Statics (FSI-3ST-A)

Introduction to solid mechanics and Statics, its relation to other courses of solid mechanics. Model and theoretical aspects of engineering mechanics, specification of basic terms and general principles. Introduction to and discussion of the elements of Statics - force, moment of force about a point, moment of force about an axis. Classification of force systems and their resultants. Equivalent force systems. Replacement of a force system by a force and a couple, replacement of a force system by a single force. Conditions for rigid-body equilibrium. Basic tasks of Statics. Centre of gravity and methods of its evaluation. Body supports and connections, their computational models, kinematic pairs. Degrees of freedom of a single body, constraints, concept of a free-body diagram. Statically determinate and indeterminate problems. Algorithm of static equilibrium solution of a body and its application to the analysis and solution of statically determinate systems, mechanisms and trusses. Basic graphical constructions. Passive resistances - their analysis and computational models, dry friction and rolling resistance. Free-body diagrams in actual states of motion. Application to engineering problems including friction forces and rolling resistances. Integral and differential approach to calculation of the resulting internal forces and moments in straight rods.

1. Definition of mechanics, basic concepts, force, moment of force about a point, moment of force about an axis.
2. Force systems, their classification and characteristic features, gravity, center of gravity.
3. Equivalent force systems.
4. Static equilibrium of a rigid body - characteristics of bonds without passive effect, basic models of body connections.
5. Numerical solutions of the static equilibrium of a bound body.
6. Graphical solutions of the static equilibrium of a bound body.
7. Solving the static equilibrium of systems of bodies – numerically and graphically.
8. Trusses structures.
9. Bonds with a passive effect - analysis and calculation models, basic models of body connections.
10. Solution of the static equilibrium of a bound body with bonds with a passive effect.
11. Solving the static balance of a system of bodies with a passive effect.
12. Bar – definition and basic characteristics, loading and bonds.
13. Internal resultant forces and moments in straight bars - an integral and differential approach.

Force, moment of force about a point and about an axis.

Force and moment resultants of force system.

Replacement of a force system by an equivalent force.

Centre of gravity determination.

Static equilibrium of a bound body.

Static equilibrium of a bound body.

Static equilibrium of movable body.

Computational solutions of equilibrium of rigid body system.

Graphical solutions of equilibrium of rigid body system.

Computational and graphical solution of trusses structures.

Static equilibrium of movable body with passive resistances.

Static equilibrium of movable body system with passive resistances.

Internal resultant forces and moments in straight bars - an integral and differential approach.

Force, moment of force about a point and about an axis.

Force and moment resultants of force system.

Replacement of a force system by an equivalent force.

Centre of gravity determination.

Static equilibrium of a bound body.

Static equilibrium of a bound body.

Static equilibrium of movable body.

Computational solutions of equilibrium of rigid body system.

Graphical solutions of equilibrium of rigid body system.

Computational and graphical solution of trusses structures.

Static equilibrium of movable body with passive resistances.

Static equilibrium of movable body system with passive resistances.

Internal resultant forces and moments in straight bars - an integral and differential approach.

Islam, M. R., Al Faruque, M. A., Zoghi, B. & Kalevela, S. A. Engineering Statics (1st ed.). CRC Press, 2020 https://doi.org/10.1201/9781003098157

Budynas, R. G. a Nisbett, J. K. Shigleyho konstruování strojních součástí. 2. vyd. Editor Martin Hartl, Miloš Vlk, VUTIUM, 2023