# 309.021 Mechanics of solid bodies, exercises 1 This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});});

2020S, UE, 2.0h, 2.0EC

## Properties

• Semester hours: 2.0
• Credits: 2.0
• Type: UE Exercise

## Learning outcomes

After successful completion of the course, students are able to:

• identify given forces like those of springs, gliding friction, gravity, and also (other) distributed forces, and to formulate them mathematically for the solution of equilibrium problems;
• apply the conditions of equilibrium both graphically and arithmetically to find the constraining forces in a statically determined system;
• determine the stress resultants in beam-like structures as functions of a characteristic coordinate and to represent them graphically;
• determine in adhesion problems the limits of equilibrium with respect both to the onset of sliding and to tilting graphically as well as arithmetically and to find the necessary minimum coefficient of adhesion for equilibrium; moreover, to check systems for self-locking behaviour; furthermore, to find the forces in systems where bodies move with sliding friction (and constant velocity) both graphically and arithmetically;
• determine the forces in (statically determined) trusses both graphically and arithmetically;
• determine the center of gravity of bodies and plane areas by integration, Guldin's rule, and appropriate combination of sub-bodies/areas with already determined centers of gravity;
• determine the moments of inertia and products of inertia both for bodies and plane areas by integration and application of Steiner's law;
• explicate the basics of linear elasticity theory and to apply Hooke's law;
• find the stresses and displacements in straight Euler-Bernoulli bars caused by tension/compression, bending, and torsion both for statically determined and undetermined systems; to this aim, to apply the principle of superposition and Mohr's method, too;
• explicate the effects of shear forces in straight bars;
• explicate the basics of the statics of ropes and chains under the influence of gravity

## Subject of course

In the exercise units, particular exercise examples are solved. The subject of each example is tailored to the topic of the respective lecture. Essential parts of each solution procedure are (i) finding adequate physical approaches, (ii) their accurate mathematical formulation and computation, (iii) the physical interpretation of the mathematical solutions, and (iv) the critical analysis of the obtained results.

## Teaching methods

Exercise

The students are encouraged to autonomously approach solutions for the exercise examples. Students are thereby guided and supported by the lecturer. In addition, tutors are in attendance to individually answer emerging questions. Conclusively, the lecturer presents a feasible solution for each example, refers briefly to the respective theoretical basis and remarks alternative solution strategies.

## Mode of examination

Immanent

Two type of groups are available to attend the course:

# 1) Small Groups (K01-K17):

• The groups are held by tutors.
• Teamwork and discussions by the participants is explicitly intended.
• One Group will be held in English (for details see group-registration).

# 2) Large Group (G)

• A lecturer introduces the examples, highlights essential steps of the solution procedure and responds to questions from the participants.
• The presentation of the lecturer are more detailed than in the small groups, yet less time for autonomous approaches and questions from the participants will be available.
• In case of exceeding numbers of participants, a second large group will be organised.

Attendance is mandatory in each group (refer to section "Examination modalities").

To participate in the exercise it is required to register to a group.
The registration process is exclusively organised via TISS and implies two stages:

First stage: Pre-registrations by the students
To acquire a seat in a small group, register to the respective pre-registration groups according to your schedule. You can also register in several pre-registration groups.
To acquire a seat in a large group, register directly to the respective group.

Second stage: Determination by the course management
In case that there are more pre-registration than seats for a small group, the seats will be drawn by lot. The seats are preferably given to students who attend the exercise for the first time. All those, who don't receive a seat in a small group, are registered to the large group.

Due to administrative reasons, it is not possible to switch groups past the pre-registration stage.

The further course is organised via TUWEL.
For general questions to the course, please consult the FAQs in TUWEL. If this does not answer your question, please use the forum in TUWEL. You are welcome to use this forum for technical discussion as well!
Please address individual questions w.r.t. the organisation of the course exclusively to mechanik1UE@tuwien.ac.at.
Individual technical questions can be discussed in the tutorial sessions, which can be booked in the TUWEL course.

On Monday, 9.3.2020, a collective demonstration unit will be held from 17:00 to 19:00 at the Audimax. Basics from vector analysis (chapter 2 of the script) will be repeated and a demonstration example will be discussed.
Attendance is not mandatory for this unit.

## Course dates

DayTimeDateLocationDescription
Fri14:00 - 16:0006.03.2020GM 1 Audi. Max.- ARCH-INF Preliminary talk - Organizational Issues
Mon17:00 - 19:0009.03.2020GM 1 Audi. Max.- ARCH-INF Collective Demonstration Exercise

## Examination modalities

The assessment consists of three elements.

# 1. Attendance

For a positive degree for the course, the attendance and active participation in at least 8 exercise units is required.
This holds for all exercise units for the large and small groups at the corresponding dates (the "Collective Demonstration Exercise" and the "Preliminary talk - Organizational Issues" at the begining of the semester as well as the test are excepted therefrom)

# 2. Peer-Review

During the semester, four example problems are to be solved as a homework and to be submitted via TUWEL. In addition, submissions of other participant are to be examined and evaluated. These problems are comparable w.r.t scope and difficulty to those of the final test, and similar criteria are to be used for the evaluation. More details on the Peer-Review procedure are found in the TUWEL section of the course.

