Ijciet 10 01_082

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 01, January 2019, pp. 891–903, Article ID: IJCIET_10_01_082
Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=10&IType=1
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
©IAEME Publication Scopus Indexed
DEVELOPMENT OF EFFICIENCY BASED
STANDARDS FOR OPTIMUM DESIGN OF
STIFFENED PLATE GIRDERS
Priya A Jacob
Associate Professor, North Malabar Institute of Technology, Kerala, India
Research Scholar, Karunya Institute of Technology and Sciences, Coimbatore, India
Justin S
Chief Engg. Manager (Civil), EDRC – Buildings & Factories,
L&T Construction, Chennai, India
R Mercy Shanthi
Associate Professor, Dept. of Civil Engineering,
Karunya Institute of Technology & Sciences, Coimbatore, India
ABSTRACT
In recent years, stiffened plate girders have been used extensively for long spans
due to its high flexural rigidity and buckling resistance. While designing, the amount
of costly steel used in a girder can be reduced by adopting optimum dimensions for
web depth, web thickness, flange thickness, flange breadth and spacing of stiffeners.
Such design can finally result in an economical design. Indian standards have code
provisions which can be used for design of stiffened plate girders. However, relatively
little attention has been devoted to developing efficiency based standards in the design
of plate girders. These efficiency based standards in the form of design charts can
help a designer in the economical design of stiffened plate girders considering
strength and serviceability conditions. Herein, relationships between the design
variables are developed using genetic algorithm (GA) based optimization formulation.
Both transversely stiffened and corrugated web plate girders are considered. The
relationships are further used to develop design charts which can be useful for design
engineers. The design charts are developed considering strength and serviceability
conditions as specified by the IS 800:2007.
Key words: Optimum design, Stiffened plate girder, Corrugated web, Design charts
Cite this Article: Priya A Jacob, Justin S, R Mercy Shanthi, Development of
Efficiency Based Standards for Optimum Design of Stiffened Plate Girders,
International Journal of Civil Engineering and Technology (IJCIET) 10(1), 2019, pp.
891–903.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=1

Development of Efficiency Based Standards for Optimum Design of Stiffened Plate Girders
1. INTRODUCTION
Plate girders are built-up flexural members made up from separate structural steel plates
which are either welded or bolted together to form the horizontal flanges and vertical web of
the girder. A plate girder has enormous flexural strength and the resistance to bending and
shear can be increased by increasing the distance between the flanges. Web buckling can be
prevented by providing stiffeners. Use of stiffeners and thin corrugated steel plates in web of
plate girder can help in achieving out-of-plane stiffness and buckling resistance in place of a
thick web plate and thus save girder production cost. Span lengths can be increased due to the
use of stiffened plate girders because of high strength to weight ratio. Due to their many
favourable properties, these plate girders are widely used in many fields of application. For
the last 25 years, there have been a remarkable use of corrugated plate girders and many
theoretical studies and experimental investigations are carried out on corrugated plate girders.
Recently in India many manufacturers started investing on cutting edge technology, to
develop corrugated plate girders to be used as main frames of single-storey steel buildings.
Figure-1 a) Stiffened Plate b) Corrugated Plate girder
Optimization of stiffened girders is necessary to take complete advantage of many
favourable properties. Majority of the investigations on stiffened plate girders mainly focused
on analytical and experimental work. Few of the significant numerical and experimental
investigations include the study of interactive shear behaviour of trapezoidally corrugated
webs by Jogwon Yi et al. [6], study of influence of geometric parameters on patch load
resistance in corrugated webs. Performance of sinusoidal corrugated plate girders when used
as main frames of single-storey steel buildings were studied by Hartmut et al. [5]. However
insufficient investigations are carried out on the optimum design of plate girders. Kuan Chen
Fu. et al. [7] used genetic algorithm (GA) with elitism in the optimum design of plate girders.
Fatima Zohra Chalal [4] developed a formulation using Generalised Reduced Gradient
method for optimum design of continuous girder with variable depth. Optimum cost design of
steel box girder by varying plate thickness was carried out by Do Dai Thang et al. [3]. They
developed design guidelines which can be useful to the designer in the first stage of the
designing procedure. Furthermore Shon S D et al. [9] and Sudeok Shon et al. [12] conducted
analytical studies on optimum structural design of sinusoidal corrugated web beam using real-
valued genetic algorithm. Shon et al. [9, 10] recently researched on the optimum design of
thin corrugated web for shear buckling using genetic algorithm.
Many algorithms based on natural phenomena have been developed since 1970s. In
particular, the genetic algorithm (GA) has often been used in the optimization problems of
civil engineering structures. GA performs effectively in performing global search. The main
purpose of this work is to identify relationship of design variables and establish design
guidelines for the optimum design of stiffened plate girders. Plate girders with transverse
stiffeners and corrugated web stiffeners are used in this work. GA based algorithm has been

