Pitched-roof Frames Research Articles

Discrete Optimum Design of Planar Steel Curved Roof and Pitched Roof Portal Frames Using Metaheuristic Algorithms

Portal frames are single-story frame buildings including columns and rafters, and their rafters can be either curved or pitched. These are used widely in the construction of industrial buildings, warehouses, gyms, fire stations, agricultural buildings, hangars, etc. The construction cost of these frames considerably depends on their weight. In the present research, the discrete optimum design of two types of portal frames including planar steel Curved Roof Frame (CRF) and Pitched Roof Frame (PRF) with tapered I-section members are presented. The optimal design aims to minimize the weight of these frame structures while satisfying some design constraints based on the requirements of ANSI/AISC 360-16 and ASCE 7-10. Four population-based metaheuristic optimization algorithms are applied to the optimal design of these frames. These algorithms consist of Teaching-Learning-Based Optimization (TLBO), Enhanced Colliding Bodies Optimization (ECBO), Shuffled Shepherd Optimization Algorithm (SSOA), and Water Strider Algorithm (WSA). Two main objectives are followed in this paper. The first one deals with comparing the optimized weight of the CRF and PRF structures with the same dimensions for height and span in two different span lengths (16.0 m and 32.0 m), and the second one is related to comparing the performance of the considered metaheuristics in the optimum design of these portal frames. The obtained results reveal that CRF is more economical than PRF in the fair comparison. Moreover, comparing the results acquired by SSOA with those of other considered metaheuristics reveals that SSOA has better performance for the optimal design of these portal frames.

Minimum Weight Design of Pitched Roof Steel Frames.(Dept.C)

The optimum elastic design of p itched roof frames has been studied. An iterative method which uses Taylor's first order series expansion to express the various required constraints is employed. The function of the problem is linear in the design variables, which enables the simp lex line ar programming algorithm to be used to solve the problem, An example of rectangular hall has been investigated. The hall is cove red by pitched roof frames with different sp ans, spacing and slop es. Stress and deflection limitations are taken into consideration and the optimum cross-sectional area of the various members of the structure has been obtained. Design charts to determine the minimum weight of p itched roof frames, with different sp ans, spacing and slopes, covering a rectangular hall are given.

Analysisof Effective Length Factors of Hinged Pitched-Roof Framed Column with Sway under Arch Effect

Aiming at the limitation of the calculated length coefficient of the gable portal rigid frame columns in the standards and regulations, which ignores the influence of the arch effect caused by the axial force of the inclined beams lope, this paper uses the elastic buckling equation of the solid-webbed articulated pitched-roof frame, considered 𝑃−𝛥 second-order effect and the arch effect of the inclined beam under uniform load together. And the length coefficient calculated is analyzed. It is concluded that the larger the slope of the inclined beam and the ratio of the rigid frame span are, the more obvious the arching effect is, and the larger the calculated length coefficient of the rigid frame column is.

Optimal Design of Pitched Roof Rigid Frames with Non-Prismatic Members Using Quantum Evolutionary Algorithm

The weight and shape of the gable and multi-span frames (mono and two-span pitched roof) with tapered members, as a familiar group of the pitched roof frames, are highly dependent on the properties of the member cross-section. In this work a quantum inspired evolutionary algorithms, so-called Quantum evolutionary algorithm (QEA) [1], are utilized for optimal design of one gable frame and a multi-span frame in five alternatives with tapered members. In order to optimize the frames, the design is performed using the AISC specifications for stress, displacement and stability constraints. The design constraints and weight of the gable and multi-span frames are computed from the cross-section of members. These optimum weights are obtained using aforementioned optimization algorithm considering the cross-section of members and design constraints as optimization variables and constraints, respectively. A comparative study of the QEA and some recently developed methods from literature is also performed to illustrate the performance of the utilized optimization algorithm and its featuring. Furthermore, optimal design of a multi-span frame is compared with the solution of other methods including the same conditions and constraints. This study indicates the power of QEA in exploring and exploitation due the search space with using Q-gate and binary code for individual representation and updating. Binary code helps the QEA to find optimal solution even with minimum number of Q-bit individuals. High speed of this method is because of such a feature.

Linear Analysis of Stability of Pitched Roof Frames

Background: In this paper, geometric nonlinear analysis of pitched roof frames was carried out by the stiffness matrix method using stability functions. Objective: This study contributes to a better knowledge of the stability of pitched roof frames, not braced, and therefore of the efficiency in their dimensioning. Method: At first, the argument of the stability functions was set as 0.01. The stiffness matrix of the frame has been assembled, as well as the nodal load vector of the frame. The boundary conditions (support restraint and wind bracing restraint) were introduced for the reduction of this matrix and the nodal load vector. At this stage, the determinant of the reduced stiffness matrix and the reduced nodal displacement vector are calculated. The argument of the stability functions is incremented by 0.01 and the operations are repeated until the determinant of the reduced stiffness matrix changes sign. The argument of the iteration preceding the sign change of the determinant and corresponding to its positive value is taken and refined by a process described in the paper. The buckling loads of the frame members are determined at this stage. Results and Conclusion: The analysis focused on four frames; the obtained results show that the increase in the inclination of the crossbar makes it possible to take full advantage of the “arch effect”. Arch effect is due to the presence of crossbars which have a linear arch shape. Furthermore, the angle as well as the length ratio, between the crossbar and post, influence critical load value.

