross-sections. Significant differences were noted between the optimal beam and column cross-sections, with the optimal column cross-section thickness being on average 74% greater, but the optimal beam cross-section height being on average 81% greater than those of the respective counterparts. In this article, a practical assembly solution for the connection of the frame members was proposed for the optimized novel closed cross-section types in portal frames. However, the strength and stiffness of these connections were not analyzed in this research.

Academic leadership and job performance: the effects of organizational citizenship behavior and informal institutional leadership

PurposeGrounded on the distributed theory and the social exchange theory, the current study investigates the determinants that positively influence job performance among educators within the realm of higher education in India. It particularly assesses the impact of perceived academic leadership on performance and explores the mediating and moderating effects of organizational citizenship behavior and informal institutional leadership.Design/methodology/approachEmploying a descriptive research design, this study encompasses a broad cross-section of faculty members from various higher educational institutions across India. Data were gathered from 826 educators using a snowball sampling technique, with questionnaires administered online. Each variable was measured using prevalidated scales.FindingsThe findings from the moderated mediation model indicate a significant indirect relationship between perceived academic leadership and job performance, which is mediated by organizational citizenship behavior. Furthermore, informal institutional leadership demonstrates significant conditional indirect effects, enhancing the link between academic leadership and job performance up to a threshold, beyond which its influence diminishes.Originality/valueThis study pioneers the exploration of academic dynamics beyond mere titles and ranks in the Indian educational sector. It delineates both the direct and indirect roles these dynamics play in enhancing faculty performance, providing a novel insight into the complexities of academic leadership.

Structural design of reinforced concrete frames for minimum amount of concrete or embodied carbon

In standard engineering practice, designers often aim to minimize the amount and volume of concrete in reinforced concrete (RC) frames by reducing the size of member cross-sections. This is done either for architectural reasons or because it is assumed to drive to more economic and environmentally friendly productions. The present study, for first time, compares the environmental footprint of RC frames designed for minimum concrete volume against designs for minimum embodied carbon. To serve this goal, six realistic 3D RC building frames are optimally designed for parametric values of the carbon factors of concrete and reinforcing steel materials. In this comparison, it is noticed that the carbon factors ratio R of reinforcing steel to concrete plays a key role. More particularly, it is found that for R ≤ 10 the designs for minimum concrete and carbon practically coincide. This is a useful observation since it signals a clear direction to designers to decrease concrete sections to achieve minimum environmental impact. Nevertheless, as R increases from 10, the two designs gradually deviate since the carbon footprint of rebars becomes more important. For high R values, the RC frames with the least amount of concrete produce, on average, up to 40 % more embodied carbon than the most environmentally clean designs.

Database of tall pre-Northridge steel moment frames for earthquake performance evaluations

This article describes a detailed database of tall steel moment frame buildings that are representative of the construction practices in San Francisco prior to the 1994 Northridge earthquake. The database contains design details that affect the structural performance of steel moment frames, including frame geometry, member cross-section sizes, and gravity system characteristics. This database also captures irregularities that might impact seismic response, such as podiums, setbacks, mass concentrations (mechanical, electrical, and plumbing (MEP) floors), interrupted column lines, and atriums. The database includes information on 89 moment frame buildings, 14 of which were built before 1960 and are constructed with riveted connections, while the remaining 75 have welded flange connections like those that suffered brittle fracture during the 1994 Northridge earthquake. The buildings are further distinguished between space frame, perimeter frame, and partial space frame systems. For about half (41/89) of the buildings in the database, section sizes of representative structural members were collected, which enabled the evaluation of the seismic design, elastic, and inelastic response using computational workflows. The design diagnostics indicate that most of the buildings meet the minimum seismic strength and strong-column weak-beam requirements of modern building codes, even though they were not necessarily designed with this intent. On the contrary, about one-third of the buildings do not meet the seismic design drift limit of current codes, and about half of them have weak beam-column panel zones. This database, associated structural analysis models, and processing scripts are published at DesignSafe https://doi.org/10.17603/ds2-wjad-r340 to facilitate collaboration and continued development of open-source data for high-resolution simulations to inform risk mitigation strategies on a regional scale.

