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
SpringerVerlag, 13. Auflage, 2017 (www.springer.com) 
Prerequisites


Teaching language

(X) German ( ) English 
Part of International Profile

( ) Yes (X) No 
Module structure

Type 1a 

For more details please click on this link: T_CL_Modulauspraegungen_SM2025 
Exams

Description 
Type 
Form 
Scope 
Grade 
Weighting 
Graded assignments during teaching semester 
exam 
written 
45 min 
mark 
20% 
Endofsemester 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 endofsemster 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. 