study & evaluation scheme...sadhu singh, “theory of elasticity” , khanna publishers, new...

SYLLABUS

OF

M. TECH

(Structural Engineering)

DEPARTMENT OF CIVIL

ENGINEERING

INTEGRAL UNIVERSITY

LUCKNOW

STARTING FROM BATCH 2016-17

STUDY AND EVALUATION SCHEME (Evening)

M.Tech. (Structural Engg.)

SYLLABUS REVISED-2016

w.e.f. July-2016

Semester – I

S.

No.

Course

Category

Code No Name of Subject PERIODS Credits EVALUATION SCHEME Subject

Total L T P SESSIONAL EXAM EXAM.

ESE CT AT Total

01 DC CEE501 Theory of Elasticity and

plasticity

3 1 - 4 25 15 40 60 100

02 DC CEE503 Advanced Concrete Design

3 1 - 4 25 15 40 60 100

03 DC CEE509 Structural Engg Lab

- - 3 2 - - 60 40 100

Total 10 300

Semester – II

01 DC CEE511 Numerical Analysis And

Finite Element Method

3 1 - 4 25 15 40 60 100

02 DC CEE513 Theory of plates and shell

3 1 - 4 25 15 40 60 100

03 DC CEE514 Seminar

- - 3 2 - - 60 40 100

Total 10 300

TA- Teacher Assessment; ESE – End Semester Examination; CT- Cumulative Test.

Note : Duration of ESE shall be 03 (Three) hours per subject.




w.e.f. July-2016

Semester – III

S.

No.

Course

Category



ESE CT AT Total

01. DC CEE502 Advanced Structural

Analysis (Matrix Approach)

3 1 - 4 25 15 40 60 100

02. DE CEE504-

CEE506

Elective – I

3 1 - 4 25 15 40 60 100

03. DE CEE601-

CEE603

Elective –II

3 1 - 4 25 15 40 60 100

Total 12 300

Semester – IV

01. DC CEE510 Structural Dynamics

3 1 - 4 25 15 40 60 100

02. DC CEE512 Advanced Steel Structures

3 1 - 4 25 15 40 60 100

03. DC CEE615 Training

- - - 2 ---- ---- 100 ---- 100

Total 10 300

TA- Teacher Assessment; ESE – End Semester Examination ; CT- Cumulative Test.





w.e.f. July-2016

Semester – V

S.

No.

Course

Category

Code No Name of Subject PERIODS Cre

dits

EVALUATION SCHEME Subject

Total

L T P SESSIONAL EXAM EXAM.

ESE CT TA Total

01. DE CEE606-

CEE608

Elective –III

3

1

-

4 25 15 40 60 100

02. DE CEE611-

CEE613

Elective –IV

3

1

-

4 25 15 40 60 100

03. DC CEE616 Dissertation (Phase –

I)

-

-

3

4 --- --- 60 40 100

Total

12

300

Semester – VI

01.

DC

CEE617

Dissertation (Phase-

II)

-

-

12

18

-

-

60 40 100

Grand Total

1600



STUDY AND EVALUATION SCHEME (Full Time)



w.e.f. July-2016

Semester – I

TA- Teacher Assessment; ESE – End Semester Examination; CT- Cumulative Test.

Note: Duration of ESE shall be 03 (Three) hours per subject

S.

No.

Course

Category



ESE CT AT Total

01. DC CE501 Theory of Elasticity and

plasticity

3 1 - 4 25 15 40 60 100

02. DC CE502 Advanced Structural

Analysis(Matrix Approach)

3 1 - 4 25 15 40 60 100

03. DC CE503 Advanced Concrete Design

3 1 - 4 25 15 40 60 100

04. DE CE504-

CE506

Elective -I

3 1 - 4 25 15 40 60 100

05. DC CE509 Structural Engg Lab

- - 3 2 - - 60 40 100

Total 18 500

Semester – II

01. DC CE510 Structural Dynamics

3 1 - 4 25 15 40 60 100

02. DC CE511 Numerical Analysis And

Finite Element Method

3 1 - 4 25 15 40 60 100

03. DC CE512 Advanced Steel Structures

3 1 - 4 25 15 40 60 100

04. DC CE513 Theory of plates and shell

3 1 - 4 25 15 40 60 100

05. DC CE514 Seminar

- - 3 2 - - 60 40 100

Total 18 500

STUDY AND EVALUATION SCHEME (Full Time)