Priya A Jacob, Justin S, R Mercy Shanthi
used to perform optimization. These guidelines can be useful for structural engineers during
the first stage of design.
2. OPTIMUM DESIGN OF PLATE GIRDERS
Optimum design of plate girders is governed by flexural strength, shear strength,
serviceability and overall girder weight. Therefore optimum design of plate girders can be
formulated as a weight minimization problem keeping in view the flexural strength, shear
strength and serviceability aspects as suggested by the design codes. To increase the buckling
strength plate girder web, they are usually reinforced with transverse stiffeners or provided
with thin corrugated webs. Optimum design of such plate girders hence helps a designer to
also optimize the parameters influencing the weight and strength. This can finally result in an
economical design which satisfies strength and serviceability conditions as specified by the
design codes.
2.1. Objective Function
The common engineering objective function involves minimization of overall cost of
manufacturing of a structure or minimization of its overall weight or maximization of its
strength. Objective function is represented in terms of the design variables and other problem
parameters. In this work the objective function used is weight minimization. Usually objective
function in a case of unconstrained optimization is f(x). The modified objective function Ф
(x) in case of constraint optimization is written as
Ф (x) =f(x) {1+KC}
where parameter K has to be judiciously selected depending on the required influence of a
violation individual in the next generation and C is the constraint coefficient.
2.1.1. Transversely Stiffened Plate Girder (TSPG)
Use of transverse stiffeners in plate girders help in safeguarding the web against local
buckling failure. A bench mark problem is identified here for carrying out the formulation
using GA. The objective function, design variables and constraints are identified.
Objective function of weight minimization in TSPG is,
( ) [( ) ( )] (1)
where
L : Span of girder ρ : Density of steel
d : Depth of web n : Number of stiffeners / folds
tw : Thickness of web bs : Breadth of stiffener
bf : Breadth of flange ts : Thickness of stiffener
tf : Thickness of flange
Figure 2 Transversely stiffened plate girder

2.1.2. Corrugated Web Plate Girder (CWPG)
Corrugated plate girders afford a significant weight reduction compared with welded I
section. Due to developments in automatic fabrication process, thin corrugated webs are
possible and this has helped engineers to design optimal structures.
The objective function, design variables and constraints are identified.
Objective function of weight minimization in CWPG is,
( ) ∑ ( ) (2)
subject to ( ) ( )
where ( ) { }
Figure 3 Corrugated web plate girder
2.2. Constraints
Constraints represent some functional relationship among the design variables and other
design parameters which satisfy certain resource limitations and physical phenomena. GA is
ideally appropriate for unconstrained optimization problems. The problem used here is a
constraint optimization problem; hence it is necessary to convert the same by using exterior or
interior penalty functions. GA performs the search in parallel using populations of points in
the given search space. Traditional transformations using penalty or barrier functions are not
appropriate for this genetic algorithm. Hence, a formulation based on the violation of
normalized constraints is generally adopted. It is found to work very well for these classes of
problems. The constraints and design checks are applied as per IS 800:2007. The constraints
used in this work are,
a) Stress constraints
b) Dimensional constraints
c) Serviceability constraints
2.2.1. Stress constraints
Stress constraints consist of shear stress, flexural stress and buckling stress. In a plate girder,
shear stress is zero at the extreme fibres, increases to a high value at flange-web intersection
and attains maximum value at the neutral axis. The nature of flexural stress distribution
indicates that flanges carry most of the bending stress. Hence from the comparison of the
shear and flexural stress distributions in a plate girder, it is observed that flanges carry a major
portion of the flexural load, whereas the web carries most of the shear load.
The following requirements shall be satisfied according to IS 800: 2007in design of plate
girders.
 The applied bending moment shall not exceed the moment capacity of the plate girder.
 The applied shear force shall not exceed the shear buckling resistance of the plate girder.

