Course content

Virtual work. Plastic hinges and collapse mechanisms for frame structures. Plastic capacity of frames. Displacement method: discretization, degrees of freedom, elements and system, stiffness matrix and load vector.

Element analysis: bar and beam element; strong and weak form; assumed displacement shapes (functions); direct and indirect interpolation; element stiffness matrix and consistent load vector (including temperature); shear deformations, transformations, arbitrary cross sections and eccentricities.

System analysis: assembly of stiffness- and load matrices; boundary conditions and reaction forces; storage schemes and equation solving; static condensation and super elements.

2nd order theory: differential equation for beam with axial force, Euler buckling and buckling length; geometric stiffness and solution of eigenvalue problem; buckling of plane frames.

Programs and their use; modelling and control.

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:

- Virtual work, plastic hinges and calculation methods for plastic collapse capacity of frame structures.

- The displacement method, including concepts such as degrees of freedom and stiffness matrix

- Important features related to the finite element method: Element, connectivity matrix, how to establish stiffness relation at structural level, treatment of loading and boundary conditions

- Structure and application of a frame analysis program (e.g. Focus konstruksjon)

- Finite element method based on direct and indirect interpolation

- Geometric non-linearity, including beam with normal (axial) force and buckling

- How to mplementate 2. order theory (geometric stiffness matrix)

- The concept of influence lines.

Skills:

- How to select adequate degrees of freedom and establish stiffness matrix for hand calculations

- Determine the response in a structure by use of the displacement method (matrix structural analysis)

- Development of the stiffness relation for bar and beam elements from equilibrium considerations as well as from the differential equations

- Perform simple 2. order calculations to determine deformations or buckling loads

- Application of influence lines to determine the response in a structure

- Application of a FEM program for frame calculations in a qualified way to analyse static problems.

General competence:

- Plastic capacity of frames

- The displacement method

- The finite element method for bars and beams

- The foundation for numerical calculations of structures

- The difference of 1. and 2. order theory

- Buckling – phenomenology and mathematical treatment.

Learning methods and activities

Lectures and problem solving by means of hand calculations or computer.

Compulsory assignments

• Exercises (hand calculations and PC)

Recommended previous knowledge

The subject requires TKT4122/TKT4123 Mechanics 2 and TMA4110/TMA4115 Calculus 3.

Course materials

Text book: Matrisestatikk, Statiske beregninger av rammekonstruksjoner, Kolbein Bell, Tapir akademiske forlag. Lecture notes.

Credit reductions