Theory of Structures I

Syllabus

1. Introduction (3 hours)
   1. Types of structures based on analysis perspective
   2. Idealization of structures, threats and responses
   3. Review of determinacy, indeterminacy and stability of plane structures
   4. Application of determinate systems in civil engineering infrastructures
2. Strain Energy Method (5 hours)
   1. Work and complementary work
   2. Strain energy and complementary strain energy
   3. Strain energy due to axial, shear, bending and torsion
   4. Deformation of beams and frames by real work method
   5. Limitations of the real work method
   6. Strain energy due to gradually and suddenly applied direct load: Dynamic multipliers
3. Virtual Work Method (6 hours)
   1. Introduction to virtual work
   2. Derivation of virtual work equation
   3. Displacements by the methods of virtual work
   4. Direct axial, shear, bending and torsion effects
   5. Deformation of trusses due to external loads, temperature effect and misfits
   6. Deformation of beams and frames due to external loads and temperature effects
   7. Deformation of beams and frames due to support settlements
   8. Betti's law and Maxwell's reciprocal theorems
   9. Application of different effects in beam, frame and truss
4. Deflection of Beams (7 hours)
   1. Importance of deflection evaluation
   2. Macaulay's method
   3. Moment-area method: Derivation of theorems
   4. Conjugate-beam method
   5. Deflections by the method of superposition
   6. Deflection evaluation of different determinate beams
   7. Application of deflection
5. Influence Lines for Simple Structures (9 hours)
   1. Importance of influence lines
   2. Concept of moving static loads and influence line diagrams (ILD)
   3. Influence lines for support reactions and support moments
   4. Influence lines for shear force and bending moment in beams
   5. Influence lines for support reactions and member forces in trusses
   6. ILD for indirect load applications (Panel loadings)
   7. Qualitative ILD using Muller-Breslau principle
   8. Use of influence line diagrams including determination of reactions, bending moments and shear forces from ILD due to different loadings, critical positioning of loading systems, and absolute maximum internal forces
6. Statically Determinate Arches (6 hours)
   1. Introduction and type of arches
   2. Three-hinged structures with supports at the same and different levels
   3. Determination of support reactions, shear forces, normal forces and bending moments
   4. Analysis of three-hinged arches by the graphical method
   5. Use of ILD for reactions, bending moments, radial shear forces and normal thrust
7. Suspension Cable Systems (7 hours)
   1. Introduction and type
   2. Funicular shape of cable
   3. Catenary cables and general cable theorem
   4. General cases of parabolic cables and their analysis
   5. Elements of a simple suspended and suspension bridges
   6. Analysis of three-hinged stiffening girder
   7. Use of influence line diagrams
   8. Basics of tower structures, wind cables and ties
8. Simple Space Truss (2 hours)
   1. Introduction and importance of space truss
   2. Boundary conditions and types of supports
   3. Analysis of simple space truss by tension coefficient methods

Practicals

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. Experimental analysis of suspension bridges under different loading arrangements
5. Simulation of influence lines for beams, girders and frames under different loading arrangements
6. Simulation of displacement measurement in statically determinate plane frame