Plane Steel Frames Research Articles

Finite Element-Based Structural Reliability Assessment Using Efficient Directional Simulation

Reliability analysis of structural systems often requires finite element (FE)-based simulation to estimate failure probabilities. Common simulation methods, even those incorporating variation reduction techniques, usually involve a very large number of FE analyses to achieve acceptable accuracy. A recently developed directional approach significantly improves the efficiency of directional simulation by utilizing deterministic point sets to preserve the underlying joint probability distribution of the random vector describing the structure and by employing neural networks to focus the simulation effort in the significant regions. This paper investigates the application of this method to structural system reliability analysis. The method is illustrated using deformation-based system limit states, proposed for performance-based engineering, for two plane steel frames.

線形座屈解析を用いた鋼構造平面骨組の座屈設計 : その2 地震荷重に対する定式化とブレース付骨組への適用

線形座屈解析を用いた鋼構造平面骨組の座屈設計 : その2 地震荷重に対する定式化とブレース付骨組への適用

Elastic Stability of Planar Steel Frames with Unsymmetrical Beam Loading

Unsymmetrical loads along the frame beams produce unequal axial forces in columns together with primary bending moments in the frame members. The combined effect of these two factors on the elastic buckling loads of the frames is studied. The case of one concentrated load acts at different locations on the frame beams is chosen as an example to study the effect of aforementioned factors. The analysis is applied on different types of structural systems such as braced and unbraced multistory frames. Parameters such as fixed and hinged bases, beam to column bending stiffness ratios, and beam span to column height ratios are considered. In addition, the effect of the axial stiffness of the bracing elements is taken into account. The matrix displacement method of analysis has been used throughout the study. The geometric nonlinear behavior of the members is considered by using the stability functions to modify the stiffness matrix of the individual members. Results clearly show that the combined action of the primary bending moments along with the variation of loads ratios on columns has considerable effect on the elastic buckling loads of the braced planar frames.

Cost function analysis in the structural optimization of steel frames

An objective function used in structural optimization should be formulated in such a way that the most economic solution can be found. However, the objective function is usually simplified to represent the weight, disregarding the fabrication and erection costs of the structure. The paper presents a very detailed objective function that considers the self-manufacturing costs of the whole structure. The cost function includes all essential fabrication and erection activities. It considers both manufacturing costs as well as material costs. It is formulated in an open manner, offering users the possibility to define their own parameters on the basis of a certain production line. The cost function is implemented into the optimization system for planar steel frames.

Analysis Of A Portal Steel Frame Subject To FireBy Use Of A Truss Model

A plane steel frame is simulated by a truss model. The bars obey uniaxial elastoplastic stress-strain laws. Yield stress and modulus of elasticity are assumed constant up to 300°C and then linearly decreasing up to zero for 900°C. Semi-rigid beam-column connection is represented by a hinge and a bar connecting column and beam; this bar has a small length and properly selected cross-section area and elasticity modulus. Three fire scenarios are considered. Numerical experiments show that heat conduction time in steel is very short and can be ignored; it is enough to assume simplified temperature distributions over the cross-sections. A short computer program, with only about 200 Fortran instructions, is documented, for the step-by-step nonlinear structural analysis of plane truss models of steel frames subjected to fire. Geometrical nonlinearities are taken into account by writing, within each time step of the algorithm, the equilibrium conditions with respect to the deformed truss. The program is applied on a typical steel portal frame. In the output of the application, it is observed that, for temperatures lower than 300°C, influence of fire appears by thermal expansion and additional stresses, as well as by thermal bowing of beams due to temperature gradient over the cross-sections. Whereas, for temperatures higher than 300°C, plastic hinges are gradually formed due to yield stress reduction with temperature, and columns may buckle due to elasticity modulus reduction with temperature. Each of the above two phenomena may lead to a collapse of the portal frame, which is shown, in the analysis, by very large displacements.

Static inelastic analysis of steel frames with flexible connections

The effects of connection flexibility and material yielding on the behavior of plane steel frames subjected to static (monotonic) loads are presented in this paper. Two types of material nonlinearities are considered: flexible nodal connections and material yielding, as well as geometric nonlinearity of the structure. To account for material yielding, a plastic hinge concept is adopted. A flexible connection is idealized by nonlinear rotational spring. Plastic hinge is also idealized by nonlinear rotational spring attached in series with the rotational spring that accounts for connection flexibility. The stiffness matrix for the beam with flexible connections and plastic hinges at its ends is obtained. To illustrate the validity and accuracy of the proposed numerical model, several examples have been conducted.

Practical second-order inelastic analysis for steel frames subjected to distributed load

A practical second-order inelastic analysis of planar steel frames subjected to distributed load is developed. This analysis realistically assesses both strength and behavior of a structural system and its component members in a direct manner. To capture second-order effects associated with P– δ and P–Δ, stability functions are used to minimize modeling and solution time. The column research council (CRC) tangent modulus concept is used to account for gradual yielding due to residual stresses. A softening plastic-hinge model is used to represent the degradation from elastic to zero stiffness associated with development of a hinge. In the proposed analysis, a member has two elements and three nodal points. A plastic-hinge location can be captured in analysis as the internal nodal point traces the maximum moment location at each load step. Maximum moments and load–displacements predicted by the proposed analysis compare well with those given by other approaches.

