Single-Course Danish 5 ECTS

# Strength of materials 2

## Overall Course Objectives

To provide the student with the necessary background to analyse and evaluate on the basis of strength and reliability considerations components/constructions such as e.g. pressure vessels, machine components, shrink fits etc. The understanding gained in the course of the 3D stress and strain description is in addition a prerequisite for e.g. to understand and interpret numerical results obtained using the finite element method (FEM).

Learning Objectives

• explain the 3D stress and strain definitions and apply these when formulating the state of stress and strain in a continuum
• apply index notation for Cartesian tensors
• describe the mechanical properties of time independent materials subjected to static, uniaxial tensile load
• determine the state of stress and strain in a loaded (mechanical and/or thermal) continuum using Hooke’s generalized law and strain gauge measures, if any
• explain the conditions for plane stress and plane strain as well as use Hooke’s law for plane stress and plane strain when applicable
• calculate principal stresses and strains and their corresponding principal angles
• determine the state of stress and strain in thick-walled cylinders and plane discs, including use of cylindrical coordinates
• calculate the strain energy in a linear elastic continuum
• apply von Mises’ and Tresca’s yield criteria in order to predict the initiation of plastic yielding and to determine the safety against yielding
• dimension against fatigue failure (“infinite” life), including make a reduced Haigh diagram and calculate a safety factor

Course Content

Cartesian tensors and index notation. 3D stress and strain. Principal values. Strength data of construction materials. Hooke’s generalized law. Plane stress and plane strain. Thick-walled tubes and plane discs. Strain energy. Mechanisms of plastic deformation. Tresca’s and v. Mises’ yield hypotheses. Dimensioning againt fatigue failure, reduced Haigh diagram.

Recommended prerequisites

41501, Basic strength of materials including statics, stresses and deformations in beams and bars.

Teaching Method

1 module, lectures, problem solving.

Faculty

Remarks

The course is a technological specialization course on the BSc in Mechanical Engineering.

See course in the course database.

## Registration

Language Danish 13 weeks DTU Lyngby Campus 41502 Bachelor Week 35 Week 48 Thurs 8-12
Price 7.500,00 DKK