Optimization of prestressed concrete girder
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This document discusses the optimization of prestressed concrete girders for bridge construction, emphasizing the advantages of using prestressed concrete, such as increased stability and reduced maintenance costs. It presents a methodology for cost minimization through design variables and constraints, employing optimization techniques in MATLAB. The findings indicate significant cost savings when using optimized designs compared to conventional methods, along with detailed examples and analysis of cost variations across different concrete grades.
![IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 04 Issue: 03 | Mar-2015, Available @ http://www.ijret.org 635
Presstressed concrete is ideally suited for the construction of
medium and long span bridges. Ever since the development
of prestressed concrete by Freyssinet in the early 1930s, the
material has found extensive application in the construction
of long-span bridges, gradually replacing steel which needs
costly maintenance due to the inherent disadvantage of
corrosion under aggressive environment conditions. One of
the most commonly used forms of superstructure in concrete
bridges is precast girders with cast-in-situ slab. This type of
superstructure is generally used for spans between 20 to 40
m. T or I-girder bridges are the most common example
under this category and are very popular because of their
simple geometry, low fabrication cost, easy erection or
casting and smaller dead loads [21].
2. METHODOLOGY
In this project gives an idea about design the prestressed
girder. For the design I section is used. This report gives the
two method of designing girder. Firstly by conventional
method and second is optimization method. With help of
mathematical analysis, manual iteration and most of human
efforts conventional design method is carried out.
2.1 Conventional Method of Design
In conventional structure design process, the design method
proposes a certain solution that is corroborated by
mathematical analysis in order to verify that the problem
requirements or specifications are satisfied. The process
undergoes many manual iterations before the design can be
finalized making it is slow and very costly process. There is
no formal attempt to reach the best design in the strict
mathematical sense of minimizing cost, weight or volume.
The process of design is relied solely on the designer’s
experience, intuition and ingenuity resulting in high cost in
terms of times and human efforts.
2.2 Design Example
Design a post tensioned PSC Girder for effective span of
20m; simply supported live load on girder is 2.5KN/m2, Use
M45 and any type of cable (Multistrand cable). Slab
thickness=115mm. Short span of slab=3m, WPL/FFL on
slab=0.75KN/m2,Ro=0.85.
Fig.1: Plan of simply supported PSC girder with deck slab
Fig. 2: Cross section of prestressed concrete girder
Fig.3: Arrangement of cable at mid span section
Fig.4:- Reinforcement details on midspan section](https://image.slidesharecdn.com/optimizationofprestressedconcretegirder-160831061814/85/Optimization-of-prestressed-concrete-girder-2-320.jpg)
![IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 04 Issue: 03 | Mar-2015, Available @ http://www.ijret.org 636
Fig.5:-Trapezoidal end block view and transition zone
2.3 Optimization Method of Design
The ultimate aim of all such decision is to either minimize
the effort required or maximize the desire benefit. Since the
effort required or the benefit desired in any practical
situation can be expressed as a function of a certain design
variables, optimization can be defined as the process of
finding the conditions that give the minimum or maximum
value of a function. Without loss of generality optimization
can be taken to mean minimization of a function since the
maximum of a function can be found be seeking the
minimum of the negative of the same function.
2.4 Problem Formulation
2.4.1. Description of Design Variables
In prestressed concrete bridge girder design five design
variables are considered. Following fig. shows cross section
of girder with design variables.
X1= Height of Girder
X2 = width of web
X3 = Width of Bottom Flange
X4= Thickness of Bottom Flange
X5 = Number of cables
Fig.6:-Cross section of post tension girder showing different
design variables
2.4.2 Description of constraints
The bound on design variable is considered as constraints.
These are specified limitation (upper or lower limit) on
design variables which are derived from geometric
requirements (superstructure depth, clearances etc.),
minimum practical dimension for construction, code
restriction etc. The lower and upper limits of deck slab
reinforcement are considered according to AASHTO
standard specification,[12,19,22] .The constraint is defined
as
XL ≤ X ≤ XU
Where
X = Design variable.
XL = Lower limit of the design variable.
XU = Upper limit of the design variable
Table 1. Design variables with constraints
Sr.
No.