For a positive assessment of the element "Peer-Review", three of four solutions and reviews have to be submitted. Incomplete or inconclusive submissions are not accepted.

No certificate for the course will be issued if you de-register from the course prior to the first Peer-Review.

# 3. Final Test

A positive assessment for the Peer-Review element is required to participate at the final test. The test covers the entire subject of the exercises and determines the grading for the course.

For a positive assessment of the test, the following items have to be documented on the test's sheet:

1. All necessary physical/mathematical approaches and relevant sketches to comprehend the chosen solution strategy.
2. The essential steps of the solution process.
3. The final result, as an expression of the given quantities.

## Group dates

GroupDayTimeDateLocationDescription
G1Mon17:00 - 19:0009.03.2020GM 1 Audi. Max.- ARCH-INF 309.021 Mechanics of solid bodies, exercises 1 G1
G2Tue12:00 - 14:0010.03.2020FH Hörsaal 1 - MWB 309.021 Mechanics of solid bodies, exercises 1 G2
Tutorensprechstunden Mittwoch (keine Anmeldung erforderlich)Wed08:00 - 09:0004.03.2020 - 11.03.2020Seminarraum BA 05 Tutorensprechstunden Mittwoch (keine Anmeldung erforderlich)
Tutorensprechstunden Montag (keine Anmeldung erforderlich)Mon15:00 - 16:0002.03.2020 - 09.03.2020Seminarraum BA 05 Tutorensprechstunden Montag (keine Anmeldung erforderlich)

## Course registration

Use Group Registration to register.

### Precondition

The student has to be enrolled for at least one of the studies listed below

## Group Registration

GroupRegistration FromTo
> Voranmeldung K01-K03 MO 13:00-15:0002.03.2020 08:0009.03.2020 08:00
> Voranmeldung K04-K05 MO 17:00-19:0002.03.2020 08:0009.03.2020 08:00
> Voranmeldung K06 (Englisch) MO 17:00-19:0002.03.2020 08:0009.03.2020 08:00
> Voranmeldung K07 DI 12:00-14:0002.03.2020 08:0009.03.2020 08:00
> Voranmeldung K08-K09 MI 13:00-15:0002.03.2020 08:0009.03.2020 08:00
> Voranmeldung K10 MI 14:00-16:0002.03.2020 08:0009.03.2020 08:00
> Voranmeldung K11-K12 MI 15:00-17:0002.03.2020 08:0009.03.2020 08:00
> Voranmeldung K13 MI 17:00-19:0002.03.2020 08:0009.03.2020 08:00
> Voranmeldung K14-K17 FR 12:00-14:0002.03.2020 08:0009.03.2020 08:00
G102.03.2020 08:0029.03.2020 18:00
G209.03.2020 18:0029.03.2020 18:00
K0109.03.2020 18:0012.03.2020 12:00
K0209.03.2020 18:0012.03.2020 12:00
K0309.03.2020 18:0012.03.2020 12:00
K0409.03.2020 18:0012.03.2020 12:00
K0509.03.2020 18:0012.03.2020 12:00
K06 (Englisch)09.03.2020 18:0012.03.2020 12:00
K0709.03.2020 18:0012.03.2020 12:00
K0809.03.2020 18:0012.03.2020 12:00
K0909.03.2020 18:0012.03.2020 12:00
K1009.03.2020 18:0012.03.2020 12:00
K1109.03.2020 18:0012.03.2020 12:00
K1209.03.2020 18:0012.03.2020 12:00
K1309.03.2020 18:0012.03.2020 12:00
K1409.03.2020 18:0012.03.2020 12:00
K1509.03.2020 18:0012.03.2020 12:00
K1609.03.2020 18:0012.03.2020 12:00
K1709.03.2020 18:0012.03.2020 12:00
Tutorensprechstunden Mittwoch (keine Anmeldung erforderlich)30.01.2020 00:0030.01.2020 00:01
Tutorensprechstunden Montag (keine Anmeldung erforderlich)30.01.2020 00:0030.01.2020 00:01

## Curricula

Study CodeSemesterPrecon.Info
033 245 Mechanical Engineering 2. Semester
Course belongs to the introductory and orientation phase ("Studieneingangs- und Orientierungsphase")
033 282 Mechanical Engineering - Management 2. Semester
Course belongs to the introductory and orientation phase ("Studieneingangs- und Orientierungsphase")
700 Mechanical Engineering 1. Semester
740 Industrial Engineering-Management 1. Semester

## Literature

Gamer, U., Mack, W.:
Mechanik – Ein einführendes Lehrbuch für Studierende der technischen Wissenschaften. Springer Verlag Wien, 1999. ISBN: 3-211-82854-0.
Mack, W. , Lugner, P. , Plöchl, M.:
Angewandte Mechanik – Aufgaben und Lösungen aus Statik und Festigkeitslehre, Springer Verlag Wien, 2006. ISBN 3-211-25672-5

## Previous knowledge

Basics in trigonometry, calculus aund vector algebra.

German