2nd year of Degree in Foundations of Architecture
6 ECTS – Core course
Description
The fundamental objective of this subject is to acquire basic knowledge of the dynamics and statics of material systems and the elastic behavior of these systems, as well as to convey a general perspective on how physics approaches the study of natural phenomena.
The course begins with several topics dedicated to some of the mathematical tools of interest in physics. It then consecutively addresses kinematics, dynamics, and statics of material systems in general, and specifically of rigid solids and solid systems. Finally, it covers the basic study of elastic media and concludes with a simple examination of stresses and strains in some fundamental material elements in architectural structures.
Course content
- Introduction. Fundamentals of Physics
- Vector Calculus
- Definition, types of vectors, and description of a vector
- Operations with vectors
- Vector systems. Characterization
- Equivalent systems. Reduction
- Fields
- Scalar fields and vector fields. Description
- Gradient of a scalar field
- Circulation. Work. Conservative fields. Potential energy
- Flux and divergence
- Kinematics
- Kinematics of the particle: position, velocity, and acceleration
- Systems of particles. The rigid body
- Elementary motions of the rigid body: translation and rotation
- Plane motion of the rigid body
- Dynamics
- Dynamics of the particle
- Center of mass and moments of inertia of the rigid body
- General dynamics of the particle system
- Dynamics of the rigid body with plane motion
- Vibrations
- General characteristics of mechanical vibrations
- Harmonic vibratory motion in one dimension
- Damped vibrations
- Forced vibrations. Resonance
- Statics
- Equilibrium. Conditions of equilibrium for a particle
- Conditions of equilibrium for the rigid body and systems of solids
- Constraints and reactions at the constraints. Statics of bars in the plane
- Method of virtual work. Stability of equilibrium
- Introduction to tensor analysis
- Transformation of Cartesian coordinates. Definition of Cartesian tensor
- Symmetric second-order Cartesian tensors. Principal axes
- Fundamental notions of elasticity
- Stresses in solids. The stress tensor
- Strains. The strain tensor
- Stress-strain diagram. Generalized Hooke’s law for isotropic solids
- Thermal strains and stresses
- Tension, bending, and torsion
- Relationship between external forces and components of the stress tensor
- Tension
- Bending
- Equation of the elasticity of a beam subjected to bending
- Torsion
Teaching planning (subject table, academic calendar, and exam schedule…)
Course coordinator
Prof. Mª de los Ángeles Navacerrada Saturio
Academic board
President: Prof. Mª de los Ángeles Navacerrada Saturio
Secretary: Prof. Óscar de Abril Torralba
Member: Prof. José Manuel García Tijero