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 och VSM090. Optional for: V4at, V4hb, 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 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.