Economization of the structural systems by optimizing the elements is the recent trend receiving much attention in structural engineering designs. In this work, a numerical study is made to arrive at the optimal proportions of the cold-formed steel (CFS) Lipped C, Lipped Z, and Rectangular Hollow Flange sections (RHFB) when used as flexural members. Web depth to developed length ratio (k) and the flange width to lip depth ratio (a) are the two parameters taken for this optimization. Genetic algorithm was used to obtain the optimum values. Investigations are carried out on the variation in the moment capacity to the changes in dimensions of web, flange and lip. In this work developed length ranging from 100 mm to 500 mm and thickness of 1 mm to 3 mm were adopted. The moment capacity and buckling behavior of (CFS) sections are verified by non-linear finite element analysis using ABAQUS.
La tendencia actual en los diseños de la ingeniería estructural es el abaratamiento de los sistemas estructurales mediante la optimización de sus elementos. En este trabajo se emplean métodos numéricos para obtener las dimensiones óptimas de secciones conformadas en frío (CFS) tipo C, Z y en I con perfiles huecos rectangulares (RHFB) que se usan para piezas en flexión. Para la optimización se usaron dos parámetros, la relación entre la dimensión del alma y la longitud del desarrollo (k) y la relación entre la longitud del ala y la longitud del labio (a). Los valores óptimos se obtuvieron mediante algoritmos genéticos. Se investiga la variación del momento resistido con las variaciones en la dimensión del alma, el ala y el labio. Las longitudes de desarrollo consideradas en este trabajo van de 100 mm a 500 mm y los espesores adoptados desde 1 mm a 3 mm. El momento resistido y el comportamiento a pandeo de las secciones conformadas en frío (CFS) se verifican mediante el análisis por elementos finitos no lineales usando ABAQUS.
In the design of any structural elements, adequate safety is to be guaranteed, and at the same time, it should be designed such that the cost is minimum. This is achieved by choosing the best geometry consistent with the functional requirements and proportioning the materials used for these structural elements in the most appropriate manner. In steel constructions, cold formed steel sections (CFS) are widely used. The modern CFS sections are quite complex, and they have a large number of independent parts. They are susceptible to different types of buckling and other constraints. Considerable scope exists in the rationalization and economization of CFS sections. In recent years this optimization receives much attention in the area of design. Engaging Genetic Algorithm, the symmetric CFS beam-column members are optimized by (
In this work, purlins in the roof system of a pre engineered steel structure is adopted for optimization. The design of a purlin has to withstand the moment arising from the combination of predominant loads like the dead, live, and wind loads. The nature of moment in a purlin may be of sagging or hogging depending upon the combination of wind load with other loads. The worst combination of loads will govern the design. In practice, the roof diaphragm connected to the compression flange of a purlin at a spacing not exceeding 300 mm through fasteners and it will act as a lateral restraint. During wind uplifting, the purlin is laterally unrestrained. To restrain the compression flange in case of wind uplift, it is a general practice to brace the bottom flange at suitable intervals with the top flange of adjacent purlins using sag rods. This bracings will act as a partial restraint and the portion of purlin between the bracings has to be designed for laterally unrestrained condition. In this study, the length between such bracing is taken as 2.5 m.
With the conditions given above, the aim of this work is to find the optimum proportion of the conventional lipped C, Z, and the newly formed Rectangular Hollow Flange sections (RHFB) for the given developed length. The RHFB sections has many advantages than the conventional sections due to tubular flanges. Research on the behaviour of the hollow flange channel beam under lateral buckling was carried out by researchers (
This work considers the advantage of flexibility in fabricating a CFS section in a local manufacturing unit. The CFS sections are optimized to achieve maximum bending and buckling resistance for the constant developed length. The shape of the CFS section is maintained, and only the dimensions are varied. Two dimensionless parameters were introduced namely the ratio of web depth to developed length (k) and flange width to lip depth ratio (a). In this work, size optimization was carried out to maximize the moment capacity for a given weight of material. This work can be used as a ready reckoner in the process of design of cold-formed steel sections. This helps in choosing the required developed length for the given moment and optimum dimensions of the CFS section for the chosen developed length.
