Course content

Principle of virtual work: Virtual work for rigid bodies, plastic hinges, plastic capacity of frames.

Displacement method: Degrees of freedom, stiffness matrix, load vector.

Finite element method: Discretization, bar and beam element, interpolation, stiffness matrix and consistent load vector at element and system level, boundary conditions and reaction forces, storage schemes, equation solving.

2nd order theory: Differential equation for beam with axial force, geometric stiffness, buckling of frames.

Programs and their use, modelling, check of results.

Learning outcome

Mechanics 3 is the first course in solid mechanics at Department of Structural Engineering exposing the students to numerical tools for calculations of structures. The course covers structures made of bars and beams, i.e. trusses and frames, and provides an introduction to basic finite element analysis for static analyses. Through the problem sets the student should gain sufficient insight and knowledge to become a qualified user of typical program tools for these types of analyses.

Mechanics 3 has these learning objectives:

Knowledge: The candidate should be able to explain basic elements in the theory for frame and truss structures, and explain how analytic and numeric methods are used in the analysis of such structures.

Skills: The candidate should be able to perform strength analyzes of frame and truss structures using the finite element method and be able to check the results by analytical considerations, for instance with the displacement method.

General competence: The candidate should be able to explain and critically discuss the use of the finite element method in the analysis of structures.

Digital competence: Skilled use of finite element program for frame and truss structures: Modeling, 1st and 2nd order analysis, interpretation of results. Programming with Python: Matrix operations, finite element method.

Sustainability competence: The course serves to give the students introductory skills to design safe and cost-effective structures. Examples of calculation methods that provide higher utilization of materials are used in exercises (incl a lab exercise). With this, increased understanding of more accurate computational methods is achieved, with the potential to obtain higher utilization of the structures. This will have a direct influence on CO2-reduction as one needs less material to get sufficient capacity.

Learning methods and activities

Lectures, problem solving by means of hand calculations, computer exercises.

Compulsory assignments

• Exercises (hand calculations and PC)

Recommended previous knowledge

The subject requires TKT4122/TKT4123 Mechanics 2 and TMA4110/TMA4115 Calculus 3, or similar knowledge.

Course materials

Kolbein Bell: Matrisestatikk - Statiske beregninger av rammekonstruksjoner, Fagbokforlaget.

Lecture notes.

Credit reductions