Course Details

Fundamentals of Structural Mechanics

BDA001 course is part of 4 study plans

Bc. full-t. program BPC-SI > spVS compulsory Summer Semester 1st year 5 credits

Bc. full-t. program BPC-MI compulsory Summer Semester 1st year 5 credits

Bc. full-t. program BPA-SI compulsory Summer Semester 1st year 5 credits

Bc. combi. program BKC-SI compulsory Summer Semester 1st year 5 credits

Students will be able to solve reactions and internal forces of the plane statically determinate structures, of plane beams with straight and broken axis, to solve three-hinged broken beam with and without a bar, the planar composed beam systems and plane truss systems, to determine the position of centroid and the second order moments of cross-section.

Course Guarantor

prof. Ing. Jiří Kala, Ph.D.

Institute

Institute of Structural Mechanics

Learning outcomes

Students get the basic knowledge of structural mechanics needed for the further study of civil engineering branch and of the following specializations.
Students will be able to solve reactions and internal forces of the plane statically determinate structures, of plane beams with straight and broken axis, to solve three-hinged broken beam with and without a bar, the planar composed beam systems and plane truss systems, to find centroid and second order moments of cross-section.

Prerequisites

The basic secondary s school knowledge from mathematics and physics.

Corequisites

Linear algebra, foundations of matrix calculus, solving of linear algebraic equations systems, foundations of vector calculus, analytical geometry, first derivative of function, indefinite integral, definite integral.

Planned educational activities and teaching methods

The subject is taught by lectures and exercises. Lectures involve the theoretical explanation of delivered matter. The theory is applied at solution of examples of real structures in exercises.
Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Forms and criteria of assessment

The subject is finished by abridged examination and final examination. For abridged exam the student should pass all written tests in exercises and elaborate correctly all given homework. The abridged exam is the necessary condition for final examination entrance.
The final examination consists of written and oral parts. The written examination may contain both examples and the theoretical questions. The positive result in written examination allows the student to pass to oral part.

Objective

The students will be acquainting with: (i) Reactions and internal forces of the plane static determinate structures, (ii) centroid and second order moments of cross-section.

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, 13 weeks, elective

Syllabus of lectures

1.Basic terms and axioms of statics. Concurrent system of forces in plane. System of parallel forces in plane.
2. General system of forces in plane. Static models of plane structures, constrains and supports, types of loading, reactions.
3. Plane lattice girders, static and kinematic certainty. Calculation of axial forces in members by general and simplified joint method, intersecting method and its Ritter modification. Approach to the solution of extra-lumbar loading of members of planar lattice structures.
4. Components of the resultant of internal forces (N, V, M) of the straight plane of the stressed member. Straight planar statically determined beams and brackets, loads, reactions in constraints, calculation of reactions and internal forces and moments, diagrams of internal forces and moments.
5. Differential dependences between loads, shear forces and bending moments, differential equilibrium conditions.
6. Plane rectangular angled beams and brackets, calculation of reactions in bonds, diagrams of internal forces.
7. Plane inclined beam, continuous load of inclined member, decomposition of inclined continuous load, planar angled beam with inclined members, reactions and diagrams of internal forces and moments. Applications to off-load loads of planar lattice structures.
8. Statics of planar systems of bodies composed of material points and rigid plates, static and kinematic certainty (also for lattice construction from lecture 2). General method for solving planar systems of bodies by decomposition into partial bodies, reactions and internal forces. Three-joint angled beam.
9. Three-joint angled beam with tie rod, Gerber beam, reactions and diagrams of internal forces.
10. Area, static moment, center of gravity (analogy to solving a system of parallel forces). Quadratic and deviation moments. Steiner's theorem.
11. Main axes of cross section, main quadratic moments. Mohr's circle. Radii of inertia, ellipse of inertia, polar quadratic moments.
12. Spatial systems of forces, spatial bundle of forces, general spatial system of forces. Bonds and reactions of a rigid body in space, calculation of reactions in bonds. Spatially stressed straight bar.
13. Spatial rectangular angled bracket and beam, reactions and diagrams of internal forces and moments. Test information.

Practice

3 hours/week, 13 weeks, compulsory

Syllabus of practice

1. Moment of force to a point, pair of forces. Concurrent system of forces in plane, general system of forces in plane.
2. System of parallel forces in plane and its static centre. Static centre of plane composed shapes.
3. Calculation of reactions of simple straight, angled and lattice beams loaded by solitary forces and moments, continuous loading.
4. Calculation of axial forces in members of planar lattice girders by the joint method.
5. Calculation of axial forces in members of planar lattice girders by the intersecting method.
6. Straight planar statically determined beams and brackets with simple load, reactions and diagrams of internal forces.
7. Plane straight beams loaded with any uniform load, calculation of reactions in bonds, calculation and drawing of internal force diagrams. The first control test - calculation of the reactions of a planar beam or axial force in the bars of a lattice structure by the intersecting method. (10 minute test)
8. Plane straight beams loaded by any combination of loads with continuous linear load, calculation of reactions in constraints, calculation and plotting of internal force diagrams.
9. Plane rectangular angled beams and brackets loaded with any load, including uniformly continuous and linear, reactions and diagrams of internal forces and moments.
10. Plane inclined beam, decomposition of inclined continuous load, reactions and diagrams of internal forces and moments. Second control test - a planar straight beam loaded with a simple combination of a solitary force, moment and a uniform continuous load. (15 minute test)
11. Plane inclined beam with overhanging end, with continuous load, forces and moments, reactions and diagrams of internal forces and moments.
12. Plane angled beam with inclined members, reactions and diagrams of internal forces and moments.
13. Three-joint angled beam with and without rod, reactions and diagrams of internal forces and moments. Third inspection test - planar angled beam with inclined bar with continuous load. (test for 20 minutes).
14. Gerber beam. Calculation of reactions and diagrams of internal forces and moments.
15. Compound beam systems of various types. Calculation of reactions and diagrams of internal forces and moments.
16. Center of gravity, quadratic and deviation moments of plane compound shapes, application of Steiner's theorem.
17. Main quadratic moments - numerical and graphical solutions. Radii of inertia, ellipse of inertia.
18. Spatially stressed straight bar and rectangular spatially angled bracket or beam - reactions and courses of internal forces. Credit test - planar composite beam system loaded with any load (test for 40 minutes).
19. Control of fulfillment of obligations and event. test correction. Reserve. Repetition of a composite beam system. Credit.