The course deals with static and deformation analysis of simple statically indeterminate beam structures. The theory and application of the principle of virtual works for the calculation of displacement of beam systems will be explained. Subsequently, students will learn how to solve plane statically indeterminate continuous beams and folded beam systems using the force method, under both force and deformation loads (effect of temperature change and support buckling).

Lecture outline

1. Introduction, course content. Moving loads. Influence lines of static quantities of statically determinate structures. Static and kinematic methods of solution. Gerber beam.
2. Evaluation of influence lines and determination of extremes. Criteria for deriving maximum moments.
3. Virtual work of external and internal forces. Lagrange's and Castigliano's principle of virtual works. Reciprocity theorems for virtual works. Maxwell-Mohr equation.
4. Determination of displacement and rotation of beams and frames by the unit dummy forces method. Effect of normal and shear internal forces. Vereshchagin's rule. Effect of temperature change and support shifts on displacements.
5. Calculation of displacement of trusses for force loads, temperature changes and support shifts. Assessment of static indeterminacy of structures.
6. Methods of solution of statically indeterminate structures. Description of the force method. Simple statically indeterminate beam, effect of axial load.
7. Open and closed plane frames solved by the force method. Choice of statically indeterminate quantities, canonical equations. Effects of uniform and non-uniform temperature change on the frame. Effect of support settlement.
8. Statically indeterminate plane truss loaded by forces temperature changes and support settlement solved by the force method.
9. Continuous beams, solved by the force method (three moment equation method) for force loads, temperature changes and support shifts.
10. Use of geometric symmetry of the frame, decomposition of the general load, restraints on the symmetry axes. Displacement and rotation of statically indeterminate structures.
11. Influence lines of a statically indeterminate continuous beam. Load distribution for the induction of extreme effects.
12. Solution of statically indeterminate structures with variable cross-sections. Redistribution of internal forces.
13. Curved beams. Planar statically determinate and indeterminate arc.

Tutorial outline:

1. Repetition of internal force calculation on plane statically determinate structures.
2. Moving loads. Application of the kinematic method to a beam with overhanging and a Gerber beam.
3. Determination of reactions and internal forces on statically determinate structures by evaluating the influence lines.
4. Calculation of displacements and rotations by the unit dummy force method on simple beams. Integration and application of Vereshchagin's rule.
5. Calculation of displacement and rotation by the unit dummy force method on more complex structures with more complex type of loading.
6. Effect of temperature change and support settlement on the displacement of beams. Calculation of displacement of trusses.
7. Degree of static indeterminacy. Creation of a basic statically determinate system.
8. Solution of simple statically indeterminate beam systems loaded by force loads.
9. Solution of more complex statically indeterminate beam systems subjected to force and deformation loads.
10. Solution of an internally and externally statically indeterminate truss loaded by force and deformation loads.
11. Solution of statically indeterminate continuous beams subjected to force loads.
12. Solution of statically indeterminate continuous beams subjected to force and deformation loads. Influence lines of support moments of a continuous beam.
13. Completion of the solution of the influence lines of a continuous beam, load distribution.

Learning outcomes

Students will learn to solve plane statically indeterminate beam structures such as continuous beams, frames or trusses using the force method. They will be able to analyze the force and deformation state of structures with constant or variable cross-sections, which are affected by both force loads and changes in temperature and support settlement. They will understand the differences and (dis)advantages in the calculation and implementation of statically determinate and indeterminate structural systems. They will be able to find the positions of moving loads to determine the extreme effects of static quantities on a structure and evaluate these effects.