w.e.f. July-2016

Semester –III

S.No. Course

Category



ESE CT AT Total

01. DE CE601-CE603 Elective -II

3 1 - 4 25 15 40 60 100

02. DE CE606-CE608 Elective -III

3 1 - 4 25 15 40 60 100

03. DE CE611-CE613 Elective -IV

3 1 - 4 25 15 40 60 100

04. DC CE615 Training

- - - 2 --- --- 100 --- 100

05. DC CE616 Dissertation (Phase –I)

- - 3 4 -- -- 60 40 100

Total 18 500

Semester – IV

01. DC CE617 Dissertation (Phase –II)

- - 12 18 - - 60 40 100

Grand Total 1600



M.Tech (Structural Engg.) (Evening)

List of the Elective Paper

Elective – I

CEE504 Concrete Technology

CEE505 Design of foundation structures

CEE506 Design of steel Concrete composite Structures

Elective – II

CEE601 Design of Bridges

CEE602 Stability of Structures

CEE603 Maintenance and Rehabilitation of Structures

Elective – III

CEE606 Design of Tall Buildings

CEE607 Industrial Structures

CEE608 Prefabricated Structures

Elective – IV

CEE611 A Seismic Design of Structures

CEE612 Computer Aided Design

CEE613 Prestressed Concrete



M.Tech (Structural Engg.) (Full Time)

List of the Elective Paper

Elective – I

CE504 Concrete Technology

CE505 Design of foundation structures

CE506 Design of steel Concrete composite Structures

Elective – II

CE601 Design of Bridges

CE602 Stability of Structures

CE603 Maintenance and Rehabilitation of Structures

Elective – III

CE606 Design of Tall Buildings

CE607 Industrial Structures

CE608 Prefabricated Structures

Elective – IV

CE611 A Seismic Design of Structures

CE612 Computer Aided Design

CE613 Prestressed Concrete



Theory of Elasticity and Plasticity (CEE-501/CE501)

L T P

3 1 0

Unit – I 10

Analysis of stress and strain, Stress strain relationship. Generalized Hooke’s Law. Plane

stress and plane stress plane strain.

Unit – II 10

Two dimensional problems in Cartesian co-ordinates for simple problems of structures.

Unit – III 10

Two dimensional problems in polar co-ordinates for simple problems of structures.

Unit – IV 10

Introduction to problems in plasticity. Physical assumption- criterion of yielding, yield

surface, Flow rule (plastic stress strain relationship). Elastic plastic problems of beams in

bending- plastic torsion.

Total No of periods: 40

References :

1. Timoshenko, S. and Goodier T.N. “Theory of Elasticity” Mc Graw Hill Book Co.

Newyork. II Edition 1988.

2. Chwo P.C. and pagano, N.J. “Elasticity Tensor, Dyadic and Engineering

applications” D.Van Nestrand Co. In Co. 1967.

3. Chenn, W.P and Henry D.J. “plasticity for structural Engineers”, Springer Verlag

New Yark 1988.

4. Sadhu Singh, “Theory of Elasticity” , Khanna publishers, New Delhi 1988.

5. Verma PDS, “Theory of Elasticity” , Vikas publishing Pvt. Ltd. New Delhi – 1997.

6. Sadhu Singh, “Theory of plasticity” , Khanna publ

Advanced Structural Analysis (Matrix Approach) (CEE-502/ CE502)

L T P

3 1 0

Unit – I 10

Introduction and Displacement Method -2D Analysis

Introduction to Matrix Methods- displacements formulation analysis of continuous

beams- co-ordinate Rigid and pin jointed plane-frames.

Unit – II 10

Force Method

Matrix flexibility methods- general formulation-application to plane rigid frames-

plane rigid frames plane trusses.

Unit – III 10

Displacement Method -3D Analysis

Displacement method for three dimensional structure-analysis of space trusses and

space frames.

Unit – IV 10

Special Problems

Analysis of large structures- sub-structuring static condensation procedure-Simple

problems only.

Total No of periods : 40

References:

1. Coates, R.C., Coutie M.G., and Kong, F.K. ,Structural Analysis,

John Wiley and Sons, 1979.

2. Mc Guire, W., and Gallagher, R.H., Matrix Structural Analysis,

John Wiley and Sons,1979.