 Shear buckling resistance of web depends on two factors.
a) Depth to web thickness
b) Spacing of intermediate web stiffeners
 Resistance to shear buckling shall be verified as specified, when
> 67 ε for stiffened web.
 IS 800:2007 specifies minimum web thickness requirement from a
serviceability point of view with regard to provision of stiffeners. The web
thickness should satisfy the following requirements with respect to
serviceability:
When only transverse stiffeners are provided
≤ 200 εw when 3d ≥ c ≥ d
≤ 200 εw when 0.74 d ≤ c < d
≤ 270 εw when c < d
web shall be considered as unstiffened when c > 3d
 In order to avoid buckling of the compression flange into the web, the web
thickness shall satisfy the following:
When transverse stiffeners are provided and
≤ 345 εf
2
when c>l.5d
≤ 345 εf when c < 1.5d
where
c : panel width
εw : √ fyw yield stress of the web
εf : √ fyf yield stress of compression flange
2.2.2. Dimensional constraints
Dimensional constraints are used to control the proportions and size of the design variables.
 The ratio between equivalent span to the full depth of plate girder is chosen such that the ratio
does not exceed 25.
 For webs with only transverse stiffeners, the maximum ratio of the web is kept below 400
in order to meet serviceability and compression flange buckling requirements.
 The flange rigidity ratio should be such that the flange is either plastic or compact or semi-
compact. Hence ratio is limited to 13.6.
 The panel aspect ratio is limited to 3 beyond which the web panel is considered as
unstiffened.

Due to headroom constraint and web buckling susceptibility, the depth of web cannot be
increased infinitely. Hence deflection limits recommended by IS 800:2007 are adopted as
constraints to check the most adverse but realistic combination of service loads.
2.2.3. Serviceability constraints
Serviceability limit state includes deflection limit and vibration limit.
 Deflection limit according to Table 6 of IS 800: 2007 is adopted as:
 Allowable deflection ≤ Span/300
 Vibration limit according to ANNEX C of IS 800:2007 is adopted as:
Natural floor frequency
√
where
= Natural floor frequency in Hz, = Maximum deflection in mm
Natural floor frequency less then 5Hz is avoided.
The stress, dimensional and serviceability constraints in normalized form is given by
≤0 ≤0 ≤0 (3)
where
σc : Stress in the member σa : Allowable stress
: Calculated dimension : Allowable dimension
: Calculated deflection : Allowable deflection
Violation coefficient C is computed as,
Ci=g(x) if g(x) > 0
Ci=0 if g(x) <= 0
C= ∑ , where n is the number of constraints.
g i(x) = g i(x) = gi(x)= (4)
Now the modified function Ф(x) is written as
Ф(x) = f(x) {1+KC}. (5)
2.3. Design variables
The design variables used in this work are depth of the web (d), thickness of the web (tw),
thickness of the flange (tf), breadth of the flange (bf) and panel width (c).
3. PROBLEM STATEMENT
To investigate the performance of GA on the optimum design of plate girder, a simply
supported beam example with transverse web as well as corrugated web were analysed with
program developed using MATLAB. Optimization was performed using the equations
mentioned in section 2.
The adopted model in the problem has a span of 24m and uniform load of w = 100kN/m is
applied. The elastic modulus E, Poisson ratio μ and yield stress fy are 210GPa, 0.3 and
250MPa. The values for the variables are set to vary from a lower bound to an upper bound.
The range of variation is selected such that there is no constraint violation in the final
optimum solution.