Design Variables Constraints
1. X1= Height of Girder 1000 ≤ X1 ≤ 3500
2. X2 = width of web b X2≤ 300
3. X3=Width of Bottom
Flange
300 X3≤ S
4. X4=Thickness of Bottom
Flange
a X4≤ 600
5. X5= No. of Cables 1 X5≤ 20
a = clear cover + duct diameter; b = clear cover + web
rebars diameter + duct diameter;, S= Girder spacing
2.4.2 Objective Function
The objective function in the present optimization problem
is the cost of PSC I girder for bridge whose main
components are cost of concrete, and pre stressing steel. The
objective function is a function of design variables the value
of which provides the basis for choice between alternate
acceptable designs [23] .In structural design the objective
function is usually cost minimization.
The cost function F ( cost) is:
F (Cost) = Qconc. x Cconc. + Qsteel x Csteel + Qcable x
Ccable
Where, Qconc. is the quantity of concrete in m3
Cconc. is the unit cost of concrete in Rs/m3
Q steel is the quantity of steel in kg.
C steel is the unit cost of steel in Rs/kg.
Qcable is the quantity of cable in kg.
Ccable is the unit cost of cable in Rs/kg.
3. RESULTS AND DISCUSSION
This is constrained nonlinear programming problem for the
numerical solution of post tension I girder structure using
MATLAB, optimtool.A bound constraint for upper & lower
limits of design variables are derived from geometric](https://image.slidesharecdn.com/optimizationofprestressedconcretegirder-160831061814/85/Optimization-of-prestressed-concrete-girder-3-320.jpg)
![IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 04 Issue: 03 | Mar-2015, Available @ http://www.ijret.org 639
4. RESULT ANALYSES
In the analysis, objective function i.e. for cost is explained
for three different grade of concrete and each case include
varies the top flange dimensions and compared with
conventional values are given in graph no. 1 to 6. In this
optimal design cost saving is same .As in four cases are
taken in that case I constant TFw and vary TFt then
conventional & optimum cost increases with increase in TFt
.then case II constant TFt and vary TFw then also
conventional & optimum cost increases with increase in
TFw.
In Case III both TFw and TFt varies then both cost
increases. and lastly the case IV TFw increases and
decreases the TFt then conventional & optimum cost
increases at certain point and then both the values decreases.
These cases are same for three different grade of concrete.
As the grade increase the conventional cost and optimum
cost is also increases.
5. CONCLUSION
From graph, for conventional and optimal design
consideration; it shows that overall cost of structure
can be reduced by using optimization technique with
stability.
The conventional design procedure aim at finding an
acceptable or adequate design which merely satisfies
the functional and other requirements of the post
tension I girder In general ,there will be more than one
acceptable design based on assumptions. So, it is
difficult to co-relate with different parameters .The
purpose of optimization has to choose the best one of
the many acceptable design.
ACKNOWLEDGEMENTS
I take this opportunity to thank H.O.D, staff members of
Civil Engineering Department, Amrutvahini college of
engineering, Sangamner, library staff for their assistance
useful views and tips. A word of thanks is also reserved for
all my batch mates for their selfless help, support and
entertaining company.
The authors can acknowledge any person/authorities in this
section. This is not mandatory.
REFERENCES
[1]. Alqedra Mamoun, Arafa Mohammed and Ismail
Mohammed, “Optimum cost of prestressed and reinforced
concrete beam using genetic algorithms”, Journal of
artificial intelligence, 2011, vol-4, pg. no. 76-88.
[2]. Barkat Samer, Salem Ali, Harthy Al and Thamer Aouf
R., “Design of prestressed concrete girder using
optimization technique”, Journal of information technology,
2002,pg no 193-201.
[3]. Beck James, Chan Eduardo, Irfanoglu Ayhan,
Papadimitriou Costas,“Multi-criteria optimal structural
design under uncertainty”, journal of earthquake engineering
and structural dynamics,1999,pg. No.-28, 741-761.
[4]. Bindra S.P., “Principles and practice of bridge
engineering”, Dhanpat rai publications, pg. no.166-170.
[5]. Branch M. A., Grace A., “Matlab: Optimization
toolbox, user’s guide", & Version 4.1, the math works inc.,
October 2008.
