Course Details

Structural Mechanics 2

Academic Year 2025/26

BDA016 course is part of 1 study plan

​ BPC-APS Summer Semester 1st year

The course deals with static and deformation analysis of simple statically indeterminate beam structures by force and direct stiffness method. Topics: Types of structures in civil engineering. Types of loads acting on a structure. Influence lines for statically determinate structures. Principle of virtual work and its application to the calculation of deflections and rotations of statically determinate beams – unit dummy force method. Statically indeterminate structures, degree of static and kinematic indeterminacy of structures. Principle of force method for analysis of indeterminate structures. Three-moment equation method for continuous beam analysis. Force method – statically indeterminate plane frames and trusses. Principle of direct stiffness method. Computational model and degree of kinematic indeterminacy. The general form of direct stiffness method – matrix form, analysis of straight beam with constant cross-section. Slope deflection method – end moments and forces, analysis of continuous beam and frame analysis.

Course Guarantor

doc. Ing. Hana Šimonová, Ph.D.

Institute

Institute of Structural Mechanics

Objective

Students will be acquainted with influence lines for statically determinate structures. The principle of virtual work and its application to the calculation of deflections and rotations of statically determinate beams (unit dummy force method) will be clarified. Students will learn how to solve statically indeterminate beam structures by force method and direct stiffness method. The solution of statically indeterminate structures will be performed on a two-sided fixed beam, continuous beam, planar frame, and truss girder. The force load, the effect of temperature changes and the support settlement are considered.

 

Students will be able to solve influence lines for statically determinate structures, calculate deflections and rotations of statically determinate beams using the unit dummy force method and solve statically indeterminate planar beam structures by force method and direct stiffness method.

Prerequisites

Linear algebra, fundamentals of matrix calculus, solutions of systems of linear algebraic equations, vector calculus, analytic geometry, derivative of a function, indefinite and definite integral, applications of the integral. Determination of reactions and internal forces of statically determinate plane beams and frames.

Language of instruction

Czech

Credits

3 credits

Semester

summer

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/289643

Lecture

13 weeks, 2 hours/week, elective

Syllabus

  1. Types of structures in civil engineering. Types of loads acting on a structure. Influence lines for statically determinate structures.
  2. Principle of virtual work, Lagrange’s equations. Maxwell–Betti reciprocal work theorem. Maxwell–Mohr’s integral. Vereshchagin’s rule.
  3. Deflections and rotations of statically determinate straight beams, frames and trusses – unit dummy force method.
  4. Methods for analysis of statically indeterminate structures, degree of static and kinematic indeterminacy of structures. Principle of force method.
  5. Three-moment equation method for continuous beam analysis. Force and deflection load. Utilisation of symmetry of beam shape.
  6. Force method – statically indeterminate plane frames. Selection of statically indeterminate variables. Effect of temperature changes and support settlement.
  7. Force method – statically indeterminate truss.
  8. Principle of direct stiffness method. Computational model and degree of kinematic indeterminacy.
  9. The general form of direct stiffness method – matrix form, analysis of straight beam with constant cross-section. Load vector and stiffness matrix.
  10. Slope deflection method – end moments and forces. Analysis of continuous beam.
  11. Slope deflection method – plane frame analysis.
  12. Direct stiffness method – continuous beam analysis.
  13. Direct stiffness method – plane frame analysis.

Exercise

13 weeks, 1 hours/week, compulsory

Syllabus

  1. Influence lines for statically determinate structures.
  2. Influence lines for statically determinate structures. Vereshchagin’s rule.
  3. Deflections and rotations of statically determinate straight beams, unit dummy force method.
  4. Unit dummy force method – frames without and with internal pins.
  5. Degree of static indeterminacy of structures. Selection of statically indeterminate variables. The first control test (calculation of the deflections and rotations of a statically determinate straight beam using unit dummy force method, Vereshchagin’s rule).
  6. Three-moment equation method – continuous beam analysis.
  7. Force method – statically indeterminate straight beams.
  8. Force method – statically indeterminate plane frame. Computational model and degree of kinematic indeterminacy.
  9. Computational model and degree of kinematic indeterminacy.
  10. Slope deflection method – straight beam analysis. The second control test (degree of static indeterminacy of structures, Computational model and degree of kinematic indeterminacy).
  11. Slope deflection method – plane frame analysis.
  12. Slope deflection method – plane frame analysis.
  13. Credit