t.BA.MT.FL1.19HS (Strength of Materials 1)
Module: Strength of Materials 1
This information was generated on: 27 September 2021
No.
t.BA.MT.FL1.19HS
Title
Strength of Materials 1
Organised by
T IMES
Credits
2

Description

Version: 2.0 start 01 February 2020

Short description

Students are familiarised with the base quantities of the strength of materials and introduced to stress calculations for simple structures subjected to tension/compression/bending. Tensors are introduced as a basic mechanical quantity, taking the example of the stress tensor.

Module coordinator

Ralf Pfrommer (pfro)

Learning objectives (competencies)

 Objectives Competences Taxonomy levels Knows the base quantities of the strength of materials and is able to list the definitions without any aids F, M K4 Is able to calculate the normal stress in rods as well as the deformations of simple rod systems F, M K4 Knows the definition of second order tensors and the difference of a second order tensor to a first order tensor (vector) F, M K4 Is able to compute the stress tensor in a rotated system as well as its eigenvalues and principal directions F, M K4 Is able to transform a biaxial stress state graphically by means of Mohr’s circle F, M K4 Is able to calculate stresses in arbitrary cross sections in the case of uniaxial bending F, M K4 Is able to determine area moments of inertia of arbitrary cross sections and their principal moments and directions F, M K4

Module contents

1.     Base quantities of the strength of materials
1.1    Function and classification of the strength of materials
1.2    Characteristic values of the tensile test
1.3    Base quantities of the strength of materials
1.3.1  Normal and shear stress
1.3.2  Change of length, strain and transversal contraction
1.3.3  Change of angle, shear
1.3.4  Young’s and shear modulus, Poisson’s ratio, thermal expansion coeff.
2.    Tension and compression of rods
2.1    Normal stresses under variable cross sections

2.2    Deformations of rod systems
2.2.1  Statically determined systems
2.2.2  Statically undetermined systems
2.2.3  Condition of compatibility
2.2.3 Examples
3.     Tensors in mechanics*
3.1    States of spatial stress
3.2    Stresses in the tetrahedral element
3.2.1  Stress and normal vector
3.2.2  Cauchy’s formula
3.3    Stress tensor
3.2.1  Stress tensor as a linear map

3.3.2  Tensor transformation under rotation of the coordinate system
3.3.3  Principal directions and eigenvalues
3.3.4  Examples
3.4    Strain tensor
3.4.1  Biaxial strain state

3.4.2  Evaluation of strain gauge measurements
3.5    Mohr's circle
3.5.1  Graphical visualization of the tensor transformation

3.5.2  Special stress states
4.     Stresses caused by bending
4.1    Introduction to calculation of bending stress
4.1.1  Neutral plane, tension and compression zone
4.2    Area moments of inertia
4.2.1  Simple cross sections

4.2.2  Parallel axis theorem
4.2.3  Area moment of inertia tensor
4.2.4  Principal directions and moments
4.3    Symmetrical and asymmetrical bending
4.4    Examples

()* This section is fundamental for all subsequent mechanics and physics classes.

Teaching materials

Blackboard script, own lecture notes, provided material for specific sections

Supplementary literature

Gross, D., Hauger, W., Schröder, J., Wall, W.A.: Technische Mechanik 2, Elastostatik
Springer-Verlag, 13. Auflage, 2017 (www.springer.com)

Teaching language

(X) German ( ) English

( ) Yes (X) No

Type 1a

Exams

 Description Type Form Scope Grade Weighting Graded assignments during teaching semester exam written 45 min mark 20% End-of-semester exam exam written 90 min mark 80%

Remarks

1. This module requires mastery of the matters of the classes Analysis 1 and 2, Algebra and Statistics 1 and 2 as well as Statics.
2.
The lecturers in MFL1 jointly create a end-of-semster exam that is the same for all classes. The lecturers create the midterm exams individually, but coordinate them with each other with respect to the level of difficulty.

Legal basis

The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester a written and communicated supplement can specify the module description in more detail.
Course: Strength of Materials 1 - Vorlesung
No.
t.BA.MT.FL1.19HS.V
Title
Strength of Materials 1 - Vorlesung

Note

• No module description is available in the system for the cut-off date of 01 August 2099.