Course Details

Structural Mechanics 1

Academic Year 2023/24

BDA015 course is part of 1 study plan

​ BPC-APS Winter Semester 1st year

The course is focused on the interpretation of basic concepts of structural mechanics and elasticity of beam structures. Topics: introduction to structural mechanics. Coplanar and non-coplanar force systems. Structural form and idealisation, loading, supports and reactions. Types of internal forces, differential equilibrium relationship, internal forces diagrams. Statically determinate plane beams – simply supported, cantilever, inclined, bent and curved beams. Frame structures with internal pins and trusses. Statically determinate beams with 3D loads and bent beams in 3D. Geometric properties of cross-sections. Basic concepts and assumptions of the linear elasticity and strength theory. Stress, displacement, deformation. Simple stresses in Civil Engineering – tension, compression, shear, bending, and torsional stress. Stability and elastic buckling of axially loaded compression members. Combined bending and direct stress.

Credits

3 credits

Language of instruction

Czech

Semester

winter

Course Guarantor

doc. Ing. Hana Šimonová, Ph.D.

Institute

Institute of Structural Mechanics

Forms and criteria of assessment

course-unit credit and examination

Entry Knowledge

Basic knowledge of mathematics and physics from secondary school is required.

Aims

Students will be acquainted with reactions and internal forces of statically determinate plane beams and frames, and geometric properties of cross-sections (centroid, second moments of area). They also will be acquainted with basic concepts and assumptions of the linear elasticity and strength theory, such as stress, displacement, and deformations and looked into dimensioning of structures.


The students will be able to solve reactions and internal forces of the plane statically determinate structures, to design centroid and second order moments of gross-section, solve simple and compound stresses to and compute strain in a section, to find materials and dimensions, to calculate deformation within bend.

Basic Literature

Kadlčák, J., Kytýr, J. Statika stavebních konstrukcí I. Základy stavební mechaniky. Staticky určité prutové konstrukce. Učebnice. Nakladatelství VUTIUM v Brně, 2001, 2010. (cs)
Šmiřák, S. Pružnost a plasticita I pro distanční studium. Skripta. Akademické nakladatelství s. r. o. Brno, 1995, 1999. (cs)

Recommended Reading

Jíra, A., Jandeková, D., Hlobilová, A., Janouchová, E., Zrůbek, A. Sbírka příkladů stavební mechaniky. České vysoké učení technické v Praze, 2021. (cs)
Jíra, A., Jandeková, D., Novotná, E., Řehounek, L, Prošek, Z, Štěpánek, J., Voříšek, J. Sbírka příkladů z Pružnosti a Pevnosti. ČVUT v Praze, 2022. (cs)
Křiváková, J. Stavební mechanika 1. Moduly AD01-MO1 až AD01-MO7. Studijní opory. VUT, FAST, Brno, 2011. (cs)
Hulse, R. Cain, J. Structural mechanics. Red Globe Press, 2000. (en)
Hulse, R. Cain, J. Structural mechanics: Worked examples. Palgrave Macmillan, 2009. (en)
Cueto E., Gonzales, D. An Introduction to Structural Mechanics for Architects. Springer, 2018. (en)

Syllabus

  1. Introduction to structural mechanics. Basic concepts, principles and axioms. Coplanar and non-coplanar force systems.
  2. Basic types of statically determinate beams. Structural form and idealisation, loading, supports and reactions. Static and kinematic determinacy of structures. Calculation of support reactions.
  3. Types of internal forces. Beam equilibrium differential equations. Internal forces diagrams.
  4. Statically determinate plane beams – simply supported, cantilever.
  5. Statically determinate plane bent beams.
  6. Statically determinate plane inclined beams.
  7. Frame structures with internal pins.
  8. Trusses and curved beams. Statically determinate beams with 3D loads, and bent beams in 3D.
  9. Geometric properties of cross-sections. The parallel axis theorem. The radius of gyration and ellipse of second-order moments of the cross-section.
  10. Basic concepts and assumptions of the linear elasticity and strength theory. Stress, displacement, deformation. Simple stresses in Civil Engineering – direct tension and compression.
  11. Simple stresses in Civil Engineering – shear and bending. Transverse shear stress. Shear stress in thin-walled members. Shear centre.
  12. Torsional stress. Stability and elastic buckling of axially loaded compression members
  13. Combined bending and direct stress.

Prerequisites

Basic knowledge of mathematics and physics from secondary school is required.

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

The definition of monitored instruction and the method of its implementation is annually updated by the guarantor of the course

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/273667

Lecture

13 weeks, 2 hours/week, elective

Syllabus

  1. Introduction to structural mechanics. Basic concepts, principles and axioms. Coplanar and non-coplanar force systems.
  2. Basic types of statically determinate beams. Structural form and idealisation, loading, supports and reactions. Static and kinematic determinacy of structures. Calculation of support reactions.
  3. Types of internal forces. Beam equilibrium differential equations. Internal forces diagrams.
  4. Statically determinate plane beams – simply supported, cantilever.
  5. Statically determinate plane bent beams.
  6. Statically determinate plane inclined beams.
  7. Frame structures with internal pins.
  8. Trusses and curved beams. Statically determinate beams with 3D loads, and bent beams in 3D.
  9. Geometric properties of cross-sections. The parallel axis theorem. The radius of gyration and ellipse of second-order moments of the cross-section.
  10. Basic concepts and assumptions of the linear elasticity and strength theory. Stress, displacement, deformation. Simple stresses in Civil Engineering – direct tension and compression.
  11. Simple stresses in Civil Engineering – shear and bending. Transverse shear stress. Shear stress in thin-walled members. Shear centre.
  12. Torsional stress. Stability and elastic buckling of axially loaded compression members
  13. Combined bending and direct stress.

Exercise

13 weeks, 1 hours/week, compulsory

Syllabus

  1. Coplanar force systems. Conditions of equilibrium.
  2. Statically determinate plane beams – simply supported, cantilever – support reactions.
  3. Statically determinate plane beams – simply supported, cantilever – internal forces diagrams.
  4. Statically determinate plane beams – bent and inclined beams. Frame structures with internal pins.
  5. Gerber beams. Trusses – method of joint and method of section.
  6. Geometric properties of cross-sections. Dimensioning of members – bending stress.
  7. Credit