Strength of Materials I (FSI-4PP)

The course-unit credit is granted under the condition of active participation in seminars and passing the seminar tests of basic knowledge (at least 10 ECTS points out of 20 must be gained). The points gained in seminar tests are included in the final course evaluation.
Final examination: Written part of the examination plays a decisive role, where the maximum of 80 ECTS points can be reached. Solution of several computational problems is demanded. The problems come from typical profile areas of given subject and supplied by a theoretical question, proof, etc. The lecturer will specify exact demands like the number and types problems during the semester preceding the examination.
Final evaluation of the course is obtained as the sum of ECTS points gained in seminars and at the examination. To pass the course, at least 50 points must be reached.

Attendance at practical training is obligatory. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge.

Definition of subject contents. Basic terms – deformation, stress, stress state, limit states, safety.
Mechanical properties of material and its computational models. Characteristics of linear elastic body. Definition of linear strength of materials.
Work done by forces, Castigliano's theorem. Saint -Venant's principle. Beam in strength of materials – definition, classification.
Geometrical characteristics of cross-section. Area moments of inertia, transformation with respect to the translated and rotated axes. Principal central area moments of inertia.
Axially loaded bars:
- Deformation, stress state and strain energy.
- Influence of deviations on deformation and stress state, notches and safety check.
- Statically indeterminate beam loaded in tension and compression.
- Truss structures and trusses.
Bars in torsion:
- Deformation, stress state, strain energy and influence of deviations on deformation and stress state.
- Statically indeterminate beam and safety check.
Beams in bending:
- Stress state, deformation, strain energy. Methods of determination of deflection.
- Influence of deviations on stress state and deformation. Shear stress resulting from shear force. Safety check.
- Statically indeterminate beam.
- Shear stress for thin-walled profiles, shear center.
Stability of columns. Influence of deviations on the critical load.
Stability of columns from real material. Eccentric compression.
Stress state in the point of a body, principal stresses.
Representation of stress state using Mohr's circle. Particular cases of stress state, plane stress state.
Criteria for materials of bodies in ductile or brittle state without a priori defects of the crack type at static loading.
Combined loading of beams.
Curved beams and frames. Closed beams (frames). Utilization of symmetry and antimetry.
Beams loaded by temperature. Non-linearity in bending.
Overview of problems solvable by analytical and numerical methods.
Examples of possibilities of contemporary methods of experimental strength of materials.
Eurocodes - Design of steel structures.

Internal forces and moments for straight bar.
Internal forces and moments for curved beam and frame.
Area moments of inertia. Mohr's circle.
Loading in tension, stress state and deformation. Statically determinate tasks.
Loading in tension, stress state and deformation. Statically indeterminate tasks.
Loading in torsion. Statically determinate and indeterminate tasks.
Loading in bending. Stress state and deformation for statically determinate beam.
Loading in bending. Stress state and deformation for statically indeterminate beam.
Stability of columns. Safety for compressive loading of bars from real material.
Calculation of trusses considering the stability of columns. Truss structures.
Combined loading.
Curved beams and frames. Closed beams (frames). Utilization of symmetry and antimetry.

Internal forces and moments for straight bar.
Internal forces and moments for curved beam and frame.
Area moments of inertia. Mohr's circle.
Loading in tension, stress state and deformation. Statically determinate tasks.
Loading in tension, stress state and deformation. Statically indeterminate tasks.
Loading in torsion. Statically determinate and indeterminate tasks.
Loading in bending. Stress state and deformation for statically determinate beam.
Loading in bending. Stress state and deformation for statically indeterminate beam.
Stability of columns. Safety for compressive loading of bars from real material.
Calculation of trusses considering the stability of columns. Truss structures.
Combined loading.
Curved beams and frames. Closed beams (frames). Utilization of symmetry and antimetry.

Janíček P., Ondráček E., Vrbka J., Burša J.: Pružnost a pevnost I,VUT-FSI,Brno,2004

Janíček P., Florian Z.: Úlohy z pružnosti a pevnosti I,2. vyd., VUT-FSI, Brno,1995

GOODNO, B. J a J. M. GERE. Mechanics of materials. Enhanced ninth edition, SI edition. Boston: Cengage, 2021, ISBN 978-0-357-37785-7.

HIBBELER, R. C a K. B. YAP. Mechanics of materials. Harlow: Pearson, 2018. ISBN 978-1-292-17820-2.

Muvdi, B.B., & Elhouar, S. (2016). Mechanics of Materials: With Applications in Excel (1st ed.). CRC Press. Dostupné z: https://doi.org/10.1201/9781315374314

Ross, C., Bird, J., & Little, A. (2021). Mechanics of Solids (3rd ed.). Routledge. Dostupné z: https://doi.org/10.1201/9781003128021