Optimal Design of Multi-Span Pitched Roof Frames with Tapered Members

Many industrial buildings require large spans and high height, and the use of a frame with inclined roofs with non-prismatic elements can reduce the usage of steel. Pitched roof frame with single spans are optimized using different meta-heuristic algorithms. In this paper, the optimal design of industrial frames with two and three spans under gravity and lateral loads is performed. Five efficient and widely accepted optimization algorithms are used to optimize each frame. The convergence histories and design results of these algorithms are compared and the most suitable algorithm is determined. In each frame, the effect of increasing the apex height is evaluated on the optimal weight and the best angle is determined for optimum weight.

Geometry and Sizing Optimization of Steel Pitched Roof Frames with Tapered Members Using Nine Metaheuristics

Steel pitched roof frames with the tapper fabricated members is the common solution for a wide range of industrial structures. In the present research, design optimization of the steel member sections is performed by different apex heights and tapered lengths for steel pitched roof frames. The effective variable definition has helped to reduce the variable domain and ignore the unwanted part of the bounds before starting the optimization process. Nine metaheuristic algorithms are used for the optimization. Results show that selecting apex height and tapered length can change optimum weight of structure by 10%. Additionally, performance of the considered metaheuristic algorithms is compared for this type of frame structures.

Optimizing Structures with Semi-Rigid Connections Using the Principle of Virtual Work

In this paper, the virtual work optimization method (VWOM) has been generalised to consider structures with semi-rigid connections. The VWOM is an automated method that minimizes the mass of a structure with a given geometry, multiple deflection criteria and load cases, while adhering to Design code requirements. In the optimization process, members are selected from a discrete database to meet all strength and stiffness criteria. Connections are modelled using rotational springs, allowing some moment transfer. The rotational stiffness of each connection can be varied form rigid to pinned. The example of a pitched roof frame is used to explain the method. Two case studies are considered: (i) a three-storey two-bay and (ii) a four-storey three-bay office building. The VWOM produced results up to 26.7% lighter than results in the literature. Furthermore, the structures were optimized for a range of rotational stiffness, where all connections in the structure were assumed to have the same rotational stiffness. Characteristic jumps in the optimized mass versus rotational stiffness were observed.

Optimal design of pitched roof frames with tapered members using ECBO algorithm

Pitched roof frames are widely used in construction of the industrial buildings, gyms, schools and colleges, fire stations, storages, hangars and many other low rise structures. The weight and shape of the gable frames with tapered members, as a familiar group of the pitched roof frames, are highly dependent on the properties of the member cross-sectional. In this work Enhanced Colliding Bodies Optimization (ECBO) is utilized for optimal design of three gable frames with tapered members. In order to optimize the frames, the design is performed using the AISC specifications for stress, displacement and stability constraints. The design constraints and weight of the gable frames are computed from the cross-section of members. These optimum weights are obtained using aforementioned optimization algorithms considering the cross-sections of the members and design constraints as optimization variables and constraints, respectively. A comparative study of the PSO and CBO with ECBO is also performed to illustrate the importance of the enhancement of the utilized optimization algorithm.

Estabilidade e vibração não linear de pórticos em aço usados em galpões industriais: análise paramétrica

Esse trabalho apresenta um estudo referente à análise da estabilidade e vibração não linear de pórticos de aço planos do tipo galpão. Especial atenção é voltada à influência do pré-carregamento estático nas frequências naturais e nos modos de vibração dessas estruturas. Nesse sentido, foi utilizada uma formulação não linear de elementos finitos de viga-coluna que permite considerar as ligações entre os membros estruturais como semirrígidas. Para resolver o problema de equilíbrio estático não linear, um processo incremental e iterativo do tipo Newton acoplado ao método do comprimento de arco é adotado. Uma vez obtida convergência em cada passo de carga, emprega-se o método de Jacobi, para se determinarem as frequências naturais e os modos de vibração da estrutura pré-carregada. Todo o processo de solução não linear adotado é detalhado em um algoritmo. A influência de um parâmetro geométrico (altura da tesoura) e outro físico (rigidez dos apoios) no comportamento do pórtico tipo galpão é destacada nas análises. Objetiva-se, assim, obter uma melhor compreensão de alguns fenômenos de instabilidade e sensibilidade estrutural e mostrar a importância desses parâmetros e do pré-carregamento estático na flambagem e na vibração dessa estrutura de grande aplicação prática.

