Syllabus 2009/2010 VSM091

Syllabus academic year 2009/2010
(Created 2009-08-11.)

BEAM THEORY

VSM091

Higher education credits: 4,5. Grading scale: TH. Level: G2 (First level). Language of instruction: The course will be given in Swedish. VSM091 overlap following cours/es: VSM090, VSM090, VSM090 och VSM090. Optional for: V4at, V4sa. Course coordinator: Per Johan Gustafsson, per_j.gustafsson@byggmek.lth.se, Byggnadsmekanik. Prerequisites: VSM141 Structural Mechanics and VSM150 Engineering Modelling: Analysis of Structures. The course might be cancelled if the numer of applicants is less than 10. Assessment: The course examination comprises a hand-in task with three sub-tasks and a written examination. Both parts have to be passed. The mark is based on the sum of the points of the two parts. Further information: The course can be cancelled if less than 10 participants. Home page: http://www.byggmek.lth.se.

Aim
The course shall give knowledge about the action of beams and about theories for calculation of stiffness, deformations, stresses and instability of beams loaded in 3D and with a cross-section of arbitrary geometrical shape, including thinn walled cross-sections.

Knowledge and understanding
For a passing grade the student must

be able to give account of different kinds of beams, their mechanical action and performance, and phenomena that limit their servicabilty.
be able to give account of the beam theories of Bernoulli-Euler, Timoshenko, St Venant and Vlasov, and for the basics of analysis instability of beams.
be able to explain the concepts, quantities and constants that are used in advanced beam calculations.

Skills and abilities
For a passing grade the student must

know how to calculate deformations, stresses and instability loads for a straight linear elastic beam with constant cross-section and loaded in 3D by forces, bending moments, torque and secondary moment.
know how to calculate the stiffness matrix for beams of the above kind and how to use this matrix for analysis of structures composed of beams.
know how to calculate the cross-section constants for a cross-section of arbitrary shape.
know how to make account of a beam design or analysis calculation.

Judgement and approach
For a passing grade the student must

be able to assess the way of action and properties of a beam (deformation pattern, stiffness properties, stress distribution and instability phenomena) based on the geometrical shape and loading of the beam.

Contents

A summary of different types of beams, phenomena that limit structural ability and theories for beam analysis.
The Bernoulli-Euler and Timoshenko theories for the response to bending moments, shear forces and normal force.
The St Venants and Vlasov theories for analysis of torsion of beams with thick and thin cross section, respectively.
Matrix formulation of beam stiffness properties for computer based analysis of 3D framework structures.
Second order theory for analysing instability phenomena such as 3D buckling and tilting.

The methods of calculation dealt with include consideration to beams with non-symmetrical, open/closed and thick/thin cross-sections exposed to loading in 3D, including torque and temperature induced deformations.

Literature
1) Map with lecture notes and exercises.
2) Austrell. P.-E. et al., CALFEM - A finite element toolbox, The Division of Structural Mechanics, Lund University, distributed by KFS i Lund AB, 2004, ISBN:91-8855823-1.