Theory of structures is a course for Bachelor’s degree students in Civil Engineering for constituent and affiliated engineering colleges in Nepal under Institute of Engineering(IOE), Tribhuvan University(TU). Its included in third year – first part for BCE and course code of Theory of structures is: CE 601. It has 3 lectures, 3 tutorial and 2/2 practicals.

Further syllabus for BCE can be grabbed from IOE Syllabus for Civil Engineering page.

Course Objectives: The threefold objective for BCE of the course is to:

• Familiarize the terminologies and concepts of displacements, stresses strains, stiffness etc. and their parameters in the context of indeterminate systems,
• Practice in examples the basic concepts and theorems on static (equilibrium), geometrical (compatibility) and physical (Force, stiffness and displacements) conditions in the context of indeterminate Systems,
• Prepare the candidates for advanced courses in structural mechanics by introducing to the necessary tools like matrix method, force method, displacement method, plastic analysis etc.
1. Introduction (8 hours)
1. Formulation of problems in theory of structure: functions of the structural systems and the corresponding requirements/conditions to be fulfilled, strength, stiffness and stability of a system
2. Conditions and equations: static, compatibility, and physical
3. Satisfaction of conditions
4. Boundary conditions, partial restraints
5. Solutions of equations
6. Structure idealization, local and global coordinate systems and static and deformation conventions of signs
7. Indeterminacy of structural systems its physical meanings and its types
8. Degree of static indeterminacy of a system and its determination/ calculation static indeterminacies, use of formula, necessity of visual Checking for plane systems only in the form of truss, frame and arch
9. Degree of kinematic indeterminacy of a system and its determination/ calculation use of formula, necessity of visual checking for plane systems only in the form of truss, frame and arch
10. Definitions and explanations of force and displacement for a structural system as operational parameters in comparison with system” parameters like dimensions of system and elements and their material properties
11. Force and displacements as cause and effect; Betti’s law and Maxwell’s reciprocal theorem, their uses and the limitations
12. Two theorems from Castigliano and their application: use of second theorem for determination of displacements in statically determinate and solution of statically indeterminate simple systems like bean truss
13. Flexibility and stiffness
14. Flexibility matrix
15. Stiffness matrices
16. Relation between Flexibility and stiffness matrices
17. Force and displacement methods
2.  Force Method (12 hours)
1. Definitions and explanations; specialties of force method and limitations
2. Primary systems with replacements of static determinacies choice of unknowns for force quantities and its limitations, primary system With unit forces for static indeterminacies, unit force diagrams
3. Compatibility conditions and formulation of equations in matrix system specific matrix and its dependency upon choice of unknown.
4. Flexibility matrix generations and calculations
5. Use of graphical method for calculation of coefficients (elemens flexibility matrix), derivation of formula for the standard case of parabo, and straight line, its extension to the case when both are straightline
6. Applications to beams and frames; three moment theorem, effects, temperature variance and settlement of supports in beams and same determination of redundant reactions or member forces in a beam (two to three spans) and frames (one storey two bay or two store of bay), consideration of settlement of support, variance in internal and external temperature for beams (up to two spans) and famo” only) involving not more than four unknowns.
7. Applications of trusses; effects of temperature variance and misfits
8. Applications to arches (parabolic and circular), simple cases of two hinged and hingeless arches, cases of yielding of support and temperature effects, influence line diagrams for two hinged arches
3. Displacement Methods (15 hours)
1. Definition and explanations, specialiteies of displacement methods and its limitation.
2. Primary system: kinematic indeterminancy and unit displacement system, unit displacement diagrams and their applications
3. Choice of unknowns and its uniqueness in comparision with force method
4. Equilibrium conditions and formulation of equations in matrix form
5. Stiffness matrix its formation, properties and application as system specific
6. Applications to beams and frames, effects of settlement of support and temperature
7. Application of trusses, effect of temperature change
8. Bending moment, shear force and normal thrust diagrams for the systems
9. Fixed end moment, slope and deflection and their uses in beam systems
10. Equilibrium conditions of the joints in beams and frames
11. Slope deflection equations and their application in beam systems
12. Stiffness of a member in a rigid joint
13. Boundary conditions
14. Distribution of unbalanced moment in a rigid joint
15. Principle of moment distribution with consideration stiffness, member stiffness (consideration of length) and bourdary conditions
16. Application of moment distribution method to solve beams frames(simple cases with one bay and two storeys or two bays and one storey)
17. Consideration of sway conditions(simple cases with one bay and two storeys or two bays and one storey)
4. Influence Line(IL) or Continuous Beams (4 hours)
1. Definitions and explanations: given section, structural quantity (support reaction, bending moment or shear force etc.) and the given structural system as the three basic elements of definition of IL, IL diagrams as system specific diagrams – independent of operational parameters like loads
2. Neutral points (focus) in an unloaded beam span of a continuous beam as fixed points with respect to load on left or right of the span, left of right focal point ratios and recurrent formula for their determination, focal point ratios for the extreme spans
3. Use of three moment equations and focal point ratios to determine support moments in a continuous beam
4. Numerical method for drawing IL diagram of support moments using focal point ratios
5. Use of Il of support moments to draw IL for other structural quantities like support reactions, bending moment and shear force in the given Section
6. Mueller Breslau principle its physical meaning and its use
7. IL diagrams for reaction, bending moment and shear force in Various sections of continuous beams (two to three spans only)
8. Loading of the IL diagrams, determination of reaction * and shear force at a section of a continuous beam forgiy form of a concentrated force, couple and distributed load
5. Introduction of Plastic Analysis (6 hours)
1. Definition and explanations
2. Plastic analysis of bending members
3. Plastic bending
4. Plastic hinge and its length
5. Load factor and shape factor
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