Theory of Structures II

Syllabus

1. Introduction (4 hours)
   1. Types of indeterminate structures
   2. Boundary conditions and degree of freedoms
   3. Static and kinematic indeterminacy
   4. Structure idealization, local and global coordinate systems, deformations and sign conventions
   5. Determination of degree of static indeterminacy
   6. Degree of kinematic indeterminacy determination
   7. Definitions of force, displacement, flexibility, stiffness and relationships
2. Theorem of Displacements (6 hours)
   1. Force and displacements as cause and effects
   2. Castigliano's theorems and applications
   3. Analyses of beams, frames and trusses
   4. Bending moment, shear force and normal thrust diagrams
3. Force Method (10 hours)
   1. Definitions and specialties; limitations
   2. Consistent deformation systems; compatibility equations; primary structures
   3. Flexibility method applications; support yielding; temperature effects; misfits
   4. Flexibility matrix method
   5. Graph multiplication approach
   6. Three moment theorem and applications
   7. Introduction to focal point method
4. Analysis of Indeterminate Arches (6 hours)
   1. Use in modern constructions
   2. Horizontal reactions for parabolic and circular two-hinged and fixed arches
   3. Bending moment, shear force and normal thrust diagrams
   4. Support yielding, temperature effects, rib shortening
   5. Influence line diagrams for various components
5. Slope Deflection Method (5 hours)
   1. Introduction and sign conventions
   2. Slope deflection equation formulation
   3. Fixed end moments
   4. Applications in beams and frames with support settlements
   5. Bending moment, shear force and normal thrust diagrams
6. Moment Distribution Method (5 hours)
   1. Introduction, terminology and method development
   2. Distribution factors
   3. Carry over moments
   4. Applications: symmetry, anti-symmetry, sway conditions, support yielding
   5. Bending moment, shear force and normal thrust diagrams
7. Stiffness Matrix Method (12 hours)
   1. Stiffness definition; choice of redundant; degree of freedoms
   2. Member stiffness matrices for springs, bars, trusses, beams
   3. Rotation matrices
   4. Multiple spring systems; bar and string combinations; two-dimensional trusses
   5. Applications to beams and frames; support settlement; temperature effects
   6. Three-dimensional truss applications
   7. Bending moment, shear force and normal thrust diagrams
   8. Introduction to structural engineering software
8. Influence Line for Indeterminate Beams (6 hours)
   1. Necessity of influence line diagrams
   2. Muller Breslau principle and applications
   3. Influence line diagrams for reactions, bending moment, shear force
   4. Calculation using concentrated forces, couples, distributed loads
9. Introduction to Plastic Analysis (6 hours)
   1. Definitions and explanations
   2. Plastic analysis of bending members
   3. Plastic hinges and their length
   4. Load factor, shape factor and plastic modulus
   5. Basic limit analysis theorems
   6. Collapse loads and conditions
   7. Collapse with tied loads for beams and portal frames

Practicals

1. Continuous beams (propped cantilever, two-span beams)
2. Two-hinged arch
3. Symmetrical portal frame
4. Unsymmetrical portal
5. Two-dimensional truss analysis (4 or more degree redundancy), flexibility matrix method
6. Two-dimensional truss analysis (4 or more degree redundancy), stiffness matrix method
7. Two-dimensional frame analysis (4 or more degree redundancy), stiffness matrix method with diagrams