Aim
Analysis of bars, beams, trusses and frames belongs to the most common computing tasks for a structural engineer. The aim of the course is to give knowledge of how to define physically correct models and to use them for solving engineering problems. The generality of the element based analysis method is emphasized by the fact that also one-dimensional scalar problems such as thermal conduction, diffusion and groundwater flow are treated.

Knowledge and understanding
For a passing grade the student must

• be able to theoretically model bars, beams, trusses, frames and one-dimensional scalar problems such as thermal conduction, diffusion and groundwater flow.

Skills and abilities
For a passing grade the student must

• be able to use element based displacement method to analyse trusses, frames and one-dimensional scalar problems.

• be able to choose suitable models for analysing structures, including dividing the structure into elements, defining degrees of freedom, and defining support conditions and loads.

• be able to perform computer based analysis of the structures in question.

• be able to present a clear written description of basic conditions, model for analysing the structure, and results from computations performed by hand and using computer, for different applications.

Judgement and approach
For a passing grade the student must

• be able to assess if the obtained results are in accordance with the assumed conditions and the defined computational model.

Contents
Matrix algebra. Introduction to discrete systems. Bar and beam elements. Element-based analysis of trusses and frames. Aspects of modelling; symmetry, hinges in frames, subsidiary conditions, static condensation, reduced systems of equations. One-dimensional scalar problems; thermal conduction, diffusion, groundwater flow, pipe network and electrical circuit. Beams and supports on elastic foundation. Frames and trusses considering geometric nonlinearity and instability. Frames and trusses considering material nonlinearity.

Literature
Dahlblom O, Olsson K.-G. och Persson K.: Bärverk - modellering och analys, Byggnadsmekanik, Lunds tekniska högskola 2006. CALFEM ver 3.4 - A finite element toolbox, KFS i Lund AB, 2004.