Course detail

Structural Analysis 1

FAST-BDA003Acad. year: 2021/2022

Moving load of static quantity of statically determinate frame structures. Solution using influence lines, analytic and kinematic method. Evaluation of influence lines and determination of extreme values.
Principle of virtual work. Clauses about virtual works reciprocity. Maxwell-Mohr integral. Solution of displacement and rotation of frame systems using method of unit forces, including the influence of temperature changes. Veresčagin’s rule.
Statically indeterminate structures. Degree of static indeterminacy. Solution methods. Force method. Elementary cantilever beam. Continuous girder is solved by three-torque equation. Moving load at continuous girder. Combinations of loads.
Planar frame using by force method, option of statically indeterminate values, canonical equations. Influence of shift of supports, effects of uniform and non-uniform temperature changes at frame structure. Utilization of shape symmetry.
Planar arc is solved by force method, influence of compression of line of arc, deflection load. Statically indeterminate truss girder is solved by force method.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

prof. Ing. Zbyněk Keršner, CSc.

Department

Institute of Structural Mechanics (STM)

Offered to foreign students

Of all faculties

Learning outcomes of the course unit

The student will learn the structural analysis of statically indeterminate bar structures by the force method, namely plane frames, planar bar systems, continuous girder, statically indeterminate trusses, including the effect of support relaxation and the temperature influence.

Prerequisites

Linear algebra, fundaments of matrix calculus, solutions of systems of linear algebraic equations, vector calculus, analytic geometry, derivative of a function, the indefinite and definite integral, applications of the integral.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

1. Introduction, content and outline of the subject. Moving load. Influence lines of static values of statically determinate frame structures.
2. Solution of kinematic method. Evaluation of influence lines and determination of extreme values. Criteria.
3. Meaning of statics, fundamental assumptions of solution. Distribution of load bearing building constructions. Planar frame structures.
4. Virtual work of internal and external forces. Lagrange’s principle of virtual works. Theorem about virtual works reciprocity. Maxwell-Mohr theorem, simplification of calculation.
5. Determination of displacement and rotation of straight and cranked girders using method of unit forces. Veresčagin’s rule. Influence of temperature changes on deformation of plate girders. Calculation of shift of truss girders using method of unit forces.
6. Methods of solution of statically indeterminate frame structures. Assessment of static indeterminacy. Interpretation of force method.
7. Planar frame is solved by force method. Option of static indeterminate values, canonical equations. Effect of uniform and non-uniform temperature changes of frame. Influence of shift of support.
8. Elementary statically indeterminate girder, influence of axis load.
9. Continuous plate girder, general form of three-moment equation for force and deflection load. Progress of internal forces.
10. Moving load acting on continuous girder. Influence lines. Combination of loads.
11. Utilization of shape symmetry of frame, decomposition of general load, substitution bonds. Curved bar.
12. Planar statically indeterminate arc solved by force method. Statically indeterminate truss girder solved by force method.

Work placements

Not applicable.

Aims

Explanation the principle of virtual work and theorem of reciprocity of virtual work. The calculation of deformations by the method of unit forces.
Information about the force method of structural analysis of statically indeterminate plane frames, planar bar systems, continuous girder, including the effect of support relaxation and the temperature influence.

Specification of controlled education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme BKC-SI Bachelor's 2 year of study, summer semester, compulsory
  • Programme BPA-SI Bachelor's 2 year of study, summer semester, compulsory

  • Programme BPC-SI Bachelor's

    specialization VS , 2 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Zbyněk Keršner, CSc.
prof. Ing. David Lehký, Ph.D.

Syllabus

1. Introduction, content and outline of the subject. Moving load. Influence lines of static values of statically determinate frame structures. 2. Solution of kinematic method. Evaluation of influence lines and determination of extreme values. Criteria. 3. Meaning of statics, fundamental assumptions of solution. Distribution of load bearing building constructions. Planar frame structures. 4. Virtual work of internal and external forces. Lagrange’s principle of virtual works. Theorem about virtual works reciprocity. Maxwell-Mohr theorem, simplification of calculation. 5. Determination of displacement and rotation of straight and cranked girders using method of unit forces. Veresčagin’s rule. Influence of temperature changes on deformation of plate girders. Calculation of shift of truss girders using method of unit forces. 6. Methods of solution of statically indeterminate frame structures. Assessment of static indeterminacy. Interpretation of force method. 7. Planar frame is solved by force method. Option of static indeterminate values, canonical equations. Effect of uniform and non-uniform temperature changes of frame. Influence of shift of support. 8. Elementary statically indeterminate girder, influence of axis load. 9. Continuous plate girder, general form of three-moment equation for force and deflection load. Progress of internal forces. 10. Moving load acting on continuous girder. Influence lines. Combination of loads. 11. Utilization of shape symmetry of frame, decomposition of general load, substitution bonds. Curved bar. 12. Planar statically indeterminate arc solved by force method. Statically indeterminate truss girder solved by force method.

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. Ing. Jiří Kytýr, CSc.
Ing. Luděk Brdečko, Ph.D.
doc. Ing. Petr Hradil, Ph.D.
Ing. Zbyněk Vlk, Ph.D.
doc. Ing. Petr Frantík, Ph.D.
Ing. Dita Vořechovská, Ph.D.
doc. Ing. Hana Šimonová, Ph.D.
Ing. Josef Martinásek, Ph.D.
Ing. Filip Hokeš, Ph.D.

Syllabus

1. Revision of diagrams of internal forces at planar cranked statically determinate frame structure. 2. Moving load. Application of kinematic method at girder with overhang and Gerber’s girder. 3. Determination of extreme values from moving load. Winkler criteria, load’s criteria, Šolín’s criteria. 4. Calculation of displacement and rotation by using method of unit forces at elementary frame structures, which are loaded by elementary loads. 5. Calculation of displacement and rotation using method of unit forces at more complicated frame structures with more complicated type of loading. 6. Influence of temperature changes on deflection of girder. Calculation of displacement at truss girders. 7. Degree of static indeterminacy. Choice of fundamental static determinate system. Solution of elementary planar statically indeterminate frame with forced loading. 8. Solution of more complicated planar statically indeterminate frame with forced and deflection loading. 9. Statically indeterminate frame with closed part. 10. Elementary statically indeterminate girder with forced loading including effect of axis loading. 11. Continuous girder with forced and deflection loading. 12. Influence lines at continuous girder. Solution of statically indeterminate truss girder.