THEORY OF STRUCTURES I (ENCE 202)

1. Introduction (3 hours)

1.1 Types of structures based on analysis perspective

1.2 Idealization of structures, threats and responses

1.3 Review of determinacy, indeterminacy and stability of plane structures

1.4 Application of determinate systems in civil engineering infrastructures

2. Strain Energy Method (5 hours)

2.1 Work and complementary work

2.2 Strain energy and complementary strain energy

2.3 Strain energy due to axial, shear, bending and torsion

2.4 Deformation of beams and frames by real work method

2.5 Limitations of the real work method

2.6 Strain energy due to gradually and suddenly applied direct load: Dynamic multipliers

3. Virtual Work Method (6 Hours)

3.1 Introduction to virtual work

3.2 Derivation of virtual work equation

3.3 Displacements by the methods of virtual work

3.4 Direct axial, shear, bending and torsion effects

3.5 Deformation of trusses due to external loads, temperature effect and misfits

3.6 Deformation of beams and fames due to external loads and temperature effects

3.7 Deformation of beams and frames due to support settlements

3.8 Betti’s law and Maxwell’s reciprocal theorems

3.9 Application of different effects in beam, frame and truss

4. Deflection of Beams (7 hours)

4.1 Importance of deflection evaluation

4.2 Macaulay’s method

4.3 Moment-area method: Derivation of theorems

4.4 Conjugate-beam method

4.5 Deflections by the method of superposition

4.6 Deflection evaluation of different determinate beams

4.7 Application of deflection

5. Influence Lines for Simple Structures (9 Hours)

5.1 Importance of influence lines

5.2 Concept of moving static loads and influence line diagrams (ILD)

5.3 Influence lines for support reactions and support moments

5.4 Influence lines for shear force and bending moment in beams

5.5 Influence lines for support reactions and member forces in trusses

5.6 ILD for indirect load applications (Panel loadings)

5.7 Qualitative ILD using Muller-Breslau principle

5.8 Use of influence line diagrams

5.8.1 Determination of reactions, bending moments and shear forces (Structural quantity diagram) from ILD due to different loadings: Point load, distributed load, couple, standard load trains

5.8.2 Most critical position of a loading system for maximum internal force/moment at a beam section

5.8.3 Determination of most critical position of a loading system for absolute maximum internal forces

6. Statically Determinate Arches (6 hours)

6.1 Introduction and type of arches

6.2 Three-hinged structures with supports at the same and different levels

6.3 Determination of support reactions, shear forces, normal forces and bending moments

6.4 Analysis of three-hinged arches by the graphical method

6.5 Use of ILD for reactions, bending moments, radial shear forces and normal thrust

7. Suspension Cable Systems (7 hours)

7.1 Introduction and type

7.2 Funicular shape of cable

7.3 Catenary cables and general cable theorem

7.4 General cases of parabolic cables and their analysis

7.5 Elements of a simple suspended and suspension bridges

7.6 Analysis of three-hinged stiffening girder

7.7 Use of influence line diagrams

7.8 Basics of tower structures, wind cables and ties

8. Simple Space Truss (2 hours)

8.1 Introduction and importance of space truss

8.2 Boundary conditions and types of supports

8.3 Analysis of simple space truss by tension coefficient methods

1. Strain energy due to axial, shear, bending, and torsion

2. Deformation of beams and frames by real work method

3. Displacements by the methods of virtual work

4. Deformation of trusses due to external loads, temperature effect and misfits

5. Deformation of beams and fames due to external loads and temperature effects

6. Deformation of beams and frames due to support settlements

7. Deflection of beams by different methods

8. Influence line diagrams for support reactions, shear force and bending moment

9. Influence lines for support reactions and member forces in trusses

10. Determination of reactions, bending moments and shear forces (Structural quantity diagram) from ILD due to different loadings: Point load, distributed load, couple, standard load trains

11. Determination of support reactions, shear forces, normal forces and bending moments of three-hinged arches

12. ILD for reactions, bending moments, radial shear forces and normal thrust of three-hinged arches

13. Analysis of parabolic cables

14. Analysis of three-hinged stiffening girder

15. Analysis of simple space truss by tension coefficient methods

1. Deflection of beams and frames

2. Measurement of reactions in three-hinged arches under different loading arrangements

3. Analysis of plane truss under different loading arrangements

4. Simulation of influence lines for beams, girders and frames under different loading arrangements

5. Experimental analysis of suspension bridges under different loading arrangements

6. Simulation of displacement measurement in statically determinate plane frame

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3. Reddy, C.S. (2017). Basic Structural Analysis. Tata McGraw-Hill Education.

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