The effect of joint flexibility on the free elastic vibration characteristics of steel plane frames

The present work offers a simplified approach for establishing the effect of joint flexibility on the free vibration characteristics of steel plane frames. Based on the beam-to-column model of Eurocode 3, the presented analysis shows that within the elastic range and under certain combinations of the parameters involved, a transition to a higher vibration mode may occur, a finding of great importance for structural design purposes. Numerical results of an L-shaped steel frame, considered either rigid or semi-rigid, in tabular and graphical form, reveal the pronounced effect of the joint’s stiffness and its specific role especially on higher vibration modes, implying that the actual flexible joint behavior should be accounted for, even in the elastic range.

Dynamic analysis of steel frames with flexible connections

This paper deals with the effects of flexibility and damping in the nodal connections on the dynamic behavior of plane steel frames. A flexible eccentric connection is idealized by nonlinear rotational spring and dashpot in parallel. Thus, the effects of viscous and hysteretic damping on dynamic response of frame structures are taken into consideration. A numerical model that includes both nonlinear connection behavior and geometric nonlinearity of the structure is developed. The complex dynamic stiffness matrix for the beam with flexible connections and linear viscous dampers at its ends is obtained. Several examples are included to illustrate the efficiency and accuracy of the present model.

Weight Optimization of Steel Frames Using Genetic Algorithm

Genetic Algorithm (GA) is a new technique in optimization procedure that works best in design problems with discrete variables. It employs the survival of the fittest philosophy in determining the optimum combination. GA optimization procedure is applied to weight optimization of steel plane frames subjected to different load cases. Database of steel beam sizes is provided as the discrete variables. Both elitist and non-elitist search procedures are used to optimize the total weight of steel frames. Crossover types used are 20- and 50-percent uniform. Optimization result using population sizes 10, 20, and 40 are compared. Elitist search procedure showed superior results when compared to non-elitist for higher population sizes search because of its faster convergence rate. Performance of non-elitist is superior when using lesser population sizes. To examine the performance of genetic algorithms, case studies are conducted by varying material groups and the results are compared with the results from other optimization techniques. Genetic optimization showed superior results when compared to other techniques especially to problems with few material groupings.

Genetic algorithm based optimum design of nonlinear planar steel frames with various semi-rigid connections

A genetic algorithm based optimum design method is presented for nonlinear multistorey steel frames with semi-rigid connections. The design algorithm obtains optimum frame by selecting appropriate sections from standard steel section tables while satisfying the serviceability and strength limitations specified in BS5950. The algorithm accounts for the effect of the flexibility of the connections and the geometric non-linearity of the members. The semi-rigid connections are modeled with the Frye–Morris polynomial model. The values of the coefficients, such as the diameter of bolts, the gauge and the geometric dimensions of angles used in the standardization constants are obtained by designing each connection in the frame during the optimum design cycles. The effective length factors for columns, which are flexibly connected to beams, are obtained from the solution of the nonlinear interaction equation. Several steel frames with different beam to column connections, such as extended end plate, and top and seat angle with and without web cleat, are designed using the algorithm. Each design is carried out twice, with and without considering the geometric non-linearity. Comparison of optimum frames has shown that consideration of geometric non-linearity results in greater economy. It is also noticed that taking the realistic behavior of beam–column connection into account produces more appropriate and in some cases even lighter designs.

Consideration of out-of-plane buckling in advanced analysis for planar steel frame design

A technique that may be used to augment most in-plane advanced analysis procedures to account for inelastic out-of-plane flexural–torsional buckling in the design of planar steel frames is presented. The linear stability theory is adopted and the finite element analysis method is used to derive the second-order stiffness matrix. The effects of material nonlinearities and geometric imperfections on out-of-plane buckling strength are accounted for by substituting the elastic rigidities ( EI y , EC w and GJ) with their effective values, which are determined from calibrations against specification equations for member strength. Based on a set of attributes found in typical building frames, it is demonstrated that out-of-plane buckling is likely to govern the strength of nonsway frames and may control the strength of sway frames. Thus, the proposed advanced analysis technique is recommended for the design of both types of planar steel frames.

Design optimization of structural steelwork using a genetic algorithm, FEM and a system of design rules

In this paper a structural optimization technique based on a modified genetic algorithm (GA) is presented. The technique is developed to deal with discrete design optimization of structural steelwork. Also, the paper discusses the effect of different approaches, employed for the determination of the effective buckling length of a column, on the optimum design. In order to consider realistic steelwork design problems, a modified GA has been linked to a system of structural design rules (British Standards BS 5950 and BS 6399), interacting with a finite element package. In the formulation of the optimization problem, the objective function is the total weight of the structural members, as it gives a reasonably accurate estimation of the cost. The cross‐sectional properties of the structural members, which form the set of design variables, are chosen from two separate catalogues (universal beams and columns) covered by the British Standard BS 4. The minimum weight designs of two plane steel frame structures subjected to realistic multiple loading cases are obtained. These examples show that the modified GA in combination with structural design rules and more accurate analysis provides an efficient tool for practicing designers of steel frame structures. Finally, it is shown that the resulting design optimization is considerably influenced by a specific choice of a technique employed for the evaluation of the effective buckling length of structural members.

