Course syllabus for Strength of materials

Basic course in rigid body mechanics.

The course aims at giving fundamental knowledge of continuum mechanical modeling with application to construction elements such as beams and shafts. It also aims at giving prerequisite knowledge for further studies in material mechanics, structural dynamics, and continuum mechanics.

* describe and discuss constitutive modells, kinematic and equilibrium equations in 3D elasticity theory * given constitutive, kinematic and equilibrium relations, derive the governing differential equations for 3D elasticity * reduce the 3D elasticity problem to 2D, assuming plane deformation or plane stress * identify and formulate the boundary conditions requiered to solve a given elasticity problem * establish kinematic and equilibrium equations for common members, such as bars, axis and beams, and use these to derive the governing differential equations * formulate boundary conditions in elasticity problems that involve bars, axes and beams * calculate stresses and deformations in structures constructed from bars, axes and beams, and determine if the structure will be able to sustain a given load * describe elastic stability and calculate the critical load for a (simple) system of compressed beams (columns) * describe the variational and minimization problems that corresponds to a given elasticity problem; use virtual work and energy methods to solve elasticity problems

We introduce the concepts of strain (deformation), stress and elasticity. The basic relations (i.e. constitutive modells, kinematics and equilibrim) for axially loaded bars, axis (shafts) subjected to a torque, and beam bending are derived. The material is considerd to be fully elastic or elastic-ideally plastic, and thermal loading is regarded. Elastic stability for compressed columns are studied. The governing partial differential equations for 3D elasticity are derived, and it is shown how these (under certain conditions) may be reduced to 2D. Finally we introduce the principle of virtual work (a variational problem) and the principle of minimum potential energy (minimization problem); the theorems Castigliano are derived.

The coure embrace 14 lectures with theoretical derivations, and 14 exercises with problem solutions; each lecture embarce approximately 2 hours. During the course, 5 assignments will be handed out; solutions should be presented in breif written reports, which subsequently are corrected and labeled "pass" or "fail". Each "pass" will grant one extra point to the written examination (subjected to a constraint). For further information, see "Examination" below.

Hans Lundh, Grundläggande hållfasthetslära, KTH, Stocholm, 2000 Peter W Möller, Exempelsamling i hållfasthetslära, Skrift U77b, Institutionen för hållfasthetslära, Chalmers, Göteborg 2010 Formelsamling delas ut vid kursstart.

Written examination with 5 tasks. Maximum score is 25; you need at least 10 to pass (grade 3); 15 and 20 give grades 4 and 5, respectively. Each successfully solved assignment, will grant 1 extra point to the result of the written examination; however, you will need a minimum score of 7 on the written examination, to pass the course.