t.BA.MT.FL2.19HS (Strength of Materials 1)
Module: Strength of Materials 1
This information was generated on: 16 September 2021
No.
t.BA.MT.FL2.19HS
Title
Strength of Materials 1
Organised by
T IMES
Credits
2

### Description

Version: 2.0 start 01 February 2020

#### Short description

Students learn to calculate the deflection curve of statically determined and statically undetermined single span and multi field beams, together with stresses and deformations resulting from torsional loading. Students are introduced to the concepts of equivalent stresses and energy methods.

#### Module coordinator

Ralf Pfrommer (pfro)

#### Learning objectives (competencies)

 Objectives Competences Taxonomy levels Can write down and integrate the differen-tial equation of the deflection curve and can explain the quantities without any aids F, M K4 Can define the deflection curve of statically determined beams under different support and loading conditions F, M K4 Can define the deflection curve of statically undetermined beams under different support and loading conditions F, M K4 Can superimpose deflection curves in order to calculate support reaction forces of statically undetermined beams F, M K4 Is able to calculate deformation and stress of circular shafts and thin walled profiles under torsional loading F, M K4 Is able to calculate the equivalent stress due to von Mises for different stress combinations and explain the use of equivalent stress F, M K4 Can define deformation energy and calculate deformations using Castigliano’s theorem F, M K4

#### Module contents

1.    Deformations due to bending load
1.1    Differential equation of the deflection curve
1.2    Solution of the differential equation of the deflection curve for statically determined beams
1.2.1  Kinematic boundary and transition conditions
1.2.2  Deflection curves of single span beams under point and section loads
1.2.3  Deflection curves of multi-field beams under point and section loads
1.3    Solution of the differential equation of the deflection curve for statically undetermined beams
1.3.1  Section load as the fourth derivative of the deflection curve
1.3.2  Dynamic boundary conditions
1.3.3  Deflection curve of single span beams under point and section loads
1.4    Superimposition and combination of deflection curves
1.4.1  Deformations of frames
1.4.2  Determination of support reactions of  statically undetermined beam systems
2.1    Basics
2.2    Torsion of cylindrical shafts
2.2.1  Polar moment of inertia
2.2.2  Torsional stress and its distribution
2.2.3   Angle of twist
2.3   Torsion in thin walled closed profiles
2.3.1  Shear flow
2.3.2  Bredt’s first and second formula
2.3.3  Stresses and twisting angles
2.3.4  Examples
2.4    Torsion dünnwandiger offener Profile
2.4.1  Stresses and twisting angles
2.4.2  Examples
3.1    Fundamentals of equivalent stress
3.1.1  Von Mises equivalent stress
3.1.2  Maximum principal stress as equivalent stress
3.2    Shear stress
3.2.1  Shear stress distribution in a rectangular cross section
3.2.2  Glued and riveted beams
3.3.1  Practical examples
4.   Introduction to energy methods
4.1   Deformation work and deformation energy
4.1.1 Deformation energy in push/pull rods
4.1.2 Deformation energy in bending beams
4.1.3 Calculation of deformations based on the deformation energy
4.2   Castigliano’s theorem
4.2.1 Examples of deformation calculations
4.3   The curved beam
4.3.1 Examples of deformation calculations

#### 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 exa, 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 and strength of materials 1.
2.
The lecturers in MFL2 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.FL2.19HS.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.