Course content

Finite element method

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); System analysis: assembly of stiffness- and load matrices; boundary conditions and reaction forces. Programs and their use; modelling and control.

Structural dynamics

The single-degree-of-freedom system. Response of dynamic loads by superposition in time and frequency domain. Time domain integration. Continuous systems, generalised single-degree-of-freedom systems, dynamic respons by modal superposition. Damping mechanisms and models. The equation of motion in a matrix format. Numeric solution to the problem of free oscillations. Direct solution of the equation of motion in time domain. Response calculations for relevant load cases (e.g. wind and earthquake).

Learning outcome

Part 1 of this course involves modeling of trusses and frames through introduction to the finite element method for static loads. Through exercises the students will become qualified users of typical softwares for this type of problems.

Part 2 of this course shall given an introduction to structural dynamics, to sufficient extent provide a basis for simplified earthquake computations.

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 -

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

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

General competence: - Plastic capacity of frames - The displacement method - 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 exercises.

Exercises by means of hand calculation, python and FOCUS/ROBOT (FEM)

Compulsory assignments

• Compulsory assignments

Further on evaluation

Written exam, 4 hours.

Specific conditions