A set of results obtained for TSPG at an intermediate iteration process is shown in table 1.
This table also gives the decoded values of design variables and the plate girder weight after
the GA process.
Table 1 Design variables, weight of the plate girder and fitness value
bf (mm) tf (mm) d(mm) tw (mm) Weight (ton)
Fitness
value
340 18 1100 12 4.6 8.83E-15
410 18 1400 6 2.9 7.76 E-15
390 18 1400 6 3.7 9.50 E-15
320 22 1100 12 3.8 1.26E-14
320 25 1250 10 3.6 1.05E-14
330 20 1400 12 3.5 8.11 E-15
380 20 1400 10 5.1 1.30E-14
320 22 1250 10 4.7 6.14E-15
380 20 1400 14 4.1 1.16E-14
310 22 1250 7 3.6 1.28E-14
Figure 4 Weight of the plate girder vs number of generations
After the convergence has occurred, a graph is plotted between weight of the plate girder
and number of generations (Figure 4). It is evident from the graph that convergence occurred
at 215 generations. Thus the obtained graph gives the optimum weight after convergence. For
evaluating the effectiveness of GA in arriving at an optimum design of plate girder, the GA
results are compared with conventional design according to IS 800:2007. These results are
shown in Table 2.
Table 2 Comparative analysis of plate girder weight using GA and conventional design
Span (m) 20 30
Loading (kN/m) GA(ton)
Conventional
Design(ton)
GA(ton)
Conventional
Design(ton)
10 1.66 2.55 2.84 3.74
15 1.84 2.83 3.14 4.13
20 2.18 3.35 3.27 4.30
25 2.31 3.55 3.49 4.59
30 2.43 3.74 3.62 4.76
35 2.65 4.08 3.74 4.92
40 2.81 4.32 3.88 5.11

A comparison between optimized weight from GA and IS 800: 2007 for varying span is
also carried out to validate the GA results.
Figure 5 Comparisons between optimized weight from GA and IS 800: 2007
From table 2 and figure 5, it can be concluded that optimized weights of the plate girder
obtained through GA are less in comparison with conventional design. Thus GA has
convincing possibilities of finding optimal solution to a problem influenced by complex
parameters.
In order to understand the independent contribution by each design variable in attaining
the optimum weight, another study using GA is carried out. Of all the design variables, the
variables which influences the optimum weight of the girder to an appreciable extend is
identified. Figure 6 shows the influence of each design variables and their ratios on optimum
weight.
Figure 6 Influence of each design variables on optimum weight
The results show that varying depth (d) and thickness (tw) of web influences more in
achieving economical weight of a plate girder. Therefore the ratio between d and tw, denoted
as web slenderness ratio (d/tw) is identified as the most influencing parameter in optimum
design of stiffened plate girder. The relation between spacing of stiffeners or folds (c) and
depth of web (d) denoted as panel aspect ratio (c/d) is the another influencing parameter.
Flange rigidity ratio which is the relation between breadth (bf) and thickness (tf) of flange is

also found to influence the design to an appreciable extend. Varying all the design variables
also influences, but this can lead to an occurrence of more noisy population in GA.
4. DESIGN CHARTS
Design charts are developed from the optimization study to outline the behaviour of these
influential design parameters on economical design of plate girders. These charts can be
utilized by structural engineers in designing economical plate girders. Design variables
common to transversely stiffened plate girder (TSPG) and corrugated web plate girder
(CWPG) are used. Design charts are developed for optimizing the following ratios:
a) Web slenderness ratio (d/tw)
b) Panel aspect ratio (c/d)
c) Flange rigidity ratio (b/tf)
4.1. Web slenderness ratio (d/tw)
Weight of the web for a TSPG is about 25%-28% of the overall weight of the girder. Since the
flanges provide most of the flexural strength, most of the steel must be concentrated in flanges
and as far as possible away from the neutral axis of the girder which consequently results in
deep, thin web. A study of relation between depth of web and thickness of flange plate is
carried out to understand the behavioural pattern.
Figure 7 Variation of web depth with flange thickness
It is observed that an increase in the web depth of the plate girder causes a decrease in the
flange plate thickness. Hence it can be understood that a deeper web reduces the flange plate
thickness thereby reducing the weight of the flanges. Flanges of a plate girder carry a major
portion of the flexural load and flange area method is often used for a quick estimation of trail
sections. Using this method, the moment resisting capacity of a plate girder is determined
from the product of depth of the girder and flange area. This relationship shown in figure 7 is
realistic since the moment capacity is dependent on depth and flange area of the girder.
According to Fatima Zohra Chalal [4], results demonstrated from the study of optimum
design of continuous plate girder with variable depth show a similar behaviour.
The depth of the plate girder for which the area of steel used is minimum, will have
minimum weight and is called optimum depth. But as the web depth increases, the thickness
of the web should also be increased to prevent lateral buckling of the web and compression
flange buckling into the web. Hence an optimum web depth to web thickness ratio need to be
identified which can minimize the total weight of stiffened girders and provide the required
buckling resistance. This result of this study is illustrated in figure 8.

