Equability conditions of 2D and 3D systems of forces
Equilibrium conditions for a solid body and a system of solid bodies
Equivalent transformation rules for systems of forces
How to take into account the laws of sliding friction and rolling friction
Ways to define centers of gravity of bodies
Are you interested in improving your mechanics or introducing yourself to the subject all together? Join our unique course, devised by the Ural Federal University. Through our innovative approach, you will receive the basic traditional material by engaging in practically-oriented tasks and learn the strictly theoretical mathematical analysis of basic concepts. You will be introduced to mathematical modelling of engineering designs, standard machines, and mechanisms using 2D and 3D diagrams. The course begins with statics, which is the science of forces.
By the end of the course you will be able to:
write down equilibrium conditions of structural elements and units of machines and mechanisms.
perform the substitution of one system of forces that acts upon the structural elements and components of mechanisms with another equivalent one.
create 2D and 3D diagrams of equilibrium in the standard engineering objects.
choose appropriate mathematical models for calculating geometric parameters and force loads in the problems related to equilibrium of the engineering structures.
apply combinations of mathematical operations according to the obtained mathematical models, when creating and solving equations describing equilibrium of the engineering structures.
The weekly course includes video lectures on theoretical concepts, video demonstrations of the solutions of practical problems, tasks for students’ training, individual task, interim and final tests.
Week 1: Basic Concepts of Statics
1.1. Mechanical system, force, system of forces
1.2. Properties of the simplest systems of forces
1.3. Constraints and their reactions
1.4. Moment of force
1.5. Moment of couple. Properties of couples. Week 2. Free Body Diagrams (FBD)
2.1. Free body diagrams (FBD) Week 3. Basic Theorem of Statics
3.1. Concurrent force system
3.2. Resultant vector and resultant moment of system of forces
3.3. Reduction of system of forces to the center Week 4. Equilibrium of a Solid Body Acted upon by a Coplanar Force System
4.1. Equability of a coplanar force system
4.2. Forms of equations for a solid body acted upon by a coplanar force system Week 5. Equilibrium of a Solid Body Acted upon by a Spatial Force System
5.1. Equability of a spatial force system
5.2. Forms of equations for a solid body acted upon by a spatial force system Week 6. Trusses (Frame Structures)
6.1. Trusses (frame structures)
6.2. Analysis of plane trusses with a method of joint isolation
6.3. Analysis of plane trusses with a method of sections Week 7. Friction
7.1. Equilibrium in the presence of sliding friction. (Amontons’ and Coulomb’s laws)
7.2. Equilibrium in the presence of forces of rolling friction Week 8. Center of Gravity
8.1. Center of parallel forces
8.2. Solid body center of gravity
8.3. Ways of finding a center of gravity
Learners should know secondary school mathematics, as well as the “Mechanics” section from Physics. They should have a developed spatial awareness and be able to use a scientific calculator.