In the Engineering field, optimization techniques are introduced for solving technical problems. Conventional techniques are complicated in nature, and it is tough to solve. To overcome this difficulty, the Evolutionary optimization technique is used. Some of the prominent Evolutionary algorithms are hill-climbing, simulated annealing and the genetic algorithm. Genetic Algorithms (GAs) are trial and error search algorithms. It is based on Darwin’s principle of natural selection. The facets are grouped as initial population, fitness function, selection, crossover, and mutation. It begins with randomly generated states. A bit string usually represents these states. For reproduction, two random pairs are selected. They are selected based on their fitness function score. For each pair to be mated, a cross over point is chosen at random from within the bit string. Exchanges between the parents actualize offspring at the cross over point. The primary advantage of GA’s comes from the cross over operation. Each location, in the bit string, can be subjected to a mutation with a small random probability. The fitness function generates the next generation of states, and it provides a score to each state. A proper fitness function should return to better states. GA is looking for a good and robust solution rated against Fitness criteria, so it avoids local optima and searches for global fitness. One may be selected more than once, whereas one may not be selected at all. The flow chart of GA is as shown in
GA is used for generating high-quality solutions in optimization and search problems. Some of the popular applications are scheduling and sequencing, reliability design, vehicle routing and scheduling, group technology, facility layout, and location and transportation. In design field, GAs are used for finding an optimum cross-section of cold-formed steel beams, steel channels, lipped channel under axial compression. (
The objective of this optimization is to obtain an economical and efficient cross section dimensions for the given developed length and thickness. The Eurocode 3 predicts the design moment of CFS sections conservatively compared to other codes. The Euro code accounts for various buckling modes such as local, distortional, and lateral torsional buckling as shown in
x1: web depth, x2: Flange width, x3: lip depth
Many researchers have investigated the buckling behavior of cold-formed steel channel section (
Cold-formed steel sections usually have less thickness compared to hot rolled sections and easily susceptible to local buckling. Local buckling occurs within the element. Effective width concept uses uniform stress distribution in an equivalent width of the element to account for non-uniform stress distribution. Hence the buckled portion is omitted in the design moment calculations. The width of the buckled portion depends upon the plate slenderness, stress ratio, and yield strength of the plate. EC3 considers all the above parameters in calculating the effective portion of elements in the compression zone. The shift of the centroid due to reduced element width is also taken into account. Equations are given separately for stiffened and unstiffened elements. The stress level at which local buckling occurs is more than the stress level for distortional and lateral torsional buckling. Investigation on the global-local buckling behavior of thin-walled channel beams was carried out by (
Where
In