3. John L. Meek., Matrix structural Analysis , Mc Graw Hill Book Company,1971.

Advance Concrete Design (CEE-503/ CE503)

L T P

3 1 0

Unit – I 10

Overall Review

Review of limit state design of beams- slabs and columns according to IS 456-2000

.Calculation of deflection and crack width according to IS 456 -2000.

Unit – II 10

Design of Special RC Element

Design of Slender columns- Design of RC walls- Ordinary and shear walls-Design of

Corbels, Deep beam and Grid floors.

Unit – III 10

Flat Slabs and Flat Plates

Design of flat slabs and flat plates according to ACI method- Design of shear load-

reinforcement and edge (spandrel) beams.

Unit – IV 10

General

Detailing for ductility, fire resistance of buildings, field control of concrete.


References:

1. Purushothaman, P, Reinforced Concrete Structure Structural Elements : Behavior

Analysis and Design,Tata Mc Graw Hill, 1986.

2. Varghese, P.C., Limit State Design of Reinforced Concrete, prentice Hall of India,

1995.

3. Drishna Raju, N.Advanced Reinforced Concrete Design, CBS publishers and

Distributors, 1986.

Structural Engineering Laboratory (CEE-509/ CE509)

L T P

0 0 3

1- Properties and testing of fresh concrete (2 experiments)

2- Properties and testing of harden concrete. (2 experiments)

3- Concrete mix design (3 experiments).

4- Strength, fracture and micro structural characteristics of mild steel.

5- Electrical resistance strain Gages (one experiment)

6- Stress analysis by photoelasticity. (one experiment)

7- Non-destructive testing (one experiment).

Structural Dynamics (CEE-510/ CE510)

L T P

3 1 0

UNIT – I 10 Types of vibration and ground motions; Free and forced vibrations of single degree of

freedom system, response to harmonic, periodic, impulsive and general dynamic loading,

response of SDOF to earthquake.

UNIT – II 10 Free vibration of lumped multi degree of freedom system. Approximate methods for

obtaining natural frequencies and mode shapes.

UNIT – III 10 Frequency domain analysis of lumped multi degree of freedom system using normal mode

theory, Time domain analysis using Numerical Integration Scheme.

UNIT – IV 10 Free and forced vibrations of continuous system; Dynamic analysis of tall and massive

structures.

Total No of period 40

References:

1. Glen V.Berg – Element of structural Dynamics.

2. Agarwal, Pankaj; & Shrikhande, Manish; Earthquake Resistant Design of

Structures.

3. Paz, Mario; Structural Dynamics – Theory and Computations.

4. Chopra ,Anil Kumar; - Dynamics of Structures.

Numerical Analysis and Finite Element Method (CEE-511/ CE511)

L T P

3 1 0

UNIT – I 10 Linear equations and Eigen value problems, Accuracy of approximate calculations; Non-

linear equations, interpolation.

UNIT – II 10 Differentiation and evaluation of single and multiple integrals; Numerical solution of

differential equation.

UNIT – III 10 Finite difference methods, initial and boundary value problems; Newton’s method,

variational and weighted residual methods.

UNIT – IV 10 Introduction of FEM.Various type of finite elements, parametric and local coordinates,

discretization, energy and variational approaches, convergence criteria, Applications: plane

stress and plane strain problems, axisymetric solids, plate and shell structures, field

problems.


Reference :

1. K.K. Jain, S.R.K. Iyengar and R.K. Jain, Numerical Methods

2. Krishnamurathy , Finite Element Analysis

3. Budvanan, G.R. Finite Element Analysis.

4. Zienkiewiez, O Finite Element Method its Basic & Fundamentals

Advanced Steel Structures (CEE-512/ CE512)

L T P

3 1 0

UNIT – I 10

Analysis and design of industrial buildings and bents – Design of bracings – Design of crane

and gantry girders.

UNIT – II 10 Analysis and design of steel towers, trestles and masts. Design of self supporting chimney.

UNIT – III 10 Types of cross sections – local and lateral buckling. Design of compression and tension

members, beams and connections.

UNIT – IV 10 Plastic design of beams, shape factors, moment distribution. Plastic analysis of fixed and

continuous beams, propped cantilevers, single bay and two bay portal frames.