Figure 8 Influence of web slenderness ratio
The results from the optimization studies indicate that web slenderness ratio between 175
and 200 is appropriate when panel aspect ratio is between 1 and 3 and web slenderness ratio
between 260 and 270 is appropriate when panel aspect ratio is less than 1 in case of TSPG. In
case of CWPG used in buildings, web slenderness ratio about 500 and more are used during
conventional design. From the present study it is observed that above web slenderness ratio of
325, the weight increases marginally. Such behaviour can be due to vertical flange buckling
for higher web slenderness ratios. For higher ratios, corrugated webs may not have adequate
strength to support flanges vertically.
4.2. Panel aspect ratio (c/d)
Web stiffeners play a critical role in achieving the ultimate capacity of the girder, even though
they contribute only about 5%-7% of the total girder weight. Higher values of aspect ratios
lead to less number of web stiffeners. But this does not reduce the overall girder weight due to
increase in flange dimensions to meet the serviceability requirements. Also as the number of
stiffeners reduces, the girder starts to undergo shear buckling. Hence the panel aspect ratio
needs to be optimized which can minimize the girder weight and prevent shear buckling. In
conventional design of stiffened plate girders, panel aspect ratio in the range of 1.2 – 1.6 is
usually chosen. Panel aspect ratio from 0.05 to 3 is adopted for this work. Beyond aspect ratio
of 3, the web panel is considered as unstiffened [IS 800: 2007, Clause 8.6.1.1.1]. In case of
CWPG, panel aspect ratio of 0.05 to 1.5 is considered.
Figure 9 Influence of panel aspect ratio

From this study of influence of panel aspect ratio on optimum weight (figure 9), it is
observed that for TSPG, the minimum panel aspect ratio of 1.1 gives an optimum weight of
the girder. Above panel aspect ratio of 1.1, the percentage reduction in optimum weight is
negligible. In a CWPG, failure in shear by local and global buckling has been usually seen.
Local buckling is predominant in course corrugations and global buckling is predominant in
dense corrugations. Considering these buckling modes within the permissible limits, optimum
girder weight is achieved for aspect ratio of 1. The percentage reduction in optimum weight is
negligible for higher values of aspect ratios above 1. Sedky et al. [11] in their work had
reported that lower values of panel aspect ratios yield higher load carrying capacities. Hence
to achieve high strength to weight ratios, these lower values of panel aspect ratios are suitable.
4.3. Flange rigidity ratio (b/tf)
Flanges are designed from the consideration of strength and rigidity. For a non-composite
plate girder, the ratio of width of the flange plate and the depth of the section is usually
adopted as 0.3 in conventional designs. Weight of the flanges of a stiffened plate girder is
55%-60% of the total girder weight. When the applied load is increased, the failure mode of a
plate girder will depend largely on the web slenderness ratio. Hence, in this work another
study is carried out to study the influence of web slenderness ratio and flange rigidity ratio on
optimum girder weight. This study is done for TSPG.
Flange rigidity ratio is represented as b/tf, where in case of TSPG.
Figure 10 Influence of web slenderness ratio and flange rigidity ratio on optimum weight
From this study (figure 10) it is concluded that for flange rigidity ratio over 8, the weight
saving increases with increase in web slenderness ratio. Shahabian et al. [8] had earlier
reported that weight savings can be achieved for a flange rigidity ratio over 14. Thus these
observations prove to be more economical.
The moment resistance capacity of a plate girder depends on the product of breadth and
thickness of flange. Increasing the flange thickness may cause a reduction in design strength
of flanges; hence during design the flange width must be increased to provide the required
design moment resistance. Also during design the flange rigidity ratio is selected such that the
flange is plastic, compact or semi-compact to avoid local buckling before reaching the yield
stress. Considering all the above mentioned constraints, another study is carried out to
identify an optimum flange rigidity ratio which can minimize the total girder weight and

