Optimum design of unbraced rigid frames
Introduction
The increase in the efficiency of structural optimization techniques and the tendency of using high strength steel have resulted in greater lateral flexibility in high-rise steel frames. It is more likely that such frames fail by instability before a plastic collapse mechanism is formed under increasing loads. This leads to the necessity of considering the instability effects in the optimum design algorithm. To study the instability of unbraced tall steel frames, it is required to take into account the effect of axial forces in the equilibrium of the structure. This renders the behaviour of the frame to be non-linear. Most of the optimum design algorithms developed for steel frames were based on the elastic behaviour of the structure1, 2, 3. While the earlier group of design algorithms used mathematical programming techniques to formulate and solve the design problem3, 4, 5, it was later found that the optimality criteria approach was more efficient for the design of practical size frames1, 2, 6. In some of the recent design procedures the non-linear behaviour of the structure was accommodated7, 8, 9, 10.
The optimum design algorithm presented in this study takes into account the non-linear response of the steel frames due to the effect of axial forces. It considers the displacement and minimum size constraints as well as combined stress limitations. The latter is included according to the American Institute of Steel Construction (AISC)[11]. During the design process, the values of design variables are updated by using two recursive relationships. The first one is obtained by making use of the optimality criteria approach for the case of dominant displacement constraints. The second one is calculated from the solution of a non-linear equation, which is obtained by expressing the combined stress constraints in terms of design variables. The largest value from these two, and the minimum size limitation, is taken as the new design variable value for the next design cycle.
The algorithm initiates the design process by carrying out the non-linear analysis of the frame. Stability functions are used in this analysis to include the effect of axial forces on the deformed shape of the members[12]. During the iterations of the non-linear analysis, the overall stability of the frame is checked. When the loss of stability is observed, the design process is terminated and then it is re-started from a different initial point. If the non-linear response of the frame is successfully obtained, the new values of design variables are computed by using the recursive relationships. The change in the values of design variables necessitates updating the non-linear response of the frame. This process of re-analysis and re-sizing is repeated until the convergence is obtained in the objective function.
Section snippets
Mathematical model
The optimum design of non-linear unbraced tall frames can be described mathematically as follows:subject towhere W is the objective function which is taken as the overall weight of the frame, Ak is the design variable representing the area of members belonging to group k, while mk is the total number of members in group k. ρi and li are the density and length of member i, respectively. gdi (Ak) represents the
Design procedure
The solution of the design problem stated in Eq. (1)is obtained in an iterative manner. The values of area variables are changed in every iteration to get an improved design. It is apparent that the new values of variables are controlled by the most severe constraints in the design problem. Hence, it becomes necessary to obtain expressions for updating the design variables depending upon whether the displacement or strength constraints are dominant. If neither of these constraints is dominant,
Design examples
The design algorithm presented is applied to the optimum design of three unbraced tall steel frames. In these examples, the yield stress was taken as 230 N/mm2. The step size of t=0.5 was found suitable for the Lagrange parameters and the value of c=4 has provided a reasonable speed of convergence for the recursive relationship of Eq. (15)for area variables.
Conclusions
The optimum design algorithm developed for multistorey unbraced rigid frames considers the displacement and combined strength constraints in the design problem. Furthermore, it also takes into account the non-linear response of the frame due to the effect of axial forces in its members. It is shown that the consideration of the non-linear behaviour in the optimum design of such frames does not only provide more economy, but it also produces more realistic results. It was noticed that the
References (15)
Optimum design of steel frames with stability constraints
J Comput Struct
(1991)Optimum design of rigidly jointed frames
Comput Struct
(1980)- et al.
Optimum design of geometrically nonlinear elastic–plastic steel frames
Comput Struct
(1991) - et al.
Optimum design of geometrically nonlinear space trusses
Comput Struct
(1992) Optimality criterion techniques applied to frames having general cross-sectional relationships
AIAA J
(1984)- Kirsch U. Optimum structural design. New York: McGraw-Hill,...
- et al.
Structural optimization by nonlinear programming
J Struct Div ASCE
(1966)
Cited by (36)
Optimum design of steel building structures using migration-based vibrating particles system
2021, StructuresCitation Excerpt :During the last decades, different optimization methods have been proposed/developed/applied and discussed by many researchers to utilize as metaheuristic techniques for optimum design of skeletal structures [1–4].
Optimization of nonlinear inelastic steel frames considering panel zones
2020, Advances in Engineering SoftwareCitation Excerpt :This fact is more notable in the case of the optimization of real steel frames where several load combinations are considered since the number of structural analysis is much greater than when only one load combination is considered. Due to the highly computational efforts, in most published studies of steel frame optimization using nonlinear analysis, the authors have tried to develop optimization methods which have fast convergence and then verify these methods using small case studies and a small number (often < 10,000) of objective function evaluations [7, 8,37–39]. Panel zone is the column web area located at a beam-to-column connection.
School based optimization algorithm for design of steel frames
2018, Engineering StructuresCitation Excerpt :In addition, statistical results show that over 100 runs, SBO has an average weight that is 3.1% lighter with a standard deviation that is 47% lower than designs developed with a SGA [31]. Table 3 summarizes the design optimization performance for SBO, GA [47], ACO [21], TLBO [26], and SGA [31]. Fig. 4 shows the convergence history plots for the SBO algorithm for both cases.
Reliability-based design optimization of nonlinear inelastic trusses using improved differential evolution algorithm
2018, Advances in Engineering SoftwareCitation Excerpt :In a linear analysis, the effects of large deflection and inelastic material are not considered, so this approach cannot accurately predict the real behaviors of structures. Recently, several studies of DDO of nonlinear steel structures have been conducted (see Refs. [13–18], among others). These works prove that using nonlinear inelastic analysis in structural optimization produces more realistic results.
Optimum topological design of geometrically nonlinear single layer latticed domes using coupled genetic algorithm
2007, Computers and StructuresOptimum geometry design of nonlinear braced domes using genetic algorithm
2007, Computers and Structures