References:

1. Duggal S.K; –Design of Steel Structures.

2. Chandra R.K; –Design of Steel Structures Vol I&II.

3. Sarvar Alam Raaz–Design of Steel Structures.

4. Kazmi and Jindal–Design of Steel Structures.

5. Limit State Design of Steel Structures by S. K. Duggal, Tata Mc-Graw-Hill

Publishing Company.

6. Steel Structures Design and Practice By N.Subramanian, Oxford University Press

7. Structural Design and Drawing Reinforced Concrete and Steel By N. Krishna Raju,

University Press

8. IS-800-2007And IS-800-1984

Theory of Plates and Shells (CEE-513/CE513)

L T P

3 1 0

UNIT – I 10

Plates; basic concept, governing equations, boundary conditions, solution of rectangular and

circular plates by classical methods, numerical methods; plates of various shapes, design

criteria.

UNIT – II 10

Shells; basic concepts, membrane and bending Analysis of cylindrical shells, shell of

revolution, edge perturbations and secondary stresses; numerical solutions.

UNIT – III 10

Approximate design methods for doubly curved shells; design criteria, code specification

and parametric proportioning, stability considerations.

UNIT – IV 10

Folded plates; forms, structural action, method of analysis, design considerations.


References :

1. S. Timoshenko – Theory of plate and shells.

2. L.G. Jaeger – Elementary theory of elastic plates.

3. G. Ramaswamy – Design of Concrete Shells.

4. Ramchandran - J.- Thin Shells –Theory and problems.

ELECTIVE –I

Concrete Technology (CEE-504/CE504)

L T P

3 1 0

Unit – I 10

Concrete Making Materials

Aggregates classification, IS specifications, properties, Grading, Methods of

combining aggregates, specified grading, Testing of aggregates, Fibers. Cement,

Grade of cement, Chemical composition, testing of concrete, Hydration of cement,

structure of hydrated cement, Special cements- Water Chemical admixtures,

Mineral admixture.

Unit – II 10

Concrete

Properties of fresh concrete, hardened concrete, strength, Elastic properties, Creep

and shrinkage, variability of concrete strength.

Unit – III 10

Mix Design

Principle of concrete mix design, Methods of concrete mix design. Ready mix

concrete and its merits & demerits

Unit – IV 10

Special Concrete & Concreting Methods

Light weight concrete, Fly ash concrete, Fiber reinforced concrete, polymer

Concrete, Super plasticized concrete, Epoxy resins and screeds for

rehabilitation- properties and Applications High performance concrete. Process of

manufacturing of concrete, Methods of transportation, placing and extreme weather

concreting, special concreting methods, vacuum dewatering underwater concrete,

special from work.


References :

1. Neville, A.M., properties of Concrete, pitman publishing Limited, London.

2. Shetty M.S., Concrete Technology, S. Chand and Company Ltd. Delhi.

3. Rudhani G., Light Weight Concrete Academic Kiado, Publishing Home of

Hungarian Academy of Sciences, 1963.

Design of Foundation Structures (CEE-505/CE505)

L T P

3 1 0

Unit – I 10

Introduction

Design of Soil Investigation report for design of foundation structures. General principles of

design of reinforced concrete shallow and deep foundations.

Unit – II 10

Design of Shallow and Deep Foundations

Shallow foundations- Beams on elastic foundations- Design of isolated & rafts and

basement design, Deep foundations- Load carrying capacity of different types of

piles and detailing of reinforcements according to IS 2911- Design of pile caps.

Unit – III 10

Design of Deep Foundations

Deep foundation well foundation design of well foundation on cohesive & non-

cohesive soils, Method of constructions

Unit – IV 10

Tower Foundations

Design of foundations for towers- Structural design of support for foundation excavation,

design of ground anchors. Well sinking, tilt & shifts


References:

1. Thomlinson, M.J. and Boorman.R., “Foundation design and construction”,

ELBS Longman VI Edt. 1995

2. Nayak, N.V., “Foundation Design manual for practicing Engineers” .

Dhanpat Rai and Sons, 1982.

3. Winterkorn H.F., and Fang H.Y., “Foundation Engineering Hand book –

Van Nostrard – Reinhold 1976.

Design of Steel concrete Composite structures (CE-506/CE506)

L T P

3 1 0

Unit – I 10

Introduction

Introduction to steel Concrete composite construction- Theory of composite

structures- Introduction to steel Concrete – Steel sandwich construction.

