Course Details

# Structural Analysis 1

BDA003 course is part of 3 study plans

Bc. full-t. program BPC-SI > spVS compulsory Summer Semester 2nd year 4 credits

Bc. full-t. program BPA-SI compulsory Summer Semester 2nd year 4 credits

Bc. combi. program BKC-SI compulsory Summer Semester 2nd year 4 credits

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.

Course Guarantor

prof. Ing. Zbyněk Keršner, CSc.

Institute

Institute of Structural Mechanics

Learning outcomes

The student will learn the structural analysis of statically indeterminate bar structures by the force method. Influence lines are solved on elementary statically determinate bars and on continuous girders. Static indeterminate bar structures that are examined are planar statically indeterminate cantilever beam, continuous girders, planar frame, planar arc and truss girder. In this course student will learn force load, influence of temperature changes and shift of supports. There is analysed the utilization of shape symmetry at the frame structure.

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.

Corequisites

Applications of the integral. Solutions of linear differential equations.

Planned educational activities and teaching methods

Teaching is divided into lectures and practice lessons. Teaching is completed by individual consultations. Individual work, which is given within the course, is a part of studying activity of each student. Participation of student on lectures is recommended. Participation of student on practice lessons is required and checked. Methods of teaching depend on way of teaching and these method are written in the article 7 – Studying and Examination rules for BUT.

Forms and criteria of assessment

Subject is finished by getting credits and passing examination. There are some control tests which are written during the semester in practice lessons. To get credit it is necessary to pass all tests during semester in practice lessons. In order to do examination it is necessary to get credit. The examination consists of written and oral part. Written part is divided into (include) example and theoretic part. To get to the oral part it is necessary to be successful in example.

Objective

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

Vymezení kontrolované výuky a způsob jejího provádění stanoví každoročně aktualizovaná vyhláška garanta předmětu.

Lecture

2 hours/week, 12 weeks, elective

Syllabus of lectures

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.

Practice

2 hours/week, 12 weeks, compulsory

Syllabus of practice

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.