Distortional buckling involves rotation of lip/flange about the flange/web junction. It induces due to local torsional buckling. In this case, the half wavelength of buckling is more than that of local buckling. This may occur in the support location also. This occurs due to insufficient stiffener in the compression zone. EC3 accounts for distortional buckling by reducing the effective thickness of stiffener elements in the compression zone. The stress level for distortional buckling to occur is more than that required for lateral torsional buckling and less than the stress in case of local buckling. This buckling occurs for members having an intermediate span. Studies on elastic lateral buckling of simply supported LiteSteel beams subject to transverse loading was addressed by (
The distortional slenderness is given by
In
Lateral torsional buckling occurs for members which are in unrestrained condition. This condition occurs when the compression flange is not supported throughout its length. This is usually observed in members having an open cross-section. LTB involves rotation of entire cross section with or without element buckling. Individual elements may undergo local or distortional buckling depending upon their participation factor with LTB. Design against LTB depends upon the effective length of the member, point of application of load, End support condition, moment gradient, and torsional stiffness of the section. The slenderness for lateral-torsional buckling
where
Any system or component is described by a set of variables which influence the characteristics of the system. In- this optimization, for a given developed length and thickness, the variables identified are flange width, web depth and lip depth. To maintain the monosymmetry, dimensions of flange and lip were maintained same at top and bottom. This reduces the total number of variables. The flange width and lip depth are related by a parameter (a) as the ratio of flange width to lip depth, and thus, one of the variables is eliminated. The web depth to developed length ratio was taken as the other parameter (k). With these parameters as design variables, the moment carrying capacity is taken as the objective function. The constraints given in EC3 guidelines were incorporated in the form of limits of design variables as given in
Objective function |
M_{crd} = W_{effy} . f_{y}/γ, For laterally restrained condition M_{brd} = χLT . W_{effy} . f_{y}/γ, For laterally unrestrained condition. χLT - reduction factor for lateral torsional buckling. |
Geometrical constraints |
0 < x1 , x2 , x3< DL x1+ x2 + x3 = DL 2 x3 ≤ x1 |
EC3 constraints |
x1/t ≤ 500 x2/t ≤ 60 x3/t ≤ 50 0.2 ≤ x3/x2 ≤ 0.6 |
Design variables |
k = x1/ DL a = x2/ x3 |
Upper and Lower limits of design parameters |
0.1 ≤ k ≤ 0.9 1.6 ≤ a ≤ 5 |
Expression for arriving dimensions of CFS |
x1 = k . DL x2 = a . x3 x3 = DL (1-k) / (1+a) |
Constants | Developed Length (DL) and thickness (t) |
Parameters in Genetic algorithm setup |
Lower bounds of search space - [0.1 , 1.6] Upper bounds of search space - [0.9, 5] Population size - 100 Maximum number of generations - 50 Mutation probability - 0.1 Crossover rate - 0.8 Migration Interval - 20 |
Hence in this optimization problem, only two non dimensional parameters are defined, and all the profile dimensions can be calculated from these parameters. The limits of Design variables are obtained to satisfy the limiting value of flat width to thickness ratios as laid down by the EC3 and the geometrical constraints as given in the
From
The graph between design moment and design parameter (k) is plotted as shown in
The effect of (a) ratio as shown in (
