Technical mechanics
Technical mechanics, as a subfield of physics, encompasses the description of fundamental relationships between the loads on technical structures and their stresses and motions. The lecture imparts knowledge on modeling components and mechanical engineering constructions, as well as on analyzing their strength and dynamics. Additionally, basic knowledge of computer-aided methods in technical mechanics is taught.
Technical Mechanics 1
Statics
Courses of study: B.Sc. Biomedizinische Technik B.Sc. Maschinenbau B.Sc. Wirtschaftsingenieurwesen Lehramt an Gymnasien - AWT
Content: 3 SWS Lecture, 2 SWS Seminar
Credit points:6
The students gain an understanding of the principles of mechanics. They are enabled to solve problems in statics in a structured manner, taking into account fundamental engineering principles.
Content:
Basic Concepts: Concept of force, axioms of mechanics
Central Force Systems: Resultant force, conditions of equilibrium
General Force Systems: Force couple, moment of a force, resultant force and resultant moment, conditions of equilibrium
Center of Gravity: Center of gravity of parallel force systems, bodies, surfaces, and lines
Equilibrium of Systems of Rigid Bodies: Support reactions, static determinacy, determination of support reactions and equilibrium states
Trusses: Static determinacy, method of joints, Ritter’s method (method of sections)
Statics of Rigid Beams: Internal forces in straight and curved beams under planar and spatial loading
Adhesion and Friction: Coulomb’s laws of friction, static and kinetic friction in statically determinate and indeterminate systems, rope friction
Tension and Compression in Straight Rods: Stress, strain, material law, single rods, rod systems
Recommended Literature:
Gross, D., Hauger, W., Schröder, J.; Wall, W.: Technische Mechanik 1: Statik; Springer-Verlag, 2011.
Richard, H.A.; Sander, M.: Technische Mechanik - Statik; Springer Vieweg, 2012.
Woernle, C.: Manuskript zur Vorlesung Technische Mechanik 1 (Foliensatz)
Technical Mechanics 2
Strength of materials
Courses of study: B.Sc. Biomedizinische Technik B.Sc. Maschinenbau B.Sc. Wirtschaftsingenieurwesen Lehramt an Gymnasien - AWT
Content: 3 SWS Lecture, 2 SWS Seminar
Credit points:6
Through this module, students gain an understanding of the principles of mechanics in the fields of elastostatics and strength of materials. They are enabled to solve problems in elastostatics and strength of materials in a structured way, taking into account static conditions.
Content:
Bending of Straight Beams: Pure bending (without shear force), axial second moments of area, straight bending with shear forces, superposition of bending cases, oblique bending
Stress State: Uniaxial, biaxial, and triaxial stress states; equilibrium conditions
Strain State and Elasticity Law: Strain state, Hooke’s law (elasticity law), stress determination through strain measurements
Shear Effects in Beam Bending: Shear stresses due to transverse forces, shear stresses in thin-walled cross-sections, deformations due to shear
Torsion of Straight Rods: Circular cylindrical rods, thin-walled closed and open profiles
Combined Loading: Stresses and deformations under combined loading, strength hypotheses (failure criteria)
Buckling of Straight Rods: Stability of equilibrium, critical buckling loads of straight rods, calculation of buckling members
Energy Methods: Work and potential energy, work of external forces, influence coefficients, strain energy, Castigliano’s theorem
Recommended Literature:
Gross, D., Hauger, W., Schröder, J.; Wall, W.: Technische Mechanik 2:Elastostatik; Springer-Verlag, 2012.
Richard, H.A.; Sander, M.: Technische Mechanik - Festigkeitslehre; Springer Vieweg, 2013.
Woernle, C.: Manuskript zur Vorlesung Technische Mechanik 2 (Foliensatz)
Technical Mechanics 3
Kinematics / Dynamics
Courses of study: B.Sc. Biomedizinische Technik B.Sc. Maschinenbau B.Sc. Wirtschaftsingenieurwesen Lehramt an Gymnasien - AWT
Content: 3 SWS Lecture, 2 SWS Seminar
Credit points:6
Through this module, students gain an understanding of the principles of dynamics within the field of engineering mechanics. They are enabled to solve problems in kinematics and dynamics in a structured manner, applying appropriate mathematical methods. Students learn to describe mechanical vibration phenomena mathematically and to interpret them from a physical perspective.
Content:
Kinematics of a Point: One-dimensional point motion; motion in Cartesian coordinates, in polar and cylindrical coordinates, and in natural coordinates
Kinematics of Rigid Bodies: Translation; rotation about a fixed axis; planar motion; instantaneous center of rotation; spatial motion; relative motion
Dynamics of a Mass Point: Linear momentum, momentum principle, d’Alembert’s principle; free and constrained mass points; angular momentum; angular momentum principle; systems of mass points
Dynamics of Rigid Bodies: Rotation about a fixed axis; planar motion; spatial motion
Work-Energy Principle in Dynamics: Kinetic and potential energy; work-energy theorem; power and efficiency
Lagrange’s Equations of the Second Kind: Degrees of freedom; virtual displacements; generalized coordinates; d’Alembert-Lagrange principle; Lagrange’s equations of the second kind
Vibrations with One Degree of Freedom: Classification; free undamped and damped vibrations; forced vibrations
Impact Phenomena: Assumptions; classification; direct central impact; planar eccentric smooth impact
Recommended Literature:
Gross, D., Hauger, W., Schröder, J.; Wall, W.: Technische Mechanik 3: Dynamik; Springer-Verlag, 2012. Richard, H.A.; Sander, M.: Technische Mechanik - Dynamik; Springer Vieweg, 2011.
Woernle, C.: Manuskript zur Vorlesung Technische Mechanik 3 (Foliensatz)