[6]. Chaitanya Kumar J.D, Lute Venkat “Genetic algorithm
based optimum design of prestressed concrete beam”,
International journal of civil and structural engineering,
2013, volume 3.
[7]. Colin M. Z., ASCE F. And Macrae A. J. “Optimization
of structural concrete beams”, Journal of structural
engineering, 1984, 110:1573-1588.
[8]. Farkas J. & Jarmai K. "Multi-objective optimal design
of welded box beams" Micro computers in civil engineering,
1995, vol.10, pg. no. 249-255.
[9]. Gene F., Sirca Jr., Hojjat Adeli, F.ASCE “Cost
optimization of prestressed concrete bridges”, Journal of
structural engineering, 2005, pg.no-131:380-388.](https://image.slidesharecdn.com/optimizationofprestressedconcretegirder-160831061814/85/Optimization-of-prestressed-concrete-girder-6-320.jpg)
Optimization of prestressed concrete girder
- 1. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 03 | Mar-2015, Available @ http://www.ijret.org 634 OPTIMIZATION OF PRESTRESSED CONCRETE GIRDER Bhawar P.D1 , Wakchaure M.R2 , Nagare P.N3 1 Student of M.E (Structural Engg.), Amrutvahini College of Engineering, Sangamner, Maharashtra, India 2 Professor, Civil Engg, Department, AVCOE, Sangamner, Maharashtra, India 3 Professor, Mechanical Engg, Department, AVCOE, Sangamner, Maharashtra, India Abstract Bridge construction today has achieved a worldwide level of importance. Bridges are the key elements in any road network Use of prestressed concrete I girder bridge is gaining popularity in bridge engineering fraternity because of its better stability, serviceability, economy, aesthetic appearance and structural efficiency. This paper concerned idea about prestressed concrete.In the method of prestressing two types are consider that pre tensioning and post tensioning .At the time of prestressing different losses are consider. These are the losses due to elastic shortening, friction losses, relaxation losses, losses due to creep and shrinkage. In this way total amount of losses in pretensioning and post tensioning calculate and detailed information has given in this report. The objective is to minimize the total cost in the design process of the bridge system considering the cost of materials like steel, concrete, tendons etc. For a particular problem the design variables considered for the cost minimization of the bridge system, are depth of girder, various cross sectional dimensions of the girder, number of tendons, A programme is developed for analysis and designing an low cost prestressed girder in MATLAB R2010a software. The optimtool is used to find out minimum cost of structure Illustrative case of prestressed girder presented and discuss by using active set method from optimtool. Optimization problem is characterized by considering design variables and bound constraints are according to AASHTOO Standards ,IRC 21- 2000 bridge specifications .The proposed cost optimization approach is compared with an existing project which leads to a considerable cost saving while resulting in feasible design. Keywords: Post tension I girder, Conventional design, Optimal design, MATLAB Software etc… ----------------------------------------------------------------------***-------------------------------------------------------------------- 1. INTRODUCTION OF PRESTRESSED CONCRETE BRIDGES The Principal of presstressed concrete has been widely applied for the design of bridges. The prestressed members are light and best suited for architectural treatment. Prestressing technique eliminates the cracking of concrete. Presence of cracks lowers the capacity of structure to bear reversal of stresses, impact, vibration and shock. This reduces the maintenance cost and provides smoother deck for high speed driving. The prestressing technique increases the shear capacity of concrete. Prestressed concrete bridges of medium and long span are generally of three basic types:- i) Precast I beam with an in-situ reinforced concrete deck either made continuous by means of in- situ pier diaphragms and continuity steel by suspending them between in situ umbrella. ii) Continuous in-situ solid post-tensioned slabs, in spans up to 35 m. iii) Continuous hollow box girder bridges, usually in-situ .These may be constructed on ground supported false work, or by free cantilever erection methods. The prestressing can be either pretensioning or post tensioning .The choice of particular method for any given bridge would depend upon the availability of and proximity of pretensioning plant and equipment, size, availability of post tensioning know-how and equipment ,size of members, number of units of similar type, etc .Pretensioning is usually economical with straight tendons. The Post-tensioning can be structurally advantageous with draped tendons. Post- tensioning is well suited for prestressing at a construction site without the need for factory type installations .The unit cost for post –tensioning is higher as compared to pretensioning .This is because post tensioning requires individual tensioning, special anchorages, sheath and grouting. The cast of post –tensioning devices is higher because they are covered by patents which restrict the user to purchase material and equipment from the patent holders only .All post-tensioned girders are invariably with bonded tendons. The precasting industry in recent years has become very popular all over the world due to efficient management and outstanding quality control procedure. The major limitations to presstressed construction when it comes to hauling and erecting have been the length and weight limits. For bridge structure two basic precast sections are produced:-I beam sections to be used with a cast –in –place deck.