The maximum design bending moment of CFS sections obtained from possible proportions using a genetic algorithm is plotted against various values of developed length as shown in
Finite element analysis (FEA) was carried out using ABAQUS to simulate the flexural behavior of CFS sections as shown in
The flexural behaviour and buckling modes of optimized CFS sections were studied. The reserve capacity of optimized CFS section available more than the predicted capacity by EC3 was investigated. The detailed geometric and material non-linear model was used in this study. In each CFS section, fifteen models with various developed length, thickness, and optimized design parameters were used. FEA has become an essential tool in any CFS related research work. Numerical study on the section moment capacity of a doubly symmetric hollow flange steel plate girder (HFSPG) for use in long span applications was carried out by (
Lipped C, Lipped Z, and Rectangular hollow flange CFS sections have been considered for this numerical analysis. All the sections were subjected to constant end moments in this numerical study. Unsupported length of the section was taken as 2500 mm. The thickness of 1 mm, 1.5 mm, 2 mm, 2.5 mm, and 3 mm have been taken into this study. Cross section dimensions of the CFS sections modeled in the finite element analysis are presented in
DL | k | a | t | dw | bf | df | M |
M |
||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
(mm) | (mm) | (mm) | (mm) | (mm) | EC 3 | FEA | FEA/EC3 | EC 3 | FEA | FEA/EC3 | ||
Lipped C Section | ||||||||||||
200 | 0.44 | 1.7 | 1 | 88 | 35 | 21 | 1.67 | 1.72 | 1.03 | 1.28 | 1.31 | 1.02 |
200 | 0.42 | 2 | 1.5 | 84 | 39 | 19 | 2.54 | 3.02 | 1.19 | 1.93 | 2.21 | 1.14 |
200 | 0.43 | 2.1 | 2 | 86 | 39 | 18 | 3.49 | 4.04 | 1.16 | 2.59 | 3.03 | 1.17 |
200 | 0.43 | 2.3 | 2.5 | 86 | 40 | 17 | 4.41 | 5.19 | 1.18 | 3.27 | 3.92 | 1.20 |
200 | 0.44 | 2.5 | 3 | 88 | 40 | 16 | 5.44 | 6.78 | 1.25 | 3.97 | 4.84 | 1.22 |
300 | 0.54 | 1.6 | 1 | 162 | 42 | 27 | 3.48 | 3.56 | 1.02 | 2.86 | 3.01 | 1.05 |
300 | 0.5 | 2 | 1.5 | 150 | 50 | 25 | 6.38 | 6.85 | 1.07 | 4.96 | 5.62 | 1.13 |
300 | 0.5 | 2.3 | 2 | 150 | 52 | 23 | 8.9 | 9.11 | 1.02 | 6.62 | 8.02 | 1.21 |
300 | 0.5 | 2.3 | 2.5 | 150 | 52 | 23 | 11.13 | 12.31 | 1.11 | 8.29 | 10.23 | 1.23 |
300 | 0.5 | 2.4 | 3 | 150 | 53 | 22 | 13.41 | 15.35 | 1.14 | 9.97 | 12.54 | 1.26 |
400 | 0.61 | 1.3 | 1 | 244 | 44 | 34 | 5.55 | 6.11 | 1.10 | 4.61 | 5.27 | 1.14 |
400 | 0.57 | 1.8 | 1.5 | 228 | 55 | 31 | 10.52 | 11.23 | 1.07 | 8.51 | 9.53 | 1.12 |
400 | 0.54 | 2.2 | 2 | 216 | 63 | 29 | 15.97 | 16.88 | 1.06 | 12.47 | 12.70 | 1.02 |
400 | 0.55 | 2.4 | 2.5 | 220 | 64 | 26 | 21.17 | 23.54 | 1.11 | 15.71 | 17.58 | 1.12 |
400 | 0.55 | 2.5 | 3 | 220 | 64 | 26 | 25.48 | 27.65 | 1.09 | 18.87 | 21.72 | 1.15 |
Lipped Z Section | ||||||||||||
200 | 0.42 | 3.7 | 1 | 84 | 46 | 12 | 1.67 | 1.70 | 1.02 | 0.99 | 1.35 | 1.36 |
200 | 0.41 | 4.9 | 1.5 | 82 | 49 | 10 | 2.54 | 2.65 | 1.04 | 1.73 | 1.95 | 1.13 |
200 | 0.41 | 5 | 2 | 82 | 49 | 10 | 3.49 | 3.78 | 1.08 | 2.48 | 2.66 | 1.07 |
200 | 0.43 | 5 | 2.5 | 86 | 48 | 10 | 4.41 | 5.00 | 1.13 | 3.28 | 3.56 | 1.08 |
200 | 0.45 | 5 | 3 | 90 | 46 | 9 | 5.44 | 6.28 | 1.15 | 4.14 | 4.54 | 1.10 |
300 | 0.51 | 2.1 | 1 | 153 | 50 | 24 | 3.48 | 3.65 | 1.05 | 2.37 | 2.74 | 1.16 |
300 | 0.48 | 3.4 | 1.5 | 144 | 60 | 18 | 6.38 | 6.78 | 1.06 | 4.58 | 5.26 | 1.15 |
300 | 0.48 | 4.5 | 2 | 144 | 64 | 14 | 8.9 | 9.67 | 1.09 | 6.6 | 7.68 | 1.16 |
300 | 0.48 | 5 | 2.5 | 144 | 65 | 13 | 11.13 | 12.50 | 1.12 | 8.48 | 9.32 | 1.10 |
300 | 0.48 | 5 | 3 | 144 | 65 | 13 | 13.41 | 15.20 | 1.13 | 10.38 | 12.22 | 1.18 |
