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Solid Mechanics

Faculty of Engineering, LTH

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Hållfasthetslära AK I

Credits: 7.5. Compulsory for: M2 and M140p. Responsible teacher: Håkan Hallberg.
Prerequisites: Engineering Mechanics, Basic Course M, and Mathematics, Basic Course.
Teaching: Lectures 42 h, exercises 14 h, laboratory-work 2 h. Individual study: 140 h.
Assessment: A written examination, one compulsory hand-in assignment and one compulsory laboratory assignment. Study period: VT1

Course Information

A detailed course programme for the course given during study spring period 1 can be downloaded in PDF format here. Note that all supplementary material is in Swedish and is provided in PDF format, i.e. Acrobat Reader (or equivalent) has to be installed on your computer.

Aims of the course

The course aims at providing the basic introduction in the concepts and principles which are prerequisites for Basic Course M, part II. After finishing the course one should be able to:

  • use the concepts normal and shear force, bending and twisting moment, as well as account for and use the concepts normal and shear stress, normal and shear strain.
  • select a relevant constitutive model based on results from material tests and the problem at hand.
  • structure and solve statically indeterminate problems
  • account for the stress distributions which arise in applications of technical beam theory, and explain how they arise from assumed strain distributions at different constitutive relations.
  • calculate sufficient dimensions of beams, rods and struts with respect to criteria like plasticity, allowed deformations and stability.
  • account for the instability phenomena which arise in beam buckling.

Topics of the course

The course covers uniaxial stress and strain analysis with application to calculation of sufficient dimensions with respect to allowable stress and deformation in beams loaded in compression, elongation and bending, as well as rods loaded in twisting.

The basic concepts normal and shear stress and strain are defined. Based on measurents from uniaxial tensile test specimens, idealized material models exhibiting elastic, plastic and viscoelastic behavior are formulated. The difference between statically determinate and indeterminate problems is discussed with respect to methods of solution, and the need for conditions of deformation is recognized.

Elementary stability theory for axially loaded struts is discussed and dimensioning using the Euler elementary cases is introduced.

Literature

C. Ljung, N.S. Ottosen och M. Ristinmaa: Introduktion till Hållfasthetslära, Enaxliga tillstånd, Studentlitteratur, 2007
Handbok och formelsamling i Hållfasthetslära, KTH.

Assessment

To qualify for a final grade in Basic Course M, students must have completed the compulsory assignment and the laboratory-work. They must also have passed the written examination of Basic Course M, part I. The final grade is the average of the grades obtained in the Basic Courses part I and II.

Pass grades for Basic Course, part I are given on the scale 3.0(0.2)6.0 on the basis of the two written examination. In the examination the ability to solve a problem as well as the understanding of the subject is judged.

Assignment

The assignment, with complete instructions, can be downloaded here. Your answers will depend on which day of the month you are born, and can be found here.

Note that deadline for handing in the assignment is on Friday 3/3.

Previous examinations with solutions

Can be found here or in the menu to the left.

Compulsory laboratory work

Schedules for the laboratory work will be announced in the first or second week. The instructions for the laboratory tasks can be downloaded as a pdf file here.

Particulars

The course is given by the division of Solid Mechanics. Questions can be addressed to the teachers in connection with lectures, seminars or exercises, or at the offices of the division.

Errata

Uppgift 4.25 a) Den vertikala kraften i stöd A skall vara positiv P/2 (den är negativ i facit). Den horisontella är rätt. Den vertikala kraften i B skall vara negativ, dvs -3P/2.
Uppgift 6.4 e) : Lösningen på s 245 skall vara omvänd, dvs ε_2 = -σ_s/E och ε_3 = -3σ_s/E

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