- 2. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 03 | Mar-2015, Available @ http://www.ijret.org 635 Presstressed concrete is ideally suited for the construction of medium and long span bridges. Ever since the development of prestressed concrete by Freyssinet in the early 1930s, the material has found extensive application in the construction of long-span bridges, gradually replacing steel which needs costly maintenance due to the inherent disadvantage of corrosion under aggressive environment conditions. One of the most commonly used forms of superstructure in concrete bridges is precast girders with cast-in-situ slab. This type of superstructure is generally used for spans between 20 to 40 m. T or I-girder bridges are the most common example under this category and are very popular because of their simple geometry, low fabrication cost, easy erection or casting and smaller dead loads [21]. 2. METHODOLOGY In this project gives an idea about design the prestressed girder. For the design I section is used. This report gives the two method of designing girder. Firstly by conventional method and second is optimization method. With help of mathematical analysis, manual iteration and most of human efforts conventional design method is carried out. 2.1 Conventional Method of Design In conventional structure design process, the design method proposes a certain solution that is corroborated by mathematical analysis in order to verify that the problem requirements or specifications are satisfied. The process undergoes many manual iterations before the design can be finalized making it is slow and very costly process. There is no formal attempt to reach the best design in the strict mathematical sense of minimizing cost, weight or volume. The process of design is relied solely on the designer’s experience, intuition and ingenuity resulting in high cost in terms of times and human efforts. 2.2 Design Example Design a post tensioned PSC Girder for effective span of 20m; simply supported live load on girder is 2.5KN/m2, Use M45 and any type of cable (Multistrand cable). Slab thickness=115mm. Short span of slab=3m, WPL/FFL on slab=0.75KN/m2,Ro=0.85. Fig.1: Plan of simply supported PSC girder with deck slab Fig. 2: Cross section of prestressed concrete girder Fig.3: Arrangement of cable at mid span section Fig.4:- Reinforcement details on midspan section
- 3. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 03 | Mar-2015, Available @ http://www.ijret.org 636 Fig.5:-Trapezoidal end block view and transition zone 2.3 Optimization Method of Design The ultimate aim of all such decision is to either minimize the effort required or maximize the desire benefit. Since the effort required or the benefit desired in any practical situation can be expressed as a function of a certain design variables, optimization can be defined as the process of finding the conditions that give the minimum or maximum value of a function. Without loss of generality optimization can be taken to mean minimization of a function since the maximum of a function can be found be seeking the minimum of the negative of the same function. 2.4 Problem Formulation 2.4.1. Description of Design Variables In prestressed concrete bridge girder design five design variables are considered. Following fig. shows cross section of girder with design variables. X1= Height of Girder X2 = width of web X3 = Width of Bottom Flange X4= Thickness of Bottom Flange X5 = Number of cables Fig.6:-Cross section of post tension girder showing different design variables 2.4.2 Description of constraints The bound on design variable is considered as constraints. These are specified limitation (upper or lower limit) on design variables which are derived from geometric requirements (superstructure depth, clearances etc.), minimum practical dimension for construction, code restriction etc. The lower and upper limits of deck slab reinforcement are considered according to AASHTO standard specification,[12,19,22] .The constraint is defined as XL ≤ X ≤ XU Where X = Design variable. XL = Lower limit of the design variable. XU = Upper limit of the design variable Table 1. Design variables with constraints Sr. No. Design Variables Constraints 1. X1= Height of