Experimental and numerical investigations of S890 and S960 ultra-high strength steel circular hollow section columns

The experimental and numerical investigations of the buckling behaviour and load-carrying capacities of S890 and S960 ultra-high strength steel (UHSS) circular hollow section (CHS) columns were conducted and reported in this paper. The experimental program encompassed tensile coupon tests, initial global and local geometric imperfection measurements and pin-ended column tests. Parallelly, the numerical modelling program was carried out, where the developed finite element (FE) models were validated with reference to the experimental observations and then employed in parametric studies to result in additional numerical data, considering various cross-sectional dimensions and member lengths. Based on the obtained FE and test data, the applicability of the relevant codified design buckling curves in the current European, Australian and American specifications to S890 and S960 UHSS CHS columns was evaluated, since the aforementioned standards only cover the design rules with steel material yield strength no greater than 700 MPa. The assessment results showed that the European code and Australian standard can generally accurately predict the resistances of S890 and S960 UHSS CHS columns, but result in some unsafe data points, while the American specification yielded accurate and consistent resistance predictions. Finally, a revised Eurocode design buckling curve was proposed, accompanied by the reliability assessment through statistical analyses, with the improved design accuracy and consistency revealed.

Analysis of equivalent substitution of rectangular stress block for nonlinear stress diagram

This article deals with the analysis of equivalency of the substitution of rectangular stress block for nonlinear stress diagram with descending branch for the calculation of flexural, eccentrically compressed and eccentrically tensioned reinforced concrete members of rectangular cross-section. The method for equivalent substitution of these diagrams is proposed. Analytical relationships of area and its centre for the nonlinear diagram with descending branch are presented. Coefficients for equivalent substitution of the said diagrams for the standard concrete strength classes are determined and given. It gives the opportunity to design reinforced concrete members using rectangular stress block model. Substitution of the diagrams applied in EC2 and in STR 2.05.05:2005 is compared with the equivalent substitution of rectangular stress diagram for nonlinear stress diagram with descending branch. It is shown that in STR 2.05.05:2005 description of the ratio between the depth of the rectangular diagram and that of the equivalent nonlinear one with descending branch is very poor. An explicit analytical relationship for this ratio and its linear approximation in respect to the concrete characteristic and design strengths are presented in this article as well.

Sustainable and Efficient Structural Systems for Tall Buildings: Exploring Timber and Steel–Timber Hybrids through a Case Study

The paper focuses on tall timber buildings. The major aim of this paper is to identify the most sustainable and efficient structural system to increase the height of timber buildings, also considering steel–timber hybrid structures. First of all, a brief review of tall buildings’ evolution is presented to understand why tall timber buildings are considered nowadays and which are the most adopted structural solutions. Then, the case study of the tallest timber building in the world is selected and utilized as an archetype. Once the model has been validated, seven alternative structural systems are considered by varying the horizontal load resisting system and preserving the same member cross-sections as the reference building. The variants are tested and compared in terms of material consumption, vibration characteristics and lateral load response. Using the best structural system, the height of the building is increased, pushing the structures beyond the current limits and identifying the most efficient option. The idea is to preserve the column cross-sections and balance the increase in gravity loads due to the additional floors by replacing the concrete floors with timber counterparts. With the same structural system, equivalent steel–timber hybrid solutions are finally tested and compared in terms of sustainability to timber-only counterparts and to the original project. The results of analyses show that the use of steel elements combined with timber can lead to optimized and sustainable structural solutions.

Ultimate bearing capacity of T-shaped retrofitting diagonal members for angle steel transmission towers

Collapse of steel latticed transmission towers under strong winds is a significant safety concern for power systems. Attaching additional members to the tower members can enhance the wind resistance of transmission towers. To establish systematic retrofitting schemes and methods for predicting the ultimate bearing capacity of T-shaped retrofitting diagonal members, static experiments and finite element analysis on various cross-sectional dimensions and member lengths were utilized in this study. The experimental results indicate that retrofitting can effectively increase the bearing capacity of diagonal members. Finite element models are developed and verified based on the discussion of load-displacement curves and failure modes. The finite element analysis reveals that the increase in capacity achieved by reducing connector spacing is relatively small when compared to the ultimate bearing capacity obtained with the spacing of two connectors, and the arrangement of connectors at both ends meets the requirement of connector spacing. The relationship between the retrofitting bearing capacity and the slenderness ratio of diagonal members can be divided into two linear stages, which correspond to different failure modes. Furthermore, a λk coefficient method based on the axial compression equation is proposed to predict the ultimate bearing capacity of T-shaped retrofitting members. The bearing capacity based on the λk method shows agreement with finite element analysis results.

Geometric Nonlinear Analysis of Angle Section Elements Based on Updated Lagrangian Formulation and Rigid Body Rule

Angle cross-section members are widely used in various transmission towers owing to their convenient connections, easy availability, simple production processes, and high efficiency. Such members are very susceptible to nonlinear behavior when subjected to abnormal or extreme loads. In this work, a new geometric stiffness matrix for thin-walled steel members with an angle cross-section is derived based on the principle of virtual displacement, rigid body rule and updated Lagrangian equations. The generalized displacement control (GDC) method is employed to deal with the issues of non-convergence at the extreme value point and rebound point in the geometric nonlinear analysis, which offers clear physical meaning and can adjust the loading direction. The geometric and the traditional elastic stiffness matrices derived in this work are applied during the prediction phase, while only the traditional elastic stiffness matrix is used in the correction phase. The comparisons of the results obtained by the proposed method with those in the previous literature and ANSYS numerical solutions show that the proposed method is sufficient to ensure the accuracy and applicability for addressing the structural geometrically nonlinear issues.

Post-fire seismic performance of reinforced concrete structures

In this study, the seismic performance of a reinforced concrete (RC) structure with 4 stories and 4 spacings exposed to high temperatures was presented. Four different fire duration, i.e., 30, 45, 60, and 90 min and different fire locations were considered. In order to obtain the temperature distributions in the cross-sections of the RC members, thermal analyses were carried out under ISO-834 standard fire curve. The mechanical and thermal properties of the materials were also obtained. Then, sectional analyses were performed for the RC members to obtain the load-deformation relations. Finally, the nonlinear static analyses were conducted after fire exposure to obtain capacity curves, and the seismic performance of the structure was evaluated by transforming the capacity curves into the capacity spectra. It was found that when the temperature level increases, the mechanical and thermal properties of materials reduce especially after 4000 C. The results show that exposure to high temperatures leads to a significant decrease of about 75% of the load-carrying capacity of a structural member after 90 min. The results also show that when the fire duration increases, the base shear forces, and the roof displacements systematically decrease for all floors. The decrease rate in the base shear forces and the roof displacements was approximately up to 60%. The fire location also affects the system response. It was observed that the global structural response for elevated temperatures followed a gradual reduction in capacity with an increase in temperature levels.

Cold-formed steel strength predictions for torsion and bending–torsion interaction

Locally slender cross-section members, such as cold-formed steel open sections, are susceptible to significant twisting and high warping torsion stresses. Torsion considerations are complicated by whether it is derived as a first-order effect from loading or a second-order effect from instability. Previous direct torsion experiments on lipped Cee sections have shown significant inelastic reserve. Furthermore, the current design for combined bending–torsion interaction has limitations, including only considering the first yield and ignoring the cross-section slenderness in torsion. Two parametric studies were conducted to predict both the torsion capacity and the combined bending–torsion interaction in locally slender cross-sections. Shell finite element analysis of lipped Cee and Zee sections for both the torsion only and the combined bending–torsion cases were created using a validated model. For the torsion-only study, various cross-section geometries, steel grades, and member lengths covering the range of practically expected torsional slenderness were investigated. A set of bimoment parameters, including yield, buckling, and plastic bimoments, were calculated and the ultimate bimoment was determined by shell finite element collapse analyses. A simple uniform equation predicting the bimoment capacity was adopted and two bimoment strength curves are proposed for local and distortional buckling-controlled cases respectively. For the combined bending–torsion case, various practical cross-sections and bracing conditions were investigated with various ratios of applied torsion and bending. Shell finite element buckling and collapse analyses were performed to determine the critical and ultimate moments and bimoments. It was found that the current AISI standard is conservative under most scenarios. Updated torsion–bending interaction equations incorporating bimoment and bending moments are proposed. The interaction equations are dependent on the cross-section, the direction of the applied torsion, and the bracing condition.

On the Capacity of Beams with U Cross Section Subjected to Bending and Torsion

AbstractBeams with singly symmetric U cross sections are often subjected to bending about the strong axis and simultaneously to scheduled torsion, since the shear center is outside the section geometry. The member capacity of such sections, which is strongly influenced by effects of lateral torsional buckling, can therefore hardly be represented with the common design regulations based on reduction factors χLT of EN 1993‐1‐1. However, numerical approaches allow analyzing deeply the structural behavior of corresponding beams. In the present study, different numerical finite element simulations (GMNIA) including simplified numerical models based on the plastic zones theory are incorporated to determine member capacities and to derive corresponding reduction factors for simplified verifications. As the load‐bearing capacity of members susceptible to stability is strongly influenced by imperfections, the straightness according to manufacturing tolerances as well as approaches for the acquisition of structural imperfections (residual stresses) are considered in the numerical analyses. The investigations are carried out for selected structural systems with different sets of parameters, such as for the member lengths and cross section types. Concluding, a capacity curve is derived and compared to different reduction factors χLT specified in EN 1993‐1‐1.