Unit – II 10

Design of Composite Members

Behavior of composite beams – Columns- Design of composite beams- steel-

concrete composite columns – Design of composite trusses.

Unit – III 10

Design of Connections

Types of connections – Design of connections in the composite structures- Shear

connections- Design of connections in composite trusses.

Unit – IV 10

Composite Box Girder Bridges

Introduction – Behavior of box girder bridges – Design concepts.


References :

1. Neville, A.M. , Properties of concrete, Pitman publishing Limited , London.

2. Shetty M.S. , Concrete Technology, S. Chand and Company Ltd. Delhi.

3. Rudhani G., Light Weight Concrete Academic Kiado, publishing Home of

Hungarian Academy of Sciences, 1963.

ELECTIVE – II

Design of Bridges (CEE-601/CE601)

L T P

3 1 0

UNIT – I 10

Introduction and selection of type, Geometric and Hydraulic design considerations, Loading

and standards for highway and railway bridges.

UNIT – II 10

Reinforced and Pre-stressed Concrete Bridges: types and standard forms, Balanced

cantilever Bridge, Arch bridges, Bowstring girder bridges.

UNIT – III 10

Steel Bridges: Plate Girder Bridge, Box girder bridge, Cable Stayed Bridge, Cantilever

bridge.

UNIT – IV 10

Design of pier and abutments, pile and well foundations, Bearings, Seismic design

considerations.


References :

1. C.Vilmaz,S.Wasti Cetin Vlmaz, Analysis and Design of Bridges .

2. Raju Krishna, Design of Bridges

3. Punia B.C., Jain A.K., Jain A.K., Design of Steel Structure

Stability of Structures (CEE-602/CE602) L T P

3 1 0

UNIT – I 10

Buckling of axial and eccentrically loaded columns, beam-column, frames;

UNIT – II 10

Torsional instability; Flexural buckling of shells,

UNIT – III 10

Local buckling of plate and shell element,

UNIT – IV 10

Post buckling behavior of columns, plates and shells.


References :

1. Gambhir M.I. Stability, Analysis & Design of Structure

2. M.C. Mahon, Jhon, Brown chuck; Design of Stability of Concrete Structure

MAINTENANCE AND REHABILITATION -STRUCTURES

(CEE603/CE603) L T P

3 1 0

UNIT – I 10

Quality assurance for concrete construction, As in built concrete properties, strength,

permeability, volume changes, thermal properties, cracking. Effects due to climate,

temperature, chemicals wear and erosion,

UNIT – II 10

Design and construction errors, corrosion mechanism, Effects of cover thickness and

cracdking, methods of corrosion protection, inhibitors, resistant steels, coatings, cathodic

protection.

UNIT – III 10

Inspection, Structural Appraisal, Economic appraisal, components of quality assurance,

conceptual bases for quality assurance schemes. Special concretes and mortar, concrete

chemicals, special elements for accelerated strength gain, expansive cement, polymer

concrete, sulphur infiltrated concrete, ferrocement, fiber reinforced concrete

UNIT – IV 10

Rust eliminators and polymers coating for rebars during repair, foamed concrete, mortar and

dry pack, vacuum concrete, Gunite and shotcrete epoxy injection, mortar repair for cracks,

shoring and underpinning.


References :

1. Venkataraman K., Maintenance of Engineering & Management.

2. Panchdhari A.C., Maintenance of Building.

ELECTIVE – III

Design of Tall Buildings (CEE603/CE603)

L T P

3 1 0

UNIT – I 10

Types of structural systems; types of loads; method of analysis; stability of tall structures;

selection of foundation for tall buildings.

UNIT – II 10

Bluff body aerodynamics; aero-elastic phenomena; wind directionality effects; structural

response and design considerations; standard provisions for wind loading.

UNIT – III 10

Introduction to earthquake engineering and earthquake resistant design of buildings;

earthquake motion and response; general principles and design criteria for buildings;

UNIT – IV 10

Codal provisions, asiesmic design of structures; dynamic analysis; effect of torsion; design

of stack like structures; earthquake forces in tall buildings. Shear in buildings; need and

location of shear walls in tall buildings; analysis and design of shear walls.