satisfy the moment constraint. The results of this study are illustrated in figures 11a and 11 b.
This study was carried out for various web slenderness ratios ranging from 220 – 270. As
weight savings can be achieved for flange rigidity ratio above 8, the lower limit for flange
rigidity ratio is taken as 8 and upper limit as 14 which are to avoid local buckling of flanges.
Figure 11 a) & b) Influence of flange rigidity ratio on optimum flange area
In this study the breadth and thickness of flanges which are sufficient to provide the
required design moment resistance are considered. It was identified that optimum flange areas
can be obtained for a flange rigidity ratio up to 13.5.
In case of CWPG, there is larger outstand at one side where web is parallel to the axis of
girder and smaller outstand on the other side. Optimum flange rigidity ratio in case of CWPG
can be identified by considering either larger or smaller outstand or average outstands. Since
IS 800:2007 does not provide guidelines for design of corrugated web plate girders, studies on
flange rigidity ratio is limited to only TSPG in this paper.
5. CONCLUSIONS
Design variables and constraints imposed by the design codes are important factors that
influence a structural design. Optimal designs of steel structures are even more complex due
to discrete sizes of steel sections in market. This paper has presented the use of Genetic
Algorithm, a robust optimization technique in solving such complex problems. Weight of
plate girder obtained using IS 800: 2007 when compared with that of GA is found to be
overestimated. Among all the design variables used for weight optimization, web slenderness
ratio (d/tw) is identified as the most influential parameter on optimum girder weight. In order
to aid a designer in effective design of stiffened plate girders both transversely stiffened and
corrugated web type, design charts were developed. These charts outline the behaviour of
influential parameters on economical design of plate girders. A study of interrelationship
between ratios of design variables reveals that for flange rigidity ratio over 8, the weight
saving increases with increase in web slenderness ratio. Suitable range of values for web
slenderness ratio, panel aspect ratio and flange rigidity ratio are attained from the design
charts for corrugated web plate girder and transversely stiffened plate girder. Thus use of GA
in optimum design of stiffened plate girders can lead to cost-effective and structurally
practicable design. The outcomes of the work are very promising as it may open a new era for
the accurate and effective use of transversely stiffened plate girders as well as corrugated web
plate girders in buildings.

REFERENCES
[1] Ajeesh S S, Sreekumar S, “Shear Behaviour of Stiffened Plate Girders”, Proceedings of
International Conference on Structural and Civil Engineering (January 2011).
[2] Chacón. R, Mirambell. E, Real. E, “Transversally stiffened plate girders subjected to patch
loading Part 1 Preliminary study”, Journal of Constructional Steel Research pp. 483–491,
(2013).
[3] Do Dai Thang, Min Se Koo, Asif Hameed, “Optimum cost design of steel box-girder by
varying plate thickness”, KSCE Journal of Civil Engineering, 13(1):31-37, (2009).
[4] Fatima Zohra Chalal, “Optimum design of continuous plate girder with variable depth”,
International Journal of Civil Engineering and Technology, Vol 8, Issue 3, , pp. 494-509,
(March 2017).
[5] Hartmut Pasternak & Gabriel Kubieniec, “Plate girders with corrugated webs”, Journal of
Civil Engineering and Management, 16:2, 166-171, (2011).
[6] Jongwon Yi, Heungbae Gil, Kwangsoo Youm, Hakeun Lee, “Interactive shear buckling
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[7] Kuan-Chen Fu, Yujia Zhai and Saijun Zhou. “Optimum design of welded steel plate
girder bridges using genetic algorithm with elitism”, Journal of Bridge Engineering, Vol.
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[8] Shahabian. F, Rajabi mashhadi, J. Farzaneh, “Optimum design of plate girders by genetic
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using real valued genetic algorithm,” Journal of Korean Society of Steel Construction,
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[10] Shon, S. D., Yoo, M. N., Ha , J. H., Kang, J. W., and Seok, K. Y, “Minimum weight
design of corrugated web girder using genetic algorithms,” Proc. Conference on
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[11] Sedky Abdullah Tohamy, Osama Mohamed Abu El Ela, Amr Bakr Saddek and Ahmed
Ibrahim Mohamed, “Efficiency of plate girder with corrugated web versus plate girder
with flat web”, Minia Journal of Engineering and Technology, Vol. 32, No 1, January
(2013).
[12] Sudeok Shon,Sangwook Jin, Seungjae Lee, “Minimum Weight Design of Sinusoidal
Corrugated Web Beam Using Real-Coded Genetic Algorithms”, Mathematical Problems
in Engineering, Article ID 9184292,(2017).
[13] Vinay Agrawala, Vinay Chandwanib, Arpit Porwala, “Optimum Design of Welded Steel
Plate Girder using Genetic Algorithms”, International Journal of Current Engineering and
Technology, Vol.3, No.4 (October 2013).
[14] IS 800-2007, Code of Practice for General Construction in Steel.

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