Experimental and numerical studies on mechanical performance of the grid unit in single-layer reticulated shells with Temcor joints

Temcor joints are widely used in aluminium alloy single-layer latticed shells. However, the research mainly focuses on the connection joints of components, the research on the mechanical performance of the grid unit in single-layer reticulated shells is limit. In this paper, the performances of grid elements in single-layer aluminum alloy latticed shells with Temcor joints are studied through two full-scale tests with different member cross-section size, member length and joint construction. In the conducted tests, the failure mode, the load-displacement curves, and the bending moment-stress curves are recorded and discussed. The results indicate that the capacity and the ductility of aluminum alloy grid cells are affected significantly by the heights of the members. The failure of the grid unit with a height of 550 mm was triggered by the tensile fracture of the bottom flange in the connected members near connection joint. In contrast, the failure of the grid unit with a height of 200 mm was induced by the compression damage of the top flange in the members connected with joint, moreover, in-plane distortion was observed in the member near the gusset region. On this basis, the numerical simulation method using non-linear spring elements is proposed, in which the actual rotational stiffness of joints is considered. The load-displacement curves obtained from the refined finite element analysis model are validated to be in good agreement with the test results.

ECONOMICAL COMPARISON OF STEEL-FRAMED GREENHOUSE SYSTEMS

Since greenhouses are highly expensive structures, they need to be designed carefully with the use of modern technology of the day. Especially in the design of high-cost steel-framed greenhouses, system selection and dimensioning play an important role in economical design of load-bearing members. This study was conducted to investigate the effects of two different roof types (gothic and gable), two different truss spacings (2.5 and 3 m) and three different truss spans (6, 8 and 9.6 m) on cross-sections of load-bearing steel members, overall weight and final cost of greenhouse systems. Overall width of the systems was 48 m, length was 60 m and height was 4.5 m. Totally, 12 different greenhouse systems were designed and analyzed with the use of SAP2000 software, AutoCAD software, Excel worksheets, relevant standards and regulations. It was concluded based on present findings that gothic roof system with 3 m truss spacing and 9.6 truss span was lighter and more economical than the other systems. In terms of safety, gothic and gable roof systems with 6 m truss span and 2.5 m truss spacing were superior to other systems.

Review of the charring rates of different timber species

AbstractDuring a fire, the load‐carrying cross section of timber members will reduce due to charring. This article summarizes experimental investigations into the charring rate of different timber species under standard fire conditions, identifies material properties that contribute to the variations of char rates across the different species, and evaluates the applicability of prescribed charring rates to solid timber, cross‐laminated timber (CLT), and glulam exposed to standard fires. Data from the literature showed that density had the greatest impact on charring rate. The charring rate of timber decreased with increasing density, particularly timber densities >700 kg/m3. Prescribed charring rates from current design standards provide reasonable estimates of the average charring rate of timber with densities <700 kg/m3 exposed to standard fire curves. A linear charring rate of 0.65 mm/min was found to be suitable for CLT and glulam exposed to a standard fire for up to 180 min if the CLT did not experience char fall‐off. The National Design Specification nonlinear charring model may underestimate the char depth of glulam exposed to standard fire curves for longer than 60 min; however, the percent underestimation was small and limited data was available. The review demonstrated the need for data on the char depths of glulam and CLT exposed to standard fire curves for longer than 60 min and particularly for longer than 120 min.

The transformation matrix in the 7DOFs beam formulation

A non-negligible percentage of steel products for civil and industrial constructions is realised with members characterised by a mono-symmetric cross-section. The non-coincidence between the centroid and the shear centre reflects in a quite complex behaviour that is remarkably influenced by the warping effects. Usually, frame design is based on the output data of commercial Finite Element Analysis Packages (FEAPs) but only few of them offer a refined beam element formulation able to reproduce the response of non-bisymmetric cross-section members (like the 7 degrees of freedom, DOFs, beam element). As a consequence, warping effects are usually neglected in routine design, leading in several cases to assess non-correct internal stresses, global displacements and critical buckling multipliers.This paper is focussed on mono-symmetric cross-section members and deals with the influence of the interaction between axial force, bending moments and bimoment in linear elastic range. In particular, the two strategies that FE developers usually adopt, in the 7 DOFs beam formulation, to pass from the local to the global reference system are herein shortly introduced and discussed. The effects of the associated transformation matrices have been investigated in few examples, also reproduced via closed expressions derived from the mixed torsion theory and FE shell models. Paper outcomes show that the results in terms of generalised displacements, internal forces and, consequently, stress distribution along the member cross-section are significantly different, strictly depending on the adopted transformation matrix. The importance of a correct evaluation of the bimoment distribution is stressed also by the fact that the new edition of the EN1993-1-1, expected in the next months, includes also the bimoment contribution for member checks.