Industrial Structures (CEE-607/CE607)

L T P

3 1 0

UNIT – I 10

Planning of industrial structures; design of single and multi-bay industrial structures in steel

and concrete;

UNIT – II 10

Design of Bunkers and Silos;

UNIT – III 10

Pressure vessels and Chimneys; Cooling towers;

UNIT – IV 10

Large span roof structures; Suspension roof structures; Structural aspect of machine

foundations.


PREFABRICATED STRUCTURES (CEE-608/CE608)

L T P

3 1 0

UNIT – I 10

Types of fabrication – Modular co-ordination, components, prefabrication systems and

structural schemes; Design considerations; Economy of prefabrication; prefabrication of

load carrying members;

UNIT – II 10

Disuniting of structures; Design of cross section of load carrying members; Structural

behavior of precast structures. Handling and erection stresses.

UNIT – III 10

Application of prestressing of roof members; floor systems; Two way load bearing slabs,

wall panels, hipped plate and shell structures. Dimensioning and detailing of joints for

different structural connections; construction and expansion joints.

UNIT – IV 10

Production, Transportation & erection; Organization of production, storing and erection

equipment; Shuttering and mould design – Dimensional tolerances; Erection of R.C.

structures, Total prefabricated buildings.


ELECTIVE – IV

A Seismic Design of Structures (CEE-611/CE611)

L T P

3 1 0

UNIT – I 10

Characteristics of earthquakes: Earthquake terminology, magnitude, intensity, measurement

of ground motion, frequency-magnitude relationship, liquefaction. Strong ground motion:

Acceleration time histories, peak parameters (peak ground acceleration / velocity /

displacement), response spectrum, and site effects.

UNIT – II 10

Earthquake analysis of structures: Idealization of structures, response spectrum analysis,

equivalent force concepts, torsionally coupled systems.

UNIT – III 10

Concepts of earthquake resistant design: objectives, ductility, ductility reduction factor,

over-strength, response reduction factor, design response spectrum, lateral stiffness, building

configuration, base isolation, concept of structural control.

UNIT – IV 10

Building codes: Performance of buildings in past earthquakes, historical perspective of code

development, Indian code (IS: 1893), provisions for buildings, Retrofitting and

strengthening of structures (IS: 13935). Detailing for reinforced concrete and masonry

buildings, provisions of IS: 13920, IS: 4326, IS: 13927, IS: 13928


References :

1. R.W. Clough and J. Penzein, Dynamics of structures, second edition, McGraw

Hill International edition1993.

2. M. Paz, Dynamics of structures, CBS pub.1987.

3. A.K. Chopra, Dynamics of structures- Theory and application to earthquake

engineering, PHI 1997.

4. T. Pauley and M.S.N. Priestly, Seismic design of reinforced concrete and masonry

buildings. John Wiley and sons, 1992

COMPUTER AIDED DESIGN (CEE-612/CE612)

L T P

3 1 0

UNIT – I 10

Elements of Computer aided design and its advantages over conventional design. Types of

hardware required for CAD works.

UNIT – II 10

Principles of Software design, Concept of modular programming, debugging and testing.

UNIT – III 10

Computer applications in analysis and design of Civil Engineering Structures.

UNIT – IV 10

Uses of Software packages in the area of Structural Engineering. Expert system, their

development and applications. Introduction to Neural Networks.


References :

1. David.F. Rogers. Mathematical elements for computer graphics, McGraw Hill

1990.

2. David F. Rogers Elements of computer graphics, Mc Graw Hill International

3. Michael E. Mortenson, Geometric modeling, john Wiley and Sons, 1989

Prestressed Concrete (CEE-613/CE613)

L T P

3 1 0

UNIT – I 10

Pre- stressed concrete, basic concept; pre-stressing material and pre-stressing systems; losses

of pre-stress, End anchorage and cable layouts.

UNIT – II 10

Analysis and design of pre-stressed concrete flexure members, simply supported beam and

slabs.

UNIT – III 10

Analysis and design for shear, bond and bearing.

UNIT – IV 10

Analysis and design of pre-stressed concrete continuous beams. Analysis and design of pre-

stressed concrete compression and tension members.

Total Period 40

References :

1. Pandit G.S., Gupta S.P., Prestressed Concrete, CBS Publisher New Delhi

2. Raju Krishna N., Prestressed concrete, Tata McGraw Hill, New Delhi.

study & evaluation scheme...sadhu singh, “theory of elasticity” , khanna publishers, new...

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