Description:

Extreme effects of live load, influence lines. Matrix form of the direct stiffness method and its computer implementation for trusses and frames. Two-dimensional elasticity and its finite element treatment. Governing equations of thin plates and their finite element treatment.

Contents:

1. Course organization; Influence lines: basic principles
2. Influence lines: applications to extreme and moving loads
3. Influence lines: qualitative diagrams, indeterminate structures
4. Matrix form of Direct Stiffness Method (DSM) for truss structures
5. Matrix form of DSM for beam structures
6. Matrix form of DSM for frame structures; Principle of Virtual Work (PVW)
7. Two-dimensional elasticity: Governing equations
8. Two-dimensional elasticity: Rectangular finite element via PVW
10. Bending of thin plates: Governing equations
11. Bending of thin plates: Boundary conditions and PVW
12. Bending of thin plates: Rectangular finite element
13. Information on the final exam; Reserve / Formulation of flat shell element

Seminar contents:

1. Recap on internal force diagrams; Influence lines I
2. Influence lines II
3. Influence lines III
4. Matrix DSM for truss structures: MATLAB implementation
5. Matrix DSM for beam structures: MATLAB implementation
6. Matrix DSM for frame structures: MATLAB implementation,
7. FE method for 2D elasticity: Strategy of MATLAB implementation
8. Mid-term review test
9. FE method for 2D elasticity: MATLAB implementation
10. FE method for thin plates: Strategy of MATLAB implementation
11. FE method for thin plates: MATLAB implementation
12. Reserve / FE method for flat shell elements

Recommended literature:

1. R. C. Hibbeler: Structural Analysis in SI Units, 10th Edition, Pearson, 2019URL
2. P. I. Kattan, MATLAB Guide to Finite Elements An Interactive Approach, Springer, 2003
3- E. O?ate, Structural Analysis with the Finite Element Method. Linear Statics Volume 2: Beams, Plates and Shells, Springer, 2013

Keywords:

live load effects, Direct Stiffness Method, 2D trusses, 2D frames, finite element method, 2D elasticity, thin plates, MATLAB implementation

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar