Course Details

Structural Mechanics 1

Academic Year 2024/25

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, plane 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, and angled beams. Frame structures with internal pins and trusses. 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.

Course Guarantor

doc. Ing. Hana Šimonová, Ph.D.

Institute

Institute of Structural Mechanics

Objective

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 look into the dimensioning of structures.

Students will be able to solve reactions and internal forces of statically determinate plane beams and frames, determine centroid and second moments of area, solve simple and combined bending and direct stresses and calculate stress in cross-section to design its dimension and material.

Prerequisites

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

Language of instruction

Czech

Credits

3 credits

Semester

winter

Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/281464

Lecture

13 weeks, 2 hours/week, elective

Syllabus

  1. Introduction to structural mechanics. Basic concepts, principles and axioms. Planar 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. Planar lattice girders. Determination of normal forces – method of joint and the method of section.
  4. Types of internal forces. Beam equilibrium differential equations. Internal forces diagrams.
  5. Statically determinate plane beams – simply supported, cantilever.
  6. Statically determinate plane angled
  7. Statically determinate plane inclined beams.
  8. Frame structures with internal pins.
  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. Concurrent system of forces in a plane. Composition and decomposition of force into orthogonal components. Resultant, equivalence, equilibrium.
  2. System of parallel forces in a plane. General system of forces in a plane. Resultant, equivalence, equilibrium.
  3. Calculation of reactions of simple straight, angled and truss beams loaded by forces, moments, and continuous loading
  4. Calculation of axial forces in members of planar lattice girders.
  5. Straight planar statically determined beams and cantilevers with simple load, reactions and diagrams of internal forces.
  6. Plane straight beams loaded with any uniform load, calculation of reactions in bonds, calculation and drawing of internal force diagrams.
  7. Plane rectangular angled beams loaded with any load, including uniformly continuous and linear, reactions and diagrams of internal forces. The first control test (calculation of the reactions of a simple planar beam).
  8. Plane inclined beams, reactions and diagrams of internal forces.
  9. Three-joint angled beam with and without rod, reactions and diagrams of internal forces.
  10. Gerber beam. Calculation of reactions and diagrams of internal forces.
  11. Centre of gravity, quadratic and deviation moments of plane compound shapes, application of Steiner's theorem.
  12. Geometric properties of compound rolled steel sections. The second control test (diagrams of internal forces of a simple planar beam).
  13. Design and assessment of bent elements – normal stresses. Credit