Second-order analysis of planar steel frames considering the effect of spread of plasticity

This paper presents a method of elastic-plastic analysis for planar steel frames that provides the accuracy of distributed plasticity methods with the computational efficiency that is greater than that of distributed plasticity methods but less than that of plastic-hinge based methods. This method accounts for the effect of spread of plasticity accurately without discretization through the cross-section of a beam-column element, which is achieved by the following procedures. First, nonlinear equations describing the relationships between generalized stresses and strains of the cross-section are derived analytically. Next, nonlinear force-deformation relationships for the beam-column element are obtained through lengthwise integration of the generalized strains. Elastic-plastic flexibility coefficients are then calculated by differentiating the above element force-deformation relationships. Finally, an elastic-plastic stiffness matrix is obtained by making use of the flexibility-stiffness transformation. Adding the conventional geometric stiffness matrix to the elastic-plastic stiffness matrix results in the tangent stiffness matrix, which can readily be used to evaluate the load carrying capacity of steel frames following standard nonlinear analysis procedures. The accuracy of the proposed method is verified by several examples that are sensitive to the effect of spread of plasticity.

Plastic-Zone Analysis of 3D Steel Frames Using Beam Elements

This paper presents a corotational formulation of a spatial beam element for the purpose of 3D plastic-zone analysis of steel frames composed of compact tubular sections and open sections with no significant torsional warping. The special features of this paper, which have not been discussed in detail by other researchers, include the proposition of a torsional strain-displacement relationship for rectangular hollow sections, and the elucidation of the proper force recovery procedure for a displacement-based plastic-zone beam element. Issues concerning the miter model and the use of a consistent tangent operator in geometrically and materially nonlinear analysis are briefly discussed. Verification against three experimental tests on planar and spatial steel frames is included in the paper. It is demonstrated that in general only three cubic elements are required to model a story column with excellent accuracy, and four or five elements are sufficient for a base column with a rigid support. Such meshes are...

Inelastic Behavior of Multistory Partially Restrained Steel Frames. Part I

This paper outlines the development of a finite element for use in the inelastic second-order analysis of partially (PR) and fully (FR) restrained planar steel frames. The finite element considers spread of plastification within the cross section and along the member length; centroidal shift of the elastic core; a variety of residual stress distributions; and P-Δ effects. Nonlinear spring elements are used in modeling beam-end connections. An arc-length technique (with iteration) is used in the analysis of individual beam-columns, while constant-work simple Euler stepping (no iteration) is used in the nonlinear analysis of frameworks. Full nonlinear load-deformation response of planar beam-columns and frames is computed. Accuracy is demonstrated through comparison with previously published analytical results. It is shown that concentrated plasticity models may lead to an overestimation of connection rotation in PR frameworks. A companion paper discusses the inelastic ultimate load analysis of large steel PR frameworks and evaluation of connection classification systems.

Seismic Damage Assessment of Steel Frames

The seismic damage analysis of steel frames based on the use of global evaluation indices is addressed. A general procedure is proposed aimed at estimating the degree of damage induced by severe earthquakes in structures not supplied with monitoring systems. Special reference is made to the Park-Ang, McCabe-Hall, and plastic fatigue indices. The procedure is characterized by a form of automatic calibration of the free coefficients contained in the expressions of these indices. This allows one to constrain the arbitrariness in the coefficient choices, representing the greatest source of uncertainties for practical damage field assessment. Story stiffness degradation and permanent interstory displacements are assumed as the a posteriori measurable quantities upon which the reliability of the computational predictions supporting damage estimation are checked. The suitability of this procedure as well as of the considered indices for seismic damage characterization are discussed with reference to two case studies, represented by one shear-type and one concentrically braced, two-story plane steel frame, experimentally tested to failure.

Computer-aided design of structural steel plane frames according to Eurocode 3

Computer-aided design of structural steel plane frames according to Eurocode 3

Non-linear analysis of steel plane frames with semirigid connections

Non-linear analysis of steel plane frames with semirigid connections

Stability design of steel plane frames by second-order elastic analysis

A new stability design method for steel plane frames using second-order elastic analysis is proposed. Although many current design methods are based on the effective buckling length concept, the effective buckling length may not always be obtained accurately. This requires that a stability design method be developed without using the effective buckling length. In this method, the introduction of equivalent initial deflection, which accounts for the reduction in strength due to various initial imperfections, is of the utmost importance. Therefore, a new formula for the equivalent initial deflection is proposed, and a methodology using the curvature of the buckling mode is introduced to allow-for a systematic application of this formula to arbitrary shaped irregular frames. The validity and efficiency of the method are demonstrated by some examples.