400 | 0.58 | 1.6 | 1 | 232 | 52 | 32 | 5.55 | 5.88 | 1.06 | 4.02 | 5.04 | 1.25 |
400 | 0.55 | 2.4 | 1.5 | 220 | 64 | 26 | 10.52 | 10.95 | 1.04 | 8.07 | 8.72 | 1.08 |
400 | 0.53 | 3.5 | 2 | 212 | 73 | 21 | 15.97 | 16.74 | 1.05 | 12.64 | 15.15 | 1.20 |
400 | 0.52 | 4.3 | 2.5 | 208 | 78 | 18 | 21.17 | 22.80 | 1.08 | 16.87 | 17.2 | 1.02 |
400 | 0.52 | 5 | 3 | 208 | 80 | 16 | 25.48 | 28.63 | 1.12 | 20.54 | 22.85 | 1.11 |
Rectangular Hollow Flange Section | ||||||||||||
200 | 0.28 | 1.7 | 1 | 56 | 23 | 13 | 1.18 | 1.32 | 1.12 | 0.87 | 1.00 | 1.15 |
200 | 0.28 | 1.7 | 1.5 | 56 | 23 | 13 | 1.77 | 1.82 | 1.03 | 1.31 | 1.58 | 1.21 |
200 | 0.28 | 1.7 | 2 | 56 | 23 | 13 | 2.37 | 2.65 | 1.12 | 1.74 | 1.97 | 1.13 |
200 | 0.28 | 1.7 | 2.5 | 56 | 23 | 13 | 2.96 | 3.11 | 1.05 | 2.18 | 2.68 | 1.23 |
200 | 0.28 | 1.7 | 3 | 56 | 23 | 13 | 3.55 | 3.84 | 1.08 | 2.62 | 2.99 | 1.14 |
300 | 0.32 | 1.6 | 1 | 96 | 31 | 20 | 2.84 | 2.95 | 1.04 | 2.2 | 2.26 | 1.03 |
300 | 0.32 | 1.8 | 1.5 | 96 | 33 | 18 | 4.27 | 4.82 | 1.13 | 3.3 | 3.8 | 1.15 |
300 | 0.32 | 1.8 | 2 | 96 | 33 | 18 | 5.7 | 6.1 | 1.07 | 4.41 | 5.16 | 1.17 |
300 | 0.32 | 1.8 | 2.5 | 96 | 33 | 18 | 7.12 | 7.53 | 1.06 | 5.51 | 6.73 | 1.22 |
300 | 0.33 | 1.8 | 3 | 99 | 32 | 18 | 8.69 | 8.87 | 1.02 | 6.62 | 8.27 | 1.25 |
400 | 0.36 | 1.6 | 1 | 144 | 39 | 25 | 5.06 | 5.32 | 1.05 | 4.02 | 4.35 | 1.08 |
400 | 0.36 | 1.9 | 1.5 | 144 | 42 | 22 | 8.09 | 8.86 | 1.09 | 6.33 | 7.28 | 1.15 |
400 | 0.36 | 1.9 | 2 | 144 | 42 | 22 | 10.79 | 12.28 | 1.14 | 8.45 | 9.21 | 1.09 |
400 | 0.36 | 1.9 | 2.5 | 144 | 42 | 22 | 13.49 | 14.95 | 1.11 | 10.56 | 11.62 | 1.10 |
400 | 0.36 | 1.9 | 3 | 144 | 42 | 22 | 16.19 | 17.12 | 1.06 | 12.68 | 15.22 | 1.20 |
For the preliminary investigation, cold-formed steel having yield stress of 350 N/mm² is considered in this study. Initially, a buckling analysis was carried out with elastic properties of standard steel. Elastic modulus and Poisson’s ratio were taken as 210 GPa and 0.3, respectively. The most realistic hardening behaviour of the material is required to simulate the post-buckling behaviour of members. For Non-linear analysis, a bilinear model having linear stress-strain relation up to 0.2% proof stress, followed by a straight line with a constant slope of E/100 was adopted as recommended in Eurocode 3 part 1-5. This model is similar to the elastic-perfect plastic model. In this study, the perfect plastic model was adopted after the elastic range since the strains at the maximum moment are less than the strains in the post-buckling stage.
The cross-section profile is developed in the XY plane and extruded along the Z-axis in the finite element model. The nodal displacements are referred to as (U1, U2, U3) and rotations as (UR1, UR2, UR3) in global X, Y and Z axis, respectively. The simply supported end conditions were modeled as shown in
In this study, buckle analysis on the perfect model and geometrically and Materially Nonlinear Analysis on imperfection models (GMNIA) (
The primary and secondary buckling modes and the corresponding critical moment are compared for these sections. It is evident that section 2 with intermediate web depth resists more significant moment compared with the shorter or deeper web. The buckling modes of these sections also compared. Section 1 with deeper web lacks in lateral torsional resistance. Section 3 with shorter web though resists lateral torsional buckling in a better way but its in-plane bending capacity is less, and compression flange suffers from local buckling. The results of optimization using a genetic algorithm for CFS sections are presented in