Analysis and Optimum Design of Self Supporting Steel Communication Tower

The present study deals with the optimum design of self supporting steel communication towers. A special technique is used to represent the tower as an equivalent hollow tapered beam with variable cross section. Then this method is employed to find the best layout of the tower among prespecified configurations. The formulation of the problem is applied to four types of tower layoutwith K and X brace, with equal and unequal panels. The objective function is the total weight of the tower. The variables are the base and the top dimensions, the number of panels for the tower and member's cross section areas. The formulations of design constraints are based on the requirements of EIA and ANSI codes for allowable stresses in the members and the allowable displacement atantenna position. The Sequential Unconstrained Minimization Technique (SUMT) is used to perform the process. Direct stiffness method is used for the analysis of the structure, with beam elements. The strain energy is used to derive the stiffness matrix for members of unsymmetrical cross section. A computer program in FORTRAN is developed to represent the tower as an equivalent beam, and generate the tower nodes and members, analysis, design and to find the optimum design. Four types of tower are studied with different load cases. The effects of earthquake and wind loadings are taken in two directions and two positions of antenna are considered in the process to seek the optimum design. The tower type of X-brace with unequal panels has the minimum weightcompared with other types of tower and the optimum design is satisfied when the angle of main leg is equal to (87O).

Optimization Design for Steel Trusses Based on a Genetic Algorithm

Steel trusses are widely utilized in engineering structures, and their optimization is essential for enhancing structural performance and reducing material consumption. Existing optimization methods for steel trusses predominantly rely on the trial-and-error method, which is not only inefficient but also inaccurate. Therefore, this study focused on the optimization of steel trusses using an efficient and accurate optimization methodology. Based on a genetic algorithm and the finite element method, both mono- and multi-parameter optimization designs for steel trusses were executed, an applicable optimization design method for steel trusses was established, and corresponding optimization design programs were developed. The analysis demonstrates that the proposed optimization method effectively optimizes truss height and member cross-section, leading to a significant reduction in material consumption. Compared to the traditional trial-and-error method, the proposed optimization method exhibits adequate calculation accuracy and superior optimization efficiency, thereby providing a robust theoretical foundation for the engineering design of steel trusses.

CFD wind tunnel investigation for wind loading on angle members in lattice tower structures

Wind loading on lattice structures is studied locally by considering the applied forces on individual angle members. This work represents a comprehensive Computational Fluid Dynamics (CFD) analysis of wind loading on angle members, which includes a quantitative evaluation of the aerodynamic drag and lift loading and also a qualitative investigation of the wake characteristics behind the angle member. The focus is on the flow around the angle member cross-section which has two equal length sides at a right angle to each other. CFD has been used to investigate the flow around a single angle member characterized by its length D, thickness T, and angle of incidence to the oncoming flow. Both Reynolds-Averaged Navier–Stokes (RANS) and Large-Eddy Simulation (LES) are evaluated for a Reynolds number of 37,700, where the k-ϵ RANS and Wall-Adapting Local Eddy-viscosity (WALE) LES models are respectively used. The results are compared with the wind tunnel experiments reported in the literature (Wardlaw, 1967; Slater, 1969; Prud’homme et al., 2014) and the National Building Code of Canada (Canadian Commission on Building and Fire Codes and National Building Code of Canada, 2005), where the drag and lift coefficients at a range of incidence angles were reported. Quantitatively, the RANS performs well when compared to experiments for the aerodynamic coefficients at a range of incidence angles and less well for angles where a cavity style flow is formed and the separation becomes influential. This is in contrast to other bluff body cases where RANS does not perform so well. The LES is thus run at selected incidence angles for comparison and to better understand the flow where the RANS performs well and less well. Details of the turbulence in the wake are difficult to interpret when using RANS modeling, but this behavior is well illustrated with the LES model and details are reported here.