Girder 1000 ≤ X1 ≤ 3500 2. X2 = width of web b X2≤ 300 3. X3=Width of Bottom Flange 300 X3≤ S 4. X4=Thickness of Bottom Flange a X4≤ 600 5. X5= No. of Cables 1 X5≤ 20 a = clear cover + duct diameter; b = clear cover + web rebars diameter + duct diameter;, S= Girder spacing 2.4.2 Objective Function The objective function in the present optimization problem is the cost of PSC I girder for bridge whose main components are cost of concrete, and pre stressing steel. The objective function is a function of design variables the value of which provides the basis for choice between alternate acceptable designs [23] .In structural design the objective function is usually cost minimization. The cost function F ( cost) is: F (Cost) = Qconc. x Cconc. + Qsteel x Csteel + Qcable x Ccable Where, Qconc. is the quantity of concrete in m3 Cconc. is the unit cost of concrete in Rs/m3 Q steel is the quantity of steel in kg. C steel is the unit cost of steel in Rs/kg. Qcable is the quantity of cable in kg. Ccable is the unit cost of cable in Rs/kg. 3. RESULTS AND DISCUSSION This is constrained nonlinear programming problem for the numerical solution of post tension I girder structure using MATLAB, optimtool.A bound constraint for upper & lower limits of design variables are derived from geometric
- 4. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 03 | Mar-2015, Available @ http://www.ijret.org 637 requirements, minimum practical dimension for construction, code restriction etc. and objective function has been prepared for various width and thickness of top flange of girder and the also according to different concrete grade. Following are the input parameters of post tension I girder which is used in the optimtool for making bound constrained equation and objective equation in optimtool. 3.1 Optimization for Post Tension I Girder The programs developed were applied to obtain optimal solution for 1300 mm height of girder. Optimal values are obtained in three cases according to three different grades of concrete. Problem is solved by M45 grade but it compares with the M50 grade. Each case includes varies the top flange dimensions and compared with conventional values. 3.1.1 For M45 grade of concrete 1) CASE-I As top flange width constant (TFw) and vary thickness (TFt). 2) CASE-II As Top flange width vary (TFw) and thickness constant (TFt). 3) CASE-III As Both top flange width (TFw) and thickness (TFt) vary. 4) CASE-IV As top flange width increases (TFw) and thickness (TFt) decreases. Table -1: CASE-I As top flange width constant (TFw) and vary thickness (TFt). Sr. No. Top Flange Width ( TFw) in mm Top Flange Thickness ( TFt) in mm Conventional Cost(Rs) Optimum Cost (Rs) 1 500 150 72,713 52,184 2 500 175 74,402 53,931 3 500 200 76,091 55,678 4 500 220 77,442 57,075 5 500 250 79,469 59,171 Graph-1:-Case-I Comparison of optimum and conventional cost Table -2: CASE-II As Top flange width vary (TFw) and thickness constant (TFt). Sr. No. Top Flange Width (TFw) in mm Top Flange Thickness ( TFt) in mm Conventional Cost(Rs) Optimum Cost (Rs) 1 500 150 72,713 52,184 2 550 150 74,919 54,173 3 600 150 77,125 56,168 4 625 150 78,228 57,155 5 650 150 79,331 58,149 Graph-2:-Case-II Comparison of optimum and conventional cost Table -3: CASE-III As Both top flange width (TFw) and thickness (TFt) vary. Sr. No. Top Flange Width ( TFw) in mm Top Flange Thickness ( TFt) in mm Conventional Cost(Rs) Optimum Cost (Rs) 1 550 175 76,859 56,175 2 575 200 80,154 59,426 3 600 225 83,700 62,933 4 625 240 86,571 65,741 5 650 260 90,081 69,205 Graph-3:-Case-III Comparison of optimum and conventional cost
- 5. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 03 | Mar-2015, Available @ http://www.ijret.org 638 Graph-4:-Case-III Comparison of optimum and conventional cost Table -4: CASE-IV As top flange width increases (TFw) and thickness (TFt) decreases. Sr. No. Top Flange Width ( TFw) in mm Top Flange Thickness ( TFt) in mm Conventional Cost(Rs) Optimum Cost (Rs) 1 500 260 80,145 59,870 2 550 240 81,904 61,380 3 600 200 81,508 60,676 4 625 175 80,545 59,540 5 650 150 79,331 58,149 Graph-5:-Case-IV Comparison of optimum and conventional cost Graph-6:-Case-IV Comparison of optimum and conventional cost 3.2 Comparison of Conventional, Optimum and Saving Cost for different Grade of Concrete with TFw = 500mm, TFt = 150 mm. For conventional design take top flange width 500mm & thickness is 150 mm.This values are taken for different grade of concrete. Calculate the conventional cost and compare result with the optimum cost and also calculate the saving cost. As conventional cost increase, optimum cost and saving cost is also increases. These are shown in table below:- Table No-5: Cost comparison of conventional and optimum cost as TFw =500 and TFt = 150 mm, changes grade of concrete (TF w) (TF ) Grade of Concre te Conventio nal Cost(Rs) Optimu m Cost (Rs) Saving cost 500 150 M45 72,713 52,184 20,529 M50 76,091 54,609 21,482 M55 79,470 57,034 22,436 Graph -7: Comparison of optimum, conventional and saving cost
- 6. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 03 | Mar-2015, Available @ http://www.ijret.org 639 4. RESULT ANALYSES In the analysis, objective function i.e. for cost is explained for three different grade of concrete and each case include varies the top flange dimensions and compared with conventional values are given in graph no. 1 to 6. In this optimal design cost saving is same .As in four cases are taken in that case I constant TFw and vary TFt then conventional & optimum cost increases with increase in TFt .then case II constant TFt and vary TFw then also conventional & optimum cost increases with increase in TFw. In Case III both TFw and TFt varies then both cost increases. and lastly the case IV TFw increases and decreases the TFt then conventional & optimum cost increases at certain point and then both the values decreases. These cases are same for three different grade of concrete. As the grade increase the conventional cost and optimum cost is also increases. 5. CONCLUSION From graph, for conventional and optimal design consideration; it shows that overall cost of structure can be reduced by using optimization technique with stability. The conventional design procedure aim at finding an acceptable or adequate design which merely satisfies the functional and other requirements of the post tension I girder In general ,there will be more than one acceptable design based on assumptions. So, it is difficult to co-relate with different parameters .The purpose of optimization has to choose the best one of the many acceptable design. ACKNOWLEDGEMENTS I take this opportunity to thank H.O.D, staff members of Civil Engineering Department, Amrutvahini college of engineering, Sangamner, library staff for their assistance useful views and tips. A word of thanks is also reserved for all my batch mates for their selfless help, support and entertaining company. The authors can acknowledge any person/authorities in this section. This is not mandatory. REFERENCES [1]. Alqedra Mamoun, Arafa Mohammed and Ismail Mohammed, “Optimum cost of prestressed and reinforced concrete beam using genetic algorithms”, Journal of artificial intelligence, 2011, vol-4, pg. no. 76-88. [2]. Barkat Samer, Salem Ali, Harthy Al and Thamer Aouf R., “Design of prestressed concrete girder using optimization technique”, Journal of information technology, 2002,pg no 193-201. [3]. Beck James, Chan Eduardo, Irfanoglu Ayhan, Papadimitriou Costas,“Multi-criteria optimal structural design under uncertainty”, journal of earthquake engineering and structural dynamics,1999,pg. No.-28, 741-761. [4]. Bindra S.P., “Principles and practice of bridge engineering”, Dhanpat rai publications, pg. no.166-170. [5]. Branch M. A., Grace A., “Matlab: Optimization toolbox, user’s guide", & Version 4.1, the math works inc., October 2008. [6]. Chaitanya Kumar J.D, Lute Venkat “Genetic algorithm based optimum design of prestressed concrete beam”, International journal of civil and structural engineering, 2013, volume 3. [7]. Colin M. Z., ASCE F. And Macrae A. J. “Optimization of structural concrete beams”, Journal of structural engineering, 1984, 110:1573-1588. [8]. Farkas J. & Jarmai K. "Multi-objective optimal design of welded box beams" Micro computers in civil engineering, 1995, vol.10, pg. no. 249-255. [9]. Gene F., Sirca Jr., Hojjat Adeli, F.ASCE “Cost optimization of prestressed concrete bridges”, Journal of structural engineering, 2005, pg.no-131:380-388.