DL (mm) | dw/DL | bf/df | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
t → | 1 | 1.5 | 2 | 2.5 | 3 | 1 | 1.5 | 2 | 2.5 | 3 |
Lipped C & Z Section-M_{crd} | ||||||||||
100 | 0.81 | 0.81 | 0.81 | 0.81 | 0.81 | 5.0 | 5.0 | 5.0 | 5.0 | 5.0 |
200 | 0.63 | 0.73 | 0.81 | 0.81 | 0.81 | 3.8 | 5.0 | 5.0 | 5.0 | 5.0 |
300 | 0.69 | 0.63 | 0.65 | 0.81 | 0.81 | 2.7 | 3.8 | 5.0 | 5.0 | 5.0 |
400 | 0.76 | 0.68 | 0.63 | 0.66 | 0.73 | 2.2 | 3 | 3.8 | 4.8 | 5.0 |
500 | 0.79 | 0.71 | 0.67 | 0.63 | 0.65 | 1.7 | 2.4 | 3.2 | 3.8 | 4.6 |
Lipped C Section- M_{brd} | ||||||||||
100 | 0.31 | 0.35 | 0.37 | 0.4 | 0.42 | 1.9 | 5.0 | 5.0 | 5.0 | 5.0 |
200 | 0.44 | 0.42 | 0.43 | 0.43 | 0.44 | 1.7 | 2.0 | 2.1 | 2.3 | 2.5 |
300 | 0.54 | 0.5 | 0.5 | 0.5 | 0.5 | 1.6 | 2.0 | 2.3 | 2.3 | 2.4 |
400 | 0.61 | 0.57 | 0.54 | 0.55 | 0.55 | 1.3 | 1.8 | 2.2 | 2.4 | 2.5 |
500 | 0.66 | 0.62 | 0.59 | 0.56 | 0.57 | 1.6 | 1.7 | 2.3 | 2.5 | 2.8 |
Lipped Z Section- M_{brd} | ||||||||||
100 | 0.30 | 0.35 | 0.38 | 0.41 | 0.43 | 5.0 | 5.0 | 5.0 | 5.0 | 5.0 |
200 | 0.42 | 0.41 | 0.41 | 0.43 | 0.45 | 3.7 | 4.9 | 5.0 | 5.0 | 5.0 |
300 | 0.51 | 0.48 | 0.48 | 0.48 | 0.48 | 2.1 | 3.4 | 4.5 | 5.0 | 5.0 |
400 | 0.58 | 0.55 | 0.53 | 0.52 | 0.52 | 1.6 | 2.4 | 3.5 | 4.3 | 5.0 |
500 | 0.63 | 0.60 | 0.58 | 0.55 | 0.56 | 1.6 | 1.8 | 2.8 | 3.5 | 4.3 |
RHFB- M_{crd} | ||||||||||
100 | 0.90 | 0.90 | 0.90 | 0.90 | 0.90 | 1.6 | 1.6 | 1.6 | 1.6 | 1.6 |
200 | 0.76 | 0.89 | 0.90 | 0.90 | 0.90 | 5.0 | 5.0 | 1.6 | 1.6 | 1.6 |
300 | 0.68 | 0.76 | 0.86 | 0.90 | 0.90 | 5.0 | 5.0 | 5.0 | 5.0 | 1.6 |
400 | 0.64 | 0.70 | 0.76 | 0.84 | 0.89 | 5.0 | 5.0 | 5.0 | 5.0 | 5.0 |
500 | 0.65 | 0.67 | 0.71 | 0.77 | 0.83 | 5.0 | 5.0 | 5.0 | 5.0 | 5.0 |
RHFB- M_{brd} | ||||||||||
100 | 0.20 | 0.20 | 0.20 | 0.20 | 0.20 | 1.6 | 1.6 | 1.6 | 1.6 | 1.6 |
200 | 0.28 | 0.28 | 0.28 | 0.28 | 0.28 | 1.7 | 1.7 | 1.7 | 1.7 | 1.7 |
300 | 0.32 | 0.32 | 0.32 | 0.32 | 0.33 | 1.6 | 1.8 | 1.8 | 1.8 | 1.8 |
400 | 0.36 | 0.36 | 0.36 | 0.36 | 0.36 | 1.6 | 1.9 | 1.9 | 1.9 | 1.9 |
500 | 0.38 | 0.38 | 0.38 | 0.38 | 0.38 | 1.7 | 1.7 | 2.0 | 2.0 | 2.0 |
In this attempt, an approach engaged a genetic algorithm for finding the optimum dimensions of cold-formed steel sections for an economical construction. The minimum requirement of developed length and thickness to resist the given bending moment is given. The optimum proportions for both laterally restrained and laterally unrestrained condition are separately investigated for various developed length and thickness. For other values of developed length, linear interpolation can be adopted. The variation in the design moment capacity due to linear interpolation for intermediate values was investigated, and it is found to be a maximum of only 5% in limited cases. All the optimum value of design parameters are within the constraints given in EC3 except for RHFB. Finite element analysis has been carried out for 45 CFS sections and compared with the design moment obtained from EC3. In future, the upper limit of parameter (a) for RHFB sections may be increased beyond the EC3 constraints to identify any improvement in the moment capacity in laterally restrained condition. This investigation indicates that there is a need to search for other practical profiles to improve the buckling resistance for the given developed length.
The author is grateful to the Government College of Technology, Coimbatore, for providing a licensed version of ABAQUS under TEQIP-II for the above work. The author is also thankful to the college for providing access to Scopus indexed journals under TEQIP II.