Nonlinear dynamic behavior and instability of slender frames with semi-rigid connections

The free and forced nonlinear vibrations of slender frames with semi-rigid connections are studied in this work. Special attention is given to the influence of static pre-load on the natural frequencies and mode shapes, nonlinear frequency–amplitude relations, and resonance curves. An efficient nonlinear finite element program for buckling and vibration analysis of slender elastic frames with semi-rigid connections is developed. The equilibrium paths are obtained by continuation techniques, in combination with the Newton-Raphson method. The ordinary differential equations of motion of the discretized frame are solved by the Newmark implicit numerical integration method using adaptive time-step strategies. Three structural systems with important practical applications are analyzed: an L-frame, a shallow arch, and a pitched-roof frame. The results highlight the importance of the static pre-load and the stiffness of the semi-rigid connections on the buckling and vibration characteristics of these structures.

Elastic buckling and second-order behaviour of pitched-roof steel frames

The aims of this work are two-fold: (i) to present the results of a study concerning the elastic in-plane stability and second-order behaviour of unbraced single-bay pitched-roof steel frames and (ii) to propose, validate and illustrate the application of an efficient methodology to design this type of commonly used frame. After (i) characterizing the relevant frame buckling modes and P – Δ second-order effects, and (ii) addressing the exact and approximate calculation of the associated bifurcation loads and secondary bending moments, the paper deals with the incorporation of these concepts in the definition of an efficient design procedure. In particular, it is clearly shown that, due to the rafter slope, the geometrically nonlinear behaviours of orthogonal beam-and-column and pitched-roof frames are qualitatively different. Finally, the proposed concepts and methodologies are illustrated through the presentation and discussion of numerical results involving fixed and pinned-base frames.

Optimum design of pitched roof steel frames with haunched rafters by genetic algorithm

The pitched roof steel frames appear to be the simplest structural form used in single storey buildings. However, its design necessitates consideration of many different structural criteria that are required in the design of complex structures. In this paper, a genetic algorithm is used to develop an optimum design method for pitched roof steel frames with haunches for the rafters in the eaves. The algorithm selects the optimum universal beam sections for columns and rafters from the available steel sections tables. Furthermore, it determines the optimum depth of the haunch at the eaves and the length of the haunch required for reaching the most cost-effective form. Formulation of the design problem is based on the elastic design method. The serviceability and the strength constraints are included in the design problem as defined in BS 5950. Furthermore, the overall buckling of columns and rafters in the torsional mode between effective torsional restraints to both flanges is also checked. A pitched roof frame is designed by the algorithm developed to demonstrate its practical application.

Optimal plastic design of pitched roof frames for multiple loading

The paper describes the use of algebraic linear programming for the minimum weight design of steel portal frames subject to the constraints of the Kinematic Theorem of plastic collapse. Minimum weight design is a classic linear programming problem which can be solved algebraically for classes of frames with arbitrary geometric dimensions and arbitrary load magnitudes. In a recent paper, the process of algebraic linear programming was reduced to the repeated application of a number of vector formulas and a computer program was developed for the derivation of the solution charts for specific classes of frames. In this paper the method is extended to the problem of frames subjected to multiple load cases. It is shown that simple problems whose solution can normally be displayed in the form of two-dimensional charts now require three-dimensional charts or a number of two-dimensional charts.

Stability of Pitched‐Roof Frames in National Building Codes

The buckling loads, buckling lengths, and P‐delta effects for pitched roof frames with different loading arrangements are examined. Results are compared to some common and internationally known code results. It was found that the load distribution significantly affects the buckling loads and hence the buckling lengths and the magnified (or added) moments. This paper clarifies a defect in some national building codes and encourages the use of computers in determining the buckling loads and/or the magnified moments. It is worth noting that although the program suggested is simple, it is robust and could be used to trace the large deformation characteristics of frames.

Stability control of pitched-roof frames by allowable member depth

Abstract This paper synthesises extensive previous research work by the author and his coworkers on a novel approach to satisfy in-plane stability of plastically designed pitched-roof steel frames. Overall sway and snap-through buckling as well as member buckling are addressed. For the first time, simple composite stability provisions in the form of allowable member depths are formulated for columns and rafters in regular frameworks of practical dimensions. Lateral and local member buckling are excluded from this study.

The finite deflection of plane frames

If the elements into which a frame is divided are small enough the large deflection behaviour of the frame can be analysed on the basis of simple bending stiffnesses for each element (without the use of stability functions), provided only that the rigid body displacements of the element are correctly allowed for in its governing equations. This thesis is developed, confirmed by comparison with the exact solution for a cantilever, and applied to the large displacement analysis of a two-bay, two-storey pitched-roof frame (see Fig. 6). The equilibrium equations are solved by the method of Dynamic Relaxation.